WorldWideScience

Sample records for singly-resonant sum frequency

  1. Singly-resonant sum frequency generation of visible light in a semiconductor disk laser

    DEFF Research Database (Denmark)

    Andersen, Martin Thalbitzer; Schlosser, P.J.; Hastie, J.E.

    2009-01-01

    In this paper a generic approach for visible light generation is presented. It is based on sum frequency generation between a semiconductor disk laser and a solid-state laser, where the frequency mixing is achieved within the cavity of the semiconductor disk laser using a singlepass of the solid......-state laser light. This exploits the good beam quality and high intra-cavity power present in the semiconductor disk laser to achieve high conversion efficiency. Combining sum frequency mixing and semiconductor disk lasers in this manner allows in principle for generation of any wavelength within the visible...

  2. Frequency control of a 1163 nm singly resonant OPO based on MgO:PPLN

    NARCIS (Netherlands)

    Gross, P.; Lindsay, I.D.; Lee, Christopher James; Nittmann, M.; Bauer, T.; Bartschke, J.; Warring, U.; Fischer, A.; Kellenbauer, A.; Boller, Klaus J.

    2010-01-01

    We report the realization of a singly resonant optical parametric oscillator (SRO) that is designed to provide narrow-bandwidth, continuously tunable radiation at a wavelength of 1163 nm for optical cooling of osmium ions. The SRO is based on periodically poled, magnesium-oxide-doped lithium niobate

  3. Second harmonic generation and sum frequency generation

    International Nuclear Information System (INIS)

    Pellin, M.J.; Biwer, B.M.; Schauer, M.W.; Frye, J.M.; Gruen, D.M.

    1990-01-01

    Second harmonic generation and sum frequency generation are increasingly being used as in situ surface probes. These techniques are coherent and inherently surface sensitive by the nature of the mediums response to intense laser light. Here we will review these two techniques using aqueous corrosion as an example problem. Aqueous corrosion of technologically important materials such as Fe, Ni and Cr proceeds from a reduced metal surface with layer by layer growth of oxide films mitigated by compositional changes in the chemical makeup of the growing film. Passivation of the metal surface is achieved after growth of only a few tens of atomic layers of metal oxide. Surface Second Harmonic Generation and a related nonlinear laser technique, Sum Frequency Generation have demonstrated an ability to probe the surface composition of growing films even in the presence of aqueous solutions. 96 refs., 4 figs

  4. Sum frequency generation for surface vibrational spectroscopy

    International Nuclear Information System (INIS)

    Hunt, J.H.; Guyot-Sionnest, P.; Shen, Y.R.

    1987-01-01

    Surface vibrational spectroscopy is one of the best means for characterizing molecular adsorbates. For this reason, many techniques have been developed in the past. However, most of them suffer from poor sensitivity, low spectral and temporal resolution, and applications limited to vacuum solid interfaces. Recently, the second harmonic generation (SHG) technique was proved repeatedly to be a simple but versatile surface probe. It is highly sensitive and surface specific; it is also capable of achieving high temporal, spatial, and spectral resolution. Being an optical technique, it can be applied to any interface accessible by light. The only serious drawback is its lack of molecular selectivity. An obvious remedy is the extension of the technique to IR-visible sum frequency generation (SFG). Surface vibrational spectroscopy with submonolayer sensitivity is then possible using SFG with the help of a tunable IR laser. The authors report here an SFG measurement of the C-H stretch vibration of monolayers of molecules at air-solid and air-liquid interfaces

  5. Efficient yellow beam generation by intracavity sum frequency ...

    Indian Academy of Sciences (India)

    2014-02-06

    Feb 6, 2014 ... We present our studies on dual wavelength operation using a single Nd:YVO4 crystal and its intracavity sum frequency generation by considering the influence of the thermal lensing effect on the performance of the laser. A KTP crystal cut for type-II phase matching was used for intracavity sum frequency ...

  6. Unidirectional ring-laser operation using sum-frequency mixing

    DEFF Research Database (Denmark)

    Tidemand-Lichtenberg, Peter; Cheng, Haynes Pak Hay; Pedersen, Christian

    2010-01-01

    A technique enforcing unidirectional operation of ring lasers is proposed and demonstrated. The approach relies on sum-frequency mixing between a single-pass laser and one of the two counterpropagating intracavity fields of the ring laser. Sum-frequency mixing introduces a parametric loss for the...... where lossless second-order nonlinear materials are available. Numerical modeling and experimental demonstration of parametric-induced unidirectional operation of a diode-pumped solid-state 1342 nm cw ring laser are presented.......A technique enforcing unidirectional operation of ring lasers is proposed and demonstrated. The approach relies on sum-frequency mixing between a single-pass laser and one of the two counterpropagating intracavity fields of the ring laser. Sum-frequency mixing introduces a parametric loss...

  7. Efficient yellow beam generation by intracavity sum frequency ...

    Indian Academy of Sciences (India)

    2014-02-06

    Feb 6, 2014 ... petition leading to instability in the output sum frequency power and ... Nd:YVO4 crystal has been identified as one of the promising laser materials for diode ... very important to achieve small laser mode size as well as proper ...

  8. Dynamical local field, compressibility, and frequency sum rules for quasiparticles

    International Nuclear Information System (INIS)

    Morawetz, Klaus

    2002-01-01

    The finite temperature dynamical response function including the dynamical local field is derived within a quasiparticle picture for interacting one-, two-, and three-dimensional Fermi systems. The correlations are assumed to be given by a density-dependent effective mass, quasiparticle energy shift, and relaxation time. The latter one describes disorder or collisional effects. This parametrization of correlations includes local-density functionals as a special case and is therefore applicable for density-functional theories. With a single static local field, the third-order frequency sum rule can be fulfilled simultaneously with the compressibility sum rule by relating the effective mass and quasiparticle energy shift to the structure function or pair-correlation function. Consequently, solely local-density functionals without taking into account effective masses cannot fulfill both sum rules simultaneously with a static local field. The comparison to the Monte Carlo data seems to support such a quasiparticle picture

  9. Sum-Frequency Generation from Chiral Media and Interfaces

    Energy Technology Data Exchange (ETDEWEB)

    Ji, Na [Univ. of California, Berkeley, CA (United States)

    2006-02-13

    Sum frequency generation (SFG), a second-order nonlinear optical process, is electric-dipole forbidden in systems with inversion symmetry. As a result, it has been used to study chiral media and interfaces, systems intrinsically lacking inversion symmetry. This thesis describes recent progresses in the applications of and new insights into SFG from chiral media and interfaces. SFG from solutions of chiral amino acids is investigated, and a theoretical model explaining the origin and the strength of the chiral signal in electronic-resonance SFG spectroscopy is discussed. An interference scheme that allows us to distinguish enantiomers by measuring both the magnitude and the phase of the chiral SFG response is described, as well as a chiral SFG microscope producing chirality-sensitive images with sub-micron resolution. Exploiting atomic and molecular parity nonconservation, the SFG process is also used to solve the Ozma problems. Sum frequency vibrational spectroscopy is used to obtain the adsorption behavior of leucine molecules at air-water interfaces. With poly(tetrafluoroethylene) as a model system, we extend the application of this surface-sensitive vibrational spectroscopy to fluorine-containing polymers.

  10. Sum-Frequency Generation from Chiral Media and Interfaces

    International Nuclear Information System (INIS)

    Ji, Na

    2006-01-01

    Sum frequency generation (SFG), a second-order nonlinear optical process, is electric-dipole forbidden in systems with inversion symmetry. As a result, it has been used to study chiral media and interfaces, systems intrinsically lacking inversion symmetry. This thesis describes recent progresses in the applications of and new insights into SFG from chiral media and interfaces. SFG from solutions of chiral amino acids is investigated, and a theoretical model explaining the origin and the strength of the chiral signal in electronic-resonance SFG spectroscopy is discussed. An interference scheme that allows us to distinguish enantiomers by measuring both the magnitude and the phase of the chiral SFG response is described, as well as a chiral SFG microscope producing chirality-sensitive images with sub-micron resolution. Exploiting atomic and molecular parity nonconservation, the SFG process is also used to solve the Ozma problems. Sum frequency vibrational spectroscopy is used to obtain the adsorption behavior of leucine molecules at air-water interfaces. With poly(tetrafluoroethylene) as a model system, we extend the application of this surface-sensitive vibrational spectroscopy to fluorine-containing polymers

  11. Sum Frequency Generation Studies of Hydrogenation Reactions on Platinum Nanoparticles

    Energy Technology Data Exchange (ETDEWEB)

    Krier, James M. [Univ. of California, Berkeley, CA (United States)

    2013-08-31

    Sum Frequency Generation (SFG) vibrational spectroscopy is used to characterize intermediate species of hydrogenation reactions on the surface of platinum nanoparticle catalysts. In contrast to other spectroscopy techniques which operate in ultra-high vacuum or probe surface species after reaction, SFG collects information under normal conditions as the reaction is taking place. Several systems have been studied previously using SFG on single crystals, notably alkene hydrogenation on Pt(111). In this thesis, many aspects of SFG experiments on colloidal nanoparticles are explored for the first time. To address spectral interference by the capping agent (PVP), three procedures are proposed: UV cleaning, H2 induced disordering and calcination (core-shell nanoparticles). UV cleaning and calcination physically destroy organic capping while disordering reduces SFG signal through a reversible structural change by PVP.

  12. Sum frequency generation for studying plasma-wall interactions

    International Nuclear Information System (INIS)

    Roke, Sylvie

    2010-01-01

    Interaction of a plasma with a surface results in chemical and physical restructuring of the surface as well as the plasma in the vicinity of the surface. Studying such a reorganization of the atoms and molecules in the surface layer requires optical tools that can penetrate the plasma environment. At the same time, surface specificity is required. Sum Frequency Generation (SFG) is an optical method that fulfills these requirements. SFG has been developed into a surface specific probe during the eighties and nineties. Nowadays SFG is routinely applied in the research of complex interfaces. In such experiments, liquid/gas, solid/gas, solid/liquid, or liquid/liquid interfaces are probed, and the chemical surface composition, orientational distribution, order and chirality can be retrieved. An application to investigate plasma-wall interactions is feasible too.

  13. Sum-frequency generation echo and grating from interface

    International Nuclear Information System (INIS)

    Volkov, Victor

    2014-01-01

    The work addresses spectroscopy of fourth-order Sum Frequency Generation Echo and Grating responses as an experimental tool to study structure and dynamics at interfaces. First, it addresses experimental geometry to extract background-free fourth-order Echo and Grating responses. Further, the article provides the analytical expressions of the response functions for these nonlinearities. The derived expressions are used to model the χ (4) two-dimensional spectral responses of a hydrated methyl acetate, which resembles a hydrated carbonyl moiety at the polar outer side of a phospholipid membrane. Orientation, transition dipole moments, and Raman tensors are obtained from the results of classical and quantum calculations, respectively. The numerical studies for the nonlinear responses under different polarization schemes and timings suggest the possibility of securely factoring of spectral contributions of χ YYYZX and χ YYYZY macroscopic susceptibilities. As such, the nonlinearities provide an experimental perspective on orientation of a generic (low-symmetry) molecular system at interfaces. Besides, the spectral properties of the tensors may reflect correlations of the in-plane and out-of-plane field components specific to the interface. For the case of a phospholipid membrane, the experiment would address in-plane and out-of-plane anisotropy of hydrogen bonding and related dynamics

  14. Sum-frequency generation echo and grating from interface

    Energy Technology Data Exchange (ETDEWEB)

    Volkov, Victor [Bereozovaya 2A, Konstantinovo, Moscow Region 140207 (Russian Federation)

    2014-10-14

    The work addresses spectroscopy of fourth-order Sum Frequency Generation Echo and Grating responses as an experimental tool to study structure and dynamics at interfaces. First, it addresses experimental geometry to extract background-free fourth-order Echo and Grating responses. Further, the article provides the analytical expressions of the response functions for these nonlinearities. The derived expressions are used to model the χ{sup (4)} two-dimensional spectral responses of a hydrated methyl acetate, which resembles a hydrated carbonyl moiety at the polar outer side of a phospholipid membrane. Orientation, transition dipole moments, and Raman tensors are obtained from the results of classical and quantum calculations, respectively. The numerical studies for the nonlinear responses under different polarization schemes and timings suggest the possibility of securely factoring of spectral contributions of χ{sub YYYZX} and χ{sub YYYZY} macroscopic susceptibilities. As such, the nonlinearities provide an experimental perspective on orientation of a generic (low-symmetry) molecular system at interfaces. Besides, the spectral properties of the tensors may reflect correlations of the in-plane and out-of-plane field components specific to the interface. For the case of a phospholipid membrane, the experiment would address in-plane and out-of-plane anisotropy of hydrogen bonding and related dynamics.

  15. Sensibility to Changes of Vibrational Modes of Excited Electron: Sum Frequency Signals Versus Difference Frequency Signals

    International Nuclear Information System (INIS)

    Gu Anna; Liang Xianting

    2011-01-01

    In this paper, we investigate a two electronic level system with vibrational modes coupled to a Brownian oscillator bath. The difference frequency generation (DFG) signals and sum frequency generation (SFG) signals are calculated. It is shown that, for the same model, the SFG signals are more sensitive than the DFG signals to the changes of the vibrational modes of the electronic two-level system. Because the SFG conversion efficiency can be improved by using the time-delay method, the findings in this paper predict that the SFG spectrum may probe the changes of the microstructure more effectively. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  16. Sum Frequency Generation Vibrational Spectroscopy of Colloidal Platinum Nanoparticle Catalysts: Disordering versus Removal of Organic Capping

    KAUST Repository

    Krier, James M.; Michalak, William D.; Baker, L. Robert; An, Kwangjin; Komvopoulos, Kyriakos; Somorjai, Gabor A.

    2012-01-01

    Recent work with nanoparticle catalysts shows that size and shape control on the nanometer scale influences reaction rate and selectivity. Sum frequency generation (SFG) vibrational spectroscopy is a powerful tool for studying heterogeneous

  17. Sum-frequency nonlinear Cherenkov radiation generated on the boundary of bulk medium crystal.

    Science.gov (United States)

    Wang, Xiaojing; Cao, Jianjun; Zhao, Xiaohui; Zheng, Yuanlin; Ren, Huaijin; Deng, Xuewei; Chen, Xianfeng

    2015-12-14

    We demonstrated experimentally a method to generate the sum-frequency Nonlinear Cherenkov radiation (NCR) on the boundary of bulk medium by using two synchronized laser beam with wavelength of 1300 nm and 800 nm. It is also an evidence that the polarization wave is always confined to the boundary. Critical conditions of surface sum-frequency NCR under normal and anomalous dispersion condition is discussed.

  18. Implementation of bright six-partite entanglement by coupled intracavity sum frequency generation

    Science.gov (United States)

    Wang, Junfeng; Liu, Le; Liu, Yuzhu; Zhang, Yanan; Wu, Hongyan; Gong, Chengxuan; Zhang, Ruofan; Zhang, Houyuan; Fan, JingYu

    2018-04-01

    Bright six-partite continuous-variable (CV) entanglement generated by the coupled intracavity sum frequency generation is investigated. The entanglement characteristics of reflected pump fields and the output sum frequency fields are discussed theoretically in symmetric and asymmetric cases by applying van Loock and Furusawa criteria for multipartite CV entanglement. Such compact tunable multipartite CV entanglement, generated from an experimentally feasible coupled system, could be used in integrated quantum communication and networks.

  19. Giant enhancement of sum-frequency yield by surface-plasmon excitation

    NARCIS (Netherlands)

    van der Ham, E. W. M.; Vrehen, Q. H. F.; Eliel, E. R.; Yakovlev, V. A.; Valieva, E. V.; Kuzik, L. A.; Petrov, J. E.; Sychugov, V. A.; van der Meer, A. F. G.

    1999-01-01

    We show experimentally that the radiation generated in infrared-visible sum-frequency mixing at an air-silver interface can be greatly enhanced when the visible input beam excites a surface plasmon-polariton at the interface. With either a prism or a grating used to couple the visible radiation with

  20. Studies of Interfacial Regions by Sum-Frequency Generation with a Free-Electron Laser

    NARCIS (Netherlands)

    Eliel, E. R.; van der Ham, E. W. M.; Vrehen, Q. H. F.; Thooft, G. W.; Barmentlo, M.; Auerhammer, J. M.; van der Meer, A. F. G.; van Amersfoort, P. W.

    1995-01-01

    The use of a Free-Electron Laser (FEL) allows the study of (non)linear optical properties of materials over unsurpassed large spectral intervals. As an example, we report on the use of a FEL as the infrared source in spectroscopic infrared-visible Sum-Frequency Generation (SFG). Employing the

  1. Theory of sum-frequency generation spectroscopy of adsorbed molecules using the density matrix method-broadband vibrational sum-frequency generation and applications

    International Nuclear Information System (INIS)

    Bonn, M; Ueba, H; Wolf, M

    2005-01-01

    A generalized theory of frequency- and time-resolved vibrational sum-frequency generation (SFG) spectroscopy of adsorbates at surfaces is presented using the density matrix formalism. Our theoretical treatment is specifically aimed at addressing issues that accompany the relatively novel SFG approach using broadband infrared pulses. The ultrashort duration of these pulses makes them ideally suited for time-resolved investigations, for which we present a complete theoretical treatment. A second key characteristic of these pulses is their large bandwidth and high intensity, which allow for highly non-linear effects, including vibrational ladder climbing of surface vibrations. We derive general expressions relating the density matrix to SFG spectra, and apply these expressions to specific experimental results by solving the coupled optical Bloch equations of the density matrix elements. Thus, we can theoretically reproduce recent experimentally demonstrated hot band SFG spectra using femtosecond broadband infrared excitation of carbon monoxide (CO) on a Ru(001) surface

  2. Sum frequency generation image reconstruction: Aliphatic membrane under spherical cap geometry

    Energy Technology Data Exchange (ETDEWEB)

    Volkov, Victor [Bereozovaya 2A, Konstantinovo, Moscow Region 140207 (Russian Federation)

    2014-10-07

    The article explores an opportunity to approach structural properties of phospholipid membranes using Sum Frequency Generation microscopy. To establish the principles of sum frequency generation image reconstruction in such systems, at first approach, we may adopt an idealistic spherical cap uniform assembly of hydrocarbon molecules. Quantum mechanical studies for decanoic acid (used here as a representative molecular system) provide necessary information on transition dipole moments and Raman tensors of the normal modes specific to methyl terminal – a typical moiety in aliphatic (and phospholipid) membranes. Relative degree of localization and frequencies of the normal modes of methyl terminals make nonlinearities of this moiety to be promising in structural analysis using Sum Frequency Generation imaging. Accordingly, the article describes derivations of relevant macroscopic nonlinearities and suggests a mapping procedure to translate amplitudes of the nonlinearities onto microscopy image plane according to geometry of spherical assembly, local molecular orientation, and optical geometry. Reconstructed images indicate a possibility to extract local curvature of bilayer envelopes of spherical character. This may have practical implications for structural extractions in membrane systems of practical relevance.

  3. Probing a molecular electronic transition by two-colour sum-frequency generation spectroscopy

    International Nuclear Information System (INIS)

    Humbert, C.; Dreesen, L.; Nihonyanagi, S.; Masuda, T.; Kondo, T.; Mani, A.A.; Uosaki, K.; Thiry, P.A.; Peremans, A.

    2003-01-01

    We demonstrate that a new emerging technique, two-colour sum-frequency generation (SFG) spectroscopy, can be used to probe the molecular electronic properties of self-assembled monolayers (SAMs). In the CH spectral range (2800-3200 cm -1 ), we show that the sum-frequency generation signal of a porphyrin alkanethiol derivative adsorbed on Pt(1 1 1) reaches a maximum intensity at ∼435 nm SFG wavelength. This wavelength corresponds to the porphyrin moiety specific π-π* molecular electronic transition which is called the Soret or B band. This resonant behaviour is not observed for 1-dodecanethiol SAMs, which are devoid of molecular electronic transition in the investigated visible spectral range

  4. Highly efficient single-pass sum frequency generation by cascaded nonlinear crystals

    DEFF Research Database (Denmark)

    Hansen, Anders Kragh; Andersen, Peter E.; Jensen, Ole Bjarlin

    2015-01-01

    , despite differences in the phase relations of the involved fields. An unprecedented 5.5 W of continuous-wave diffraction-limited green light is generated from the single-pass sum frequency mixing of two diode lasers in two periodically poled nonlinear crystals (conversion efficiency 50%). The technique......The cascading of nonlinear crystals has been established as a simple method to greatly increase the conversion efficiency of single-pass second-harmonic generation compared to a single-crystal scheme. Here, we show for the first time that the technique can be extended to sum frequency generation...... is generally applicable and can be applied to any combination of fundamental wavelengths and nonlinear crystals....

  5. Vibrational sum frequency generation (SFG) spectroscopic study of crystalline cellulose in biomass

    Science.gov (United States)

    Kim, Seong H.; Lee, Christopher M.; Kafle, Kabindra; Park, Yong Bum; Xi, Xiaoning

    2013-09-01

    The noncentrosymmetry requirement of sum frequency generation (SFG) spectroscopy allows selective detection of crystalline cellulose in plant cell walls and lignocellulose biomass without spectral interferences from hemicelluloses and lignin. In addition, the phase synchronization requirement of the SFG process allows noninvasive investigation of spatial arrangement of crystalline cellulose microfibrils in the sample. This paper reviews how these principles are applied to reveal structural information of crystalline cellulose in plant cell walls and biomass.

  6. Tunable, continuous-wave, ultraviolet source based on intracavity sum-frequency-generation in an optical parametric oscillator using BiB₃O₆.

    Science.gov (United States)

    Devi, Kavita; Kumar, S Chaitanya; Ebrahim-Zadeh, M

    2013-10-21

    We report a continuous-wave (cw) source of tunable radiation across 333-345 nm in the ultraviolet (UV) using bismuth triborate, BiB₃O₆ (BIBO) as the nonlinear gain material. The source is based on internal sum-frequency-generation (SFG) in a cw singly-resonant optical parametric oscillator (OPO) pumped at 532 nm. The compact tunable source employs a 30-mm-long MgO:sPPLT crystal as the OPO gain medium and a 5-mm-long BIBO crystal for intracavity SFG of the signal and pump, providing up to 21.6 mW of UV power at 339.7 nm, with >15 mW over 64% of the SFG tuning range. The cw OPO is also tunable across 1158-1312 nm in the idler, delivering as much as 1.7 W at 1247 nm, with >1W over 65% of the tuning range. The UV output at maximum power exhibits passive power stability better than 3.4% rms and frequency stability of 193 GHz over more than one minute.

  7. Toward a simple molecular understanding of sum frequency generation at air-water interfaces

    Energy Technology Data Exchange (ETDEWEB)

    Noah-Vanhoucke, Joyce; Smith, Jared D.; Geissler, Phillip L.

    2009-01-13

    Second-order vibrational spectroscopies successfully isolate signals from interfaces, but they report on intermolecular structure in a complicated and indirect way. Here we adapt a perspective on vibrational response developed for bulk spectroscopies to explore the microscopic fluctuations to which sum frequency generation (SFG), a popular surface-specific measurement, is most sensitive. We focus exclusively on inhomogeneous broadening of spectral susceptibilities for OH stretching of HOD as a dilute solute in D{sub 2}O. Exploiting a simple connection between vibrational frequency shifts and an electric field variable, we identify several functions of molecular orientation whose averages govern SFG. The frequency-dependence of these quantities is well captured by a pair of averages, involving alignment of OH and OD bonds with the surface normal at corresponding values of the electric field. The approximate form we obtain for SFG susceptibility highlights a dramatic sensitivity to the way a simulated liquid slab is partitioned for calculating second-order response.

  8. Efficient generation of 509 nm light by sum-frequency mixing between two tapered diode lasers

    DEFF Research Database (Denmark)

    Tawfieq, Mahmoud; Jensen, Ole Bjarlin; Hansen, Anders Kragh

    2015-01-01

    We demonstrate a concept for visible laser sources based on sum-frequency generation of beam com- bined tapered diode lasers. In this specific case, a 1.7 W sum-frequency generated green laser at 509 nm is obtained, by frequency adding of 6.17 W from a 978 nm tapered diode laser with 8.06 W from...... a 1063 nm tapered diode laser, inside a periodically poled MgO doped lithium niobate crystal. This corresponds to an optical to optical conversion ef fi ciency of 12.1%. As an example of potential applica- tions, the generated nearly diffraction-limited green light is used for pumping a Ti:sapphire laser......, thus demonstrating good beam quality and power stability. The maximum output powers achieved when pumping the Ti:sapphire laser are 226 mW (CW) and 185 mW (mode-locked) at 1.7 W green pump power. The optical spectrum emitted by the mode-locked Ti:sapphire laser shows a spectral width of about 54 nm...

  9. Photon wave function formalism for analysis of Mach–Zehnder interferometer and sum-frequency generation

    Energy Technology Data Exchange (ETDEWEB)

    Ritboon, Atirach, E-mail: atirach.3.14@gmail.com [School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ (United Kingdom); Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112 (Thailand); Daengngam, Chalongrat, E-mail: chalongrat.d@psu.ac.th [Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112 (Thailand); Pengpan, Teparksorn, E-mail: teparksorn.p@psu.ac.th [Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112 (Thailand)

    2016-08-15

    Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.

  10. Nonlinear beam clean-up using resonantly enhanced sum-frequency mixing

    DEFF Research Database (Denmark)

    Karamehmedovic, Emir; Pedersen, Christian; Jensen, Ole Bjarlin

    2009-01-01

    We investigate the possibility of improving the beam quality and obtaining high conversion efficiency in nonlinear sum-frequency generation. A 765 nm beam from an external cavity tapered diode laser is single-passed through a nonlinear crystal situated in the high intracavity field of a 1342 nm N......:YVO4 laser, generating a SFG beam at 488 nm. The ECDL have MH^2=1.9 and MV^2=2.4 and the solid-state laser has M^2...

  11. All-solid-state continuous-wave doubly resonant all-intracavity sum-frequency mixer.

    Science.gov (United States)

    Kretschmann, H M; Heine, F; Huber, G; Halldórsson, T

    1997-10-01

    A new resonator design for doubly resonant continuous-wave intracavity sum-frequency mixing is presented. We generated 212 mW of coherent radiation at 618 nm by mixing the radiation of a 1080-nm Nd(3+):YAlO(3) laser and a 1444-nm Nd(3+):YAG laser. Two different mixing resonator setups and several nonlinear-optical crystals were investigated. So far output is limited by unequal performance of the two fundamental lasers and coating problems of the nonlinear crystals.

  12. Orientations of nonlocal vibrational modes from combined experimental and theoretical sum frequency spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Chase, Hilary M.; Chen, Shunli; Fu, Li; Upshur, Mary Alice; Rudshteyn, Benjamin; Thomson, Regan J.; Wang, Hong-Fei; Batista, Victor S.; Geiger, Franz M.

    2017-09-01

    Inferring molecular orientations from vibrational sum frequency generation (SFG) spectra is challenging in polarization combinations that result in low signal intensities, or when the local point group symmetry approximation fails. While combining experiments with density functional theory (DFT) could overcome this problem, the scope of the combined method has yet to be established. Here, we assess its feasibility of determining the distributions of molecular orientations for one monobasic ester, two epoxides and three alcohols at the vapor/fused silica interface. We find that molecular orientations of nonlocal vibrational modes cannot be determined using polarization-resolved SFG measurements alone.

  13. Photon wave function formalism for analysis of Mach–Zehnder interferometer and sum-frequency generation

    International Nuclear Information System (INIS)

    Ritboon, Atirach; Daengngam, Chalongrat; Pengpan, Teparksorn

    2016-01-01

    Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.

  14. Conformation, orientation and interaction in molecular monolayers: A surface second harmonic and sum frequency generation study

    International Nuclear Information System (INIS)

    Superfine, R.; Huang, J.Y.; Shen, Y.R.

    1988-12-01

    We have used sum frequency generation (SFG) to study the order in a silane monolayer before and after the deposition of a coadsorbed liquid crystal monolayer. We observe an increase in the order of the chain of the silane molecule induced by the interpenetration of the liquid crystal molecules. By using second harmonic generation (SHG) and SFG, we have studied the orientation and conformation of the liquid crystal molecule on clean and silane coated glass surfaces. On both surfaces, the biphenyl group is tilted by 70 degree with the alkyl chain end pointing away from the surface. The shift in the C-H stretch frequencies in the coadsorbed system indicates a significant interaction between molecules. 9 refs., 3 figs

  15. Quantitative Surface Chirality Detection with Sum Frequency Generation Vibrational Spectroscopy: Twin Polarization Angle Approach

    International Nuclear Information System (INIS)

    Wei, Feng; Xu, Yanyan; Guo, Yuan; Liu, Shi-lin; Wang, Hongfei

    2009-01-01

    Here we report a novel twin polarization angle (TPA) approach in the quantitative chirality detection with the surface sum-frequency generation vibrational spectroscopy (SFG-VS). Generally, the achiral contribution dominates the surface SFG-VS signal, and the pure chiral signal is usually two or three orders of magnitude smaller. Therefore, it has been difficult to make quantitative detection and analysis of the chiral contributions to the surface SFG-VS signal. In the TPA method, by varying together the polarization angles of the incoming visible light and the sum frequency signal at fixed s or p polarization of the incoming infrared beam, the polarization dependent SFG signal can give not only direct signature of the chiral contribution in the total SFG-VS signal, but also the accurate measurement of the chiral and achiral components in the surface SFG signal. The general description of the TPA method is presented and the experiment test of the TPA approach is also presented for the SFG-VS from the S- and R-limonene chiral liquid surfaces. The most accurate degree of chiral excess values thus obtained for the 2878 cm -1 spectral peak of the S- and R-limonene liquid surfaces are (23.7±0.4)% and (25.4±1.3)%, respectively.

  16. Optical sum-frequency generation in a whispering-gallery-mode resonator

    International Nuclear Information System (INIS)

    Strekalov, Dmitry V; Kowligy, Abijith S; Huang, Yu-Ping; Kumar, Prem

    2014-01-01

    We demonstrate sum-frequency generation between a telecom wavelength and the Rb D2 line, achieved through natural phase matching in a nonlinear whispering gallery mode resonator. Due to the strong optical field confinement and ultra high Q of the cavity, the process saturates already at sub-mW pump peak power, at least two orders of magnitude lower than in existing waveguide-based devices. The experimental data are in agreement with the nonlinear dynamics and phase matching theory based on spherical geometry. Our experimental and theoretical results point toward a new platform for manipulating the color and quantum states of light waves for applications such as atomic memory based quantum networking and logic operations with optical signals. (paper)

  17. Combined IR-Raman vs vibrational sum-frequency heterospectral correlation spectroscopy

    Science.gov (United States)

    Roy, Sandra; Beutier, Clémentine; Hore, Dennis K.

    2018-06-01

    Vibrational sum-frequency generation spectroscopy is a valuable probe of surface structure, particularly when the same molecules are present in one of the adjacent bulk solid or solution phases. As a result of the non-centrosymmetric requirement of SFG, the signal generated is a marker of the extent to which the molecules are ordered in an arrangement that breaks the up-down symmetry at the surface. In cases where the accompanying changes in the bulk are of interest in understanding and interpreting the surface structure, simultaneous analysis of the bulk IR absorption or bulk Raman scattering is helpful, and may be used in heterospectral surface-bulk two-dimensional correlation. We demonstrate that, in such cases, generating a new type of bulk spectrum that combines the IR and Raman amplitudes is a better candidate than the individual IR and Raman spectra for the purpose of correlation with the SFG signal.

  18. Circularly polarized infrared and visible sum-frequency-generation spectroscopy: Vibrational optical activity measurement

    International Nuclear Information System (INIS)

    Cheon, Sangheon; Cho, Minhaeng

    2005-01-01

    Vibrational optical activity spectroscopies utilizing either circularly polarized ir or circularly polarized visible beams were theoretically investigated by considering the infrared and visible sum-frequency-generation (IV-SFG) schemes. In addition to the purely electric dipole-allowed chiral component of the IV-SFG susceptibility, the polarizability-electric quadrupole hyperpolarizability term also contributes to the vibrationally resonant IV-SFG susceptibility. The circular-intensity-difference signal is shown to be determined by the interferences between the all-electric dipole-allowed chiral component and the polarizability-electric-dipole or electric-dipole-electric-quadrupole Raman optical activity tensor components. The circularly polarized SFG methods are shown to be potentially useful coherent spectroscopic tools for determining absolute configurations of chiral molecules in condensed phases

  19. Theoretical study of sum-frequency vibrational spectroscopy on limonene surface

    International Nuclear Information System (INIS)

    Zheng, Ren-Hui; Liu, Hao; Jing, Yuan-Yuan; Wang, Bo-Yang; Shi, Qiang; Wei, Wen-Mei

    2014-01-01

    By combining molecule dynamics (MD) simulation and quantum chemistry computation, we calculate the surface sum-frequency vibrational spectroscopy (SFVS) of R-limonene molecules at the gas-liquid interface for SSP, PPP, and SPS polarization combinations. The distributions of the Euler angles are obtained using MD simulation, the ψ-distribution is between isotropic and Gaussian. Instead of the MD distributions, different analytical distributions such as the δ-function, Gaussian and isotropic distributions are applied to simulate surface SFVS. We find that different distributions significantly affect the absolute SFVS intensity and also influence on relative SFVS intensity, and the δ-function distribution should be used with caution when the orientation distribution is broad. Furthermore, the reason that the SPS signal is weak in reflected arrangement is discussed

  20. Theoretical study of sum-frequency vibrational spectroscopy on limonene surface

    Energy Technology Data Exchange (ETDEWEB)

    Zheng, Ren-Hui, E-mail: zrh@iccas.ac.cn; Liu, Hao; Jing, Yuan-Yuan; Wang, Bo-Yang; Shi, Qiang [Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190 (China); Wei, Wen-Mei [Department of Chemistry, College of Basic Medicine, Anhui Medical University, Hefei, Anhui 230032 (China)

    2014-03-14

    By combining molecule dynamics (MD) simulation and quantum chemistry computation, we calculate the surface sum-frequency vibrational spectroscopy (SFVS) of R-limonene molecules at the gas-liquid interface for SSP, PPP, and SPS polarization combinations. The distributions of the Euler angles are obtained using MD simulation, the ψ-distribution is between isotropic and Gaussian. Instead of the MD distributions, different analytical distributions such as the δ-function, Gaussian and isotropic distributions are applied to simulate surface SFVS. We find that different distributions significantly affect the absolute SFVS intensity and also influence on relative SFVS intensity, and the δ-function distribution should be used with caution when the orientation distribution is broad. Furthermore, the reason that the SPS signal is weak in reflected arrangement is discussed.

  1. Combining total internal reflection sum frequency spectroscopy spectral imaging and confocal fluorescence microscopy.

    Science.gov (United States)

    Allgeyer, Edward S; Sterling, Sarah M; Gunewardene, Mudalige S; Hess, Samuel T; Neivandt, David J; Mason, Michael D

    2015-01-27

    Understanding surface and interfacial lateral organization in material and biological systems is critical in nearly every field of science. The continued development of tools and techniques viable for elucidation of interfacial and surface information is therefore necessary to address new questions and further current investigations. Sum frequency spectroscopy (SFS) is a label-free, nonlinear optical technique with inherent surface specificity that can yield critical organizational information on interfacial species. Unfortunately, SFS provides no spatial information on a surface; small scale heterogeneities that may exist are averaged over the large areas typically probed. Over the past decade, this has begun to be addressed with the advent of SFS microscopy. Here we detail the construction and function of a total internal reflection (TIR) SFS spectral and confocal fluorescence imaging microscope directly amenable to surface investigations. This instrument combines, for the first time, sample scanning TIR-SFS imaging with confocal fluorescence microscopy.

  2. Broadband short pulse measurement by autocorrelation with a sum-frequency generation set-up

    International Nuclear Information System (INIS)

    Glotin, F.; Jaroszynski, D.; Marcouille, O.

    1995-01-01

    Previous spectral and laser pulse length measurements carried out on the CLIO FEL at wavelength λ=8.5 μm suggested that very short light pulses could be generated, about 500 fs wide (FWHM). For these measurements a Michelson interferometer with a Te crystal, as a non-linear detector, was used as a second order autocorrelation device. More recent measurements in similar conditions have confirmed that the laser pulses observed are indeed single: they are not followed by other pulses distant by the slippage length Nλ. As the single micropulse length is likely to depend on the slippage, more measurements at different wavelengths would be useful. This is not directly possible with our actual interferometer set-up, based on a phase-matched non-linear crystal. However, we can use the broadband non-linear medium provided by one of our users' experiments: Sum-Frequency Generation over surfaces. With such autocorrelation set-up, interference fringes are no more visible, but this is largely compensated by the frequency range provided. First tests at 8 μm have already been performed to validate the technic, leading to results similar to those obtained with our previous Michelson set-up

  3. Sum frequency generation spectroscopy of tetraalkylphosphonium ionic liquids at the air-liquid interface

    Science.gov (United States)

    Peñalber-Johnstone, Chariz; Adamová, Gabriela; Plechkova, Natalia V.; Bahrami, Maryam; Ghaed-Sharaf, Tahereh; Ghatee, Mohammad Hadi; Seddon, Kenneth R.; Baldelli, Steven

    2018-05-01

    Sum frequency generation (SFG) spectroscopy is a nonlinear vibrational spectroscopic technique used in the study of interfaces, due to its unique ability to distinguish surface molecules that have preferential ordering compared to the isotropic bulk. Here, a series of alkyltrioctylphosphonium chloride ionic liquids, systematically varied by cation structure, were characterized at the air-liquid interface by SFG. The effect on surface structure resulting from molecular variation (i.e., addition of cyano- and methoxy-functional groups) of the cation alkyl chain was investigated. SFG spectra in the C—H stretching region (2750-3100 cm-1) for [P8 8 8 n][Cl], where n = 4, 5, 8, 10, 12, or 14, showed characteristic changes as the alkyl chain length was increased. Spectral profiles for n = 4, 5, 8, or 10 appeared similar; however, when the fourth alkyl chain was sufficiently long (as in the case of n = 12 or n = 14), abrupt changes occurred in the spectra. Molecular dynamics (MD) simulation of a slab of each ionic liquid (with n = 8, 10, or 12) confirmed gauche defects, with enhancement for the long alkyl chain and an abrupt increase of gauche occurrence from n = 8 to n = 10. A comparison of the tilt angle distribution from the simulation and the SFG analysis show a broad distribution of angles. Using experimental SFG spectra in conjunction with MD simulations, a comprehensive molecular picture at the surface of this unique class of liquids is presented.

  4. Sum Frequency Generation Vibrational Spectroscopy of Colloidal Platinum Nanoparticle Catalysts: Disordering versus Removal of Organic Capping

    KAUST Repository

    Krier, James M.

    2012-08-23

    Recent work with nanoparticle catalysts shows that size and shape control on the nanometer scale influences reaction rate and selectivity. Sum frequency generation (SFG) vibrational spectroscopy is a powerful tool for studying heterogeneous catalysis because it enables the observation of surface intermediates during catalytic reactions. To control the size and shape of catalytic nanoparticles, an organic ligand was used as a capping agent to stabilize nanoparticles during synthesis. However, the presence of an organic capping agent presents two major challenges in SFG and catalytic reaction studies: it blocks a significant fraction of active surface sites and produces a strong signal that prevents the detection of reaction intermediates with SFG. Two methods for cleaning Pt nanoparticles capped with poly (vinylpyrrolidone) (PVP) are examined in this study: solvent cleaning and UV cleaning. Solvent cleaning leaves more PVP intact and relies on disordering with hydrogen gas to reduce the SFG signal of PVP. In contrast, UV cleaning depends on nearly complete removal of PVP to reduce SFG signal. Both UV and solvent cleaning enable the detection of reaction intermediates by SFG. However, solvent cleaning also yields nanoparticles that are stable under reaction conditions, whereas UV cleaning results in aggregation during reaction. The results of this study indicate that solvent cleaning is more advantageous for studying the effects of nanoparticle size and shape on catalytic selectivity by SFG vibrational spectroscopy. © 2012 American Chemical Society.

  5. Structure and orientation of interfacial proteins determined by sum frequency generation vibrational spectroscopy: method and application.

    Science.gov (United States)

    Ye, Shuji; Wei, Feng; Li, Hongchun; Tian, Kangzhen; Luo, Yi

    2013-01-01

    In situ and real-time characterization of molecular structures and orientation of proteins at interfaces is essential to understand the nature of interfacial protein interaction. Such work will undoubtedly provide important clues to control biointerface in a desired manner. Sum frequency generation vibrational spectroscopy (SFG-VS) has been demonstrated to be a powerful technique to study the interfacial structures and interactions at the molecular level. This paper first systematically introduced the methods for the calculation of the Raman polarizability tensor, infrared transition dipole moment, and SFG molecular hyperpolarizability tensor elements of proteins/peptides with the secondary structures of α-helix, 310-helix, antiparallel β-sheet, and parallel β-sheet, as well as the methodology to determine the orientation of interfacial protein secondary structures using SFG amide I spectra. After that, recent progresses on the determination of protein structure and orientation at different interfaces by SFG-VS were then reviewed, which provides a molecular-level understanding of the structures and interactions of interfacial proteins, specially understanding the nature of driving force behind such interactions. Although this review has focused on analysis of amide I spectra, it will be expected to offer a basic idea for the spectral analysis of amide III SFG signals and other complicated molecular systems such as RNA and DNA. Copyright © 2013 Elsevier Inc. All rights reserved.

  6. Sum frequency and second harmonic generation from the surface of a liquid microjet

    Energy Technology Data Exchange (ETDEWEB)

    Smolentsev, Nikolay; Chen, Yixing; Roke, Sylvie, E-mail: sylvie.roke@epfl.ch [Laboratory for Fundamental Biophotonics (LBP), Institute of Bioengineering (IBI), School of Engineering STI, École Polytechnique Fédérale de Lausanne EPFL, 1015 Lausanne (Switzerland); Jena, Kailash C. [Laboratory for Fundamental Biophotonics (LBP), Institute of Bioengineering (IBI), School of Engineering STI, École Polytechnique Fédérale de Lausanne EPFL, 1015 Lausanne (Switzerland); Department of Physics, Indian Institute of Technology Ropar, Rupnagar, 140001 (India); Brown, Matthew A. [Laboratory for Surface Science and Technology, Department of Materials, ETH Zürich, CH-8093 Zurich (Switzerland)

    2014-11-14

    The use of a liquid microjet as a possible source of interest for Second Harmonic Generation (SHG) and Sum Frequency Generation (SFG) spectroscopy is examined. We measured non-resonant SHG scattering patterns from the air/water interface of a microjet of pure water and observe a strong enhancement of the SHG signal for certain scattering angles. These enhancements can be explained by the optical properties and the shape of the liquid microjet. SFG experiments at the surface of a liquid microjet of ethanol in air show that it is also possible to measure the coherent vibrational SFG spectrum of the ethanol/air interface in this way. Our findings are useful for future far-UV or X-ray based nonlinear optical surface experiments on liquid jets. In addition, combined X-ray photoelectron spectroscopy and SHG/SFG measurements are feasible, which will be very useful in improving our understanding of the molecular foundations of electrostatic and chemical surface properties and phenomena.

  7. Sum frequency and second harmonic generation from the surface of a liquid microjet

    Science.gov (United States)

    Smolentsev, Nikolay; Chen, Yixing; Jena, Kailash C.; Brown, Matthew A.; Roke, Sylvie

    2014-11-01

    The use of a liquid microjet as a possible source of interest for Second Harmonic Generation (SHG) and Sum Frequency Generation (SFG) spectroscopy is examined. We measured non-resonant SHG scattering patterns from the air/water interface of a microjet of pure water and observe a strong enhancement of the SHG signal for certain scattering angles. These enhancements can be explained by the optical properties and the shape of the liquid microjet. SFG experiments at the surface of a liquid microjet of ethanol in air show that it is also possible to measure the coherent vibrational SFG spectrum of the ethanol/air interface in this way. Our findings are useful for future far-UV or X-ray based nonlinear optical surface experiments on liquid jets. In addition, combined X-ray photoelectron spectroscopy and SHG/SFG measurements are feasible, which will be very useful in improving our understanding of the molecular foundations of electrostatic and chemical surface properties and phenomena.

  8. Elucidation of Compression-Induced Surface Crystallization in Amorphous Tablets Using Sum Frequency Generation (SFG) Microscopy.

    Science.gov (United States)

    Mah, Pei T; Novakovic, Dunja; Saarinen, Jukka; Van Landeghem, Stijn; Peltonen, Leena; Laaksonen, Timo; Isomäki, Antti; Strachan, Clare J

    2017-05-01

    To investigate the effect of compression on the crystallization behavior in amorphous tablets using sum frequency generation (SFG) microscopy imaging and more established analytical methods. Tablets containing neat amorphous griseofulvin with/without excipients (silica, hydroxypropyl methylcellulose acetate succinate (HPMCAS), microcrystalline cellulose (MCC) and polyethylene glycol (PEG)) were prepared. They were analyzed upon preparation and storage using attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy, scanning electron microscopy (SEM) and SFG microscopy. Compression-induced crystallization occurred predominantly on the surface of the neat amorphous griseofulvin tablets, with minimal crystallinity being detected in the core of the tablets. The presence of various types of excipients was not able to mitigate the compression-induced surface crystallization of the amorphous griseofulvin tablets. However, the excipients affected the crystallization rate of amorphous griseofulvin in the core of the tablet upon compression and storage. SFG microscopy can be used in combination with ATR-FTIR spectroscopy and SEM to understand the crystallization behaviour of amorphous tablets upon compression and storage. When selecting excipients for amorphous formulations, it is important to consider the effect of the excipients on the physical stability of the amorphous formulations.

  9. Small Molecules and Sum Frequency Generation Probes of Nanoparticulate TiO2

    Science.gov (United States)

    Shultz, Mary Jane

    2006-03-01

    Anatase TiO2 is known to photo catalytically mineralize a wide variety of pollutants and pathogens, both airborne and in aqueous solution. One of the major benefits of basing water treatment systems on TiO2 is that it is environmentally benign and so non toxic that it is used as a colorant in creamy salad dressing. The primary impediment to wide spread implementation of a TiO2 based system for water decontamination is that the quantum efficiency in contact with condense phase water is less than 5%. Since the quantum efficiency for destruction of airborne materials is greater than 80%, the potential for increased efficiency is very real. To convert the potential to practice, the oxidation mechanism needs to be more fully understood. We will report on the results of using a nonlinear optical spectroscopy, sum frequency generation (SFG) as an in situ probe of interactions at the TiO2 surface. Results suggest that the dominant oxidation mechanism converts from a direct to an indirect mechanism as the water content (vapor pressure) increases. This presentation will discuss the probe technique as well as the results.

  10. Sum frequency and second harmonic generation from the surface of a liquid microjet

    International Nuclear Information System (INIS)

    Smolentsev, Nikolay; Chen, Yixing; Roke, Sylvie; Jena, Kailash C.; Brown, Matthew A.

    2014-01-01

    The use of a liquid microjet as a possible source of interest for Second Harmonic Generation (SHG) and Sum Frequency Generation (SFG) spectroscopy is examined. We measured non-resonant SHG scattering patterns from the air/water interface of a microjet of pure water and observe a strong enhancement of the SHG signal for certain scattering angles. These enhancements can be explained by the optical properties and the shape of the liquid microjet. SFG experiments at the surface of a liquid microjet of ethanol in air show that it is also possible to measure the coherent vibrational SFG spectrum of the ethanol/air interface in this way. Our findings are useful for future far-UV or X-ray based nonlinear optical surface experiments on liquid jets. In addition, combined X-ray photoelectron spectroscopy and SHG/SFG measurements are feasible, which will be very useful in improving our understanding of the molecular foundations of electrostatic and chemical surface properties and phenomena

  11. Sum frequency generation (SFG) vibrational spectroscopy of planar phosphatidylethanolamine hybrid bilayer membranes under water.

    Science.gov (United States)

    Kett, Peter J N; Casford, Michael T L; Davies, Paul B

    2010-06-15

    Sum frequency generation (SFG) spectroscopy has been used to study the structure of phosphatidylethanolamine hybrid bilayer membranes (HBMs) under water at ambient temperatures. The HBMs were formed using a modified Langmuir-Schaefer technique and consisted of a layer of dipalmitoyl phosphatidylethanolamine (DPPE) physisorbed onto an octadecanethiol (ODT) self-assembled monolayer (SAM) at a series of surface pressures from 1 to 40 mN m(-1). The DPPE and ODT were selectively deuterated so that the contributions to the SFG spectra from the two layers could be determined separately. SFG spectra in both the C-H and C-D stretching regions confirmed that a monolayer of DPPE had been adsorbed to the ODT SAM and that there were gauche defects within the alkyl chains of the phospholipid. On adsorption of a layer of DPPE, methylene modes from the ODT SAM were detected, indicating that the phospholipid had partially disordered the alkanethiol monolayer. SFG spectra recorded in air indicated that removal of water from the surface of the HBM resulted in disruption of the DPPE layer and the formation of phospholipid bilayers.

  12. Polarization entanglement of sum-frequency photons: A tool to probe the Markovian limit

    Science.gov (United States)

    Volkov, Victor; Chelli, Riccardo

    2015-06-01

    The article addresses the possibility of entanglement-specific infrared-visible sum-frequency generation spectroscopy. In the case of an anisotropic interface, it is possible to employ SSS and PSS polarizations to detect responses not only specific to χY Y Y and χX Y Y nonlinearities, but also to higher-order χ(Y Y Y )(X Y Y ) and χ(X Y Y )(Y Y Y ) nonlinearities. Using quantum mechanical studies of the rhenium complex [Re (OH) 3(CO) 3] as a molecular model, we demonstrate that if such complexes would form an anisotropic orientational distribution at a surface, under the considered geometry and the polarization settings, we may prepare quantum correlated C =O vibrational states to emit polarization-entangled photons. Accordingly, we explore the possibility of a polarization-measurement protocol to extract spectral signatures of the entangled states. The response would be informative on intramolecular interactions. As a result, we discuss the possible practical implications in probing dynamics at interfaces, and different opportunities in the preparation of entangled vibrational states of quantified fidelity.

  13. Sum-Frequency-Generation-Based Laser Sidebands for Tunable Femtosecond Raman Spectroscopy in the Ultraviolet

    Directory of Open Access Journals (Sweden)

    Liangdong Zhu

    2015-04-01

    Full Text Available Femtosecond stimulated Raman spectroscopy (FSRS is an emerging molecular structural dynamics technique for functional materials characterization typically in the visible to near-IR range. To expand its applications we have developed a versatile FSRS setup in the ultraviolet region. We use the combination of a narrowband, ~400 nm Raman pump from a home-built second harmonic bandwidth compressor and a tunable broadband probe pulse from sum-frequency-generation-based cascaded four-wave mixing (SFG-CFWM laser sidebands in a thin BBO crystal. The ground state Raman spectrum of a laser dye Quinolon 390 in methanol that strongly absorbs at ~355 nm is systematically studied as a standard sample to provide previously unavailable spectroscopic characterization in the vibrational domain. Both the Stokes and anti-Stokes Raman spectra can be collected by selecting different orders of SFG-CFWM sidebands as the probe pulse. The stimulated Raman gain with the 402 nm Raman pump is >21 times larger than that with the 550 nm Raman pump when measured at the 1317 cm−1 peak for the aromatic ring deformation and ring-H rocking mode of the dye molecule, demonstrating that pre-resonance enhancement is effectively achieved in the unique UV-FSRS setup. This added tunability in the versatile and compact optical setup enables FSRS to better capture transient conformational snapshots of photosensitive molecules that absorb in the UV range.

  14. Theoretical vibrational sum-frequency generation spectroscopy of water near lipid and surfactant monolayer interfaces

    Energy Technology Data Exchange (ETDEWEB)

    Roy, S.; Gruenbaum, S. M.; Skinner, J. L. [Theoretical Chemistry Institute and Department of Chemistry, 1101 University Ave., University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States)

    2014-11-14

    Understanding the structure of water near cell membranes is crucial for characterizing water-mediated events such as molecular transport. To obtain structural information of water near a membrane, it is useful to have a surface-selective technique that can probe only interfacial water molecules. One such technique is vibrational sum-frequency generation (VSFG) spectroscopy. As model systems for studying membrane headgroup/water interactions, in this paper we consider lipid and surfactant monolayers on water. We adopt a theoretical approach combining molecular dynamics simulations and phase-sensitive VSFG to investigate water structure near these interfaces. Our simulated spectra are in qualitative agreement with experiments and reveal orientational ordering of interfacial water molecules near cationic, anionic, and zwitterionic interfaces. OH bonds of water molecules point toward an anionic interface leading to a positive VSFG peak, whereas the water hydrogen atoms point away from a cationic interface leading to a negative VSFG peak. Coexistence of these two interfacial water species is observed near interfaces between water and mixtures of cationic and anionic lipids, as indicated by the presence of both negative and positive peaks in their VSFG spectra. In the case of a zwitterionic interface, OH orientation is toward the interface on the average, resulting in a positive VSFG peak.

