Factorization with Gauss sums: scaling properties of ghost factors
International Nuclear Information System (INIS)
Stefanak, M; Merkel, W; Schleich, W P; Haase, D; Maier, H
2007-01-01
Recent experiments have shown that truncated Gauss sums allow us to find the factors of an integer N. This method relies on the fact that for a factor the absolute value of the Gauss sum is unity. However, for every integer N there exist integers which are not factors, but where the Gauss sum reaches a value which is arbitrarily close to unity. In order to distinguish such ghost factors from real factors we need to amplify this difference. We show that a proper choice of the truncation parameter of the Gauss sum suppresses the ghost factors below a threshold value. We derive the scaling law of the truncation parameter on the number to be factored. Moreover, we show that this scaling law is also necessary for the success of our factorization scheme, even if we relax the threshold or allow limited error tolerance
Factorization of numbers with Gauss sums: I. Mathematical background
International Nuclear Information System (INIS)
Woelk, S; Merkel, W; Schleich, W P; Averbukh, I Sh; Girard, B
2011-01-01
We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially.
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.
A new sum analogous to Gauss sums and its fourth power mean.
Ru, Shaofeng; Zhang, Wenpeng
2014-01-01
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.
On the structure of quadratic Gauss sums in the Talbot effect.
Fernández-Pousa, Carlos R
2017-05-01
We report on the detailed derivation of the Gauss sums leading to the weighting phase factors in the fractional Talbot effect. In contrast to previous approaches, the derivation is directly based on the two coprime integers p and q that define the fractional Talbot effect so that, using standard techniques from the number theory, the computation is reduced, up to a global phase, to the trivial completion of the exponential of the square of a sum. In addition, it is shown that the Gauss sums can be reduced to only two cases, depending on the parity of integer q. Explicit and simpler expressions for the two forms of the Talbot weighting phases are also provided. The Gauss sums are presented as a discrete Fourier transform pair between quadratic phase sequences showing perfect periodic autocorrelation and a connection with the theory of biunimodular sequences is presented. In addition, the Talbot weighting factors of orders 1/q and 2/q are reduced to a closed form, and the equivalence to existing characterizations of Talbot weighting phases is also discussed. The relationship with one-dimensional multilevel phase structures is exemplified by the study of Talbot array illuminators. These results simplify and extend the description of the role played by Gauss sums in the fractional Talbot effect, providing a compact synthesis of previous results.
Greybody factors for a spherically symmetric Einstein-Gauss-Bonnet-de Sitter black hole
Zhang, Cheng-Yong; Li, Peng-Cheng; Chen, Bin
2018-02-01
We study the greybody factors of the scalar fields in spherically symmetric Einstein-Gauss-Bonnet-de Sitter black holes in higher dimensions. We derive the greybody factors analytically for both minimally and nonminimally coupled scalar fields. Moreover, we discuss the dependence of the greybody factor on various parameters including the angular momentum number, the nonminimally coupling constant, the spacetime dimension, the cosmological constant, and the Gauss-Bonnet coefficient in detail. We find that the nonminimal coupling may suppress the greybody factor and the Gauss-Bonnet coupling could enhance it, but they both suppress the energy emission rate of Hawking radiation.
International Nuclear Information System (INIS)
Ivashchuk, V.D.
2016-01-01
A (n + 1)-dimensional gravitational model with Gauss-Bonnet term and a cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with an exponential dependence of the scale factors, a i ∝ exp(v i t), i = 1,.., n, are analyzed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. K(v) = sum k=1 n v k ≠ 0. We prove that under a certain restriction R imposed solutions with K(v) > 0 are stable, while solutions with K(v) < 0 are unstable. Certain examples of stable solutions are presented. We show that the solutions with v 1 = v 2 = v 3 = H > 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Ivashchuk, V.D. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia (RUDN University), Institute of Gravitation and Cosmology, Moscow (Russian Federation)
2016-08-15
A (n + 1)-dimensional gravitational model with Gauss-Bonnet term and a cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with an exponential dependence of the scale factors, a{sub i} ∝ exp(v{sup i}t), i = 1,.., n, are analyzed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. K(v) = sum {sub k=1}{sup n} v{sup k} ≠ 0. We prove that under a certain restriction R imposed solutions with K(v) > 0 are stable, while solutions with K(v) < 0 are unstable. Certain examples of stable solutions are presented. We show that the solutions with v{sup 1} = v{sup 2} = v{sup 3} = H > 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed. (orig.)
Beam propagation factors and kurtosis parameters of a Lorentz-Gauss vortex beam.
Zhou, Guoquan
2014-06-01
Based on the second-order and the higher-order moments, analytical expressions for the beam propagation factors of a Lorentz-Gauss vortex beam with l=1 have been derived, and analytical propagation expressions for the kurtosis parameters of a Lorentz-Gauss vortex beam with l=1 through a paraxial and real ABCD optical system have also been presented. The M² factor is determined by the parameters a and b and decreases with increasing the parameter a or b. The M² factor is validated to be larger than 2. The kurtosis parameters depend on the diffraction-free ranges of the Lorentz part, the parameters a and b, and the ratio A/B. The kurtosis parameters of a Lorentz-Gauss vortex beam propagating in free space are demonstrated in different reference planes. In the far field, the kurtosis parameter K decreases with increasing one of the parameters a and b. Upon propagation, the kurtosis parameter K first decreases, then increases, and finally tends to a saturated value. In any case, the kurtosis parameter K is larger than 2. This research is beneficial to optical trapping, guiding, and manipulation of microscopic particles and atoms using Lorentz-Gauss vortex beams.
Charm and bottom hadronic form factors with QCD sum rules
International Nuclear Information System (INIS)
Bracco, M. E.; Rodrigues, B. O.; Cerqueira, A. Jr.
2013-01-01
We present a brief review of some calculations of form factors and coupling constants in vertices with charm and bottom mesons in the framework of QCD sum rules. We first discuss the motivation for this work, describing possible applications of these form factors to charm and bottom decays processes. We first make a summarize of the QCD sum rules method. We give special attention to the uncertainties of the method introducing by the intrinsic variation of the parameters. Finally we conclude.
B-decay form factors from QCD sum rules
International Nuclear Information System (INIS)
Offen, Nils
2008-01-01
In the Standard Model of particle physics there is only one source of CP-violation. Namely, a single complex phase in the unitary 3 x 3 CKM-Matrix governing flavor transitions in the weak interaction. The unitarity is usually visualized by a triangle in the complex ρ - η-plane. Therefore testing this framework comes down to measuring weak decays, relating observables to sides and angles of this so called Unitarity Triangle(UT). Particular interest in this respect is payed to decays of mesons containing a heavy b-quark, giving the opportunity to alone determine all parameters of the UT. Doing this is far from easy. Besides tedious experimental measurements the theoretical calculations are plagued by hadronic quantities which cannot be determined by perturbation theory. In this work several of these quantities so called form factors are computed using the well known method of light cone sum rules(LCSR). Two different setups have been used. One, established in this work, utilizing a correlation function with an on-shell B-Meson and one following the traditional calculation by taking the light meson on-shell. Both using light cone expansion in the respective on-shell mesons distribution amplitudes. While the first approach allows to calculate a whole bunch of phenomenologically interesting quantities by just changing Dirac-structures of the relevant currents it has the drawback that it does not have access to the well developed twist expansion of the latter. To incorporate higher Fock-state contributions the first models for three-particle distribution amplitudes of the B-Meson have been derived. α s -corrections remain out of the scope of this work. Nevertheless does a comparison with more sophisticated methods show an encouraging numerical agreement. In the second setup all known corrections especially the never verified α s -corrections to Twist three terms have been recalculated and a competitive result for the CKM-matrixelement vertical stroke V ub vertical
Noncoaxial Bessel-Gauss beams.
Huang, Chaohong; Zheng, Yishu; Li, Hanqing
2016-04-01
We proposed a new family of noncoaxial Gauss-truncated Bessel beams through multiplying conventional symmetrical Bessel beams by a noncoaxial Gauss function. These beams can also be regarded as the exponential-truncated version of Bessel-Gauss beams since they can be transformed into the product of Bessel-Gauss beams and an exponential window function along a certain Cartesian axis. The closed-form solutions of the angular spectra and paraxial propagation of these beams were derived. These beams have asymmetrical intensity distributions and carry the same orbit angular momentum per photon as the corresponding Bessel-Gauss beams. While propagating along the z axis, the mth (m≠0) noncoaxial Bessel-Gauss beams rotate their intensity distributions and the mth-order vortex at the beam center has a transverse shift along the direction perpendicular to the offset axis. Depending on the product of the transverse scalar factor of the Bessel beams and the offset between the Gaussian window function and the center of the Bessel beams, the noncoaxial Bessel-Gauss beams can produce unit vortices with opposite signs in pairs during propagation.
Rice, Kathryn; Scott, Paul
2005-01-01
This article presents a brief biography of Johann Carl Friedrich Gauss. Gauss was born on April 30, 1777, in the German city of Braunschweig (Brunswick). He was the only child of Gebhard Dietrich Gauss and Dorothea Benze. Neither of Gauss's parents had much education, his father could read and write, but earned his living doing menial jobs such as…
International Nuclear Information System (INIS)
Ivashchuk, V D; Ernazarov, K K
2017-01-01
A ( n + 1)-dimensional gravitational model with cosmological constant and Gauss-Bonnet term is studied. The ansatz with diagonal cosmological metrics is adopted and solutions with exponential dependence of scale factors: a i ∼ exp ( v i t ), i = 1, …, n , are considered. The stability analysis of the solutions with non-static volume factor is presented. We show that the solutions with v 1 = v 2 = v 3 = H > 0 and small enough variation of the effective gravitational constant G are stable if certain restriction on ( v i ) is obeyed. New examples of stable exponential solutions with zero variation of G in dimensions D = 1 + m + 2 with m > 2 are presented. (paper)
Indian Academy of Sciences (India)
was born into the family of Gebhard Dietrich Gauss, a bricklayer at the German town of Brunswick, on 30 April 1777. Gauss was a child prodigy whose calculating prowess showed itself fairly early in his life. Stories of his ... his studies anymore, Gauss began to look for a patron who would finance his education beyond the ...
Indian Academy of Sciences (India)
D Surya Ramana. Carl Friedrich Gauss, whose mathematical work in the 19th century earned him the title of Prince among Mathematicians ,1 was born into the family of Gebhard Dietrich Gauss, a bricklayer at the German town of Brunswick, on 30 April 1777. Gauss was a child prodigy whose calculating prowess showed.
QCD sum rule calculation of the Isgur-Wise form factor
International Nuclear Information System (INIS)
Radyushkin, A.V.
1991-01-01
Within the QCD sum rule approach, we develop a formalism that enables one to calculate the form factors of the heavy-light mesons in the m Q → ∞ limit. It is shown that the behavior of the universal Isgur-Wise form factor is determined by the quark propagation function in imaginary time. (orig.)
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
$B \\to D^{(*)}$ Form Factors from QCD Light-Cone Sum Rules
Faller, S; Klein, Ch; Mannel, T
2009-01-01
We derive new QCD sum rules for $B\\to D$ and $B\\to D^*$ form factors. The underlying correlation functions are expanded near the light-cone in terms of $B$-meson distribution amplitudes defined in HQET, whereas the $c$-quark mass is kept finite. The leading-order contributions of two- and three-particle distribution amplitudes are taken into account. From the resulting light-cone sum rules we calculate all $B\\to \\Dst $ form factors in the region of small momentum transfer (maximal recoil). In the infinite heavy-quark mass limit the sum rules reduce to a single expression for the Isgur-Wise function. We compare our predictions with the form factors extracted from experimental $B\\to \\Dst l \
Light Cone Sum Rules for gamma*N ->Delta Transition Form Factors
Energy Technology Data Exchange (ETDEWEB)
V.M. Braun; A. Lenz; G. Peters; A. Radyushkin
2006-02-01
A theoretical framework is suggested for the calculation of {gamma}* N {yields} {Delta} transition form factors using the light-cone sum rule approach. Leading-order sum rules are derived and compared with the existing experimental data. We find that the transition form factors in a several GeV region are dominated by the ''soft'' contributions that can be thought of as overlap integrals of the valence components of the hadron wave functions. The ''minus'' components of the quark fields contribute significantly to the result, which can be reinterpreted as large contributions of the quark orbital angular momentum.
Calculation of Coincidence Summing Correction Factors for an HPGe detector using GEANT4
International Nuclear Information System (INIS)
Giubrone, G.; Ortiz, J.; Gallardo, S.; Martorell, S.; Bas, M.C.
2016-01-01
The aim of this paper was to calculate the True Coincidence Summing Correction Factors (TSCFs) for an HPGe coaxial detector in order to correct the summing effect as a result of the presence of 88 Y and 60 Co in a multigamma source used to obtain a calibration efficiency curve. Results were obtained for three volumetric sources using the Monte Carlo toolkit, GEANT4. The first part of this paper deals with modeling the detector in order to obtain a simulated full energy peak efficiency curve. A quantitative comparison between the measured and simulated values was made across the entire energy range under study. The True Summing Correction Factors were calculated for 88 Y and 60 Co using the full peak efficiencies obtained with GEANT4. This methodology was subsequently applied to 134 Cs, and presented a complex decay scheme. - Highlights: • True Summing Correction Factors have been calculated for an HPGe detector. • GEANT4 toolkit has been used to calculate the efficiency curve for different source geometries. • Quantitative comparisons have been made using appropriate statistical tests to validate the simulations. • The average differences between simulated and measurement efficiencies are lower than 2%.
Oort, F.
We present one of the shortest examples of a statement with a visionary impact: we discuss an expectation by Gauss. His idea preludes developments only started more than a century later. Several proofs were given for the prediction by Gauss. We show where this statements fits into modern
An automated Monte-Carlo based method for the calculation of cascade summing factors
Jackson, M. J.; Britton, R.; Davies, A. V.; McLarty, J. L.; Goodwin, M.
2016-10-01
A versatile method has been developed to calculate cascade summing factors for use in quantitative gamma-spectrometry analysis procedures. The proposed method is based solely on Evaluated Nuclear Structure Data File (ENSDF) nuclear data, an X-ray energy library, and accurate efficiency characterisations for single detector counting geometries. The algorithm, which accounts for γ-γ, γ-X, γ-511 and γ-e- coincidences, can be applied to any design of gamma spectrometer and can be expanded to incorporate any number of nuclides. Efficiency characterisations can be derived from measured or mathematically modelled functions, and can accommodate both point and volumetric source types. The calculated results are shown to be consistent with an industry standard gamma-spectrometry software package. Additional benefits including calculation of cascade summing factors for all gamma and X-ray emissions, not just the major emission lines, are also highlighted.
Degenerate Gauss hypergeometric functions
Vidunas, Raimundas
2004-01-01
This is a study of terminating and ill-defined Gauss hypergeometric functions. Corresponding hypergeometric equations have a degenerate set of of 24 Kummer's solutions. We describe those solutions and relations between them.
Homotopy invariants of Gauss words
Gibson, Andrew
2009-01-01
By defining combinatorial moves, we can define an equivalence relation on Gauss words called homotopy. In this paper we define a homotopy invariant of Gauss words. We use this to show that there exist Gauss words that are not homotopically equivalent to the empty Gauss word, disproving a conjecture by Turaev. In fact, we show that there are an infinite number of equivalence classes of Gauss words under homotopy.
Microscopic calculation of the enhancement factor in the electric dipole sum rule
International Nuclear Information System (INIS)
Fabrocini, A.; Lagaris, I.E.; Viviani, M.; Fantoni, S.
1985-01-01
Correlated basis function perturbation theory with state-dependent correlations is used to calculate the nuclear photoabsorption enhancement factor K in the electric dipole sum rule for some realistic models of nuclear matter. The contribution due to 2p-2h admixtures in the ground state wave function turns out to be only a few percent of the unperturbed value. The values obtained for K are about 1.8 at experimental equilibrium density and increase almost linearly with density. We also give estimates of K for finite nuclei, obtained within the local density approximation framework. The surface effects give a contribution which is proportional 20% of the volume term. (orig.)
Equivalence of computer codes for calculation of coincidence summing correction factors
International Nuclear Information System (INIS)
Vidmar, T.; Capogni, M.; Hult, M.; Hurtado, S.; Kastlander, J.; Lutter, G.; Lépy, M.-C.; Martinkovič, J.; Ramebäck, H.; Sima, O.; Tzika, F.; Vidmar, G.
2014-01-01
The aim of the study was to check for equivalence of computer codes that can perform calculations of true coincidence summing correction factors. All calculations were performed for a set of well-defined detector and sample parameters, without any reference to empirical data. For a p-type detector model the application of different codes resulted in satisfactory agreement in the calculated correction factors. For high-efficiency geometries in combination with an n-type detector and a radionuclide emitting abundant X-rays the results were scattered. - Highlights: • Measured and calculated true coincidence corrections differ in recent study. • We checked for equivalence of computer codes that can perform such calculations. • Codes compared with each other for a set of well-defined detector and sample models. • Satisfactory agreement between the codes for a p-type detector model. • Large differences for an n-type detector model and X-ray emitting radionuclides
Di Fazio, Antonella; Vernucci, Antonio; Rossini, Eugenio
2003-07-01
GAUSS is a Research and Technological Development project co-funded by European Commission, within the frame of the IST (Information Society Technologies) V Programme. It is a two-year project, starting from December 2000, and successfully completed.The GAUSS Team involves a Consortium of nine European companies, including ARNI (Azienda Regionale per la Navigazione Interna, I), ASCOM (CH), ERICSSON Telecomunicazioni (I), GMV (E), TELEFONICA (E), THALES Navigation (F), TTI Norte (E), Space Engineering (I) and TELESPAZIO (I) as project co-ordinator.GAUSS objective was to design and demonstrate the feasibility of a system providing Location-based services, from the integration of Satellite Navigation and Communications, within the contexts of GALILEO and the UMTS technology. The GAUSS proposed solution supports highly reliable, near real-time two-way communication between Mobile Users and Service Centre/Provider. The services considered for GAUSS are based on exchange at low data rate transmission of small data packets carrying very accurate positioning & timing information, as typically required by Info-Mobility and Inter-Modality oriented applications. These services are characterised by bursty and unbalanced traffic, generated by a large number of Mobile Users towards a relatively small number of Service Providers, and viceversa from the Service Providers towards widely geographically sparse Mobile Users (i.e. greater amount of traffic in the return link with respect to the forward link). The GAUSS system supports both asynchronous and synchronous communication, based on: ß broad-casting (i.e. data distribution from a Service Provider to Mobile Users)ß broad-catching (i.e. data collection from MUs to a SP)ß point-to-point schemes.Resource access is based on CDMA (Code Division Multiple Access), according to the UMTS standard. A Demonstrator was built up by combining existing facilities with innovative hardware and software components, ad-hoc developed by some of
The solid angle factor sum method for stability prediction of technetium complex compound
International Nuclear Information System (INIS)
Sunanti, S. T.; Susanto, I. R.; Harjoto, D.
1996-01-01
Based on literature study have been performed the solid angle factor sum (SAS) calculations to predict the characteristic and stability of technitium (V) nitrido diethylene triamine penta acetic acid [Tc V N(DTPA)] complex compound. The compound [Tc V NCl 2 (PPh 3 ) 2 ] with SAS value 0.8223 is chosen as initial target and diethylene triamine penta acetic acid (DTPA) is the substitute ligand. It is found that, [Tc V N(DTPA)] can be synthesized through exchange ligand reaction. There are several alternative to the compound [Tc V N(DTPA)] formed, namely [Tc V N(DTPA)] + , [Tc V N(DTPA)], [Tc V N (DTPA)] - and [Tc V N(DTPA)] = , with coordination numbers 5, 6, 7 dan 8. Respectively. The SAS values of those compound are 0.7729, 0.9122, 1.0515 dan 1.1908. Based on these SAS value, the [Tc V N(DTPA)] - complex with coordination number 7 is predicted to be the most stable, with pentagonal bipyramidal structure. (author)
Directory of Open Access Journals (Sweden)
Mohammed Larbi Labbi
2007-12-01
Full Text Available The $(2k$-th Gauss-Bonnet curvature is a generalization to higher dimensions of the $(2k$-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for $k = 1$. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known as the Lagrangian of Lovelock gravity, Gauss-Bonnet Gravity and Lanczos gravity. In this paper we present various aspects of these curvature invariants and review their variational properties. In particular, we discuss natural generalizations of the Yamabe problem, Einstein metrics and minimal submanifolds.
Student difficulties with Gauss' law
Kanim, Stephen
2000-09-01
Many students in introductory courses have difficulty solving Gauss' law problems. Through interviews with students and analysis of solutions to homework and examination questions we have identified some specific conceptual difficulties that often contribute to students' inability to solve quantitative Gauss' law problems. We give examples of common difficulties and discuss instructional implications.
Energy Technology Data Exchange (ETDEWEB)
Peters, Gerhard
2008-05-15
In this work the leading-twist next-to-leading order (NLO) correction to the light-cone sum rules prediction for the electromagnetic form factors of the nucleon are calculated. Here the Ioffe nucleon interpolation current is used and it is worked in the M{sub N}=0 approximation, with M{sub N} being the mass of the nucleon. In this approximation, only the Pauli form factor F{sub 2} receives a correction and the calculated correction is quite sizable. The numerical results for the proton form factors show the improved agreement with the experimental data. Furthermore the problems encountered when going away from M{sub N}=0 approximation at NLO, as well as, gauge invariance of the perturbative results are discussed. This work presents the first step towards the NLO accuracy in the light-cone sum rules for baryon form factors. (orig.)
Renormalization group analysis of B →π form factors with B -meson light-cone sum rules
Shen, Yue-Long; Wei, Yan-Bing; Lü, Cai-Dian
2018-03-01
Within the framework of the B -meson light-cone sum rules, we review the calculation of radiative corrections to the three B →π transition form factors at leading power in Λ /mb. To resum large logarithmic terms, we perform the complete renormalization group evolution of the correlation function. We employ the integral transformation which diagonalizes evolution equations of the jet function and the B -meson light-cone distribution amplitude to solve these evolution equations and obtain renormalization group improved sum rules for the B →π form factors. Results of the form factors are extrapolated to the whole physical q2 region and are compared with that of other approaches. The effect of B -meson three-particle light-cone distribution amplitudes, which will contribute to the form factors at next-to-leading power in Λ /mb at tree level, is not considered in this paper.
On Sensitivity of Gauss-Christoffel Quadrature
Czech Academy of Sciences Publication Activity Database
O'Leary, D.P.; Strakoš, Zdeněk; Tichý, Petr
2007-01-01
Roč. 107, č. 1 (2007), s. 147-174 ISSN 0029-599X R&D Projects: GA AV ČR 1ET400300415 Grant - others:NSF(US) CCR -0204084; NSF(US) CCF-0514213 Institutional research plan: CEZ:AV0Z10300504 Keywords : Gauss-Christoffel quadrature * sensitivity * moments Subject RIV: BA - General Mathematics Impact factor: 1.376, year: 2007
International Nuclear Information System (INIS)
Tannheimer, Stacey L; Rehemtulla, Alnawaz; Ethier, Stephen P
2000-01-01
The fibroblast growth factor receptor (FGFR)2 gene has been shown to be amplified in 5-10% of breast cancer patients. A breast cancer cell line developed in our laboratory, SUM-52PE, was shown to have a 12-fold amplification of the FGFR2 gene, and FGFR2 message was found to be overexpressed 40-fold in SUM-52PE cells as compared with normal human mammary epithelial (HME) cells. Both human breast cancer (HBC) cell lines and HME cells expressed two FGFR2 isoforms, whereas SUM-52PE cells overexpressed those two isoforms, as well as several unique FGFR2 polypeptides. SUM-52PE cells expressed exclusively FGFR2-IIIb isoforms, which are high-affinity receptors for fibroblast growth factor (FGF)-1 and FGF-7. Differences were identified in the expression of the extracellular Ig-like domains, acid box and carboxyl termini, and several variants not previously reported were isolated from these cells. The FGFR family of receptor tyrosine kinases includes four members, all of which are highly alternatively spliced and glycosylated. For FGFR2, alternative splicing of the second half of the third Ig-like domain, involving exons IIIb and IIIc, is a mutually exclusive choice that affects ligand binding specificity and affinity [1,2,3]. It appears that the second half of the third Ig-like domain can dictate high affinity for FGF-2 or keratinocyte growth factor (KGF), whereas affinity for FGF-1 appears to remain the same [3]. Alternative splicing of the carboxyl terminus has been shown to involve at least two different exons that can produce at least three different variants. The C1-type and C2-type carboxyl termini are encoded by the same exon, and have two different splice acceptor sites, whereas the C3-type carboxyl terminus is encoded by a separate exon [4]. The biologic significance of the C1 carboxyl terminus, as compared with the shorter C3 variant found primarily in tumorigenic samples, has been studied in NIH3T3 transfection assays, in which C3 variants were able to produce
Multivariate curve-fitting in GAUSS
Bunck, C.M.; Pendleton, G.W.
1988-01-01
Multivariate curve-fitting techniques for repeated measures have been developed and an interactive program has been written in GAUSS. The program implements not only the one-factor design described in Morrison (1967) but also includes pairwise comparisons of curves and rates, a two-factor design, and other options. Strategies for selecting the appropriate degree for the polynomial are provided. The methods and program are illustrated with data from studies of the effects of environmental contaminants on ducklings, nesting kestrels and quail.
Colon Cancer Risk Assessment - Gauss Program
An executable file (in GAUSS) that projects absolute colon cancer risk (with confidence intervals) according to NCI’s Colorectal Cancer Risk Assessment Tool (CCRAT) algorithm. GAUSS is not needed to run the program.
Doster, Timothy; Watnik, Abbie T
2016-12-20
As a means of increasing the channel capacity in free-space optical communication systems, two types of orbital angular momentum carrying beams, Bessel-Gauss and Laguerre-Gauss, are studied. In a series of numerical simulations, we show that Bessel-Gauss beams, pseudo-nondiffracting beams, outperform Laguerre-Gauss beams of various orders in channel efficiency and bit error rates.
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)
The AGS Ggamma Meter and Calibrating the Gauss Clock
Energy Technology Data Exchange (ETDEWEB)
Ahrens, Leif [Brookhaven National Laboratory (BNL), Upton, NY (United States). Collider-Accelerator Dept.
2014-03-31
During AGS Polarized Proton acceleration periods, one output from the AGS Ggamma Meter, namely the energy (or Ggamma) calculated from the magnetic field in the AGS main magnets and the beam radius- both measured in particular instant, is used to figure out the times in the AGS magnet acceleration cycle when the beam passes through a particular set of depolarizing resonances. The resonance set occur whenever a particle’s Ggamma (energy*(G/m) becomes nearly equal to n*Qx (i.e. any integer multiplied by the horizontal betatron tune). This deliverable is why the machinery is referred to as the ''Ggamma Meter'' rather than the AGS energy meter. The Ggamma Meter takes as inputs a set of measurements of frequency (F(t)), radius (r(t)), and gauss clock counts (GCC(t)). The other energy (GgammaBr) assumes the field when the gauss clock starts counting is known. The change in field to time t is given by the measured accumulated gauss clock counts multiplied by the gauss clock calibration (gauss/GCC). In order to deal with experimental data, this calibration factor gets an added ad hoc complication, namely a correction dependent on the rate of change the counting rate. The Ggamma meter takes GCC(t) and together with the past history for this cycle calculates B(t).
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.)
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.
Storner-Cowell: straight, summed and split; An overview
Frankena, J.F.
1995-01-01
In this paper we consider the relationship between some (forms of) specific numerical methods for (second-order) initial value problems. In particular, the Störmer-Cowell method in second-sum form is shown to be the Gauss-Jackson method (and analogously, for the sake of completeness, we relate
Multiresolution Hilbert Approach to Multidimensional Gauss-Markov Processes
Directory of Open Access Journals (Sweden)
Thibaud Taillefumier
2011-01-01
Full Text Available The study of the multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practically important Gauss-Markov processes, are ordinarily defined through the theory of stochastic integration. Here, inspired by the Lévy-Ciesielski construction of the Wiener process, we propose an alternative representation of multidimensional Gauss-Markov processes as expansions on well-chosen Schauder bases, with independent random coefficients of normal law with zero mean and unit variance. We thereby offer a natural multiresolution description of the Gauss-Markov processes as limits of finite-dimensional partial sums of the expansion, that are strongly almost-surely convergent. Moreover, such finite-dimensional random processes constitute an optimal approximation of the process, in the sense of minimizing the associated Dirichlet energy under interpolating constraints. This approach allows for a simpler treatment of problems in many applied and theoretical fields, and we provide a short overview of applications we are currently developing.
Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.
Kiselev, Aleksei P; Plachenov, Alexandr B
2016-04-01
The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given.
Asymmetric Bessel-Gauss beams.
Kotlyar, V V; Kovalev, A A; Skidanov, R V; Soifer, V A
2014-09-01
We propose a three-parameter family of asymmetric Bessel-Gauss (aBG) beams with integer and fractional orbital angular momentum (OAM). The aBG beams are described by the product of a Gaussian function by the nth-order Bessel function of the first kind of complex argument, having finite energy. The aBG beam's asymmetry degree depends on a real parameter c≥0: at c=0, the aBG beam is coincident with a conventional radially symmetric Bessel-Gauss (BG) beam; with increasing c, the aBG beam acquires a semicrescent shape, then becoming elongated along the y axis and shifting along the x axis for c≫1. In the initial plane, the intensity distribution of the aBG beams has a countable number of isolated optical nulls on the x axis, which result in optical vortices with unit topological charge and opposite signs on the different sides of the origin. As the aBG beam propagates, the vortex centers undergo a nonuniform rotation with the entire beam about the optical axis (c≫1), making a π/4 turn at the Rayleigh range and another π/4 turn after traveling the remaining distance. At different values of the c parameter, the optical nulls of the transverse intensity distribution change their position, thus changing the OAM that the beam carries. An isolated optical null on the optical axis generates an optical vortex with topological charge n. A vortex laser beam shaped as a rotating semicrescent has been generated using a spatial light modulator.
International Nuclear Information System (INIS)
Ji Changyu
2001-01-01
This article introduces the relativity between the coincidence summing correction factor of the HPGe detector surface and the efficiency of 137 Cs almighty apex. By calculation, the function relation between the accordance addition correction factor for 110m Ag(657.8 keV) and the efficiency of 137 Cs almighty apex is gained, by which can calculate the accordance addition correction factor for 110m Ag (657.8 keV). The results are satisfactory to analysis the fixed value ash samples by adapting the factor
Nonextensive entropies derived from Gauss' principle
International Nuclear Information System (INIS)
Wada, Tatsuaki
2011-01-01
Gauss' principle in statistical mechanics is generalized for a q-exponential distribution in nonextensive statistical mechanics. It determines the associated stochastic and statistical nonextensive entropies which satisfy Greene-Callen principle concerning on the equivalence between microcanonical and canonical ensembles. - Highlights: → Nonextensive entropies are derived from Gauss' principle and ensemble equivalence. → Gauss' principle is generalized for a q-exponential distribution. → I have found the condition for satisfying Greene-Callen principle. → The associated statistical q-entropy is found to be normalized Tsallis entropy.
Complex source point theory of paraxial and nonparaxial cosine-Gauss and Bessel-Gauss beams.
Sheppard, Colin J R
2013-02-15
It shown how cosine-Gauss and Bessel-Gauss beams can be generated using the complex source point theory. Paraxial beams are treated first. An analytic expression is derived for the nonparaxial cosine-Gaussian beam, based on the complex source point approach, and numerical results are presented to illustrate its behavior. A way to generate nonparaxial Bessel-Gauss beams is also indicated.
Generation of pulsed Bessel-Gauss beams using passive axicon-theoretical and experimental studies.
Parsa, Shahrzad; Fallah, Hamid Reza; Ramezani, Mohsen; Soltanolkotabi, Mahmood
2012-10-20
We studied the conditions for generating passive Bessel-Gauss beams by using an axicon. We designed an appropriate Gaussian resonator and extracted a quasi-fundamental Gaussian mode from a pulsed Nd:YAG laser pumped by a Xenon flash lamp and measured its parameters, such as propagation factor, divergence angle, and Rayleigh range. Then we generated passive Bessel-Gauss beams using an axicon and investigated their propagation properties, theoretically and experimentally. For example, for the axicon of 1°, the output energy and the Rayleigh range of the generated Bessel-Gauss beams were measured to be 58 mJ and 229.3 mm, respectively. We compared these properties with our results of the Gaussian mode. Finally, by using axicons with different apex angles, and also by changing the beam spot size on the axicon, we generated Bessel-Gauss beams and studied their properties theoretically and experimentally.
Instability of black holes with a Gauss-Bonnet term
International Nuclear Information System (INIS)
Ahn, Wha-Keun; Gwak, Bogeun; Lee, Wonwoo; Lee, Bum-Hoon
2015-01-01
We investigate the fragmentation instability of hairy black holes in the theory with a Gauss-Bonnet (GB) term in asymptotically flat spacetime. Our approach is through the non-perturbative fragmentation instability. By this approach, we investigate whether the initial black hole can be broken into two black holes by comparing the entropy of the initial black hole with the sum of those of two fragmented black holes. The relation between the black hole instability and the GB coupling with dilaton hair are presented. We describe the phase diagrams with respect to the mass of the black hole solutions and coupling constants. We find that a perturbatively stable black hole can be unstable under fragmentation. (orig.)
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.
The Arithmetico-geometric Mean of Gauss
Indian Academy of Sciences (India)
2000-08-01
Aug 1, 2000 ... where these functions are assumed to have continuous first derivatives. This condition is indeed enough to en- force rectifiability as we show now. Let a = to < t1 < ... The same problem persists with the integrals of their derivatives etc. ..... There is a transformation similar to the one used by. Gauss in the ...
Demystifying Electric Flux and Gauss's Law
McManus, Jeff
2017-01-01
Many physics students have experienced the difficulty of internalizing concepts in electrostatics. After studying concrete, measurable details in mechanics, they are challenged by abstract ideas such as electric fields, flux, Gauss's law, and electric potential. There are a few well-known hands-on activities that help students get experience with…
Transformations of some Gauss hypergeometric functions.
Vidûnas, R.
2005-01-01
This paper presents explicit algebraic transformations of some Gauss hypergeometric functions. Specifically, the transformations considered apply to hypergeometric solutions of hypergeometric differential equations with the local exponent differences 1/k,1/l,1/m such that k,l,m are positive integers
Explorations of the Gauss-Lucas Theorem
Brilleslyper, Michael A.; Schaubroeck, Beth
2017-01-01
The Gauss-Lucas Theorem is a classical complex analysis result that states the critical points of a single-variable complex polynomial lie inside the closed convex hull of the zeros of the polynomial. Although the result is well-known, it is not typically presented in a first course in complex analysis. The ease with which modern technology allows…
Galileo, Gauss, and the Green Monster
Kalman, Dan; Teague, Daniel J.
2013-01-01
Galileo dropped cannonballs from the leaning tower of Pisa to demonstrate something about falling bodies. Gauss was a giant of mathematics and physics who made unparalleled contributions to both fields. More contemporary (and not a person), the Green Monster is the left-field wall at the home of the Boston Red Sox, Fenway Park. Measuring 37 feet…
The Archimedes Principle and Gauss's Divergence Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 3; Issue 11. The Archimedes Principle and Gauss's Divergence Theorem. Subhashis Nag. General Article Volume 3 Issue 11 November 1998 pp 18-29. Fulltext. Click here to view fulltext PDF. Permanent link:
Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
Hale, Nicholas
2013-03-06
An efficient algorithm for the accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton\\'s root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100. © 2013 Society for Industrial and Applied Mathematics.
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.
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.
Sum rules for quasifree scattering of hadrons
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.
Driving corrugated donut rotors with Laguerre-Gauss beams.
Loke, Vincent L Y; Asavei, Theodor; Stilgoe, Alexander B; Nieminen, Timo A; Rubinsztein-Dunlop, Halina
2014-08-11
Tightly-focused laser beams that carry angular momentum have been used to trap and rotate microrotors. In particular, a Laguerre-Gauss mode laser beam can be used to transfer its orbital angular momentum to drive microrotors. We increase the torque efficiency by a factor of about 2 by designing the rotor such that its geometry is compatible with the driving beam, when driving the rotation with the optimum beam, rather than beams of higher or lower orbital angular momentum. Based on Floquet's theorem, the order of discrete rotational symmetry of the rotor can be made to couple with the azimuthal mode of the Laguerre-Gauss beam. We design corrugated donut rotors, that have a flat disc-like profile, with the help of the discrete dipole approximation and the T-matrix methods in parallel with experimental demonstrations of stable trapping and torque measurement. We produce and test such a rotor using two-photon photopolymerization. With a rotor that has 8-fold discrete rotational symmetry, an outer radius of 1.85 μm and a hollow core radius of 0.5 μm, we were able to transfer approximately 0.3 h̄ per photon of the orbital angular momentum from an LG04 beam.
On zero sum subsequences of restricted size
Indian Academy of Sciences (India)
Additive number theory, factorization theory and graph theory provide a good source for combinatorial problems in finite abelian groups (for instance, see [2, 4, 16–18]. Among them, zero sum problems have been of growing interest. The cornerstone of almost all recent combinatorial research on zero-sum problems is a ...
Efficient generation of Hermite-Gauss and Ince-Gauss beams through kinoform phase elements.
Aguirre-Olivas, Dilia; Mellado-Villaseñor, Gabriel; Sánchez-de-la-Llave, David; Arrizón, Victor
2015-10-01
We discuss the generation of Hermite-Gauss and Ince-Gauss beams employing phase elements whose transmittances coincide with the phase modulations of such beams. A scaled version of the desired field appears, distorted by marginal optical noise, at the element's Fourier domain. The motivation to perform this study is that, in the context of the proposed approach, the desired beams are generated with the maximum possible efficiency. A disadvantage of the method is the distortion of the desired beams by the influence of several nondesired beam modes generated by the phase elements. We evaluate such distortion employing the root mean square deviation as a figure of merit.
Laguerre-Gauss basis functions in observer models
Burgess, Arthur E.
2003-05-01
Observer models based on linear classifiers with basis functions (channels) are useful for evaluation of detection performance with medical images. They allow spatial domain calculations with a covariance matrix of tractable size. The term "channelized Fisher-Hotelling observer" will be used here. It is also called the "channelized Hotelling observer" model. There are an infinite number of basis function (channel ) sets that could be employed. Examples of channel sets that have been used include: difference of Gaussian (DOG) filters, difference of Mesa (DOM) filters and Laguerre-Gauss (LG) basis functions. Another option, sums of LG functions (LGS), will also be presented here. This set has the advantage of having no DC response. The effect of the number of images used to estimate model observer performance will be described, for both filtered 1/f3 noise and GE digital mammogram backgrounds. Finite sample image sets introduce both bias and variance to the estimate. The results presented here agree with previous work on linear classifiers. The LGS basis set gives a small but statistically significant reduction in bias. However, this may not be of much practical benefit. Finally, the effect of varying the number of basis functions included in the set will be addressed. It was found that four LG bases or three LGS bases are adequate.
Does the Gauss-Bonnet term stabilize wormholes?
Kokubu, Takafumi; Maeda, Hideki; Harada, Tomohiro
2015-01-01
The effect of the Gauss-Bonnet term on the existence and dynamical stability of thin-shell wormholes as negative tension branes is studied in the arbitrary dimensional spherically, planar, and hyperbolically symmetric spacetimes. We consider radial perturbations against the shell for the solutions which have the Z${}_2$ symmetry and admit the general relativistic limit. It is shown that the Gauss-Bonnet term shrinks the parameter region admitting static wormholes. The effect of the Gauss-Bonn...
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....
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...
Narison, Stéphan
The aim of the book is to give an introduction to the method of QCD Spectral Sum Rules and to review its developments. After some general introductory remarks, Chiral Symmetry, the Historical Developments of the Sum Rules and the necessary materials for perturbative QCD including the MS regularization and renormalization schemes are discussed. The book also gives a critical review and some improvements of the wide uses of the QSSR in Hadron Physics and QSSR beyond the Standard Hadron Phenomenology. The author has participated actively in this field since 1978 just before the expanding success
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....
Cylindrically polarized Bessel–Gauss beams
International Nuclear Information System (INIS)
Madhi, Daena; Aiello, Andrea; Ornigotti, Marco
2015-01-01
We present a study of radially and azimuthally polarized Bessel–Gauss (BG) beams in both the paraxial and nonparaxial regime. We discuss the validity of the paraxial approximation and the form of the nonparaxial corrections for BG beams. We show that independently on the ratio between the Bessel aperture cone angle ϑ 0 and the Gaussian beam divergence θ 0 , the nonparaxial corrections are alway very small and therefore negligible. The explicit expressions for the nonparaxial vector electric field components are also reported. (paper)
Gauss-Bonnet Supergravity in Six Dimensions.