  15. Generation and tunable enhancement of a sum-frequency signal in lithium niobate nanowires

    Science.gov (United States)

    Sergeyev, Anton; Reig Escalé, Marc; Grange, Rachel

    2017-02-01

    Recent developments in the fabrication of lithium niobate (LiNbO3) structures down to the nanoscale opens up novel applications of this versatile material in nonlinear optics. Current nonlinear optical studies in sub-micron waveguides are mainly restricted to the generation of second and third harmonics. In this work, we demonstrate the generation and waveguiding of the sum-frequency generation (SFG) signal in a single LiNbO3 nanowire with a cross-section of 517 nm  ×  654 nm. Furthermore, we enhance the guided SFG signal 17.9 times by means of modal phase matching. We also display tuning of the phase-matched wavelength by varying the nanowire cross-section and changing the polarization of the incident laser. The results prove that LiNbO3 nanowires can be successfully used for nonlinear wave-mixing applications and assisting the miniaturization of optical devices. , which features invited work from the best early-career researchers working within the scope of J Phys D. This project is part of the Journal of Physics series’ 50th anniversary celebrations in 2017. Rachel Grange was selected by the Editorial Board of J Phys D as an Emerging Leader.

  16. High-order sum and difference-frequency generation in helium

    International Nuclear Information System (INIS)

    Crane, J.K.; Perry, M.D.

    1993-01-01

    High-order harmonic generation provides a new method for generating coherent, XUV radiation. These harmonics are characterized by a rapid, pertubative drop at low orders, followed by a broad plateau extending to photon energies of 150 eV in the lighter, rare gas atoms. An experimentally observed limit coincides with the theoretical limit for harmonic generation in neutral atoms given by the expression E c (eV)=IP(0)+3U p (I), where E c is the energy cutoff of the harmonic plateau, IP(O) is the field-free ionization potential and U p is the electron quiver energy at the maximum intensity, I seen by the atom. As part of an effort to develop this technique into a general purpose XUV source, extensive work to understand the phase-matching between the harmonic and driving fields, and the resulting effect on the conversion efficiency, angular distribution and spectral brightness has been undertaken at several. Though, certain aspects of the harmonically generated radiation such as the polarization, relative strength of a given harmonic, and the plateau extent, are defined by the single atom-field interaction. Specifically, the single-atom harmonic spectrum is determined primarily by the interaction of a driven, quasi-free electron with the atomic potential. Using two, independent fields one can affect the electron motion by controlling the relative strength, polarization, and phase of the fields and alter the harmonic spectrum. In this paper we discuss initial, two-color experiments where we drive the atom with two fields of different frequencies: 1053 nm (1ω) and 526 nm (2ω). In addition to the higher, odd harmonics, we observe sets of three additional peaks that we attribute to sum and difference-frequency generation between the two fields. By controlling the relative polarization between the two fields we can control the relative strength of the harmonic and mixing components, as well as the polarization of the output XUV photon

  17. Efficient generation of continuous-wave yellow-orange light using sum-frequency in periodically poled KTP

    DEFF Research Database (Denmark)

    Janousek, Jiri; Johansson, Sandra; Tidemand-Lichtenberg, Peter

    We present highly efficient sum-frequency generation between two CW 1064 and 1342 nm laser lines of two Nd:YVO4 lasers using periodically poled KTP. This is an all solid-state light source in the yellow-orange spectral range....

  18. Determining In Situ Protein Conformation and Orientation from the Amide-I Sum-Frequency Generation Spectrum: Theory and Experiment

    NARCIS (Netherlands)

    Roeters, S.J.; van Dijk, C.N.; Torres Knoop, A.; Backus, E.H.G.; Campen, R.K.; Bonn, M.; Woutersen, S.

    2013-01-01

    Vibrational sum-frequency generation (VSFG) spectra of the amide-I band of proteins can give detailed insight into biomolecular processes near membranes. However, interpreting these spectra in terms of the conformation and orientation of a protein can be difficult, especially in the case of complex

  19. Multimodal Broadband Vibrational Sum Frequency Generation (MM-BB-V-SFG) Spectrometer and Microscope.

    Science.gov (United States)

    Lee, Christopher M; Kafle, Kabindra; Huang, Shixin; Kim, Seong H

    2016-01-14

    A broadband sum frequency generation (BB-SFG) spectrometer with multimodal (MM) capabilities was constructed, which could be routinely reconfigured for tabletop experiments in reflection, transmission, and total internal reflection (TIR) geometries, as well as microscopic imaging. The system was constructed using a Ti:sapphire amplifier (800 nm, pulse width = 85 fs, repetition rate = 2 kHz), an optical parameter amplification (OPA) system for production of broadband IR pulses tunable between 1000 and 4000 cm(-1), and two Fabry-Pérot etalons arranged in series for production of narrowband 800 nm pulses. The key feature allowing the MM operation was the nearly collinear alignment of the visible (fixed, 800 nm) and infrared (tunable, 1000-4000 cm(-1)) pulses which were spatially separated. Physical insights discussed in this paper include the comparison of spectral bandwidth produced with 40 and 85 fs pump beams, the improvement of spectral resolution using etalons, the SFG probe volume in bulk analysis, the normalization of SFG signals, the stitching of multiple spectral segments, and the operation in different modes for air/liquid and adsorbate/solid interfaces, bulk samples, as well as spectral imaging combined with principle component analysis (PCA). The SFG spectral features obtained with the MM-BB-SFG system were compared with those obtained with picosecond-scanning-SFG system and high-resolution BB-SFG system (HR-BB-SFG) for dimethyl sulfoxide, α-pinene, and various samples containing cellulose (purified commercial products, Cladophora cell wall, cotton and flax fibers, and onion epidermis cell wall).

  20. Atmospheric pressure reaction cell for operando sum frequency generation spectroscopy of ultrahigh vacuum grown model catalysts

    Science.gov (United States)

    Roiaz, Matteo; Pramhaas, Verena; Li, Xia; Rameshan, Christoph; Rupprechter, Günther

    2018-04-01

    A new custom-designed ultrahigh vacuum (UHV) chamber coupled to a UHV and atmospheric-pressure-compatible spectroscopic and catalytic reaction cell is described, which allows us to perform IR-vis sum frequency generation (SFG) vibrational spectroscopy during catalytic (kinetic) measurements. SFG spectroscopy is an exceptional tool to study vibrational properties of surface adsorbates under operando conditions, close to those of technical catalysis. This versatile setup allows performing surface science, SFG spectroscopy, catalysis, and electrochemical investigations on model systems, including single crystals, thin films, and deposited metal nanoparticles, under well-controlled conditions of gas composition, pressure, temperature, and potential. The UHV chamber enables us to prepare the model catalysts and to analyze their surface structure and composition by low energy electron diffraction and Auger electron spectroscopy, respectively. Thereafter, a sample transfer mechanism moves samples under UHV to the spectroscopic cell, avoiding air exposure. In the catalytic cell, SFG spectroscopy and catalytic tests (reactant/product analysis by mass spectrometry or gas chromatography) are performed simultaneously. A dedicated sample manipulation stage allows the model catalysts to be examined from LN2 temperature to 1273 K, with gaseous reactants in a pressure range from UHV to atmospheric. For post-reaction analysis, the SFG cell is rapidly evacuated and samples are transferred back to the UHV chamber. The capabilities of this new setup are demonstrated by benchmark results of CO adsorption on Pt and Pd(111) single crystal surfaces and of CO adsorption and oxidation on a ZrO2 supported Pt nanoparticle model catalyst grown by atomic layer deposition.

  1. Sum-frequency spectroscopic studies: I. Surface melting of ice, II. Surface alignment of polymers

    Energy Technology Data Exchange (ETDEWEB)

    Wei, Xing [Univ. of California, Berkeley, CA (United States)

    2000-01-01

    Surface vibrational spectroscopy via infrared-visible sum-frequency generation (SFG) has been established as a useful tool to study the structures of different kinds of surfaces and interfaces. This technique was used to study the (0001) face of hexagonal ice (Ih). SFG spectra in the O-H stretch frequency range were obtained at various sample temperatures. For the vapor(air)/ice interface, the degree of orientational order of the dangling OH bonds at the surface was measured as a function of temperature. Disordering sets in around 200 K and increases dramatically with temperature, which is strong evidence of surface melting of ice. For the other ice interfaces (silica/OTS/ice and silica/ice), a similar temperature dependence of the hydrogen bonded OH stretch peak was observed; the free OH stretch mode, however, appears to be different from that of the vapor (air)/ice interface due to interactions at the interfaces. The technique was also used to measure the orientational distributions of the polymer chains on a rubbed polyvinyl alcohol surface. Results show that the polymer chains at the surface appear to be well aligned by rubbing, and the adsorbed liquid crystal molecules are aligned, in turn, by the surface polymer chains. A strong correlation exists between the orientational distributions of the polymer chains and the liquid crystal molecules, indicating that the surface-induced bulk alignment of a liquid crystal film by rubbed polymer surfaces is via an orientational epitaxy-like mechanism. This thesis also contains studies on some related issues that are crucial to the above applications. An experiment was designed to measure SFG spectra in both reflection and transmission. The result confirms that SFG in reflection is generally dominated by the surface contribution. Another issue is the motional effect due to fast orientational motion of molecules at a surface or interface. Calculations show that the effect is significant if the molecular orientation varies

  2. Quantitative spectral and orientational analysis in surface sum frequency generation vibrational spectroscopy (SFG-VS)

    Science.gov (United States)

    Wang, Hong-Fei; Gan, Wei; Lu, Rong; Rao, Yi; Wu, Bao-Hua

    Sum frequency generation vibrational spectroscopy (SFG-VS) has been proven to be a uniquely effective spectroscopic technique in the investigation of molecular structure and conformations, as well as the dynamics of molecular interfaces. However, the ability to apply SFG-VS to complex molecular interfaces has been limited by the ability to abstract quantitative information from SFG-VS experiments. In this review, we try to make assessments of the limitations, issues and techniques as well as methodologies in quantitative orientational and spectral analysis with SFG-VS. Based on these assessments, we also try to summarize recent developments in methodologies on quantitative orientational and spectral analysis in SFG-VS, and their applications to detailed analysis of SFG-VS data of various vapour/neat liquid interfaces. A rigorous formulation of the polarization null angle (PNA) method is given for accurate determination of the orientational parameter D = /, and comparison between the PNA method with the commonly used polarization intensity ratio (PIR) method is discussed. The polarization and incident angle dependencies of the SFG-VS intensity are also reviewed, in the light of how experimental arrangements can be optimized to effectively abstract crucial information from the SFG-VS experiments. The values and models of the local field factors in the molecular layers are discussed. In order to examine the validity and limitations of the bond polarizability derivative model, the general expressions for molecular hyperpolarizability tensors and their expression with the bond polarizability derivative model for C3v, C2v and C∞v molecular groups are given in the two appendixes. We show that the bond polarizability derivative model can quantitatively describe many aspects of the intensities observed in the SFG-VS spectrum of the vapour/neat liquid interfaces in different polarizations. Using the polarization analysis in SFG-VS, polarization selection rules or

  3. Effect of surface structure on catalytic reactions: A sum frequency generation surface vibrational spectroscopy study

    International Nuclear Information System (INIS)

    McCrea, Keith R.

    2001-01-01

    In the results discussed above, it is clear that Sum Frequency Generation (SFG) is a unique tool that allows the detection of vibrational spectra of adsorbed molecules present on single crystal surfaces under catalytic reaction conditions. Not only is it possible to detect active surface intermediates, it is also possible to detect spectator species which are not responsible for the measured turnover rates. By correlating high-pressure SFG spectra under reaction conditions and gas chromatography (GC) kinetic data, it is possible to determine which species are important under reaction intermediates. Because of the flexibility of this technique for studying surface intermediates, it is possible to determine how the structures of single crystal surfaces affect the observed rates of catalytic reactions. As an example of a structure insensitive reaction, ethylene hydrogenation was explored on both Pt(111) and Pt(100). The rates were determined to be essentially the same. It was observed that both ethylidyne and di-(sigma) bonded ethylene were present on the surface under reaction conditions on both crystals, although in different concentrations. This result shows that these two species are not responsible for the measured turnover rate, as it would be expected that one of the two crystals would be more active than the other, since the concentration of the surface intermediate would be different on the two crystals. The most likely active intermediates are weakly adsorbed molecules such as(pi)-bonded ethylene and ethyl. These species are not easily detected because their concentration lies at the detection limit of SFG. The SFG spectra and GC data essentially show that ethylene hydrogenation is structure insensitive for Pt(111) and Pt(100). SFG has proven to be a unique and excellent technique for studying adsorbed species on single crystal surfaces under high-pressure catalytic reactions. Coupled with kinetic data obtained from gas chromatography measurements, it can

  4. Direct comparison of phase-sensitive vibrational sum frequency generation with maximum entropy method: case study of water.

    Science.gov (United States)

    de Beer, Alex G F; Samson, Jean-Sebastièn; Hua, Wei; Huang, Zishuai; Chen, Xiangke; Allen, Heather C; Roke, Sylvie

    2011-12-14

    We present a direct comparison of phase sensitive sum-frequency generation experiments with phase reconstruction obtained by the maximum entropy method. We show that both methods lead to the same complex spectrum. Furthermore, we discuss the strengths and weaknesses of each of these methods, analyzing possible sources of experimental and analytical errors. A simulation program for maximum entropy phase reconstruction is available at: http://lbp.epfl.ch/. © 2011 American Institute of Physics

  5. Study of confinement and sliding friction of fluids using sum frequency generation spectroscopy

    Science.gov (United States)

    Nanjundiah, Kumar

    2007-12-01

    Friction and wear are important technologically. Tires on wet roads, windshield wipers and human joints are examples where nanometer-thick liquids are confined between flexible-rigid contact interfaces. Fundamental understanding of the structure of these liquids can assist in the design of products such as artificial joints and lubricants for Micro-electromechanical systems [MEMS]. Prior force measurements have suggested an increase in apparent viscosity of confined liquid and sometimes solid-like responses. But, these have not given the state of molecules under confinement. In the present study, we have used a surface sensitive, non-linear optical technique (infrared-visible sum frequency generation spectroscopy [SFG]) to investigate molecular structure at hidden interfaces. SFG can identify chemical groups, concentration and orientation of molecules at an interface. A friction cell was developed to study sliding of a smooth elastomeric lens against a sapphire surface. Experiments were done with dry sliding as well as lubricated sliding in the presence of linear alkane liquids. SFG spectra at the alkane/sapphire interface revealed ordering of the confined alkane molecules. These were more ordered than alkane liquid, but less ordered than alkane crystal. Cooling of the confined alkane below its melting temperature [TM] led to molecular orientation that was different from that of bulk crystal next to a sapphire surface. Molecules were oriented with their symmetry axis parallel to the surface normal. In addition, the melting temperature [Tconf] under confinement for a series of linear alkanes (n =15--27) showed a surprising trend. Intermediate molecular weights showed melting point depression. The T conf values suggested that melting started at the alkane/sapphire interface. In another investigation, confinement of water between an elastomeric PDMS lens and sapphire was studied. SFG spectra at the sapphire/water/PDMS interface revealed a heterogeneous morphology. The

  6. Single-frequency blue light generation by single-pass sum-frequency generation in a coupled ring cavity tapered laser

    DEFF Research Database (Denmark)

    Jensen, Ole Bjarlin; Petersen, Paul Michael

    2013-01-01

    A generic approach for generation of tunable single frequency light is presented. 340 mW of near diffraction limited, single-frequency, and tunable blue light around 459 nm is generated by sum-frequency generation (SFG) between two tunable tapered diode lasers. One diode laser is operated in a ring...... cavity and another tapered diode laser is single-passed through a nonlinear crystal which is contained in the coupled ring cavity. Using this method, the single-pass conversion efficiency is more than 25%. In contrast to SFG in an external cavity, the system is entirely self-stabilized with no electronic...

  7. Effects of cations and cholesterol with sphingomyelin membranes investigated by high-resolution broadband sum frequency vibrational spectroscopy

    Science.gov (United States)

    Zhang, Zhen; Feng, Rong-juan; Li, Yi-yi; Liu, Ming-hua; Guo, Yuan

    2017-08-01

    Sphingomyelin(SM) is specifically enriched in the plasma membrane of mammalian cells. Its molecular structure is compose by N-acyl-Derythro-sphingosylphosphorylcholine. The function of the SM related to membrane signaling and protein trafficking are relied on the interactions of the SM, cations, cholesterol and proteins. In this report, the interaction of three different nature SMs, cations and cholesterol at air/aqueous interfaces studied by high-resolution broadband sum frequency vibrational spectroscopy, respectively. Our results shed lights on understanding the relationship between SMs monolayer, cholesterol and Cations.

  8. All-solid-state quasi-CW yellow laser with intracavity self-Raman conversion and sum frequency generation

    International Nuclear Information System (INIS)

    Kananovich, A; Grabtchikov, A; Orlovich, V; Demidovich, A; Danailov, M

    2010-01-01

    Quasi continuous-wave (qCW) yellow emission (pulse duration 5 ms, repetition rate 20 Hz) at 559 nm is demonstrated through intracavity sum frequency generation (SFG) of Stokes and fundamental fields in Nd:YVO 4 diode pumped self-Raman laser for the first time. Average in pulse output power at 559 nm was 0.47 W for 22 W of pump power, which corresponds to 2.1% of diode-to-yellow efficiency. The pulsed mode of operation was due to diode pump modulation and was used to reduce thermal stress of the crystal

  9. Sum frequency generation of CO on (III) and polycrystalline platinum electrode surfaces: Evidence for SFG invisible surface CO

    Energy Technology Data Exchange (ETDEWEB)

    Baldelli, S.; Markovic, N.; Ross, P.; Shen, Y.R.; Somorjai, G.

    1999-10-21

    The vibrational spectroscopy sum frequency generation (SFG) is used to investigate the adsorption of carbon monoxide on the single crystal (111) and polycrystalline platinum surfaces. By varying the frequency and polarization of the light beams, different surface species of CO species are probed. SFG signal intensities for different polarization indicate that adsorbed CO polarizability is significantly perturbed from the gas-phase molecule. The SFG signal of CO disappears well below the main oxidation potential of CO to CO{sub 2}. The disappearance of the CO signal is interpreted as a transformation in the CO layer to a state which is invisible to SFG. The invisible state is suggested to be CO with the bond axis nearly parallel to the platinum surface.

  10. Sum Frequency Generation Vibrational Spectroscopy and Kinetic Study of 2-Methylfuran and 2,5-Dimethylfuran Hydrogenation over 7 nm Platinum Cubic Nanoparticles

    KAUST Repository

    Aliaga, Cesar; Tsung, Chia-Kuang; Alayoglu, Selim; Komvopoulos, Kyriakos; Yang, Peidong; Somorjai, Gabor A.

    2011-01-01

    Sum frequency generation vibrational spectroscopy and kinetic measurements obtained from gas chromatography were used to study the adsorption and hydrogenation of 2-methylfuran (MF) and 2,5-dimethylfuran (DMF) over cubic Pt nanoparticles of 7 nm

  11. Sum-frequency generation from molecular monolayers using 14 μm radiation from the FELIX free-electron laser

    International Nuclear Information System (INIS)

    Van der Ham, E.W.M.; Vrehen, Q.H.F.; Eliel, E.R.

    1995-01-01

    Sum-frequency generation (SFG) has developed into a widely applied tool for study of surfaces and interfaces where molecules are present. It combines the surface specificity of a second-order nonlinear optical technique with the power of a spectroscopic method, and it can be used under widely varying experimental conditions ranging from UHV to electrochemical cells. The important characteristic of SFG is that it allows one to study the average spatial orientation of a molecular bond in a monolayer of molecules at an interface. Until recently SFG measurements were confined to the frequency interval Y μ > 1700 cm -1 because of a lack of suitable laser sources at wave-lengths λ > 6 μm. So for most molecules only a few vibrational modes and thus intramolecular bonds can be studied. We have developed a universal sum-frequency spectrometer around the FELIX free-electron law that covers the complete molecular fingerprint since we can generate any IR wavelength between 2.75 and 110 fμ at the FELIX facility. We have used this setup for a series of exploratory SFG experiments in a frequency range that was hitherto unexplored in the study of molecular monolayers. We have studied thiol monolayers chemisorbed on a variety of noble metals (Au, Ag, Pt) where we focussed on the C-S stretch vibration at ν = 702 cm -1 (λ = 14.3 μm). We have found spectroscopic features revealing the presence of both the trane and gauche conformers of the adsorbed molecules. The present measurements open a whole new wavelength range for nonlinear optical studies of interfaces

  12. Phase distortions in sum- and difference-frequency mixing in crystals

    International Nuclear Information System (INIS)

    Smith, A.V.; Bowers, M.S.

    1995-01-01

    We show that if two waves are incident on a quadratically nonlinear crystal, with the third wave generated entirely within the crystal, a phase-velocity mismatch (Δk ≠ 0) leads to intensity-dependent phase shifts of the generated wave only if there is walk-off, linear absorption, or significant diffraction of at least one of the waves as well as significant energy exchange among the waves. The result is frequency broadening and wave-front distortion of the generated wave. Although the induced phase distortions are usually quite small, they may be significant in applications that require high spectral resolution or pointing accuracy

  13. A new approach to sum frequency generation of single-frequency blue light in a coupled ring cavity

    DEFF Research Database (Denmark)

    Jensen, Ole Bjarlin; Petersen, Paul Michael

    2014-01-01

    We present a generic approach for the generation of tunable single-frequency light and demonstrate generation of more than 300 mW tunable light around 460 nm. One tapered diode laser is operated in a coupled ring cavity containing the nonlinear crystal and another tapered diode laser is sent thro...... through the nonlinear crystal in a single pass. A high conversion efficiency of more than 25 % of the single-pass laser is enabled by the high circulating power in the coupled cavity. The system is entirely self-stabilized with no need for electronic locking....

  14. Collective excitations of strongly coupled bilayer charged Bose liquids in the third-frequency-moment sum rule

    International Nuclear Information System (INIS)

    Tas, Murat; Tanatar, B.

    2008-01-01

    We calculate the collective excitation modes of strongly coupled bilayer charged Bose systems. We employ the dielectric matrix formulation to study the correlation effects within the random-phase approximation (RPA), the self consistent field approximation Singwi, Tosi, Land, and Sjoelander (STLS), and the quasilocalized charge approximation (QLCA), which satisfies the third-frequency-moment ( 3 >) sum rule. We find that the QLCA predicts a long-wavelength correlation-induced energy gap in the out-of-phase plasmon mode, similar to the situation in electronic bilayer systems. The energy gap and the plasmon density of states are studied as a function of interlayer separation and coupling parameter r s . The results should be helpful for experimental investigations

  15. Salt Effects on Surface Structures of Polyelectrolyte Multilayers (PEMs) Investigated by Vibrational Sum Frequency Generation (SFG) Spectroscopy.

    Science.gov (United States)

    Ge, Aimin; Matsusaki, Michiya; Qiao, Lin; Akashi, Mitsuru; Ye, Shen

    2016-04-26

    Sum frequency generation (SFG) vibrational spectroscopy was employed to investigate the surface structures of polyelectrolyte multilayers (PEMs) constructed by sequentially alternating adsorption of poly(diallyldimethylammonium chloride) (PDDA) and poly(styrenesulfonate) (PSS). It was found that the surface structures and surface charge density of the as-deposited PEMs of PDDA/PSS significantly depend on the concentration of sodium chloride (NaCl) present in the polyelectrolyte solutions. Furthermore, it was found that the surface structure of the as-deposited PEMs is in a metastable state and will reach the equilibrium state by diffusion of the polyelectrolyte chain after an aging process, resulting in a polyelectrolyte mixture on the PEM surfaces.

  16. Quantification of crystalline cellulose in lignocellulosic biomass using sum frequency generation (SFG) vibration spectroscopy and comparison with other analytical methods.

    Science.gov (United States)

    Barnette, Anna L; Lee, Christopher; Bradley, Laura C; Schreiner, Edward P; Park, Yong Bum; Shin, Heenae; Cosgrove, Daniel J; Park, Sunkyu; Kim, Seong H

    2012-07-01

    The non-centrosymmetry requirement of sum frequency generation (SFG) vibration spectroscopy allows the detection and quantification of crystalline cellulose in lignocellulose biomass without spectral interferences from hemicelluloses and lignin. This paper shows a correlation between the amount of crystalline cellulose in biomass and the SFG signal intensity. Model biomass samples were prepared by mixing commercially available cellulose, xylan, and lignin to defined concentrations. The SFG signal intensity was found sensitive to a wide range of crystallinity, but varied non-linearly with the mass fraction of cellulose in the samples. This might be due to the matrix effects such as light scattering and absorption by xylan and lignin, as well as the non-linear density dependence of the SFG process itself. Comparison with other techniques such as XRD, FT-Raman, FT-IR and NMR demonstrate that SFG can be a complementary and sensitive tool to assess crystalline cellulose in biomass. Copyright © 2012 Elsevier Ltd. All rights reserved.

  17. Total internal reflection sum-frequency generation spectroscopy and dense gold nanoparticles monolayer: a route for probing adsorbed molecules

    International Nuclear Information System (INIS)

    Tourillon, Gerard; Dreesen, Laurent; Volcke, Cedric; Sartenaer, Yannick; Thiry, Paul A; Peremans, Andre

    2007-01-01

    We show that sum-frequency generation spectroscopy performed in the total internal reflection configuration (TIR-SFG) combined with a dense gold nanoparticles monolayer allows us to study, with an excellent signal to noise ratio and high signal to background ratio, the conformation of adsorbed molecules. Dodecanethiol (DDT) was used as probe molecules in order to assess the potentialities of the approach. An enhancement of more than one order of magnitude of the SFG signals arising from the adsorbed species is observed with the TIR geometry compared to the external reflection one while the SFG non-resonant contribution remains the same for both configurations. Although further work is required to fully understand the origin of the SFG process on nanoparticles, our work opens new possibilities for studying nanostructures

  18. Selective detection of crystalline cellulose in plant cell walls with sum-frequency-generation (SFG) vibration spectroscopy.

    Science.gov (United States)

    Barnette, Anna L; Bradley, Laura C; Veres, Brandon D; Schreiner, Edward P; Park, Yong Bum; Park, Junyeong; Park, Sunkyu; Kim, Seong H

    2011-07-11

    The selective detection of crystalline cellulose in biomass was demonstrated with sum-frequency-generation (SFG) vibration spectroscopy. SFG is a second-order nonlinear optical response from a system where the optical centrosymmetry is broken. In secondary plant cell walls that contain mostly cellulose, hemicellulose, and lignin with varying concentrations, only certain vibration modes in the crystalline cellulose structure can meet the noninversion symmetry requirements. Thus, SFG can be used to detect and analyze crystalline cellulose selectively in lignocellulosic biomass without extraction of noncellulosic species from biomass or deconvolution of amorphous spectra. The selective detection of crystalline cellulose in lignocellulosic biomass is not readily achievable with other techniques such as XRD, solid-state NMR, IR, and Raman analyses. Therefore, the SFG analysis presents a unique opportunity to reveal the cellulose crystalline structure in lignocellulosic biomass.

  19. Characterization of polymer surface structure and surface mechanical behaviour by sum frequency generation surface vibrational spectroscopy and atomic force microscopy

    International Nuclear Information System (INIS)

    Opdahl, Aric; Koffas, Telly S; Amitay-Sadovsky, Ella; Kim, Joonyeong; Somorjai, Gabor A

    2004-01-01

    Sum frequency generation (SFG) vibrational spectroscopy and atomic force microscopy (AFM) have been used to study polymer surface structure and surface mechanical behaviour, specifically to study the relationships between the surface properties of polymers and their bulk compositions and the environment to which the polymer is exposed. The combination of SFG surface vibrational spectroscopy and AFM has been used to study surface segregation behaviour of polyolefin blends at the polymer/air and polymer/solid interfaces. SFG surface vibrational spectroscopy and AFM experiments have also been performed to characterize the properties of polymer/liquid and polymer/polymer interfaces, focusing on hydrogel materials. A method was developed to study the surface properties of hydrogel contact lens materials at various hydration conditions. Finally, the effect of mechanical stretching on the surface composition and surface mechanical behaviour of phase-separated polyurethanes, used in biomedical implant devices, has been studied by both SFG surface vibrational spectroscopy and AFM. (topical review)

  20. Wetting effect on optical sum frequency generation (SFG) spectra of D-glucose, D-fructose, and sucrose

    Science.gov (United States)

    Hieu, Hoang Chi; Li, Hongyan; Miyauchi, Yoshihiro; Mizutani, Goro; Fujita, Naoko; Nakamura, Yasunori

    2015-03-01

    We report a sum frequency generation (SFG) spectroscopy study of D-glucose, D-fructose and sucrose in the Csbnd H stretching vibration regime. Wetting effect on the SFG spectra was investigated. The SFG spectrum of D-glucose changed from that of α-D-glucose into those of α-D-glucose monohydrate by wetting. The SFG spectra showed evidence of a small change of β-D-fructopyranose into other anomers by wetting. SFG spectra of sucrose did not change by wetting. Assignments of the vibrational peaks in the SFG spectra of the three sugars in the dry and wet states were performed in the Csbnd H stretching vibration region near 3000 cm-1.

  1. Two-dimensional sum-frequency generation (2D SFG) reveals structure and dynamics of a surface-bound peptide

    Science.gov (United States)

    Laaser, Jennifer E.; Skoff, David R.; Ho, Jia-Jung; Joo, Yongho; Serrano, Arnaldo L.; Steinkruger, Jay D.; Gopalan, Padma; Gellman, Samuel H.; Zanni, Martin T.

    2014-01-01

    Surface-bound polypeptides and proteins are increasingly used to functionalize inorganic interfaces such as electrodes, but their structural characterization is exceedingly difficult with standard technologies. In this paper, we report the first two-dimensional sum-frequency generation (2D SFG) spectra of a peptide monolayer, which is collected by adding a mid-IR pulse shaper to a standard femtosecond SFG spectrometer. On a gold surface, standard FTIR spectroscopy is inconclusive about the peptide structure because of solvation-induced frequency shifts, but the 2D lineshapes, anharmonic shifts, and lifetimes obtained from 2D SFG reveal that the peptide is largely α-helical and upright. Random coil residues are also observed, which do not themselves appear in SFG spectra due to their isotropic structural distribution, but which still absorb infrared light and so can be detected by cross-peaks in 2D SFG spectra. We discuss these results in the context of peptide design. Because of the similar way in which the spectra are collected, these 2D SFG spectra can be directly compared to 2D IR spectra, thereby enabling structural interpretations of surface-bound peptides and biomolecules based on the well-studied structure/2D IR spectra relationships established from soluble proteins. PMID:24372101

  2. Study of the Imidazolium-Based Ionic Liquid - ag Electrified Interface on the CO_{2} Electroreduction by Sum Frequency Spectroscopy.

    Science.gov (United States)

    Garcia Rey, Natalia; Dlott, Dana

    2017-06-01

    Imidazolium based ionic liquids (ILs) have been used as a promising system to improve the CO_{2} electroreduction at lower overpotential than other organic or aqueous electrolytes^{1}. Although the detailed mechanism of the CO_{2} electroreduction on Ag has not been elucidated yet, we have developed a methodology to study the electrified interface during the CO_{2} electroreduction using sum frequency generation (SFG) spectroscopy in combination with cyclic voltammetry^{2}. In this work, we tuned the composition of imidazolium-based ILs by exchanging the anion or the functional groups of the imidazolium. We use the nonresonant SFG (NR-SFG) to study the IL-Ag interface and resonant SFG (RES-SFG) to identify the CO adsorbed on the electrode and monitor the Stark shift as a function of cell potential. In previous studies on CO_{2} electroreduction in the IL: 1-ethyl-3-methylimidazolium tetrafluorborate (EMIM-BF_{4}) on Ag, we showed three events occurred at the same potential (-1.33 V vs. Ag/AgCl): the current associated with CO_{2} electroreduction increased, the Stark shift of the adsorbed atop CO doubled in magnitude and the EMIM-BF_{4} underwent a structural transition^{3}. In addition, we also observed how the structural transition of the EMIM-BF_{4} electrolyte shift to lower potentials when the IL is mixed with water. It is known that water enhances the CO_{2} electroreduction producing more CO^{4}. Moreover, the CO is adsorbed in multi-bonded and in atop sites when more water is present in the electrolyte. ^{1}Lau, G. P. S.; Schreier, M.; Vasilyev, D.; Scopelliti, R.; Grätzel, M.; Dyson, P. J., New Insights into the Role of Imidazolium-Based Promoters for the Electroreduction of CO_{2} on a Silver Electrode. J. Am. Chem. Soc. 2016, 138, 7820-7823. ^{2}Garcia Rey, N.; Dlott, D. D., Studies of Electrochemical Interfaces by Broadband Sum Frequency Generation. J. Electroanal. Chem. 2016. DOI:10.1016/j.jelechem.2016.12.023. ^{3}Garcia Rey, N.; Dlott, D. D

  3. Nonlinear optical response of a gold surface in the visible range: A study by two-color sum-frequency generation spectroscopy. I. Experimental determination.

    Science.gov (United States)

    Dalstein, L; Revel, A; Humbert, C; Busson, B

    2018-04-07

    We experimentally determine the effective nonlinear second-order susceptibility of gold over the visible spectral range. To reach that goal, we probe by vibrational two-color sum-frequency generation spectroscopy the methyl stretching region of a dodecanethiol self-assembled monolayer adsorbed on a gold film. The sum-frequency generation spectra show a remarkable shape reversal when the visible probe wavelength is tuned from 435 to 705 nm. After correcting from Fresnel effects, the methyl stretching vibrations serve as an internal reference, allowing to extract the dispersion of the absolute phase and relative amplitude of the effective nonlinear optical response of gold in the visible range.

  4. Cooperative Effects of Zwitterionic-Ionic Surfactant Mixtures on the Interfacial Water Structure Revealed by Sum Frequency Generation Vibrational Spectroscopy.

    Science.gov (United States)

    Pan, Xuecong; Yang, Fangyuan; Chen, Shunli; Zhu, Xuefeng; Wang, Chuanyi

    2018-05-08

    Cooperative effects of a series of equimolar binary zwitterionic-ionic surfactant mixtures on the interfacial water structure at the air-water interfaces have been studied by sum frequency generation vibrational spectroscopy (SFG-VS). For zwitterionic surfactant palmityl sulfobetaine (SNC 16 ), anionic surfactant sodium hexadecyl sulfate (SHS), and cationic surfactant cetyltrimethylammonium bromide (CTAB) with the same length of alkyl chain, significantly enhanced ordering of interfacial water molecules was observed for the zwitterionic-anionic surfactant mixtures SNC 16 -SHS, indicating that SNC 16 interacts more strongly with SHS than with CTAB because of the strong headgroup-headgroup electrostatic attraction for SNC 16 -SHS. Meanwhile, the SFG amplitude ratio of methyl and methylene symmetric stretching modes was used to verify the stronger interaction between SNC 16 and SHS. The conformational order indicator increased from 0.64 for SNC 16 to 7.17 for SNC 16 -SHS but only 0.94 for SNC 16 -CTAB. In addition, another anionic surfactant sodium dodecyl sulfate (SDS) was introduced to study the influence of chain-chain interaction. Decreased SFG amplitude of interfacial water molecules for SNC 16 -SDS was observed. Therefore, both the headgroup-headgroup electrostatic interaction and chain-chain van der Waals attractive interaction of the surfactants play an important role in enhancing the ordering of interfacial water molecules. The results provided experimental and theoretical bases for practical applications of the surfactants.

  5. Sum Frequency Generation Vibrational Spectroscopy of Adsorbed Amino Acids, Peptides and Proteins of Hydrophilic and Hydrophobic Solid-Water Interfaces

    Energy Technology Data Exchange (ETDEWEB)

    Holinga IV, George Joseph [Univ. of California, Berkeley, CA (United States)

    2010-09-01

    Sum frequency generation (SFG) vibrational spectroscopy was used to investigate the interfacial properties of several amino acids, peptides, and proteins adsorbed at the hydrophilic polystyrene solid-liquid and the hydrophobic silica solid-liquid interfaces. The influence of experimental geometry on the sensitivity and resolution of the SFG vibrational spectroscopy technique was investigated both theoretically and experimentally. SFG was implemented to investigate the adsorption and organization of eight individual amino acids at model hydrophilic and hydrophobic surfaces under physiological conditions. Biointerface studies were conducted using a combination of SFG and quartz crystal microbalance (QCM) comparing the interfacial structure and concentration of two amino acids and their corresponding homopeptides at two model liquid-solid interfaces as a function of their concentration in aqueous solutions. The influence of temperature, concentration, equilibration time, and electrical bias on the extent of adsorption and interfacial structure of biomolecules were explored at the liquid-solid interface via QCM and SFG. QCM was utilized to quantify the biological activity of heparin functionalized surfaces. A novel optical parametric amplifier was developed and utilized in SFG experiments to investigate the secondary structure of an adsorbed model peptide at the solid-liquid interface.

  6. Facet-specific interaction between methanol and TiO2 probed by sum-frequency vibrational spectroscopy.

    Science.gov (United States)

    Yang, Deheng; Li, Yadong; Liu, Xinyi; Cao, Yue; Gao, Yi; Shen, Y Ron; Liu, Wei-Tao

    2018-04-24

    The facet-specific interaction between molecules and crystalline catalysts, such as titanium dioxides (TiO 2 ), has attracted much attention due to possible facet-dependent reactivity. Using surface-sensitive sum-frequency vibrational spectroscopy, we have studied how methanol interacts with different common facets of crystalline TiO 2 , including rutile(110), (001), (100), and anatase(101), under ambient temperature and pressure. We found that methanol adsorbs predominantly in the molecular form on all of the four surfaces, while spontaneous dissociation into methoxy occurs preferentially when these surfaces become defective. Extraction of Fermi resonance coupling between stretch and bending modes of the methyl group in analyzing adsorbed methanol spectra allows determination of the methanol adsorption isotherm. The isotherms obtained for the four surfaces are nearly the same, yielding two adsorbed Gibbs free energies associated with two different adsorption configurations singled out by ab initio calculations. They are ( i ) ∼-20 kJ/mol for methanol with its oxygen attached to a low-coordinated surface titanium, and ( ii ) ∼-5 kJ/mol for methanol hydrogen-bonded to a surface oxygen and a neighboring methanol molecule. Despite similar adsorption energetics, the Fermi resonance coupling strength for adsorbed methanol appears to depend sensitively on the surface facet and coverage.

  7. Vibrational sum-frequency generation spectroscopy of lipid bilayers at repetition rates up to 100 kHz

    Science.gov (United States)

    Yesudas, Freeda; Mero, Mark; Kneipp, Janina; Heiner, Zsuzsanna

    2018-03-01

    Broadband vibrational sum-frequency generation (BB-VSFG) spectroscopy has become a well-established surface analytical tool capable of identifying the orientation and structure of molecular layers. A straightforward way to boost the sensitivity of the technique could be to increase the laser repetition rate beyond that of standard BB-VSFG spectrometers, which rely on Ti:sapphire lasers operating at repetition rates of 1-5 kHz. Nevertheless, possible thermally induced artifacts in the vibrational spectra due to higher laser average powers are unexplored. Here, we discuss laser power induced temperature accumulation effects that distort the BB-VSFG spectra of 1,2-diacyl-sn-glycero-3-phosphocholine at an interface between two transparent phases at repetition rates of 5, 10, 50, and 100 kHz at constant pulse energy. No heat-induced distortions were found in the spectra, suggesting that the increase in the laser repetition rate provides a feasible route to an improved signal-to-noise ratio or shorter data acquisition times in BB-VSFG spectroscopy for thin films on transparent substrates. The results have implications for future BB-VSFG spectrometers pushing the detection limit for molecular layers with low surface coverage.

  8. Surface and buried interfacial structures of epoxy resins used as underfills studied by sum frequency generation vibrational spectroscopy.

    Science.gov (United States)

    Vázquez, Anne V; Holden, Brad; Kristalyn, Cornelius; Fuller, Mike; Wilkerson, Brett; Chen, Zhan

    2011-05-01

    Flip chip technology has greatly improved the performance of semiconductor devices, but relies heavily on the performance of epoxy underfill adhesives. Because epoxy underfills are cured in situ in flip chip semiconductor devices, understanding their surface and interfacial structures is critical for understanding their adhesion to various substrates. Here, sum frequency generation (SFG) vibrational spectroscopy was used to study surface and buried interfacial structures of two model epoxy resins used as underfills in flip chip devices, bisphenol A digylcidyl ether (BADGE) and 1,4-butanediol diglycidyl ether (BDDGE). The surface structures of these epoxies were compared before and after cure, and the orientations of their surface functional groups were deduced to understand how surface structural changes during cure may affect adhesion properties. Further, the effect of moisture exposure, a known cause of adhesion failure, on surface structures was studied. It was found that the BADGE surface significantly restructured upon moisture exposure while the BDDGE surface did not, showing that BADGE adhesives may be more prone to moisture-induced delamination. Lastly, although surface structure can give some insight into adhesion, buried interfacial structures more directly correspond to adhesion properties of polymers. SFG was used to study buried interfaces between deuterated polystyrene (d-PS) and the epoxies before and after moisture exposure. It was shown that moisture exposure acted to disorder the buried interfaces, most likely due to swelling. These results correlated with lap shear adhesion testing showing a decrease in adhesion strength after moisture exposure. The presented work showed that surface and interfacial structures can be correlated to adhesive strength and may be helpful in understanding and designing optimized epoxy underfill adhesives.

  9. Nanoscale chemical and mechanical characterization of thin films:sum frequency generation (SFG) vibrational spectroscopy at buriedinterfaces

    Energy Technology Data Exchange (ETDEWEB)

    Kweskin, Sasha Joseph [Univ. of California, Berkeley, CA (United States)

    2006-01-01

    Sum frequency generation (SFG) surface vibrational spectroscopy was used to characterize interfaces pertinent to current surface engineering applications, such as thin film polymers and novel catalysts. An array of advanced surface science techniques like scanning probe microscopy (SPM), x-ray photoelectron spectroscopy (XPS), gas chromatography (GC) and electron microscopy were used to obtain experimental measurements complementary to SFG data elucidating polymer and catalyst surface composition, surface structure, and surface mechanical behavior. Experiments reported in this dissertation concentrate on three fundamental questions: (1) How does the interfacial molecular structure differ from that of the bulk in real world applications? (2) How do differences in chemical environment affect interface composition or conformation? (3) How do these changes correlate to properties such as mechanical or catalytic performance? The density, surface energy and bonding at a solid interface dramatically alter the polymer configuration, physics and mechanical properties such as surface glass transition, adhesion and hardness. The enhanced sensitivity of SFG at the buried interface is applied to three systems: a series of acrylates under compression, the compositions and segregation behavior of binary polymer polyolefin blends, and the changes in surface structure of a hydrogel as a function of hydration. In addition, a catalytically active thin film of polymer coated nanoparticles is investigated to evaluate the efficacy of SFG to provide in situ information for catalytic reactions involving small mass adsorption and/or product development. Through the use of SFG, in situ total internal reflection (TIR) was used to increase the sensitivity of SFG and provide the necessary specificity to investigate interfaces of thin polymer films and nanostructures previously considered unfeasible. The dynamic nature of thin film surfaces is examined and it is found that the non

  10. Coupled-cluster sum-frequency generation nonlinear susceptibilities of methyl (CH3) and methylene (CH2) groups.

    Science.gov (United States)

    Tetsassi Feugmo, Conrard Giresse; Liégeois, Vincent; Champagne, Benoît

    2017-11-15

    The first vibrational sum frequency generation (SFG) spectra based on molecular properties calculated at the coupled cluster singles and doubles (CCSD) level of approximation have been simulated for interfacial model alkyl chains, providing benchmark data for comparisons with approximate methods, including density functional theory (DFT). The approach proceeds in three steps. In the first two steps, the molecular spectral properties are determined: the vibrational normal modes and frequencies and then the derivatives of the dipole moment and of the polarizability with respect to the normal coordinates. These derivatives are evaluated with a numerical differentiation approach, of which the accuracy was monitored using Romberg's procedure. Then, in the last step, a three-layer model is employed to evaluate the macroscopic second-order nonlinear optical responses and thereby the simulated SFG spectra of the alkyl interface. Results emphasize the following facts: (i) the dipole and polarizability derivatives calculated at the DFT level with the B3LYP exchange-correlation functional can differ, with respect to CCSD, by as much as ±10 to 20% and ±20 to 50% for the CH 3 and CH 2 vibrations, respectively; (ii) these differences are enhanced when considering the SFG intensities as well as their variations as a function of the experimental configuration (ppp versus ssp) and as a function of the tilt and rotation angles, defining the orientation of the alkyl chain at the interface; (iii) these differences originate from both the vibrational normal coordinates and the Cartesian derivatives of the dipole moment and polarizability; (iv) freezing the successive fragments of the alkyl chain strongly modifies the SFG spectrum and enables highlighting the delocalization effects between the terminal CH 3 group and its neighboring CH 2 units; and finally (v) going from the free chain to the free methyl model, and further to C 3v constraints on leads to large variations of two ratios

  11. Combined wide pump tuning and high power of a continuous-wave, singly resonant optical parametric oscillator

    NARCIS (Netherlands)

    Herpen, M.M.J.W. van; Bisson, S.E.; Ngai, A.K.Y.; Harren, F.J.M.

    2004-01-01

    A new singly resonant, single-frequency optical parametric oscillator (OPO) has been developed for the 2.6-4.7 mum infrared wavelength region, using a high power (>20 W), widely tunable (1024-1034 nm) Yb:YAG pump source. With the OPO frequency stabilized with an intracavity etalon, the OPO achieved

  12. Correlation of zero-point energy with molecular structure and molecular forces. 3. Approximation for H/D isotope shifts and linear frequency sum rule

    International Nuclear Information System (INIS)

    Oi, T.; Ishida, T.

    1984-01-01

    The approximation methods for the zero-point energy (ZPE) previously developed using the Lanczo's tau method have been applied to the shifts in ZPE due to hydrogen isotope substitutions. Six types of approximation methods have been compared and analyzed on the basis of a weighing function Ω(lambda) varies as lambda/sup k/ and the actual eigenvalue shift spectra. The method generated by the most general optimzation treatment yields a predictable and generally satisfactory precision of the order of 1% or better. A linear frequency sum rule has been derived, which approximately holds for the sets of isotopic molecules which satisfy the second-order frequency sum rule. 19 references, 3 figures, 3 tables

  13. Efficient near diffraction limited blue light source by sum-frequency mixing of a BAL and a solid-state laser

    DEFF Research Database (Denmark)

    Sørensen, Knud Palmelund; Tidemand-Lichtenberg, Peter; Pedersen, Christian

    2011-01-01

    and slow axis of the diode, respectively. The BAL output beam is single-passed through a periodically poled KTiOPO4 (PPKTP) crystal placed in an intra-cavity beam waist of a 1064 nm Nd:YVO4 laser, resulting in 100 mW of sum-frequency generated blue output power. This corresponds to a power conversion......Sum-frequency mixing of an 808 nm broad area laser (BAL) with a build-in grating structure for spectral control and a 1064 nm solid-state laser is experimentally investigated. The spectrally improved 20 mu m wide BAL can deliver up to 700 mW of output power with an M-2 of 1.4 and 5.3 in the fast...

  14. Efficient concept for generation of diffraction-limited green light by sum-frequency generation of spectrally combined tapered diode lasers

    DEFF Research Database (Denmark)

    Müller, André; Jensen, Ole Bjarlin; Hasler, Karl-Heinz

    2012-01-01

    In order to increase the power of visible diode laser systems in an efficient manner, we propose spectral beam combining with subsequent sum-frequency generation. We show that this approach, in comparison with second harmonic generation of single emitters, can enhance the available power signific......In order to increase the power of visible diode laser systems in an efficient manner, we propose spectral beam combining with subsequent sum-frequency generation. We show that this approach, in comparison with second harmonic generation of single emitters, can enhance the available power...... significantly. By combining two distributed Bragg reflector tapered diode lasers we achieve a 2.5–3.2 fold increase in power and a maximum of 3.9 W of diffraction-limited green light. At this power level, green diode laser systems have a high application potential, e.g., within the biomedical field. Our concept...

  15. Characterisation of the membrane affinity of an isoniazide peptide conjugate by tensiometry, atomic force microscopy and sum-frequency vibrational spectroscopy, using a phospholipid Langmuir monolayer model.

    Science.gov (United States)

    Hill, Katalin; Pénzes, Csanád Botond; Schnöller, Donát; Horváti, Kata; Bosze, Szilvia; Hudecz, Ferenc; Keszthelyi, Tamás; Kiss, Eva

    2010-10-07

    Tensiometry, sum-frequency vibrational spectroscopy, and atomic force microscopy were employed to assess the cell penetration ability of a peptide conjugate of the antituberculotic agent isoniazide. Isoniazide was conjugated to peptide (91)SEFAYGSFVRTVSLPV(106), a functional T-cell epitope of the immunodominant 16 kDa protein of Mycobacterium tuberculosis. As a simple but versatile model of the cell membrane a phospholipid Langmuir monolayer at the liquid/air interface was used. Changes induced in the structure of the phospholipid monolayer by injection of the peptide conjugate into the subphase were followed by tensiometry and sum-frequency vibrational spectroscopy. The drug penetrated lipid films were transferred to a solid support by the Langmuir-Blodgett technique, and their structures were characterized by atomic force microscopy. Peptide conjugation was found to strongly enhance the cell penetration ability of isoniazide.

  16. In situ speciation of the functional groups at mineral/electrolyte interfaces by sum frequency vibrational spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Floersheimer, M.; Kruse, K.; Klenze, R.; Kim, J.I. [Institut fuer Nukleare Entsorgung, Forschungszentrum Karlsruhe, Postfach 3640, D-76021 Karlsruhe (Germany); Fanghaenel, Th. [Institut fuer Nukleare Entsorgung, Forschungszentrum Karlsruhe, Postfach 3640, D-76021 Karlsruhe (Germany); Physikalisch-Chemisches Institut, Ruprecht-Karls-Universitaet Heidelberg, Im Neuenheimer Feld 253, D-69120, Heidelberg (Germany)

    2005-07-01

    Full text of publication follows: In order to describe surface reactivity and adsorption/desorption processes on the molecular level, a large number of functional groups has been postulated. In most cases, however, a direct proof for the existence of these species in real aquatic environment is lacking because it is difficult to obtain chemical analytical information in situ under electrolyte with interface selectivity. Here we apply interface selective sum frequency (SF) vibrational spectroscopy to study the (001) and (110) surfaces of sapphire ({alpha}-Al{sub 2}O{sub 3}) under water between pH 4 and 12. This work is part of an ongoing fundamental study of the sorption mechanism of actinides on single crystals faces of sapphire by various experimental and theoretical techniques. Sapphire is used as a simple model for natural clay minerals and related iron phases. In the O-H stretch region of the infrared spectrum between 2800 and 4000 cm{sup -1}, we observe a surprisingly large number of 8 SF bands in total. Two of them are due to the polar ordered water film near the mineral surface which is well known from various aquatic interfaces. The other bands originate from up to 6 different aluminol species or from specifically [1] bound water molecules. The prominent peak of the (001) surface (SF intensity maximum at 3690 cm{sup -1}), we attribute to an OH species bridging two [1-4] aluminium atoms. At the (110) surface, the concentration of this species is considerably smaller. Another aluminol species that can be detected at the (001) and the (110) surface (signal maximum near 3450 cm{sup -1}) exhibits O-H bonds which are almost parallel to the interface plane. This species is probably the in-plane aluminol group predicted in recent molecular dynamics calculations [4]. SF spectroscopy allows us also to measure the absolute polar orientation of the water molecules adjacent to the mineral surface. The inversion of the molecules polar orientation upon alteration of the p

  17. Effects of Second-Order Sum- and Difference-Frequency Wave Forces on the Motion Response of a Tension-Leg Platform Considering the Set-down Motion

    Science.gov (United States)

    Wang, Bin; Tang, Yougang; Li, Yan; Cai, Runbo

    2018-04-01

    This paper presents a study on the motion response of a tension-leg platform (TLP) under first- and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function (QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.