Novak, Joseph; Ozkan, Mehmet; Pang, Yi; Tartaglino-Mazzucchelli, Gabriele
2017-09-15
The supersymmetrization of curvature squared terms is important in the study of the low-energy limit of compactified superstrings where a distinguished role is played by the Gauss-Bonnet combination, which is ghost-free. In this Letter, we construct its off-shell N=(1,0) supersymmetrization in six dimensions for the first time. By studying this invariant together with the supersymmetric Einstein-Hilbert term, we confirm and extend known results of the α^{'}-corrected string theory compactified to six dimensions. Finally, we analyze the spectrum about the AdS_{3}×S^{3} solution.
Twisting formula of epsilon factors
Indian Academy of Sciences (India)
Sazzad Ali Biswas
2017-08-07
mail: sabiswas@cmi.ac.in; sazzad.jumath@gmail.com ...... [1] Berndt B C, Evans R J, Williams K S, Gauss and Jacobi sums, Canadian Mathematical Society. Series of Monographs and Advanced Texts 21 (1998) (Wiley).
Scalar modified Bessel-Gauss beams and waves.
Seshadri, S R
2007-09-01
For modified Bessel-Gauss beams, the modulating function for the Gaussian, instead of a Bessel function of real argument, is a Bessel function of imaginary argument. The modified Bessel-Gauss beams and their full wave generalizations are treated with particular attention to the spreading properties on propagation for the azimuthal mode numbers m=0 and m=1. The spreading on propagation of the peak and the null in the radiation pattern obtained in the propagation direction for m=0 and m=1, respectively, is substantially less for the modified Bessel-Gauss waves than that for the corresponding Bessel-Gauss waves. The total power transported by the waves is determined and compared with that of the corresponding paraxial beam to assess the quality of the paraxial beam approximation for the wave. The powers in the Bessel-Gauss wave and the modified Bessel-Gauss wave are finite in contrast to that in the Bessel wave. With respect to both the spreading properties and the quality of the paraxial beam approximation, the modified Bessel-Gauss beam is an improvement over the Bessel-Gauss beam.
African Journals Online (AJOL)
Tracie1
Résumé. 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 ...
International Nuclear Information System (INIS)
Radyushkin, A.V.; Ruskov, R.
1992-01-01
We extend the QCD sum rule analysis of the form factor F γ* γ *→π 0 (q 1 2 ,q 2 2 ) into the region of small virtuality of one of the photons, where one should perform more precisely an OPE to factorize large and small distance contributions. As a first step the form factor is investigated in the region of moderate virtualities and the full corrections in the sum rule are obtained. It is shown that the infrared mass singularities are subtracted in the corresponding OPE for essentially nonsymmetric kinematics due to the operators of lowest two twists. On a simple scalar example the most important steps of the further calculations are demonstrated. 26 refs.; 8 figs
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.
In the paper `On GCD and LCM in Domains { A Conjecture of Gauss ...
Indian Academy of Sciences (India)
In the paper `On GCD and LCM in Domains {. A Conjecture of Gauss' in Resonance [1], some elegant proofs for the fact that ZZ[√−d] (d ≥ 3, square-free) is not a UFD are given. The aim of this note is to provide an alternative proof for this theorem. 1. Introduction. A unique factorization domain (UFD) is an integral do-.
Indeterminacy points for superposed Yukawa and Gauss potentials
International Nuclear Information System (INIS)
Choubey, Jyoti; Sharma, L.K.
1981-01-01
Eigenenergy expansion for the superposition of Yukawa and Gauss potentials for calculating the first indeterminacy points is derived. Behaviour of Regge trajectories for the superposed potential is also studied. (author)
Bessel–Gauss resonator with internal amplitude filter
CSIR Research Space (South Africa)
Litvin, IA
2008-05-01
Full Text Available The authors investigate a conventional resonator configuration, using only spherical curvature optical elements, for the generation of Bessel–Gauss beams. This is achieved through the deployment of a suitable amplitude filter at a Fourier plane...
The Gauss-Bonnet identity in quartic gravitation theories
International Nuclear Information System (INIS)
Gomes, M.
1989-01-01
The possible modifications in Gauss-Bonnet relation due to quantum oscillations are studied. The introduction of quantum operator correspondent in the function of two points, in space without singularities is calculated. (M.C.K.)
Composite Gauss-Legendre Quadrature with Error Control
Prentice, J. S. C.
2011-01-01
We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)
Directory of Open Access Journals (Sweden)
Young-Doo Kwon
2013-01-01
Full Text Available This study examined the characteristics of a variable three-point Gauss quadrature using a variable set of weighting factors and corresponding optimal sampling points. The major findings were as follows. The one-point, two-point, and three-point Gauss quadratures that adopt the Legendre sampling points and the well-known Simpson’s 1/3 rule were found to be special cases of the variable three-point Gauss quadrature. In addition, the three-point Gauss quadrature may have out-of-domain sampling points beyond the domain end points. By applying the quadratically extrapolated integrals and nonlinearity index, the accuracy of the integration could be increased significantly for evenly acquired data, which is popular with modern sophisticated digital data acquisition systems, without using higher-order extrapolation polynomials.
Gauss-Green cubature and moment computation over arbitrary geometries
Sommariva, Alvise; Vianello, Marco
2009-09-01
We have implemented in Matlab a Gauss-like cubature formula over arbitrary bivariate domains with a piecewise regular boundary, which is tracked by splines of maximum degree p (spline curvilinear polygons). The formula is exact for polynomials of degree at most 2n-1 using N~cmn2 nodes, 1directly on univariate Gauss-Legendre quadrature via Green's integral formula. Several numerical tests are presented, including computation of standard as well as orthogonal moments over a nonstandard planar region.
Directory of Open Access Journals (Sweden)
Danilo Bedoya Valencia
2011-12-01
Full Text Available In this article, we have derived the probability density functions of the productand the quotient of two independent random variables having Gauss hypergeometricdistribution. These densities have been expressed in terms of Appell'srst hypergeometric function F1. Further, Renyi and Shannon entropies havealso been derived for the Gauss hypergeometric distribution.En este artículo, hemos derivado las funciones de densidad de probabilidad del producto y el cociente de dos variables aleatorias independientes que tienen una distribución hipergeométrica de Gauss. Estas densidades se han expresada en términos de la primera función hipergeométrica de Appell F1. Además, entropías Rényi y Shannon también se han derivado de la distribución hipergeométrica de Gauss.
Ricci-Gauss-Bonnet holographic dark energy
Saridakis, Emmanuel N.
2018-03-01
We present a model of holographic dark energy in which the infrared cutoff is determined by both the Ricci and the Gauss-Bonnet invariants. Such a construction has the significant advantage that the infrared cutoff, and consequently the holographic dark energy density, does not depend on the future or the past evolution of the universe, but only on its current features, and moreover it is determined by invariants, whose role is fundamental in gravitational theories. We extract analytical solutions for the behavior of the dark energy density and equation-of-state parameters as functions of the redshift. These reveal the usual thermal history of the universe, with the sequence of radiation, matter and dark energy epochs, resulting in the future to a complete dark energy domination. The corresponding dark energy equation-of-state parameter can lie in the quintessence or phantom regime, or experience the phantom-divide crossing during the cosmological evolution, and its asymptotic value can be quintessencelike, phantomlike, or be exactly equal to the cosmological-constant value. Finally, we extract the constraints on the model parameters that arise from big bang nucleosynthesis.
Cosmology of modified Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Li Baojiu; Barrow, John D.; Mota, David F.
2007-01-01
We consider the cosmology where some function f(G) of the Gauss-Bonnet term G is added to the gravitational action to account for the late-time accelerating expansion of the universe. The covariant and gauge invariant perturbation equations are derived with a method which could also be applied to general f(R,R ab R ab ,R abcd R abcd ) gravitational theories. It is pointed out that, despite their fourth-order character, such f(G) gravity models generally cannot reproduce arbitrary background cosmic evolutions; for example, the standard ΛCDM paradigm with Ω DE =0.76 cannot be realized in f(G) gravity theories unless f is a true cosmological constant because it imposes exclusionary constraints on the form of f(G). We analyze the perturbation equations and find that, as in the f(R) model, the stability of early-time perturbation growth puts some constraints on the functional form of f(G), in this case ∂ 2 f/∂G 2 <0. Furthermore, the stability of small-scale perturbations also requires that f not deviate significantly from a constant. These analyses are illustrated by numerically propagating the perturbation equations with a specific model reproducing a representative ΛCDM cosmic history. Our results show how the f(G) models are highly constrained by cosmological data
Jäntschi, Lorentz; Bálint, Donatella; Bolboacă, Sorana D
2016-01-01
Multiple linear regression analysis is widely used to link an outcome with predictors for better understanding of the behaviour of the outcome of interest. Usually, under the assumption that the errors follow a normal distribution, the coefficients of the model are estimated by minimizing the sum of squared deviations. A new approach based on maximum likelihood estimation is proposed for finding the coefficients on linear models with two predictors without any constrictive assumptions on the distribution of the errors. The algorithm was developed, implemented, and tested as proof-of-concept using fourteen sets of compounds by investigating the link between activity/property (as outcome) and structural feature information incorporated by molecular descriptors (as predictors). The results on real data demonstrated that in all investigated cases the power of the error is significantly different by the convenient value of two when the Gauss-Laplace distribution was used to relax the constrictive assumption of the normal distribution of the error. Therefore, the Gauss-Laplace distribution of the error could not be rejected while the hypothesis that the power of the error from Gauss-Laplace distribution is normal distributed also failed to be rejected.
Social Security Administration — Staging Instance for all SUMs Counts related projects including: Redeterminations/Limited Issue, Continuing Disability Resolution, CDR Performance Measures, Initial...
Gauss-Bonnet black holes in dS spaces
International Nuclear Information System (INIS)
Cai Ronggen; Guo Qi
2004-01-01
We study the thermodynamic properties associated with the black hole horizon and cosmological horizon for the Gauss-Bonnet solution in de Sitter space. When the Gauss-Bonnet coefficient is positive, a locally stable small black hole appears in the case of spacetime dimension d=5, the stable small black hole disappears, and the Gauss-Bonnet black hole is always unstable quantum mechanically when d≥6. On the other hand, the cosmological horizon is found to be always locally stable independent of the spacetime dimension. But the solution is not globally preferred; instead, the pure de Sitter space is globally preferred. When the Gauss-Bonnet coefficient is negative, there is a constraint on the value of the coefficient, beyond which the gravity theory is not well defined. As a result, there is not only an upper bound on the size of black hole horizon radius at which the black hole horizon and cosmological horizon coincide with each other, but also a lower bound depending on the Gauss-Bonnet coefficient and spacetime dimension. Within the physical phase space, the black hole horizon is always thermodynamically unstable and the cosmological horizon is always stable; furthermore, as in the case of the positive coefficient, the pure de Sitter space is still globally preferred. This result is consistent with the argument that the pure de Sitter space corresponds to an UV fixed point of dual field theory
Resolution enhancement in confocal microscopy using Bessel-Gauss beams.
Thibon, Louis; Lorenzo, Louis E; Piché, Michel; De Koninck, Yves
2017-02-06
Laser scanning microscopy is limited in lateral resolution by the diffraction of light. We show that we can obtain twenty percent improvement in the resolution of confocal microscopy using Bessel-Gauss beams with the right pinhole size compared to conventional Gaussian beam based confocal microscopy. Advantages of this strategy include simplicity of installation and use, linear polarization compatibility, possibility to combine it with other resolution enhancement and superresolution strategies. We demonstrate the resolution enhancement capabilities of Bessel-Gauss beams both theoretically and experimentally on nano-spheres and biological tissue samples without any residual artifacts coming from the Bessel-Gauss beam side lobes with a resolution of 0.39λ. We also show that the resolution enhancement of Bessel-Gauss beams yields a better statistical colocalization analysis with fewer false positive results than when using Gaussian beams. We have also used Bessel-Gauss beams of different orders to further improve the resolution by combining them in SLAM microscopy (Switching LAser Modes : Dehez, Optics Express, 2013) achieving a resolution of 0.2λ.
Concentration inequalities for sums and martingales
Bercu, Bernard; Rio, Emmanuel
2015-01-01
The purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales. The first chapter is devoted to classical asymptotic results in probability such as the strong law of large numbers and the central limit theorem. Our goal is to show that it is really interesting to make use of concentration inequalities for sums and martingales. The second chapter deals with classical concentration inequalities for sums of independent random variables such as the famous Hoeffding, Bennett, Bernstein and Talagrand inequalities. Further results and improvements are also provided such as the missing factors in those inequalities. The third chapter concerns concentration inequalities for martingales such as Azuma-Hoeffding, Freedman and De la Pena inequalities. Several extensions are also provided. The fourth chapter is devoted to applications of concentration inequalities in probability and statistics.
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.
Braneworld dynamics in Einstein-Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Maeda, Hideki; Sahni, Varun; Shtanov, Yuri
2007-01-01
We discuss the cosmological evolution of a braneworld in five-dimensional Gauss-Bonnet gravity. Our discussion allows the fifth (bulk) dimension to be spacelike as well as timelike. The resulting equations of motion have the form of a cubic equation in the (H 2 ,(ρ+σ) 2 ) plane, where σ is the brane tension and ρ is the matter density. This allows us to conduct a comprehensive pictorial analysis of cosmological evolution for the Gauss-Bonnet brane. The many interesting properties of this braneworld include the possibility of accelerated expansion at late times. For a finite region in parameter space the accelerated expansion can be phantomlike so that w<-1. At late times, this branch approaches de Sitter space (w=-1) and avoids the big-rip singularities usually present in phantom models. For a timelike extra dimension the Gauss-Bonnet brane can bounce and avoid the initial singularity
Framed 4-graphs: Euler tours, Gauss circuits and rotating circuits
International Nuclear Information System (INIS)
Il'yutko, Denis P
2011-01-01
We consider connected finite 4-valent graphs with the structure of opposite edges at each vertex (framed 4-graphs). For any of such graphs there exist Euler tours, in travelling along which at each vertex we turn from an edge to a nonopposite one (rotating circuits); and at the same time, it is not true that for any such graph there exists an Euler tour passing from an edge to the opposite one at each vertex (a Gauss circuit). The main result of the work is an explicit formula connecting the adjacency matrices of the Gauss circuit and an arbitrary Euler tour. This formula immediately gives us a criterion for the existence of a Gauss circuit on a given framed 4-graph. It turns out that the results are also valid for all symmetric matrices (not just for matrices realisable by a chord diagram). Bibliography: 24 titles.
Gravitational perfect fluid collapse in Gauss-Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Abbas, G.; Tahir, M. [The Islamia University of Bahawalpur, Department of Mathematics, Bahawalpur (Pakistan)
2017-08-15
The Einstein Gauss-Bonnet theory of gravity is the low-energy limit of heterotic super-symmetric string theory. This paper deals with gravitational collapse of a perfect fluid in Einstein-Gauss-Bonnet gravity by considering the Lemaitre-Tolman-Bondi metric. For this purpose, the closed form of the exact solution of the equations of motion has been determined by using the conservation of the stress-energy tensor and the condition of marginally bound shells. It has been investigated that the presence of a Gauss-Bonnet coupling term α > 0 and the pressure of the fluid modifies the structure and time formation of singularity. In this analysis a singularity forms earlier than a horizon, so the end state of the collapse is a naked singularity depending on the initial data. But this singularity is weak and timelike, which goes against the investigation of general relativity. (orig.)
Gauss-Bonnet chameleon mechanism of dark energy
International Nuclear Information System (INIS)
Ito, Yusaku; Nojiri, Shin'ichi
2009-01-01
As a model of the current accelerated expansion of the Universe, we consider a model of the scalar-Einstein-Gauss-Bonnet gravity. This model includes the propagating scalar modes, which might give a large correction to the Newton law. In order to avoid this problem, we propose an extension of the chameleon mechanism where the scalar mode becomes massive due to the coupling with the Gauss-Bonnet term. Since the Gauss-Bonnet invariant does not vanish near the Earth or in the Solar System, even in the vacuum, the scalar mode is massive even in the vacuum and the correction to the Newton law could be small. We also discuss the possibility that the model could describe simultaneously the inflation in the early Universe, in addition to the current accelerated expansion.
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 ...
Rotating black holes in dilatonic Einstein-Gauss-Bonnet theory.
Kleihaus, Burkhard; Kunz, Jutta; Radu, Eugen
2011-04-15
We construct generalizations of the Kerr black holes by including higher-curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. We show that the domain of existence of these Einstein-Gauss-Bonnet-dilaton (EGBD) black holes is bounded by the Kerr black holes, the critical EGBD black holes, and the singular extremal EGBD solutions. The angular momentum of the EGBD black holes can exceed the Kerr bound. The EGBD black holes satisfy a generalized Smarr relation. We also compare their innermost stable circular orbits with those of the Kerr black holes and show the existence of differences which might be observable in astrophysical systems.
Asymptotics of weighted random sums
DEFF Research Database (Denmark)
Corcuera, José Manuel; Nualart, David; Podolskij, Mark
2014-01-01
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral...... of the weight process with respect to the Brownian motion when the distance between observations goes to zero. The result is obtained with the help of fractional calculus showing the power of this technique. This study, though interesting by itself, is motivated by an error found in the proof of Theorem 4...
Directory of Open Access Journals (Sweden)
Abel W. de Albuquerque
2005-06-01
Full Text Available Para se alcançar os objetivos previstos neste trabalho, determinaram-se os fatores da Equação Universal de Perda de Solo (EUPS em condições de chuva natural, num Luvissolo de Sumé, PB, em que os dados relativos aos anos de 1983-1990 foram obtidos na Estação Experimental de Sumé, PB, pertencente à Universidade Federal da Paraíba - UFPB, cujos tratamentos foram os seguintes: parcela descoberta e em alqueive contínuo, parcela com caatinga nativa, parcela com caatinga nova, parcelas em pousio, parcela com palma cultivada morro abaixo e parcela com palma cultivada em nível. Os valores médios anuais do fator erosividade da chuva expressos em EI30 e PI30 foram de 4.928 MJ mm ha-1 h-1 e 19.734 mm-2 h-1, respectivamente. Os valores do fator erodibilidade do solo (K foram calculados em 0,013 t h MJ-1 mm-1 e 0,003 t ha-1 mm-2, enquanto os valores determinados para o fator uso e manejo do solo foram os seguintes: 0,0015 (caatinga nativa, 0,0174 (caatinga nova, 0,0133 (cobertura morta, 0,0056 (cobertura morta, 0,5103 (palma cultivada morro abaixo e 0,2355 (palma cultivada em nível. O valor do fator práticas conservacionistas para palma cultivada em nível foi de 0,46The Universal Soil Loss Equation (USLE factors were determined in a Haplargs under natural rainfall conditions. Data concerning to the years of 1983 -1990 were obtained at the Sumé Experimental Station (Paraíba State - Brazil of the Federal University of Paraíba (UFPB. The treatments consisted of runoff plots with bare soil, native semiarid vegetation runoff plot, mulch runoff plot, palm leaf under downhill runoff plot and under contour palm leaf runoff plot. The annual average of the rainfall erosivity factors EI30 and PI30 were 4,928 MJ mm ha-1 h-1 and 19,734 mm-2 h-1, respectively. The calculated annual mean values of the erodibility parameters were calculated in 0.013 t h MJ-1 mm-1 and 0.003 t h ha-1 mm-2. The calculated values for the support practice factor cropping
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.
A Generalization of Riemann Sums
Kouba, Omran
2014-01-01
We generalize the property that Riemann sums of a continuous function corresponding to equidistant subdivision of an interval converge to the integral of that function, and we give some applications of this generalization.
CLOSED FORM OF THE STEERED ELONGATED HERMITE-GAUSS WAVELETS
Papari, Giuseppe; Campisi, Patrizio; Petkov, Nicolai
2010-01-01
We provide a closed form, both in the spatial and in the frequency domain, of a family of wavelets which arise from steering elongated Hermite-Gauss filters. These wavelets have interesting mathematical properties, as they form new dyadic families of eigenfunctions of the 2D Fourier transform, and
Gauss law constraints on Debye–Hückel screening
Indian Academy of Sciences (India)
Abstract. We demand that the Gauss law at the edge must be obeyed by the electric potential φ(r) generated within a neutral plasma/electrolyte of strictly finite size by the in- troduction of a test charge qb. Our proposal has the nice features that total ionic numbers are conserved, the point-Coulomb behaviour of φ(r) is ...
Maximum entropy estimation via Gauss-LP quadratures
Thély, Maxime; Sutter, Tobias; Mohajerin Esfahani, P.; Lygeros, John; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri
2017-01-01
We present an approximation method to a class of parametric integration problems that naturally appear when solving the dual of the maximum entropy estimation problem. Our method builds up on a recent generalization of Gauss quadratures via an infinite-dimensional linear program, and utilizes a
Gauss law constraints on Debye–Hückel screening
Indian Academy of Sciences (India)
We demand that the Gauss law at the edge must be obeyed by the electric potential () generated within a neutral plasma/electrolyte of strictly ﬁnite size by the introduction of a test charge b. Our proposal has the nice features that total ionic numbers are conserved, the point-Coulomb behaviour of () is guaranteed at ...
Wormholes in Dilatonic Einstein-Gauss-Bonnet Theory
Kanti, Panagiota; Kleihaus, Burkhard; Kunz, Jutta
2011-01-01
We construct traversable wormholes in dilatonic Einstein-Gauss-Bonnet theory in four spacetime dimensions, without needing any form of exotic matter. We determine their domain of existence, and show that these wormholes satisfy a generalised Smarr relation. We demonstrate linear stability with respect to radial perturbations for a subset of these wormholes.
Wormholes in dilatonic Einstein-Gauss-Bonnet theory.
Kanti, Panagiota; Kleihaus, Burkhard; Kunz, Jutta
2011-12-30
We construct traversable wormholes in dilatonic Einstein-Gauss-Bonnet theory in four spacetime dimensions, without needing any form of exotic matter. We determine their domain of existence, and show that these wormholes satisfy a generalized Smarr relation. We demonstrate linear stability with respect to radial perturbations for a subset of these wormholes.
Interpolation on sparse Gauss-Chebyshev grids in higher dimensions
F. Sprengel
1998-01-01
textabstractIn this paper, we give a unified approach to error estimates for interpolation on sparse Gauss--Chebyshev grids for multivariate functions from Besov--type spaces with dominating mixed smoothness properties. The error bounds obtained for this method are almost optimal for the considered
Holographic vector superconductor in Gauss-Bonnet gravity
Lu, Jun-Wang; Wu, Ya-Bo; Cai, Tuo; Liu, Hai-Min; Ren, Yin-Shuan; Liu, Mo-Lin
2016-02-01
In the probe limit, we numerically study the holographic p-wave superconductor phase transitions in the higher curvature theory. Concretely, we study the influences of Gauss-Bonnet parameter α on the Maxwell complex vector model (MCV) in the five-dimensional Gauss-Bonnet-AdS black hole and soliton backgrounds, respectively. In the two backgrounds, the improving Gauss-Bonnet parameter α and dimension of the vector operator Δ inhibit the vector condensate. In the black hole, the condensate quickly saturates a stable value at lower temperature. Moreover, both the stable value of condensate and the ratio ωg /Tc increase with α. In the soliton, the location of the second pole of the imaginary part increases with α, which implies that the energy of the quasiparticle excitation increases with the improving higher curvature correction. In addition, the influences of the Gauss-Bonnet correction on the MCV model are similar to the ones on the SU(2) p-wave model, which confirms that the MCV model is a generalization of the SU(2) Yang-Mills model even without the applied magnetic field to some extent.
Composite Gauss-Legendre Formulas for Solving Fuzzy Integration
Directory of Open Access Journals (Sweden)
Xiaobin Guo
2014-01-01
Full Text Available Two numerical integration rules based on composition of Gauss-Legendre formulas for solving integration of fuzzy numbers-valued functions are investigated in this paper. The methods' constructions are presented and the corresponding convergence theorems are shown in detail. Two numerical examples are given to illustrate the proposed algorithms finally.
Understanding Gauss's Law Using Spreadsheets
Baird, William H.
2013-01-01
Some of the results from the electrostatics portion of introductory physics are particularly difficult for students to understand and/or believe. For students who have yet to take vector calculus, Gauss's law is far from obvious and may seem more difficult than Coulomb's. When these same students are told that the minimum potential…
Gauss-Bonnet's Theorem and Closed Frenet Frames
DEFF Research Database (Denmark)
Røgen, Peter
1997-01-01
curves are found using Gauss-Bonnet's Theorem after cutting the curve into simple closed sub-curves. At this point an error in the litterature is corrected. If the spherecal curve is the tangent indicatrix of a space-curve we obtain a new short proof of a formula for integrated torsion presented...
Automatic classification of protein structure by using Gauss integrals
DEFF Research Database (Denmark)
Røgen, Peter; Fain, B.
2003-01-01
We introduce a method of looking at, analyzing, and comparing protein structures. The topology of a protein is captured by 30 numbers inspired by Vassiliev knot invariants. To illustrate the simplicity and power of this topological approach, we construct a measure (scaled Gauss metric, SGM...
Small-displacement measurements using high-order Hermite-Gauss modes
Energy Technology Data Exchange (ETDEWEB)
Sun, Hengxin; Liu, Kui; Liu, Zunlong; Guo, Pengliang; Zhang, Junxiang; Gao, Jiangrui, E-mail: jrgao@sxu.edu.cn [State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006 (China)
2014-03-24
We present a scheme for small-displacement measurements using high-order Hermite-Gauss modes and balanced homodyne detection. We demonstrate its use with experimental results of displacement measurements using fundamental transverse mode TEM{sub 00} and first order transverse mode TEM{sub 10} as signal modes. The results show a factor of 1.41 improvement in measurement precision with the TEM{sub 10} mode compared with that with the TEM{sub 00} mode. This scheme has potential applications in precision metrology, atomic force microscopy, and optical imaging.
On zero sum subsequences of restricted size
Indian Academy of Sciences (India)
. Jhunsi, Allahabad 211 019, ... Zero sum problems; Kemnitz' conjecture; sequence sums. 1. Introduction and notations ... The cornerstone of almost all recent combinatorial research on zero-sum problems is a theorem of Erdös, Ginzburg and.
Directory of Open Access Journals (Sweden)
Jamieson D.S.
2014-03-01
Full Text Available Cadmium isotopes have been presented for decades as excellent examples of vibrational nuclei, with low-lying levels interpreted as multi-phonon quadrupole, octupole, and mixed-symmetry states. A large amount of spectroscopic data has been obtained through various experimental studies of cadmiumisotopes. In the present work, the 111Cd(d→$\\overrightarrow {\\rm{d}} $,p112Cd reaction was used to investigate the single-particle structure of the 112Cd nucleus. A 22 MeV beam of polarized deuterons was obtained at the Maier-Leibnitz laboratory in Garching, Germany. The reaction ejectiles were momentum analyzed using a Q3D spectrograph, and 130 levels have been identified up to 4.2 MeV of excitation energy. Using DWBA analysis with optical model calculations, spin-parity assignments have been made for observed levels, and spectroscopic factors have been extracted from the experimental angular distributions of differential cross section and analyzing power. In this high energy resolution investigation, many additional levels have been observed compared with the previous (d,p study using 8 MeV deuterons [1]. There were a total of 44 new levels observed, and the parity assignments of 34 levels were improved.
Directory of Open Access Journals (Sweden)
Anne M. Hofmeister
2017-11-01
Full Text Available Galactic mass consistent with luminous mass is obtained by fitting rotation curves (RC = tangential velocities vs. equatorial radius r using Newtonian force models, or can be unambiguously calculated from RC data using a model based on spin. In contrast, mass exceeding luminous mass is obtained from multi-parameter fits using potentials associated with test particles orbiting in a disk around a central mass. To understand this disparity, we explore the premises of these mainstream disk potential models utilizing the theorem of Gauss, thermodynamic concepts of Gibbs, the findings of Newton and Maclaurin, and well-established techniques and results from analytical mathematics. Mainstream models assume that galactic density in the axial (z and r directions varies independently: we show that this is untrue for self-gravitating objects. Mathematics and thermodynamic principles each show that modifying Poisson’s equation by summing densities is in error. Neither do mainstream models differentiate between interior and exterior potentials, which is required by potential theory and has been recognized in seminal astronomical literature. The theorem of Gauss shows that: (1 density in Poisson’s equation must be averaged over the interior volume; (2 logarithmic gravitational potentials implicitly assume that mass forms a long, line source along the z axis, unlike any astronomical object; and (3 gravitational stability for three-dimensional shapes is limited to oblate spheroids or extremely tall cylinders, whereas other shapes are prone to collapse. Our findings suggest a mechanism for the formation of the flattened Solar System and of spiral galaxies from gas clouds. The theorem of Gauss offers many advantages over Poisson’s equation in analyzing astronomical problems because mass, not density, is the key parameter.
Grassmannians and Gauss maps in piecewise-linear topology
Levitt, Norman
1989-01-01
The book explores the possibility of extending the notions of "Grassmannian" and "Gauss map" to the PL category. They are distinguished from "classifying space" and "classifying map" which are essentially homotopy-theoretic notions. The analogs of Grassmannian and Gauss map defined incorporate geometric and combinatorial information. Principal applications involve characteristic class theory, smoothing theory, and the existence of immersion satifying certain geometric criteria, e.g. curvature conditions. The book assumes knowledge of basic differential topology and bundle theory, including Hirsch-Gromov-Phillips theory, as well as the analogous theories for the PL category. The work should be of interest to mathematicians concerned with geometric topology, PL and PD aspects of differential geometry and the geometry of polyhedra.
Noncommutative Wormhole Solutions in Einstein Gauss-Bonnet Gravity
Directory of Open Access Journals (Sweden)
Shamaila Rani
2016-01-01
Full Text Available We explore static spherically symmetric wormhole solutions in the framework of n-dimensional Einstein Gauss-Bonnet gravity. Our objective is to find out wormhole solutions that satisfy energy conditions. For this purpose, we consider two frameworks such as Gaussian distributed and Lorentzian distributed noncommutative geometry. Taking into account constant redshift function, we obtain solutions in the form of shape function. The fifth and sixth dimensional solutions with positive as well as negative Gauss-Bonnet coefficient are discussed. Also, we check the equilibrium condition for the wormhole solutions with the help of generalized Tolman-Oppenheimer-Volkoff equation. It is interesting to mention here that we obtain fifth dimensional stable wormhole solutions in both distributions that satisfy the energy conditions.
Noether symmetries in Gauss-Bonnet-teleparallel cosmology
Energy Technology Data Exchange (ETDEWEB)
Capozziello, Salvatore [Universita' di Napoli' ' Federico II' ' , Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica ' ' E. Pancini' ' , Napoli (Italy); INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Napoli (Italy); Gran Sasso Science Institute (INFN), L' Aquila (Italy); Tomsk State Pedagogical University, Tomsk (Russian Federation); De Laurentis, Mariafelicia [INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Napoli (Italy); Tomsk State Pedagogical University, Tomsk (Russian Federation); Goethe University, Institute for Theoretical Physics, Frankfurt (Germany); Laboratory of Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), Tomsk (Russian Federation); Dialektopoulos, Konstantinos F. [Universita' di Napoli' ' Federico II' ' , Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica ' ' E. Pancini' ' , Napoli (Italy); INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Napoli (Italy)
2016-11-15
A generalized teleparallel cosmological model, f(T{sub G},T), containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant T{sub G}, is studied in the framework of the Noether symmetry approach. As f(G, R) gravity, where G is the Gauss-Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, f(T{sub G},T) contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function f(T{sub G},T) and to derive exact cosmological solutions. (orig.)
Noether symmetries in Gauss-Bonnet-teleparallel cosmology.
Capozziello, Salvatore; De Laurentis, Mariafelicia; Dialektopoulos, Konstantinos F
2016-01-01
A generalized teleparallel cosmological model, [Formula: see text], containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant [Formula: see text], is studied in the framework of the Noether symmetry approach. As [Formula: see text] gravity, where [Formula: see text] is the Gauss-Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, [Formula: see text] contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function [Formula: see text] and to derive exact cosmological solutions.
Laguerre-Gauss beams versus Bessel beams showdown: peer comparison.
Mendoza-Hernández, Job; Arroyo-Carrasco, Maximino Luis; Iturbe-Castillo, Marcelo David; Chávez-Cerda, Sabino
2015-08-15
We present for the first time a comparison under similar circumstances between Laguerre-Gauss beams (LGBs) and Bessel beams (BB), and show that the former can be a better option for many applications in which BBs are currently used. By solving the Laguerre-Gauss differential equation in the asymptotic limit of a large radial index, we find the parameters to perform a peer comparison, showing that LGBs can propagate quasi-nondiffracting beams within the same region of space where the corresponding BBs do. We also demonstrate that LGBs, which have the property of self-healing, are more robust in the sense that they can propagate further than BBs under similar initial conditions.
From Foucault's Pendulum to the Gauss--Bonnet Theorem
Stoytchev, Orlin
2017-01-01
We present a self-contained proof of the Gauss-Bonnet theorem for two-dimensional surfaces embedded in $R^3$ using just classical vector calculus. The exposition should be accessible to advanced undergraduate and non-expert graduate students. It may be viewed as an illustration and exercise in multivariate calculus and a motivation to go deeper into the fields of geometry and topology.
Accurate Numerical Approximation to the Gauss-Lorentz Lineshape
Grivet
1997-03-01
The Gauss-Lorentz lineshape often observed in EPR or NMR is shown to be simply related to the complex error function. Using numerical algorithms developed for the evaluation of this function, experimental lineshapes can be accurately and rapidly simulated. Formulas are presented for the derivatives of the line profile with respect to the parameters and for the approximate computation of the overall linewidth. It is observed that accurate integrals require use of a wide integration interval.
Model checking sum and product
van Ditmarsch, H; Ruan, H; Verbrugge, L.C.; Zhang, S.; Jarvis, R.
2005-01-01
We model the well-known Sum-and-Product problem in a modal logic, and verify its solution in a model checker. The modal logic is public announcement logic. The riddle is then implemented and its solution verified in the epistemic model checker DEMO.
Path integrals as discrete sums
Bitar, Khalil; Khuri, N. N.; Ren, H. C.
1991-08-01
We present a new formulation of Feynman's path integral, based on Voronin's theorems on the universality of the Riemann zeta function. The result is a discrete sum over ``paths,'' each given by a zeta function. A new measure which leads to the correct quantum mechanics is explicitly given.
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 ... Keywords. Riemann zeta function; integral representation; Basel problem.
Reevaluation of the Gottfried sum
International Nuclear Information System (INIS)
Arneodo, M.; Arvidson, A.; Badelek, B.; Ballintijn, M.; Baum, G.; Beaufays, J.; Bird, I.G.; Bjoerkholm, P.; Botje, M.; Broggini, C.; Brueckner, W.; Bruell, A.; Burger, W.J.; Ciborowski, J.; van Dantzig, R.; Dyring, A.; Engelien, H.; Ferrero, M.I.; Fluri, L.; Gaul, U.; Granier, T.; von Harrach, D.; van der Heijden, M.; Heusch, C.; Ingram, Q.; Janson-Prytz, K.; de Jong, M.; Kabuss, E.M.; Kaiser, R.; Ketel, T.J.; Klein, F.; Kullander, S.; Landgraf, U.; Lindqvist, T.; Mallot, G.K.; Mariotti, C.; van Middelkoop, G.; Milsztajn, A.; Mizuno, Y.; Nassalski, J.; Oberski, J.; Nowotny, D.; Paic, A.; Peroni, C.; Povh, B.; Rieger, R.; Rith, K.; Roehrich, K.; Rondio, E.; Ropelewski, L.; Sandacz, A.; Sanders, D.; Scholz, C.; Schumacher, R.; Seitz, R.; Sever, F.; Shibata, T.; Siebler, M.; Simon, A.; Staiano, A.; Szleper, M.; Tzamouranis, Y.; Virchaux, M.; Vuilleumier, J.L.; Walcher, T.; Windmolders, R.; Witzmann, A.; Zetsche, F.; CERN, CH-1211, Geneva 23; Freiburg University, Hermann-Herder-Strasse 3, D-79104 Freiburg; Max-Planck Institut fuer Kernphysik, Postf. 103980, D-69029, Heidelberg; Heidelberg University, D-69120, Heidelberg; Mainz University, D-55099, Mainz; Mons University, Mons, Hainaut; Neuchatel University, Neuchatel; NIKHEF-K, P.O. Box 41882, NL-1009DB, Amsterdam; DAPNIA/SPP, CEN-Saclay, F-91191 Gif-sur-Yvette; University of California, Santa Cruz, California, 95064; Paul Scherrer Institute, CH-5232 Villigen PSI; Torino University, Via Pietro Giuria 1, 10125, Torino; Istituto Nazionale di Fisica Nucleare, Torino; Uppsala University, S-75121, Uppsala)
1994-01-01
We present a new determination of the nonsinglet structure function F p 2 - F n 2 at Q 2 =4 GeV 2 using recently measured values of F d 2 and F n 2 /F p 2 . A new evaluation of the Gottfried sum is given, which remains below the simple quark-parton model value of 1/3
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:
Energy Technology Data Exchange (ETDEWEB)
Pavluchenko, Sergey A. [Universidade Federal do Maranhao (UFMA), Programa de Pos-Graduacao em Fisica, Sao Luis, Maranhao (Brazil)
2017-08-15
In this paper we perform a systematic study of spatially flat [(3+D)+1]-dimensional Einstein-Gauss-Bonnet cosmological models with Λ-term. We consider models that topologically are the product of two flat isotropic subspaces with different scale factors. One of these subspaces is three-dimensional and represents our space and the other is D-dimensional and represents extra dimensions. We consider no ansatz of the scale factors, which makes our results quite general. With both Einstein-Hilbert and Gauss-Bonnet contributions in play, D = 3 and the general D ≥ 4 cases have slightly different dynamics due to the different structure of the equations of motion. We analytically study the equations of motion in both cases and describe all possible regimes with special interest on the realistic regimes. Our analysis suggests that the only realistic regime is the transition from high-energy (Gauss-Bonnet) Kasner regime, which is the standard cosmological singularity in that case, to the anisotropic exponential regime with expanding three and contracting extra dimensions. Availability of this regime allows us to put a constraint on the value of Gauss-Bonnet coupling α and the Λ-term - this regime appears in two regions on the (α, Λ) plane: α < 0, Λ > 0, αΛ ≤ -3/2 and α > 0, αΛ ≤ (3D{sup 2} - 7D + 6)/(4D(D-1)), including the entire Λ < 0 region. The obtained bounds are confronted with the restrictions on α and Λ from other considerations, like causality, entropy-to-viscosity ratio in AdS/CFT and others. Joint analysis constrains (α, Λ) even further: α > 0, D ≥ 2 with (3D{sup 2} - 7D + 6)/(4D(D-1)) ≥ αΛ ≥ -(D+2)(D+3)(D{sup 2} + 5D + 12)/(8(D{sup 2} + 3D + 6){sup 2}). (orig.)
Self-similar propagation of Hermite-Gauss water-wave pulses.
Fu, Shenhe; Tsur, Yuval; Zhou, Jianying; Shemer, Lev; Arie, Ady
2016-01-01
We demonstrate both theoretically and experimentally propagation dynamics of surface gravity water-wave pulses, having Hermite-Gauss envelopes. We show that these waves propagate self-similarly along an 18-m wave tank, preserving their general Hermite-Gauss envelopes in both the linear and the nonlinear regimes. The measured surface elevation wave groups enable observing the envelope phase evolution of both nonchirped and linearly frequency chirped Hermite-Gauss pulses, hence allowing us to measure Gouy phase shifts of high-order Hermite-Gauss pulses for the first time. Finally, when increasing pulse amplitude, nonlinearity becomes essential and the second harmonic of Hermite-Gauss waves was observed. We further show that these generated second harmonic bound waves still exhibit self-similar Hermite-Gauss shapes along the tank.
Generalizing higher-order Bessel-Gauss beams: analytical description and demonstration.
Schimpf, Damian N; Schulte, Jan; Putnam, William P; Kärtner, Franz X
2012-11-19
We report on a novel class of higher-order Bessel-Gauss beams in which the well-known Bessel-Gauss beam is the fundamental mode and the azimuthally symmetric Laguerre-Gaussian beams are special cases. We find these higher-order Bessel-Gauss beams by superimposing decentered Hermite-Gaussian beams. We show analytically and experimentally that these higher-order Bessel-Gauss beams resemble higher-order eigenmodes of optical resonators consisting of aspheric mirrors. This work is relevant for the many applications of Bessel-Gauss beams in particular the more recently proposed high-intensity Bessel-Gauss enhancement cavities for strong-field physics applications.