  18. A Tunable CW Orange Laser Based on a Cascaded MgO:PPLN Single-Pass Sum-Frequency Generation Module

    OpenAIRE

    Dismas K. Choge; Huai-Xi Chen; Bao-Lu Tian; Yi-Bin Xu; Guang-Wei Li; Wan-Guo Liang

    2018-01-01

    We report an all-solid-state continuous wave (CW) tunable orange laser based on cascaded single-pass sum-frequency generation with fundamental wavelengths at 1545.7 and 975.2 nm using two quasi-phase-matched (QPM) MgO-doped periodically poled lithium niobate (MgO:PPLN) crystals. Up to 10 mW of orange laser is generated in the cascaded module corresponding to a 10.4%/W nonlinear conversion efficiency. The orange output showed a temperature tuning rate of ~0.05 nm/°C, and the beam quality (M2) ...

  19. Correlation of molecular conformation with adhesion at AlOx/poly (ethylene terephthalate) interface studied by sum-frequency generation spectroscopy

    International Nuclear Information System (INIS)

    Miyamae, Takayuki; Nozoye, Hisakazu

    2004-01-01

    The interface between AlO x and poly(ethylene terephthalate) has been investigated by sum-frequency generation (SFG). A considerable improvement in adhesion strength was achieved by short time Ar plasma modification. The increase of the adhesion strength shows good correlation with the increase of the SFG peak strength. By depositing AlO x , the increase of SFG intensities and appearance of a new peak are observed, indicating the formation of a C=O···Al bond at the interface. Surface-modification and interfacial adhesion property are discussed

  20. NOLM-based all-optical 40 Gbit/s format conversion through sum-frequency generation (SFG) in a PPLN waveguide

    Science.gov (United States)

    Wang, Jian; Sun, Junqiang

    2005-11-01

    A novel all-optical format conversion scheme from NRZ to RZ based on sum-frequency generation (SFG) in a periodically poled LiNbO 3 (PPLN) waveguide is proposed, using a nonlinear optical loop mirror (NOLM). The conversion mechanism relies on the combination of attenuation and nonlinear phase shift induced on the clockwise signal field during the SFG process. The SFG between pump, and co- and counter- propagating signals in the PPLN waveguide are numerically studied, showing that counter-propagating SFG can be ignored when quasi-phase matching (QPM) for SFG during co-propagating interaction. The nonlinear phase shift induced on the clockwise signal field is analyzed in detail, showing that it is more effective to yield large values for nonlinear phase shift when appropriately phase mismatched for the SFG process. Two tuning schemes are proposed depend on whether the sum-frequency wavelength is variable or fixed. It is found that the latter has a rather wide 3dB signal conversion bandwidth approximately 154nm. Finally, the influence of reversible process of SFG is discussed and the optimum arrangement of pump and signal peak powers is theoretically demonstrated. The result shows that proper power arrangement, pump width, and waveguide length are necessary for achieving a good conversion effect.

  1. Intrinsic Chirality and Prochirality at Air/R-(+)- and S-(-)-Limonene Interfaces: Spectral Signatures with Interference Chiral Sum-Frequency Generation Vibrational Spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Fu, Li; Zhang, Yun; Wei, Zhehao; Wang, Hongfei

    2014-06-04

    We report in this work detailed measurements on the chiral and achiral sum-frequency vibrational spectra in the C-H stretching vibration region (2800-3050cm-1) of the air/liquid interfaces of R-limonene and S-limonene, using the recently developed high-resolution broadband sum-frequency generation vibrational spectroscopy (HR-BB-SFG-VS). The achiral SFG spectra of R-limonene and S-limonene, as well as the equal amount (50/50) racemic mixture show that the enantiomers are with the same interfacial orientations. The interference chiral SFG spectra of the limonene enantiomers exhibit spectral signature from chiral response of the Cα-H stretching mode, and spectral signature from prochiral response of the CH2 asymmetric stretching mode, respectively. The chiral spectral feature of the Cα-H stretching mode changes sign from R-limonene to S-limonene, and disappears for the 50/50 racemic mixture. While the prochiral spectral feature of the CH2 asymmetric stretching mode is the same for R-limonene and S-limonene, and also surprisingly remains the same for the 50/50 racemic mixture. These results provided detail information in understanding the structure and chirality of molecular interfaces, and demonstrated the sensitivity and potential of SFG-VS as unique spectroscopic tool for chirality characterization and chiral recognition at the molecular interface.

  2. Sum Frequency Generation Vibrational Spectroscopy of 1,3-Butadiene Hydrogenation on 4 nm Pt@SiO 2 , Pd@SiO 2 , and Rh@SiO 2 Core–Shell Catalysts

    KAUST Repository

    Krier, James M.; Michalak, William D.; Cai, Xiaojun; Carl, Lindsay; Komvopoulos, Kyriakos; Somorjai, Gabor A.

    2015-01-01

    NPs (Stöber encapsulation) prepared by colloidal synthesis. Sum frequency generation (SFG) vibrational spectroscopy was performed to correlate surface intermediates observed in situ with reaction selectivity. It is shown that calcination is effective

  3. CW light sources at the 589 nm sodium D2 line by sum-frequency mixing of diode pumped neodymium lasers

    International Nuclear Information System (INIS)

    Lü, Y F; Lu, J; Xu, L J; Sun, G C; Zhao, Z M; Gao, X; Lin, J Q

    2010-01-01

    We present a laser architecture to obtain continuous-wave (CW) light sources at the 589 nm sodium D2 line. A 808 nm diode-pumped a Nd:YLiF 4 (Nd:YLF) crystal emitting at 1053 nm. A part of the pump power was then absorbed by the Nd:YLF crystal. The remaining was used to pump a Nd:YAG crystal emitting at 1338 nm. Intracavity sum-frequency mixing at 1053 and 1338 nm was then realized in a LiB 3 O 5 (LBO) crystal to reach the yellow-orange radiation. We obtained a CW output power of 235 mW at 589 nm with a pump laser diode emitting 17.8 W at 808 nm

  4. Diode-pumped quasi-three-level Nd:GdV O4–Nd:YAG sum-frequency laser at 464 nm

    International Nuclear Information System (INIS)

    Lu, Jie

    2014-01-01

    We report a laser architecture to obtain continuous-wave (cw) blue radiation at 464 nm. A 808 nm diode pumped a Nd:GdV O 4 crystal emitting at 912 nm. A part of the pump power was then absorbed by the Nd:GdV O 4 crystal. The remainder was used to pump a Nd:YAG crystal emitting at 946 nm. Intracavity sum-frequency mixing at 912 and 946 nm was then realized in a LiB 3 O 5 (LBO) crystal to produce blue radiation. We obtained a cw output power of 1.52 W at 464 nm with a pump laser diode emitting 18.4 W at 808 nm. (letter)

  5. Sum frequency generation and catalytic reaction studies of the removal of the organic capping agents from Pt nanoparticles by UV-ozone treatment

    Energy Technology Data Exchange (ETDEWEB)

    Aliaga, Cesar; Park, Jeong Y.; Yamada, Yusuke; Lee, Hyun Sook; Tsung, Chia-Kuang; Yang, Peidong; Somorjai, Gabor A.

    2009-12-10

    We report the structure of the organic capping layers of platinum colloid nanoparticles and their removal by UV-ozone exposure. Sum frequency generation vibrational spectroscopy (SFGVS) studies identify the carbon-hydrogen stretching modes on poly(vinylpyrrolidone) (PVP) and tetradecyl tributylammonium bromide (TTAB)-capped platinum nanoparticles. We found that the UV-ozone treatment technique effectively removes the capping layer on the basis of several analytical measurements including SFGVS, X-ray photoelectron spectroscopy, and diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS). The overall shape of the nanoparticles was preserved after the removal of capping layers, as confirmed by transmission electron microscopy (TEM). SFGVS of ethylene hydrogenation on the clean platinum nanoparticles demonstrates the existence of ethylidyne and di-{sigma}-bonded species, indicating the similarity between single-crystal and nanoparticle systems.

  6. Continuous-wave sodium D2 resonance radiation generated in single-pass sum-frequency generation with periodically poled lithium niobate.

    Science.gov (United States)

    Yue, J; She, C-Y; Williams, B P; Vance, J D; Acott, P E; Kawahara, T D

    2009-04-01

    With two cw single-mode Nd:YAG lasers at 1064 and 1319 nm and a periodically poled lithium niobate crystal, 11 mW of 2 kHz/100 ms bandwidth single-mode tunable 589 nm cw radiation has been detected using single-pass sum-frequency generation. The demonstrated conversion efficiency is approximately 3.2%[W(-1) cm(-1)]. This compact solid-state light source has been used in a solid-state-dye laser hybrid sodium fluorescence lidar transmitter to measure temperatures and winds in the upper atmosphere (80-105 km); it is being implemented into the transmitter of a mobile all-solid-state sodium temperature and wind lidar under construction.

  7. Sum frequency generation vibrational spectroscopy (SFG-VS) for complex molecular surfaces and interfaces: Spectral lineshape measurement and analysis plus some controversial issues

    Science.gov (United States)

    Wang, Hong-Fei

    2016-12-01

    Sum-frequency generation vibrational spectroscopy (SFG-VS) was first developed in the 1980s and it has been proven a uniquely sensitive and surface/interface selective spectroscopic probe for characterization of the structure, conformation and dynamics of molecular surfaces and interfaces. In recent years, there have been many progresses in the development of methodology and instrumentation in the SFG-VS toolbox that have significantly broadened the application to complex molecular surfaces and interfaces. In this review, after presenting a unified view on the theory and methodology focusing on the SFG-VS spectral lineshape, as well as the new opportunities in SFG-VS applications with such developments, some of the controversial issues that have been puzzling the community are discussed. The aim of this review is to present to the researchers and students interested in molecular surfaces and interfacial sciences up-to-date perspectives complementary to the existing textbooks and reviews on SFG-VS.

  8. Experimental demonstration of wavelength conversion between ps-pulses based on cascaded sum- and difference frequency generation (SFG+DFG) in LiNbO3 waveguides

    Science.gov (United States)

    Wang, Jian; Sun, Junqiang; Lou, Chuanhong; Sun, Qizhen

    2005-09-01

    All-optical wavelength conversion between ps-pulses based on cascaded sum- and difference frequency generation (SFG+DFG) is proposed and experimentally demonstrated in periodically poled LiNbO3 (PPLN) waveguides. The signal pulse with 40-GHz repetition rate and 1.57- ps pulse width is adopted. The converted idler wavelength can be tuned from 1527.4 to 1540.5nm as the signal wavelength is varied from 1561.9 to 1548.4nm. No obvious changes of the pulse shape and width, also no chirp are observed in the converted idler pulse. The results imply that single-to-multiple channel wavelength conversions can be achieved by appropriately tuning the two pump wavelengths.

  9. IR visible sum-frequency vibrational spectroscopy of Biphenyl-3 methylene thiol monolayer on gold and silver: effect of the visible wavelength on the SFG spectrum

    Science.gov (United States)

    Humbert, C.; Dreesen, L.; Mani, A. A.; Caudano, Y.; Lemaire, J.-J.; Thiry, P. A.; Peremans, A.

    2002-04-01

    We measured IR-visible sum-frequency generation spectra of CH 3-(C 6H 4) 2-(CH 2) 3-S-H (Biphenyl-3) self-assembled monolayers on a silver and a gold substrate. For the latter substrate, we observed different interference patterns between the resonant signal of the CH vibration and the non-resonant contribution of the substrate as a function of the visible beam wavelength. The non-linear response of the gold substrate is enhanced around 480 nm corresponding to the s-d interband transition. Such effect is not observed for the silver substrate the interband transition of which is located out of the investigated visible spectral range of 450-700 nm.

  10. Amine Chemistry at Aqueous Interfaces: The Study of Organic Amines in Neutralizing Acidic Gases at an Air/Water Surface Using Vibrational Sum Frequency Spectroscopy

    Science.gov (United States)

    McWilliams, L.; Wren, S. N.; Valley, N. A.; Richmond, G.

    2014-12-01

    Small organic bases have been measured in atmospheric samples, with their sources ranging from industrial processing to animal husbandry. These small organic amines are often highly soluble, being found in atmospheric condensed phases such as fogwater and rainwater. Additionally, they display acid-neutralization ability often greater than ammonia, yet little is known regarding their kinetic and thermodynamic properties. This presentation will describe the molecular level details of a model amine system at the vapor/liquid interface in the presence of acidic gas. We find that this amine system shows very unique properties in terms of its bonding, structure, and orientation at aqueous surfaces. The results of our studies using a combination of computation, vibrational sum frequency spectroscopy, and surface tension will report the properties inherent to these atmospherically relevant species at aqueous surfaces.

  11. Sum Frequency Generation Vibrational Spectroscopy and Kinetic Study of 2-Methylfuran and 2,5-Dimethylfuran Hydrogenation over 7 nm Platinum Cubic Nanoparticles

    KAUST Repository

    Aliaga, Cesar

    2011-04-28

    Sum frequency generation vibrational spectroscopy and kinetic measurements obtained from gas chromatography were used to study the adsorption and hydrogenation of 2-methylfuran (MF) and 2,5-dimethylfuran (DMF) over cubic Pt nanoparticles of 7 nm average size, synthesized by colloidal methods and cleaned by ultraviolet light and ozone treatment. Reactions carried out at atmospheric pressure in the temperature range of 20-120 °C produced dihydro and tetrahydro species, as well as ring-opening products (alcohols) and ring-cracking products, showing high selectivity toward ring opening throughout the entire temperature range. The aromatic rings (MF and DMF) adsorbed parallel to the nanoparticle surface. Results yield insight into various surface reaction intermediates and the reason for the significantly lower selectivity for ring cracking in DMF hydrogenation compared to MF hydrogenation. © 2011 American Chemical Society.

  12. Investigation on phase noise of the signal from a singly resonant optical parametric oscillator

    Science.gov (United States)

    Jinxia, Feng; Yuanji, Li; Kuanshou, Zhang

    2018-04-01

    The phase noise of the signal from a singly resonant optical parametric oscillator (SRO) is investigated theoretically and experimentally. An SRO based on periodically poled lithium niobate is built up that generates the signal with a maximum power of 5.2 W at 1.5 µm. The intensity noise of the signal reaches the shot noise level for frequencies above 5 MHz. The phase noise of the signal oscillates depending on the analysis frequency, and there are phase noise peaks above the shot noise level at the peak frequencies. To explain the phase noise feature of the signal, a semi-classical theoretical model of SROs including the guided acoustic wave Brillouin scattering effect within the nonlinear crystal is developed. The theoretical predictions are in good agreement with the experimental results.

  13. Intrinsic chirality and prochirality at Air/R-(+)- and S-(-)-limonene interfaces: spectral signatures with interference chiral sum-frequency generation vibrational spectroscopy.

    Science.gov (United States)

    Fu, Li; Zhang, Yun; Wei, Zhe-Hao; Wang, Hong-Fei

    2014-09-01

    We report in this work detailed measurements of the chiral and achiral sum-frequency vibrational spectra in the C-H stretching vibration region (2800-3050 cm(-1)) of the air/liquid interfaces of R-(+)-limonene and S-(-)-limonene, using the recently developed high-resolution broadband sum-frequency generation vibrational spectroscopy (HR-BB-SFG-VS). The achiral SFG spectra of R-limonene and S-limonene, as well as the RS racemic mixture (50/50 equal amount mixture), show that the corresponding molecular groups of the R and S enantiomers are with the same interfacial orientations. The interference chiral SFG spectra of the limonene enantiomers exhibit a spectral signature from the chiral response of the Cα-H stretching mode, and a spectral signature from the prochiral response of the CH(2) asymmetric stretching mode, respectively. The chiral spectral feature of the Cα-H stretching mode changes sign from R-(+)-limonene to S-(-)-limonene surfaces, and disappears for the RS racemic mixture surface. While the prochiral spectral feature of the CH(2) asymmetric stretching mode is the same for R-(+)-limonene and S-(-)-limonene surfaces, and also surprisingly remains the same for the RS racemic mixture surface. Therefore, the structures of the R-(+)-limonene and the S-(-)-limonene at the liquid interfaces are nevertheless not mirror images to each other, even though the corresponding groups have the same tilt angle from the interfacial normal, i.e., the R-(+)-limonene and the S-(-)-limonene at the surface are diastereomeric instead of enantiomeric. These results provide detailed information in understanding the structure and chirality of molecular interfaces and demonstrate the sensitivity and potential of SFG-VS as a unique spectroscopic tool for chirality characterization and chiral recognition at the molecular interface. © 2014 Wiley Periodicals, Inc.

  14. Catalyzed hydrogenation of nitrogen and ethylene on metal (Fe, Pt) single crystal surfaces and effects of coadsorption: A sum frequency generation vibrational spectroscopy study

    Energy Technology Data Exchange (ETDEWEB)

    Westerberg, Staffan Per Gustav [Univ. of California, Berkeley, CA (United States)

    2004-01-01

    High-pressure catalytic reactions and associated processes, such as adsorption have been studied on a molecular level on single crystal surfaces. Sum Frequency Generation (SFG) vibrational spectroscopy together with Auger Electron Spectroscopy (AES), Temperature Programmed Desorption (TPD) and Gas Chromatography (GC) were used to investigate the nature of species on catalytic surfaces and to measure the catalytic reaction rates. Special attention has been directed at studying high-pressure reactions and in particular, ammonia synthesis in order to identify reaction intermediates and the influence of adsorbates on the surface during reaction conditions. The adsorption of gases N2, H2, O2 and NH3 that play a role in ammonia synthesis have been studied on the Fe(111) crystal surface by sum frequency generation vibrational spectroscopy using an integrated Ultra-High Vacuum (UHV)/high-pressure system. SFG spectra are presented for the dissociation intermediates, NH2 (~3325 cm-1) and NH (~3235 cm-1) under high pressure of ammonia (200 Torr) on the clean Fe(111) surface. Addition of 0.5 Torr of oxygen to 200 Torr of ammonia does not significantly change the bonding of dissociation intermediates to the surface. However, it leads to a phase change of nearly 180° between the resonant and non-resonant second order non-linear susceptibility of the surface, demonstrated by the reversal of the SFG spectral features. Heating the surface in the presence of 200 Torr ammonia and 0.5 Torr oxygen reduces the oxygen coverage, which can be seen from the SFG spectra as another relative phase change of 180°. The reduction of the oxide is also supported by Auger electron spectroscopy. The result suggests that the phase change of the spectral features could serve as a sensitive indicator of the chemical environment of the adsorbates.

  15. Spectrally- and Time-Resolved Sum Frequency Generation (STiR-SFG): a new tool for ultrafast hydrogen bond dynamics at interfaces.

    Science.gov (United States)

    Benderskii, Alexander; Bordenyuk, Andrey; Weeraman, Champika

    2006-03-01

    The recently developed spectrally- and time-resolved Sum Frequency Generation (STiR-SFG) is a surface-selective 3-wave mixing (IR+visible) spectroscopic technique capable of measuring ultrafast spectral evolution of vibrational coherences. A detailed description of this measurement will be presented, and a noniterative method or deconvolving the laser pulses will be introduced to obtain the molecular response function. STiR-SFG, combined with the frequency-domain SFG spectroscopy, was applied to study hydrogen bonding dynamics at aqueous interfaces (D2O/CaF2). Spectral dynamics of the OD-stretch on the 50-150 fs time scale provides real-time observation of ultrafast H-bond rearrangement. Tuning the IR wavelength to the blue or red side of the OD-stretch transition, we selectively monitor the dynamics of different sub-ensembles in the distribution of the H-bond structures. The blue-side excitation (weaker H-bonding) shows monotonic red-shift of the OD-frequency. In contrast, the red-side excitation (stronger H-bonding structures) produces a blue-shift and a recursion, which may indicate the presence of an underdamped intermolecular mode of interfacial water. Effect of electrolyte concentration on the H-bond dynamics will be discussed.

  16. Summing skyrmions

    International Nuclear Information System (INIS)

    Jackson, A.D.; Weiss, C.; Wirzba, A.

    1990-01-01

    The Skyrme model has the same high density behavior as a free quark gas. However, the inclusion of higher-order terms spoils this agreement. We consider the all-order sum of a class of chiral invariant Lagrangians of even order in L μ suggested by Marleau. We prove Marleau's conjecture that these terms are of second order in the derivatives of the chiral angle for the hedgehog case and show the terms are unique under the additional condition that, for each order, the identity map on the 3-sphere S 3 (L) is a solution. The general form of the summation can be restricted by physical constraints leading to stable results. Under the assumption that the Lagrangian scales like the non-linear sigma model at low densities and like the free quark gas at high densities, we prove that a chiral phase transition must occur. (orig.)

  17. Adding a dimension to the infrared spectra of interfaces using heterodyne detected 2D sum-frequency generation (HD 2D SFG) spectroscopy.

    Science.gov (United States)

    Xiong, Wei; Laaser, Jennifer E; Mehlenbacher, Randy D; Zanni, Martin T

    2011-12-27

    In the last ten years, two-dimensional infrared spectroscopy has become an important technique for studying molecular structures and dynamics. We report the implementation of heterodyne detected two-dimensional sum-frequency generation (HD 2D SFG) spectroscopy, which is the analog of 2D infrared (2D IR) spectroscopy, but is selective to noncentrosymmetric systems such as interfaces. We implement the technique using mid-IR pulse shaping, which enables rapid scanning, phase cycling, and automatic phasing. Absorptive spectra are obtained, that have the highest frequency resolution possible, from which we extract the rephasing and nonrephasing signals that are sometimes preferred. Using this technique, we measure the vibrational mode of CO adsorbed on a polycrystalline Pt surface. The 2D spectrum reveals a significant inhomogenous contribution to the spectral line shape, which is quantified by simulations. This observation indicates that the surface conformation and environment of CO molecules is more complicated than the simple "atop" configuration assumed in previous work. Our method can be straightforwardly incorporated into many existing SFG spectrometers. The technique enables one to quantify inhomogeneity, vibrational couplings, spectral diffusion, chemical exchange, and many other properties analogous to 2D IR spectroscopy, but specifically for interfaces.

  18. 2D heterodyne-detected sum frequency generation study on the ultrafast vibrational dynamics of H{sub 2}O and HOD water at charged interfaces

    Energy Technology Data Exchange (ETDEWEB)

    Inoue, Ken-ichi; Singh, Prashant C. [Molecular Spectroscopy Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Nihonyanagi, Satoshi; Tahara, Tahei, E-mail: tahei@riken.jp [Molecular Spectroscopy Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Ultrafast Spectroscopy Research Team, RIKEN Center for Advanced Photonics, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Yamaguchi, Shoichi [Molecular Spectroscopy Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Department of Applied Chemistry, Saitama University, 255 Shimo-Okubo, Saitama 338-8570 (Japan)

    2015-06-07

    Two-dimensional heterodyne-detected vibrational sum-frequency generation (2D HD-VSFG) spectroscopy is applied to study the ultrafast vibrational dynamics of water at positively charged aqueous interfaces, and 2D HD-VSFG spectra of cetyltrimethylammonium bromide (CTAB)/water interfaces in the whole hydrogen-bonded OH stretch region (3000 cm{sup −1} ≤ ω{sub pump} ≤ 3600 cm{sup −1}) are measured. 2D HD-VSFG spectrum of the CTAB/isotopically diluted water (HOD-D{sub 2}O) interface exhibits a diagonally elongated bleaching lobe immediately after excitation, which becomes round with a time constant of ∼0.3 ps due to spectral diffusion. In contrast, 2D HD-VSFG spectrum of the CTAB/H{sub 2}O interface at 0.0 ps clearly shows two diagonal peaks and their cross peaks in the bleaching region, corresponding to the double peaks observed at 3230 cm{sup −1} and 3420 cm{sup −1} in the steady-state HD-VSFG spectrum. Horizontal slices of the 2D spectrum show that the relative intensity of the two peaks of the bleaching at the CTAB/H{sub 2}O interface gradually change with the change of the pump frequency. We simulate the pump-frequency dependence of the bleaching feature using a model that takes account of the Fermi resonance and inhomogeneity of the OH stretch vibration, and the simulated spectra reproduce the essential features of the 2D HD-VSFG spectra of the CTAB/H{sub 2}O interface. The present study demonstrates that heterodyne detection of the time-resolved VSFG is critically important for studying the ultrafast dynamics of water interfaces and for unveiling the underlying mechanism.

  19. Low energy electron diffraction (LEED) and sum frequency generation (SFG) vibrational spectroscopy studies of solid-vacuum, solid-air and solid-liquid interfaces

    Energy Technology Data Exchange (ETDEWEB)

    Hoffer, Saskia [Univ. of California, Berkeley, CA (United States)

    2002-01-01

    Electron based surface probing techniques can provide detailed information about surface structure or chemical composition in vacuum environments. The development of new surface techniques has made possible in situ molecular level studies of solid-gas interfaces and more recently, solid-liquid interfaces. The aim of this dissertation is two-fold. First, by using novel sample preparation, Low Energy Electron Diffraction (LEED) and other traditional ultra high vacuum (UHV) techniques are shown to provide new information on the insulator/vacuum interface. The surface structure of the classic insulator NaCl has been determined using these methods. Second, using sum frequency generation (SFG) surface specific vibrational spectroscopy studies were performed on both the biopolymer/air and electrode/electrolyte interfaces. The surface structure and composition of polyetherurethane-silicone copolymers were determined in air using SFG, atomic force microscopy (AFM), and X-ray photoelectron spectroscopy (XPS). SFG studies of the electrode (platinum, gold and copper)/electrolyte interface were performed as a function of applied potential in an electrochemical cell.

  20. Self-assembled organic monolayers on gold nanoparticles: A study by sum-frequency generation combined with UV-vis spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Humbert, C. [LURE, CNRS-UMR 130, Centre Universitaire Paris-Sud, Ba-hat t. 209D, B.P. 34, 91898 Orsay Cedex (France) and Laboratoire de Spectroscopie Moleculaire de Surface, University of Namur, 61 Rue de Bruxelles, B-5000 Namur (Belgium)]. E-mail: christophe.humbert@fundp.ac.be; Busson, B. [LURE, CNRS-UMR 130, Centre Universitaire Paris-Sud, Ba-hat t. 209D, B.P. 34, 91898 Orsay Cedex (France); Abid, J.-P. [Ecole Polytechnique Federale de Lausanne, Laboratoire d' Electrochimie Physique et Analytique, CH-1015 Lausanne (Switzerland); Six, C. [LURE, CNRS-UMR 130, Centre Universitaire Paris-Sud, Ba-hat t. 209D, B.P. 34, 91898 Orsay Cedex (France); Girault, H.H. [Ecole Polytechnique Federale de Lausanne, Laboratoire d' Electrochimie Physique et Analytique, CH-1015 Lausanne (Switzerland); Tadjeddine, A. [LURE, CNRS-UMR 130, Centre Universitaire Paris-Sud, Ba-hat t. 209D, B.P. 34, 91898 Orsay Cedex (France)

    2005-05-20

    We use sum-frequency generation spectroscopy (SFG) in the infrared 2800-3000 cm{sup -1} spectral range and UV-vis spectroscopy (transmission) in the 450-650 nm spectral range in order to characterize vibrational and electronic properties of various interfaces composed of organic monolayers adsorbed on gold nanoparticles (AuNPs) with 19 nm average diameter. SFG signal is observed for AuNPs films deposited on glass substrates using the following silane intermediates: 3-(aminopropyl) triethoxysilane and 3-(mercaptopropyl) trimethoxysilane. The density of AuNPs and their aggregates are measured with a scanning electron microscope. For the samples showing a strong well-defined surface plasmon resonance (SPR), we also observe an enhancement of their non-linear optical properties. Furthermore, the SFG measurements show that 1-dodecanethiol films are rather well ordered on specific AuNPs substrates. In this way, the presence of the SFG signal, which comes from both the bulk electronic s-d interband transition and the vibrational states of the adsorbed molecules, depends on a SPR process. This phenomenon is evidenced on the AuNPs by the incident visible beam located at 532 nm, i.e. near the SPR energy maximum of these interfaces. These results open the door to experiments involving macromolecular and biological materials networks deposited on ultrathin metal electrodes in a controlled electrochemical environment.

  1. Synthesis and characterization of aromatic self-assembled monolayers containing methylene and ethyleneglycol entities by means of sum-frequency generation spectroscopy

    International Nuclear Information System (INIS)

    Dreesen, L.; Sartenaer, Y.; Peremans, A.; Thiry, P.A.; Humbert, C.; Grugier, J.; Marchand-Brynaert, J.

    2006-01-01

    We use infrared-visible sum-frequency generation (SFG) spectroscopy in order to investigate the adsorption properties on Pt(111) of molecules having CH 3 -C 6 H 4 -(O-CH 2 -CH 2 ) n -O-(CH 2 ) m -SH as general chemical formula. We synthesized three molecules defined by the values m = 5 n = 4, m = 11 n = 4, m = 11 n = 8 and characterized them by Nuclear Magnetic Resonance spectroscopy. Thanks to spectroscopic measurements, we show that these molecules build self-assembled monolayers on Pt(111). First, the weak SFG signals arising from the ad-layer indicate low order and surface coverage of the substrate by these molecules. Next, the vibrational fingerprints of the aforementioned molecules are determined between 2825 and 3125 cm - 1 and the observed SFG spectral features are ascribed on the basis of the analysis of shorter and simpler molecules (1-dodecanethiol, 4-methylbenzenethiol and CH 3 -C 6 H 4 -O-(CH 2 ) 11 -SH) also adsorbed on Pt(111). The occurrence of methylene vibration modes indicates a significant amount of chain defects whatever the n and m numbers are. Finally, the identification of a particular vibration mode, characteristic of the aromatic ring, enables us to qualitatively discuss the effect of the number of methylene and ethylene glycol entities on its orientation. More precisely, higher these numbers, more tilted (with respect to the substrate normal) the aromatic ring plane is

  2. Water Orientation at Ceramide/Water Interfaces Studied by Heterodyne-Detected Vibrational Sum Frequency Generation Spectroscopy and Molecular Dynamics Simulation

    KAUST Repository

    Adhikari, Aniruddha

    2016-10-10

    Lipid/water interaction is essential for many biological processes. The water structure at the nonionic lipid interface remains little known, and there is no scope of a priori prediction of water orientation at nonionic interfaces, either. Here, we report our study combining advanced nonlinear spectroscopy and molecular dynamics simulation on the water orientation at the ceramide/water interface. We measured χ spectrum in the OH stretch region of ceramide/isotopically diluted water interface using heterodyne-detected vibrational sum-frequency generation spectroscopy and found that the interfacial water prefers an overall hydrogen-up orientation. Molecular dynamics simulation indicates that this preferred hydrogen-up orientation of water is determined by a delicate balance between hydrogen-up and hydrogen-down orientation induced by lipid-water and intralipid hydrogen bonds. This mechanism also suggests that water orientation at neutral lipid interfaces depends highly on the chemical structure of the lipid headgroup, in contrast to the charged lipid interfaces where the net water orientation is determined solely by the charge of the lipid headgroup.

  3. Studies of Heterogeneously Catalyzed Liquid-Phase Alcohol Oxidation on Platinum bySum-frequency Generation Vibrational Spectroscopy and Reaction Rate Measurements

    Energy Technology Data Exchange (ETDEWEB)

    Thompson, Christopher [Univ. of California, Berkeley, CA (United States)

    2014-05-15

    Compared to many branches of chemistry, the molecular level study of catalytically active surfaces is young. Only with the invention of ultrahigh vacuum technology in the past half century has it been possible to carry out experiments that yield useful molecular information about the reactive occurrences at a surface. The reason is two-fold: low pressure is necessary to keep a surface clean for an amount of time long enough to perform an experiment, and most atomic scale techniques that are surface speci c (x-ray photoelectron spectroscopy, electron energy loss spectroscopy, Auger electron spectroscopy, etc.) cannot be used at ambient pressures, because electrons, which act as chemical probes in these techniques, are easily scattered by molecules. Sum-frequency generation (SFG) vibrational spectroscopy is one technique that can provide molecular level information from the surface without the necessity for high vacuum. Since the advent of SFG as a surface spectroscopic tool it has proved its worth in the studies of surface catalyzed reactions in the gas phase, with numerous reactions in the gas phase having been investigated on a multitude of surfaces. However, in situ SFG characterization of catalysis at the solid-liquid interface has yet to be thoroughly pursued despite the broad interest in the use of heterogeneous catalysts in the liquid phase as replacements for homogeneous counterparts. This work describes an attempt to move in that direction, applying SFG to study the solid-liquid interface under conditions of catalytic alcohol oxidation on platinum.

  4. Vibrational Dynamics of Interfacial Water by Free Induction Decay Sum Frequency Generation (FID-SFG) at the Al2O3(1120)/H2O Interface.

    Science.gov (United States)

    Boulesbaa, Abdelaziz; Borguet, Eric

    2014-02-06

    The dephasing dynamics of a vibrational coherence may reveal the interactions of chemical functional groups with their environment. To investigate this process at a surface, we employ free induction decay sum frequency generation (FID-SFG) to measure the time that it takes for free OH stretch oscillators at the charged (pH ≈ 13, KOH) interface of alumina/water (Al2O3/H2O) to lose their collective coherence. By employing noncollinear optical parametric amplification (NOPA) technology and nonlinear vibrational spectroscopy, we showed that the single free OH peak actually corresponds to two distinct oscillators oriented opposite to each other and measured the total dephasing time, T2, of the free OH stretch modes at the Al2O3/H2O interface with a sub-40 fs temporal resolution. Our results suggested that the free OH oscillators associated with interfacial water dephase on the time scale of 89.4 ± 6.9 fs, whereas the homogeneous dephasing of interfacial alumina hydroxyls is an order of magnitude slower.

  5. Two-dimensional sum-frequency generation (2D SFG) spectroscopy: summary of principles and its application to amyloid fiber monolayers.

    Science.gov (United States)

    Ghosh, Ayanjeet; Ho, Jia-Jung; Serrano, Arnaldo L; Skoff, David R; Zhang, Tianqi; Zanni, Martin T

    2015-01-01

    By adding a mid-infrared pulse shaper to a sum-frequency generation (SFG) spectrometer, we have built a 2D SFG spectrometer capable of measuring spectra analogous to 2D IR spectra but with monolayer sensitivity and SFG selection rules. In this paper, we describe the experimental apparatus and provide an introduction to 2D SFG spectroscopy to help the reader interpret 2D SFG spectra. The main aim of this manuscript is to report 2D SFG spectra of the amyloid forming peptide FGAIL. FGAIL is a critical segment of the human islet amyloid polypeptide (hIAPP or amylin) that aggregates in people with type 2 diabetes. FGAIL is catalyzed into amyloid fibers by many types of surfaces. Here, we study the structure of FGAIL upon deposition onto a gold surface covered with a self-assembled monolayer of methyl-4-mercaptobenzoate (MMB) that produces an ester coating. FGAIL deposited on bare gold does not form ordered layers. The measured 2D SFG spectrum is consistent with amyloid fiber formation, exhibiting both the parallel (a+) and perpendicular (a-) symmetry modes associated with amyloid β-sheets. Cross peaks are observed between the ester stretches of the coating and the FGAIL peptides. Simulations are presented for two possible structures of FGAIL amyloid β-sheets that illustrate the sensitivity of the 2D SFG spectra to structure and orientation. These results provide some of the first molecular insights into surface catalyzed amyloid fiber structure.

  6. Self-assembled organic monolayers on gold nanoparticles: A study by sum-frequency generation combined with UV-vis spectroscopy

    International Nuclear Information System (INIS)

    Humbert, C.; Busson, B.; Abid, J.-P.; Six, C.; Girault, H.H.; Tadjeddine, A.

    2005-01-01

    We use sum-frequency generation spectroscopy (SFG) in the infrared 2800-3000 cm -1 spectral range and UV-vis spectroscopy (transmission) in the 450-650 nm spectral range in order to characterize vibrational and electronic properties of various interfaces composed of organic monolayers adsorbed on gold nanoparticles (AuNPs) with 19 nm average diameter. SFG signal is observed for AuNPs films deposited on glass substrates using the following silane intermediates: 3-(aminopropyl) triethoxysilane and 3-(mercaptopropyl) trimethoxysilane. The density of AuNPs and their aggregates are measured with a scanning electron microscope. For the samples showing a strong well-defined surface plasmon resonance (SPR), we also observe an enhancement of their non-linear optical properties. Furthermore, the SFG measurements show that 1-dodecanethiol films are rather well ordered on specific AuNPs substrates. In this way, the presence of the SFG signal, which comes from both the bulk electronic s-d interband transition and the vibrational states of the adsorbed molecules, depends on a SPR process. This phenomenon is evidenced on the AuNPs by the incident visible beam located at 532 nm, i.e. near the SPR energy maximum of these interfaces. These results open the door to experiments involving macromolecular and biological materials networks deposited on ultrathin metal electrodes in a controlled electrochemical environment

  7. Hydrogenation of the alpha,beta-Unsaturated Aldehydes Acrolein, Crotonaldehyde, and Prenal over Pt Single Crystals: A Kinetic and Sum-Frequency Generation Vibrational Spectroscopy Study

    Energy Technology Data Exchange (ETDEWEB)

    Kliewer, C.J.; Somorjai, G.A.

    2008-11-26

    Sum-frequency generation vibrational spectroscopy (SFG-VS) and kinetic measurements using gas chromatography have been used to study the surface reaction intermediates during the hydrogenation of three {alpha},{beta}-unsaturated aldehydes, acrolein, crotonaldehyde, and prenal, over Pt(111) at Torr pressures (1 Torr aldehyde, 100 Torr hydrogen) in the temperature range of 295K to 415K. SFG-VS data showed that acrolein has mixed adsorption species of {eta}{sub 2}-di-{sigma}(CC)-trans, {eta}{sub 2}-di-{sigma}(CC)-cis as well as highly coordinated {eta}{sub 3} or {eta}{sub 4} species. Crotonaldehyde adsorbed to Pt(111) as {eta}{sub 2} surface intermediates. SFG-VS during prenal hydrogenation also suggested the presence of the {eta}{sub 2} adsorption species, and became more highly coordinated as the temperature was raised to 415K, in agreement with its enhanced C=O hydrogenation. The effect of catalyst surface structure was clarified by carrying out the hydrogenation of crotonaldehyde over both Pt(111) and Pt(100) single crystals while acquiring the SFG-VS spectra in situ. Both the kinetics and SFG-VS showed little structure sensitivity. Pt(100) generated more decarbonylation 'cracking' product while Pt(111) had a higher selectivity for the formation of the desired unsaturated alcohol, crotylalcohol.

  8. Experimental evidence for an optical interference model for vibrational sum frequency generation on multilayer organic thin film systems. I. Electric dipole approximation

    International Nuclear Information System (INIS)

    O’Brien, Daniel B.; Massari, Aaron M.

    2015-01-01

    In the field of vibrational sum frequency generation spectroscopy (VSFG) applied to organic thin film systems, a significant challenge to data analysis is in the accurate description of optical interference effects. Herein, we provide experimental evidence that a model recently developed in our lab provides an accurate description of this phenomenon. We studied the organic small molecule N,N′-dioctyl-3,4,9,10-perylenedicarboximide vapor deposited as a thickness gradient on silicon wafer substrates with two oxide thicknesses and two surface preps. VSFG data were obtained using the ssp and the sps polarization combinations in the imide carbonyl stretching region as a function of organic thickness. In this first of two reports, the data are modeled and interpreted within the ubiquitous electric dipole approximation for VSFG. The intrinsic sample responses are parameterized during the fitting routines while optical interference effects are simply calculated from the model using known refractive indices, thin film thicknesses, and beam angles. The results indicate that the thin film model provides a good description of optical interferences, indicating that interfacial terms are significant. Inconsistencies between the fitting results within the bounds of the electric dipole response motivate deliberation for additional effects to be considered in the second report

  9. Experimental evidence for an optical interference model for vibrational sum frequency generation on multilayer organic thin film systems. I. Electric dipole approximation.

    Science.gov (United States)

    O'Brien, Daniel B; Massari, Aaron M

    2015-01-14

    In the field of vibrational sum frequency generation spectroscopy (VSFG) applied to organic thin film systems, a significant challenge to data analysis is in the accurate description of optical interference effects. Herein, we provide experimental evidence that a model recently developed in our lab provides an accurate description of this phenomenon. We studied the organic small molecule N,N'-dioctyl-3,4,9,10-perylenedicarboximide vapor deposited as a thickness gradient on silicon wafer substrates with two oxide thicknesses and two surface preps. VSFG data were obtained using the ssp and the sps polarization combinations in the imide carbonyl stretching region as a function of organic thickness. In this first of two reports, the data are modeled and interpreted within the ubiquitous electric dipole approximation for VSFG. The intrinsic sample responses are parameterized during the fitting routines while optical interference effects are simply calculated from the model using known refractive indices, thin film thicknesses, and beam angles. The results indicate that the thin film model provides a good description of optical interferences, indicating that interfacial terms are significant. Inconsistencies between the fitting results within the bounds of the electric dipole response motivate deliberation for additional effects to be considered in the second report.

  10. Experimental evidence for an optical interference model for vibrational sum frequency generation on multilayer organic thin film systems. I. Electric dipole approximation

    Energy Technology Data Exchange (ETDEWEB)

    O’Brien, Daniel B.; Massari, Aaron M., E-mail: massari@umn.edu [Department of Chemistry, University of Minnesota—Twin Cities, 207 Pleasant Street SE, Minneapolis, Minnesota 55455 (United States)

    2015-01-14

    In the field of vibrational sum frequency generation spectroscopy (VSFG) applied to organic thin film systems, a significant challenge to data analysis is in the accurate description of optical interference effects. Herein, we provide experimental evidence that a model recently developed in our lab provides an accurate description of this phenomenon. We studied the organic small molecule N,N′-dioctyl-3,4,9,10-perylenedicarboximide vapor deposited as a thickness gradient on silicon wafer substrates with two oxide thicknesses and two surface preps. VSFG data were obtained using the ssp and the sps polarization combinations in the imide carbonyl stretching region as a function of organic thickness. In this first of two reports, the data are modeled and interpreted within the ubiquitous electric dipole approximation for VSFG. The intrinsic sample responses are parameterized during the fitting routines while optical interference effects are simply calculated from the model using known refractive indices, thin film thicknesses, and beam angles. The results indicate that the thin film model provides a good description of optical interferences, indicating that interfacial terms are significant. Inconsistencies between the fitting results within the bounds of the electric dipole response motivate deliberation for additional effects to be considered in the second report.

  11. Phase transition behaviors of the supported DPPC bilayer investigated by sum frequency generation (SFG) vibrational spectroscopy and atomic force microscopy (AFM).

    Science.gov (United States)

    Wu, Heng-Liang; Tong, Yujin; Peng, Qiling; Li, Na; Ye, Shen

    2016-01-21

    The phase transition behaviors of a supported bilayer of dipalmitoylphosphatidyl-choline (DPPC) have been systematically evaluated by in situ sum frequency generation (SFG) vibrational spectroscopy and atomic force microscopy (AFM). By using an asymmetric bilayer composed of per-deuterated and per-protonated monolayers, i.e., DPPC-d75/DPPC and a symmetric bilayer of DPPC/DPPC, we were able to probe the molecular structural changes during the phase transition process of the lipid bilayer by SFG spectroscopy. It was found that the DPPC bilayer is sequentially melted from the top (adjacent to the solution) to bottom leaflet (adjacent to the substrate) over a wide temperature range. The conformational ordering of the supported bilayer does not decrease (even slightly increases) during the phase transition process. The conformational defects in the bilayer can be removed after the complete melting process. The phase transition enthalpy for the bottom leaflet was found to be approximately three times greater than that for the top leaflet, indicating a strong interaction of the lipids with the substrate. The present SFG and AFM observations revealed similar temperature dependent profiles. Based on these results, the temperature-induced structural changes in the supported lipid bilayer during its phase transition process are discussed in comparison with previous studies.

  12. Up to 30 mW of broadly tunable CW green-to-orange light, based on sum-frequency mixing of Cr4+:forsterite and Nd:YVO4 lasers

    DEFF Research Database (Denmark)

    Mortensen, Jesper Liltorp; McWilliam, Allan; G. Leburn, Christopher

    2006-01-01

    Efficient generation of continuous-wave (CW) tunable light in the yellow region is reported. The method is based on sum-frequency mixing of a tunable Cr4+:forsterite laser with a Nd:YVO4 laser. A periodically poled lithium niobate crystal was placed intra-cavity in a Nd:YVO4 laser, and the Cr4...

  13. Adsorption of 1- and 2-butylimidazoles at the copper/air and steel/air interfaces studied by sum frequency generation vibrational spectroscopy.

    Science.gov (United States)

    Casford, Michael T L; Davies, Paul B

    2012-07-24

    The structure of thin films of 1- and 2-butylimidazoles adsorbed on copper and steel surfaces under air was examined using sum frequency generation (SFG) vibrational spectroscopy in the ppp and ssp polarizations. Additionally, the SFG spectra of both isomers were recorded at 55 °C at the liquid imidazole/air interface for reference. Complementary bulk infrared, reflection-absorption infrared spectroscopy (RAIRS), and Raman spectra of both imidazoles were recorded for assignment purposes. The SFG spectra in the C-H stretching region at the liquid/air interface are dominated by resonances from the methyl end group of the butyl side chain of the imidazoles, indicating that they are aligned parallel or closely parallel to the surface normal. These are also the most prominent features in the SFG spectra on copper and steel. In addition, both the ppp and ssp spectra on copper show resonances from the C-H stretching modes of the imidazole ring for both isomers. The ring C-H resonances are completely absent from the spectra on steel and at the liquid/air interface. The relative intensities of the SFG spectra can be interpreted as showing that, on copper, under air, both butylimidazoles are adsorbed with their butyl side chains perpendicular to the interface and with the ring significantly inclined away from the surface plane and toward the surface normal. The SFG spectra of both imidazoles on steel indicate an orientation where the imidazole rings are parallel or nearly parallel to the surface. The weak C-H resonances from the ring at the liquid/air interface suggest that the tilt angle of the ring from the surface normal at this interface is significantly greater than it is on copper.

  14. Hydration of Sulphobetaine (SB) and Tetra(ethylene glycol) (EG4)-Terminated Self-Assembled Monolayers Studied by Sum Frequency Generation (SFG) Vibrational Spectroscopy

    Science.gov (United States)

    Stein, M. Jeanette; Weidner, Tobias; McCrea, Keith; Castner, David G.; Ratner, Buddy D.

    2010-01-01

    Sum frequency generation (SFG) vibrational spectroscopy is used to study the surface and the underlying substrate of both homogeneous and mixed self-assembled monolayers (SAMs) of 11-mercaptoundecyl-1-sulphobetainethiol (HS(CH2)11N+(CH3)2(CH2)3SO3−, SB) and 1-mercapto-11-undecyl tetra(ethylene glycol) (HS(CH2)11O(CH2CH2O)4OH, EG4) with an 11-mercapto-1-undecanol (HS(CH2)11OH, MCU) diluent. SFG results on the C–H region of the dry and hydrated SAMs gave an in situ look into the molecular orientation and suggested an approach to maximize signal-to-noise ratio on these difficult to analyze hydrophilic SAMs. Vibrational fingerprint studies in the 3000–3600 cm−1 spectral range for the SAMs exposed serially to air, water, and deuterated water revealed that a layer of tightly-bound structured water was associated with the surface of a non-fouling monolayer but was not present on a hydrophobic N-undecylmercaptan (HS(CH2)10CH3, UnD) control. The percentage of water retained upon submersion in D2O correlated well with the relative amount of protein that was previously shown to absorb onto the monolayers. These results provide evidence supporting the current theory regarding the role of a tightly-bound vicinal water layer in the protein resistance of a non-fouling group. PMID:19639981

  15. Discovery of deep and shallow trap states from step structures of rutile TiO2 vicinal surfaces by second harmonic and sum frequency generation spectroscopy

    International Nuclear Information System (INIS)

    Takahashi, Hiroaki; Watanabe, Ryosuke; Miyauchi, Yoshihiro; Mizutani, Goro

    2011-01-01

    In this report, local electronic structures of steps and terraces on rutile TiO 2 single crystal faces were studied by second harmonic and sum frequency generation (SHG/SFG) spectroscopy. We attained selective measurement of the local electronic states of the step bunches formed on the vicinal (17 18 1) and (15 13 0) surfaces using a recently developed step-selective probing technique. The electronic structures of the flat (110)-(1x1) (the terrace face of the vicinal surfaces) and (011)-(2x1) surfaces were also discussed. The SHG/SFG spectra showed that step structures are mainly responsible for the formation of trap states, since significant resonances from the trap states were observed only from the vicinal surfaces. We detected deep hole trap (DHT) states and shallow electron trap (SET) states selectively from the step bunches on the vicinal surfaces. Detailed analysis of the SHG/SFG spectra showed that the DHT and SET states are more likely to be induced at the top edges of the step bunches than on their hillsides. Unlike the SET states, the DHT states were observed only at the step bunches parallel to [1 1 1][equivalent to the step bunches formed on the (17 18 1) surface]. Photocatalytic activity for each TiO 2 sample was also measured through methylene blue photodegradation reactions and was found to follow the sequence: (110) < (17 18 1) < (15 13 0) < (011), indicating that steps along [0 0 1] are more reactive than steps along [1 1 1]. This result implies that the presence of the DHT states observed from the step bunches parallel to [1 1 1] did not effectively contribute to the methylene blue photodegradation reactions.

  16. Sum-frequency generation spectroscopy on metals, oxides, and oxide-supported metal particles; Summenfrequenzerzeugungsspektroskopie an Metallen, Oxiden und oxidgetraegerten Metallpartikeln

    Energy Technology Data Exchange (ETDEWEB)

    Aumer, Andreas

    2010-06-21

    This thesis focuses on 4 different model systems of surface science. The experimental techniques used for the measurements include sum frequency generation (SFG), thermal desorption spectroscopy (TDS), low energy electron diffraction (LEED), Auger electron spectroscopy (AES), infrared adsorption spectrosocopy (IRAS) and scanning tunneling microscopy (STM). By using SFG, measurements could be performed up to a pressure of 50 mbar. The systems under investigation were: CO on Pt(111), water on Ag(001) and on MgO/Ag(001), CO on Au/MgO/Ag(001), and CO on Au-Pd/MgO/Ag(001). The system of CO on Pt(111) exhibits a two peak-pattern under certain pressure and temperature conditions which has not been studied so far. Various experiments helped to elucidate the origin of this distinct behaviour. The measurements of water on Ag(001) and MgO/Ag(001) show that on MgO, water first adsorbs as a monolayer with a following multilayer, whereas on Ag(001) it adsorbs as a multilayer from the beginning. The monolayer can be studied below the multilayer and some resonances can be identified. For the case of Au/MgO/Ag(001), STM shows that the growth mode of Au depends on the thickness of the supporting MgO film, which can not be seen with spectroscopic methods. For mixed Au-Pd particles on MgO/Ag(001) a clear difference in the adsorption behaviour between pure metal particles and mixed particles can be seen, which is explained by an interaction between these metals. Annealing the mixed particles to 600 K leads to a segregation of the metals, where the Au atoms diffuse to the shell and the Pd atoms make up the core. The results of all these measurements are discussed in the light of recent publications. (orig.)