African Journals Online (AJOL)
AKA Boko
Résumé. Le rendement, la composition chimique et les propriétés antibactérienne et antifongique de l'huile essentielle extraite de la biomasse foliaire de Tetraclinis articulata (Vahl) du. Khémisset (Maroc) ont été étudiés. La teneur moyenne en huile essentielle des feuilles de cette espèce est 0,22 % par rapport à la ...
Torque-Summing Brushless Motor
Vaidya, J. G.
1986-01-01
Torque channels function cooperatively but electrically independent for reliability. Brushless, electronically-commutated dc motor sums electromagnetic torques on four channels and applies them to single shaft. Motor operates with any combination of channels and continues if one or more of channels fail electrically. Motor employs single stator and rotor and mechanically simple; however, each of channels electrically isolated from other so that failure of one does not adversely affect others.
African Journals Online (AJOL)
ISONIC
Résumé. 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 ...
Inner Structure of Gauss-Bonnet-Chern Theorem and the Morse Theory
Duan, Yi-Shi; Zhang, Peng-Ming
We define a new one-form HA based on the second fundamental tensor HabA¯, the Gauss-Bonnet-Chern form can be novelly expressed with this one-form. Using the φ-mapping theory we find that the Gauss-Bonnet-Chern density can be expressed in terms of the δ-function δ(φ) and the relationship between the Gauss-Bonnet-Chern theorem and Hopf-Poincaré theorem is given straightforwardly. The topological current of the Gauss-Bonnet-Chern theorem and its topological structure are discussed in details. At last, the Morse theory formula of the Euler characteristic is generalized.
International Nuclear Information System (INIS)
Zhou, J.; Li, S.; Liu, Y.
1993-01-01
Mitra's regularization of the masslike term, which was originally discussed in an Abelian model, is used to calculate the anomaly in the commutator of the Gauss-law operators for anomalous d=2 non-Abelian chiral theory. The Schwinger term in the commutator of the different Gauss-law operator is shifted, because of regularization ambiguities, to the commutator of the Gauss-law operators with themselves. The Poisson brackets of the Gauss-law constraints correspond to the Kac-Moody algebra, and the Gauss-law constraints are similar to the chiral constraints. In a sense, this kind of Gauss-law constraint structure differs from what Faddeev suggested
QCD Sum Rules and Models for Generalized Parton Distributions
Energy Technology Data Exchange (ETDEWEB)
Anatoly Radyushkin
2004-10-01
I use QCD sum rule ideas to construct models for generalized parton distributions. To this end, the perturbative parts of QCD sum rules for the pion and nucleon electromagnetic form factors are interpreted in terms of GPDs and two models are discussed. One of them takes the double Borel transform at adjusted value of the Borel parameter as a model for nonforward parton densities, and another is based on the local duality relation. Possible ways of improving these Ansaetze are briefly discussed.
Automatic classification of protein structure by using Gauss integrals
DEFF Research Database (Denmark)
Røgen, Peter; Fain, B.
2003-01-01
We introduce a method of looking at, analyzing, and comparing protein structures. The topology of a protein is captured by 30 numbers inspired by Vassiliev knot invariants. To illustrate the simplicity and power of this topological approach, we construct a measure (scaled Gauss metric, SGM......) of similarity of protein shapes. Under this metric, protein chains naturally separate into fold clusters. We use SGM to construct an automatic classification procedure for the CATH2.4 database. The method is very fast because it requires neither alignment of the chains nor any chain-chain comparison. It also...
Mode structure analysis of a Bessel-Gauss resonator
CSIR Research Space (South Africa)
Litvin, IA
2006-08-01
Full Text Available each other (F – focal length of mirrors). The core zone of mirror L1 is blinded by diaphragm with radius R1. As a whole this scheme is similar to scheme of resonator which was investigated by work [23]. Figure 1: Illustration... (circle with gauss field distribution of cross section) for all mode numbers23, then increasing or decreasing of diaphragm R1 or mirror L1 itself, we can expect an increasing or decreasing losses for each modes simultaneous only. We have another...
Extension of Gauss' method for the solution of Kepler's equation
Battin, R. H.; Fill, T. J.
1978-01-01
Gauss' method for solving Kepler's equation is extended to arbitrary epochs and orbital eccentricities. Although originally developed for near parabolic orbits in the vicinity of pericenter, a generalization of the method leads to a highly efficient algorithm which compares favorably to other methods in current use. A key virtue of the technique is that convergence is obtained by a method of successive substitutions with an initial approximation that is independent of the orbital parameters. The equations of the algorithm are universal, i.e., independent of the nature of the orbit whether elliptic, hyperbolic, parabolic or rectilinear.
Gravity Aided Navigation Precise Algorithm with Gauss Spline Interpolation
Directory of Open Access Journals (Sweden)
WEN Chaobin
2015-01-01
Full Text Available The gravity compensation of error equation thoroughly should be solved before the study on gravity aided navigation with high precision. A gravity aided navigation model construction algorithm based on research the algorithm to approximate local grid gravity anomaly filed with the 2D Gauss spline interpolation is proposed. Gravity disturbance vector, standard gravity value error and Eotvos effect are all compensated in this precision model. The experiment result shows that positioning accuracy is raised by 1 times, the attitude and velocity accuracy is raised by 1～2 times and the positional error is maintained from 100~200 m.
Gauss's law test of gravity at short range
Moody, M. V.; Paik, H. J.
1993-01-01
A null test of the gravitational inverse-square law can be performed by testing Gauss's law for the field. We have constructed a three-axis superconducting gravity gradiometer and carried out such a test. A lead pendulum weighing 1500 kg was used to produce a time-varying field. This experiment places a new (2-sigma) limit of alpha = (0.9 + or - 4.6) x 10 exp -4 at lambda of 1.5 m, where alpha and lambda are parameters for the generalized potential phi = -(GM/r)(l + alpha e exp -r/lambda).
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
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....
International Nuclear Information System (INIS)
Ivashchuk, V.D.; Kobtsev, A.A.
2015-01-01
A D-dimensional gravitational model with Gauss.Bonnet term is considered. When an ansatz with diagonal cosmological type metrics is adopted, we find solutions with an exponential dependence of the scale factors (with respect to a @gsynchronous-like@h variable) which describe an exponential expansion of @gour@h 3-dimensional factor space and obey the observational constraints on the temporal variation of effective gravitational constant G. Among them there are two exact solutions in dimensions D = 22, 28 with constant G and also an infinite series of solutions in dimensions D ≥ 2690 with the variation of G obeying the observational data. (orig.)
Nonparaxial Bessel and Bessel–Gauss pincers light-sheets
Energy Technology Data Exchange (ETDEWEB)
Mitri, F.G., E-mail: F.G.Mitri@ieee.org
2017-01-23
Highlights: • Bessel and Bessel–Gauss autofocusing light sheets (i.e. beams in 2D) are developed. • The light-sheets are synthesized based on the angular spectrum decomposition method. • Computations of the scattering, radiation force and torque benefit from the solutions. - Abstract: Nonparaxial optical Bessel and Bessel–Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.
Nonparaxial Bessel and Bessel–Gauss pincers light-sheets
International Nuclear Information System (INIS)
Mitri, F.G.
2017-01-01
Highlights: • Bessel and Bessel–Gauss autofocusing light sheets (i.e. beams in 2D) are developed. • The light-sheets are synthesized based on the angular spectrum decomposition method. • Computations of the scattering, radiation force and torque benefit from the solutions. - Abstract: Nonparaxial optical Bessel and Bessel–Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.
Phase space of modified Gauss-Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Carloni, Sante [Universidade de Lisboa-UL, Centro Multidisciplinar de Astrofisica-CENTRA, Instituto Superior Tecnico-IST, Lisbon (Portugal); Mimoso, Jose P. [Instituto de Astrofisica e Ciencias do Espaco, Universidade de Lisboa, Departamento de Fisica, Faculdade de Ciencias, Lisbon (Portugal)
2017-08-15
We investigate the evolution of non-vacuum Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the emergence of accelerated expansion. As in f(R) gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations. (orig.)
A note on the viability of Gauss-Bonnet cosmology
International Nuclear Information System (INIS)
Chingangbam, R.; Sami, M.; Tretyakov, P.V.; Toporensky, A.V.
2008-01-01
In this Letter, we analyze the viability of a vacuum Gauss-Bonnet cosmology by examining the dynamics of the homogeneous and anisotropic background in 4+1 dimensions. The trajectories of the system either originate from the standard singularity or from non-standard type, the later is characterized by the divergence of time derivative of the Hubble parameters for its finite value. At the onset, the system should relax to Einstein phase at late times as the effect of Gauss-Bonnet term becomes negligible in the low energy regime. However, we find that most of the trajectories emerging from the standard big-bang singularity lead to future re-collapse whereas the system beginning its evolution from the non-standard singularity enters the Kasner regime at late times. This leads to the conclusion that the measure of trajectories giving rise to a smooth evolution from a standard singularity to the Einstein phase is negligibly small for generic initial conditions
Controllable light capsules employing modified Bessel-Gauss beams.
Gong, Lei; Liu, Weiwei; Zhao, Qian; Ren, Yuxuan; Qiu, Xingze; Zhong, Mincheng; Li, Yinmei
2016-07-08
We report, in theory and experiment, on a novel class of controlled light capsules with nearly perfect darkness, directly employing intrinsic properties of modified Bessel-Gauss beams. These beams are able to naturally create three-dimensional bottle-shaped region during propagation as long as the parameters are properly chosen. Remarkably, the optical bottle can be controlled to demonstrate various geometries through tuning the beam parameters, thereby leading to an adjustable light capsule. We provide a detailed insight into the theoretical origin and characteristics of the light capsule derived from modified Bessel-Gauss beams. Moreover, a binary digital micromirror device (DMD) based scheme is first employed to shape the bottle beams by precise amplitude and phase manipulation. Further, we demonstrate their ability for optical trapping of core-shell magnetic microparticles, which play a particular role in biomedical research, with holographic optical tweezers. Therefore, our observations provide a new route for generating and controlling bottle beams and will widen the potentials for micromanipulation of absorbing particles, aerosols or even individual atoms.
Phase space of modified Gauss-Bonnet gravity.
Carloni, Sante; Mimoso, José P
2017-01-01
We investigate the evolution of non-vacuum Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the emergence of accelerated expansion. As in f ( R ) gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations.
Lascu, Dan
2014-01-01
We consider a family {τ m : m ≥ 2} of interval maps which are generalizations of the Gauss transformation. For the continued fraction expansion arising from τ m , we solve a Gauss-Kuzmin-type problem.
Gauss-Bonnet braneworld cosmological effect on relic density of dark matter
International Nuclear Information System (INIS)
Okada, Nobuchika; Okada, Satomi
2009-01-01
In Gauss-Bonnet braneworld cosmology, the Friedmann equation of our four-dimensional Universe on 3-brane is modified in a high energy regime (Gauss-Bonnet regime), while the standard expansion law is reproduced in low energies (standard regime). We investigate the Gauss-Bonnet braneworld cosmological effect on the thermal relic density of cold dark matter when the freeze-out of the dark matter occurs in the Gauss-Bonnet regime. We find that the resultant relic density is considerably reduced when the transition temperature, which connects the Gauss-Bonnet regime with the standard regime, is low enough. This result is in sharp contrast with the result previously obtained in the Randall-Sundrum braneworld cosmology, where the relic density is enhanced.
Anisotopic inflation with a non-abelian gauge field in Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Lahiri, Sayantani
2017-01-01
In presence of Gauss-Bonnet corrections, we study anisotropic inflation aided by a massless SU(2) gauge field where both the gauge field and the Gauss-Bonnet term are non-minimally coupled to the inflaton. In this scenario, under slow-roll approximations, the anisotropic inflation is realized as an attractor solution with quadratic forms of inflaton potential and Gauss-Bonnet coupling function. We show that the degree of anisotropy is proportional to the additive combination of two slow-roll parameters of the theory. The anisotropy may become either positive or negative similar to the non-Gauss-Bonnet framework, a feature of the model for anisotropic inflation supported by a non-abelian gauge field but the effect of Gauss-Bonnet term further enhances or suppresses the generated anisotropy.
Bessel-Gauss beam enhancement cavities for high-intensity applications.
Putnam, William P; Schimpf, Damian N; Abram, Gilberto; Kärtner, Franz X
2012-10-22
We introduce Bessel-Gauss beam enhancement cavities that may circumvent the major obstacles to more efficient cavity-enhanced high-field physics such as high-harmonic generation. The basic properties of Bessel-Gauss beams are reviewed and their transformation properties through simple optical systems (consisting of spherical and conical elements) are presented. A general Bessel-Gauss cavity design strategy is outlined, and a particular geometry, the confocal Bessel-Gauss cavity, is analyzed in detail. We numerically simulate the confocal Bessel-Gauss cavity and present an example cavity with 300 MHz repetition rate supporting an effective waist of 33 μm at the focus and an intensity ratio from the focus to the cavity mirror surfaces of 1.5 × 10(4).
The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1
Directory of Open Access Journals (Sweden)
Shuguo Shi
2008-03-01
Full Text Available In this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfaces in S1n+1, and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 and S1n+1. Particularly, we discuss the surfaces with conformal normal Gauss map in H³ and S³1, and prove a duality property. We give a Weierstrass representation formula for space-like surfaces in S³1 with conformal normal Gauss map. We also state the similar results for time-like surfaces in S³1. Some examples of surfaces in S³1 with conformal normal Gauss map are given and a fully nonlinear equation of Monge-Ampère type for the graphs in S³1 with conformal normal Gauss map is derived.Neste artigo, introduzimos a quarta forma fundamental de uma hipersuperfície em Hn+1 de uma hipersuperfície tipo-espaço em S1n+1, e discutimos a conformalidade da aplicação normal de Gauss de tais hipersuperfícies. Em particular, investigamos o caso de superfícies com aplicação normal de Gauss conforme em H³ e S³1, e provamos um teorema de dualidade. Apresentamos uma representação de Weierstrass para superfícies tipo-espaço em S³1 com aplicação de Gauss conforme. Enunciamos também resultados semelhantes para superfícies tipo-tempo em S³1. São dados alguns exemplos de superfícies em S³1 com aplicações de Gauss conformes, e é deduzida uma equação totalmente não-linear do tipo Monge-Ampère para gráficos em S³1 com aplicações de Gauss conformes.
Research algorithm for synthesis of double conjugation optical systems in the Gauss region
Directory of Open Access Journals (Sweden)
A. B. Ostrun
2014-01-01
Full Text Available The article focuses on the research of variable magnification optical systems of sophistic class - so-called double conjugation systems. When the magnification changes, they provide two pairs of fixed conjugate planes, namely object and image, as well as entrance and exit pupils. Similar systems are used in microscopy and complex schemes, where it is necessary to conform the pupils of contiguous removable optical components. Synthesis of double conjugation systems in Gauss region is not an easy task. To ensure complete immobility of the exit pupil in the system there should be three movable components or components with variable optical power.Analysis of the literature shows that the design of double conjugation optical system in the paraxial region has been neglected, all methods are not completely universal and suitable for automation.Based on the foregoing, the research and development of a universal method for automated synthesis of double conjugation systems in Gauss region formulated as an objective of the present work seem to be a challenge.To achieve this goal a universal algorithm is used. It is based on the fact that the output coordinates of paraxial rays are multilinear functions of optical surfaces and of axial thicknesses between surfaces. It allows us to create and solve a system of multilinear equations in semi-automatic mode to achieve the chosen values of paraxial characteristics.As a basic scheme for the synthesis a five-component system has been chosen with extreme fixed components and three mobile "internal" ones. The system was considered in two extreme states of moving parts. Initial values of axial thicknesses were taken from Hopkins' patent. Optical force five components were considered unknown. For calculation the system of five equations was created, which allowed us to obtain a certain back focal length, to provide the specified focal length and a fixed position of the exit pupil at a fixed entrance pupil.The scheme
Nonparaxial Bessel and Bessel-Gauss pincers light-sheets
Mitri, F. G.
2017-01-01
Nonparaxial optical Bessel and Bessel-Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.
Gauss decomposition, Wakimoto realisation and gauged WZNW models
International Nuclear Information System (INIS)
Arfaei, H.; Mohammedi, N.
1993-10-01
The implications of gauging the Wess-Zumino-Novikov-Witten (WZNW) model using the Gauss decomposition of the group elements are explored. We show that, contrary to standard gauging of WZNW models, this gauging is carried out by minimally coupling the gauge fields. We find that this gauging, in the case of gauging an abelian vector subgroup, differs from the standard one by terms proportional to the field strength of the gauge fields. We prove that gauging an abelian vector subgroup does not have a nonlinear sigma model interpretation. This is because the target-space metric resulting from the integration over the gauge fields is degenerate. We demonstrate, however, that this kind of gauging has a natural interpretation in terms of Wakimoto variables. (orig.)
The Cousins of Stuxnet: Duqu, Flame, and Gauss
Directory of Open Access Journals (Sweden)
Márk Félegyházi
2012-11-01
Full Text Available Stuxnet was the first targeted malware that received worldwide attention forcausing physical damage in an industrial infrastructure seemingly isolated from the onlineworld. Stuxnet was a powerful targeted cyber-attack, and soon other malware samples were discovered that belong to this family. In this paper, we will first present our analysis of Duqu, an information-collecting malware sharing striking similarities with Stuxnet. Wedescribe our contributions in the investigation ranging from the original detection of Duquvia finding the dropper file to the design of a Duqu detector toolkit. We then continue with the analysis of the Flame advanced information-gathering malware. Flame is unique in thesense that it used advanced cryptographic techniques to masquerade as a legitimate proxyfor the Windows Update service. We also present the newest member of the family, called Gauss, whose unique feature is that one of its modules is encrypted such that it can onlybe decrypted on its target system; hence, the research community has not yet been able to analyze this module. For this particular malware, we designed a Gauss detector serviceand we are currently collecting intelligence information to be able to break its very specialencryption mechanism. Besides explaining the operation of these pieces of malware, wealso examine if and how they could have been detected by vigilant system administrators manually or in a semi-automated manner using available tools. Finally, we discuss lessonsthat the community can learn from these incidents. We focus on technical issues, and avoidspeculations on the origin of these threats and other geopolitical questions.
Alternating sums of reciprocal generalized Fibonacci numbers.
Kuhapatanakul, Kantaphon
2014-01-01
Recently Holliday and Komatsu extended the results of Ohtsuka and Nakamura on reciprocal sums of Fibonacci numbers to reciprocal sums of generalized Fibonacci numbers. The aim of this work is to give similar results for the alternating sums of reciprocals of the generalized Fibonacci numbers with indices in arithmetic progression. Finally we note our generalizations of some results of Holliday and Komatsu. Primary 11B37; secondary 11B39.
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.)
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
Directory of Open Access Journals (Sweden)
Simoens Frederik
2006-01-01
Full Text Available This paper concerns channel tracking in a multiantenna context for correlated flat-fading channels obeying a Gauss-Markov model. It is known that data-aided tracking of fast-fading channels requires a lot of pilot symbols in order to achieve sufficient accuracy, and hence decreases the spectral efficiency. To overcome this problem, we design a code-aided estimation scheme which exploits information from both the pilot symbols and the unknown coded data symbols. The algorithm is derived based on a factor graph representation of the system and application of the sum-product algorithm. The sum-product algorithm reveals how soft information from the decoder should be exploited for the purpose of estimation and how the information bits can be detected. Simulation results illustrate the effectiveness of our approach.
Propagation of partially coherent Lorentz-Gauss vortex beam through oceanic turbulence.
Liu, Dajun; Yin, Hongming; Wang, Guiqiu; Wang, Yaochuan
2017-11-01
The partially coherent Lorentz-Gauss vortex beam generated by a Schell-model source has been introduced. Based on the extended Huygens-Fresnel principle, the cross-spectral density function of a partially coherent Lorentz-Gauss vortex beam propagating in oceanic turbulence is derived. The influences of coherence length, topological charge M, and oceanic turbulence on the spreading properties and position of the coherence vortex for a partially coherent Lorentz-Gauss vortex beam are analyzed in detail. The results show that a partially coherent Lorentz-Gauss vortex beam propagating in stronger oceanic turbulence will evolve into a Gaussian-like beam more rapidly as the propagation distance increases, and the number of coherent vortices will change.
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 (−12+1 involving the generalized Fibonacci and Lucas numbers.
Absolutely summing multilinear operators: a Panorama | Pellegrino ...
African Journals Online (AJOL)
This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective search of “perfect” multilinear extensions of the ideal of absolutely summing operators.
Euler Sums and Contour Integral Representations
Flajolet, Philippe; Salvy, Bruno
1996-01-01
This paper develops an approach to the evaluation of Euler sums involving harmonic numbers either linearly or nonlinearly. We give explicit formul{æ} for certain classes of Euler sums in terms of values of the Riemann zeta function at positive integers. The approach is based on simple contour integral representations and residue computations.