  17. High-Pressure Catalytic Reactions of C6 Hydrocarbons on PlatinumSingle-Crystals and nanoparticles: A Sum Frequency Generation VibrationalSpectroscopic and Kinetic Study

    Energy Technology Data Exchange (ETDEWEB)

    Bratlie, Kaitlin [Univ. of California, Berkeley, CA (United States)

    2007-01-01

    Catalytic reactions of cyclohexene, benzene, n-hexane, 2-methylpentane, 3-methylpentane, and 1-hexene on platinum catalysts were monitored in situ via sum frequency generation (SFG) vibrational spectroscopy and gas chromatography (GC). SFG is a surface specific vibrational spectroscopic tool capable of monitoring submonolayer coverages under reaction conditions without gas-phase interference. SFG was used to identify the surface intermediates present during catalytic processes on Pt(111) and Pt(100) single-crystals and on cubic and cuboctahedra Pt nanoparticles in the Torr pressure regime and at high temperatures (300K-450K). At low pressures (<10-6 Torr), cyclohexene hydrogenated and dehydrogenates to form cyclohexyl (C6H11) and π-allyl C6H9, respectively, on Pt(100). Increasing pressures to 1.5 Torr form cyclohexyl, π-allyl C6H9, and 1,4-cyclohexadiene, illustrating the necessity to investigate catalytic reactions at high-pressures. Simultaneously, GC was used to acquire turnover rates that were correlated to reactive intermediates observed spectroscopically. Benzene hydrogenation on Pt(111) and Pt(100) illustrated structure sensitivity via both vibrational spectroscopy and kinetics. Both cyclohexane and cyclohexene were produced on Pt(111), while only cyclohexane was formed on Pt(100). Additionally, π-allyl c-C6H9 was found only on Pt(100), indicating that cyclohexene rapidly dehydrogenates on the (100) surface. The structure insensitive production of cyclohexane was found to exhibit a compensation effect and was analyzed using the selective energy transfer (SET) model. The SET model suggests that the Pt-H system donates energy to the E2u mode of free benzene, which leads to catalysis. Linear C6 (n-hexane, 2-methylpentane, 3-methylpentane, and 1-hexene) hydrocarbons were also investigated in the presence and absence of excess hydrogen on Pt

  18. Sum Frequency Generation Vibrational Spectroscopy Studies on ModelPeptide Adsorption at the Hydrophobic Solid-Water and HydrophilicSolid-Water Interfaces

    Energy Technology Data Exchange (ETDEWEB)

    York, Roger L. [Univ. of California, Berkeley, CA (United States)

    2007-01-01

    Sum frequency generation (SFG) vibrational spectroscopy has been used to study the interfacial structure of several polypeptides and amino acids adsorbed to hydrophobic and hydrophilic surfaces under a variety of experimental conditions. Peptide sequence, peptide chain length, peptide hydrophobicity, peptide side-chain type, surface hydrophobicity, and solution ionic strength all affect an adsorbed peptide's interfacial structure. Herein, it is demonstrated that with the choice of simple, model peptides and amino acids, surface specific SFG vibrational spectroscopy can be a powerful tool to elucidate the interfacial structure of these adsorbates. Herein, four experiments are described. In one, a series of isosequential amphiphilic peptides are synthesized and studied when adsorbed to both hydrophobic and hydrophilic surfaces. On hydrophobic surfaces of deuterated polystyrene, it was determined that the hydrophobic part of the peptide is ordered at the solid-liquid interface, while the hydrophilic part of the peptide appears to have a random orientation at this interface. On a hydrophilic surface of silica, it was determined that an ordered peptide was only observed if a peptide had stable secondary structure in solution. In another experiment, the interfacial structure of a model amphiphilic peptide was studied as a function of the ionic strength of the solution, a parameter that could change the peptide's secondary structure in solution. It was determined that on a hydrophobic surface, the peptide's interfacial structure was independent of its structure in solution. This was in contrast to the adsorbed structure on a hydrophilic surface, where the peptide's interfacial structure showed a strong dependence on its solution secondary structure. In a third experiment, the SFG spectra of lysine and proline amino acids on both hydrophobic and hydrophilic surfaces were obtained by using a different experimental geometry that increases the SFG signal

  19. Support Effects in Catalysis Studied by in-situ Sum Frequency Generation Vibrational Spectroscopy and in-situ X-Ray Spectroscopies

    Science.gov (United States)

    Kennedy, Griffin John

    Kinetic measurements are paired with in-situ spectroscopic characterization tools to investigate colloidally based, supported Pt catalytic model systems in order to elucidate the mechanisms by which metal and support work in tandem to dictate activity and selectivity. The results demonstrate oxide support materials, while inactive in absence of Pt nanoparticles, possess unique active sites for the selective conversion of gas phase molecules when paired with an active metal catalyst. In order to establish a paradigm for metal-support interactions using colloidally synthesized Pt nanoparticles the ability of the organic capping agent to inhibit reactivity and interaction with the support must first be assessed. Pt nanoparticles capped by poly(vinylpyrrolidone) (PVP), and those from which the PVP is removed by UV light exposure, are investigated for two reactions, the hydrogenation of ethylene and the oxidation of methanol. It is shown that prior to PVP removal the particles are moderately active for both reactions. Following removal, the activity for the two reactions diverges, the ethylene hydrogenation rate increases 10-fold, while the methanol oxidation rate decreases 3-fold. To better understand this effect the capping agent prior to, and the residual carbon remaining after UV treatment are probed by sum frequency generation vibrational spectroscopy. Prior to removal no major differences are observed when the particles are exposed to alternating H2 and O2 environments. When the PVP is removed, carbonaceous fragments remain on the surface that dynamically restructure in H2 and O2. These fragments create a tightly bound shell in an oxygen environment and a porous coating of hydrogenated carbon in the hydrogen environment. Reaction rate measurements of thermally cleaned PVP and oleic acid capped particles show this effect to be independent of cleaning method or capping agent. In all this demonstrates the ability of the capping agent to mediate nanoparticle catalysis

  20. Characterization of the molecular structure and mechanical properties of polymer surfaces and protein/polymer interfaces by sum frequency generation vibrational spectroscopy and atomic force microscopy

    Energy Technology Data Exchange (ETDEWEB)

    Koffas, Telly Stelianos [Univ. of California, Berkeley, CA (United States)

    2004-01-01

    Sum frequency generation (SFG) vibrational spectroscopy, atomic force microscopy (AFM), and other complementary surface-sensitive techniques have been used to study the surface molecular structure and surface mechanical behavior of biologically-relevant polymer systems. SFG and AFM have emerged as powerful analytical tools to deduce structure/property relationships, in situ, for polymers at air, liquid and solid interfaces. The experiments described in this dissertation have been performed to understand how polymer surface properties are linked to polymer bulk composition, substrate hydrophobicity, changes in the ambient environment (e.g., humidity and temperature), or the adsorption of macromolecules. The correlation of spectroscopic and mechanical data by SFG and AFM can become a powerful methodology to study and engineer materials with tailored surface properties. The overarching theme of this research is the interrogation of systems of increasing structural complexity, which allows us to extend conclusions made on simpler model systems. We begin by systematically describing the surface molecular composition and mechanical properties of polymers, copolymers, and blends having simple linear architectures. Subsequent chapters focus on networked hydrogel materials used as soft contact lenses and the adsorption of protein and surfactant at the polymer/liquid interface. The power of SFG is immediately demonstrated in experiments which identify the chemical parameters that influence the molecular composition and ordering of a polymer chain's side groups at the polymer/air and polymer/liquid interfaces. In general, side groups with increasingly greater hydrophobic character will be more surface active in air. Larger side groups impose steric restrictions, thus they will tend to be more randomly ordered than smaller hydrophobic groups. If exposed to a hydrophilic environment, such as water, the polymer chain will attempt to orient more of its hydrophilic groups to

  1. Composite Finite Sums

    KAUST Repository

    Alabdulmohsin, Ibrahim M.

    2018-01-01

    In this chapter, we extend the previous results of Chap. 2 to the more general case of composite finite sums. We describe what composite finite sums are and how their analysis can be reduced to the analysis of simple finite sums using the chain rule. We apply these techniques, next, on numerical integration and on some identities of Ramanujan.

  2. Composite Finite Sums

    KAUST Repository

    Alabdulmohsin, Ibrahim M.

    2018-03-07

    In this chapter, we extend the previous results of Chap. 2 to the more general case of composite finite sums. We describe what composite finite sums are and how their analysis can be reduced to the analysis of simple finite sums using the chain rule. We apply these techniques, next, on numerical integration and on some identities of Ramanujan.

  3. Blue and Orange Two-Color CW Laser Based on Single-Pass Second-Harmonic and Sum-Frequency Generation in MgO:PPLN

    Directory of Open Access Journals (Sweden)

    Dismas K. Choge

    2018-04-01

    Full Text Available We demonstrate a compact blue and orange-two color continuous wave laser source emitting at 487 nm and from 597.4 to 600.3 nm, respectively. The temperature tunable coherent orange radiation is achieved by frequency mixing 974 nm laser diode (LD and a C-band amplified spontaneous emission laser source while the temperature insensitive blue radiation is generated by second-order quasi-phase-matching frequency doubling of 974 nm LD. We implement the simultaneous nonlinear processes in a single magnesium oxide doped periodically poled lithium niobate bulk crystal without the need of an aperiodic design.

  4. Observation of sum-frequency-generation-induced cascaded four-wave mixing using two crossing femtosecond laser pulses in a 0.1 mm beta-barium-borate crystal.

    Science.gov (United States)

    Liu, Weimin; Zhu, Liangdong; Fang, Chong

    2012-09-15

    We demonstrate the simultaneous generation of multicolor femtosecond laser pulses spanning the wavelength range from UV to near IR in a 0.1 mm Type I beta-barium borate crystal from 800 nm fundamental and weak IR super-continuum white light (SCWL) pulses. The multicolor broadband laser pulses observed are attributed to two concomitant cascaded four-wave mixing (CFWM) processes as corroborated by calculation: (1) directly from the two incident laser pulses; (2) by the sum-frequency generation (SFG) induced CFWM process (SFGFWM). The latter signal arises from the interaction between the frequency-doubled fundamental pulse (400 nm) and the SFG pulse generated in between the fundamental and IR-SCWL pulses. The versatility and simplicity of this spatially dispersed multicolor self-compressed laser pulse generation offer compact and attractive methods to conduct femtosecond stimulated Raman spectroscopy and time-resolved multicolor spectroscopy.

  5. Simple Finite Sums

    KAUST Repository

    Alabdulmohsin, Ibrahim M.

    2018-03-07

    We will begin our treatment of summability calculus by analyzing what will be referred to, throughout this book, as simple finite sums. Even though the results of this chapter are particular cases of the more general results presented in later chapters, they are important to start with for a few reasons. First, this chapter serves as an excellent introduction to what summability calculus can markedly accomplish. Second, simple finite sums are encountered more often and, hence, they deserve special treatment. Third, the results presented in this chapter for simple finite sums will, themselves, be used as building blocks for deriving the most general results in subsequent chapters. Among others, we establish that fractional finite sums are well-defined mathematical objects and show how various identities related to the Euler constant as well as the Riemann zeta function can actually be derived in an elementary manner using fractional finite sums.

  6. Simple Finite Sums

    KAUST Repository

    Alabdulmohsin, Ibrahim M.

    2018-01-01

    We will begin our treatment of summability calculus by analyzing what will be referred to, throughout this book, as simple finite sums. Even though the results of this chapter are particular cases of the more general results presented in later chapters, they are important to start with for a few reasons. First, this chapter serves as an excellent introduction to what summability calculus can markedly accomplish. Second, simple finite sums are encountered more often and, hence, they deserve special treatment. Third, the results presented in this chapter for simple finite sums will, themselves, be used as building blocks for deriving the most general results in subsequent chapters. Among others, we establish that fractional finite sums are well-defined mathematical objects and show how various identities related to the Euler constant as well as the Riemann zeta function can actually be derived in an elementary manner using fractional finite sums.

  7. Electronuclear sum rules

    International Nuclear Information System (INIS)

    Arenhoevel, H.; Drechsel, D.; Weber, H.J.

    1978-01-01

    Generalized sum rules are derived by integrating the electromagnetic structure functions along lines of constant ratio of momentum and energy transfer. For non-relativistic systems these sum rules are related to the conventional photonuclear sum rules by a scaling transformation. The generalized sum rules are connected with the absorptive part of the forward scattering amplitude of virtual photons. The analytic structure of the scattering amplitudes and the possible existence of dispersion relations have been investigated in schematic relativistic and non-relativistic models. While for the non-relativistic case analyticity does not hold, the relativistic scattering amplitude is analytical for time-like (but not for space-like) photons and relations similar to the Gell-Mann-Goldberger-Thirring sum rule exist. (Auth.)

  8. Over 8 W high peak power UV laser with a high power Q-switched Nd:YVO4 oscillator and the compact extra-cavity sum-frequency mixing

    International Nuclear Information System (INIS)

    Yan, X P; Liu, Q; Gong, M; Wang, D S; Fu, X

    2009-01-01

    A 8.2 W UV laser was reported with the compact extra-cavity sum-frequency mixing. The IR fundamental frequency source was a high power and high beam quality Q-switched Nd:YVO 4 oscillator. 38 W fundamental frequency laser at 1064 nm was obtained at the pulse repetition rate of 450 kHz with the beam quality factors of M 2 x = 1.27, M 2 y = 1.21. The type I and type II phase-matched LBO crystals were used as the extra-cavity frequency doubling and mixing crystals respectively. At 38 kHz, 8.2 W UV laser at 355 nm was achieved with the pulse duration of 8 ns corresponding to the pulse peak power as high as 27 kW, and the optical-optical conversion efficiency from IR to UV was 25.6%. The output characteristics of the IR and the harmonic generations varying with the pulse repetition rate were also investigated detailedly

  9. Observation of self-pulsing in singly resonant optical second-harmonic generation with competing nonlinearities

    DEFF Research Database (Denmark)

    Bache, Morten; Lodahl, Peter; Mamaev, Alexander V.

    2002-01-01

    We predict and experimentally observe temporal self-pulsing in singly resonant intracavity second-harmonic generation under conditions of simultaneous parametric oscillation. The threshold for self-pulsing as a function of cavity tuning and phase mismatch are found from analysis of a three...

  10. Fiber Laser Pumped Continuous-wave Singly-resonant Optical Parametric Oscillator

    NARCIS (Netherlands)

    Klein, M.E.; Gross, P.; Walde, T.; Boller, Klaus J.; Auerbach, M.; Wessels, P.; Fallnich, C.; Fejer, Martin M.

    2002-01-01

    We report on the first fiber-pumped CW LiNbO/sub 3/ optical parametric oscillator (OPO). The OPO is singly resonant (SRO) and generates idler wavelengths in the range of 3.0 /spl mu/m to 3.7 /spl mu/m with a maximum output power of 1.9 watt.

  11. Sums and Gaussian vectors

    CERN Document Server

    Yurinsky, Vadim Vladimirovich

    1995-01-01

    Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.

  12. Quantum Mechanical Calculations of Vibrational Sum-Frequency-Generation (SFG) Spectra of Cellulose: Dependence of the CH and OH Peak Intensity on the Polarity of Cellulose Chains within the SFG Coherence Domain.

    Science.gov (United States)

    Lee, Christopher M; Chen, Xing; Weiss, Philip A; Jensen, Lasse; Kim, Seong H

    2017-01-05

    Vibrational sum-frequency-generation (SFG) spectroscopy is capable of selectively detecting crystalline biopolymers interspersed in amorphous polymer matrices. However, the spectral interpretation is difficult due to the lack of knowledge on how spatial arrangements of crystalline segments influence SFG spectra features. Here we report time-dependent density functional theory (TD-DFT) calculations of cellulose crystallites in intimate contact with two different polarities: parallel versus antiparallel. TD-DFT calculations reveal that the CH/OH intensity ratio is very sensitive to the polarity of the crystallite packing. Theoretical calculations of hyperpolarizability tensors (β abc ) clearly show the dependence of SFG intensities on the polarity of crystallite packing within the SFG coherence length, which provides the basis for interpretation of the empirically observed SFG features of native cellulose in biological systems.

  13. An efficient continuous-wave 591 nm light source based on sum-frequency mixing of a diode pumped Nd:GdVO4–Nd:CNGG laser

    International Nuclear Information System (INIS)

    Zhao, Y D; Liu, J H

    2013-01-01

    We report a laser architecture to obtain continuous-wave (CW) yellow-orange light sources at the 591 nm wavelength. An 808 nm diode pumped a Nd:GdVO 4 crystal emitting at 1063 nm. A part of the pump power was then absorbed by the Nd:CNGG crystal. The remaining pump power was used to pump a Nd:CNGG crystal emitting at 1329 nm. Intracavity sum-frequency mixing at 1063 and 1329 nm was then realized in a LiB 3 O 5 (LBO) crystal to reach the yellow-orange radiation. We obtained a CW output power of 494 mW at 591 nm with a pump laser diode emitting 17.8 W at 808 nm. (paper)

  14. Selecting Sums in Arrays

    DEFF Research Database (Denmark)

    Brodal, Gerth Stølting; Jørgensen, Allan Grønlund

    2008-01-01

    In an array of n numbers each of the \\binomn2+nUnknown control sequence '\\binom' contiguous subarrays define a sum. In this paper we focus on algorithms for selecting and reporting maximal sums from an array of numbers. First, we consider the problem of reporting k subarrays inducing the k largest...... sums among all subarrays of length at least l and at most u. For this problem we design an optimal O(n + k) time algorithm. Secondly, we consider the problem of selecting a subarray storing the k’th largest sum. For this problem we prove a time bound of Θ(n · max {1,log(k/n)}) by describing...... an algorithm with this running time and by proving a matching lower bound. Finally, we combine the ideas and obtain an O(n· max {1,log(k/n)}) time algorithm that selects a subarray storing the k’th largest sum among all subarrays of length at least l and at most u....

  15. Multiparty symmetric sum types

    DEFF Research Database (Denmark)

    Nielsen, Lasse; Yoshida, Nobuko; Honda, Kohei

    2010-01-01

    This paper introduces a new theory of multiparty session types based on symmetric sum types, by which we can type non-deterministic orchestration choice behaviours. While the original branching type in session types can represent a choice made by a single participant and accepted by others...... determining how the session proceeds, the symmetric sum type represents a choice made by agreement among all the participants of a session. Such behaviour can be found in many practical systems, including collaborative workflow in healthcare systems for clinical practice guidelines (CPGs). Processes...... with the symmetric sums can be embedded into the original branching types using conductor processes. We show that this type-driven embedding preserves typability, satisfies semantic soundness and completeness, and meets the encodability criteria adapted to the typed setting. The theory leads to an efficient...

  16. Single frequency intracavity SRO

    DEFF Research Database (Denmark)

    Abitan, Haim; Buchhave, Preben

    2000-01-01

    Summary form only given. A single resonance optical parametric oscillator (SRO) is inserted intracavity to a CW high power, single frequency, and ring Nd:YVO4 laser. We obtain a stable single frequency CW SRO with output at 1.7-1.9 μm (idler) and a resonating signal at 2.3-2.6 μm. The behavior...

  17. Cosmic Sum Rules

    DEFF Research Database (Denmark)

    T. Frandsen, Mads; Masina, Isabella; Sannino, Francesco

    2011-01-01

    We introduce new sum rules allowing to determine universal properties of the unknown component of the cosmic rays and show how it can be used to predict the positron fraction at energies not yet explored by current experiments and to constrain specific models.......We introduce new sum rules allowing to determine universal properties of the unknown component of the cosmic rays and show how it can be used to predict the positron fraction at energies not yet explored by current experiments and to constrain specific models....

  18. Capturing inhomogeneous broadening of the -CN stretch vibration in a Langmuir monolayer with high-resolution spectra and ultrafast vibrational dynamics in sum-frequency generation vibrational spectroscopy (SFG-VS)

    Science.gov (United States)

    Velarde, Luis; Wang, Hong-fei

    2013-08-01

    While in principle the frequency-domain and time-domain spectroscopic measurements should generate identical information for a given molecular system, the inhomogeneous character of surface vibrations in sum-frequency generation vibrational spectroscopy (SFG-VS) studies has only been studied with time-domain SFG-VS by mapping the decay of the vibrational polarization using ultrafast lasers, this due to the lack of SFG vibrational spectra with high enough spectral resolution and accurate enough lineshape. Here, with the recently developed high-resolution broadband SFG-VS (HR-BB-SFG-VS) technique, we show that the inhomogeneous lineshape can be obtained in the frequency-domain for the anchoring CN stretch of the 4-n-octyl-4'-cyanobiphenyl (8CB) Langmuir monolayer at the air-water interface, and that an excellent agreement with the time-domain SFG free-induction-decay can be established. We found that the 8CB CN stretch spectrum consists of a single peak centered at 2234.00 ± 0.01 cm-1 with a total linewidth of 10.9 ± 0.3 cm-1 at half maximum. The Lorentzian contribution accounts only for 4.7 ± 0.4 cm-1 to this width and the Gaussian (inhomogeneous) broadening for as much as 8.1 ± 0.2 cm-1. Polarization analysis of the -CN spectra showed that the -CN group is tilted 57° ± 2° from the surface normal. The large heterogeneity in the -CN spectrum is tentatively attributed to the -CN group interactions with the interfacial water molecules penetrated/accommodated into the 8CB monolayer, a unique phenomenon for the nCB Langmuir monolayers reported previously.

  19. Sum Frequency Generation Vibrational Spectroscopy of 1,3-Butadiene Hydrogenation on 4 nm Pt@SiO 2 , Pd@SiO 2 , and Rh@SiO 2 Core–Shell Catalysts

    KAUST Repository

    Krier, James M.

    2015-01-14

    © 2014 American Chemical Society. 1,3-Butadiene (1,3-BD) hydrogenation was performed on 4 nm Pt, Pd, and Rh nanoparticles (NPs) encapsulated in SiO2 shells at 20, 60, and 100 °C. The core-shells were grown around polyvinylpyrrolidone (PVP) coated NPs (Stöber encapsulation) prepared by colloidal synthesis. Sum frequency generation (SFG) vibrational spectroscopy was performed to correlate surface intermediates observed in situ with reaction selectivity. It is shown that calcination is effective in removing PVP, and the SFG signal can be generated from the metal surface. Using SFG, it is possible to compare the surface vibrational spectrum of Pt@SiO2 (1,3-BD is hydrogenated through multiple paths and produces butane, 1-butene, and cis/trans-2-butene) to Pd@SiO2 (1,3-BD favors one path and produces 1-butene and cis/trans-2-butene). In contrast to Pt@SiO2 and Pd@SiO2, SFG and kinetic experiments of Rh@SiO2 show a permanent accumulation of organic material.

  20. sumé

    African Journals Online (AJOL)

    Tracie1

    sumé. L'activité traduisant est un processus très compliqué qui exige la connaissance extralinguistique chez le traducteur. Ce travail est basé sur la traduction littéraire. La traduction littéraire consistedes textes littéraires que comprennent la poésie, le théâtre, et la prose. La traduction littéraire a quelques problèmes ...

  1. Oscillating Finite Sums

    KAUST Repository

    Alabdulmohsin, Ibrahim M.

    2018-03-07

    In this chapter, we use the theory of summability of divergent series, presented earlier in Chap. 4, to derive the analogs of the Euler-Maclaurin summation formula for oscillating sums. These formulas will, in turn, be used to perform many remarkable deeds with ease. For instance, they can be used to derive analytic expressions for summable divergent series, obtain asymptotic expressions of oscillating series, and even accelerate the convergence of series by several orders of magnitude. Moreover, we will prove the notable fact that, as far as the foundational rules of summability calculus are concerned, summable divergent series behave exactly as if they were convergent.

  2. Oscillating Finite Sums

    KAUST Repository

    Alabdulmohsin, Ibrahim M.

    2018-01-01

    In this chapter, we use the theory of summability of divergent series, presented earlier in Chap. 4, to derive the analogs of the Euler-Maclaurin summation formula for oscillating sums. These formulas will, in turn, be used to perform many remarkable deeds with ease. For instance, they can be used to derive analytic expressions for summable divergent series, obtain asymptotic expressions of oscillating series, and even accelerate the convergence of series by several orders of magnitude. Moreover, we will prove the notable fact that, as far as the foundational rules of summability calculus are concerned, summable divergent series behave exactly as if they were convergent.

  3. Analysis and optimization with ecological objective function of irreversible single resonance energy selective electron heat engines

    International Nuclear Information System (INIS)

    Zhou, Junle; Chen, Lingen; Ding, Zemin; Sun, Fengrui

    2016-01-01

    Ecological performance of a single resonance ESE heat engine with heat leakage is conducted by applying finite time thermodynamics. By introducing Nielsen function and numerical calculations, expressions about power output, efficiency, entropy generation rate and ecological objective function are derived; relationships between ecological objective function and power output, between ecological objective function and efficiency as well as between power output and efficiency are demonstrated; influences of system parameters of heat leakage, boundary energy and resonance width on the optimal performances are investigated in detail; a specific range of boundary energy is given as a compromise to make ESE heat engine system work at optimal operation regions. Comparing performance characteristics with different optimization objective functions, the significance of selecting ecological objective function as the design objective is clarified specifically: when changing the design objective from maximum power output into maximum ecological objective function, the improvement of efficiency is 4.56%, while the power output drop is only 2.68%; when changing the design objective from maximum efficiency to maximum ecological objective function, the improvement of power output is 229.13%, and the efficiency drop is only 13.53%. - Highlights: • An irreversible single resonance energy selective electron heat engine is studied. • Heat leakage between two reservoirs is considered. • Power output, efficiency and ecological objective function are derived. • Optimal performance comparison for three objective functions is carried out.

  4. In Situ Adsorption Studies at the Solid/Liquid Interface: Characterization of Biological Surfaces and Interfaces Using Sum Frequency Generation Vibrational Spectroscopy, Atomic Force Microscopy, and Quartz Crystal Microbalance

    International Nuclear Information System (INIS)

    Phillips, D.C.

    2006-01-01

    Sum frequency generation (SFG) vibrational spectroscopy, atomic force microscopy (AFM), and quartz crystal microbalance (QCM) have been used to study the molecular surface structure, surface topography and mechanical properties, and quantitative adsorbed amount of biological molecules at the solid-liquid interface. The molecular-level behavior of designed peptides adsorbed on hydrophobic polystyrene and hydrophilic silica substrates has been examined as a model of protein adsorption on polymeric biomaterial surfaces. Proteins are such large and complex molecules that it is difficult to identify the features in their structure that lead to adsorption and interaction with solid surfaces. Designed peptides which possess secondary structure provide simple model systems for understanding protein adsorption. Depending on the amino acid sequence of a peptide, different secondary structures (α-helix and β-sheet) can be induced at apolar (air/liquid or air/solid) interfaces. Having a well-defined secondary structure allows experiments to be carried out under controlled conditions, where it is possible to investigate the affects of peptide amino acid sequence and chain length, concentration, buffering effects, etc. on adsorbed peptide structure. The experiments presented in this dissertation demonstrate that SFG vibrational spectroscopy can be used to directly probe the interaction of adsorbing biomolecules with a surface or interface. The use of well designed model systems aided in isolation of the SFG signal of the adsorbing species, and showed that surface functional groups of the substrate are sensitive to surface adsorbates. The complementary techniques of AFM and QCM allowed for deconvolution of the effects of surface topography and coverage from the observed SFG spectra. Initial studies of biologically relevant surfaces are also presented: SFG spectroscopy was used to study the surface composition of common soil bacteria for use in bioremediation of nuclear waste

  5. In Situ Adsorption Studies at the Solid/Liquid Interface:Characterization of Biological Surfaces and Interfaces Using SumFrequency Generation Vibrational Spectroscopy, Atomic Force Microscopy,and Quartz Crystal Microbalance

    Energy Technology Data Exchange (ETDEWEB)

    Phillips, Diana Christine [Univ. of California, Berkeley, CA (United States)

    2006-01-01

    Sum frequency generation (SFG) vibrational spectroscopy, atomic force microscopy (AFM), and quartz crystal microbalance (QCM) have been used to study the molecular surface structure, surface topography and mechanical properties, and quantitative adsorbed amount of biological molecules at the solid-liquid interface. The molecular-level behavior of designed peptides adsorbed on hydrophobic polystyrene and hydrophilic silica substrates has been examined as a model of protein adsorption on polymeric biomaterial surfaces. Proteins are such large and complex molecules that it is difficult to identify the features in their structure that lead to adsorption and interaction with solid surfaces. Designed peptides which possess secondary structure provide simple model systems for understanding protein adsorption. Depending on the amino acid sequence of a peptide, different secondary structures (α-helix and β-sheet) can be induced at apolar (air/liquid or air/solid) interfaces. Having a well-defined secondary structure allows experiments to be carried out under controlled conditions, where it is possible to investigate the affects of peptide amino acid sequence and chain length, concentration, buffering effects, etc. on adsorbed peptide structure. The experiments presented in this dissertation demonstrate that SFG vibrational spectroscopy can be used to directly probe the interaction of adsorbing biomolecules with a surface or interface. The use of well designed model systems aided in isolation of the SFG signal of the adsorbing species, and showed that surface functional groups of the substrate are sensitive to surface adsorbates. The complementary techniques of AFM and QCM allowed for deconvolution of the effects of surface topography and coverage from the observed SFG spectra. Initial studies of biologically relevant surfaces are also presented: SFG spectroscopy was used to study the surface composition of common soil bacteria for use in bioremediation of nuclear waste.

  6. Broader energy distribution of CO adsorbed at polycrystalline Pt electrode in comparison with that at Pt(111) electrode in H_2SO_4 solution confirmed by potential dependent IR/visible double resonance sum frequency generation spectroscopy

    International Nuclear Information System (INIS)

    Yang, Shuo; Noguchi, Hidenori; Uosaki, Kohei

    2017-01-01

    Highlights: • Electrochemical SFG spectroscopy is an efficient in situ probe of electronic structure at electrochemical interface. • Electrooxidation performances of CO adsorbed on polycrystalline Pt and Pt(111) electrodes were compared. • The enhanced SFG signal of CO on Pt electrodes was observed due to a vibrational-electronic double resonance effect. • The broader energy distribution of 5sa state of CO on polycrystalline Pt than on Pt(111) is proved by SFG results. - Abstract: Electrochemical cyclic voltammetry and potential dependent double resonance sum frequency generation (DR-SFG) spectroscopy were performed on CO adsorbed on polycrystalline Pt and Pt(111) electrodes in H_2SO_4 solution to examine the effect of substrate on the electronic structure of CO. The dependence of SFG intensity on potential and visible energy for atop CO band was observed on both polycrystalline and single crystalline Pt electrodes. Enhancement of the SFG intensity was determined to be a direct result of a surface electronic resonance of the visible/SF light with the electronic transition from Fermi level of Pt to the 5σ_a anti-bonding state of adsorbed CO, in agreement with previous results. Interestingly, when compared to the Pt(111) electrode, the distribution width of the intensity enhancement region on polycrystalline Pt is broader than on Pt(111). This suggests that the energy distribution of the 5σ_a state of CO on polycrystalline Pt surface is broader than that on Pt(111) due to the complex surface structure of the polycrystalline Pt electrode.

  7. Femtosecond nonlinear spectroscopy at surfaces: Second-harmonic probing of hole burning at the Si(111)7x7 surface and Fourier-transform sum-frequency vibrational spectroscopy

    International Nuclear Information System (INIS)

    McGuire, John Andrew

    2004-01-01

    The high temporal resolution and broad bandwidth of a femtosecond laser system are exploited in a pair of nonlinear optical studies of surfaces. The dephasing dynamics of resonances associated with the adatom dangling bonds of the Si(111)7 x 7 surface are explored by transient second-harmonic hole burning, a process that can be described as a fourth-order nonlinear optical process. Spectral holes produced by a 100 fs pump pulse at about 800 nm are probed by the second harmonic signal of a 100 fs pulse tunable around 800 nm. The measured spectral holes yield homogeneous dephasing times of a few tens of femtoseconds. Fits with a Lorentzian spectral hole centered at zero probe detuning show a linear dependence of the hole width on pump fluence, which suggests that charge carrier-carrier scattering dominates the dephasing dynamics at the measured excitation densities. Extrapolation of the deduced homogeneous dephasing times to zero excitation density yields an intrinsic dephasing time of ∼ 70 fs. The presence of a secondary spectral hole indicates that scattering of the surface electrons with surface optical phonons at 570 cm -1 occurs within the first 200 fs after excitation. The broad bandwidth of femtosecond IR pulses is used to perform IR-visible sum frequency vibrational spectroscopy. By implementing a Fourier-transform technique, we demonstrate the ability to obtain sub-laser-bandwidth spectral resolution. FT-SFG yields a greater signal when implemented with a stretched visible pulse than with a femtosecond visible pulse. However, when compared with multichannel spectroscopy using a femtosecond IR pulse but a narrowband visible pulse, Fourier-transform SFG is found to have an inferior signal-to-noise ratio. A mathematical analysis of the signal-to-noise ratio illustrates the constraints on the Fourier-transform approach

  8. Femtosecond nonlinear spectroscopy at surfaces: Second-harmonic probing of hole burning at the Si(111)7x7 surface and fourier-transform sum-frequency vibrational spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    McGuire, John Andrew [Univ. of California, Berkeley, CA (United States)

    2004-11-24

    The high temporal resolution and broad bandwidth of a femtosecond laser system are exploited in a pair of nonlinear optical studies of surfaces. The dephasing dynamics of resonances associated with the adatom dangling bonds of the Si(111)7 x 7 surface are explored by transient second-harmonic hole burning, a process that can be described as a fourth-order nonlinear optical process. Spectral holes produced by a 100 fs pump pulse at about 800 nm are probed by the second harmonic signal of a 100 fs pulse tunable around 800 nm. The measured spectral holes yield homogeneous dephasing times of a few tens of femtoseconds. Fits with a Lorentzian spectral hole centered at zero probe detuning show a linear dependence of the hole width on pump fluence, which suggests that charge carrier-carrier scattering dominates the dephasing dynamics at the measured excitation densities. Extrapolation of the deduced homogeneous dephasing times to zero excitation density yields an intrinsic dephasing time of {approx} 70 fs. The presence of a secondary spectral hole indicates that scattering of the surface electrons with surface optical phonons at 570 cm-1 occurs within the first 200 fs after excitation. The broad bandwidth of femtosecond IR pulses is used to perform IR-visible sum frequency vibrational spectroscopy. By implementing a Fourier-transform technique, we demonstrate the ability to obtain sub-laser-bandwidth spectral resolution. FT-SFG yields a greater signal when implemented with a stretched visible pulse than with a femtosecond visible pulse. However, when compared with multichannel spectroscopy using a femtosecond IR pulse but a narrowband visible pulse, Fourier-transform SFG is found to have an inferior signal-to-noise ratio. A mathematical analysis of the signal-to-noise ratio illustrates the constraints on the Fourier-transform approach.

  9. The Subset Sum game.

    Science.gov (United States)

    Darmann, Andreas; Nicosia, Gaia; Pferschy, Ulrich; Schauer, Joachim

    2014-03-16

    In this work we address a game theoretic variant of the Subset Sum problem, in which two decision makers (agents/players) compete for the usage of a common resource represented by a knapsack capacity. Each agent owns a set of integer weighted items and wants to maximize the total weight of its own items included in the knapsack. The solution is built as follows: Each agent, in turn, selects one of its items (not previously selected) and includes it in the knapsack if there is enough capacity. The process ends when the remaining capacity is too small for including any item left. We look at the problem from a single agent point of view and show that finding an optimal sequence of items to select is an [Formula: see text]-hard problem. Therefore we propose two natural heuristic strategies and analyze their worst-case performance when (1) the opponent is able to play optimally and (2) the opponent adopts a greedy strategy. From a centralized perspective we observe that some known results on the approximation of the classical Subset Sum can be effectively adapted to the multi-agent version of the problem.

  10. Counting Triangles to Sum Squares

    Science.gov (United States)

    DeMaio, Joe

    2012-01-01

    Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.

  11. Using Squares to Sum Squares

    Science.gov (United States)

    DeTemple, Duane

    2010-01-01

    Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2]…

  12. Premium Pricing of Liability Insurance Using Random Sum Model

    OpenAIRE

    Kartikasari, Mujiati Dwi

    2017-01-01

    Premium pricing is one of important activities in insurance. Nonlife insurance premium is calculated from expected value of historical data claims. The historical data claims are collected so that it forms a sum of independent random number which is called random sum. In premium pricing using random sum, claim frequency distribution and claim severity distribution are combined. The combination of these distributions is called compound distribution. By using liability claim insurance data, we ...

  13. Least square regularized regression in sum space.

    Science.gov (United States)

    Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu

    2013-04-01

    This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.

  14. Continuous-wave singly resonant optical parametric oscillator placed inside a ring laser

    DEFF Research Database (Denmark)

    Abitan, Haim; Buchhave, Preben

    2003-01-01

    A cw singly resonant optical parametric oscillator (SRO) was built and placed inside the cavity of a ring laser. The system consists of a diode-end-pumped Nd:YVO4 ring laser with intracavity periodically poled lithium niobate as the nonlinear gain medium of the SRO. When the laser was operated...... in a unidirectional mode, we obtained more than 520 mW of signal power in one beam. When the laser was operated in a bidirectional mode, we obtained 600 mW of signal power (300 mW in two separate beams). The power and the spectral features of the laser in the unidirectional and bidirectional modes were measured while...... the laser was coupled with the SRO. The results show that it is preferable to couple a SRO with a unidirectional ring laser....

  15. The structure of oleamide films at the aluminum/oil interface and aluminum/air interface studied by Sum Frequency Generation (SFG) vibrational spectroscopy and Reflection Absorption Infrared Spectroscopy (RAIRS).

    Science.gov (United States)

    Casford, Michael T L; Davies, Paul B

    2009-08-01

    The structure of oleamide (cis-9-octadecenamide) films on aluminum has been investigated by sum frequency generation vibrational spectroscopy (SFG) and reflection absorption infrared spectroscopy (RAIRS). Three different film deposition strategies were investigated: (i) films formed by equilibrium adsorption from oleamide solutions in oil, (ii) Langmuir-Blodgett films cast at 1 and 25 mN m(-1), (iii) thick spin-cast films. Both L-B and spin-cast films were examined in air and under oil. The adsorbate formed in the 1 mN m(-1) film in air showed little orientational order. For this film, the spectroscopic results and the ellipsometric thickness point to a relatively conformationally disordered monolayer that is oriented principally in the plane of the interface. Direct adsorption to the metal interface from oil results in SFG spectra of oleamide that are comparable to those observed for the 1 mN m(-1) L-B film in air. In contrast, SFG and RAIRS results for the 25 mN m(-1) film in air and SFG spectra of the spin-cast film in air both show strong conformational ordering and orientational alignment normal to the interface. The 25 mN m(-1) film has an ellipsometric thickness almost twice that of the 1 mN m(-1) L-B film. Taken in combination with the spectroscopic results, this is indicative of a well packed monolayer in air in which the hydrocarbon chain is in an essentially defect-free extended conformation with the methyl terminus oriented away from the surface. A similar structure is also deduced for the surface of the spin-cast film in air. Upon immersion of the 25 mN m(-1) L-B film in oil the SFG spectra show that this film rapidly adopts a relatively disordered structure similar to that seen for the 1 mN m(-1) L-B film in air. Immersion of the spin-cast film in oil results in the gradual disordering of the amide film over a period of several days until the observed spectra become essentially identical to those observed for direct adsorption of oleamide from oil.

  16. In-situ Studies of the Reactions of Bifunctional and Heterocyclic Molecules over Noble Metal Single Crystal and Nanoparticle Catalysts Studied with Kinetics and Sum-Frequency Generation Vibrational Spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Kliewer, Christopher J. [Univ. of California, Berkeley, CA (United States)

    2009-06-30

    Sum frequency generation surface vibrational spectroscopy (SFG-VS) in combination with gas chromatography (GC) was used in-situ to monitor surface bound reaction intermediates and reaction selectivities for the hydrogenation reactions of pyrrole, furan, pyridine, acrolein, crotonaldehyde, and prenal over Pt(111), Pt(100), Rh(111), and platinum nanoparticles under Torr reactant pressures and temperatures of 300K to 450K. The focus of this work is the correlation between the SFG-VS observed surface bound reaction intermediates and adsorption modes with the reaction selectivity, and how this is affected by catalyst structure and temperature. Pyrrole hydrogenation was investigated over Pt(111) and Rh(111) single crystals at Torr pressures. It was found that pyrrole adsorbs to Pt(111) perpendicularly by cleaving the N-H bond and binding through the nitrogen. However, over Rh(111) pyrrole adsorbs in a tilted geometry binding through the {pi}-aromatic orbitals. A surface-bound pyrroline reaction intermediate was detected over both surfaces with SFG-VS. It was found that the ring-cracking product butylamine is a reaction poison over both surfaces studied. Furan hydrogenation was studied over Pt(111), Pt(100), 10 nm cubic platinum nanoparticles and 1 nm platinum nanoparticles. The product distribution was observed to be highly structure sensitive and the acquired SFG-VS spectra reflected this sensitivity. Pt(100) exhibited more ring-cracking to form butanol than Pt(111), while the nanoparticles yielded higher selectivities for the partially saturated ring dihydrofuran. Pyridine hydrogenation was investigated over Pt(111) and Pt(100). The α-pyridyl surface adsorption mode was observed with SFG-VS over both surfaces. 1,4-dihydropyridine was seen as a surface intermediate over Pt(100) but not Pt(111). Upon heating the surfaces to 350K, the adsorbed pyridine changes to a flat-lying adsorption mode. No evidence was found for the pyridinium cation. The hydrogenation of the

  17. Premium Pricing of Liability Insurance Using Random Sum Model

    Directory of Open Access Journals (Sweden)

    Mujiati Dwi Kartikasari

    2017-03-01

    Full Text Available Premium pricing is one of important activities in insurance. Nonlife insurance premium is calculated from expected value of historical data claims. The historical data claims are collected so that it forms a sum of independent random number which is called random sum. In premium pricing using random sum, claim frequency distribution and claim severity distribution are combined. The combination of these distributions is called compound distribution. By using liability claim insurance data, we analyze premium pricing using random sum model based on compound distribution

  18. SUMS Counts-Related Projects

    Data.gov (United States)

    Social Security Administration — Staging Instance for all SUMs Counts related projects including: Redeterminations/Limited Issue, Continuing Disability Resolution, CDR Performance Measures, Initial...

  19. Neutrino mass sum-rule

    Science.gov (United States)

    Damanik, Asan

    2018-03-01

    Neutrino mass sum-rele is a very important research subject from theoretical side because neutrino oscillation experiment only gave us two squared-mass differences and three mixing angles. We review neutrino mass sum-rule in literature that have been reported by many authors and discuss its phenomenological implications.

  20. Credal Sum-Product Networks

    NARCIS (Netherlands)

    Maua, Denis Deratani; Cozman, Fabio Gagli; Conaty, Diarmaid; de Campos, Cassio P.

    2017-01-01

    Sum-product networks are a relatively new and increasingly popular class of (precise) probabilistic graphical models that allow for marginal inference with polynomial effort. As with other probabilistic models, sum-product networks are often learned from data and used to perform classification.

  1. Sums of squares of integers

    CERN Document Server

    Moreno, Carlos J

    2005-01-01

    Introduction Prerequisites Outline of Chapters 2 - 8 Elementary Methods Introduction Some Lemmas Two Fundamental Identities Euler's Recurrence for Sigma(n)More Identities Sums of Two Squares Sums of Four Squares Still More Identities Sums of Three Squares An Alternate Method Sums of Polygonal Numbers Exercises Bernoulli Numbers Overview Definition of the Bernoulli Numbers The Euler-MacLaurin Sum Formula The Riemann Zeta Function Signs of Bernoulli Numbers Alternate The von Staudt-Clausen Theorem Congruences of Voronoi and Kummer Irregular Primes Fractional Parts of Bernoulli Numbers Exercises Examples of Modular Forms Introduction An Example of Jacobi and Smith An Example of Ramanujan and Mordell An Example of Wilton: t (n) Modulo 23 An Example of Hamburger Exercises Hecke's Theory of Modular FormsIntroduction Modular Group ? and its Subgroup ? 0 (N) Fundamental Domains For ? and ? 0 (N) Integral Modular Forms Modular Forms of Type Mk(? 0(N);chi) and Euler-Poincare series Hecke Operators Dirichlet Series and ...

  2. Proximinality in generalized direct sums

    Directory of Open Access Journals (Sweden)

    Darapaneni Narayana

    2004-01-01

    Full Text Available We consider proximinality and transitivity of proximinality for subspaces of finite codimension in generalized direct sums of Banach spaces. We give several examples of Banach spaces where proximinality is transitive among subspaces of finite codimension.

  3. 'Sum rules' for preequilibrium reactions

    International Nuclear Information System (INIS)

    Hussein, M.S.

    1981-03-01

    Evidence that suggests a correct relationship between the optical transmission matrix, P, and the several correlation widths, gamma sub(n), found in nsmission matrix, P, and the several correlation widths, n, found in multistep compound (preequilibrium) nuclear reactions, is presented. A second sum rule is also derived within the shell model approach to nuclear reactions. Indications of the potential usefulness of the sum rules in preequilibrium studies are given. (Author) [pt

  4. Sum rules in classical scattering

    International Nuclear Information System (INIS)

    Bolle, D.; Osborn, T.A.

    1981-01-01

    This paper derives sum rules associated with the classical scattering of two particles. These sum rules are the analogs of Levinson's theorem in quantum mechanics which provides a relationship between the number of bound-state wavefunctions and the energy integral of the time delay of the scattering process. The associated classical relation is an identity involving classical time delay and an integral over the classical bound-state density. We show that equalities between the Nth-order energy moment of the classical time delay and the Nth-order energy moment of the classical bound-state density hold in both a local and a global form. Local sum rules involve the time delay defined on a finite but otherwise arbitrary coordinate space volume S and the bound-state density associated with this same region. Global sum rules are those that obtain when S is the whole coordinate space. Both the local and global sum rules are derived for potentials of arbitrary shape and for scattering in any space dimension. Finally the set of classical sum rules, together with the known quantum mechanical analogs, are shown to provide a unified method of obtaining the high-temperature expansion of the classical, respectively the quantum-mechanical, virial coefficients

  5. Small sum privacy and large sum utility in data publishing.

    Science.gov (United States)

    Fu, Ada Wai-Chee; Wang, Ke; Wong, Raymond Chi-Wing; Wang, Jia; Jiang, Minhao

    2014-08-01

    While the study of privacy preserving data publishing has drawn a lot of interest, some recent work has shown that existing mechanisms do not limit all inferences about individuals. This paper is a positive note in response to this finding. We point out that not all inference attacks should be countered, in contrast to all existing works known to us, and based on this we propose a model called SPLU. This model protects sensitive information, by which we refer to answers for aggregate queries with small sums, while queries with large sums are answered with higher accuracy. Using SPLU, we introduce a sanitization algorithm to protect data while maintaining high data utility for queries with large sums. Empirical results show that our method behaves as desired. Copyright © 2014 Elsevier Inc. All rights reserved.

  6. Sum rules for collisional processes

    International Nuclear Information System (INIS)

    Oreg, J.; Goldstein, W.H.; Bar-Shalom, A.; Klapisch, M.

    1991-01-01

    We derive level-to-configuration sum rules for dielectronic capture and for collisional excitation and ionization. These sum rules give the total transition rate from a detailed atomic level to an atomic configuration. For each process, we show that it is possible to factor out the dependence on continuum-electron wave functions. The remaining explicit level dependence of each rate is then obtained from the matrix element of an effective operator acting on the bound orbitals only. In a large class of cases, the effective operator reduces to a one-electron monopole whose matrix element is proportional to the statistical weight of the level. We show that even in these cases, nonstatistical level dependence enters through the dependence of radial integrals on continuum orbitals. For each process, explicit analytic expressions for the level-to-configuration sum rules are given for all possible cases. Together with the well-known J-file sum rule for radiative rates [E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (University Press, Cambridge, 1935)], the sum rules offer a systematic and efficient procedure for collapsing high-multiplicity configurations into ''effective'' levels for the purpose of modeling the population kinetics of ionized heavy atoms in plasma

  7. Polarizability sum rules in QED

    International Nuclear Information System (INIS)

    Llanta, E.; Tarrach, R.

    1978-01-01

    The well founded total photoproduction and the, assumed subtraction free, longitudinal photoproduction polarizability sum rules are checked in QED at the lowest non-trivial order. The first one is shown to hold, whereas the second one turns out to need a subtraction, which makes its usefulness for determining the electromagnetic polarizabilities of the nucleons quite doubtful. (Auth.)

  8. Cosmic-ray sum rules

    International Nuclear Information System (INIS)

    Frandsen, Mads T.; Masina, Isabella; Sannino, Francesco

    2011-01-01

    We introduce new sum rules allowing to determine universal properties of the unknown component of the cosmic rays; we show how they can be used to predict the positron fraction at energies not yet explored by current experiments, and to constrain specific models.

  9. Sum rules for neutrino oscillations

    International Nuclear Information System (INIS)

    Kobzarev, I.Yu.; Martemyanov, B.V.; Okun, L.B.; Schepkin, M.G.

    1981-01-01

    Sum rules for neutrino oscillations are obtained. The derivation of the general form of the s matrix for two stage process lsub(i)sup(-)→ν→lsub(k)sup(+-) (where lsub(i)sup(-)e, μ, tau, ... are initial leptons with flavor i and lsub(k)sup(+-) is final lepton) is presented. The consideration of two stage process lsub(i)sup(-)→ν→lsub(k)sup(+-) gives the possibility to take into account neutrino masses and to obtain the expressions for the oscillating cross sections. In the case of Dirac and left-handed Majorana neutrino is obtained the sum rule for the quantities 1/Vsub(K)σ(lsub(i)sup(-)→lsub(K)sup(+-)), (where Vsub(K) is a velocity of lsub(K)). In the left-handed Majorana neutrino case there is an additional antineutrino admixture leading to lsub(i)sup(-)→lsub(K)sup(+) process. Both components (neutrino and antineutrino) oscillate independently. The sums Σsub(K)1/Vsub(k)σ(lsub(i)sup(-) - lsub(K)sup(+-) then oscillate due to the presence of left-handed antineutrinos and right-handed neutrinos which do not take part in weak interactions. If right-handed currents are added sum rules analogous to considered above may be obtained. All conclusions are valid in the general case when CP is not conserved [ru

  10. Sums of Generalized Harmonic Series

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 9. Sums of Generalized Harmonic Series: For Kids from Five to Fifteen. Zurab Silagadze. General Article Volume 20 Issue 9 September 2015 pp 822-843. Fulltext. Click here to view fulltext PDF. Permanent link:

  11. Dispersion relations and sum rules for natural optical activity

    International Nuclear Information System (INIS)

    Thomaz, M.T.; Nussenzveig, H.M.

    1981-06-01

    Dispersion relations and sum rules are derived for the complex rotatory power of an arbitrary linear (nonmagnetic) isotropic medium showing natural optical activity. Both previously known dispersion relations and sum rules as well as new ones are obtained. It is shown that the Rosenfeld-Condon dispersion formula is inconsistent with the expected asymptotic behavior at high frequencies. A new dispersion formula based on quantum eletro-dynamics removes this inconsistency; however, it still requires modification in the low-frequency limit. (Author) [pt

  12. 338 Résumé

    African Journals Online (AJOL)

    ISONIC

    sumé. Cardisoma armatum, est une espèce de crabe de terre rencontrée en Afrique de l'ouest en particulier en ... optique suite au traitement histologique ont permis la mise en évidence de quelques critères d'identification de l'espèce et ...... En Côte d'Ivoire il n'est pas rare de voir durant les saisons propices. Cardisoma ...

  13. The Sum of the Parts

    DEFF Research Database (Denmark)

    Gross, Fridolin; Green, Sara

    2017-01-01

    Systems biologists often distance themselves from reductionist approaches and formulate their aim as understanding living systems “as a whole”. Yet, it is often unclear what kind of reductionism they have in mind, and in what sense their methodologies offer a more comprehensive approach. To addre......-up”. Specifically, we point out that system-level properties constrain lower-scale processes. Thus, large-scale modeling reveals how living systems at the ​same time ​ are ​more and ​less than the sum of the parts....

  14. Lattice sums then and now

    CERN Document Server

    Borwein, J M; McPhedran, R C

    2013-01-01

    The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of

  15. Alkyl chain interaction at the surface of room temperature ionic liquids: systematic variation of alkyl chain length (R = C(1)-C(4), C(8)) in both cation and anion of [RMIM][R-OSO(3)] by sum frequency generation and surface tension.

    Science.gov (United States)

    Santos, Cherry S; Baldelli, Steven

    2009-01-29

    The gas-liquid interface of halide-free 1,3-dialkylimidazolium alkyl sulfates [RMIM][R-OSO(3)] with R chain length from C(1)-C(4) and C(8) has been studied systematically using the surface-specific sum frequency generation (SFG) vibrational spectroscopy and surface tension measurements. From the SFG spectra, vibrational modes from the methyl group of both cation and anion are observed for all ionic liquid samples considered in the present study. These results suggest the presence of both ions at the gas-liquid interface, which is further supported by surface tension measurements. Surface tension data show a decreasing trend as the alkyl chain in the imidazolium cation is varied from methyl to butyl chain, with a specific anion. A similar trend is observed when the alkyl chain of the anion is modified and the cation is fixed.

  16. High quality-factor fano metasurface comprising a single resonator unit cell

    Science.gov (United States)

    Sinclair, Michael B.; Warne, Larry K.; Basilio, Lorena I.; Langston, William L.; Campione, Salvatore; Brener, Igal; Liu, Sheng

    2017-06-20

    A new monolithic resonator metasurface design achieves ultra-high Q-factors while using only one resonator per unit cell. The metasurface relies on breaking the symmetry of otherwise highly symmetric resonators to induce intra-resonator mixing of bright and dark modes (rather than inter-resonator couplings), and is scalable from the near-infrared to radio frequencies and can be easily implemented in dielectric materials. The resulting high-quality-factor Fano metasurface can be used in many sensing, spectral filtering, and modulation applications.

  17. Statistical sums of strings on hyperellyptic surfaces

    International Nuclear Information System (INIS)

    Lebedev, D.; Morozov, A.

    1987-01-01

    Contributions of hyperellyptic surfaces to statistical sums of string theories are presented. Available results on hyperellyptic surface give the apportunity to check factorization of three-loop statsum. Some remarks on the vanishing statistical sum are presented

  18. Efficient continuous-wave eye-safe region signal output from intra-cavity singly resonant optical parametric oscillator

    International Nuclear Information System (INIS)

    Li Bin; Ding Xin; Sheng Quan; Yin Su-Jia; Shi Chun-Peng; Li Xue; Wen Wu-Qi; Yao Jian-Quan; Yu Xuan-Yi

    2012-01-01

    We report an efficient continuous-wave (CW) tunable intra-cavity singly resonant optical parametric oscillator based on the multi-period periodically poled lithium niobate and using a laser diode (LD) end-pumped CW 1064 nm Nd:YVO 4 laser as the pump source. A highly efficiency CW operation is realized through a careful cavity design for mode matching and thermal stability. The signal tuning range is 1401–1500 nm obtained by varying the domain period. The maximum output power of 2.2 W at 1500 nm is obtained with a 17.1 W 808 nm LD power and the corresponding conversion efficiency is 12.9%. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  19. Momentum sum rules for fragmentation functions

    International Nuclear Information System (INIS)

    Meissner, S.; Metz, A.; Pitonyak, D.

    2010-01-01

    Momentum sum rules for fragmentation functions are considered. In particular, we give a general proof of the Schaefer-Teryaev sum rule for the transverse momentum dependent Collins function. We also argue that corresponding sum rules for related fragmentation functions do not exist. Our model-independent analysis is supplemented by calculations in a simple field-theoretical model.

  20. Highly efficient deep ultraviolet generation by sum-frequency mixing ...

    Indian Academy of Sciences (India)

    Ultraviolet laser radiation; walk-off compensation; third harmonic generation; nonlinear optical material. ... Because of its large birefringence, BBO crystal permits the generation of UV radiation near 200 nm by THG ... A, B and C are three different configurations for THG, A – Single crystal, B – two crystals (B2 and B3 in.

  1. Scattering and; Delay, Scale, and Sum Migration

    Energy Technology Data Exchange (ETDEWEB)

    Lehman, S K

    2011-07-06

    How do we see? What is the mechanism? Consider standing in an open field on a clear sunny day. In the field are a yellow dog and a blue ball. From a wave-based remote sensing point of view the sun is a source of radiation. It is a broadband electromagnetic source which, for the purposes of this introduction, only the visible spectrum is considered (approximately 390 to 750 nanometers or 400 to 769 TeraHertz). The source emits an incident field into the known background environment which, for this example, is free space. The incident field propagates until it strikes an object or target, either the yellow dog or the blue ball. The interaction of the incident field with an object results in a scattered field. The scattered field arises from a mis-match between the background refractive index, considered to be unity, and the scattering object refractive index ('yellow' for the case of the dog, and 'blue' for the ball). This is also known as an impedance mis-match. The scattering objects are referred to as secondary sources of radiation, that radiation being the scattered field which propagates until it is measured by the two receivers known as 'eyes'. The eyes focus the measured scattered field to form images which are processed by the 'wetware' of the brain for detection, identification, and localization. When time series representations of the measured scattered field are available, the image forming focusing process can be mathematically modeled by delayed, scaled, and summed migration. This concept of optical propagation, scattering, and focusing have one-to-one equivalents in the acoustic realm. This document is intended to present the basic concepts of scalar scattering and migration used in wide band wave-based remote sensing and imaging. The terms beamforming and (delayed, scaled, and summed) migration are used interchangeably but are to be distinguished from the narrow band (frequency domain) beamforming to determine

  2. Sum rules for quasifree scattering of hadrons

    Science.gov (United States)

    Peterson, R. J.

    2018-02-01

    The areas d σ /d Ω of fitted quasifree scattering peaks from bound nucleons for continuum hadron-nucleus spectra measuring d2σ /d Ω d ω are converted to sum rules akin to the Coulomb sums familiar from continuum electron scattering spectra from nuclear charge. Hadronic spectra with or without charge exchange of the beam are considered. These sums are compared to the simple expectations of a nonrelativistic Fermi gas, including a Pauli blocking factor. For scattering without charge exchange, the hadronic sums are below this expectation, as also observed with Coulomb sums. For charge exchange spectra, the sums are near or above the simple expectation, with larger uncertainties. The strong role of hadron-nucleon in-medium total cross sections is noted from use of the Glauber model.

  3. Extremum uncertainty product and sum states

    Energy Technology Data Exchange (ETDEWEB)

    Mehta, C L; Kumar, S [Indian Inst. of Tech., New Delhi. Dept. of Physics

    1978-01-01

    The extremum product states and sum states of the uncertainties in non-commuting observables have been examined. These are illustrated by two specific examples of harmonic oscillator and the angular momentum states. It shows that the coherent states of the harmonic oscillator are characterized by the minimum uncertainty sum <(..delta..q)/sup 2/>+<(..delta..p)/sup 2/>. The extremum values of the sums and products of the uncertainties of the components of the angular momentum are also obtained.

  4. QCD Sum Rules, a Modern Perspective

    CERN Document Server

    Colangelo, Pietro; Colangelo, Pietro; Khodjamirian, Alexander

    2001-01-01

    An introduction to the method of QCD sum rules is given for those who want to learn how to use this method. Furthermore, we discuss various applications of sum rules, from the determination of quark masses to the calculation of hadronic form factors and structure functions. Finally, we explain the idea of the light-cone sum rules and outline the recent development of this approach.

  5. Decompounding random sums: A nonparametric approach

    DEFF Research Database (Denmark)

    Hansen, Martin Bøgsted; Pitts, Susan M.

    Observations from sums of random variables with a random number of summands, known as random, compound or stopped sums arise within many areas of engineering and science. Quite often it is desirable to infer properties of the distribution of the terms in the random sum. In the present paper we...... review a number of applications and consider the nonlinear inverse problem of inferring the cumulative distribution function of the components in the random sum. We review the existing literature on non-parametric approaches to the problem. The models amenable to the analysis are generalized considerably...

  6. Sum rules in the response function method

    International Nuclear Information System (INIS)

    Takayanagi, Kazuo

    1990-01-01

    Sum rules in the response function method are studied in detail. A sum rule can be obtained theoretically by integrating the imaginary part of the response function over the excitation energy with a corresponding energy weight. Generally, the response function is calculated perturbatively in terms of the residual interaction, and the expansion can be described by diagrammatic methods. In this paper, we present a classification of the diagrams so as to clarify which diagram has what contribution to which sum rule. This will allow us to get insight into the contributions to the sum rules of all the processes expressed by Goldstone diagrams. (orig.)

  7. Single-resonance optical pumping spectroscopy and application in dressed-state measurement with atomic vapor cell at room temperature.

    Science.gov (United States)

    Liang, Qiangbing; Yang, Baodong; Zhang, Tiancai; Wang, Junmin

    2010-06-21

    By monitoring the transmission of probe laser beam (also served as coupling laser beam) which is locked to a cycling hyperfine transition of cesium D(2) line, while pumping laser is scanned across cesium D(1) or D(2) lines, the single-resonance optical pumping (SROP) spectra are obtained with atomic vapor cell. The SROP spectra indicate the variation of the zero-velocity atoms population of one hyperfine fold of ground state, which is optically pumped into another hyperfine fold of ground state by pumping laser. With the virtue of Doppler-free linewidth, high signal-to-noise ratio (SNR), flat background and elimination of crossover resonance lines (CRLs), the SROP spectra with atomic vapor cell around room temperature can be employed to measure dressed-state splitting of ground state, which is normally detected with laser-cooled atomic sample only, even if the dressed-state splitting is much smaller than the Doppler-broaden linewidth at room temperature.

  8. Some Finite Sums Involving Generalized Fibonacci and Lucas Numbers

    Directory of Open Access Journals (Sweden)

    E. Kılıç

    2011-01-01

    Full Text Available By considering Melham's sums (Melham, 2004, we compute various more general nonalternating sums, alternating sums, and sums that alternate according to (−12+1 involving the generalized Fibonacci and Lucas numbers.

  9. Where Does Latin "Sum" Come From?

    Science.gov (United States)

    Nyman, Martti A.

    1977-01-01

    The derivation of Latin "sum,""es(s),""est" from Indo-European "esmi,""est,""esti" involves methodological problems. It is claimed here that the development of "sum" from "esmi" is related to the origin of the variation "est-st" (less than"esti"). The study is primarily concerned with this process, but chronological suggestions are also made. (CHK)

  10. Compound sums and their applications in finance

    NARCIS (Netherlands)

    R. Helmers (Roelof); B. Tarigan

    2003-01-01

    textabstractCompound sums arise frequently in insurance (total claim size in a portfolio) and in accountancy (total error amount in audit populations). As the normal approximation for compound sums usually performs very badly, one may look for better methods for approximating the distribution of a

  11. Gauss Sum Factorization with Cold Atoms

    International Nuclear Information System (INIS)

    Gilowski, M.; Wendrich, T.; Mueller, T.; Ertmer, W.; Rasel, E. M.; Jentsch, Ch.; Schleich, W. P.

    2008-01-01

    We report the first implementation of a Gauss sum factorization algorithm by an internal state Ramsey interferometer using cold atoms. A sequence of appropriately designed light pulses interacts with an ensemble of cold rubidium atoms. The final population in the involved atomic levels determines a Gauss sum. With this technique we factor the number N=263193

  12. Shapley Value for Constant-sum Games

    NARCIS (Netherlands)

    Khmelnitskaya, A.B.

    2002-01-01

    It is proved that Young's axiomatization for the Shapley value by marginalism, efficiency, and symmetry is still valid for the Shapley value defined on the class of nonnegative constant-sum games and on the entire class of constant-sum games as well. To support an interest to study the class of

  13. Superconvergent sum rules for the normal reflectivity

    International Nuclear Information System (INIS)

    Furuya, K.; Zimerman, A.H.; Villani, A.

    1976-05-01

    Families of superconvergent relations for the normal reflectivity function are written. Sum rules connecting the difference of phases of the reflectivities of two materials are also considered. Finally superconvergence relations and sum rules for magneto-reflectivity in the Faraday and Voigt regimes are also studied

  14. Sums and products of sets and estimates of rational trigonometric sums in fields of prime order

    Energy Technology Data Exchange (ETDEWEB)

    Garaev, Mubaris Z [National Autonomous University of Mexico, Institute of Mathematics (Mexico)

    2010-11-16

    This paper is a survey of main results on the problem of sums and products of sets in fields of prime order and their applications to estimates of rational trigonometric sums. Bibliography: 85 titles.

  15. Current algebra sum rules for Reggeons

    CERN Document Server

    Carlitz, R

    1972-01-01

    The interplay between the constraints of chiral SU/sub 2/*SU/sub 2/ symmetry and Regge asymptotic behaviour is investigated. The author reviews the derivation of various current algebra sum rules in a study of the reaction pi + alpha to pi + beta . These sum rules imply that all particles may be classified in multiplets of SU/sub 2/*SU/sub 2/ and that each of these multiplets may contain linear combinations of an infinite number of physical states. Extending his study to the reaction pi + alpha to pi + pi + beta , he derives new sum rules involving commutators of the axial charge with the reggeon coupling matrices of the rho and f Regge trajectories. Some applications of these new sum rules are noted, and the general utility of these and related sum rules is discussed. (17 refs).

  16. Study of QCD medium by sum rules

    Energy Technology Data Exchange (ETDEWEB)

    Mallik, S [Saha Institute of Nuclear Physics, Calcutta (India)

    1998-08-01

    Though it has no analogue in condensed matter physics, the thermal QCD sum rules can, nevertheless, answer questions of condensed matter type about the QCD medium. The ingredients needed to write such sum rules, viz. the operator product expansion and the spectral representation at finite temperature, are reviewed in detail. The sum rules are then actually written for the case of correlation function of two vector currents. Collecting information on the thermal average of the higher dimension operators from other sources, we evaluate these sum rules for the temperature dependent {rho}-meson parameters. Possibility of extracting more information from the combined set of all sum rules from different correlation functions is also discussed. (author) 30 refs., 2 figs.

  17. Coloring sums of extensions of certain graphs

    Directory of Open Access Journals (Sweden)

    Johan Kok

    2017-12-01

    Full Text Available We recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted $\\chi(G$. Motivated by the introduction of the concept of the $b$-chromatic sum of a graph the concept of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum are introduced in this paper. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. This paper furthers the concepts of $\\chi'$-chromatic sum and $\\chi^+$-chromatic sum to extended paths and cycles. Bipartite graphs also receive some attention. The paper concludes with patterned structured graphs. These last said graphs are typically found in chemical and biological structures.

  18. Sum Rules, Classical and Quantum - A Pedagogical Approach

    Science.gov (United States)

    Karstens, William; Smith, David Y.

    2014-03-01

    Sum rules in the form of integrals over the response of a system to an external probe provide general analytical tools for both experiment and theory. For example, the celebrated f-sum rule gives a system's plasma frequency as an integral over the optical-dipole absorption spectrum regardless of the specific spectral distribution. Moreover, this rule underlies Smakula's equation for the number density of absorbers in a sample in terms of the area under their absorption bands. Commonly such rules are derived from quantum-mechanical commutation relations, but many are fundamentally classical (independent of ℏ) and so can be derived from more transparent mechanical models. We have exploited this to illustrate the fundamental role of inertia in the case of optical sum rules. Similar considerations apply to sum rules in many other branches of physics. Thus, the ``attenuation integral theorems'' of ac circuit theory reflect the ``inertial'' effect of Lenz's Law in inductors or the potential energy ``storage'' in capacitors. These considerations are closely related to the fact that the real and imaginary parts of a response function cannot be specified independently, a result that is encapsulated in the Kramers-Kronig relations. Supported in part by the US Department of Energy, Office of Nuclear Physics under contract DE-AC02-06CH11357.

  19. A New Sum Analogous to Gauss Sums and Its Fourth Power Mean

    Directory of Open Access Journals (Sweden)

    Shaofeng Ru

    2014-01-01

    Full Text Available The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it.

  20. Zero-Sum Flows in Designs

    International Nuclear Information System (INIS)

    Akbari, S.; Khosrovshahi, G.B.; Mofidi, A.

    2010-07-01

    Let D be a t-(v, k, λ) design and let N i (D), for 1 ≤ i ≤ t, be the higher incidence matrix of D, a (0, 1)-matrix of size (v/i) x b, where b is the number of blocks of D. A zero-sum flow of D is a nowhere-zero real vector in the null space of N 1 (D). A zero-sum k-flow of D is a zero-sum flow with values in {±,...,±(k-1)}. In this paper we show that every non-symmetric design admits an integral zero-sum flow, and consequently we conjecture that every non-symmetric design admits a zero-sum 5-flow. Similarly, the definition of zero-sum flow can be extended to N i (D), 1 ≤ i ≤ t. Let D = t-(v,k, (v-t/k-t)) be the complete design. We conjecture that N t (D) admits a zero-sum 3-flow and prove this conjecture for t = 2. (author)

  1. Fixed mass and scaling sum rules

    International Nuclear Information System (INIS)

    Ward, B.F.L.

    1975-01-01

    Using the correspondence principle (continuity in dynamics), the approach of Keppell-Jones-Ward-Taha to fixed mass and scaling current algebraic sum rules is extended so as to consider explicitly the contributions of all classes of intermediate states. A natural, generalized formulation of the truncation ideas of Cornwall, Corrigan, and Norton is introduced as a by-product of this extension. The formalism is illustrated in the familiar case of the spin independent Schwinger term sum rule. New sum rules are derived which relate the Regge residue functions of the respective structure functions to their fixed hadronic mass limits for q 2 → infinity. (Auth.)

  2. Sumário/Editorial

    Directory of Open Access Journals (Sweden)

    Irene Machado

    2008-11-01

    Full Text Available Nem sempre os temas candentes da investigação, numa determinada área do conhecimento, são colocados de maneira orgânica e organizada para o conjunto dos pesquisadores que sobre eles se debruçam. Quase nunca as edições cientí­cas, que se propõem a torná-los acessí­veis a seus leitores, conseguem harmonizá-los sem correr os riscos de aproximações indevidas. A única forma de não incorrer em equí­vocos perigosos é assumir a idiossincrasia do temário diversificado que constitui o campo em questão. O leitor que ora inicia seu diálogo com este sétimo número de Galáxia não deve tomar esse preâmbulo por alerta, mas sim como tentativa de a revista manter a coerência face a seu compromisso de ser porta-voz dos temas e problemas da comunicação e da cultura pelo prisma das teorias semióticas que orientam o olhar dos vários colaboradores que encontram neste espaço uma tribuna aberta ao trânsito das diferenças. Basta um relance pelo sumário desta edição para que tal armação possa ser confirmada. Os textos que constituem o Fórum, respeitadas as singularidades, tratam de temas que são caros para as abordagens da comunicação e da semiótica na cultura. Temos o privilégio de publicar o texto inédito em português de Jakob von Uexküll em que o autor apresenta sua teoria da Umwelt, caracterizando formulações da biossemiótica sobre o signi.cado do entorno ou do espaço circundante, que são valiosas para compreender a percepção, a interação, o contexto, a informação, os códigos em ambientes de semiose. De um outro lugar - aquele modulado pela lógica da linguagem - Lucrécia Ferrara perscruta o campo conceitual que entende o design não pelo viés da operatividade, mas como processo semiótico-cognitivo. A outra ponta deste que pode ser um triálogo nos é dado pela comunicologia de Vilém Flusser. Para Michael Hanke, Flusser foi um dos grandes teóricos a investigar a importância da mí­dia para os

  3. A fast summation method for oscillatory lattice sums

    Science.gov (United States)

    Denlinger, Ryan; Gimbutas, Zydrunas; Greengard, Leslie; Rokhlin, Vladimir

    2017-02-01

    We present a fast summation method for lattice sums of the type which arise when solving wave scattering problems with periodic boundary conditions. While there are a variety of effective algorithms in the literature for such calculations, the approach presented here is new and leads to a rigorous analysis of Wood's anomalies. These arise when illuminating a grating at specific combinations of the angle of incidence and the frequency of the wave, for which the lattice sums diverge. They were discovered by Wood in 1902 as singularities in the spectral response. The primary tools in our approach are the Euler-Maclaurin formula and a steepest descent argument. The resulting algorithm has super-algebraic convergence and requires only milliseconds of CPU time.

  4. A Bayesian analysis of QCD sum rules

    International Nuclear Information System (INIS)

    Gubler, Philipp; Oka, Makoto

    2011-01-01

    A new technique has recently been developed, in which the Maximum Entropy Method is used to analyze QCD sum rules. This approach has the virtue of being able to directly generate the spectral function of a given operator, without the need of making an assumption about its specific functional form. To investigate whether useful results can be extracted within this method, we have first studied the vector meson channel, where QCD sum rules are traditionally known to provide a valid description of the spectral function. Our results show a significant peak in the region of the experimentally observed ρ-meson mass, which is in agreement with earlier QCD sum rules studies and suggests that the Maximum Entropy Method is a strong tool for analyzing QCD sum rules.

  5. Sum rules for nuclear collective excitations

    International Nuclear Information System (INIS)

    Bohigas, O.

    1978-07-01

    Characterizations of the response function and of integral properties of the strength function via a moment expansion are discussed. Sum rule expressions for the moments in the RPA are derived. The validity of these sum rules for both density independent and density dependent interactions is proved. For forces of the Skyrme type, analytic expressions for the plus one and plus three energy weighted sum rules are given for isoscalar monopole and quadrupole operators. From these, a close relationship between the monopole and quadrupole energies is shown and their dependence on incompressibility and effective mass is studied. The inverse energy weighted sum rule is computed numerically for the monopole operator, and an upper bound for the width of the monopole resonance is given. Finally the reliability of moments given by the RPA with effective interactions is discussed using simple soluble models for the hamiltonian, and also by comparison with experimental data

  6. 3He electron scattering sum rules

    International Nuclear Information System (INIS)

    Kim, Y.E.; Tornow, V.

    1982-01-01

    Electron scattering sum rules for 3 He are derived with a realistic ground-state wave function. The theoretical results are compared with the experimentally measured integrated cross sections. (author)

  7. Sum formulas for reductive algebraic groups

    DEFF Research Database (Denmark)

    Andersen, Henning Haahr; Kulkarni, Upendra

    2008-01-01

    \\supset V^1 \\cdots \\supset V^r = 0$. The sum of the positive terms in this filtration satisfies a well known sum formula. If $T$ denotes a tilting module either for $G$ or $U_q$ then we can similarly filter the space $\\Hom_G(V,T)$, respectively $\\Hom_{U_q}(V,T)$ and there is a sum formula for the positive...... terms here as well. We give an easy and unified proof of these two (equivalent) sum formulas. Our approach is based on an Euler type identity which we show holds without any restrictions on $p$ or $l$. In particular, we get rid of previous such restrictions in the tilting module case....

  8. Gaussian sum rules for optical functions

    International Nuclear Information System (INIS)

    Kimel, I.

    1981-12-01

    A new (Gaussian) type of sum rules (GSR) for several optical functions, is presented. The functions considered are: dielectric permeability, refractive index, energy loss function, rotatory power and ellipticity (circular dichroism). While reducing to the usual type of sum rules in a certain limit, the GSR contain in general, a Gaussian factor that serves to improve convergence. GSR might be useful in analysing experimental data. (Author) [pt

  9. Structural relations between nested harmonic sums

    International Nuclear Information System (INIS)

    Bluemlein, J.

    2008-07-01

    We describe the structural relations between nested harmonic sums emerging in the description of physical single scale quantities up to the 3-loop level in renormalizable gauge field theories. These are weight w=6 harmonic sums. We identify universal basic functions which allow to describe a large class of physical quantities and derive their complex analysis. For the 3-loop QCD Wilson coefficients 35 basic functions are required, whereas a subset of 15 describes the 3-loop anomalous dimensions. (orig.)

  10. Structural relations between nested harmonic sums

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, J.

    2008-07-15

    We describe the structural relations between nested harmonic sums emerging in the description of physical single scale quantities up to the 3-loop level in renormalizable gauge field theories. These are weight w=6 harmonic sums. We identify universal basic functions which allow to describe a large class of physical quantities and derive their complex analysis. For the 3-loop QCD Wilson coefficients 35 basic functions are required, whereas a subset of 15 describes the 3-loop anomalous dimensions. (orig.)

  11. The Gross-Llewellyn Smith sum rule

    International Nuclear Information System (INIS)

    Scott, W.G.

    1981-01-01

    We present the most recent data on the Gross-Llewellyn Smith sum rule obtained from the combined BEBC Narrow Band Neon and GGM-PS Freon neutrino/antineutrino experiments. The data for the Gross-Llewellyn Smith sum rule as a function of q 2 suggest a smaller value for the QCD coupling constant parameter Λ than is obtained from the analysis of the higher moments. (author)

  12. Electronuclear sum rules for the lightest nuclei

    International Nuclear Information System (INIS)

    Efros, V.D.

    1992-01-01

    It is shown that the model-independent longitudinal electronuclear sum rules for nuclei with A = 3 and A = 4 have an accuracy on the order of a percent in the traditional single-nucleon approximation with free nucleons for the nuclear charge-density operator. This makes it possible to test this approximation by using these sum rules. The longitudinal sum rules for A = 3 and A = 4 are calculated using the wave functions of these nuclei corresponding to a large set of realistic NN interactions. The values of the model-independent sum rules lie in the range of values calculated by this method. Model-independent expressions are obtained for the transverse sum rules for nuclei with A = 3 and A = 4. These sum rules are calculated using a large set of realistic wave functions of these nuclei. The contribution of the convection current and the changes in the results for different versions of realistic NN forces are given. 29 refs., 4 tabs

  13. Transition sum rules in the shell model

    Science.gov (United States)

    Lu, Yi; Johnson, Calvin W.

    2018-03-01

    An important characterization of electromagnetic and weak transitions in atomic nuclei are sum rules. We focus on the non-energy-weighted sum rule (NEWSR), or total strength, and the energy-weighted sum rule (EWSR); the ratio of the EWSR to the NEWSR is the centroid or average energy of transition strengths from an nuclear initial state to all allowed final states. These sum rules can be expressed as expectation values of operators, which in the case of the EWSR is a double commutator. While most prior applications of the double commutator have been to special cases, we derive general formulas for matrix elements of both operators in a shell model framework (occupation space), given the input matrix elements for the nuclear Hamiltonian and for the transition operator. With these new formulas, we easily evaluate centroids of transition strength functions, with no need to calculate daughter states. We apply this simple tool to a number of nuclides and demonstrate the sum rules follow smooth secular behavior as a function of initial energy, as well as compare the electric dipole (E 1 ) sum rule against the famous Thomas-Reiche-Kuhn version. We also find surprising systematic behaviors for ground-state electric quadrupole (E 2 ) centroids in the s d shell.

  14. Expansion around half-integer values, binomial sums, and inverse binomial sums

    International Nuclear Information System (INIS)

    Weinzierl, Stefan

    2004-01-01

    I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a symbolic computer algebra system. The method is an extension of the technique of nested sums. The algorithms allow in addition the evaluation of binomial sums, inverse binomial sums and generalizations thereof

  15. Fast fundamental frequency estimation

    DEFF Research Database (Denmark)

    Nielsen, Jesper Kjær; Jensen, Tobias Lindstrøm; Jensen, Jesper Rindom

    2017-01-01

    Modelling signals as being periodic is common in many applications. Such periodic signals can be represented by a weighted sum of sinusoids with frequencies being an integer multiple of the fundamental frequency. Due to its widespread use, numerous methods have been proposed to estimate the funda...

  16. QCD sum rules in a Bayesian approach

    International Nuclear Information System (INIS)

    Gubler, Philipp; Oka, Makoto

    2011-01-01

    A novel technique is developed, in which the Maximum Entropy Method is used to analyze QCD sum rules. The main advantage of this approach lies in its ability of directly generating the spectral function of a given operator. This is done without the need of making an assumption about the specific functional form of the spectral function, such as in the 'pole + continuum' ansatz that is frequently used in QCD sum rule studies. Therefore, with this method it should in principle be possible to distinguish narrow pole structures form continuum states. To check whether meaningful results can be extracted within this approach, we have first investigated the vector meson channel, where QCD sum rules are traditionally known to provide a valid description of the spectral function. Our results exhibit a significant peak in the region of the experimentally observed ρ-meson mass, which agrees with earlier QCD sum rules studies and shows that the Maximum Entropy Method is a useful tool for analyzing QCD sum rules.

  17. A bayesian approach to QCD sum rules

    International Nuclear Information System (INIS)

    Gubler, Philipp; Oka, Makoto

    2010-01-01

    QCD sum rules are analyzed with the help of the Maximum Entropy Method. We develop a new technique based on the Bayesion inference theory, which allows us to directly obtain the spectral function of a given correlator from the results of the operator product expansion given in the deep euclidean 4-momentum region. The most important advantage of this approach is that one does not have to make any a priori assumptions about the functional form of the spectral function, such as the 'pole + continuum' ansatz that has been widely used in QCD sum rule studies, but only needs to specify the asymptotic values of the spectral function at high and low energies as an input. As a first test of the applicability of this method, we have analyzed the sum rules of the ρ-meson, a case where the sum rules are known to work well. Our results show a clear peak structure in the region of the experimental mass of the ρ-meson. We thus demonstrate that the Maximum Entropy Method is successfully applied and that it is an efficient tool in the analysis of QCD sum rules. (author)

  18. Vacuum structure and QCD sum rules

    International Nuclear Information System (INIS)

    Shifman, M.A.

    1992-01-01

    The method of the QCD sum rules was and still is one of the most productive tools in a wide range of problems associated with the hadronic phenomenology. Many heuristic ideas, computational devices, specific formulae which are useful to theorists working not only in hadronic physics, have been accumulated in this method. Some of the results and approaches which have originally been developed in connection with the QCD sum rules can be and are successfully applied in related fields, as supersymmetric gauge theories, nontraditional schemes of quarks and leptons, etc. The amount of literature on these and other more basic problems in hadronic physics has grown enormously in recent years. This volume presents a collection of papers which provide an overview of all basic elements of the sum rule approach and priority has been given to the works which seemed most useful from a pedagogical point of view

  19. Experimental results of the betatron sum resonance

    International Nuclear Information System (INIS)

    Wang, Y.; Ball, M.; Brabson, B.

    1993-06-01

    The experimental observations of motion near the betatron sum resonance, ν x + 2ν z = 13, are presented. A fast quadrupole (Panofsky-style ferrite picture-frame magnet with a pulsed power supplier) producing a betatron tune shift of the order of 0.03 at rise time of 1 μs was used. This quadrupole was used to produce betatron tunes which jumped past and then crossed back through a betatron sum resonance line. The beam response as function of initial betatron amplitudes were recorded turn by turn. The correlated growth of the action variables, J x and J z , was observed. The phase space plots in the resonance frame reveal the features of particle motion near the nonlinear sum resonance region

  20. Inverse-moment chiral sum rules

    International Nuclear Information System (INIS)

    Golowich, E.; Kambor, J.

    1996-01-01

    A general class of inverse-moment sum rules was previously derived by the authors in a chiral perturbation theory (ChPT) study at two-loop order of the isospin and hypercharge vector-current propagators. Here, we address the evaluation of the inverse-moment sum rules in terms of existing data and theoretical constraints. Two kinds of sum rules are seen to occur: those which contain as-yet undetermined O(q 6 ) counterterms and those free of such quantities. We use the former to obtain phenomenological evaluations of two O(q 6 ) counterterms. Light is shed on the important but difficult issue regarding contributions of higher orders in the ChPT expansion. copyright 1996 The American Physical Society

  1. Systematics of strength function sum rules

    Directory of Open Access Journals (Sweden)

    Calvin W. Johnson

    2015-11-01

    Full Text Available Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink–Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink–Axel hypothesis is unsurprising: one expects sum rules to evolve with excitation energy. Furthermore, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive or negative (attractive.

  2. Vacuum structure and QCD sum rules

    International Nuclear Information System (INIS)

    Shifman, M.A.

    1992-01-01

    The method of the QCD sum rules was and still is one of the most productive tools in a wide range of problems associated with the hadronic phenomenology. Many heuristic ideas, computational devices, specific formulae which are useful to theorists working not only in hadronic physics, have been accumulated in this method. Some of the results and approaches which have been originally developed in connection with the QCD sum rules can be and are successfully applied in related fields, such as supersymmetric gauge theories, nontraditional schemes of quarks and leptons, etc. The amount of literature on these and other more basic problems in hadronic physics has grown enormously in recent years. This collection of papers provides an overview of all basic elements of the sum rule approach. Priority has been given to those works which seemed most useful from a pedagogical point of view

  3. On the Computation of Correctly Rounded Sums

    DEFF Research Database (Denmark)

    Kornerup, Peter; Lefevre, Vincent; Louvet, Nicolas

    2012-01-01

    This paper presents a study of some basic blocks needed in the design of floating-point summation algorithms. In particular, in radix-2 floating-point arithmetic, we show that among the set of the algorithms with no comparisons performing only floating-point additions/subtractions, the 2Sum...... algorithm introduced by Knuth is minimal, both in terms of number of operations and depth of the dependency graph. We investigate the possible use of another algorithm, Dekker's Fast2Sum algorithm, in radix-10 arithmetic. We give methods for computing, in radix 10, the floating-point number nearest...... the average value of two floating-point numbers. We also prove that under reasonable conditions, an algorithm performing only round-to-nearest additions/subtractions cannot compute the round-to-nearest sum of at least three floating-point numbers. Starting from an algorithm due to Boldo and Melquiond, we also...

  4. Sum rules for the quarkonium systems

    International Nuclear Information System (INIS)

    Burnel, A.; Caprasse, H.

    1980-01-01

    In the framework of the radial Schroedinger equation we derive in a very simple way sum rules relating the potential to physical quantities such as the energy eigenvalues and the square of the lth derivative of the eigenfunctions at the origin. These sum rules contain as particular cases well-known results such as the quantum version of the Clausius theorem in classical mechanics as well as Kramers's relations for the Coulomb potential. Several illustrations are given and the possibilities of applying them to the quarkonium systems are considered

  5. Integrals of Lagrange functions and sum rules

    Energy Technology Data Exchange (ETDEWEB)

    Baye, Daniel, E-mail: dbaye@ulb.ac.be [Physique Quantique, CP 165/82, Universite Libre de Bruxelles, B 1050 Bruxelles (Belgium); Physique Nucleaire Theorique et Physique Mathematique, CP 229, Universite Libre de Bruxelles, B 1050 Bruxelles (Belgium)

    2011-09-30

    Exact values are derived for some matrix elements of Lagrange functions, i.e. orthonormal cardinal functions, constructed from orthogonal polynomials. They are obtained with exact Gauss quadratures supplemented by corrections. In the particular case of Lagrange-Laguerre and shifted Lagrange-Jacobi functions, sum rules provide exact values for matrix elements of 1/x and 1/x{sup 2} as well as for the kinetic energy. From these expressions, new sum rules involving Laguerre and shifted Jacobi zeros and weights are derived. (paper)

  6. Pentaquarks in QCD Sum Rule Approach

    International Nuclear Information System (INIS)

    Rodrigues da Silva, R.; Matheus, R.D.; Navarra, F.S.; Nielsen, M.

    2004-01-01

    We estimate the mass of recently observed pentaquak staes Ξ- (1862) and Θ+(1540) using two kinds of interpolating fields, containing two highly correlated diquarks, in the QCD sum rule approach. We obtained good agreement with the experimental value, using standard continuum threshold

  7. Sums of two-dimensional spectral triples

    DEFF Research Database (Denmark)

    Christensen, Erik; Ivan, Cristina

    2007-01-01

    construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in. The metric is recovered exactly...

  8. Summing threshold logs in a parton shower

    International Nuclear Information System (INIS)

    Nagy, Zoltan; Soper, Davison E.

    2016-05-01

    When parton distributions are falling steeply as the momentum fractions of the partons increases, there are effects that occur at each order in α s that combine to affect hard scattering cross sections and need to be summed. We show how to accomplish this in a leading approximation in the context of a parton shower Monte Carlo event generator.

  9. On Learning Ring-Sum-Expansions

    DEFF Research Database (Denmark)

    Fischer, Paul; Simon, H. -U.

    1992-01-01

    The problem of learning ring-sum-expansions from examples is studied. Ring-sum-expansions (RSE) are representations of Boolean functions over the base {#123;small infinum, (+), 1}#125;, which reflect arithmetic operations in GF(2). k-RSE is the class of ring-sum-expansions containing only monomials...... of length at most k:. term-RSE is the class of ring-sum-expansions having at most I: monomials. It is shown that k-RSE, k>or=1, is learnable while k-term-RSE, k>2, is not learnable if RPnot=NP. Without using a complexity-theoretical hypothesis, it is proven that k-RSE, k>or=1, and k-term-RSE, k>or=2 cannot...... be learned from positive (negative) examples alone. However, if the restriction that the hypothesis which is output by the learning algorithm is also a k-RSE is suspended, then k-RSE is learnable from positive (negative) examples only. Moreover, it is proved that 2-term-RSE is learnable by a conjunction...

  10. Stark resonances: asymptotics and distributional Borel sum

    International Nuclear Information System (INIS)

    Caliceti, E.; Grecchi, V.; Maioli, M.

    1993-01-01

    We prove that the Stark effect perturbation theory of a class of bound states uniquely determines the position and the width of the resonances by Distributional Borel Sum. In particular the small field asymptotics of the width is uniquely related to the large order asymptotics of the perturbation coefficients. Similar results apply to all the ''resonances'' of the anharmonic and double well oscillators. (orig.)

  11. Fibonacci Identities via the Determinant Sum Property

    Science.gov (United States)

    Spivey, Michael

    2006-01-01

    We use the sum property for determinants of matrices to give a three-stage proof of an identity involving Fibonacci numbers. Cassini's and d'Ocagne's Fibonacci identities are obtained at the ends of stages one and two, respectively. Catalan's Fibonacci identity is also a special case.

  12. Summing threshold logs in a parton shower

    Energy Technology Data Exchange (ETDEWEB)

    Nagy, Zoltán [DESY,Notkestrasse 85, 22607 Hamburg (Germany); Soper, Davison E. [Institute of Theoretical Science, University of Oregon,Eugene, OR 97403-5203 (United States)

    2016-10-05

    When parton distributions are falling steeply as the momentum fractions of the partons increases, there are effects that occur at each order in α{sub s} that combine to affect hard scattering cross sections and need to be summed. We show how to accomplish this in a leading approximation in the context of a parton shower Monte Carlo event generator.

  13. Demonstration of a Quantum Nondemolition Sum Gate

    DEFF Research Database (Denmark)

    Yoshikawa, J.; Miwa, Y.; Huck, Alexander

    2008-01-01

    The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum nondemolition (QND) interaction between the quadrature...

  14. Sum rule approach to nuclear vibrations

    International Nuclear Information System (INIS)

    Suzuki, T.

    1983-01-01

    Velocity field of various collective states is explored by using sum rules for the nuclear current. It is shown that an irrotational and incompressible flow model is applicable to giant resonance states. Structure of the hydrodynamical states is discussed according to Tomonaga's microscopic theory for collective motions. (author)

  15. Generalizations of some zero sum theorems

    Indian Academy of Sciences (India)

    Let G be an abelian group of order n, written additively. The Davenport constant D(G) is defined to be the smallest natural number t such that any sequence of length t over G has a non-empty subsequence whose sum is zero. Another combinatorial invariant E(G). (known as the EGZ constant) is the smallest natural number t ...

  16. Succinct partial sums and fenwick trees

    DEFF Research Database (Denmark)

    Bille, Philip; Christiansen, Anders Roy; Prezza, Nicola

    2017-01-01

    We consider the well-studied partial sums problem in succint space where one is to maintain an array of n k-bit integers subject to updates such that partial sums queries can be efficiently answered. We present two succint versions of the Fenwick Tree – which is known for its simplicity...... and practicality. Our results hold in the encoding model where one is allowed to reuse the space from the input data. Our main result is the first that only requires nk + o(n) bits of space while still supporting sum/update in O(logbn)/O(blogbn) time where 2 ≤ b ≤ log O(1)n. The second result shows how optimal...... time for sum/update can be achieved while only slightly increasing the space usage to nk + o(nk) bits. Beyond Fenwick Trees, the results are primarily based on bit-packing and sampling – making them very practical – and they also allow for simple optimal parallelization....

  17. QCD sum-rules analysis of vector (1-) heavy quarkonium meson-hybrid mixing

    Science.gov (United States)

    Palameta, A.; Ho, J.; Harnett, D.; Steele, T. G.

    2018-02-01

    We use QCD Laplace sum rules to study meson-hybrid mixing in vector (1-) heavy quarkonium. We compute the QCD cross-correlator between a heavy meson current and a heavy hybrid current within the operator product expansion. In addition to leading-order perturbation theory, we include four- and six-dimensional gluon condensate contributions as well as a six-dimensional quark condensate contribution. We construct several single and multiresonance models that take known hadron masses as inputs. We investigate which resonances couple to both currents and so exhibit meson-hybrid mixing. Compared to single resonance models that include only the ground state, we find that models that also include excited states lead to significantly improved agreement between QCD and experiment. In the charmonium sector, we find that meson-hybrid mixing is consistent with a two-resonance model consisting of the J /ψ and a 4.3 GeV resonance. In the bottomonium sector, we find evidence for meson-hybrid mixing in the ϒ (1 S ) , ϒ (2 S ), ϒ (3 S ), and ϒ (4 S ).

  18. Limiting law excess sum rule for polyelectrolytes.

    Science.gov (United States)

    Landy, Jonathan; Lee, YongJin; Jho, YongSeok

    2013-11-01

    We revisit the mean-field limiting law screening excess sum rule that holds for rodlike polyelectrolytes. We present an efficient derivation of this law that clarifies its region of applicability: The law holds in the limit of small polymer radius, measured relative to the Debye screening length. From the limiting law, we determine the individual ion excess values for single-salt electrolytes. We also consider the mean-field excess sum away from the limiting region, and we relate this quantity to the osmotic pressure of a dilute polyelectrolyte solution. Finally, we consider numerical simulations of many-body polymer-electrolyte solutions. We conclude that the limiting law often accurately describes the screening of physical charged polymers of interest, such as extended DNA.

  19. Geometric optimization and sums of algebraic functions

    KAUST Repository

    Vigneron, Antoine E.

    2014-01-01

    We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls.

  20. Old tensor mesons in QCD sum rules

    International Nuclear Information System (INIS)

    Aliev, T.M.; Shifman, M.A.

    1981-01-01

    Tensor mesons f, A 2 and A 3 are analyzed within the framework of QCD sum rules. The effects of gluon and quark condensate is accounted for phenomenologically. Accurate estimates of meson masses and coupling constants of the lowest-lying states are obtained. It is shown that the masses are reproduced within theoretical uncertainty of about 80 MeV. The coupling of f meson to the corresponding quark current is determined. The results are in good aqreement with experimental data [ru

  1. Disjoint sum forms in reliability theory

    Directory of Open Access Journals (Sweden)

    B. Anrig

    2014-01-01

    Full Text Available The structure function f of a binary monotone system is assumed to be known and given in a disjunctive normal form, i.e. as the logical union of products of the indicator variables of the states of its subsystems. Based on this representation of f, an improved Abraham algorithm is proposed for generating the disjoint sum form of f. This form is the base for subsequent numerical reliability calculations. The approach is generalized to multivalued systems. Examples are discussed.

  2. Singlet axial constant from QCD sum rules

    International Nuclear Information System (INIS)

    Belitskij, A.V.; Teryaev, O.V.

    1995-01-01

    We analyze the singlet axial form factor of the proton for small momentum transferred in the framework of QCD sum rules using the interpolating nucleon current which explicitly accounts for the gluonic degrees of freedom. As the result we come to the quantitative prediction of the singlet axial constant. It is shown that the bilocal power corrections play the most important role in the analysis. 21 refs., 3 figs

  3. Beautiful mesons from QCD spectral sum rules

    International Nuclear Information System (INIS)

    Narison, S.

    1991-01-01

    We discuss the beautiful meson from the point of view of the QCD spectral sum rules (QSSR). The bottom quark mass and the mixed light quark-gluon condensates are determined quite accurately. The decay constant f B is estimated and we present some arguments supporting this result. The decay constants and the masses of the other members of the beautiful meson family are predicted. (orig.)

  4. A 2-categorical state sum model

    Energy Technology Data Exchange (ETDEWEB)

    Baratin, Aristide, E-mail: abaratin@uwaterloo.ca [Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, Ontario N2L 3G1 (Canada); Freidel, Laurent, E-mail: lfreidel@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline Str. N, Waterloo, Ontario N2L 2Y5 (Canada)

    2015-01-15

    It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here, we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6j-symbols. These weights solve a hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in A. Baratin and L. Freidel [Classical Quantum Gravity 24, 2027–2060 (2007)] which was shown to lead after gauge-fixing to Korepanov’s invariant of 4-manifolds.

  5. Separation of radiation from two sources from their known radiated sum field

    DEFF Research Database (Denmark)

    Laitinen, Tommi; Pivnenko, Sergey

    2011-01-01

    This paper presents a technique for complete and exact separation of the radiated fields of two sources (at the same frequency) from the knowledge of their radiated sum field. The two sources can be arbitrary but it must be possible to enclose the sources inside their own non-intersecting minimum...

  6. Resource allocation via sum-rate maximization in the uplink of multi-cell OFDMA networks

    KAUST Repository

    Tabassum, Hina; Alouini, Mohamed-Slim; Dawy, Zaher

    2012-01-01

    In this paper, we consider maximizing the sum rate in the uplink of a multi-cell orthogonal frequency-division multiple access network. The problem has a non-convex combinatorial structure and is known to be NP-hard. Because of the inherent

  7. Remark on the computation of mode sums

    International Nuclear Information System (INIS)

    Allen, Theodore J.; Olsson, M. G.; Schmidt, Jeffrey R.

    2000-01-01

    The computation of mode sums of the types encountered in basic quantum field theoretic applications is addressed with an emphasis on their expansions into functions of distance that can be interpreted as potentials. We show how to regularize and calculate the Casimir energy for the continuum Nambu-Goto string with massive ends as well as for the discrete Isgur-Paton non-relativistic string with massive ends. As an additional example, we examine the effect on the interquark potential of a constant Kalb-Ramond field strength interacting with a QCD string. (c) 2000 The American Physical Society

  8. Sum rules in extended RPA theories

    International Nuclear Information System (INIS)

    Adachi, S.; Lipparini, E.

    1988-01-01

    Different moments m k of the excitation strength function are studied in the framework of the second RPA and of the extended RPA in which 2p2h correlations are explicitly introduced into the ground state by using first-order perturbation theory. Formal properties of the equations of motion concerning sum rules are derived and compared with those exhibited by the usual 1p1h RPA. The problem of the separation of the spurious solutions in extended RPA calculations is also discussed. (orig.)

  9. Playing a zero-sum game?

    DEFF Research Database (Denmark)

    Triantafillou, Peter

    2017-01-01

    Supreme audit institutions (SAIs) are fundamental institutions in liberal democracies as they enable control of the exercise of state power. In order to maintain this function, SAIs must enjoy a high level of independence. Moreover, SAIs are increasingly expected to be also relevant for government...... and the execution of its policies by way of performance auditing. This article examines how and why the performance auditing of the Danish SAI pursues independence and relevance. It is argued that, in general, the simultaneous pursuit of independence and relevance is highly challenging and amounts to a zero-sum or...

  10. Nuclear Symmetry Energy with QCD Sum Rule

    International Nuclear Information System (INIS)

    Jeong, K.S.; Lee, S.H.

    2013-01-01

    We calculate the nucleon self-energies in an isospin asymmetric nuclear matter using QCD sum rule. Taking the difference of these for the neutron and proton enables us to express an important part of the nuclear symmetry energy in terms of local operators. Calculating the operator product expansion up to mass dimension six operators, we find that the main contribution to the difference comes from the iso-vector scalar and vector operators, which is reminiscent to the case of relativistic mean field type theories where mesons with aforementioned quantum numbers produce the difference and provide the dominant mechanism for nuclear symmetry energy. (author)

  11. Statistical sum of bosonic string, compactified on an orbifold

    International Nuclear Information System (INIS)

    Morozov, A.; Ol'shanetskij, M.

    1986-01-01

    Expression for statistical sum of bosonic string, compactified on a singular orbifold, is presented. All the information about the orbifold is encoded the specific combination of theta-functions, which the statistical sum is expressed through

  12. Robinson's radiation damping sum rule: Reaffirmation and extension

    International Nuclear Information System (INIS)

    Mane, S.R.

    2011-01-01

    Robinson's radiation damping sum rule is one of the classic theorems of accelerator physics. Recently Orlov has claimed to find serious flaws in Robinson's proof of his sum rule. In view of the importance of the subject, I have independently examined the derivation of the Robinson radiation damping sum rule. Orlov's criticisms are without merit: I work through Robinson's derivation and demonstrate that Orlov's criticisms violate well-established mathematical theorems and are hence not valid. I also show that Robinson's derivation, and his damping sum rule, is valid in a larger domain than that treated by Robinson himself: Robinson derived his sum rule under the approximation of a small damping rate, but I show that Robinson's sum rule applies to arbitrary damping rates. I also display more concise derivations of the sum rule using matrix differential equations. I also show that Robinson's sum rule is valid in the vicinity of a parametric resonance.

  13. A new generalization of Hardy–Berndt sums

    Indian Academy of Sciences (India)

    4,11,18]. Berndt and Goldberg [4] found analytic properties of these sums and established infinite trigonometric series representations for them. The most important properties of Hardy–. Berndt sums are reciprocity theorems due to Berndt [3] ...

  14. Isospin sum rules for inclusive cross-sections

    NARCIS (Netherlands)

    Rotelli, P.; Suttorp, L.G.

    1972-01-01

    A systematic analysis of isospin sum rules is presented for the distribution functions of strong, electromagnetic weak inclusive processes. The general expression for these sum rules is given and some new examples are presented.

  15. QCD sum-rules for V-A spectral functions

    International Nuclear Information System (INIS)

    Chakrabarti, J.; Mathur, V.S.

    1980-01-01

    The Borel transformation technique of Shifman et al is used to obtain QCD sum-rules for V-A spectral functions. In contrast to the situation in the original Weinberg sum-rules and those of Bernard et al, the problem of saturating the sum-rules by low lying resonances is brought under control. Furthermore, the present sum-rules, on saturation, directly determine useful phenomenological parameters

  16. 7 CFR 42.132 - Determining cumulative sum values.

    Science.gov (United States)

    2010-01-01

    ... 7 Agriculture 2 2010-01-01 2010-01-01 false Determining cumulative sum values. 42.132 Section 42... Determining cumulative sum values. (a) The parameters for the on-line cumulative sum sampling plans for AQL's... 3 1 2.5 3 1 2 1 (b) At the beginning of the basic inspection period, the CuSum value is set equal to...

  17. Deriving the Normalized Min-Sum Algorithm from Cooperative Optimization

    OpenAIRE

    Huang, Xiaofei

    2006-01-01

    The normalized min-sum algorithm can achieve near-optimal performance at decoding LDPC codes. However, it is a critical question to understand the mathematical principle underlying the algorithm. Traditionally, people thought that the normalized min-sum algorithm is a good approximation to the sum-product algorithm, the best known algorithm for decoding LDPC codes and Turbo codes. This paper offers an alternative approach to understand the normalized min-sum algorithm. The algorithm is derive...

  18. Bulk stress auto-correlation function in simple liquids-sum rules

    International Nuclear Information System (INIS)

    Tankeshwar, K.; Bhandari, R.; Pathak, K.N.

    1990-10-01

    Expressions for the zeroth, second and fourth frequency sum rules of the bulk stress auto correlation function have been derived. The exact expressions involve static correlation function up to four particles. Because of the non availability of any information about static quadruplet correlation function we use a low order decoupling approximation for this. In this work, we have obtained, separately, the sum rules for the different mechanism of momentum transfer in the fluids. The results are expected to be useful in the study of bulk viscosity of the fluids. (author). 9 refs

  19. Gottfried sum rule and mesonic exchanges in deuteron

    International Nuclear Information System (INIS)

    Kaptari, L.P.

    1991-01-01

    Recent NMC data on the experimental value of the Gottfried Sum are discussed. It is shown that the Gottfried Sum is sensitive to the nuclear structure corrections, viz. themesonic exchanges and binding effects. A new estimation of the Gottfried Sum is given. The obtained result is close to the quark-parton prediction of 1/3. 11 refs.; 2 figs

  20. Extremal extensions for the sum of nonnegative selfadjoint relations

    NARCIS (Netherlands)

    Hassi, Seppo; Sandovici, Adrian; De Snoo, Henk; Winkler, Henrik

    2007-01-01

    The sum A + B of two nonnegative selfadjoint relations (multivalued operators) A and B is a nonnegative relation. The class of all extremal extensions of the sum A + B is characterized as products of relations via an auxiliary Hilbert space associated with A and B. The so-called form sum extension

  1. Moments of the weighted sum-of-digits function | Larcher ...

    African Journals Online (AJOL)

    The weighted sum-of-digits function is a slight generalization of the well known sum-of-digits function with the difference that here the digits are weighted by some weights. So for example in this concept also the alternated sum-of-digits function is included. In this paper we compute the first and the second moment of the ...

  2. 7 CFR 1726.205 - Multiparty lump sum quotations.

    Science.gov (United States)

    2010-01-01

    ... 7 Agriculture 11 2010-01-01 2010-01-01 false Multiparty lump sum quotations. 1726.205 Section 1726....205 Multiparty lump sum quotations. The borrower or its engineer must contact a sufficient number of... basis of written lump sum quotations, the borrower will select the supplier or contractor based on the...