On the equivalence of Gaussian elimination and Gauss-Jordan reduction in solving linear equations
Tsao, Nai-Kuan
1989-01-01
A novel general approach to round-off error analysis using the error complexity concepts is described. This is applied to the analysis of the Gaussian Elimination and Gauss-Jordan scheme for solving linear equations. The results show that the two algorithms are equivalent in terms of our error complexity measures. Thus the inherently parallel Gauss-Jordan scheme can be implemented with confidence if parallel computers are available.
Transformations and invariants for dihedral Gauss hypergeometric functions
Vidunas, Raimundas
2011-01-01
Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a generalization of Clausen's formula and terminating double hypergeometric sums. Besides, pull-back transformations for the dihedral hypergeometric equations are presented, including Klein's pullback transformations for the equations with a finite (dihedral) monodromy...
Gauss-Bonnet's Formula and Closed Frenet Frames
DEFF Research Database (Denmark)
Røgen, Peter
1998-01-01
Our main result is that integrated geodesic curvature of a (non-simple) closed curve on the unit 2-sphere equals a half integer weighted sum of the areas of the connected components of the complement of the curve. These weights that gives a spherical analogy to the winding number of closed plane ...
40 CFR 91.508 - Cumulative Sum (CumSum) procedure.
2010-07-01
... × σ, and is a function of the standard deviation, σ. σ = is the sample standard deviation and is... + F))] Where: Ci = The current CumSum statistic Ci-1 = The previous CumSum statistic. Prior to any testing, the CumSum statistic = 0 (i.e. C0 = 0) Xi = The current emission test result for an individual...
Nonlinear dynamics in the Einstein-Gauss-Bonnet gravity
Shinkai, Hisa-aki; Torii, Takashi
2017-08-01
We numerically investigated how nonlinear dynamics depends on the dimensionality and on the higher-order curvature corrections in the form of Gauss-Bonnet (GB) terms. We especially monitored the processes of appearances of a singularity (or black hole) in two models: (i) a perturbed wormhole throat in spherically symmetric space-time, and (ii) colliding scalar pulses in plane-symmetric space-time. We used a dual-null formulation for evolving the field equations, which enables us to locate the trapping horizons directly, and also enables us to follow close to the large-curvature region due to its causal integrating scheme. We observed that the fate of a perturbed wormhole is either a black hole or an expanding throat depending on the total energy of the structure, and its threshold depends on the coupling constant of the GB terms (αGB ). We also observed that a collision of large scalar pulses will produce a large-curvature region, of which the magnitude also depends on αGB. For both models, the normal corrections (αGB>0 ) work for avoiding the appearance of singularity, although it is inevitable. We also found that in the critical situation for forming a black hole, the existence of the trapped region in the Einstein-GB gravity does not directly indicate the formation of a black hole.
Uniform Gauss-Weight Quadratures for Discrete Ordinate Transport Calculations
International Nuclear Information System (INIS)
Carew, John F.; Hu, Kai; Zamonsky, Gabriel
2000-01-01
Recently, a uniform equal-weight quadrature set, UE n , and a uniform Gauss-weight quadrature set, UG n , have been derived. These quadratures have the advantage over the standard level-symmetric LQ n quadrature sets in that the weights are positive for all orders,and the transport solution may be systematically converged by increasing the order of the quadrature set. As the order of the quadrature is increased,the points approach a uniform continuous distribution on the unit sphere,and the quadrature is invariant with respect to spatial rotations. The numerical integrals converge for continuous functions as the order of the quadrature is increased.The numerical characteristics of the UE n quadrature set have been investigated previously. In this paper, numerical calculations are performed to evaluate the application of the UG n quadrature set in typical transport analyses. A series of DORT transport calculations of the >1-MeV neutron flux have been performed for a set of pressure-vessel fluence benchmark problems. These calculations employed the UG n (n = 8, 12, 16, 24, and 32) quadratures and indicate that the UG n solutions have converged to within ∼0.25%. The converged UG n solutions are found to be comparable to the UE n results and are more accurate than the level-symmetric S 16 predictions
African Journals Online (AJOL)
This study aimed to examine perceptual factors associated with condom use, and the relationship between condom use and the timing of sexual ... Interventions to increase awareness about the role of condoms in preventing HIV, delay sexual initiation, and .... Health Belief Model (HBM) that were significantly associated.
Generalized Simplified Variable-Scaled Min Sum LDPC decoder for irregular LDPC Codes
Emran, Ahmed A.; Elsabrouty, Maha
2015-01-01
In this paper, we propose a novel low complexity scaling strategy of min-sum decoding algorithm for irregular LDPC codes. In the proposed method, we generalize our previously proposed simplified Variable Scaled Min-Sum (SVS-min-sum) by replacing the sub-optimal starting value and heuristic update for the scaling factor sequence by optimized values. Density evolution and Nelder-Mead optimization are used offline, prior to the decoding, to obtain the optimal starting point and per iteration upd...
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
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.)
Bs⁎BK vertex from QCD sum rules
International Nuclear Information System (INIS)
Cerqueira, A.; Osório Rodrigues, B.; Bracco, M.E.
2012-01-01
The form factors and the coupling constant of the B s ⁎ BK vertex are calculated using the QCD sum rules method. Three-point correlation functions are computed considering both K and B mesons off-shell and, after an extrapolation of the QCDSR results, we obtain the coupling constant of the vertex. We study the uncertainties in our result by calculating a third form factor obtained when the B s ⁎ is the off-shell meson, considering other acceptable structures and computing the variations of the sum rules' parameters. The form factors obtained have different behaviors but their simultaneous extrapolations reach to the same value of the coupling constant g B s ⁎ BK =10.6±1.7. We compare our result with other theoretical estimates.
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...... and the properties of the proposed estimators are studied. Bootstrap methods are suggested to provide confidence bounds. Finally a number of algorithms are suggested to make the methods operational and tested on simulated data. In particular we show how Panjer recursion in general can be inverted for the Panjer...
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....
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...
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)
Transition sum rules in the shell model
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.
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
Liu, Dajun; Wang, Guiqiu; Wang, Yaochuan
2018-01-01
Based on the Huygens-Fresnel integral and the relationship of Lorentz distribution and Hermite-Gauss function, the average intensity and coherence properties of a partially coherent Lorentz-Gauss beam propagating through oceanic turbulence have been investigated by using numerical examples. The influences of beam parameters and oceanic turbulence on the propagation properties are also discussed in details. It is shown that the partially coherent Lorentz-Gauss beam with smaller coherence length will spread faster in oceanic turbulence, and the stronger oceanic turbulence will accelerate the spreading of partially coherent Lorentz-Gauss beam in oceanic turbulence.
International Nuclear Information System (INIS)
Zhou, Guoquan
2010-01-01
Based on the generalized Huygens–Fresnel integral and the Hermite–Gaussian expansion of a Lorentzian distribution, analytical expressions for the mutual coherence functions and the spatial complex degrees of coherence of the partially coherent super-Lorentz–Gauss (SLG) modes SLG 01 and SLG 11 through a paraxial and real ABCD optical system are derived. As a numerical example, the focusing of the partially coherent SLG 01 and SLG 11 modes is illustrated, and the influence of the spatial correlation length on the normalized intensity distributions and the spatial complex degrees of coherence is examined. The analytical formulae of the beam propagation factors of the partially coherent SLG 01 and SLG 11 modes are also presented. The effects of the beam parameter and the coherent parameter on the beam propagation factors are numerically investigated
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.)
Nonparaxial propagation of Lorentz-Gauss beams in uniaxial crystal orthogonal to the optical axis.
Wang, Xun; Liu, Zhirong; Zhao, Daomu
2014-04-01
Analytical expressions for the three components of nonparaxial propagation of a polarized Lorentz-Gauss beam in uniaxial crystal orthogonal to the optical axis are derived and used to investigate its propagation properties in uniaxial crystal. The influences of the initial beam parameters and the parameters of the uniaxial crystal on the evolution of the beam-intensity distribution in the uniaxial crystal are examined in detail. Results show that the statistical properties of a nonparaxial Lorentz-Gauss beam in a uniaxial crystal orthogonal to the optical axis are closely determined by the initial beam's parameters and the parameters of the crystal: the beam waist sizes-w(0), w(0x), and w(0y)-not only affect the size and shape of the beam profile in uniaxial crystal but also determine the nonparaxial effect of a Lorentz-Gauss beam; the beam profile of a Lorentz-Gauss beam in uniaxial crystal is elongated in the x or y direction, which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index; with increasing deviation of the ratio from unity, the extension of the beam profile augments. The results indicate that uniaxial crystal provides an effective and convenient method for modulating the Lorentz-Gauss beams. Our results may be valuable in some fields, such as optical trapping and nonlinear optics, where a light beam with a special profile and polarization is required.
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
40 CFR 90.708 - Cumulative Sum (CumSum) procedure.
2010-07-01
... is 5.0×σ, and is a function of the standard deviation, σ. σ=is the sample standard deviation and is... i -1+X i−(FEL+F))] Where: Ci=The current CumSum statistic. Ci -1=The previous CumSum statistic. Prior to any testing, the CumSum statistic=0 (i.e. C0=0). Xi=The current emission test result for an...
Effects of backreaction on power-Maxwell holographic superconductors in Gauss-Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Salahi, Hamid Reza; Montakhab, Afshin [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Sheykhi, Ahmad [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P.O. Box 55134-441, Maragha (Iran, Islamic Republic of)
2016-10-15
We analytically and numerically investigate the properties of s-wave holographic superconductors by considering the effects of scalar and gauge fields on the background geometry in five-dimensional Einstein-Gauss-Bonnet gravity. We assume the gauge field to be in the form of the power-Maxwell nonlinear electrodynamics. We employ the Sturm-Liouville eigenvalue problem for analytical calculation of the critical temperature and the shooting method for the numerical investigation. Our numerical and analytical results indicate that higher curvature corrections affect condensation of the holographic superconductors with backreaction. We observe that the backreaction can decrease the critical temperature of the holographic superconductors, while the power-Maxwell electrodynamics and Gauss-Bonnet coefficient term may increase the critical temperature of the holographic superconductors. We find that the critical exponent has the mean-field value β = 1/2, regardless of the values of Gauss-Bonnet coefficient, backreaction and power-Maxwell parameters. (orig.)
Shear sum rules at finite chemical potential
David, Justin R.; Jain, Sachin; Thakur, Somyadip
2012-03-01
We derive sum rules which constrain the spectral density corresponding to the retarded propagator of the T xy component of the stress tensor for three gravitational duals. The shear sum rule is obtained for the gravitational dual of the mathcal{N} = {4} Yang-Mills, theory of the M2-branes and M5-branes all at finite chemical potential. We show that at finite chemical potential there are additional terms in the sum rule which involve the chemical potential. These modifications are shown to be due to the presence of scalars in the operator product expansion of the stress tensor which have non-trivial vacuum expectation values at finite chemical potential.
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...
The Gauss and Ampere laws: different laws but similar difficulties for student learning
International Nuclear Information System (INIS)
Guisasola, Jenaro; AlmudI, Jose M; Zuza, Kristina; Ceberio, Mikel; Salinas, Julia
2008-01-01
This study aims to analyse university students' reasoning regarding two laws of electromagnetism: Gauss's law and Ampere's law. It has been supposed that the problems seen in understanding and applying both laws do not spring from students' misconceptions. Students habitually use reasoning known in the literature as 'common sense' methodology that leads to incorrect forms of reasoning. To test our hypothesis, questionnaires were designed emphasizing explanations. The results obtained show the low level of students' reasoning in both electricity and magnetism in terms of Gauss's and Ampere's laws
Gauss: La revolución de las matemáticas del siglo XIX
Gutierrez, Santiago
2005-01-01
Hace 150 años, el 23 de febrero de 1855, moría, en Gotinga, a la edad de setenta y siete años, Johan Friedrich Carl Gauss o, simplemente, Carl Friedrich Gauss, como él mismo quiso ser llamado. Eran tiempos de revolución y progreso: comenzaba la revolución industrial en Inglaterra, en Estados Unidos se perforaba el primer pozo de petróleo (1859), la economía estaba dominada por las teorías liberales de Adam Smith mientras se gestaba la creación de la Internacional Socialista, Darwin publicaba ...
Holographic Thermalization in Gauss-Bonnet Gravity with de Sitter Boundary
Zhang, Shao-Jun; Abdalla, Elcio; Papantonopoulos, Eleftherios
2015-01-01
We introduce higher-derivative Gauss-Bonnet correction terms in the gravity sector and we relate the modified gravity theory in the bulk to the strongly coupled quantum field theory on a de Sitter boundary. We study the process of holographic thermalization by examining three non-local observables, the two-point function, the Wilson loop and the holographic entanglement entropy. We study the time evolution of these three observables and we find that the modification of the gravity side with the Gauss-Bonnet correction terms influences the saturation time to reach thermal equilibrium with the dominant effect given by the holographic entanglement entropy since it contains more bulk information.
Gauss-Bonnet black holes at new colliders beyond the dimensionality of space
Alexeyev, S; Grain, J
2005-01-01
The Gauss-Bonnet invariant is one of the most promising candidates for a quadratic curvature correction to the Einstein action in expansions of supersymmetric string theory. We study the evaporation of such Schwarzschild-Gauss-Bonnet black holes which could be formed at future colliders if the Planck scale is of the order of TeV, as predicted by some modern brane world models. We show that, apart from the dimensionality of space, the corresponding coupling constant could be measured by the LHC. This opens new windows for physics investigation in spite of the possible screening of microphysics due to the event horizon.
The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature
Directory of Open Access Journals (Sweden)
PEDRO A. HINOJOSA
2013-11-01
Full Text Available In this paper we are concerned with the image of the normal Gauss map of a minimal surface immersed in ℝ3 with finite total curvature. We give a different proof of the following theorem of R. Osserman: The normal Gauss map of a minimal surface immersed in ℝ3 with finite total curvature, which is not a plane, omits at most three points of2 Moreover, under an additional hypothesis on the type of ends, we prove that this number is exactly 2.
Non-diffractive Bessel-Gauss beams for the detection of rotating object free of obstructions.
Fu, Shiyao; Wang, Tonglu; Zhang, Zheyuan; Zhai, Yanwang; Gao, Chunqing
2017-08-21
Bessel-Gauss beams carrying orbital angular momentum are widely known for their non-diffractive or self-reconstructing performance, and have been applied in lots of domains. Here we demonstrate that, by illuminating a rotating object with high-order Bessel-Gauss beams, a frequency shift proportional to the rotating speed and the topological charge is observed. Moreover, the frequency shift is still present once an obstacle exists in the path, in spite of the decreasing of received signals. Our work indicates the feasibility of detecting rotating objects free of obstructions, and has potential as obstruction-immune rotation sensors in engine monitoring, aerological sounding, and so on.
Partial sum approaches to mathematical parameters of some growth models
Korkmaz, Mehmet
2016-04-01
Growth model is fitted by evaluating the mathematical parameters, a, b and c. In this study, the method of partial sums were used. For finding the mathematical parameters, firstly three partial sums were used, secondly four partial sums were used, thirdly five partial sums were used and finally N partial sums were used. The purpose of increasing the partial decomposition is to produce a better phase model which gives a better expected value by minimizing error sum of squares in the interval used.
A new look at the free electromagnetic field. The Gauss law as a hamiltonian equation of motion
International Nuclear Information System (INIS)
Aldaya, V.; Navarro-Salas, J.
1992-01-01
A new canonical formalism for the free electromagnetic field is proposed in terms of an infinite-dimensional Lie group. The Gauss law is derived as a hamiltonian equation of motion and the quantum theory is obtained by constructing the irreducible representation of the group. The quantum Gauss law thus appears as an additional polarization equation and not as a constraint equation. (orig.)
Almost Sure Central Limit Theory for Self-Normalized Products of Sums of Partial Sums
Directory of Open Access Journals (Sweden)
Qunying Wu
2012-01-01
Full Text Available Let X,X1,X2,… be a sequence of independent and identically distributed random variables in the domain of attraction of a normal law. An almost sure limit theorem for the self-normalized products of sums of partial sums is established.
Almost Sure Central Limit Theory for Self-Normalized Products of Sums of Partial Sums
Wu, Qunying
2012-01-01
Let $X,{X}_{1},{X}_{2},\\dots $ be a sequence of independent and identically distributed random variables in the domain of attraction of a normal law. An almost sure limit theorem for the self-normalized products of sums of partial sums is established.
International Nuclear Information System (INIS)
Zhou, Yimin; Zhou, Guoquan; Dai, Chaoqing; Ru, Guoyun
2015-01-01
Based on the Collins integral formula and the Hermite–Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function (WDF) of a Lorentz–Gauss vortex beam passing through a paraxial ABCD optical system is derived. The WDF properties of a Lorentz–Gauss vortex beam propagating in free space are also demonstrated. During propagation, the WDF pattern shrinks in the direction of the spatial frequency variables and elongates in the direction of the transverse spatial coordinates. With given the transverse spatial coordinates or the spatial frequency variables, the evolvement of the WDF of a Lorentz–Gauss vortex beam during propagation is examined in detail. To show the WDF application, the second-order moments of the WDF for a Lorentz–Gauss vortex beam in free space are also presented. This research exhibits the propagation properties of a Lorentz–Gauss vortex beam from the phase space. (paper)
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
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)
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...
Some zero-sum constants with weights
Indian Academy of Sciences (India)
to zero-sum problems, Discrete Math. 306 (2006) 1–10. [2] Adhikari S D and Chen Y G, Davenport constant with weights and some related ques- tions – II, J. Combin. Theory A115 (2008) 178–184. [3] Adhikari Sukumar Das and Rath Purusottam, Davenport constant with weights and some related questions, Integers 6 ...
DEFF Research Database (Denmark)
Triantafillou, Peter
2017-01-01
, at the very best, a very modest plus-sum game. More specifically, while the Danish SAI actively pursues both objectives, it has persistently prioritized independence over relevance. This priority seems to be the most effective strategy for the Danish SAI to maintain its legitimacy in a situation where...
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.)
Sums of two-dimensional spectral triples
DEFF Research Database (Denmark)
Christensen, Erik; Ivan, Cristina
2007-01-01
We study countable sums of two dimensional modules for the continuous complex functions on a compact metric space and show that it is possible to construct a spectral triple which gives the original metric back. This spectral triple will be finitely summable for any positive parameter. We also co...
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 ...
5D black hole solution in Einstein-Yang-Mills-Gauss-Bonnet theory
International Nuclear Information System (INIS)
Mazharimousavi, S. Habib; Halilsoy, M.
2007-01-01
By adopting the 5D version of the Wu-Yang ansatz we present in closed form a black hole solution in the Einstein-Yang-Mills-Gauss-Bonnet theory. In the Einstein-Yang-Mills limit, we recover the 5D black hole solution already known
Horizons of radiating black holes in Einstein-Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Ghosh, S. G.; Deshkar, D. W.
2008-01-01
A Vaidya-based model of a radiating black hole is studied in a 5-dimensional Einstein gravity with Gauss-Bonnet contribution of quadratic curvature terms. The structure and locations of the apparent and event horizons of the radiating black hole are determined
Generation of J_0-Bessel-Gauss beam by a heterogeneous refractive index map
San Roman Alerigi, Damian
2012-07-01
In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a Si/Si1-yOy/Si1-x-yGexCy platform or by photo-refractive media. The proposed device is 200 ?m in length and 25 ?m in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and -0.457 dB, respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a J0-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers. © 2012 Optical Society of America.
From Lintearia to Lemniscate II: Gauss and Landen's Work -R-ES ...
Indian Academy of Sciences (India)
Gauss and Landen's Work. R Sridharan. In the first part [1], we introduced and discussed the. 'elastic curve' and the related algebraic curve, the' Lem- niscate'. The name 'elastic curve' was given due to the fact that it is the shape assulued by a uniform elastic rod when bent in to a plane curve under a stress of a certain kind.
Thin-shell wormholes supported by ordinary matter in Einstein--Gauss--Bonnet gravity
Richarte, Martin; Simeone, Claudio
2007-01-01
The generalized Darmois--Israel formalism for Einstein--Gauss--Bonnet theory is applied to construct thin-shell Lorentzian wormholes with spherical symmetry. We calculate the energy localized on the shell, and we find that for certain values of the parameters wormholes could be supported by matter not violating the energy conditions.