  3. Sum rules for charge transition density

    Energy Technology Data Exchange (ETDEWEB)

    Gul' karov, I S [Tashkentskij Politekhnicheskij Inst. (USSR)

    1979-01-01

    The form factors of the quadrupole and octupole oscillations of the /sup 12/C nucleus are compared with the predictions of the sum rules for the charge transition density (CTD). These rules allow one to obtain various CTDs which contain the components k: r/sup lambda + 2k-2/rho(r) and r/sup lambda + 2k-1)(drho(r)/dr) (k = 0, 1, 2...) and can be applied to analyze the inelastic scattering of high energy particles by nuclei. It is shown that the CTD under consideration have different radius dependence and describe the data essentially better (though ambiguously) than the Tassy and Steinwedel-Jensen models do. Recurrence formulas are derived for the ratios of the higher-order transition matrix elements and CTD. These formulas can be used to predict the CTD behavior for highly excited nuclear states.

  4. Neutron matter within QCD sum rules

    Science.gov (United States)

    Cai, Bao-Jun; Chen, Lie-Wen

    2018-05-01

    The equation of state (EOS) of pure neutron matter (PNM) is studied in QCD sum rules (QCDSRs ). It is found that the QCDSR results on the EOS of PNM are in good agreement with predictions by current advanced microscopic many-body theories. Moreover, the higher-order density terms in quark condensates are shown to be important to describe the empirical EOS of PNM in the density region around and above nuclear saturation density although they play a minor role at subsaturation densities. The chiral condensates in PNM are also studied, and our results indicate that the higher-order density terms in quark condensates, which are introduced to reasonably describe the empirical EOS of PNM at suprasaturation densities, tend to hinder the appearance of chiral symmetry restoration in PNM at high densities.

  5. On sum rules for charge transition density

    International Nuclear Information System (INIS)

    Gul'karov, I.S.

    1979-01-01

    The form factors of the quadrupole and octupole oscillations of the 12 C nucleus are compared with the predictions of the sum rules for the charge transition density (CTD). These rules allow to obtain various CTD which contain the components k: rsup(lambda+2k-2)rho(r) and rsup(lambda+2k-1)(drho(r)/dr) (k=0, 1, 2...) and can be applied to analyze the inelastic scattering of high energy particles by nuclei. It is shown that the CTD under consideration have different radius dependence and describe the data essentially better (though ambiguously) than the Tassy and Steinwedel-Jensen models do. The recurrent formulas are derived for the ratios of the higher order transition matrix elements and CTD. These formulas can be used to predict the CTD behaviour for highly excited nuclear states

  6. Sum rules for four-spinon dynamic structure factor in XXX model

    International Nuclear Information System (INIS)

    Si Lakhal, B.; Abada, A.

    2005-01-01

    In the context of the antiferromagnetic spin 12 Heisenberg quantum spin chain (XXX model), we estimate the contribution of the exact four-spinon dynamic structure factor S 4 by calculating a number of sum rules the total dynamic structure factor S is known to satisfy exactly. These sum rules are: the static susceptibility, the integrated intensity, the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that the contribution of S 4 is between 1% and 2.5%, depending on the sum rule, whereas the contribution of the exact two-spinon dynamic structure factor S 2 is between 70% and 75%. The calculations are numerical and Monte Carlo based. Good statistics are obtained

  7. Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52

    Directory of Open Access Journals (Sweden)

    Ntienjem Ebénézer

    2017-04-01

    \\end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms are used to achieve these evaluations. Since the modular space of level 22 is contained in that of level 44, we almost completely use the basis elements of the modular space of level 44 to carry out the evaluation of the convolution sums for αβ = 22. We then use these convolution sums to determine formulae for the number of representations of a positive integer by the octonary quadratic forms a(x12+x22+x32+x42+b(x52+x62+x72+x82, $a\\,(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+b\\,(x_{5}^{2}+x_{6}^{2}+x_{7}^{2}+x_{8}^{2},$ where (a, b = (1, 11, (1, 13.

  8. Methods for the analysis of complex fluorescence decays: sum of Becquerel functions versus sum of exponentials

    International Nuclear Information System (INIS)

    Menezes, Filipe; Fedorov, Alexander; Baleizão, Carlos; Berberan-Santos, Mário N; Valeur, Bernard

    2013-01-01

    Ensemble fluorescence decays are usually analyzed with a sum of exponentials. However, broad continuous distributions of lifetimes, either unimodal or multimodal, occur in many situations. A simple and flexible fitting function for these cases that encompasses the exponential is the Becquerel function. In this work, the applicability of the Becquerel function for the analysis of complex decays of several kinds is tested. For this purpose, decays of mixtures of four different fluorescence standards (binary, ternary and quaternary mixtures) are measured and analyzed. For binary and ternary mixtures, the expected sum of narrow distributions is well recovered from the Becquerel functions analysis, if the correct number of components is used. For ternary mixtures, however, satisfactory fits are also obtained with a number of Becquerel functions smaller than the true number of fluorophores in the mixture, at the expense of broadening the lifetime distributions of the fictitious components. The quaternary mixture studied is well fitted with both a sum of three exponentials and a sum of two Becquerel functions, showing the inevitable loss of information when the number of components is large. Decays of a fluorophore in a heterogeneous environment, known to be represented by unimodal and broad continuous distributions (as previously obtained by the maximum entropy method), are also measured and analyzed. It is concluded that these distributions can be recovered by the Becquerel function method with an accuracy similar to that of the much more complex maximum entropy method. It is also shown that the polar (or phasor) plot is not always helpful for ascertaining the degree (and kind) of complexity of a fluorescence decay. (paper)

  9. The Asymptotic Joint Distribution of Self-Normalized Censored Sums and Sums of Squares

    OpenAIRE

    Hahn, Marjorie G.; Kuelbs, Jim; Weiner, Daniel C.

    1990-01-01

    Empirical versions of appropriate centering and scale constants for random variables which can fail to have second or even first moments are obtainable in various ways via suitable modifications of the summands in the partial sum. This paper discusses a particular modification, called censoring (which is a kind of winsorization), where the (random) number of summands altered tends to infinity but the proportion altered tends to zero as the number of summands increases. Some analytic advantage...

  10. Sum rules and constraints on passive systems

    International Nuclear Information System (INIS)

    Bernland, A; Gustafsson, M; Luger, A

    2011-01-01

    A passive system is one that cannot produce energy, a property that naturally poses constraints on the system. A system in convolution form is fully described by its transfer function, and the class of Herglotz functions, holomorphic functions mapping the open upper half-plane to the closed upper half-plane, is closely related to the transfer functions of passive systems. Following a well-known representation theorem, Herglotz functions can be represented by means of positive measures on the real line. This fact is exploited in this paper in order to rigorously prove a set of integral identities for Herglotz functions that relate weighted integrals of the function to its asymptotic expansions at the origin and infinity. The integral identities are the core of a general approach introduced here to derive sum rules and physical limitations on various passive physical systems. Although similar approaches have previously been applied to a wide range of specific applications, this paper is the first to deliver a general procedure together with the necessary proofs. This procedure is described thoroughly and exemplified with examples from electromagnetic theory.

  11. Sum-rule analysis of long-wavelength excitations in electron liquids

    International Nuclear Information System (INIS)

    Ichimaru, Setsuo; Totsuji, Hiroo; Tange, Toshio; Pines, D.

    1975-01-01

    The properties of the plasma oscillations, the single-particle excitations and the collisional excitations in the classical one-component plasma are investigated in the long-wave-length domain with the aid of moment sum rules. The frequency moments of the dynamic form factor are calculated up to that term which involves the ternary correlation function. The dispersion in the plasma-wave frequency and the strengths of the single-particle and collisional excitations are computed over the thermodynamically stable domain of the plasma parameter, epsilon<=10. It is emphasized that inclusion of the collisional excitations plays a vital part in satisfying various moment-sum rules and in securing agreement with known boundary conditions such as the Vlasov description and molecular-dynamics computations. (auth.)

  12. Light cone sum rules in nonabelian gauge field theory

    Energy Technology Data Exchange (ETDEWEB)

    Mallik, S [Bern Univ. (Switzerland). Inst. fuer Theoretische Physik

    1981-03-24

    The author examines, in the context of nonabelian gauge field theory, the derivation of the light cone sum rules which were obtained earlier on the assumption of dominance of canonical singularity in the current commutator on the light cone. The retarded scaling functions appearing in the sum rules are numbers known in terms of the charges of the quarks and the number of quarks and gluons in the theory. Possible applications of the sum rules are suggested.

  13. On the Laplace transform of the Weinberg type sum rules

    International Nuclear Information System (INIS)

    Narison, S.

    1981-09-01

    We consider the Laplace transform of various sum rules of the Weinberg type including the leading non-perturbative effects. We show from the third type Weinberg sum rules that 7.5 to 8.9 1 coupling to the W boson, while the second sum rule gives an upper bound on the A 1 mass (Msub(A 1 ) < or approx. 1.25 GeV). (author)

  14. On poisson-stopped-sums that are mixed poisson

    OpenAIRE

    Valero Baya, Jordi; Pérez Casany, Marta; Ginebra Molins, Josep

    2013-01-01

    Maceda (1948) characterized the mixed Poisson distributions that are Poisson-stopped-sum distributions based on the mixing distribution. In an alternative characterization of the same set of distributions here the Poisson-stopped-sum distributions that are mixed Poisson distributions is proved to be the set of Poisson-stopped-sums of either a mixture of zero-truncated Poisson distributions or a zero-modification of it. Peer Reviewed

  15. Inclusive sum rules and spectra of neutrons at the ISR

    International Nuclear Information System (INIS)

    Grigoryan, A.A.

    1975-01-01

    Neutron spectra in pp collisions at ISR energies are studied in the framework of sum rules for inclusive processes. The contributions of protons, π- and E- mesons to the energy sum rule are calculated at √5 = 53 GeV. It is shown by means of this sum rule that the spectra of neutrons at the ISR are in contradiction with the spectra of other particles also measured at the ISR

  16. Singular f-sum rule for superfluid 4He

    International Nuclear Information System (INIS)

    Wong, V.K.

    1979-01-01

    The validity and applicability to inelastic neutron scattering of a singular f-sum rule for superfluid helium, proposed by Griffin to explain the rhosub(s) dependence in S(k, ω) as observed by Woods and Svensson, are examined in the light of similar sum rules rigorously derived for anharmonic crystals and Bose liquids. It is concluded that the singular f-sum rules are only of microscopic interest. (Auth,)

  17. Compound Poisson Approximations for Sums of Random Variables

    OpenAIRE

    Serfozo, Richard F.

    1986-01-01

    We show that a sum of dependent random variables is approximately compound Poisson when the variables are rarely nonzero and, given they are nonzero, their conditional distributions are nearly identical. We give several upper bounds on the total-variation distance between the distribution of such a sum and a compound Poisson distribution. Included is an example for Markovian occurrences of a rare event. Our bounds are consistent with those that are known for Poisson approximations for sums of...

  18. Coulomb sum rules in the relativistic Fermi gas model

    International Nuclear Information System (INIS)

    Do Dang, G.; L'Huillier, M.; Nguyen Giai, Van.

    1986-11-01

    Coulomb sum rules are studied in the framework of the Fermi gas model. A distinction is made between mathematical and observable sum rules. Differences between non-relativistic and relativistic Fermi gas predictions are stressed. A method to deduce a Coulomb response function from the longitudinal response is proposed and tested numerically. This method is applied to the 40 Ca data to obtain the experimental Coulomb sum rule as a function of momentum transfer

  19. QCD sum rules and applications to nuclear physics

    International Nuclear Information System (INIS)

    Cohen, T.D.; Xuemin, J.

    1994-12-01

    Applications of QCD sum-rule methods to the physics of nuclei are reviewed, with an emphasis on calculations of baryon self-energies in infinite nuclear matter. The sum-rule approach relates spectral properties of hadrons propagating in the finite-density medium, such as optical potentials for quasinucleons, to matrix elements of QCD composite operators (condensates). The vacuum formalism for QCD sum rules is generalized to finite density, and the strategy and implementation of the approach is discussed. Predictions for baryon self-energies are compared to those suggested by relativistic nuclear physics phenomenology. Sum rules for vector mesons in dense nuclear matter are also considered. (author)

  20. Adler Function, DIS sum rules and Crewther Relations

    International Nuclear Information System (INIS)

    Baikov, P.A.; Chetyrkin, K.G.; Kuehn, J.H.

    2010-01-01

    The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(α s 4 ). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(α s 4 ) contribution to the singlet part of the Adler function.

  1. An electrophysiological signature of summed similarity in visual working memory.

    Science.gov (United States)

    van Vugt, Marieke K; Sekuler, Robert; Wilson, Hugh R; Kahana, Michael J

    2013-05-01

    Summed-similarity models of short-term item recognition posit that participants base their judgments of an item's prior occurrence on that item's summed similarity to the ensemble of items on the remembered list. We examined the neural predictions of these models in 3 short-term recognition memory experiments using electrocorticographic/depth electrode recordings and scalp electroencephalography. On each experimental trial, participants judged whether a test face had been among a small set of recently studied faces. Consistent with summed-similarity theory, participants' tendency to endorse a test item increased as a function of its summed similarity to the items on the just-studied list. To characterize this behavioral effect of summed similarity, we successfully fit a summed-similarity model to individual participant data from each experiment. Using the parameters determined from fitting the summed-similarity model to the behavioral data, we examined the relation between summed similarity and brain activity. We found that 4-9 Hz theta activity in the medial temporal lobe and 2-4 Hz delta activity recorded from frontal and parietal cortices increased with summed similarity. These findings demonstrate direct neural correlates of the similarity computations that form the foundation of several major cognitive theories of human recognition memory. PsycINFO Database Record (c) 2013 APA, all rights reserved.

  2. Model dependence of energy-weighted sum rules

    International Nuclear Information System (INIS)

    Kirson, M.W.

    1977-01-01

    The contribution of the nucleon-nucleon interaction to energy-weighted sum rules for electromagnetic multipole transitions is investigated. It is found that only isoscalar electric transitions might have model-independent energy-weighted sum rules. For these transitions, explicit momentum and angular momentum dependence of the nuclear force give rise to corrections to the sum rule which are found to be negligibly small, thus confirming the model independence of these specific sum rules. These conclusions are unaffected by correlation effects. (author)

  3. Direct and reverse inclusions for strongly multiple summing operators

    Indian Academy of Sciences (India)

    and strongly multiple summing operators under the assumption that the range has finite cotype. Keywords. .... multiple (q, p)-summing, if there exists a constant C ≥ 0 such that for every choice of systems (x j i j )1≤i j ≤m j ...... Ideals and their Applications in Theoretical Physics (1983) (Leipzig: Teubner-Texte) pp. 185–199.

  4. 29 CFR 4044.75 - Other lump sum benefits.

    Science.gov (United States)

    2010-07-01

    ... sum benefits. The value of a lump sum benefit which is not covered under § 4044.73 or § 4044.74 is equal to— (a) The value under the qualifying bid, if an insurer provides the benefit; or (b) The present value of the benefit as of the date of distribution, determined using reasonable actuarial assumptions...

  5. Lattice QCD evaluation of baryon magnetic moment sum rules

    International Nuclear Information System (INIS)

    Leinweber, D.B.

    1991-05-01

    Magnetic moment combinations and sum rules are evaluated using recent results for the magnetic moments of octet baryons determined in a numerical simulation of quenched QCD. The model-independent and parameter-free results of the lattice calculations remove some of the confusion and contradiction surrounding past magnetic moment sum rule analyses. The lattice results reveal the underlying quark dynamics investigated by magnetic moment sum rules and indicate the origin of magnetic moment quenching for the non-strange quarks in Σ. In contrast to previous sum rule analyses, the magnetic moments of nonstrange quarks in Ξ are seen to be enhanced in the lattice results. In most cases, the spin-dependent dynamics and center-of-mass effects giving rise to baryon dependence of the quark moments are seen to be sufficient to violate the sum rules in agreement with experimental measurements. In turn, the sum rules are used to further examine the results of the lattice simulation. The Sachs sum rule suggests that quark loop contributions not included in present lattice calculations may play a key role in removing the discrepancies between lattice and experimental ratios of magnetic moments. This is supported by other sum rules sensitive to quark loop contributions. A measure of the isospin symmetry breaking in the effective quark moments due to quark loop contributions is in agreement with model expectations. (Author) 16 refs., 2 figs., 2 tabs

  6. Luttinger and Hubbard sum rules: are they compatible?

    International Nuclear Information System (INIS)

    Matho, K.

    1992-01-01

    A so-called Hubbard sum rule determines the weight of a satellite in fermionic single-particle excitations with strong local repulsion (U→∞). Together with the Luttinger sum rule, this imposes two different energy scales on the remaining finite excitations. In the Hubbard chain, this has been identified microscopically as being due to a separation of spin and charge. (orig.)

  7. Chain hexagonal cacti with the extremal eccentric distance sum.

    Science.gov (United States)

    Qu, Hui; Yu, Guihai

    2014-01-01

    Eccentric distance sum (EDS), which can predict biological and physical properties, is a topological index based on the eccentricity of a graph. In this paper we characterize the chain hexagonal cactus with the minimal and the maximal eccentric distance sum among all chain hexagonal cacti of length n, respectively. Moreover, we present exact formulas for EDS of two types of hexagonal cacti.

  8. A sum rule description of giant resonances at finite temperature

    International Nuclear Information System (INIS)

    Meyer, J.; Quentin, P.; Brack, M.

    1983-01-01

    A generalization of the sum rule approach to collective motion at finite temperature is presented. The m 1 and msub(-1) sum rules for the isovector dipole and the isoscalar monopole electric modes have been evaluated with the modified SkM force for the 208 Pb nucleus. The variation of the resulting giant resonance energies with temperature is discussed. (orig.)

  9. Finding Sums for an Infinite Class of Alternating Series

    Science.gov (United States)

    Chen, Zhibo; Wei, Sheng; Xiao, Xuerong

    2012-01-01

    Calculus II students know that many alternating series are convergent by the Alternating Series Test. However, they know few alternating series (except geometric series and some trivial ones) for which they can find the sum. In this article, we present a method that enables the students to find sums for infinitely many alternating series in the…

  10. Partial sums of arithmetical functions with absolutely convergent ...

    Indian Academy of Sciences (India)

    Keywords. Ramanujan expansions; average order; error terms; sum-of-divisors functions; Jordan's totient functions. 2010 Mathematics Subject Classification. 11N37, 11A25, 11K65. 1. Introduction. The theory of Ramanujan sums and Ramanujan expansions has emerged from the seminal article [10] of Ramanujan. In 1918 ...

  11. 28 CFR 523.16 - Lump sum awards.

    Science.gov (United States)

    2010-07-01

    ... satisfactory performance of an unusually hazardous assignment; (c) An act which protects the lives of staff or... TRANSFER COMPUTATION OF SENTENCE Extra Good Time § 523.16 Lump sum awards. Any staff member may recommend... award is calculated. No seniority is accrued for such awards. Staff may recommend lump sum awards of...

  12. Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms

    International Nuclear Information System (INIS)

    Ablinger, Jakob; Schneider, Carsten

    2013-01-01

    In recent three-loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short S-sums) arise. They are characterized by rational (or real) numerator weights also different from ±1. In this article we explore the algorithmic and analytic properties of these sums systematically. We work out the Mellin and inverse Mellin transform which connects the sums under consideration with the associated Poincare iterated integrals, also called generalized harmonic polylogarithms. In this regard, we obtain explicit analytic continuations by means of asymptotic expansions of the S-sums which started to occur frequently in current QCD calculations. In addition, we derive algebraic and structural relations, like differentiation w.r.t. the external summation index and different multi-argument relations, for the compactification of S-sum expressions. Finally, we calculate algebraic relations for infinite S-sums, or equivalently for generalized harmonic polylogarithms evaluated at special values. The corresponding algorithms and relations are encoded in the computer algebra package HarmonicSums.

  13. On contribution of instantons to nucleon sum rules

    International Nuclear Information System (INIS)

    Dorokhov, A.E.; Kochelev, N.I.

    1989-01-01

    The contribution of instantons to nucleon QCD sum rules is obtained. It is shown that this contribution does provide stabilization of the sum rules and leads to formation of a nucleon as a bound state of quarks in the instanton field. 17 refs.; 3 figs

  14. Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2013-01-15

    In recent three-loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short S-sums) arise. They are characterized by rational (or real) numerator weights also different from {+-}1. In this article we explore the algorithmic and analytic properties of these sums systematically. We work out the Mellin and inverse Mellin transform which connects the sums under consideration with the associated Poincare iterated integrals, also called generalized harmonic polylogarithms. In this regard, we obtain explicit analytic continuations by means of asymptotic expansions of the S-sums which started to occur frequently in current QCD calculations. In addition, we derive algebraic and structural relations, like differentiation w.r.t. the external summation index and different multi-argument relations, for the compactification of S-sum expressions. Finally, we calculate algebraic relations for infinite S-sums, or equivalently for generalized harmonic polylogarithms evaluated at special values. The corresponding algorithms and relations are encoded in the computer algebra package HarmonicSums.

  15. Sum formula for SL2 over imaginary quadratic number fields

    NARCIS (Netherlands)

    Lokvenec-Guleska, H.

    2004-01-01

    The subject of this thesis is generalization of the classical sum formula of Bruggeman and Kuznetsov to the upper half-space H3. The derivation of the preliminary sum formula involves computation of the inner product of two specially chosen Poincar´e series in two different ways: the spectral

  16. An electrophysiological signature of summed similarity in visual working memory

    NARCIS (Netherlands)

    Van Vugt, Marieke K.; Sekuler, Robert; Wilson, Hugh R.; Kahana, Michael J.

    Summed-similarity models of short-term item recognition posit that participants base their judgments of an item's prior occurrence on that item's summed similarity to the ensemble of items on the remembered list. We examined the neural predictions of these models in 3 short-term recognition memory

  17. Faraday effect revisited: sum rules and convergence issues

    DEFF Research Database (Denmark)

    Cornean, Horia; Nenciu, Gheorghe

    2010-01-01

    This is the third paper of a series revisiting the Faraday effect. The question of the absolute convergence of the sums over the band indices entering the Verdet constant is considered. In general, sum rules and traces per unit volume play an important role in solid-state physics, and they give...

  18. Semiempirical search for oxide superconductors based on bond valence sums

    International Nuclear Information System (INIS)

    Tanaka, S.; Fukushima, N.; Niu, H.; Ando, K.

    1992-01-01

    Relationships between crystal structures and electronic states of layered transition-metal oxides are analyzed in the light of bond valence sums. Correlations between the superconducting transition temperature T c and the bond-valence-sum parameters are investigated for the high-T c cuprate compounds. Possibility of making nonsuperconducting oxides superconducting is discussed. (orig.)

  19. Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Schneider, Carsten [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040, Linz (Austria); Blümlein, Johannes [Deutsches Elektronen–Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany)

    2013-08-15

    In recent three-loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short S-sums) arise. They are characterized by rational (or real) numerator weights also different from ±1. In this article we explore the algorithmic and analytic properties of these sums systematically. We work out the Mellin and inverse Mellin transform which connects the sums under consideration with the associated Poincaré iterated integrals, also called generalized harmonic polylogarithms. In this regard, we obtain explicit analytic continuations by means of asymptotic expansions of the S-sums which started to occur frequently in current QCD calculations. In addition, we derive algebraic and structural relations, like differentiation with respect to the external summation index and different multi-argument relations, for the compactification of S-sum expressions. Finally, we calculate algebraic relations for infinite S-sums, or equivalently for generalized harmonic polylogarithms evaluated at special values. The corresponding algorithms and relations are encoded in the computer algebra package HarmonicSums.

  20. Volume sums of polar Blaschke–Minkowski homomorphisms

    Indian Academy of Sciences (India)

    In this article, we establish Minkowski and Aleksandrov–Fenchel type inequalities for the volume sum of polars of Blaschke–Minkowski homomorphisms. Keywords. Blaschke–Minkowski homomorphism; volume differences; volume sum; projection body operator. 2010 Mathematics Subject Classification. 52A40, 52A30. 1.

  1. Harmonic sums, polylogarithms, special numbers, and their generalizations

    International Nuclear Information System (INIS)

    Ablinger, Jakob

    2013-04-01

    In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops. These quantities are elements of stuffle and shuffle algebras implying algebraic relations being widely independent of the special quantities considered. They are supplemented by structural relations. The generalizations are given in terms of generalized harmonic sums, (generalized) cyclotomic sums, and sums containing in addition binomial and inverse-binomial weights. To all these quantities iterated integrals and special numbers are associated. We also discuss the analytic continuation of nested sums of different kind to complex values of the external summation bound N.

  2. Evaluation of the multi-sums for large scale problems

    International Nuclear Information System (INIS)

    Bluemlein, J.; Hasselhuhn, A.; Schneider, C.

    2012-02-01

    A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t. the dimension parameter ε can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we present a general summation method based on difference fields that simplifies these multi--sums by transforming them from inside to outside to representations in terms of indefinite nested sums and products. In particular, we present techniques that assist in the task to simplify huge expressions of such multi-sums in a completely automatic fashion. The ideas are illustrated on new calculations coming from 3-loop topologies of gluonic massive operator matrix elements containing two fermion lines, which contribute to the transition matrix elements in the variable flavor scheme. (orig.)

  3. Harmonic sums, polylogarithms, special numbers, and their generalizations

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2013-04-15

    In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops. These quantities are elements of stuffle and shuffle algebras implying algebraic relations being widely independent of the special quantities considered. They are supplemented by structural relations. The generalizations are given in terms of generalized harmonic sums, (generalized) cyclotomic sums, and sums containing in addition binomial and inverse-binomial weights. To all these quantities iterated integrals and special numbers are associated. We also discuss the analytic continuation of nested sums of different kind to complex values of the external summation bound N.

  4. Evaluation of the multi-sums for large scale problems

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, J.; Hasselhuhn, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation

    2012-02-15

    A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t. the dimension parameter {epsilon} can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we present a general summation method based on difference fields that simplifies these multi--sums by transforming them from inside to outside to representations in terms of indefinite nested sums and products. In particular, we present techniques that assist in the task to simplify huge expressions of such multi-sums in a completely automatic fashion. The ideas are illustrated on new calculations coming from 3-loop topologies of gluonic massive operator matrix elements containing two fermion lines, which contribute to the transition matrix elements in the variable flavor scheme. (orig.)

  5. CAMAC programmable-control frequency synthesizer

    International Nuclear Information System (INIS)

    Yumaguzin, T.Kh.; Vyazovkin, D.E.; Nazirov, Eh.P.; Tuktarov, R.F.

    1989-01-01

    Synthesizer allows to set frequency with 0.015% accuracy and to scan it with variable step. Frequency controlled divider with further summing-up of divided frequency with fundamental one is used in synthesizer, and it has allowed to use digit of the input code and to obtain 3-4 MHz frequency range. Variation of operation flowsheet in the other frequency range is possible. K-155 and K-531 series microcircuits were used during development

  6. The End of Academia?: From "Cogito Ergo Sum" to "Consumo Ergo Sum" Germany and Malaysia in Comparison

    Science.gov (United States)

    Lim, Kim-Hui,; Har, Wai-Mun

    2008-01-01

    The lack of academic and thinking culture is getting more worried and becomes a major challenge to our academia society this 21st century. Few directions that move academia from "cogito ergo sum" to "consumo ergo sum" are actually leading us to "the end of academia". Those directions are: (1) the death of dialectic;…

  7. Zero-sum bias: perceived competition despite unlimited resources

    Directory of Open Access Journals (Sweden)

    Daniel V Meegan

    2010-11-01

    Full Text Available Zero-sum bias describes intuitively judging a situation to be zero-sum (i.e., resources gained by one party are matched by corresponding losses to another party when it is actually non-zero-sum. The experimental participants were students at a university where students’ grades are determined by how the quality of their work compares to a predetermined standard of quality rather than to the quality of the work produced by other students. This creates a non-zero-sum situation in which high grades are an unlimited resource. In three experiments, participants were shown the grade distribution after a majority of the students in a course had completed an assigned presentation, and asked to predict the grade of the next presenter. When many high grades had already been given, there was a corresponding increase in low grade predictions. This suggests a zero-sum bias, in which people perceive a competition for a limited resource despite unlimited resource availability. Interestingly, when many low grades had already been given, there was not a corresponding increase in high grade predictions. This suggests that a zero-sum heuristic is only applied in response to the allocation of desirable resources. A plausible explanation for the findings is that a zero-sum heuristic evolved as a cognitive adaptation to enable successful intra-group competition for limited resources. Implications for understanding inter-group interaction are also discussed.

  8. Zero-sum bias: perceived competition despite unlimited resources.

    Science.gov (United States)

    Meegan, Daniel V

    2010-01-01

    Zero-sum bias describes intuitively judging a situation to be zero-sum (i.e., resources gained by one party are matched by corresponding losses to another party) when it is actually non-zero-sum. The experimental participants were students at a university where students' grades are determined by how the quality of their work compares to a predetermined standard of quality rather than to the quality of the work produced by other students. This creates a non-zero-sum situation in which high grades are an unlimited resource. In three experiments, participants were shown the grade distribution after a majority of the students in a course had completed an assigned presentation, and asked to predict the grade of the next presenter. When many high grades had already been given, there was a corresponding increase in low grade predictions. This suggests a zero-sum bias, in which people perceive a competition for a limited resource despite unlimited resource availability. Interestingly, when many low grades had already been given, there was not a corresponding increase in high grade predictions. This suggests that a zero-sum heuristic is only applied in response to the allocation of desirable resources. A plausible explanation for the findings is that a zero-sum heuristic evolved as a cognitive adaptation to enable successful intra-group competition for limited resources. Implications for understanding inter-group interaction are also discussed.

  9. Harmonic sums and polylogarithms generated by cyclotomic polynomials

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2011-05-15

    The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin transforms of Poincare-iterated integrals including denominators of higher cyclotomic polynomials. We derive the cyclotomic harmonic polylogarithms and harmonic sums and study their algebraic and structural relations. The analytic continuation of cyclotomic harmonic sums to complex values of N is performed using analytic representations. We also consider special values of the cyclotomic harmonic polylogarithms at argument x=1, resp., for the cyclotomic harmonic sums at N{yields}{infinity}, which are related to colored multiple zeta values, deriving various of their relations, based on the stuffle and shuffle algebras and three multiple argument relations. We also consider infinite generalized nested harmonic sums at roots of unity which are related to the infinite cyclotomic harmonic sums. Basis representations are derived for weight w=1,2 sums up to cyclotomy l=20. (orig.)

  10. Measurement sum theory and application - Application to low level measurements

    International Nuclear Information System (INIS)

    Puydarrieux, S.; Bruel, V.; Rivier, C.; Crozet, M.; Vivier, A.; Manificat, G.; Thaurel, B.; Mokili, M.; Philippot, B.; Bohaud, E.

    2015-09-01

    In laboratories, most of the Total Sum methods implemented today use substitution or censure methods for nonsignificant or negative values, and thus create biases which can sometimes be quite large. They are usually positive, and generate, for example, becquerel (Bq) counting or 'administrative' quantities of materials (= 'virtual'), thus artificially falsifying the records kept by the laboratories under regulatory requirements (environment release records, waste records, etc.). This document suggests a methodology which will enable the user to avoid such biases. It is based on the following two fundamental rules: - The Total Sum of measurement values must be established based on all the individual measurement values, even those considered non-significant including the negative values. Any modification of these values, under the pretext that they are not significant, will inevitably lead to biases in the accumulated result and falsify the evaluation of its uncertainty. - In Total Sum operations, the decision thresholds are arrived at in a similar way to the approach used for uncertainties. The document deals with four essential aspects of the notion of 'measurement Total Sums': - The expression of results and associated uncertainties close to Decision Thresholds, and Detection or Quantification Limits, - The Total Sum of these measurements: sum or mean, - The calculation of the uncertainties associated with the Total Sums, - Result presentation (particularly when preparing balance sheets or reports, etc.) Several case studies arising from different situations are used to illustrate the methodology: environmental monitoring reports, release reports, and chemical impurity Total Sums for the qualification of a finished product. The special case of material balances, in which the measurements are usually all significant and correlated (the covariance term cannot then be ignored) will be the subject of a future second document. This

  11. Light cone sum rules for single-pion electroproduction

    International Nuclear Information System (INIS)

    Mallik, S.

    1978-01-01

    Light cone dispersion sum rules (of low energy and superconvergence types) are derived for nucleon matrix elements of the commutator involving electromagnetic and divergence of axial vector currents. The superconvergence type sum rules in the fixed mass limit are rewritten without requiring the knowledge of Regge subtractions. The retarded scaling functions occurring in these sum rules are evaluated within the framework of quark light cone algebra of currents. Besides a general consistency check of the framework underlying the derivation, the author infers, on the basis of crude evaluation of scaling functions, an upper limit of 100 MeV for the bare mass of nonstrange quarks. (Auth.)

  12. Parity of Θ+(1540) from QCD sum rules

    International Nuclear Information System (INIS)

    Lee, Su Houng; Kim, Hungchong; Kwon, Youngshin

    2005-01-01

    The QCD sum rule for the pentaquark Θ + , first analyzed by Sugiyama, Doi and Oka, is reanalyzed with a phenomenological side that explicitly includes the contribution from the two-particle reducible kaon-nucleon intermediate state. The magnitude for the overlap of the Θ + interpolating current with the kaon-nucleon state is obtained by using soft-kaon theorem and a separate sum rule for the ground state nucleon with the pentaquark nucleon interpolating current. It is found that the K-N intermediate state constitutes only 10% of the sum rule so that the original claim that the parity of Θ + is negative remains valid

  13. The Eccentric-distance Sum of Some Graphs

    OpenAIRE

    P, Padmapriya; Mathad, Veena

    2017-01-01

    Let $G = (V,E)$ be a simple connected graph. Theeccentric-distance sum of $G$ is defined as$\\xi^{ds}(G) =\\ds\\sum_{\\{u,v\\}\\subseteq V(G)} [e(u)+e(v)] d(u,v)$, where $e(u)$ %\\dsis the eccentricity of the vertex $u$ in $G$ and $d(u,v)$ is thedistance between $u$ and $v$. In this paper, we establish formulaeto calculate the eccentric-distance sum for some graphs, namelywheel, star, broom, lollipop, double star, friendship, multi-stargraph and the join of $P_{n-2}$ and $P_2$.

  14. The eccentric-distance sum of some graphs

    Directory of Open Access Journals (Sweden)

    Padmapriya P

    2017-04-01

    Full Text Available Let $G = (V,E$ be a simple connected graph. Theeccentric-distance sum of $G$ is defined as$\\xi^{ds}(G =\\ds\\sum_{\\{u,v\\}\\subseteq V(G} [e(u+e(v] d(u,v$, where $e(u$ %\\dsis the eccentricity of the vertex $u$ in $G$ and $d(u,v$ is thedistance between $u$ and $v$. In this paper, we establish formulaeto calculate the eccentric-distance sum for some graphs, namelywheel, star, broom, lollipop, double star, friendship, multi-stargraph and the join of $P_{n-2}$ and $P_2$.

  15. Neutrino mass sum rules and symmetries of the mass matrix

    Energy Technology Data Exchange (ETDEWEB)

    Gehrlein, Julia [Karlsruhe Institute of Technology, Institut fuer Theoretische Teilchenphysik, Karlsruhe (Germany); Universidad Autonoma de Madrid, Departamento de Fisica Teorica, Madrid (Spain); Instituto de Fisica Teorica UAM/CSIC, Madrid (Spain); Spinrath, Martin [Karlsruhe Institute of Technology, Institut fuer Theoretische Teilchenphysik, Karlsruhe (Germany); National Center for Theoretical Sciences, Physics Division, Hsinchu (China)

    2017-05-15

    Neutrino mass sum rules have recently gained again more attention as a powerful tool to discriminate and test various flavour models in the near future. A related question which has not yet been discussed fully satisfactorily was the origin of these sum rules and if they are related to any residual or accidental symmetry. We will address this open issue here systematically and find previous statements confirmed. Namely, the sum rules are not related to any enhanced symmetry of the Lagrangian after family symmetry breaking but they are simply the result of a reduction of free parameters due to skillful model building. (orig.)

  16. Moessbauer sum rules for use with synchrotron sources

    International Nuclear Information System (INIS)

    Lipkin, Harry J.

    1999-01-01

    The availability of tunable synchrotron radiation sources with millivolt resolution has opened new prospects for exploring dynamics of complex systems with Moessbauer spectroscopy. Early Moessbauer treatments and moment sum rules are extended to treat inelastic excitations measured in synchrotron experiments, with emphasis on the unique new conditions absent in neutron scattering and arising in resonance scattering: prompt absorption, delayed emission, recoil-free transitions and coherent forward scattering. The first moment sum rule normalizes the inelastic spectrum. New sum rules obtained for higher moments include the third moment proportional to the second derivative of the potential acting on the Moessbauer nucleus and independent of temperature in the the harmonic approximation

  17. Derivation of sum rules for quark and baryon fields

    International Nuclear Information System (INIS)

    Bongardt, K.

    1978-01-01

    In an analogous way to the Weinberg sum rules, two spectral-function sum rules for quark and baryon fields are derived by means of the concept of lightlike charges. The baryon sum rules are valid for the case of SU 3 as well as for SU 4 and the one-particle approximation yields a linear mass relation. This relation is not in disagreement with the normal linear GMO formula for the baryons. The calculated masses of the first resonance states agree very well with the experimental data

  18. Adler-Weisberger sum rule for WLWL→WLWL scattering

    International Nuclear Information System (INIS)

    Pham, T.N.

    1991-01-01

    We analyse the Adler-Weisberger sum rule for W L W L →W L W L scattering. We find that at some energy, the W L W L total cross section must be large to saturate the sum rule. Measurements at future colliders would be needed to check the sum rule and to obtain the decay rates Γ(H→W L W L , Z L Z L ) which would be modified by the existence of a P-wave vector meson resonance in the standard model with strongly interacting Higgs sector or in technicolour models. (orig.)

  19. A toolbox for Harmonic Sums and their analytic continuations

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Schneider, Carsten [RISC, J. Kepler University, Linz (Austria); Bluemlein, Johannes [DESY, Zeuthen (Germany)

    2010-07-01

    The package HarmonicSums implemented in the computer algebra system Mathematica is presented. It supports higher loop calculations in QCD and QED to represent single-scale quantities like anomalous dimensions and Wilson coefficients. The package allows to reduce general harmonic sums due to their algebraic and different structural relations. We provide a general framework for these reductions and the explicit representations up to weight w=8. For the use in experimental analyzes we also provide an analytic formalism to continue the harmonic sums form their integer arguments into the complex plane, which includes their recursions and asymptotic representations. The main ideas are illustrated by specific examples.

  20. Compton scattering from nuclei and photo-absorption sum rules

    International Nuclear Information System (INIS)

    Gorchtein, Mikhail; Hobbs, Timothy; Londergan, J. Timothy; Szczepaniak, Adam P.

    2011-01-01

    We revisit the photo-absorption sum rule for real Compton scattering from the proton and from nuclear targets. In analogy with the Thomas-Reiche-Kuhn sum rule appropriate at low energies, we propose a new 'constituent quark model' sum rule that relates the integrated strength of hadronic resonances to the scattering amplitude on constituent quarks. We study the constituent quark model sum rule for several nuclear targets. In addition, we extract the α=0 pole contribution for both proton and nuclei. Using the modern high-energy proton data, we find that the α=0 pole contribution differs significantly from the Thomson term, in contrast with the original findings by Damashek and Gilman.

  1. A simple derivation of new sum rules of Bessel functions

    International Nuclear Information System (INIS)

    Ciocci, F.; Dattoli, G.; Dipace, A.

    1985-01-01

    In this note it is exploited a recently suggested technique to get simple expressions for a class of sum rules of Bessel functions appearing in plasma physics; their relevance to the numerical evaluation of the Turkin function is also discussed

  2. Asymptotic distribution of products of sums of independent random ...

    Indian Academy of Sciences (India)

    integrable random variables (r.v.) are asymptotically log-normal. This fact ... the product of the partial sums of i.i.d. positive random variables as follows. .... Now define ..... by Henan Province Foundation and Frontier Technology Research Plan.

  3. QCD sum rules and applications to nuclear physics

    Energy Technology Data Exchange (ETDEWEB)

    Cohen, T D [Maryland Univ., College Park, MD (United States). Dept. of Physics; [Washington Univ., Seattle, WA (United States). Dept. of Physics and Inst. for Nuclear Theory; Furnstahl, R J [Ohio State Univ., Columbus, OH (United States). Dept. of Physics; Griegel, D K [Maryland Univ., College Park, MD (United States). Dept. of Physics; [TRIUMF, Vancouver, BC (Canada); Xuemin, J

    1994-12-01

    Applications of QCD sum-rule methods to the physics of nuclei are reviewed, with an emphasis on calculations of baryon self-energies in infinite nuclear matter. The sum-rule approach relates spectral properties of hadrons propagating in the finite-density medium, such as optical potentials for quasinucleons, to matrix elements of QCD composite operators (condensates). The vacuum formalism for QCD sum rules is generalized to finite density, and the strategy and implementation of the approach is discussed. Predictions for baryon self-energies are compared to those suggested by relativistic nuclear physics phenomenology. Sum rules for vector mesons in dense nuclear matter are also considered. (author). 153 refs., 8 figs.

  4. Effectiveness evaluation of contingency sum as a risk management ...

    African Journals Online (AJOL)

    Ethiopian Journal of Environmental Studies and Management ... manage risks prone projects have adopted several methods, one of which is contingency sum. ... initial project cost, cost overrun and percentage allowed for contingency.

  5. Power sums of fibonacci and Lucas numbers | Chu | Quaestiones ...

    African Journals Online (AJOL)

    Lucas numbers are established, which include, as special cases, four for-mulae for odd power sums of Melham type on Fibonacci and Lucas numbers, obtained recently by Ozeki and Prodinger (2009). Quaestiones Mathematicae 34(2011), 75- ...

  6. The black hole interior and a curious sum rule

    International Nuclear Information System (INIS)

    Giveon, Amit; Itzhaki, Nissan; Troost, Jan

    2014-01-01

    We analyze the Euclidean geometry near non-extremal NS5-branes in string theory, including regions beyond the horizon and beyond the singularity of the black brane. The various regions have an exact description in string theory, in terms of cigar, trumpet and negative level minimal model conformal field theories. We study the worldsheet elliptic genera of these three superconformal theories, and show that their sum vanishes. We speculate on the significance of this curious sum rule for black hole physics

  7. QCD sum rule for nucleon in nuclear matter

    International Nuclear Information System (INIS)

    Mallik, S.; Sarkar, Sourav

    2010-01-01

    We consider the two-point function of nucleon current in nuclear matter and write a QCD sum rule to analyse the residue of the nucleon pole as a function of nuclear density. The nucleon self-energy needed for the sum rule is taken as input from calculations using phenomenological N N potential. Our result shows a decrease in the residue with increasing nuclear density, as is known to be the case with similar quantities. (orig.)

  8. Convolutional Codes with Maximum Column Sum Rank for Network Streaming

    OpenAIRE

    Mahmood, Rafid; Badr, Ahmed; Khisti, Ashish

    2015-01-01

    The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We introduce a metric known as the column sum rank, that parallels column Hamming distance when streaming over a network with link failures. We prove rank analogues of several known column Hamming distance properties and introduce a new family of convolutional codes that maximize the column sum rank up to the code memory. Our construction invol...

  9. The black hole interior and a curious sum rule

    Energy Technology Data Exchange (ETDEWEB)

    Giveon, Amit [Racah Institute of Physics, The Hebrew University,Jerusalem, 91904 (Israel); Itzhaki, Nissan [Physics Department, Tel-Aviv University,Ramat-Aviv, 69978 (Israel); Troost, Jan [Laboratoire de Physique Théorique,Unité Mixte du CRNS et de l’École Normale Supérieure,associée à l’Université Pierre et Marie Curie 6,UMR 8549 École Normale Supérieure,24 Rue Lhomond Paris 75005 (France)

    2014-03-12

    We analyze the Euclidean geometry near non-extremal NS5-branes in string theory, including regions beyond the horizon and beyond the singularity of the black brane. The various regions have an exact description in string theory, in terms of cigar, trumpet and negative level minimal model conformal field theories. We study the worldsheet elliptic genera of these three superconformal theories, and show that their sum vanishes. We speculate on the significance of this curious sum rule for black hole physics.

  10. GDH sum rule measurement at low Q2

    International Nuclear Information System (INIS)

    Bianchi, N.

    1996-01-01

    The Gerasimov-Drell-Hearn (GDH) sum rule is based on a general dispersive relation for the forward Compton scattering. Multipole analysis suggested the possible violation of the sum rule. Some propositions have been made to modify the original GDH expression. An effort is now being made in several laboratories to shred some light on this topic. The purposes of the different planned experiments are briefly presented according to their Q 2 range

  11. A Quantum Approach to Subset-Sum and Similar Problems

    OpenAIRE

    Daskin, Ammar

    2017-01-01

    In this paper, we study the subset-sum problem by using a quantum heuristic approach similar to the verification circuit of quantum Arthur-Merlin games. Under described certain assumptions, we show that the exact solution of the subset sum problem my be obtained in polynomial time and the exponential speed-up over the classical algorithms may be possible. We give a numerical example and discuss the complexity of the approach and its further application to the knapsack problem.

  12. Spectral sum rule for time delay in R2

    International Nuclear Information System (INIS)

    Osborn, T.A.; Sinha, K.B.; Bolle, D.; Danneels, C.

    1985-01-01

    A local spectral sum rule for nonrelativistic scattering in two dimensions is derived for the potential class velement ofL 4 /sup // 3 (R 2 ). The sum rule relates the integral over all scattering energies of the trace of the time-delay operator for a finite region Σis contained inR 2 to the contributions in Σ of the pure point and singularly continuous spectra

  13. Light-cone sum rules: A SCET-based formulation

    CERN Document Server

    De Fazio, F; Hurth, Tobias; Feldmann, Th.

    2007-01-01

    We describe the construction of light-cone sum rules (LCSRs) for exclusive $B$-meson decays into light energetic hadrons from correlation functions within soft-collinear effective theory (SCET). As an example, we consider the SCET sum rule for the $B \\to \\pi$ transition form factor at large recoil, including radiative corrections from hard-collinear loop diagrams at first order in the strong coupling constant.

  14. A Global Optimization Algorithm for Sum of Linear Ratios Problem

    OpenAIRE

    Yuelin Gao; Siqiao Jin

    2013-01-01

    We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the c...

  15. An Algorithm to Solve the Equal-Sum-Product Problem

    OpenAIRE

    Nyblom, M. A.; Evans, C. D.

    2013-01-01

    A recursive algorithm is constructed which finds all solutions to a class of Diophantine equations connected to the problem of determining ordered n-tuples of positive integers satisfying the property that their sum is equal to their product. An examination of the use of Binary Search Trees in implementing the algorithm into a working program is given. In addition an application of the algorithm for searching possible extra exceptional values of the equal-sum-product problem is explored after...

  16. Hadronic final states and sum rules in deep inelastic processes

    International Nuclear Information System (INIS)

    Pal, B.K.

    1977-01-01

    In order to get maximum information on the hadronic final states and sum rules in deep inelastic processes, Regge phenomenology and quarks parton model have been used. The unified picture for the production of hadrons of type i as a function of Bjorken and Feyman variables with only one adjustable parameter is formulated. The results of neutrino experiments and the production of charm particles are discussed in sum rules. (author)

  17. Comment on QCD sum rules and weak bottom decays

    International Nuclear Information System (INIS)

    Guberina, B.; Machet, B.

    1982-07-01

    QCD sum rules derived by Bourrely et al. are applied to B-decays to get a lower and an upper bound for the decay rate. The sum rules are shown to be essentially controlled by the large mass scales involved in the process. These bounds combined with the experimental value of BR (B→eνX) provide an upper bound for the lifetime of the B + meson. A comparison is made with D-meson decays

  18. On the general Dedekind sums and its reciprocity formula

    Indian Academy of Sciences (India)

    if x is an integer. The various properties of S(h, q) were investigated by many authors. Maybe the most famous property of Dedekind sums is the reciprocity formula (see [2–4]):. S(h, q) + S(q, h) = h2 + q2 + 1. 12hq. −. 1. 4. (1) for all (h, q) = 1,q > 0,h> 0. The main purpose of this paper is to introduce a general. Dedekind sum:.

  19. Root and Critical Point Behaviors of Certain Sums of Polynomials

    Indian Academy of Sciences (India)

    13

    There is an extensive literature concerning roots of sums of polynomials. Many papers and books([5], [6],. [7]) have written about these polynomials. Perhaps the most immediate question of sums of polynomials,. A + B = C, is “given bounds for the roots of A and B, what bounds can be given for the roots of C?” By. Fell [3], if ...

  20. Chiral corrections to the Adler-Weisberger sum rule

    Science.gov (United States)

    Beane, Silas R.; Klco, Natalie

    2016-12-01

    The Adler-Weisberger sum rule for the nucleon axial-vector charge, gA , offers a unique signature of chiral symmetry and its breaking in QCD. Its derivation relies on both algebraic aspects of chiral symmetry, which guarantee the convergence of the sum rule, and dynamical aspects of chiral symmetry breaking—as exploited using chiral perturbation theory—which allow the rigorous inclusion of explicit chiral symmetry breaking effects due to light-quark masses. The original derivations obtained the sum rule in the chiral limit and, without the benefit of chiral perturbation theory, made various attempts at extrapolating to nonvanishing pion masses. In this paper, the leading, universal, chiral corrections to the chiral-limit sum rule are obtained. Using PDG data, a recent parametrization of the pion-nucleon total cross sections in the resonance region given by the SAID group, as well as recent Roy-Steiner equation determinations of subthreshold amplitudes, threshold parameters, and correlated low-energy constants, the Adler-Weisberger sum rule is confronted with experimental data. With uncertainty estimates associated with the cross-section parametrization, the Goldberger-Treimann discrepancy, and the truncation of the sum rule at O (Mπ4) in the chiral expansion, this work finds gA=1.248 ±0.010 ±0.007 ±0.013 .

  1. Identification of scalp EEG circadian variation using a novel correlation sum measure

    Science.gov (United States)

    Shahidi Zandi, Ali; Boudreau, Philippe; Boivin, Diane B.; Dumont, Guy A.

    2015-10-01

    Objective. In this paper, we propose a novel method to determine the circadian variation of scalp electroencephalogram (EEG) in both individual and group levels using a correlation sum measure, quantifying self-similarity of the EEG relative energy across waking epochs. Approach. We analysed EEG recordings from central-parietal and occipito-parietal montages in nine healthy subjects undergoing a 72 h ultradian sleep-wake cycle protocol. Each waking epoch (˜1 s) of every nap opportunity was decomposed using the wavelet packet transform, and the relative energy for that epoch was calculated in the desired frequency band using the corresponding wavelet coefficients. Then, the resulting set of energy values was resampled randomly to generate different subsets with equal number of elements. The correlation sum of each subset was then calculated over a range of distance thresholds, and the average over all subsets was computed. This average value was finally scaled for each nap opportunity and considered as a new circadian measure. Main results. According to the evaluation results, a clear circadian rhythm was identified in some EEG frequency ranges, particularly in 4-8 Hz and 10-12 Hz. The correlation sum measure not only was able to disclose the circadian rhythm on the group data but also revealed significant circadian variations in most individual cases, as opposed to previous studies only reporting the circadian rhythms on a population of subjects. Compared to a naive measure based on the EEG absolute energy in the frequency band of interest, the proposed measure showed a clear superiority using both individual and group data. Results also suggested that the acrophase (i.e., the peak) of the circadian rhythm in 10-12 Hz occurs close to the core body temperature minimum. Significance. These results confirm the potential usefulness of the proposed EEG-based measure as a non-invasive circadian marker.