Boundary causality versus hyperbolicity for spherical black holes in Gauss-Bonnet gravity
Andrade, Tomás; Cáceres, Elena; Keeler, Cynthia
2017-07-01
We explore the constraints boundary causality places on the allowable Gauss-Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss-Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coupling, as we tune the Gauss-Bonnet coupling away from zero, both spherical and planar black holes violate hyperbolicity before they violate boundary causality. For positive coupling, the only hyperbolicity-respecting spherical black holes which violate boundary causality do not do so appreciably far from the planar bound. Consequently, eliminating hyperbolicity-violating solutions means the bound on Gauss-Bonnet couplings from the boundary causality of spherical black holes is no tighter than that from planar black holes.
Automatic detection of the optimal ejecting direction based on a discrete Gauss map
Directory of Open Access Journals (Sweden)
Masatomo Inui
2014-01-01
Full Text Available In this paper, the authors propose a system for assisting mold designers of plastic parts. With a CAD model of a part, the system automatically determines the optimal ejecting direction of the part with minimum undercuts. Since plastic parts are generally very thin, many rib features are placed on the inner side of the part to give sufficient structural strength. Our system extracts the rib features from the CAD model of the part, and determines the possible ejecting directions based on the geometric properties of the features. The system then selects the optimal direction with minimum undercuts. Possible ejecting directions are represented as discrete points on a Gauss map. Our new point distribution method for the Gauss map is based on the concept of the architectural geodesic dome. A hierarchical structure is also introduced in the point distribution, with a higher level “rough” Gauss map with rather sparse point distribution and another lower level “fine” Gauss map with much denser point distribution. A system is implemented and computational experiments are performed. Our system requires less than 10 seconds to determine the optimal ejecting direction of a CAD model with more than 1 million polygons.
International Nuclear Information System (INIS)
Bouferguene, Ahmed
2005-01-01
When computing multicentre integrals over Slater-type orbitals (STOs) by means of the Shavitt and Karplus Gaussian integral transforms (Shavitt and Karplus 1962 J. Chem. Phys. 36 550), one usually ends up with a multiple integral of the form ∫ 0 1 du ∫ 0 1 dv ...∫ 0 ∞ dz F(u, v, ..., z) (Shavitt and Karplus 1965 J. Chem. Phys. 43 398) in which all the integrals are inter-related. The most widely used approach for computing such an integral is to apply a product of Gauss-Legendre quadratures for the integrals over [0, 1] while the semi-infinite term is evaluated by a special procedure. Although numerous approaches have been developed to accurately perform the integration over [0, ∞) efficiently, it is the aim of this work to add a new tool that could be of some benefit in carrying out the hard task of multicentre integrals over STOs. The new approach relies on a special Gauss quadrature referred to as Gauss-Bessel to accurately evaluate the semi-infinite integral of interest. In this work, emphasis is put on accuracy rather than efficiency since its aim is essentially to bring a proof of concept showing that Gauss-Bessel quadrature can successfully be applied in the context of multicentre integrals over STOs. The obtained accuracy is comparable to that obtained with other methods available in the literature
New higher-derivative invariants in N=2 supergravity and the Gauss-Bonnet term
Butter, D.; de Wit, B.; Kuzenko, S.M.; Lodato, I.|info:eu-repo/dai/nl/357520890
2013-01-01
A new class of N = 2 locally supersymmetric higher-derivative invariants is constructed based on logarithms of conformal primary chiral superfields. They characteristically involve a coupling to Rμν 2 − 1 3 R2, which equals the non-conformal part of the Gauss-Bonnet term. Upon combining one such
Cudeck, Robert; And Others
1993-01-01
An implementation of the Gauss-Newton algorithm for the analysis of covariance structure that is specifically adapted for high-level computer languages is reviewed. This simple method for estimating structural equation models is useful for a variety of standard models, as is illustrated. (SLD)
An Alternative Method to Gauss-Jordan Elimination: Minimizing Fraction Arithmetic
Smith, Luke; Powell, Joan
2011-01-01
When solving systems of equations by using matrices, many teachers present a Gauss-Jordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row reduce matrices that does not introduce additional…
The geometric Cauchy problem for surfaces with Lorentzian harmonic Gauss maps
DEFF Research Database (Denmark)
Brander, David; Svensson, Martin
2013-01-01
The geometric Cauchy problem for a class of surfaces in a pseudo-Riemannian manifold of dimension 3 is to find the surface which contains a given curve with a prescribed tangent bundle along the curve. We consider this problem for constant negative Gauss curvature surfaces (pseudospherical surfaces...
A Modified Gauss-Jordan Procedure as an Alternative to Iterative Procedures in Multiple Regression.
Roscoe, John T.; Kittleson, Howard M.
Correlation matrices involving linear dependencies are common in educational research. In such matrices, there is no unique solution for the multiple regression coefficients. Although computer programs using iterative techniques are used to overcome this problem, these techniques possess certain disadvantages. Accordingly, a modified Gauss-Jordan…
Basic full-wave generalization of the real-argument Hermite-Gauss beam.
Seshadri, S R
2010-05-01
The linearly polarized real-argument Hermite-Gauss beam is investigated by the Fourier transform method. The complex power is obtained and the reactive power of the paraxial beam is found to be zero. The complex space source required for the full-wave generalization of the real-argument Hermite-Gauss beam is deduced. The resulting basic full real-argument Hermite-Gauss wave is determined. The real and the reactive powers of the full wave are evaluated. The reactive power of the basic full real-argument Hermite-Gauss wave is infinite, and the reasons for this singularity are described. The real power depends on kw(0), m, and n, where k is the wavenumber, w(0) is the e-folding distance of the Gaussian part of the input distribution, and m and n are the mode numbers. The variation in the real power with respect to changes in kw(0) for specified m and n as well as with respect to changes in m and n for a specified kw(0) is examined.
The Gauss and Ampere Laws: Different Laws but Similar Difficulties for Student Learning
Guisasola, Jenaro; Almudi, Jose M.; Salinas, Julia; Zuza, Kristina; Ceberio, Mikel
2008-01-01
This study aims to analyse university students' reasoning regarding two laws of electromagnetism: Gauss's law and Ampere's law. It has been supposed that the problems seen in understanding and applying both laws do not spring from students' misconceptions. Students habitually use reasoning known in the literature as 'common sense' methodology that…
Goos-Hanchen and Imbert-Fedorov shifts for Hermite-Gauss beams.
Prajapati, Chandra; Ranganathan, D
2012-07-01
We study the lateral Goos-Hanchen and the transverse Imbert-Fedorov shift produced during the reflection of Hermite-Gauss beams H(m0) or H(0m) at a plane interface. The vector angular spectrum method for a light beam in terms of a two-form angular spectrum consisting of the two orthogonal polarized components was used. We have carried out a detailed numerical calculation of these shifts at different angles of incidence, over the whole range of incidence without making the usual approximations. The shift variation as a function of refractive index and order of the Hermite-Gauss beam is studied. We also compare the shift variations with the orientation of the lobes of the Hermite-Gauss beam. We observed that the shifts are nearly equal for the two cases H(m0) (lobe oriented in the plane of incidence) and H(0m) (lobe oriented perpendicular to plane of incidence). These are the first quantitative estimates of the shifts for Hermite-Gauss beams as per our knowledge and are relevant for all cases of slab geometry.
Generation of J0-Bessel-Gauss beam by a heterogeneous refractive index map.
San-Roman-Alerigi, Damian P; Ng, Tien K; Zhang, Yaping; Ben Slimane, Ahmed; Alsunaidi, Mohammad; Ooi, Boon S
2012-07-01
In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a J(0)-Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a Si/Si(1-y)O(y)/Si(1-x-y)Ge(x)C(y) platform or by photo-refractive media. The proposed device is 200 μm in length and 25 μm in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and -0.457 dB, respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a J(0)-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers.
A new generalization of Hardy–Berndt sums
Indian Academy of Sciences (India)
Abstract. In this paper, we construct a new generalization of Hardy–Berndt sums which are explicit extensions of Hardy–Berndt sums. We express these sums in terms of Dedekind sums s r ( h , k : x , y | ) with ==0 and obtain corresponding reciprocity formulas.
Gravitational quasinormal modes of static Einstein-Gauss-Bonnet anti-de Sitter black holes
Ma, Hong; Li, Jin
2018-04-01
In this paper, we describe quasinormal modes (QNMs) for gravitational perturbations of Einstein-Gauss-Bonnet black holes (BHs) in higher dimensional spacetimes, and derive the corresponding parameters of such black holes in three types of spacetime (flat, de Sitter (dS) and anti-de Sitter (AdS)). Our attention is concentrated on discussing the (in)stability of Einstein-Gauss-Bonnet AdS BHs through the temporal evolution of all types of gravitational perturbation fields (tensor, vector and scalar). It is concluded that the potential functions in vector and scalar gravitational perturbations have negative regions, which suppress quasinormal ringing. Furthermore, the influences of the Gauss-Bonnet coupling parameter α, the number of dimensions n and the angular momentum quantum number l on the Einstein-Gauss-Bonnet AdS BHs quasinormal spectrum are analyzed. The QNM frequencies have greater oscillation and lower damping rate with the growth of α. This indicates that QNM frequencies become increasingly unstable with large α. Meanwhile, the dynamic evolutions of the perturbation field are compliant with the results of computation from the Horowitz and Hubeny method. Because the number of extra dimensions is connected with the string scale, the relationship between α and properties of Einstein-Gauss-Bonnet AdS BHs might be beneficial for the exploitation of string theory and extra-dimensional brane worlds. Supported by FAPESP (2012/08934-0), National Natural Science Foundation of China (11205254, 11178018, 11375279, 11605015), the Natural Science Foundation Project of CQ CSTC (2011BB0052), and the Fundamental Research Funds for the Central Universities (106112016CDJXY300002, 106112017CDJXFLX0014, CDJRC10300003)
Limiting law excess sum rule for polyelectrolytes.
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.
Geometric optimization and sums of algebraic functions
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.
Strong sum distance in fuzzy graphs.
Tom, Mini; Sunitha, Muraleedharan Shetty
2015-01-01
In this paper the idea of strong sum distance which is a metric, in a fuzzy graph is introduced. Based on this metric the concepts of eccentricity, radius, diameter, center and self centered fuzzy graphs are studied. Some properties of eccentric nodes, peripheral nodes and central nodes are obtained. A characterisation of self centered complete fuzzy graph is obtained and conditions under which a fuzzy cycle is self centered are established. We have proved that based on this metric, an eccentric node of a fuzzy tree G is a fuzzy end node of G and a node is an eccentric node of a fuzzy tree if and only if it is a peripheral node of G and the center of a fuzzy tree consists of either one or two neighboring nodes. The concepts of boundary nodes and interior nodes in a fuzzy graph based on strong sum distance are introduced. Some properties of boundary nodes, interior nodes and complete nodes are studied.
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.
Remarks on some zero-sum theorems
Indian Academy of Sciences (India)
(1996) 100–103. [9] Griffiths Simon, The Erd˝os-Ginzburg-Ziv theorem with units, Discrete Math. 308(23). (2008) 5473–5484, doi:10.1016/j.disc.2007.09.060. [10] Luca Florian, A generalization of a classical zero-sum problem, Discrete Math. 307(13). (2007) 1672–1678. [11] Nathanson Melvyn B, Additive number theory.
Gao's conjecture on zero-sum sequences
Indian Academy of Sciences (India)
M. Senthilkumar (Newgen Imaging) 1461 1996 Oct 15 13:05:22
Davenport's constant is connected with algebraic number theory as follows. Let K be a number field (i.e., a finite extension of Q) and ... maps a sequence to the sum of its elements. Let S = ∏l ν=1 gν ∈ F(G) be a sequence. Then S has a .... A more general application analogous to the E–G–Z theorem for a finite group had ...
Hybrid quarkonia from QCD sum rules
International Nuclear Information System (INIS)
Govaerts, J.; Reinders, L.J.; Rubinstein, H.R.; Weyers, J.
1985-01-01
We present calculations of the vacuum polarization functions in QCD induced by heavy-quark anti qqG currents with the quantum numbers Jsup(PC)=1 +- , 0 ++ , 1 -+ and 0 -- . In the framework of QCD sum rules we investigate the possible resonance structure in these channels. We obtain definite predictions for the masses of resonances in the channels 0 -- , 0 ++ and 1 +- , but not in the exotic 1 -+ channel. The resulting mass values are unexpectedly high. (orig.)
Dadhich, Naresh; Pons, Josep M
We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet gravity with the topology of the product of two spheres, [Formula: see text], in higher dimensions. There is an unusual new feature of the Gauss-Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of [Formula: see text]. For an Einstein-Gauss-Bonnet black hole a limited window of negative values for [Formula: see text] is also permitted. This topology encompasses black strings, branes, and generalized Nariai metrics. We also give new solutions with the product of two spheres of constant curvature.
Directory of Open Access Journals (Sweden)
Ali H. Bhrawy
2014-01-01
Full Text Available The modified generalized Laguerre-Gauss collocation (MGLC method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.
New Results on the Sum of Two Generalized Gaussian Random Variables
Soury, Hamza
2016-01-06
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based on this results, the probability density function (PDF) and the cumulative distribution function (CDF) of the sum distribution are obtained. These functions are expressed in terms of the bivariate Fox H function. Next, the statistics of the distribution of the sum, such as the moments, the cumulant, and the kurtosis, are analyzed and computed. Due to the complexity of bivariate Fox H function, a solution to reduce such complexity is to approximate the sum of two independent GG random variables by one GG random variable with suitable shape factor. The approximation method depends on the utility of the system so three methods of estimate the shape factor are studied and presented [1].
New Results On the Sum of Two Generalized Gaussian Random Variables
Soury, Hamza
2015-01-01
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based on this results, the probability density function (PDF) and the cumulative distribution function (CDF) of the sum distribution are obtained. These functions are expressed in terms of the bivariate Fox H function. Next, the statistics of the distribution of the sum, such as the moments, the cumulant, and the kurtosis, are analyzed and computed. Due to the complexity of bivariate Fox H function, a solution to reduce such complexity is to approximate the sum of two independent GG random variables by one GG random variable with suitable shape factor. The approximation method depends on the utility of the system so three methods of estimate the shape factor are studied and presented.
Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun
2017-03-01
H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.
Smith, H. V.
2008-01-01
A method is derived for the numerical evaluation of the error term arising in some Gauss-type formulae modified so as to approximate Cauchy Principal Value integrals. The method uses Chebyshev polynomials of the first kind. (Contains 1 table.)
Global Structure of Black Holes in String Theory with Gauss-Bonnet Correction in Various Dimensions
Ohta, N.; Torii, T.
2010-08-01
We study global structures of black hole solutions in Einstein gravity with Gauss-Bonnet term coupled to dilaton in various dimensions. In particular we focus on the problem whether the singularity is weakened due to the Gauss-Bonnet term and dilaton. We find that there appears the non-central singularity between horizon and the center in many cases, where the metric does not diverge but the Kretschmann invariant does diverge. Hence this is a singularity, but we find the singularity is much milder than the Schwarzschild solution and the non-dilatonic one. We discuss the origin of this ``fat'' singularity. In other cases, we encounter singularity at the center which is much stronger than the usual one. We find that our black hole solutions have three different types of the global structures; the Schwarzschild, Schwarzschild-AdS and ``regular AdS black hole" types.
The effect of the Gauss-Bonnet term on Hawking radiation from arbitrary dimensional black brane
Energy Technology Data Exchange (ETDEWEB)
Kuang, Xiao-Mei [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Valparaiso (Chile); Yangzhou University, Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou (China); Saavedra, Joel [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Valparaiso (Chile); Oevguen, Ali [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Valparaiso (Chile); Eastern Mediterranean University, Physics Department, Famagusta, Northern Cyprus (Country Unknown)
2017-09-15
We investigate the probabilities of the tunneling and the radiation spectra of massive spin-1 particles from arbitrary dimensional Gauss-Bonnet-Axions (GBA) Anti-de Sitter (AdS) black branes, via using the WKB approximation to the Proca spin-1 field equation. The tunneling probabilities and Hawking temperature of the arbitrary dimensional GBA AdS black brane is calculated via the Hamilton-Jacobi approach. We also compute the Hawking temperature via the Parikh-Wilczek tunneling approach. The results obtained from the two methods are consistent. In our setup, the Gauss-Bonnet (GB) coupling affects the Hawking temperature if and only if the momentum of the axion fields is non-vanishing. (orig.)
Reconstruction of the Scalar Field Potential in Inflationary Models with a Gauss-Bonnet term
Koh, Seoktae; Lee, Bum-Hoon; Tumurtushaa, Gansukh
2017-06-01
We consider inflationary models with a Gauss-Bonnet term to reconstruct the scalar-field potentials and the Gauss-Bonnet coupling functions. Both expressions are derived from the observationally favored configurations of ns and r . Our result implies that, for the reconstructed potentials and coupling functions, the blue tilt of inflationary tensor fluctuations can be realized. To achieve a blue tilt for the inflationary tensor fluctuations, a scalar field must climb up its potential before rolling down. We further investigate the properties of propagation of the perturbation modes in Friedmann-Robertson-Walker spacetime. For the reconstructed configurations that give rise to the blue tilt for the inflationary tensor fluctuations, we show that the ghosts and instabilities are absent with the superluminal propagation speeds for the scalar perturbation modes, whereas the propagation speeds of the tensor perturbations are subluminal.
History of cosmic evolution with modified Gauss-Bonnet-dilatonic coupled term
Energy Technology Data Exchange (ETDEWEB)
Debnath, Subhra; Sanyal, Abhik Kumar [Jangipur College, Department of Physics, Murshidabad (India); Ruz, Soumendra Nath [Ramananda Centenary College, Department of Physics, Purulia (India); Mandal, Ranajit [University of Kalyani, Department of Physics, Nadia (India)
2017-05-15
Gauss-Bonnet-dilatonic coupling in four dimensions plays an important role to explain late-time cosmic evolution. However, this term is an outcome of the low energy string effective action and thus ought to be important in the early universe too. Unfortunately, a phase-space formulation of such a theory does not exist in the literature due to branching. We therefore consider a modified theory of gravity, which contains a nonminimally coupled scalar-tensor sector in addition to a higher-order scalar curvature invariant term with Gauss-Bonnet-dilatonic coupling. Such an action unifies early inflation with late-time cosmic acceleration. The quantum version of the theory is also well behaved. (orig.)
Reconstruction of inflation from scalar field non-minimally coupled with the Gauss-Bonnet term
Sebastiani, Lorenzo; Myrzakul, Shynaray; Myrzakulov, Ratbay
2017-12-01
In this paper, we analyze the early time inflation in a scalar-tensor theory of gravity where the scalar field is minimally coupled with the Gauss-Bonnet four-dimensional topological invariant. The theory belongs to a class of Horndeski models where the field equations are at the second order, like in General Relativity. A viable inflationary scenario must correctly reproduce the last Plank satellite data. By starting from some simple assumptions on the field and on the coupling function between the field and the Gauss-Bonnet term, we derive the spectral index and the tensor-to-scalar ratio of the model. Once the model is viable, it is finally possible to fully reconstruct its Lagrangian.
Higher-dimensional thin-shell wormholes in Einstein-Yang-Mills-Gauss-Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Mazharimousavi, S Habib; Halilsoy, M; Amirabi, Z, E-mail: habib.mazhari@emu.edu.tr, E-mail: mustafa.halilsoy@emu.edu.tr, E-mail: zahra.amirabi@emu.edu.tr [Department of Physics, Eastern Mediterranean University, G. Magusa, North Cyprus, Mersin 10 (Turkey)
2011-01-21
We present thin-shell wormhole solutions in the Einstein-Yang-Mills-Gauss-Bonnet (EYMGB) theory in higher dimensions d {>=} 5. Exact black hole solutions are employed for this purpose where the radius of the thin shell lies outside the event horizon. For some reasons the cases d = 5 and d > 5 are treated separately. The surface energy-momentum of the thin shell creates surface pressures to resist against collapse and rendering stable wormholes possible. We test the stability of the wormholes against spherical perturbations through a linear energy-pressure relation and plot stability regions. Apart from this restricted stability we investigate the possibility of normal (i.e. non-exotic) matter which satisfies the energy conditions. For negative values of the Gauss-Bonnet (GB) parameter we obtain such physical wormholes.