  2. Sum rule and hydrodynamic analyses of the velocity autocorrelation function in strongly coupled plasmas

    International Nuclear Information System (INIS)

    Nagano, Seido; Ichimaru, Setsuo

    1980-01-01

    The memory function for the velocity autocorrelation function in a strongly coupled, one-component plasma is analyzed in the short time and long time domains, respectively, with the aid of the frequency-moment sum rules and the hydrodynamic consideration evoking the idea of the generalized Stokes friction. A series of interpolation schemes with successively improved accuracies are then introduced. Numerical investigations of those interpolation schemes clarify the physical origin of the three different types of the velocity autocorrelation function observed in the molecular dynamics simulation at different regimes of the coupling constant. (author)

  3. Closed-form summations of Dowker's and related trigonometric sums

    International Nuclear Information System (INIS)

    Cvijović, Djurdje; Srivastava, H M

    2012-01-01

    Through a unified and relatively simple approach which uses complex contour integrals, particularly convenient integration contours and calculus of residues, closed-form summation formulas for 12 very general families of trigonometric sums are deduced. One of them is a family of cosecant sums which was first summed in closed form in a series of papers by Dowker (1987 Phys. Rev. D 36 3095–101; 1989 J. Math. Phys. 30 770–3; 1992 J. Phys. A: Math. Gen. 25 2641–8), whose method has inspired our work in this area. All of the formulas derived here involve the higher-order Bernoulli polynomials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (paper)

  4. A Bayesian analysis of the nucleon QCD sum rules

    International Nuclear Information System (INIS)

    Ohtani, Keisuke; Gubler, Philipp; Oka, Makoto

    2011-01-01

    QCD sum rules of the nucleon channel are reanalyzed, using the maximum-entropy method (MEM). This new approach, based on the Bayesian probability theory, does not restrict the spectral function to the usual ''pole + continuum'' form, allowing a more flexible investigation of the nucleon spectral function. Making use of this flexibility, we are able to investigate the spectral functions of various interpolating fields, finding that the nucleon ground state mainly couples to an operator containing a scalar diquark. Moreover, we formulate the Gaussian sum rule for the nucleon channel and find that it is more suitable for the MEM analysis to extract the nucleon pole in the region of its experimental value, while the Borel sum rule does not contain enough information to clearly separate the nucleon pole from the continuum. (orig.)

  5. Subset-sum phase transitions and data compression

    Science.gov (United States)

    Merhav, Neri

    2011-09-01

    We propose a rigorous analysis approach for the subset-sum problem in the context of lossless data compression, where the phase transition of the subset-sum problem is directly related to the passage between ambiguous and non-ambiguous decompression, for a compression scheme that is based on specifying the sequence composition. The proposed analysis lends itself to straightforward extensions in several directions of interest, including non-binary alphabets, incorporation of side information at the decoder (Slepian-Wolf coding), and coding schemes based on multiple subset sums. It is also demonstrated that the proposed technique can be used to analyze the critical behavior in a more involved situation where the sequence composition is not specified by the encoder.

  6. Limit theorems for multi-indexed sums of random variables

    CERN Document Server

    Klesov, Oleg

    2014-01-01

    Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who ...

  7. Power loss analysis in altered tooth-sum spur gearing

    Directory of Open Access Journals (Sweden)

    Sachidananda H. K.

    2018-01-01

    Full Text Available The main cause of power loss or dissipation of heat in case of meshed gears is due to friction existing between gear tooth mesh and is a major concern in low rotational speed gears, whereas in case of high operating speed the power loss taking place due to compression of air-lubricant mixture (churning losses and windage losses due to aerodynamic trial of air lubricant mixture which controls the total efficiency needs to be considered. Therefore, in order to improve mechanical efficiency it is necessary for gear designer during gear tooth optimization to consider these energy losses. In this research paper the power loss analysis for a tooth-sum of 100 altered by ±4% operating between a specified center distance is considered. The results show that negative altered tooth-sum gearing performs better as compared to standard and positive altered tooth-sum gearing.

  8. Efficient simulation of tail probabilities of sums of correlated lognormals

    DEFF Research Database (Denmark)

    Asmussen, Søren; Blanchet, José; Juneja, Sandeep

    We consider the problem of efficient estimation of tail probabilities of sums of correlated lognormals via simulation. This problem is motivated by the tail analysis of portfolios of assets driven by correlated Black-Scholes models. We propose two estimators that can be rigorously shown to be eff......We consider the problem of efficient estimation of tail probabilities of sums of correlated lognormals via simulation. This problem is motivated by the tail analysis of portfolios of assets driven by correlated Black-Scholes models. We propose two estimators that can be rigorously shown...... optimize the scaling parameter of the covariance. The second estimator decomposes the probability of interest in two contributions and takes advantage of the fact that large deviations for a sum of correlated lognormals are (asymptotically) caused by the largest increment. Importance sampling...

  9. Convergence problems of Coulomb and multipole sums in crystals

    International Nuclear Information System (INIS)

    Kholopov, Evgenii V

    2004-01-01

    Different ways of calculating Coulomb and dipole sums over crystal lattices are analyzed comparatively. It is shown that the currently alleged disagreement between various approaches originates in ignoring the requirement for the self-consistency of surface conditions, which are of fundamental importance due to the long-range nature of the bulk interactions that these sums describe. This is especially true of surfaces arising when direct sums for infinite translation-invariant structures are truncated. The charge conditions for actual surfaces being self-consistently adjusted to the bulk state are formally the same as those on the truncation surface, consistent with the concept of the thermodynamic limit for the bulk-state absolute equilibrium and with the fact that the surface energy contribution in this case is, naturally, statistically small compared to the bulk contribution. Two-point multipole expansions are briefly discussed, and the problems associated with the boundary of their convergence circle are pointed out. (reviews of topical problems)

  10. Closed-form summations of Dowker's and related trigonometric sums

    Science.gov (United States)

    Cvijović, Djurdje; Srivastava, H. M.

    2012-09-01

    Through a unified and relatively simple approach which uses complex contour integrals, particularly convenient integration contours and calculus of residues, closed-form summation formulas for 12 very general families of trigonometric sums are deduced. One of them is a family of cosecant sums which was first summed in closed form in a series of papers by Dowker (1987 Phys. Rev. D 36 3095-101 1989 J. Math. Phys. 30 770-3 1992 J. Phys. A: Math. Gen. 25 2641-8), whose method has inspired our work in this area. All of the formulas derived here involve the higher-order Bernoulli polynomials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.

  11. Spectral sum rules for the three-body problem

    International Nuclear Information System (INIS)

    Bolle, D.; Osborn, T.A.

    1982-01-01

    This paper derives a number of sum rules for nonrelativistic three-body scattering. These rules are valid for any finite region μ in the six-dimensional coordinate space. They relate energy moments of the trace of the onshell time-delay operator to the energy-weighted probability for finding the three-body bound-state wave functions in the region μ. If μ is all of the six-dimensional space, the global form of the sum rules is obtained. In this form the rules constitute higher-order Levinson's theorems for the three-body problem. Finally, the sum rules are extended to allow the energy momtns have complex powers

  12. Moessbauer sum rules for use with synchrotron sources

    International Nuclear Information System (INIS)

    Lipkin, H.J.

    1995-01-01

    The availability of tunable synchrotron radiation sources with millivolt resolution has opened prospects for exploring dynamics of complex systems with Moessbauer spectroscopy. Early Moessbauer treatments and moment sum rules are extended to treat inelastic excitations measured in synchrotron experiments, with emphasis on the unique conditions absent in neutron scattering and arising in resonance scattering: prompt absorption, delayed emission, recoilfree transitions, and coherent forward scattering. The first moment sum rule normalizes the inelastic spectrum. Sum rules obtained for higher moments include the third moment proportional to the second derivative of the potential acting on the Moessbauer nucleus and independent of temperature in the harmonic approximation. Interesting information may be obtained on the behavior of the potential acting on this nucleus in samples not easily investigated with neutron scattering, e.g., small samples, thin films, time-dependent structures, and amorphous-metallic high pressure phases

  13. Ramanujan sums via generalized Möbius functions and applications

    Directory of Open Access Journals (Sweden)

    Vichian Laohakosol

    2006-01-01

    Full Text Available A generalized Ramanujan sum (GRS is defined by replacing the usual Möbius function in the classical Ramanujan sum with the Souriau-Hsu-Möbius function. After collecting basic properties of a GRS, mostly containing existing ones, seven aspects of a GRS are studied. The first shows that the unique representation of even functions with respect to GRSs is possible. The second is a derivation of the mean value of a GRS. The third establishes analogues of the remarkable Ramanujan's formulae connecting divisor functions with Ramanujan sums. The fourth gives a formula for the inverse of a GRS. The fifth is an analysis showing when a reciprocity law exists. The sixth treats the problem of dependence. Finally, some characterizations of completely multiplicative function using GRSs are obtained and a connection of a GRS with the number of solutions of certain congruences is indicated.

  14. A Shuttle Upper Atmosphere Mass Spectrometer /SUMS/ experiment

    Science.gov (United States)

    Blanchard, R. C.; Duckett, R. J.; Hinson, E. W.

    1982-01-01

    A magnetic mass spectrometer is currently being adapted to the Space Shuttle Orbiter to provide repeated high altitude atmosphere data to support in situ rarefied flow aerodynamics research, i.e., in the high velocity, low density flight regime. The experiment, called Shuttle Upper Atmosphere Mass Spectrometer (SUMS), is the first attempt to design mass spectrometer equipment for flight vehicle aerodynamic data extraction. The SUMS experiment will provide total freestream atmospheric quantitites, principally total mass density, above altitudes at which conventional pressure measurements are valid. Experiment concepts, the expected flight profile, tradeoffs in the design of the total system and flight data reduction plans are discussed. Development plans are based upon a SUMS first flight after the Orbiter initial development flights.

  15. Chiral symmetry breaking parameters from QCD sum rules

    Energy Technology Data Exchange (ETDEWEB)

    Mallik, S [Karlsruhe Univ. (T.H.) (Germany, F.R.). Inst. fuer Theoretische Kernphysik; Bern Univ. (Switzerland). Inst. fuer Theoretische Physik)

    1982-10-04

    We obtain new QCD sum rules by considering vacuum expectation values of two-point functions, taking all the five quark bilinears into account. These sum rules are employed to extract values of different chiral symmetry breaking parameters in QCD theory. We find masses of light quarks, m=1/2msub(u)+msub(d)=8.4+-1.2 MeV, msub(s)=205+-65 MeV. Further, we obtain corrections to certain soft pion (kaon) PCAC relations and the violation of SU(3) flavour symmetry by the non-strange and strange quark-antiquark vacuum condensate.

  16. Chiral restoration and the extended photoabsorption sum rule in nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Ericson, M [Lyon-1 Univ., 69 - Villeurbanne (France). Inst. de Physique Nucleaire; [European Organization for Nuclear Research, Geneva (Switzerland); Rosa-Clot, M [Florence Univ. (Italy). Ist. di Fisica; [Istituto Nazionale di Fisica Nucleare, Florence (Italy); Kulagin, S A [Akademiya Meditsinskikh Nauk SSSR, Moscow (Russian Federation)

    1996-07-01

    The Bethe-Levinger sum rule is extended beyond the potential model. The pion degrees of freedom are taken into account and the modifications of the potential theory are analyzed within two different approaches: dipole sum rule and dispersion relation on the Compton amplitude. Our aim is to extract from the photon data experimental information on the expectation value of the square of the pion field, a quantity which enters also in the restoration of chiral symmetry in nuclei and in pion-nucleus scattering. We are led to incorporate in the description the {Delta} resonance, which is strongly excited by the pion degrees of freedom. 11 refs.

  17. Chiral restoration and the extended photoabsorption sum rule in nuclei

    International Nuclear Information System (INIS)

    Ericson, M.; Rosa-Clot, M.; Kulagin, S.A.

    1996-07-01

    The Bethe-Levinger sum rule is extended beyond the potential model. The pion degrees of freedom are taken into account and the modifications of the potential theory are analyzed within two different approaches: dipole sum rule and dispersion relation on the Compton amplitude. Our aim is to extract from the photon data experimental information on the expectation value of the square of the pion field, a quantity which enters also in the restoration of chiral symmetry in nuclei and in pion-nucleus scattering. We are led to incorporate in the description the Δ resonance, which is strongly excited by the pion degrees of freedom

  18. A zero-sum monetary system, interest rates, and implications

    OpenAIRE

    Hanley, Brian P.

    2015-01-01

    To the knowledge of the author, this is the first time it has been shown that interest rates that are extremely high by modern standards (100% and higher) are necessary within a zero-sum monetary system, and not just driven by greed. Extreme interest rates that appeared in various places and times reinforce the idea that hard money may have contributed to high rates of interest. Here a model is presented that examines the interest rate required to succeed as an investor in a zero-sum fixed qu...

  19. Computation and theory of Euler sums of generalized hyperharmonic numbers

    OpenAIRE

    Xu, Ce

    2017-01-01

    Recently, Dil and Boyadzhiev \\cite{AD2015} proved an explicit formula for the sum of multiple harmonic numbers whose indices are the sequence $\\left( {{{\\left\\{ 0 \\right\\}}_r},1} \\right)$. In this paper we show that the sums of multiple harmonic numbers whose indices are the sequence $\\left( {{{\\left\\{ 0 \\right\\}}_r,1};{{\\left\\{ 1 \\right\\}}_{k-1}}} \\right)$ can be expressed in terms of (multiple) zeta values, multiple harmonic numbers and Stirling numbers of the first kind, and give an explic...

  20. A Global Optimization Algorithm for Sum of Linear Ratios Problem

    Directory of Open Access Journals (Sweden)

    Yuelin Gao

    2013-01-01

    Full Text Available We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.

  1. Second-harmonic and sum-frequency generation for surface studies

    International Nuclear Information System (INIS)

    Hunt, J.H.; Guyot-Sionnest, P.; Shen, Y.R.

    1987-07-01

    Second harmonic generation (SHG) has now been well established as a versatile surface-sensitive probe. It has been used to study electrochemical processes at electrode surfaces, molecular adsorption and desorption at metal and semiconductor surfaces, orientational phase transition of molecular monolayers on water, surface reconstruction and epitaxial growth, and so on. More recently, it has been employed as a tool to monitor monolayer polymerization and other surface reactions, to probe polar order of molecules at interfaces, and to measure molecular nonlinearity. While most surface techniques are restricted to the solid/vacuum environment, SHG is applicable to nearly all interfaces as long as the interfaces are accessible by light. In addition, SHG has the advantages of being capable of in-situ measurements with high temporal, spatial, and spectral resolutions

  2. Interpreting intensities in vibrational sum frequency generation (SFG) spectroscopy: CO adsorption on Pd surfaces

    Science.gov (United States)

    Morkel, M.; Unterhalt, H.; Klüner, T.; Rupprechter, G.; Freund, H.-J.

    2005-07-01

    The lineshape and intensity of SFG signals of CO adsorbed on supported Pd nanoparticles and Pd(1 1 1) are analyzed. For CO/Pd(1 1 1) nearly symmetric lorentzian lineshapes were observed. Applying two different visible wavelengths for excitation, asymmetric lineshapes observed for the CO/Pd/Al 2O 3/NiAl(1 1 0) system are explained by a lower resonant and a higher non-resonant SFG signal and a change in the phase between resonant and non-resonant signals, most likely originating from an interband transition in the NiAl substrate. The relative intensity of different CO species (hollow, bridge, on-top) was modeled by DFT calculations of IR transition moments and Raman activities. While the (experimental) sensitivity of SFG towards different CO species strongly varies, the calculated IR and Raman activities are rather similar. The inability to exactly reproduce experimental SFG intensities suggests a strong coverage dependence of Raman activities or that non-linear effects occur that can currently not be properly accounted for.

  3. Highly efficient deep ultraviolet generation by sum-frequency mixing ...

    Indian Academy of Sciences (India)

    Generation of deep ultraviolet radiation at 210 nm by Type-I third harmonic generation is achieved in a pair of BBO crystals with conversion efficiency as high as 36%. The fundamental source is the dye laser radiation pumped by the second harmonic of a Q-switched Nd : YAG laser. A walk-off compensated configuration ...

  4. Coincidence summing corrections for positron emitters in germanium gamma spectrometry

    International Nuclear Information System (INIS)

    Richardson, A.E.; Sallee, W.W.; New Mexico State Univ., Las Cruces

    1990-01-01

    For positron emitters, 511 keV annihilation quanta are in coincidence with other gamma rays in the decay scheme. If the positrons are not localized at the point of decay, annihilation quanta will be produced at a site some distance from the point of emission. The magnitude of the summing coincidence effect will depend upon the position of annihilation. A method for determining the magnitude of the summing effect for a single gamma of energy E in coincidence with the annihilation gammas from non-localized positrons has been developed which makes use of the counting data for the full energy peaks for both the gamma ray (E) and the 511 keV annihilation gammas. With this data and efficiency calibration data one can determine the average total efficiency for the annihilation positions from which 511 keV gammas originate, and thereby obtain the summing correction factor, SCF, for gamma ray (E). Application of the method to a 22 Na NIST standard gave excellent agreement of observed emission rates for the 1275 keV gamma with the NIST value for wide ranging degrees of positron localization having summing correction factors ranging from 1.021 to 1.505. The method was also applied successfully to 58 Co in neutron-irradiated nickel foils. The method shows promise as a check on the accuracy of the efficiency calibration for a particular detector geometry at the 511 keV energy and energies for other gammas associated with positron emission. (orig.)

  5. TAIL ASYMPTOTICS OF LIGHT-TAILED WEIBULL-LIKE SUMS

    DEFF Research Database (Denmark)

    Asmussen, Soren; Hashorva, Enkelejd; Laub, Patrick J.

    2017-01-01

    We consider sums of n i.i.d. random variables with tails close to exp{-x(beta)} for some beta > 1. Asymptotics developed by Rootzen (1987) and Balkema, Kluppelberg, and Resnick (1993) are discussed from the point of view of tails rather than of densities, using a somewhat different angle...

  6. Numerical Radius Inequalities for Finite Sums of Operators

    Directory of Open Access Journals (Sweden)

    Mirmostafaee Alireza Kamel

    2014-12-01

    Full Text Available In this paper, we obtain some sharp inequalities for numerical radius of finite sums of operators. Moreover, we give some applications of our result in estimation of spectral radius. We also compare our results with some known results.

  7. Standardization of I-125. Sum-Peak Coincidence Counting

    International Nuclear Information System (INIS)

    Grau Carles, A.; Grau Malonda, A.

    2011-01-01

    I-125 is a nuclide which presents difficulties for standardization. The sum-peak method is one of the procedures used to standardize this radionuclide. Initially NaI (Tl)detectors and then the semiconductor detectors with higher resolution have been used.This paper describes the different methods based on the sum-peak procedure and the different expressions used to calculate the activity are deduced. We describe a general procedure for obtaining all of the above equations and many more. We analyze the influence of uncertainties in the used parameters in the uncertainty of the activity. We give a complete example of the transmission of uncertainty and the effects of correlations in the uncertainty of the activity of the sample. High-resolution spectra show an unresolved doublet of 62.0 keV and 62.8 keV. The paper presents two approaches to solve this problem. One is based on the calculation of area ratio and the sum of peak areas obtained from atomic and nuclear data, in the other we modify the equations so that the sum of the peak areas doublet, rather than its components, is present. (Author) 19 refs.

  8. Root and critical point behaviors of certain sums of polynomials

    Indian Academy of Sciences (India)

    Seon-Hong Kim

    2018-04-24

    Apr 24, 2018 ... Root and critical point behaviors of certain sums of polynomials. SEON-HONG KIM1,∗. , SUNG YOON KIM2, TAE HYUNG KIM2 and SANGHEON LEE2. 1Department of Mathematics, Sookmyung Women's University, Seoul 140-742, Korea. 2Gyeonggi Science High School, Suwon 440-800, Korea.

  9. A Critique of Zero-sum Games and Palliative Economics

    African Journals Online (AJOL)

    Africa's economic growth and dependence since independence has been characterised by a zero-sum economic interaction with the West. This was no more than a continuation of the Centre-Periphery relationship that existed during colonial times. The result of the zerosum game interaction between Africa and the West ...

  10. Counter-ions at single charged wall: Sum rules.

    Science.gov (United States)

    Samaj, Ladislav

    2013-09-01

    For inhomogeneous classical Coulomb fluids in thermal equilibrium, like the jellium or the two-component Coulomb gas, there exists a variety of exact sum rules which relate the particle one-body and two-body densities. The necessary condition for these sum rules is that the Coulomb fluid possesses good screening properties, i.e. the particle correlation functions or the averaged charge inhomogeneity, say close to a wall, exhibit a short-range (usually exponential) decay. In this work, we study equilibrium statistical mechanics of an electric double layer with counter-ions only, i.e. a globally neutral system of equally charged point-like particles in the vicinity of a plain hard wall carrying a fixed uniform surface charge density of opposite sign. At large distances from the wall, the one-body and two-body counter-ion densities go to zero slowly according to the inverse-power law. In spite of the absence of screening, all known sum rules are shown to hold for two exactly solvable cases of the present system: in the weak-coupling Poisson-Boltzmann limit (in any spatial dimension larger than one) and at a special free-fermion coupling constant in two dimensions. This fact indicates an extended validity of the sum rules and provides a consistency check for reasonable theoretical approaches.

  11. Counting Your Way to the Sum of Squares Formula

    Indian Academy of Sciences (India)

    IAS Admin

    This gives us a brand new formula for the sum of the squares of the first n positive integers! A small tweak gives us a second formula, for free! For, we have the following identity for the binomial coeffi- cients which comes from the well known recursive rela- tion which the binomial coefficients satisfy: (n + 1. 3 )+ ( n + 1. 2 )= (.

  12. Sums over geometries and improvements on the mean field approximation

    International Nuclear Information System (INIS)

    Sacksteder, Vincent E. IV

    2007-01-01

    The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels

  13. Λ-bar from QCD sum rules for heavy quarkonium

    International Nuclear Information System (INIS)

    Kiselev, V.V.

    1994-01-01

    Using a specific scheme of the QCD sum rules for heavy quarkonium int he leading approximation over the inverse heavy quark, one gets the estimate of the difference between the masses of the heavy meson and heavy quark Λ=o.59+-0.02 GeV. 10 refs

  14. Isospin sum rule for nuclear photoabsorption: Effect of retardation

    International Nuclear Information System (INIS)

    Maize, M.A.; Fallieros, S.

    1987-01-01

    Motivated by the close similarity between a sum rule originally derived by Cabibbo and Radicati and a simplified version based on nonrelativistic nuclear physics in the long-wavelength limit, we have investigated the effect of retardation corrections. An account of the contributions due to higher multipolarities is presented, together with a physical interpretation of the results

  15. QCD Sum Rule External Field Approach and Vacuum Susceptibilities

    Institute of Scientific and Technical Information of China (English)

    ZONG Hong-Shi; PING Jia-Lun; CHANG Chao-His; WANG Fan; ZHAO En-Guang

    2002-01-01

    Based on QCD sum rule three-point and two-point external field formulas respectively, the vector vacuumsusceptibilities are calculated at the mean-field level in the framework of the global color symmetry model. It is shownthat the above two approaches of determination of the vector vacuum susceptibility may lead to different results. Thereason of this contradiction is discussed.

  16. Stable limits for sums of dependent infinite variance random variables

    DEFF Research Database (Denmark)

    Bartkiewicz, Katarzyna; Jakubowski, Adam; Mikosch, Thomas

    2011-01-01

    The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to hold are known in the literature. However, most of these...

  17. Lump Sum Moving Cost and Aggregate Office Space Use

    NARCIS (Netherlands)

    G. Romijn

    1997-01-01

    textabstractWhen firms decide to change office space use, in many instances this involves relocation. Relocation involves sizable costs to the firm that can to a large extent be characterized as lump sum, i.e. independent of the change in demand. In this paper we propose and solve a model of the

  18. Madhava, Gregory, Leibnitz, and Sums of Two Squares

    Indian Academy of Sciences (India)

    IAS Admin

    Keywords. Gregory–Leibnitz series, lattice points, sums of two squares,. Gauss circle problem. Shailesh Shirali heads the. Community Math Centre in Rishi Valley School and works in the field of teacher education. He is the author of many books and articles in mathemat- ics, written for interested students in the age range.

  19. The Distribution of the Sum of Signed Ranks

    Science.gov (United States)

    Albright, Brian

    2012-01-01

    We describe the calculation of the distribution of the sum of signed ranks and develop an exact recursive algorithm for the distribution as well as an approximation of the distribution using the normal. The results have applications to the non-parametric Wilcoxon signed-rank test.

  20. Lower limits for distribution tails of randomly stopped sums

    NARCIS (Netherlands)

    Denisov, D.E.; Korshunov, D.A.; Foss, S.G.

    2008-01-01

    We study lower limits for the ratio $\\overline{F^{*\\tau}}(x)/\\,\\overline F(x)$ of tail distributions, where $F^{*\\tau}$ is a distribution of a sum of a random size $\\tau$ of independent identically distributed random variables having a common distribution $F$, and a random variable $\\tau$ does not

  1. Large-Nc quantum chromodynamics and harmonic sums

    Indian Academy of Sciences (India)

    In the large- limit of QCD, two-point functions of local operators become harmonic sums. I review some properties which follow from this fact and which are relevant for phenomenological applications. This has led us to consider a class of analytic number theory functions as toy models of large- QCD which also is ...

  2. QCD sum rule studies at finite density and temperature

    Energy Technology Data Exchange (ETDEWEB)

    Kwon, Youngshin

    2010-01-21

    In-medium modifications of hadronic properties have a strong connection to the restoration of chiral symmetry in hot and/or dense medium. The in-medium spectral functions for vector and axial-vector mesons are of particular interest in this context, considering the experimental dilepton production data which signal the in-medium meson properties. In this thesis, finite energy sum rules are employed to set constraints for the in-medium spectral functions of vector and axial-vector mesons. Finite energy sum rules for the first two moments of the spectral functions are investigated with emphasis on the role of a scale parameter related to the spontaneous chiral symmetry breaking in QCD. It is demonstrated that these lowest moments of vector current spectral functions do permit an accurate sum rule analysis with controlled inputs, such as the QCD condensates of lowest dimensions. In contrast, the higher moments contain uncertainties from the higher dimensional condensates. It turns out that the factorization approximation for the four-quark condensate is not applicable in any of the cases studied in this work. The accurate sum rules for the lowest two moments of the spectral functions are used to clarify and classify the properties of vector meson spectral functions in a nuclear medium. Possible connections with the Brown-Rho scaling hypothesis are also discussed. (orig.)

  3. Standardization of I-125. Sum-Peak Coincidence Counting

    Energy Technology Data Exchange (ETDEWEB)

    Grau Carles, A.; Grau Malonda, A.

    2011-07-01

    I-125 is a nuclide which presents difficulties for standardization. The sum-peak method is one of the procedures used to standardize this radionuclide. Initially NaI (Tl)detectors and then the semiconductor detectors with higher resolution have been used.This paper describes the different methods based on the sum-peak procedure and the different expressions used to calculate the activity are deduced. We describe a general procedure for obtaining all of the above equations and many more. We analyze the influence of uncertainties in the used parameters in the uncertainty of the activity. We give a complete example of the transmission of uncertainty and the effects of correlations in the uncertainty of the activity of the sample. High-resolution spectra show an unresolved doublet of 62.0 keV and 62.8 keV. The paper presents two approaches to solve this problem. One is based on the calculation of area ratio and the sum of peak areas obtained from atomic and nuclear data, in the other we modify the equations so that the sum of the peak areas doublet, rather than its components, is present. (Author) 19 refs.

  4. Generalized Sum of Fuzzy Subgroup and α-cut Subgroup

    OpenAIRE

    Daher Waly Freh Al-Rekabi; Alia Shany Hassan

    2012-01-01

    p>In this paper we study some results of the generalized sum of a fuzzynbsp;subgroup and alpha;-cut subgroup, we define a alpha;-cut subset and alpha;-cut subgroup, and then. We study some of their properties./p>

  5. 27 CFR 24.148 - Penal sums of bonds.

    Science.gov (United States)

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Penal sums of bonds. 24.148 Section 24.148 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU... Vinegar Plant Bond, TTB F 5510.2 Not less than the tax on all wine on hand, in transit, or unaccounted for...

  6. Melham's conjecture on odd power sums of fibonacci numbers | Sun ...

    African Journals Online (AJOL)

    Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at a certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish at 1, and will be an integer polynomial after multiplying it by a ...

  7. Tight bounds on angle sums of nonobtuse simplices

    Czech Academy of Sciences Publication Activity Database

    Brandts, J.; Cihangir, A.; Křížek, Michal

    2015-01-01

    Roč. 267, 15 September (2015), s. 397-408 ISSN 0096-3003 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : nonobtuse simplex * angle sum s * spherical geometry * polar simplex Subject RIV: BA - General Mathematics Impact factor: 1.345, year: 2015 http://www.sciencedirect.com/science/article/pii/S0096300315002155

  8. Partial sums of arithmetical functions with absolutely convergent ...

    Indian Academy of Sciences (India)

    For an arithmetical function f with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the ∑ n ≤ N f(n)$ with explicit error term. As a corollary we obtain new results about sum-of-divisors functions and Jordan's totient functions.

  9. Beauty vector meson decay constants from QCD sum rules

    Energy Technology Data Exchange (ETDEWEB)

    Lucha, Wolfgang [Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria); Melikhov, Dmitri [Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria); D. V. Skobeltsyn Institute of Nuclear Physics, M. V. Lomonosov Moscow State University, 119991, Moscow (Russian Federation); Simula, Silvano [Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146, Roma (Italy)

    2016-01-22

    We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity.

  10. Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

    Science.gov (United States)

    Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet

    2015-01-01

    When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating

  11. On QCD sum rules of the Laplace transform type and light quark masses

    International Nuclear Information System (INIS)

    Narison, S.

    1981-04-01

    We discuss the relation between the usual dispersion relation sum rules and the Laplace transform type sum rules in quantum chromodynamics. Two specific examples corresponding to the S-coupling constant sum rule and the light quark masses sum rules are considered. An interpretation, within QCD, of Leutwyler's formula for the current algebra quark masses is also given

  12. Regularised integrals, sums and traces an analytic point of view

    CERN Document Server

    Paycha, Sylvie

    2012-01-01

    "Regularization techniques" is the common name for a variety of methods used to make sense of divergent series, divergent integrals, or traces of linear operators in infinite-dimensional spaces. Such methods are often indispensable in problems of number theory, geometry, quantum field theory, and other areas of mathematics and theoretical physics. However arbitrary and noncanonical they might seem at first glance, regularized sums, integrals, and traces often contain canonical concepts, and the main purpose of this book is to illustrate and explain this. This book provides a unified and self-contained mathematical treatment of various regularization techniques. The author shows how to derive regularized sums, integrals, and traces from certain canonical building blocks of the original divergent object. In the process of putting together these "building blocks", one encounters many problems and ambiguities caused by various so-called anomalies, which are investigated and explained in detail. Nevertheless, it t...

  13. Path-sum calculations for rf current drive

    International Nuclear Information System (INIS)

    Belo, Jorge H.; Bizarro, Joao P.S.; Rodrigues, Paulo

    2001-01-01

    Path sums and Gaussian short-time propagators are used to solve two-dimensional Fokker-Planck models of lower-hybrid (LH) and electron-cyclotron (EC) current drive (CD), and are shown to be well suited to the two limiting situations where the rf quasilinear diffusion coefficient is either relatively small, D rf ≅0.1, or very large, D rf →∞, the latter case enabling a special treatment. Results are given for both LHCD and ECCD in the small D rf case, whereas the limiting situation is illustrated only for ECCD. To check the accuracy of path-sum calculations, comparisons with finite difference solutions are provided

  14. Spectral representation and QCD sum rules in hot nuclear matter

    International Nuclear Information System (INIS)

    Mallik, S.; Sarkar, Sourav

    2009-01-01

    We construct the spectral representation of spinsor two-point functions in medium, that is, at finite temperature and chemical potential. We first deal with the free spinor two-point function. Then we construct the same for interacting fields leading to the Kaellen-Lehmann representation. It is emphasised that although these two point functions have the structure of 2 x 2 matrices in the real time formulation of field theory, any one component actually suffices to describe the dynamics of the system. Our construction is then applied to write the QCD sum rules for two-point function of nucleon currents in medium. We discuss a subtracted version to increase the sensitivity of such a sum rule and point out how it differs from a conventional one. (author)

  15. Direct sum matrix game with prisoner's dilemma and snowdrift game.

    Directory of Open Access Journals (Sweden)

    Chengzhang Ma

    Full Text Available A direct sum form is proposed for constructing a composite game from two 2 x 2 games, prisoner's dilemma and snowdrift game. This kind of direct sum form game is called a multiple roles game. The replicator dynamics of the multiple roles game with will-mixed populations is explored. The dynamical behaviors on square lattice are investigated by numerical simulation. It is found that the dynamical behaviors of population on square lattice depend on the mixing proportion of the two simple games. Mixing SD activities to pure PD population inhibits the proportion of cooperators in PD, and mixing PD activities to pure SD population stimulates the proportion of cooperators in SD. Besides spatial reciprocity, our results show that there are roles reciprocities between different types of individuals.

  16. Summability calculus a comprehensive theory of fractional finite sums

    CERN Document Server

    Alabdulmohsin, Ibrahim M

    2018-01-01

    This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergr...

  17. Parton model (Moessbauer) sum rules for b → c decays

    International Nuclear Information System (INIS)

    Lipkin, H.J.

    1993-01-01

    The parton model is a starting point or zero-order approximation in many treatments. The author follows an approach previously used for the Moessbauer effect and shows how parton model sum rules derived for certain moments of the lepton energy spectrum in b → c semileptonic decays remain valid even when binding effects are included. The parton model appears as a open-quote semiclassical close-quote model whose results for certain averages also hold (correspondence principle) in quantum mechanics. Algebraic techniques developed for the Moessbauer effect exploit simple features of the commutator between the weak current operator and the bound state Hamiltonian to find the appropriate sum rules and show the validity of the parton model in the classical limit, ℎ → 0, where all commutators vanish

  18. One-Loop BPS amplitudes as BPS-state sums

    CERN Document Server

    Angelantonj, Carlo; Pioline, Boris

    2012-01-01

    Recently, we introduced a new procedure for computing a class of one-loop BPS-saturated amplitudes in String Theory, which expresses them as a sum of one-loop contributions of all perturbative BPS states in a manifestly T-duality invariant fashion. In this paper, we extend this procedure to all BPS-saturated amplitudes of the form \\int_F \\Gamma_{d+k,d} {\\Phi}, with {\\Phi} being a weak (almost) holomorphic modular form of weight -k/2. We use the fact that any such {\\Phi} can be expressed as a linear combination of certain absolutely convergent Poincar\\'e series, against which the fundamental domain F can be unfolded. The resulting BPS-state sum neatly exhibits the singularities of the amplitude at points of gauge symmetry enhancement, in a chamber-independent fashion. We illustrate our method with concrete examples of interest in heterotic string compactifications.

  19. Fast Inference with Min-Sum Matrix Product.

    Science.gov (United States)

    Felzenszwalb, Pedro F; McAuley, Julian J

    2011-12-01

    The MAP inference problem in many graphical models can be solved efficiently using a fast algorithm for computing min-sum products of n × n matrices. The class of models in question includes cyclic and skip-chain models that arise in many applications. Although the worst-case complexity of the min-sum product operation is not known to be much better than O(n(3)), an O(n(2.5)) expected time algorithm was recently given, subject to some constraints on the input matrices. In this paper, we give an algorithm that runs in O(n(2) log n) expected time, assuming that the entries in the input matrices are independent samples from a uniform distribution. We also show that two variants of our algorithm are quite fast for inputs that arise in several applications. This leads to significant performance gains over previous methods in applications within computer vision and natural language processing.

  20. QCD sum rules for the decay amplitudes of pseudoscalar mesons

    International Nuclear Information System (INIS)

    Narison, S.

    1981-07-01

    Bounds on the π and K meson decay amplitudes are obtained to a good accuracy from QCD sum rules of the Laplace transform type. A relation between fsub(π) and the rho meson coupling to the photon is given. Using the heavy quarks q 2 =0 sum rule to two loops we find our best bounds: fsub(D) approximately < (101+-25) MeV and fsub(F) approximately < (147+-41.6) MeV to be compared to fsub(π) approximately 93.3 MeV. We also derive a relation between the D and F meson masses and the charm quark mass. Our results are extended to the beautiful B mesons. (author)

  1. The partially alternating ternary sum in an associative dialgebra

    International Nuclear Information System (INIS)

    Bremner, Murray R; Sanchez-Ortega, Juana

    2010-01-01

    The alternating ternary sum in an associative algebra, abc - acb - bac + bca + cab - cba, gives rise to the partially alternating ternary sum in an associative dialgebra with products dashv and vdash by making the argument a the center of each term. We use computer algebra to determine the polynomial identities in degree ≤9 satisfied by this new trilinear operation. In degrees 3 and 5, these identities define a new variety of partially alternating ternary algebras. We show that there is a 49-dimensional space of multilinear identities in degree 7, and we find equivalent nonlinear identities. We use the representation theory of the symmetric group to show that there are no new identities in degree 9.

  2. Sum rule limitations of kinetic particle-production models

    International Nuclear Information System (INIS)

    Knoll, J.; CEA Centre d'Etudes Nucleaires de Grenoble, 38; Guet, C.

    1988-04-01

    Photoproduction and absorption sum rules generalized to systems at finite temperature provide a stringent check on the validity of kinetic models for the production of hard photons in intermediate energy nuclear collisions. We inspect such models for the case of nuclear matter at finite temperature employed in a kinetic regime which copes those encountered in energetic nuclear collisions, and find photon production rates which significantly exceed the limits imposed by the sum rule even under favourable concession. This suggests that coherence effects are quite important and the production of photons cannot be considered as an incoherent addition of individual NNγ production processes. The deficiencies of present kinetic models may also apply for the production of probes such as the pion which do not couple perturbatively to the nuclear currents. (orig.)

  3. Spectral function sum rules in quantum chromodynamics. I. Charged currents sector

    International Nuclear Information System (INIS)

    Floratos, E.G.; Narison, Stephan; Rafael, Eduardo de.

    1978-07-01

    The Weinberg sum rules of the algebra of currents are reconsidered in the light of quantum chromodynamics (QCD). The authors derive new finite energy sum rules which replace the old Weinberg sum rules. The new sum rules are convergent and the rate of convergence is explicitly calculated in perturbative QCD at the one loop approximation. Phenomenological applications of these sum rules in the charged current sector are also discussed

  4. Inequalities for finite trigonometric sums. An interplay: with some series related to harmonic numbers

    Directory of Open Access Journals (Sweden)

    Omran Kouba

    2016-07-01

    Full Text Available Abstract An interplay between the sum of certain series related to harmonic numbers and certain finite trigonometric sums is investigated. This allows us to express the sum of these series in terms of the considered trigonometric sums, and permits us to find sharp inequalities bounding these trigonometric sums. In particular, this answers positively an open problem of Chen (Excursions in Classical Analysis, 2010.

  5. More sum rules for quark and lepton masses

    International Nuclear Information System (INIS)

    Terazawa, Hidezumi.

    1990-04-01

    Sum rules for quark and lepton masses are derived from the Ward identity of Chanowitz and Ellis for the vertex function of the trace of the energy-momentum tensor and the two axial-vector currents and the partially conserved axial-vector current hypothesis. They indicate, among other things, that the constituent quark masses of u and d and those of the techniquarks, if any, are about 300 MeV and 300 GeV, respectively. (author)

  6. On degree sums of a triangle-free graph

    DEFF Research Database (Denmark)

    Brandt, Stephan; Harant, J.; Naumann, S.

    2014-01-01

    For a simple triangle-free k-chromatic graph G with k >= 2 the upper bound m(n-f (k-2)) on the sum Sigma(2)(G) = Sigma(x is an element of V(G))d(2)(x) of the squares of the degrees of G is proved, where n, m, and f(1) are the order of G, the size of G, and the minimum order of a triangle-free l-c...

  7. Algebraic K-theory and sums-of-squares formulas

    OpenAIRE

    Dugger, Daniel; Isaksen, Daniel C.

    2004-01-01

    We prove a result about the non-existence of certain sums-of-squares formulas over a field. This generalizes an old theorem which used topological K-theory to obtain obstruction conditions when the field is the real numbers. Our result applies to arbitrary fields not of characteristic 2, making use of algebraic K-theory in place of topological K-theory.

  8. Modified Adler sum rule and violation of charge symmetry

    International Nuclear Information System (INIS)

    Dominguez, C.A.; Moreno, H.; Zepeda, A.

    The consequences of a once subtracted dispersion relation in the derivation of the Adler sum rule are investigated. It is shown that one can expect a breakdown of charge symmetry, of the isotriplet current hypothesis, and of scaling of the structure functions. These breakdowns are related to the possible presence of a non-zero subtraction function at asymptotic energies and arbitrary q 2 . Second class currents and PCAC relations are also discussed

  9. Signal anomaly detection using modified CUSUM [cumulative sum] method

    International Nuclear Information System (INIS)

    Morgenstern, V.; Upadhyaya, B.R.; Benedetti, M.

    1988-01-01

    An important aspect of detection of anomalies in signals is the identification of changes in signal behavior caused by noise, jumps, changes in band-width, sudden pulses and signal bias. A methodology is developed to identify, isolate and characterize these anomalies using a modification of the cumulative sum (CUSUM) approach. The new algorithm performs anomaly detection at three levels and is implemented on a general purpose computer. 7 refs., 4 figs

  10. Approximation of sums of oscillating summands in certain physical problems

    International Nuclear Information System (INIS)

    Karatsuba, Ekatherina A.

    2004-01-01

    The motion of a one-dimensional harmonic oscillator caused by recurring pushes in the absence of friction is considered. In particular, two cases are studied: the case when the pushes become more frequent and the other one when the pushes become less frequent. By means of an application of the Hardy-Littlewood-Vinogradov-Van der Corput theorem on the approximation of exponential sums by shorter ones, new asymptotic formulas for the solution of the problem are obtained

  11. Finite temperature QCD sum rule and the ρ-meson

    International Nuclear Information System (INIS)

    Liu Jueping; Jin Yaping

    1995-01-01

    The contributions from the three-gluon condensates to the finite temperature QCD sum rule for the ρ-meson are calculated, and then the dependence of the properties of the ρ-meson upon temperature is investigated in a string model of condensates. The results show that the parameters characterizing the properties of the ρ-meson change noticeably when the temperature closes to the critical temperature of the condensates, and if the critical temperatures of condensates are the same

  12. Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule.

    Science.gov (United States)

    Cloët, Ian C; Bentz, Wolfgang; Thomas, Anthony W

    2016-01-22

    In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we find a dramatic quenching of the Coulomb sum rule for momentum transfers |q|≳0.5  GeV. The main driver of this effect lies in changes to the proton Dirac form factor induced by the nuclear medium. Such a dramatic quenching of the Coulomb sum rule was not seen in a recent quantum Monte Carlo calculation for carbon, suggesting that the Jefferson Lab data may well shed new light on the explicit role of QCD in nuclei.

  13. Evaluating chiral symmetry restoration through the use of sum rules

    Directory of Open Access Journals (Sweden)

    Rapp Ralf

    2012-11-01

    Full Text Available We pursue the idea of assessing chiral restoration via in-medium modifications of hadronic spectral functions of chiral partners. The usefulness of sum rules in this endeavor is illustrated, focusing on the vector/axial-vector channel. We first present an update on obtaining quantitative results for pertinent vacuum spectral functions. These serve as a basis upon which the in-medium spectral functions can be constructed. A novel feature of our analysis of the vacuum spectral functions is the need to include excited resonances, dictated by satisfying the Weinberg-type sum rules. This includes excited states in both the vector and axial-vector channels.We also analyze the QCD sum rule for the finite temperature vector spectral function, based on a ρ spectral function tested in dilepton data which develops a shoulder at low energies.We find that the ρ′ peak flattens off which may be a sign of chiral restoration, though a study of the finite temperature axial-vector spectral function remains to be carried out.

  14. Sum-Trigger-II status and prospective physics

    Energy Technology Data Exchange (ETDEWEB)

    Dazzi, Francesco; Mirzoyan, Razmik; Schweizer, Thomas; Teshima, Masahiro [Max Planck Institut fuer Physik, Munich (Germany); Herranz, Diego; Lopez, Marcos [Universidad Complutense, Madrid (Spain); Mariotti, Mose [Universita degli Studi di Padova (Italy); Nakajima, Daisuke [The University of Tokio (Japan); Rodriguez Garcia, Jezabel [Max Planck Institut fuer Physik, Munich (Germany); Instituto Astrofisico de Canarias, Tenerife (Spain)

    2015-07-01

    MAGIC is a stereoscopic system of 2 Imaging Air Cherenkov Telescopes (IACTs) for very high energy gamma-ray astronomy, located at La Palma (Spain). Lowering the energy threshold of IACTs is crucial for the observation of Pulsars, high redshift AGNs and GRBs. A novel trigger strategy, based on the analogue sum of a patch of pixels, can lead to a lower threshold compared to conventional digital triggers. In the last years, a major upgrade of the MAGIC telescopes took place in order to optimize the performances, mainly in the low energy domain. The PMTs camera and the reflective surface of MAGIC-I, as well as both readout systems, have been deeply renovated. The last important milestone is the implementation of a new stereoscopic analogue trigger, dubbed Sum-Trigger-II. The installation successfully ended in 2014 and the first data set has been already taken. Currently the fine-tuning of the main parameters as well as the comparison with Monte Carlo studies is ongoing. In this talk the status of Sum-Trigger-II and the future prospective physics cases at very low energy are presented.

  15. On the Latent Variable Interpretation in Sum-Product Networks.

    Science.gov (United States)

    Peharz, Robert; Gens, Robert; Pernkopf, Franz; Domingos, Pedro

    2017-10-01

    One of the central themes in Sum-Product networks (SPNs) is the interpretation of sum nodes as marginalized latent variables (LVs). This interpretation yields an increased syntactic or semantic structure, allows the application of the EM algorithm and to efficiently perform MPE inference. In literature, the LV interpretation was justified by explicitly introducing the indicator variables corresponding to the LVs' states. However, as pointed out in this paper, this approach is in conflict with the completeness condition in SPNs and does not fully specify the probabilistic model. We propose a remedy for this problem by modifying the original approach for introducing the LVs, which we call SPN augmentation. We discuss conditional independencies in augmented SPNs, formally establish the probabilistic interpretation of the sum-weights and give an interpretation of augmented SPNs as Bayesian networks. Based on these results, we find a sound derivation of the EM algorithm for SPNs. Furthermore, the Viterbi-style algorithm for MPE proposed in literature was never proven to be correct. We show that this is indeed a correct algorithm, when applied to selective SPNs, and in particular when applied to augmented SPNs. Our theoretical results are confirmed in experiments on synthetic data and 103 real-world datasets.

  16. Simulation approach to coincidence summing in {gamma}-ray spectrometry

    Energy Technology Data Exchange (ETDEWEB)

    Dziri, S., E-mail: samir.dziri@iphc.cnrs.fr [Groupe RaMsEs, Institut Pluridisciplinaire Hubert Curien (IPHC), University of Strasbourg, CNRS, IN2P3, UMR 7178, 23 rue de Loess, BP 28, 67037 Strasbourg Cedex 2 (France); Nourreddine, A.; Sellam, A.; Pape, A.; Baussan, E. [Groupe RaMsEs, Institut Pluridisciplinaire Hubert Curien (IPHC), University of Strasbourg, CNRS, IN2P3, UMR 7178, 23 rue de Loess, BP 28, 67037 Strasbourg Cedex 2 (France)

    2012-07-15

    Some of the radionuclides used for efficiency calibration of a HPGe spectrometer are subject to coincidence-summing (CS) and account must be taken of the phenomenon to obtain quantitative results when counting samples to determine their activity. We have used MCNPX simulations, which do not take CS into account, to obtain {gamma}-ray peak intensities that were compared to those observed experimentally. The loss or gain of a measured peak intensity relative to the simulated peak is attributed to CS. CS correction factors are compared with those of ETNA and GESPECOR. Application to a test sample prepared with known radionuclides gave values close to the published activities. - Highlights: Black-Right-Pointing-Pointer Coincidence summing occurs when the solid angle is increased. Black-Right-Pointing-Pointer The loss of counts gives rise to an approximative efficiency curves, this means a wrong quantitative data. Black-Right-Pointing-Pointer To overcome this problem we need mono-energetic source, otherwise, the MCNPX simulation allows by comparison with the experiment data to get the coincidence summing correction factors. Black-Right-Pointing-Pointer By multiplying these factors by the approximative efficiency, we obtain the accurate efficiency.

  17. B --> K$*\\gamma$ from hybrid sum rule

    CERN Document Server

    Narison, Stéphan

    1994-01-01

    Using the {\\it hybrid} moments-Laplace sum rule (HSR), which is well-defined for M_b \\rar \\infty, in contrast with the popular double Borel (Laplace) sum rule (DLSR), which blows up in this limit when applied to the heavy-to-light processes, we show that the form factor of the B \\rar K^* \\ \\gamma radiative transition is dominated by the light-quark condensate for M_b \\rar \\infty and behaves like \\sqrt M_b. The form factor is found to be F^{B\\rar K^*}_1(0) \\simeq (30.8 \\pm 1.3 \\pm 3.6 \\pm 0.6)\\times 10^{-2}, where the errors come respectively from the procedure in the sum rule analysis, the errors in the input and in the SU(3)_f-breaking parameters. This result leads to Br(B\\rar K^* \\ \\gamma) \\simeq (4.45 \\pm 1.12) \\times 10^{-5} in agreement with the recent CLEO data. Parametrization of the M_b-dependence of the form factor including the SU(3)_f-breaking effects is given in (26), which leads to F^{B\\rar K^*}_1(0)/ F^{B\\rar \\rho}_1(0) \\simeq (1.14 \\pm 0.02).

  18. Spectral energy transfer of atmospheric gravity waves through sum and difference nonlinear interactions

    Energy Technology Data Exchange (ETDEWEB)

    Huang, K.M. [Wuhan Univ. (China). School of Electronic Information; Chinese Academey of Sciences, Hefei (China). Key Lab. of Geospace Environment; Embry Riddle Aeronautical Univ., Daytona Beach, FL (United States). Dept. of Physical Science; Ministry of Education, Wuhan (China). Key Lab. of Geospace Environment and Geodesy; State Observatory for Atmospheric Remote Sensing, Wuhan (China); Liu, A.Z.; Li, Z. [Embry Riddle Aeronautical Univ., Daytona Beach, FL (United States). Dept. of Physical Science; Zhang, S.D.; Yi, F. [Wuhan Univ. (China). School of Electronic Information; Ministry of Education, Wuhan (China). Key Lab. of Geospace Environment and Geodesy; State Observatory for Atmospheric Remote Sensing, Wuhan (China)

    2012-07-01

    Nonlinear interactions of gravity waves are studied with a two-dimensional, fully nonlinear model. The energy exchanges among resonant and near-resonant triads are examined in order to understand the spectral energy transfer through interactions. The results show that in both resonant and near-resonant interactions, the energy exchange between two high frequency waves is strong, but the energy transfer from large to small vertical scale waves is rather weak. This suggests that the energy cascade toward large vertical wavenumbers through nonlinear interaction is inefficient, which is different from the rapid turbulence cascade. Because of considerable energy exchange, nonlinear interactions can effectively spread high frequency spectrum, and play a significant role in limiting wave amplitude growth and transferring energy into higher altitudes. In resonant interaction, the interacting waves obey the resonant matching conditions, and resonant excitation is reversible, while near-resonant excitation is not so. Although near-resonant interaction shows the complexity of match relation, numerical experiments show an interesting result that when sum and difference near-resonant interactions occur between high and low frequency waves, the wave vectors tend to approximately match in horizontal direction, and the frequency of the excited waves is also close to the matching value. (orig.)

  19. A vibration energy harvesting device with bidirectional resonance frequency tunability

    International Nuclear Information System (INIS)

    Challa, Vinod R; Prasad, M G; Shi Yong; Fisher, Frank T

    2008-01-01

    Vibration energy harvesting is an attractive technique for potential powering of wireless sensors and low power devices. While the technique can be employed to harvest energy from vibrations and vibrating structures, a general requirement independent of the energy transfer mechanism is that the vibration energy harvesting device operate in resonance at the excitation frequency. Most energy harvesting devices developed to date are single resonance frequency based, and while recent efforts have been made to broaden the frequency range of energy harvesting devices, what is lacking is a robust tunable energy harvesting technique. In this paper, the design and testing of a resonance frequency tunable energy harvesting device using a magnetic force technique is presented. This technique enabled resonance tuning to ± 20% of the untuned resonant frequency. In particular, this magnetic-based approach enables either an increase or decrease in the tuned resonant frequency. A piezoelectric cantilever beam with a natural frequency of 26 Hz is used as the energy harvesting cantilever, which is successfully tuned over a frequency range of 22–32 Hz to enable a continuous power output 240–280 µW over the entire frequency range tested. A theoretical model using variable damping is presented, whose results agree closely with the experimental results. The magnetic force applied for resonance frequency tuning and its effect on damping and load resistance have been experimentally determined

  20. Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect

    Energy Technology Data Exchange (ETDEWEB)

    Golkar, Siavash; Nguyen, Dung X.; Son, Dam T. [Enrico Fermi Institute, James Franck Institute and Department of Physics,University of Chicago, Chicago, Illinois 60637 (United States)

    2016-01-05

    We consider gapped fractional quantum Hall states on the lowest Landau level when the Coulomb energy is much smaller than the cyclotron energy. We introduce two spectral densities, ρ{sub T}(ω) and ρ̄{sub T}(ω), which are proportional to the probabilities of absorption of circularly polarized gravitons by the quantum Hall system. We prove three sum rules relating these spectral densities with the shift S, the q{sup 4} coefficient of the static structure factor S{sub 4}, and the high-frequency shear modulus of the ground state μ{sub ∞}, which is precisely defined. We confirm an inequality, first suggested by Haldane, that S{sub 4} is bounded from below by |S−1|/8. The Laughlin wavefunction saturates this bound, which we argue to imply that systems with ground state wavefunctions close to Laughlin’s absorb gravitons of predominantly one circular polarization. We consider a nonlinear model where the sum rules are saturated by a single magneto-roton mode. In this model, the magneto-roton arises from the mixing between oscillations of an internal metric and the hydrodynamic motion. Implications for experiments are briefly discussed.

  1. Implementation of Layered Decoding Architecture for LDPC Code using Layered Min-Sum Algorithm

    Directory of Open Access Journals (Sweden)

    Sandeep Kakde

    2017-12-01

    Full Text Available For binary field and long code lengths, Low Density Parity Check (LDPC code approaches Shannon limit performance. LDPC codes provide remarkable error correction performance and therefore enlarge the design space for communication systems.In this paper, we have compare different digital modulation techniques and found that BPSK modulation technique is better than other modulation techniques in terms of BER. It also gives error performance of LDPC decoder over AWGN channel using Min-Sum algorithm. VLSI Architecture is proposed which uses the value re-use property of min-sum algorithm and gives high throughput. The proposed work has been implemented and tested on Xilinx Virtex 5 FPGA. The MATLAB result of LDPC decoder for low bit error rate (BER gives bit error rate in the range of 10-1 to 10-3.5 at SNR=1 to 2 for 20 no of iterations. So it gives good bit error rate performance. The latency of the parallel design of LDPC decoder has also reduced. It has accomplished 141.22 MHz maximum frequency and throughput of 2.02 Gbps while consuming less area of the design.

  2. Interference Mitigation and Sum Rate Optimization for MIMO Downlink Small Cells

    Directory of Open Access Journals (Sweden)

    H. H. Kha

    2016-12-01

    Full Text Available This paper addresses interference issues in multiuser multiple-input multiple-output (MIMO downlink heterogeneous networks in which multiple small cells are deployed in macrocell coverage. With the higher priority to access the frequency bands, the macro base station (MBS will exploit eigenmode transmission along with water-filling based power allocation to maximize its data rate. To avoid harmful interference to macro users, we propose structures of the precoders at the small cell BSs (SBSs as cascades of two precoding matrices. In addition, to mitigate intra-tier inference in small cells, the SBSs exploit the user scheduling schemes for their associated users. We investigate two user scheduling schemes using the minimum interference leakage and maximum signal to noise ratio criteria. The sum rate of the selected users can be further improved by power allocation. We develop an iterative algorithm using difference of convex functions (d.c. programming to tackle the mathematical challenges of the nonconvex power allocation problem, Numerical simulation results show that the proposed strategy outperforms the conventional methods in terms of the achievable sum rate.

  3. Generalization of the Lord-Wingersky Algorithm to Computing the Distribution of Summed Test Scores Based on Real-Number Item Scores

    Science.gov (United States)

    Kim, Seonghoon

    2013-01-01

    With known item response theory (IRT) item parameters, Lord and Wingersky provided a recursive algorithm for computing the conditional frequency distribution of number-correct test scores, given proficiency. This article presents a generalized algorithm for computing the conditional distribution of summed test scores involving real-number item…

  4. Primal Decomposition-Based Method for Weighted Sum-Rate Maximization in Downlink OFDMA Systems

    Directory of Open Access Journals (Sweden)

    Weeraddana Chathuranga

    2010-01-01

    Full Text Available We consider the weighted sum-rate maximization problem in downlink Orthogonal Frequency Division Multiple Access (OFDMA systems. Motivated by the increasing popularity of OFDMA in future wireless technologies, a low complexity suboptimal resource allocation algorithm is obtained for joint optimization of multiuser subcarrier assignment and power allocation. The algorithm is based on an approximated primal decomposition-based method, which is inspired from exact primal decomposition techniques. The original nonconvex optimization problem is divided into two subproblems which can be solved independently. Numerical results are provided to compare the performance of the proposed algorithm to Lagrange relaxation based suboptimal methods as well as to optimal exhaustive search-based method. Despite its reduced computational complexity, the proposed algorithm provides close-to-optimal performance.

  5. Sum rates of asynchronous GFDMA and SC-FDMA for 5G uplink

    Directory of Open Access Journals (Sweden)

    Woojin Park

    2015-12-01

    Full Text Available The fifth generation (5G of mobile communication envisions ultralow latency less than 1 ms for radio interface. To this end, frameless asynchronous multiple access may be needed to allow users to transmit instantly without waiting for the next frame start. In this paper, generalized frequency division multiple-access (GFDMA, one of the promising multiple-access candidates for 5G mobile, is compared with the conventional single-carrier FDMA (SC-FDMA in terms of the uplink sum rate when both techniques are adapted for the asynchronous scenario. In particular, a waveform windowing technique is applied to both schemes to mitigate the inter-user interference due to non-zero out-of-band emission.

  6. What do QCD sum rules tell us about dense matter?

    International Nuclear Information System (INIS)

    Cohen, T.D.; Washington Univ., Seattle, WA

    1995-01-01

    The QCD sum rule approach to the properties of hadrons in both the vacuum and in nuclear matter is discussed. The primary limitation for the nuclear matter case is the absence of reliable phenomenological information about the form of the spectral function and about the value of certain four quark condensates. The approach gives moderate evidence in support of the Dirac phenomenology picture of strong attractive Lorentz scalar and repulsive Lorentz vector optical potentials. The approach gives weak evidence for decreasing vector meson masses in medium. (orig.)

  7. Cyclotomy and Ramanujan sums in quantum phase locking

    International Nuclear Information System (INIS)

    Planat, Michel; Rosu, Haret C.

    2003-01-01

    Phase-locking governs the phase noise in classical clocks through effects described in precise mathematical terms. We seek here a quantum counterpart of these effects by working in a finite Hilbert space. We use a coprimality condition to define phase-locked quantum states and the corresponding Pegg-Barnett type phase operator. Cyclotomic symmetries in matrix elements are revealed and related to Ramanujan sums in the theory of prime numbers. The employed mathematical procedures also emphasize the isomorphism between algebraic number theory and the theory of quantum entanglement

  8. Optimum amount of an insurance sum in life insurance

    Directory of Open Access Journals (Sweden)

    Janez Balkovec

    2001-01-01

    Full Text Available Personal insurance represents one of the sources of personal social security as a category of personal property. How to get a proper life insurance is a frequently asked question. When insuring material objects (car, house..., the problem is usually not in the amount of the taken insurance. With life insurance (abstract goods, problems as such occur. In this paper, we wish to present a model that, according to the financial situation and the anticipated future, makes it possible to calculate the optimum insurance sum in life insurance.

  9. Sum rules and exclusive processes in quantum chromodynamics

    International Nuclear Information System (INIS)

    Radyushkin, A.V.

    1983-01-01

    A brief review of results of analyzing hadron form factors is presented. The analysis of hardron form factors was conducted by the method of QCD sum rules. The method is based on the concept of quark-hadron duality. Correlation of calculation results with available experimental data was performed. The conclusion is made that it is sufficient to consider only the contribution of the simplest diagrams which don't contain gluon exchanges in order to describe experimental data on pion, proton and neutron form factors

  10. Automatic oscillator frequency control system

    Science.gov (United States)

    Smith, S. F. (Inventor)

    1985-01-01

    A frequency control system makes an initial correction of the frequency of its own timing circuit after comparison against a frequency of known accuracy and then sequentially checks and corrects the frequencies of several voltage controlled local oscillator circuits. The timing circuit initiates the machine cycles of a central processing unit which applies a frequency index to an input register in a modulo-sum frequency divider stage and enables a multiplexer to clock an accumulator register in the divider stage with a cyclical signal derived from the oscillator circuit being checked. Upon expiration of the interval, the processing unit compares the remainder held as the contents of the accumulator against a stored zero error constant and applies an appropriate correction word to a correction stage to shift the frequency of the oscillator being checked. A signal from the accumulator register may be used to drive a phase plane ROM and, with periodic shifts in the applied frequency index, to provide frequency shift keying of the resultant output signal. Interposition of a phase adder between the accumulator register and phase plane ROM permits phase shift keying of the output signal by periodic variation in the value of a phase index applied to one input of the phase adder.

  11. Computing the Distribution of Pareto Sums Using Laplace Transformation and Stehfest Inversion

    Science.gov (United States)

    Harris, C. K.; Bourne, S. J.

    2017-05-01

    In statistical seismology, the properties of distributions of total seismic moment are important for constraining seismological models, such as the strain partitioning model (Bourne et al. J Geophys Res Solid Earth 119(12): 8991-9015, 2014). This work was motivated by the need to develop appropriate seismological models for the Groningen gas field in the northeastern Netherlands, in order to address the issue of production-induced seismicity. The total seismic moment is the sum of the moments of individual seismic events, which in common with many other natural processes, are governed by Pareto or "power law" distributions. The maximum possible moment for an induced seismic event can be constrained by geomechanical considerations, but rather poorly, and for Groningen it cannot be reliably inferred from the frequency distribution of moment magnitude pertaining to the catalogue of observed events. In such cases it is usual to work with the simplest form of the Pareto distribution without an upper bound, and we follow the same approach here. In the case of seismicity, the exponent β appearing in the power-law relation is small enough for the variance of the unbounded Pareto distribution to be infinite, which renders standard statistical methods concerning sums of statistical variables, based on the central limit theorem, inapplicable. Determinations of the properties of sums of moderate to large numbers of Pareto-distributed variables with infinite variance have traditionally been addressed using intensive Monte Carlo simulations. This paper presents a novel method for accurate determination of the properties of such sums that is accurate, fast and easily implemented, and is applicable to Pareto-distributed variables for which the power-law exponent β lies within the interval [0, 1]. It is based on shifting the original variables so that a non-zero density is obtained exclusively for non-negative values of the parameter and is identically zero elsewhere, a property

  12. Spin Sum Rules and Polarizabilities: Results from Jefferson Lab

    International Nuclear Information System (INIS)

    Jian-Ping Chen

    2006-01-01

    The nucleon spin structure has been an active, exciting and intriguing subject of interest for the last three decades. Recent experimental data on nucleon spin structure at low to intermediate momentum transfers provide new information in the confinement regime and the transition region from the confinement regime to the asymptotic freedom regime. New insight is gained by exploring moments of spin structure functions and their corresponding sum rules (i.e. the generalized Gerasimov-Drell-Hearn, Burkhardt-Cottingham and Bjorken). The Burkhardt-Cottingham sum rule is verified to good accuracy. The spin structure moments data are compared with Chiral Perturbation Theory calculations at low momentum transfers. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function g 1 at momentum transfer of 0.05 to 0.1 GeV 2 but fail to reproduce the neutron data in the case of the generalized polarizability (delta) LT (the (delta) LT puzzle). New data have been taken on the neutron ( 3 He), the proton and the deuteron at very low Q 2 down to 0.02 GeV 2 . They will provide benchmark tests of Chiral dynamics in the kinematic region where the Chiral Perturbation theory is expected to work

  13. Strategy complexity of two-player, zero-sum games

    DEFF Research Database (Denmark)

    Ibsen-Jensen, Rasmus

    on the algorithms. I consider a wide assortment of different two-player, zero-sum game classes, e.g. matrix games, uni-chain concurrent mean-payoff games, concurrent mean-payoff games, concurrent reachability games and one-clock priced timed games. In all game classes considered, except for one-clock priced timed...... non-zero probability used in one of the probability distributions. In each case I provide relatively tight bounds on the patience of the “good” strategy that requires the least patience in the worst game of the game class. I will give an improved bound on the patience of concurrent reachability games......This dissertation considers two-player, zero-sum games with a focus on how complicated they are to play; a notion I will call strategy complexity. Often, knowing good bounds on the strategy complexity indicates bounds on the run time of various algorithms. In such cases I will also derive bounds...

  14. Efficient Strategy Computation in Zero-Sum Asymmetric Repeated Games

    KAUST Repository

    Li, Lichun

    2017-03-06

    Zero-sum asymmetric games model decision making scenarios involving two competing players who have different information about the game being played. A particular case is that of nested information, where one (informed) player has superior information over the other (uninformed) player. This paper considers the case of nested information in repeated zero-sum games and studies the computation of strategies for both the informed and uninformed players for finite-horizon and discounted infinite-horizon nested information games. For finite-horizon settings, we exploit that for both players, the security strategy, and also the opponent\\'s corresponding best response depend only on the informed player\\'s history of actions. Using this property, we refine the sequence form, and formulate an LP computation of player strategies that is linear in the size of the uninformed player\\'s action set. For the infinite-horizon discounted game, we construct LP formulations to compute the approximated security strategies for both players, and provide a bound on the performance difference between the approximated security strategies and the security strategies. Finally, we illustrate the results on a network interdiction game between an informed system administrator and uniformed intruder.

  15. Borel sum rules for octet baryons in nuclear medium

    International Nuclear Information System (INIS)

    Kondo, Y.; Morimatsu, O.

    1992-06-01

    Borel sum rules are examined for octet baryons in the nuclear medium. First, it is noticed that in the medium the dispersion relation is realized for the retarded correlation Π R (ω, q 2 ) in the energy ω. Then, Π R (ω, q 2 ) is split into even and odd parts of ω in order to apply the Borel transformation. The obtained Borel sum rules differ from those of previous works. The mass shifts of octet baryons are calculated in the leading order of the operator product expansion with linear density approximation for the condensates. It is found that both scalar and vector condensates of the quark field, and + q>, induce attraction to the octet baryons in the medium in contrast to the results of previous works. It is also found that |δM N | > |δM Λ | > |δM Σ | ∼ |δM Ξ |. The absolute values, however, turn out to be one order of magnitude larger than those empirically known if a Borel mass of around 1 GeV is used in the present approximation. (author)

  16. Bottom mass from nonrelativistic sum rules at NNLL

    Energy Technology Data Exchange (ETDEWEB)

    Stahlhofen, Maximilian

    2013-01-15

    We report on a recent determination of the bottom quark mass from nonrelativistic (large-n) {Upsilon} sum rules with renormalization group improvement (RGI) at next-to-next-to-leading logarithmic (NNLL) order. The comparison to previous fixed-order analyses shows that the RGI computed in the vNRQCD framework leads to a substantial stabilization of the theoretical sum rule moments with respect to scale variations. A single moment fit (n=10) to the available experimental data yields M{sub b}{sup 1S}=4.755{+-}0.057{sub pert}{+-}0.009{sub {alpha}{sub s}}{+-}0.003{sub exp} GeV for the bottom 1S mass and anti m{sub b}(anti m{sub b})=4.235{+-}0.055{sub pert}{+-}0.003{sub exp} GeV for the bottom MS mass. The quoted uncertainties refer to the perturbative error and the uncertainties associated with the strong coupling and the experimental input.

  17. Renormalized sum rules for structure functions of heavy meson decays

    International Nuclear Information System (INIS)

    Grozin, A.G.; Korchemsky, G.P.

    1996-01-01

    We consider the properties of the structure functions of inclusive heavy meson decays B→X c and treat the c quark mass as a free parameter. We show that in two extreme cases of heavy and light c quarks the structure functions of heavy-heavy and heavy-light transitions are given by a Fourier transform of the matrix elements of Wilson lines containing a timelike and a lightlike segment, correspondingly. Using the renormalization properties of Wilson lines we find the dependence of the structure functions on the factorization scale, the structure function of the heavy-heavy transition is renormalized multiplicatively, while that of the heavy-light transition obeys the GLAP-type evolution equation. We propose a generalization of the sum rules for the moments of the structure functions (Bjorken, Voloshin, and the open-quote open-quote third close-quote close-quote sum rules) with a soft exponential factorization cutoff, which correctly incorporates both perturbative and nonperturbative effects. We analyze nonperturbative corrections by first considering infrared renormalon contributions to the Wilson lines. Uncertainties induced by the leading renormalon pole at u=1/2 are exactly canceled by a similar uncertainty in the heavy quark pole mass. The leading nonperturbative corrections associated with the next renormalon at u=1 are parametrized by the matrix element μ π 2 which is proportional to the heavy quark kinetic energy. copyright 1996 The American Physical Society

  18. Spectral sum rules and search for periodicities in DNA sequences

    International Nuclear Information System (INIS)

    Chechetkin, V.R.

    2011-01-01

    Periodic patterns play the important regulatory and structural roles in genomic DNA sequences. Commonly, the underlying periodicities should be understood in a broad statistical sense, since the corresponding periodic patterns have been strongly distorted by the random point mutations and insertions/deletions during molecular evolution. The latent periodicities in DNA sequences can be efficiently displayed by Fourier transform. The criteria of significance for observed periodicities are obtained via the comparison versus the counterpart characteristics of the reference random sequences. We show that the restrictions imposed on the significance criteria by the rigorous spectral sum rules can be rationally described with De Finetti distribution. This distribution provides the convenient intermediate asymptotic form between Rayleigh distribution and exact combinatoric theory. - Highlights: → We study the significance criteria for latent periodicities in DNA sequences. → The constraints imposed by sum rules can be described with De Finetti distribution. → It is intermediate between Rayleigh distribution and exact combinatoric theory. → Theory is applicable to the study of correlations between different periodicities. → The approach can be generalized to the arbitrary discrete Fourier transform.

  19. On the divergence of triangular and eccentric spherical sums of double Fourier series

    Energy Technology Data Exchange (ETDEWEB)

    Karagulyan, G A [Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan (Armenia)

    2016-01-31

    We construct a continuous function on the torus with almost everywhere divergent triangular sums of double Fourier series. We also prove an analogous theorem for eccentric spherical sums. Bibliography: 14 titles.

  20. On the divergence of triangular and eccentric spherical sums of double Fourier series

    International Nuclear Information System (INIS)

    Karagulyan, G A

    2016-01-01

    We construct a continuous function on the torus with almost everywhere divergent triangular sums of double Fourier series. We also prove an analogous theorem for eccentric spherical sums. Bibliography: 14 titles

  1. Frequency conversion of structured light.

    Science.gov (United States)

    Steinlechner, Fabian; Hermosa, Nathaniel; Pruneri, Valerio; Torres, Juan P

    2016-02-15

    Coherent frequency conversion of structured light, i.e. the ability to manipulate the carrier frequency of a wave front without distorting its spatial phase and intensity profile, provides the opportunity for numerous novel applications in photonic technology and fundamental science. In particular, frequency conversion of spatial modes carrying orbital angular momentum can be exploited in sub-wavelength resolution nano-optics and coherent imaging at a wavelength different from that used to illuminate an object. Moreover, coherent frequency conversion will be crucial for interfacing information stored in the high-dimensional spatial structure of single and entangled photons with various constituents of quantum networks. In this work, we demonstrate frequency conversion of structured light from the near infrared (803 nm) to the visible (527 nm). The conversion scheme is based on sum-frequency generation in a periodically poled lithium niobate crystal pumped with a 1540-nm Gaussian beam. We observe frequency-converted fields that exhibit a high degree of similarity with the input field and verify the coherence of the frequency-conversion process via mode projection measurements with a phase mask and a single-mode fiber. Our results demonstrate the suitability of exploiting the technique for applications in quantum information processing and coherent imaging.

  2. Energy-weighted sum rules for mesons in hot and dense matter

    NARCIS (Netherlands)

    Cabrera, D.; Polls, A.; Ramos, A.; Tolos Rigueiro, Laura

    2009-01-01

    We study energy-weighted sum rules of the pion and kaon propagator in nuclear matter at finite temperature. The sum rules are obtained from matching the Dyson form of the meson propagator with its spectral Lehmann representation at low and high energies. We calculate the sum rules for specific

  3. On the coupling of statistic sum of canonical and large canonical ensemble of interacting particles

    International Nuclear Information System (INIS)

    Vall, A.N.

    2000-01-01

    Potentiality of refining the known result based on analytic properties of a great statistical sum, as a function of the absolute activity of the boundary integral contribution into statistical sum, is considered. A strict asymptotic ratio between statistical sums of canonical and large canonical ensemble of interacting particles was derived [ru

  4. A Finer Classification of the Unit Sum Number of the Ring of Integers ...

    Indian Academy of Sciences (India)

    Here we introduce a finer classification for the unit sum number of a ring and in this new classification we completely determine the unit sum number of the ring of integers of a quadratic field. Further we obtain some results on cubic complex fields which one can decide whether the unit sum number is or ∞. Then we ...

  5. Sum rules for baryonic vertex functions and the proton wave function in QCD

    International Nuclear Information System (INIS)

    Lavelle, M.J.

    1985-01-01

    We consider light-cone sum rules for vertex functions involving baryon-meson couplings. These sum rules relate the non-perturbative, and experimentally known, coupling constants to the moments of the wave function of the proton state. Our results for these moments are consistent with those obtained from QCD sum rules for two-point functions. (orig.)

  6. Ordering individuals with sum scores: the introduction of the nonparametric Rasch model

    NARCIS (Netherlands)

    Zwitser, R.J.; Maris, G.

    2016-01-01

    When a simple sum or number-correct score is used to evaluate the ability of individual testees, then, from an accountability perspective, the inferences based on the sum score should be the same as the inferences based on the complete response pattern. This requirement is fulfilled if the sum score

  7. An Efficient Algorithm to Calculate the Minkowski Sum of Convex 3D Polyhedra

    NARCIS (Netherlands)

    Bekker, Henk; Roerdink, Jos B.T.M.

    2001-01-01

    A new method is presented to calculate the Minkowski sum of two convex polyhedra A and B in 3D. These graphs are given edge attributes. From these attributed graphs the attributed graph of the Minkowski sum is constructed. This graph is then transformed into the Minkowski sum of A and B. The running

  8. Frequency standards

    CERN Document Server

    Riehle, Fritz

    2006-01-01

    Of all measurement units, frequency is the one that may be determined with the highest degree of accuracy. It equally allows precise measurements of other physical and technical quantities, whenever they can be measured in terms of frequency.This volume covers the central methods and techniques relevant for frequency standards developed in physics, electronics, quantum electronics, and statistics. After a review of the basic principles, the book looks at the realisation of commonly used components. It then continues with the description and characterisation of important frequency standards

  9. Pixel 2010: A résumé

    CERN Document Server

    Wermes, Norbert

    2011-01-01

    The Pixel 2010 conference focused on semiconductor pixel detectors for particle tracking/vertexing as well as for imaging, in particular for synchrotron light sources and XFELs. The big LHC hybrid pixel detectors have impressively started showing their capabilities. X-ray imaging detectors, also using the hybrid pixel technology, have greatly advanced the experimental possibilities for diffraction experiments. Monolithic or semi-monolithic devices like CMOS active pixels and DEPFET pixels have now reached a state such that complete vertex detectors for RHIC and superKEKB are being built with these technologies. Finally, new advances towards fully monolithic active pixel detectors, featuring full CMOS electronics merged with efficient signal charge collection, exploiting standard CMOS technologies, SOI and/or 3D integration, show the path for the future. This résumé attempts to extract the main statements of the results and developments presented at this conference.

  10. Improved hadronic measurements and spectral sums on the lattice

    Energy Technology Data Exchange (ETDEWEB)

    Hagen, Christian

    2008-05-15

    the order parameter for the confinement-deconfinement transition is the Polyakov loop. The order parameter for the spontaneous breaking of chiral symmetry is given by the chiral condensate, which is related to the eigenvalues of the Dirac operator. It has been shown that also the Polyakov loop can be expressed in terms of these eigenvalues, as a spectral sum. In a first step we perform a numerical study of these sums. We find that the ordinary Polyakov loop is governed by the ultraviolet modes of the Dirac operator. Therefore, in a second step we define a new order parameter for confinement, the ''dressed Polyakov loop''. This quantity has two advantages: It can be expressed as a spectral sum which has a better convergence behavior (infrared dominated) and it is closely related to the quark condensate via a Fourier transformation. Also the spectral sums for the dressed Polyakov loop are investigated numerically. (orig.)

  11. A probabilistic approach of sum rules for heat polynomials

    International Nuclear Information System (INIS)

    Vignat, C; Lévêque, O

    2012-01-01

    In this paper, we show that the sum rules for generalized Hermite polynomials derived by Daboul and Mizrahi (2005 J. Phys. A: Math. Gen. http://dx.doi.org/10.1088/0305-4470/38/2/010) and by Graczyk and Nowak (2004 C. R. Acad. Sci., Ser. 1 338 849) can be interpreted and easily recovered using a probabilistic moment representation of these polynomials. The covariance property of the raising operator of the harmonic oscillator, which is at the origin of the identities proved in Daboul and Mizrahi and the dimension reduction effect expressed in the main result of Graczyk and Nowak are both interpreted in terms of the rotational invariance of the Gaussian distributions. As an application of these results, we uncover a probabilistic moment interpretation of two classical integrals of the Wigner function that involve the associated Laguerre polynomials. (paper)

  12. Origin of the violation of the Gottfried sum rule

    International Nuclear Information System (INIS)

    Hwang, W.P.; Speth, J.

    1992-01-01

    Using generalized Sullivan processes to generate sea-quark distributions of a nucleon at Q 2 =4 GeV 2 , we find that the recent finding by the New Muon Collaboration on the violation of the Gottfried sum rule can be understood quantitatively, including the shape of F 2 p (x)-F 2 n (x) as a function of x. The agreement may be seen as a clear evidence toward the validity of a recent suggestion of Hwang, Speth, and Brown that the sea distributions of a hadron, at low and moderate Q 2 (at least up to a few GeV 2 ), may be attributed primarily to generalized Sullivan processes

  13. LP formulation of asymmetric zero-sum stochastic games

    KAUST Repository

    Li, Lichun

    2014-12-15

    This paper provides an efficient linear programming (LP) formulation of asymmetric two player zero-sum stochastic games with finite horizon. In these stochastic games, only one player is informed of the state at each stage, and the transition law is only controlled by the informed player. Compared with the LP formulation of extensive stochastic games whose size grows polynomially with respect to the size of the state and the size of the uninformed player\\'s actions, our proposed LP formulation has its size to be linear with respect to the size of the state and the size of the uninformed player, and hence greatly reduces the computational complexity. A travelling inspector problem is used to demonstrate the efficiency of the proposed LP formulation.

  14. Approximating a wavefunction as an unconstrained sum of Slater determinants

    International Nuclear Information System (INIS)

    Beylkin, Gregory; Perez, Fernando; Mohlenkamp, Martin J.

    2008-01-01

    The wavefunction for the multiparticle Schroedinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they impose additional structural constraints on the determinants, such as orthogonality between orbitals or an excitation pattern. We present a method without any such constraints, by which we hope to obtain much more efficient expansions and insight into the inherent structure of the wavefunction. We use an integral formulation of the problem, a Green's function iteration, and a fitting procedure based on the computational paradigm of separated representations. The core procedure is the construction and solution of a matrix-integral system derived from antisymmetric inner products involving the potential operators. We show how to construct and solve this system with computational complexity competitive with current methods

  15. Isovector giant monopole resonances: A sum-rule approach

    International Nuclear Information System (INIS)

    Goeke, K.; Bonn Univ.; Castel, B.

    1980-01-01

    Several useful sum rules associated with isovector giant monopole resonances are calculated for doubly closed shell nuclei. The calculation is based on techniques known from constrained and adiabatic time-dependent Hartree-Fock theories and assume various Skyrme interactions. The results obtained form, together with the compiled literature, the basis for a quantitative description of the RPA strength distribution in terms of energy-weighted moments. These, together with strength distribution properties, are determined by a hierarchy of determinantal relations between moments. The isovector giant monopole resonance turns out to be a rather broad resonance centered at E = 46 Asup(-1/10) MeV with an extended width of more than 16 MeV. The consequences regarding isospin impurities in the nuclear ground state are discussed. (orig.)

  16. Sum-Rate Maximization of Coordinated Direct and Relay Systems

    DEFF Research Database (Denmark)

    Sun, Fan; Popovski, Petar; Thai, Chan

    2012-01-01

    Joint processing of multiple communication flows in wireless systems has given rise to a number of novel transmission techniques, notably the two-way relaying based on wireless network coding. Recently, a related set of techniques has emerged, termed coordinated direct and relay (CDR) transmissions......, where the constellation of traffic flows is more general than the two-way. Regardless of the actual traffic flows, in a CDR scheme the relay has a central role in managing the interference and boosting the overall system performance. In this paper we investigate the novel transmission modes, based...... on amplify-and-forward, that arise when the relay is equipped with multiple antennas and can use beamforming. We focus on one representative traffic type, with one uplink and one downlink users and consider the achievable sum-rate maximization relay beamforming. The beamforming criterion leads to a non...

  17. Scalar Hidden-Charm Tetraquark States with QCD Sum Rules

    Science.gov (United States)

    Di, Zun-Yan; Wang, Zhi-Gang; Zhang, Jun-Xia; Yu, Guo-Liang

    2018-02-01

    In this article, we study the masses and pole residues of the pseudoscalar-diquark-pseudoscalar-antidiquark type and vector-diquark-vector-antidiquark type scalar hidden-charm cu\\bar{c}\\bar{d} (cu\\bar{c}\\bar{s}) tetraquark states with QCD sum rules by taking into account the contributions of the vacuum condensates up to dimension-10 in the operator product expansion. The predicted masses can be confronted with the experimental data in the future. Possible decays of those tetraquark states are also discussed. Supported by the National Natural Science Foundation of China under Grant No. 11375063, the Fundamental Research Funds for the Central Universities under Grant Nos. 2016MS155 and 2016MS133

  18. Thermal Properties of Light Tensor Mesons via QCD Sum Rules

    Directory of Open Access Journals (Sweden)

    K. Azizi

    2015-01-01

    Full Text Available The thermal properties of f2(1270, a2(1320, and K2*(1430 light tensor mesons are investigated in the framework of QCD sum rules at finite temperature. In particular, the masses and decay constants of the light tensor mesons are calculated taking into account the new operators appearing at finite temperature. The numerical results show that, at the point at which the temperature-dependent continuum threshold vanishes, the decay constants decrease with amount of (70–85% compared to their vacuum values, while the masses diminish about (60–72% depending on the kinds of the mesons under consideration. The results obtained at zero temperature are in good consistency with the experimental data as well as the existing theoretical predictions.

  19. Sum rules and systematics for baryon magnetic moments

    International Nuclear Information System (INIS)

    Lipkin, H.J.

    1983-11-01

    The new experimental values of hyperon magnetic moments are compared with sum rules predicted from general quark models. Three difficulties encountered are not easily explained by simple models. The isovector contributions of nonstrange quarks to hyperon moments are smaller than the corresponding contribution to nucleon moments, indicating either appreciable configuration mixing in hyperon wave functions and absent in nucleons or an additional isovector contribution beyond that of valence quarks; e.g. from a pion cloud. The large magnitude of the THETA - moment may indicate that the strange quark contribution to the THETA moments is considerably larger than the value μ(Λ) predicted by simple models which have otherwise been very successful. The set of controversial values from different experiments of the Σ - moment include a value very close to -(1/2)μ(Σ + ) which would indicate that strange quarks do not contribute at all to the Σ moments. (author)

  20. Sum rules and systematics for baryon magnetic moments

    International Nuclear Information System (INIS)

    Lipkin, H.J.

    1984-01-01

    The new experimental values of hyperon magnetic moments are compared with sum rules predicted from general quark models. Three difficulties encountered are not easily explained by simple models. The isovector contributions of nonstrange quarks to hyperon moments are smaller than the corresponding contribution to nucleon moments, indicating either appreciable configuration mixing in hyperon wave functions and absent in nucleons or an additional isovector contribution beyond that of valence quarks, e.g. from a pion cloud. The large magnitude of the Ψ - moment may indicate that the strange quark contribution to the Ψ moments is considerably larger than the value μ(Λ) predicted by simple models which have otherwise been very successful. The set of controversial values from different experiments of the Σ - moment include a value very close to -1/2μ(Σ + ) which would indicate that strange quarks do not contribute at all to the Σ moments. (orig.)

  1. Improved hadronic measurements and spectral sums on the lattice

    International Nuclear Information System (INIS)

    Hagen, Christian

    2008-05-01

    the order parameter for the confinement-deconfinement transition is the Polyakov loop. The order parameter for the spontaneous breaking of chiral symmetry is given by the chiral condensate, which is related to the eigenvalues of the Dirac operator. It has been shown that also the Polyakov loop can be expressed in terms of these eigenvalues, as a spectral sum. In a first step we perform a numerical study of these sums. We find that the ordinary Polyakov loop is governed by the ultraviolet modes of the Dirac operator. Therefore, in a second step we define a new order parameter for confinement, the ''dressed Polyakov loop''. This quantity has two advantages: It can be expressed as a spectral sum which has a better convergence behavior (infrared dominated) and it is closely related to the quark condensate via a Fourier transformation. Also the spectral sums for the dressed Polyakov loop are investigated numerically. (orig.)

  2. A sum rule approach to the violation of Dashen's theorem

    International Nuclear Information System (INIS)

    Moussallam, B.

    1999-01-01

    A classic sum rule by Das et al. is extended to seven of the low-energy constant K i , introduced by Urech, which parameterizes electromagnetic corrections at chiral order O(e 2 p 2 ). Using the spurion formalism, a simple convolution representation is shown to hold and the structure in terms of the chiral renormalization scale, QCD renormalization scale and the QED gauge parameter is displayed. The role of the resonances is studied as providing rational interpolants to relevant QCD n-point functions in the Euclidean domain. A variety of asymptotic constraints must be implemented which have phenomenological consequences. A current assumption concerning the dominance of the lowest-lying resonances is shown clearly to fail in some cases. (author)

  3. Splitting of electrons and violation of the Luttinger sum rule

    Science.gov (United States)

    Quinn, Eoin

    2018-03-01

    We obtain a controlled description of a strongly correlated regime of electronic behavior. We begin by arguing that there are two ways to characterize the electronic degree of freedom, either by the canonical fermion algebra or the graded Lie algebra su (2 |2 ) . The first underlies the Fermi liquid description of correlated matter, and we identify a regime governed by the latter. We exploit an exceptional central extension of su (2 |2 ) to employ a perturbative scheme recently developed by Shastry and obtain a series of successive approximations for the electronic Green's function. We then focus on the leading approximation, which reveals a splitting in two of the electronic dispersion. The Luttinger sum rule is violated, and a Mott metal-insulator transition is exhibited. We offer a perspective.

  4. LP formulation of asymmetric zero-sum stochastic games

    KAUST Repository

    Li, Lichun; Shamma, Jeff S.

    2014-01-01

    This paper provides an efficient linear programming (LP) formulation of asymmetric two player zero-sum stochastic games with finite horizon. In these stochastic games, only one player is informed of the state at each stage, and the transition law is only controlled by the informed player. Compared with the LP formulation of extensive stochastic games whose size grows polynomially with respect to the size of the state and the size of the uninformed player's actions, our proposed LP formulation has its size to be linear with respect to the size of the state and the size of the uninformed player, and hence greatly reduces the computational complexity. A travelling inspector problem is used to demonstrate the efficiency of the proposed LP formulation.

  5. The DHG sum rule measured with medium energy photons

    International Nuclear Information System (INIS)

    Hicks, K.; Ardashev, K.; Babusci, D.

    1997-01-01

    The structure of the nucleon has many important features that are yet to be uncovered. Of current interest is the nucleon spin-structure which can be measured by doing double-polarization experiments with photon beams of medium energies (0.1 to 2 GeV). One such experiment uses dispersion relations, applied to the Compton scattering amplitude, to relate measurement of the total reaction cross section integrated over the incident photon energy to the nucleon anomalous magnetic moment. At present, no single facility spans the entire range of photon energies necessary to test this sum rule. The Laser-Electron Gamma Source (LEGS) facility will measure the double-polarization observables at photon energies between 0.15--0.47 MeV. Either the SPring8 facility, the GRAAL facility (France), or Jefferson Laboratory could make similar measurements at higher photon energies. A high-precision measurement of the spin-polarizability and the Drell-Hearn-Gerasimov sum rule is now possible with the advent of high-polarization solid HD targets at medium energy polarized photon facilities such as LEGS, GRAAL and SPring8. Other facilities with lower polarization in either the photon beam or target (or both) are also pursuing these measurements because of the high priority associated with this physics. The Spin-asymmetry (SASY) detector that will be used at LEGS has been briefly outlined in this paper. The detector efficiencies have been explored with simulations studies using the GEANT software, with the result that both charged and uncharged pions can be detected with a reasonable efficiency (> 30%) over a large solid angle. Tracking with a TPC, which will be built at LEGS over the next few years, will improve the capabilities of these measurements

  6. Frequency Synthesiser

    NARCIS (Netherlands)

    Drago, Salvatore; Sebastiano, Fabio; Leenaerts, Dominicus M.W.; Breems, Lucien J.; Nauta, Bram

    2016-01-01

    A low power frequency synthesiser circuit (30) for a radio transceiver, the synthesiser circuit comprising: a digital controlled oscillator configured to generate an output signal having a frequency controlled by an input digital control word (DCW); a feedback loop connected between an output and an

  7. Frequency synthesiser

    NARCIS (Netherlands)

    Drago, S.; Sebastiano, Fabio; Leenaerts, Dominicus Martinus Wilhelmus; Breems, Lucien Johannes; Nauta, Bram

    2010-01-01

    A low power frequency synthesiser circuit (30) for a radio transceiver, the synthesiser circuit comprising: a digital controlled oscillator configured to generate an output signal having a frequency controlled by an input digital control word (DCW); a feedback loop connected between an output and an

  8. Method of detecting system function by measuring frequency response

    Science.gov (United States)

    Morrison, John L [Butte, MT; Morrison, William H [Manchester, CT; Christophersen, Jon P [Idaho Falls, ID

    2012-04-03

    Real-time battery impedance spectrum is acquired using a one-time record. Fast Summation Transformation (FST) is a parallel method of acquiring a real-time battery impedance spectrum using a one-time record that enables battery diagnostics. An excitation current to a battery is a sum of equal amplitude sine waves of frequencies that are octave harmonics spread over a range of interest. A sample frequency is also octave and harmonically related to all frequencies in the sum. The time profile of this signal has a duration that is a few periods of the lowest frequency. The voltage response of the battery, average deleted, is the impedance of the battery in the time domain. Since the excitation frequencies are known and octave and harmonically related, a simple algorithm, FST, processes the time record by rectifying relative to the sine and cosine of each frequency. Another algorithm yields real and imaginary components for each frequency.

  9. Method of detecting system function by measuring frequency response

    Science.gov (United States)

    Morrison, John L.; Morrison, William H.; Christophersen, Jon P.; Motloch, Chester G.

    2013-01-08

    Methods of rapidly measuring an impedance spectrum of an energy storage device in-situ over a limited number of logarithmically distributed frequencies are described. An energy storage device is excited with a known input signal, and a response is measured to ascertain the impedance spectrum. An excitation signal is a limited time duration sum-of-sines consisting of a select number of frequencies. In one embodiment, magnitude and phase of each frequency of interest within the sum-of-sines is identified when the selected frequencies and sample rate are logarithmic integer steps greater than two. This technique requires a measurement with a duration of one period of the lowest frequency. In another embodiment, where selected frequencies are distributed in octave steps, the impedance spectrum can be determined using a captured time record that is reduced to a half-period of the lowest frequency.

  10. Impact of Duality Violations on Spectral Sum Rule analyses

    International Nuclear Information System (INIS)

    Cata, Oscar

    2007-01-01

    Recent sum rule analyses on the two-point correlator have led to significant discrepancies in the values found for the OPE condensates, most dramatically in the dimension eight condensate and to a lesser extent in the dimension six one [R. Barate et al., ALEPH Collaboration, Eur. Phys. J. C 4 (1998) 409; K. Ackerstaff et al., OPAL Collaboration, Eur. Phys. J. C 7 (1999) 571, (arXiv:hep-ex/9808019); S. Peris, B. Phily and E. de Rafael, Phys. Rev. Lett. 86 (2001) 14, (arXiv:hep-ph/0007338); S. Friot, D. Greynat and E. de Rafael, JHEP 0410 (2004) 043, (arXiv:hep-ph/0408281); M. Davier, L. Girlanda, A. Hocker and J. Stern, Phys. Rev. D 58 (1998) 096014, (arXiv:hep-ph/9802447); B.L. Ioffe and K.N. Zyablyuk, Nucl. Phys. A 687 (2001) 437, (arXiv:hep-ph/0010089). K.N. Zyablyuk, Eur. Phys. J. C 38 (2004) 215, (arXiv:hep-ph/0404230); J. Bijnens, E. Gamiz and J. Prades, JHEP 0110 (2001) 009, (arXiv:hep-ph/0108240); C.A. Dominguez and K. Schilcher, Phys. Lett. B 581 (2004) 193, (arXiv:hep-ph/0309285); J. Rojo and J. I. Latorre, JHEP 0401 (2004) 055, (arXiv:hep-ph/0401047); V. Cirigliano, E. Golowich and K. Maltman, Phys. Rev. D 68 (2003) 054013, (arXiv:hep-ph/0305118); S. Ciulli, C. Sebu, K. Schilcher and H. Spiesberger, Phys. Lett. B 595 (2004) 359, (arXiv:hep-ph/0312212). S. Narison, (arXiv:hep-ph/0412152)]. Precise knowledge of these condensates is of relevance in kaon decays [M. Knecht, S. Peris and E. de Rafael, Phys. Lett. B 457 (1999) 227, (arXiv:hep-ph/9812471); J.F. Donoghue and E. Golowich, Phys. Lett. B 478 (2000) 172, (arXiv:hep-ph/9911309); M. Knecht, S. Peris and E. de Rafael, Phys. Lett. B 508 (2001) 117, (arXiv:hep-ph/0102017)] and therefore it seems mandatory to assess the actual impact of what is commonly neglected in spectral sum rules, most prominently the issue of duality violations. We will explicitly compute them in a toy model and show that they are a priori non-negligible

  11. Scaled unscented transform Gaussian sum filter: Theory and application

    KAUST Repository

    Luo, Xiaodong

    2010-05-01

    In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT) (Julier and Uhlmann (2004) [16]), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf (Arulampalam et al. (2002) [7]). In applications, a potential problem of a Gaussian sum filter is that the number of Gaussian distributions may increase very rapidly. To this end, we also propose an auxiliary algorithm to conduct pdf re-approximation so that the number of Gaussian distributions can be reduced. With the auxiliary algorithm, in principle the SUT-GSF can achieve almost the same computational speed as the SUKF if the SUT-GSF is implemented in parallel. As an example, we will use the SUT-GSF to assimilate a 40-dimensional system due to

  12. An Analysis of the Effect of the U. S. Marine Corps' Lump Sum Selective Reenlistment Bonus Program on Reenlistment Decisions

    National Research Council Canada - National Science Library

    Barry, Robert

    2001-01-01

    ... the impact of personal characteristics, civilian pay, unemployment, and the lump sum bonus on reenlistment decisions, Marine retention probabilities under the lump sum payment program are compared...

  13. Structural relations of harmonic sums and Mellin transforms up to weight w=5

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, Johannes

    2009-01-15

    We derive the structural relations between the Mellin transforms of weighted Nielsen integrals emerging in the calculation of massless or massive single-scale quantities in QED and QCD, such as anomalous dimensions and Wilson coefficients, and other hard scattering cross sections depending on a single scale. The set of all multiple harmonic sums up to weight five cover the sums needed in the calculation of the 3-loop anomalous dimensions. The relations extend the set resulting from the quasi-shuffle product between harmonic sums studied earlier. Unlike the shuffle relations, they depend on the value of the quantities considered. Up to weight w=5, 242 nested harmonic sums contribute. In the present physical applications it is sufficient to consider the sub-set of harmonic sums not containing an index i=-1, which consists out of 69 sums. The algebraic relations reduce this set to 30 sums. Due to the structural relations a final reduction of the number of harmonic sums to 15 basic functions is obtained. These functions can be represented in terms of factorial series, supplemented by harmonic sums which are algebraically reducible. Complete analytic representations are given for these 15 meromorphic functions in the complex plane deriving their asymptotic- and recursion relations. A general outline is presented on the way nested harmonic sums and multiple zeta values emerge in higher order calculations of zero- and single scale quantities. (orig.)

  14. Cambodia–China Relations: A Positive-Sum Game?

    Directory of Open Access Journals (Sweden)

    Pheakdey Heng

    2012-01-01

    Full Text Available China has re-emerged to become a dominant foreign player in Cambodia. Politically, Cambodia is one of China’s oldest and closest allies. Economically, China is Cambodia’s top foreign investor, a major donor, and an increasingly important trading partner. Culturally, Chinese values are deeply embedded in many aspects of Cambodian society. However, China’s dominance is surrounded by renewed controversies. While the government warmly welcomes Chinese aid, saying that it comes with no strings attached, many experts are concerned that China is providing aid for more nefarious reasons. Critics also accuse Chinese investment and aid of having exacerbated corruption, weakened governance and harmed human rights, and of ruining Cambodia’s natural resources and environment. With such controversies, it is relevant and significant to assess the roles that China has played and continues to play in Cambodia’s socio-economic development. Using expert interviews, media analysis and an extensive literature review, this paper uniquely contributes to the existing discussion on China–Cambodia relations by closely examining the controversies of China’s investment and aid, critically analysing China’s interests in Cambodia, and asking if the relationship between the two nations is a positive-sum game.

  15. Cumulative sum quality control for calibrated breast density measurements

    International Nuclear Information System (INIS)

    Heine, John J.; Cao Ke; Beam, Craig

    2009-01-01

    Purpose: Breast density is a significant breast cancer risk factor. Although various methods are used to estimate breast density, there is no standard measurement for this important factor. The authors are developing a breast density standardization method for use in full field digital mammography (FFDM). The approach calibrates for interpatient acquisition technique differences. The calibration produces a normalized breast density pixel value scale. The method relies on first generating a baseline (BL) calibration dataset, which required extensive phantom imaging. Standardizing prospective mammograms with calibration data generated in the past could introduce unanticipated error in the standardized output if the calibration dataset is no longer valid. Methods: Sample points from the BL calibration dataset were imaged approximately biweekly over an extended timeframe. These serial samples were used to evaluate the BL dataset reproducibility and quantify the serial calibration accuracy. The cumulative sum (Cusum) quality control method was used to evaluate the serial sampling. Results: There is considerable drift in the serial sample points from the BL calibration dataset that is x-ray beam dependent. Systematic deviation from the BL dataset caused significant calibration errors. This system drift was not captured with routine system quality control measures. Cusum analysis indicated that the drift is a sign of system wear and eventual x-ray tube failure. Conclusions: The BL calibration dataset must be monitored and periodically updated, when necessary, to account for sustained system variations to maintain the calibration accuracy.

  16. Cumulative sum quality control for calibrated breast density measurements

    Energy Technology Data Exchange (ETDEWEB)

    Heine, John J.; Cao Ke; Beam, Craig [Cancer Prevention and Control Division, Moffitt Cancer Center, 12902 Magnolia Drive, Tampa, Florida 33612 (United States); Division of Epidemiology and Biostatistics, School of Public Health, University of Illinois at Chicago, 1603 W. Taylor St., Chicago, Illinois 60612 (United States)

    2009-12-15

    Purpose: Breast density is a significant breast cancer risk factor. Although various methods are used to estimate breast density, there is no standard measurement for this important factor. The authors are developing a breast density standardization method for use in full field digital mammography (FFDM). The approach calibrates for interpatient acquisition technique differences. The calibration produces a normalized breast density pixel value scale. The method relies on first generating a baseline (BL) calibration dataset, which required extensive phantom imaging. Standardizing prospective mammograms with calibration data generated in the past could introduce unanticipated error in the standardized output if the calibration dataset is no longer valid. Methods: Sample points from the BL calibration dataset were imaged approximately biweekly over an extended timeframe. These serial samples were used to evaluate the BL dataset reproducibility and quantify the serial calibration accuracy. The cumulative sum (Cusum) quality control method was used to evaluate the serial sampling. Results: There is considerable drift in the serial sample points from the BL calibration dataset that is x-ray beam dependent. Systematic deviation from the BL dataset caused significant calibration errors. This system drift was not captured with routine system quality control measures. Cusum analysis indicated that the drift is a sign of system wear and eventual x-ray tube failure. Conclusions: The BL calibration dataset must be monitored and periodically updated, when necessary, to account for sustained system variations to maintain the calibration accuracy.

  17. One decade after Chernobyl: Summing up the consequences

    International Nuclear Information System (INIS)

    Kaul, A.; Landfermann, H.; Thieme, M.

    1996-01-01

    During the week 8-12 April 1996, an international conference summing up the consequences of the Chernobyl disaster after one decade took place in Vienna. Organizers were the European Commission (EC), the International Atomic Energy Agency (IAEA) and the World Health Organization (WHO) (EC/IAEA/WHO 1996). One of the authors, A. Kaul, presented the outcome of the conference as given below to the IPRA 9 congress which was held in Vienna the following week. Two caveats have to be mentioned here: firstly, only facts actually reported and reviewed at the conference can be accounted for, and, secondly, according to the groundrules of the conference, the deadline for the background papers of the conference was the 9 February 1996, meaning that facts materializing after that time are not covered in this paper. The same applied to information given at the conference that was not properly reviewed and published. Reports, for example, given at the conference on an observed increase of thyroid cancers and leukemia among liquidators and of diabetes mellitus among children are not yet substantiated and are, therefore, not yet recognized as consequences. If corroborated, and it is obvious that all higher exposed groups should be closely monitored in the future, an update on the consequences will have to take this into account. 2 refs., 1 fig., 4 tabs

  18. Summing over Feynman histories by functional contour integration

    International Nuclear Information System (INIS)

    Garrison, J.C.; Wright, E.M.

    1986-01-01

    The authors show how complex paths can be consistently introduced into sums for Feynman histories by using the notion of functional contour integration. For a kappa-dimensional system specified by a potential with suitable analyticity properties, each coordinate axis is replaced by a copy of the complex plane, and at each instant of time a contour is chosen in each plane. This map from the time axis into the set of complex contours defines a functional contour. The family of contours labelled by time generates a (kappa+1)-dimensional submanifold of the (2kappa+1)-dimensional space defined by the cartesian product of the time axis and the coordinate planes. The complex Feynman paths lie on this submanifold. An application of this idea to systems described by absorptive potentials yields a simple derivation of the correct WKB result in terms of a complex path that extremalises the action. The method can also be applied to spherically symmetric potentials by using a partial wave expansion and restricting the contours appropriately. (author)

  19. Harmonic generation with a dual frequency pulse.

    Science.gov (United States)

    Keravnou, Christina P; Averkiou, Michalakis A

    2014-05-01

    Nonlinear imaging was implemented in commercial ultrasound systems over the last 15 years offering major advantages in many clinical applications. In this work, pulsing schemes coupled with a dual frequency pulse are presented. The pulsing schemes considered were pulse inversion, power modulation, and power modulated pulse inversion. The pulse contains a fundamental frequency f and a specified amount of its second harmonic 2f. The advantages and limitations of this method were evaluated with both acoustic measurements of harmonic generation and theoretical simulations based on the KZK equation. The use of two frequencies in a pulse results in the generation of the sum and difference frequency components in addition to the other harmonic components. While with single frequency pulses, only power modulation and power modulated pulse inversion contained odd harmonic components, with the dual frequency pulse, pulse inversion now also contains odd harmonic components.

  20. Frequency spirals

    International Nuclear Information System (INIS)

    Ottino-Löffler, Bertrand; Strogatz, Steven H.

    2016-01-01

    We study the dynamics of coupled phase oscillators on a two-dimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phase-locking, we find localized spatiotemporal patterns that we call “frequency spirals.” These patterns cannot be seen under time averaging; they become visible only when we examine the spatial variation of the oscillators' instantaneous frequencies, where they manifest themselves as two-armed rotating spirals. In the more familiar phase representation, they appear as wobbly periodic patterns surrounding a phase vortex. Unlike the stationary phase vortices seen in magnetic spin systems, or the rotating spiral waves seen in reaction-diffusion systems, frequency spirals librate: the phases of the oscillators surrounding the central vortex move forward and then backward, executing a periodic motion with zero winding number. We construct the simplest frequency spiral and characterize its properties using analytical and numerical methods. Simulations show that frequency spirals in large lattices behave much like this simple prototype.