Study on effective anchorage length of anchor cable based on Gauss's function
Ren, Feng; WuShuai; Liu, Yan; Liu, Jun-yan
2017-11-01
In the current relevant codes and technical standards, the design of anchor cables (bars) is based on the assumption that the shear stress is distributed uniformly along the anchor segment. However, according to this assumption, the super-deep pit need a large uplift bearing capacity, which will lead to the long anchor segment and has great hidden danger in the actual engineering design. Therefore, this paper, based on the previous derived shear stress function between τ and the anchor length, we get a research suitable model-Gauss curve distribution model through the analysis of saturated clay drawing data, and strata anchor shear stress distribution is more suitable for the Gauss function model in saturated clay; at the same time, through the FLAC numerical simulation of Jinan Government Affairs Center project, we obtained the optimal anchor effective anchor length is about 10~12m, the foundation pit anchor is optimized.
Quintessence background for 5D Einstein-Gauss-Bonnet black holes
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Sushant G. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa); Centre for Theoretical Physics, New Delhi (India); Amir, Muhammed [Centre for Theoretical Physics, New Delhi (India); Maharaj, Sunil D. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)
2017-08-15
As we know that the Lovelock theory is an extension of the general relativity to the higher-dimensions, in this theory the first- and the second-order terms correspond to general relativity and the Einstein-Gauss-Bonnet gravity, respectively. We obtain a 5D black hole solution in Einstein-Gauss-Bonnet gravity surrounded by the quintessence matter, and we also analyze their thermodynamical properties. Owing to the quintessence corrected black hole, the thermodynamic quantities have also been corrected except for the black hole entropy, and a phase transition is achievable. The phase transition for the thermodynamic stability is characterized by a discontinuity in the specific heat at r = r{sub C}, with the stable (unstable) branch for r < (>) r{sub C}. (orig.)
Modified teleparallel theories of gravity: Gauss-Bonnet and trace extensions.
Bahamonde, Sebastian; Böhmer, Christian G
2016-01-01
We investigate modified theories of gravity in the context of teleparallel geometries with possible Gauss-Bonnet contributions. The possible coupling of gravity with the trace of the energy-momentum tensor is also taken into account. This is motivated by the various different theories formulated in the teleparallel approach and the metric approach without discussing the exact relationship between them. Our formulation clarifies the connections between different well-known theories. For instance, we are able to formulate the correct teleparallel equivalent of Gauss-Bonnet modified general relativity, amongst other results. Finally, we are able to identify modified gravity models which have not been studied in the past. These appear naturally within our setup and would make a interesting starting point for further studies.
Application of Gauss-Seidel multilevel control to a single axis torsional model
Chichester, F. D.
1981-01-01
An approach to the application of multilevel control techniques for large space structures is presented. Gauss-Seidel second level controls and an extension of standard linear quadratic regulator techniques are applied to a model consisting of a flexible space vehicle comprising three rigid bodies rotating about a common axis. The method incorporates second order derivatives with respect to time, entailing the use of a two level hierarchy of subsystems. Gauss-Seidel second level control formulations were chosen to avoid the necessity of having as many controls as constraints or using gradient techniques in the choice of the Hamiltonian. The modular nature of the resulting control system allows applications for spacecraft with larger numbers of modules.
Stability of anti-de sitter space in Einstein-Gauss-Bonnet gravity.
Deppe, Nils; Kolly, Allison; Frey, Andrew; Kunstatter, Gabor
2015-02-20
Recently it has been argued that in Einstein gravity anti-de Sitter spacetime is unstable against the formation of black holes for a large class of arbitrarily small perturbations. We examine the effects of including a Gauss-Bonnet term. In five dimensions, spherically symmetric Einstein-Gauss-Bonnet gravity has two key features: Choptuik scaling exhibits a radius gap, and the mass function goes to a finite value as the horizon radius vanishes. These suggest that black holes will not form dynamically if the total mass-energy content of the spacetime is too small, thereby restoring the stability of anti-de Sitter spacetime in this context. We support this claim with numerical simulations and uncover a rich structure in horizon radii and formation times as a function of perturbation amplitude.
Magnetic fields greater than 10 to the 20th power gauss. [in astrophysical systems
Lerche, I.; Schramm, D. N.
1977-01-01
Zaumen (1976) found that spontaneous pair production in a uniform magnetic field should be a feasible process for field strengths at least of the order of 10 to the 20th power gauss. This note points out that a magnetic field of this order of magnitude is most unlikely to occur in realistic astrophysical situations because of the large dynamical and quantum-mechanical effects such a field would produce. It is suggested that Zaumen's calculation would probably have little bearing on the suspected evolution of astrophysical systems since other processes (either dynamical or quantum-mechanical) apparently limit the field strength before such high magnetic fields would be reached. An upper limit of about 10 to the 16th power gauss is obtained by considering the isotropy of the 3-K blackbody radiation, the formation of collapsed objects in very high magnetic fields, and magnetic bremsstrahlung processes in quantum electrodynamics.
Spontaneous Scalarization of Black Holes and Compact Stars from a Gauss-Bonnet Coupling
Silva, Hector O.; Sakstein, Jeremy; Gualtieri, Leonardo; Sotiriou, Thomas P.; Berti, Emanuele
2018-03-01
We identify a class of scalar-tensor theories with coupling between the scalar and the Gauss-Bonnet invariant that exhibit spontaneous scalarization for both black holes and compact stars. In particular, these theories formally admit all of the stationary solutions of general relativity, but these are not dynamically preferred if certain conditions are satisfied. Remarkably, black holes exhibit scalarization if their mass lies within one of many narrow bands. We find evidence that scalarization can occur in neutron stars as well.
Geophex Airborne Unmanned Survey System (GAUSS). Topical report, October 1993--September 1996
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-12-31
This document is a Final Technical Report that describes the results of the Geophex Airborne Unmanned Survey System (GAUSS) research project. The objectives were to construct a geophysical data acquisition system that uses a remotely operated unmanned aerial vehicle (UAV) and to evaluate its effectiveness for characterization of hazardous environmental sites. The GAUSS is a data acquisition system that mitigates the potential risk to personnel during geophysical characterization of hazardous or radioactive sites. The fundamental basis of the GAUSS is as follows: (1) an unmanned survey vehicle carries geophysical sensors into a hazardous location, (2) the pilot remains outside the hazardous site and operates the vehicle using radio control, (3) geophysical measurements and their spatial locations are processed by an automated data-acquisition system which displays data on an off-site monitor in real-time, and (4) the pilot uses the display to direct the survey vehicle for complete site coverage. The objective of our Phase I research was to develop a data acquisition and processing (DAP) subsystem and geophysical sensors suitable for UAV deployment. We integrated these two subsystems to produce an automated, hand-held geophysical surveying system. The objective of the Phase II effort was to modify the subsystems and integrate them into an airborne prototype. The completed GAUSS DAP system consists of a UAV platform, a laser tracking and ranging subsystem, a telemetry subsystem, light-weight geophysical sensors, a base-station computer (BC), and custom-written survey control software (SCS). We have utilized off-the-shelf commercial products, where possible, to reduce cost and design time.
Extremal dyonic black holes in D=4 Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Chen, C.-M.; Gal'tsov, Dmitri V.; Orlov, Dmitry G.
2008-01-01
We investigate extremal dyon black holes in the Einstein-Maxwell-dilaton theory with higher curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. In the same theory without the Gauss-Bonnet term the extremal dyon solutions exist only for discrete values of the dilaton coupling constant a. We show that the Gauss-Bonnet term acts as a dyon hair tonic enlarging the allowed values of a to continuous domains in the plane (a,q m ) where q m is the magnetic charge. In the limit of the vanishing curvature coupling (a large magnetic charge) the dyon solutions obtained tend to the Reissner-Nordstroem solution but not to the extremal dyons of the Einstein-Maxwell-dilaton theory. Both solutions have the same dependence of the horizon radius in terms of charges. The entropy of new dyonic black holes interpolates between the Bekenstein-Hawking value in the limit of the large magnetic charge (equivalent to the vanishing Gauss-Bonnet coupling) and twice this value for the vanishing magnetic charge. Although an expression for the entropy can be obtained analytically using purely local near-horizon solutions, its interpretation as the black hole entropy is legitimate only once the global black hole solution is known to exist, and we obtain numerically the corresponding conditions on the parameters. Thus, a purely local analysis is insufficient to fully understand the entropy of the curvature-corrected black holes. We also find dyon solutions which are not asymptotically flat, but approach the linear dilaton background at infinity. They describe magnetic black holes on the electric linear dilaton background.
Spontaneous Scalarization of Black Holes and Compact Stars from a Gauss-Bonnet Coupling.
Silva, Hector O; Sakstein, Jeremy; Gualtieri, Leonardo; Sotiriou, Thomas P; Berti, Emanuele
2018-03-30
We identify a class of scalar-tensor theories with coupling between the scalar and the Gauss-Bonnet invariant that exhibit spontaneous scalarization for both black holes and compact stars. In particular, these theories formally admit all of the stationary solutions of general relativity, but these are not dynamically preferred if certain conditions are satisfied. Remarkably, black holes exhibit scalarization if their mass lies within one of many narrow bands. We find evidence that scalarization can occur in neutron stars as well.
Modified Gauss rules for approximate calculation of some strongly singular integrals
Berriochoa Esnaola, Elias Manuel Maria; Cachafeiro López, María Alicia; Illán González, Jesús Ricardo; Rebollido Lorenzo, José Manuel
2013-01-01
The approach we follow consists in transforming the numerical evaluation of hyper-singular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are presented. Ministerio de Educación | Ref. MTM2011-22713
Thin-shell wormholes in Einstein-Yang-Mills-Gauss-Bonnet theory
Energy Technology Data Exchange (ETDEWEB)
Bandyopadhyay, Tanwi; Chakraborty, Subenoy, E-mail: tanwib@gmail.co, E-mail: schakraborty@math.jdvu.ac.i [Department of Mathematics, Jadavpur University, Kolkata 32 (India)
2009-04-21
A thin-shell Lorentzian wormhole with spherical symmetry has been constructed in Einstein-Yang-Mills-Gauss-Bonnet theory. The generalized Darmois-Israel matching conditions are applied to the bounding shell and energy localized on the shell has been calculated. The amount of exotic matter for the existence of the wormhole has been evaluated and it has been shown graphically for certain choices of the parameters involved that ordinary matter is sufficient for the formation of thin-shell wormholes.
On the Gauss Map of Surfaces of Revolution with Lightlike Axis in Minkowski 3-Space
Directory of Open Access Journals (Sweden)
Minghao Jin
2013-01-01
Full Text Available By studying the Gauss map G and Laplace operator Δh of the second fundamental form h, we will classify surfaces of revolution with a lightlike axis in 3-dimensional Minkowski space and also obtain the surface of Enneper of the 2nd kind, the surface of Enneper of the 3rd kind, the de Sitter pseudosphere, and the hyperbolic pseudosphere that satisfy condition ΔhG=ΛG, Λ being a 3×3 real matrix.
Power function inflation potential analysis for cosmological model with Gauss-Bonnet term
Hikmawan, Getbogi; Suroso, Agus; Zen, Freddy P.
2017-05-01
Inflation is still an interesting topic in the study of our universe. An interesting inflation scenario named Gauss-Bonnet inflation proposed without inflation potential has been shown unstable. In this work, we consider the general power function inflation potential, V(ϕ) = mϕn in the model, then the solution is analyzed according to the inflation scenario. Using the stability condition, inflation potential with m positive and 0 ≤ n < 5 give proper solution for the inflation scenario.
Scalar hair around charged black holes in Einstein-Gauss-Bonnet gravity
Grandi, Nicolás; Landea, Ignacio Salazar
2018-02-01
We explore charged black hole solutions in Einstein-Gauss-Bonnet gravity in five dimensions, with a charged scalar hair. We interpret such hairy black holes as the final state of the superradiant instability previously reported for this system. We explore the relation of the hairy black hole solutions with the nonbackreacting quasibound states and scalar clouds, as well as with the boson star solutions.
Eikonal instability of Gauss-Bonnet-(anti-)-de Sitter black holes
Konoplya, R. A.; Zhidenko, A.
2017-05-01
Here we have shown that asymptotically anti-de Sitter (AdS) black holes in the Einstein-Gauss-Bonnet (GB) theory are unstable under linear perturbations of space-time in some region of parameters. This (eikonal) instability develops at high multipole numbers. We found the exact parametric regions of the eikonal instability and extended this consideration to asymptotically flat and de Sitter cases. The approach to the threshold of instability is driven by purely imaginary quasinormal modes, which are similar to those found recently in Grozdanov, Kaplis, and Starinets, [J. High Energy Phys. 07 (2016) 151, 10.1007/JHEP07(2016)151] for the higher curvature corrected black hole with the planar horizon. The found instability may indicate limits of holographic applicability of the GB-AdS backgrounds. Recently, through the analysis of critical behavior in AdS space-time in the presence of the Gauss-Bonnet term, it was shown [Deppe et al, Phys. Rev. Lett. 114, 071102 (2015), 10.1103/PhysRevLett.114.071102], that, if the total energy content of the AdS space-time is small, then no black holes can be formed with mass less than some critical value. A similar mass gap was also found when considering collapse of mass shells in asymptotically flat Gauss-Bonnet theories [Frolov, Phys. Rev. Lett. 115, 051102 (2015), 10.1103/PhysRevLett.115.051102]. The found instability of all sufficiently small Einstein-Gauss-Bonnet-AdS, dS and asymptotically flat black holes may explain the existing mass gaps in their formation.
Chapman, G.; Kirk, D.
1974-01-01
The parameter identification scheme being used is a differential correction least squares procedure (Gauss-Newton method). The position, orientation, and derivatives of these quantities with respect to the parameters of interest (i.e., sensitivity coefficients) are determined by digital integration of the equations of motion and the parametric differential equations. The application of this technique to three vastly different sets of data is used to illustrate the versatility of the method and to indicate some of the problems that still remain.
Dynamical manipulation of Cosine-Gauss beams in a graphene plasmonic waveguide.
He, Xueqing; Ning, Tigang; Li, Rujiang; Pei, Li; Zheng, Jingjing; Li, Jing
2017-06-12
In this paper, we theoretically propose for the first time that graphene monolayer can be used to manipulate the Cosine-Gauss beams (CGBs). We show that both the transverse oscillation period and propagation length of a CGB can be dynamically manipulated by utilizing the tunability of the graphene's chemical potential. The graphene-based planar plasmonic waveguide provides a good platform to investigate the propagation properties of CGBs, which is potentially compatible to the microelectronic technology.
Rotational hypersurfaces with $L_r$-pointwise 1-type Gauss map
Directory of Open Access Journals (Sweden)
Akram Mohammadpouri
2018-07-01
Full Text Available In this paper, we study hypersurfaces in $\\E^{n+1}$ which Gauss map $G$ satisfies the equation $L_rG = f(G + C$ for a smooth function $f$ and a constant vector $C$, where $L_r$ is the linearized operator of the $(r + 1$th mean curvature of the hypersurface, i.e., $L_r(f=tr(P_r\\circ\
Clinical Profile of Statin Intolerance in the Phase 3 GAUSS-2 Study.
Cho, Leslie; Rocco, Michael; Colquhoun, David; Sullivan, David; Rosenson, Robert S; Dent, Ricardo; Xue, Allen; Scott, Rob; Wasserman, Scott M; Stroes, Erik
2016-06-01
Recent evidence suggests that statin intolerance may be more common than reported in randomized trials. However, the statin-intolerant population is not well characterized. The goal of this report is to characterize the population enrolled in the phase 3 Goal Achievement after Utilizing an anti-PCSK9 antibody in Statin Intolerant Subjects Study (GAUSS-2; NCT 01763905). GAUSS-2 compared evolocumab, a fully human monoclonal antibody to proprotein convertase subtilisin/kexin type 9 (PCSK9) to ezetimibe in hypercholesterolemic patients who discontinued statin therapy due to statin-associated muscle symptoms (SAMS). GAUSS-2 was a 12-week, double-blind, placebo-controlled, randomized study that enrolled patients with elevated LDL-C who were either not on a statin or able to tolerate only a low-dose due to SAMS. Patients had received ≥2 statins and were unable to tolerate any statin dose or increase in dose above a specified weekly dose due to SAMS. Three hundred seven patients (mean [SD] age, 62 [10] years; 54 % males) were randomized 2:1 (evolocumab:ezetimibe). Mean (SD) LDL-C was 4.99 (1.51) mmol/L. Patients had used ≥2 (100 %), ≥3 (55 %), or ≥4 (21 %) statins. Coronary artery disease was present in 29 % of patients. Statin-intolerant symptoms were myalgia in 80 % of patients, weakness in 39 %, and more serious complications in 20 %. In 98 % of patients, SAMS interfered with normal daily activity; in 52 %, symptoms precluded moderate exertion. Evaluation of the GAUSS-2 trial population of statin-intolerant patients demonstrates that most patients were high risk with severely elevated LDL-C and many had statin-associated muscle symptoms that interfered with their quality of life.
Directory of Open Access Journals (Sweden)
Junesang Choi
2014-01-01
Full Text Available A remarkably large number of integral transforms and fractional integral formulas involving various special functions have been investigated by many authors. Very recently, Agarwal gave some integral transforms and fractional integral formulas involving the Fp(α,β(·. In this sequel, using the same technique, we establish certain integral transforms and fractional integral formulas for the generalized Gauss hypergeometric functions Fp(α,β,m(·. Some interesting special cases of our main results are also considered.
Xu, H; Bai, P D; Hu, M B; Mao, S H; Zhu, W H; Hu, J M; Liu, S H; Yang, T; Hou, J Y; Hu, Y; Ding, Q; Jiang, H W
2017-04-01
To assess the risk factors of Gleason sum upgrading between biopsy and radical prostatectomy (RP) and update the nomogram for the prediction of Gleason sum upgrading. The study cohort consisted of 237 Chinese prostate adenocarcinoma patients who underwent 10-core prostate biopsy and subsequently received RP in Huashan Hospital from February 2011 to May 2015. The main outcome of our study was Gleason sum upgrading between biopsy and RP pathology. Univariate and multivariate logistic regression models were conducted to explore the potential predictors, and ultimately to build the nomograms. The prediction model was further evaluated for its ability to predict significant upgrading in patients with biopsy Gleason sum<8. In the main cohort of all the patients, Gleason sum upgrading was observed in 62 (26.16%) patients. The pre-operative prostate-specific antigen (PSA) level, biopsy Gleason sum, and digital rectal examination were used in building the nomogram, which was validated internally with a bootstrap-corrected concordance index of 0.787. In the sub-cohort of 115 patients with standardized biopsy details, Gleason sum upgrading was observed in 31 (26.96%) patients. The pre-operative PSA level, biopsy Gleason sum, and number of positive cores were used in the nomogram, which was also validated internally with a bootstrap-corrected concordance index of 0.833. These two nomograms both demonstrated satisfactory statistical performance for predicting significant upgrading. Updated nomograms to predict Gleason sum upgrading in Chinese population between biopsy and RP were developed, demonstrating good statistical performance upon internal validation. Copyright © 2016 AEU. Publicado por Elsevier España, S.L.U. All rights reserved.
On the frequency spectra of the core magnetic field Gauss coefficients
Lesur, Vincent; Wardinski, Ingo; Baerenzung, Julien; Holschneider, Matthias
2018-03-01
From monthly mean observatory data spanning 1957-2014, geomagnetic field secular variation values were calculated by annual differences. Estimates of the spherical harmonic Gauss coefficients of the core field secular variation were then derived by applying a correlation based modelling. Finally, a Fourier transform was applied to the time series of the Gauss coefficients. This process led to reliable temporal spectra of the Gauss coefficients up to spherical harmonic degree 5 or 6, and down to periods as short as 1 or 2 years depending on the coefficient. We observed that a k-2 slope, where k is the frequency, is an acceptable approximation for these spectra, with possibly an exception for the dipole field. The monthly estimates of the core field secular variation at the observatory sites also show that large and rapid variations of the latter happen. This is an indication that geomagnetic jerks are frequent phenomena and that significant secular variation signals at short time scales - i.e. less than 2 years, could still be extracted from data to reveal an unexplored part of the core dynamics.
Error bounds on block Gauss-Seidel solutions of coupled multiphysics problems
Whiteley, J. P.
2011-05-09
Mathematical models in many fields often consist of coupled sub-models, each of which describes a different physical process. For many applications, the quantity of interest from these models may be written as a linear functional of the solution to the governing equations. Mature numerical solution techniques for the individual sub-models often exist. Rather than derive a numerical solution technique for the full coupled model, it is therefore natural to investigate whether these techniques may be used by coupling in a block Gauss-Seidel fashion. In this study, we derive two a posteriori bounds for such linear functionals. These bounds may be used on each Gauss-Seidel iteration to estimate the error in the linear functional computed using the single physics solvers, without actually solving the full, coupled problem. We demonstrate the use of the bound first by using a model problem from linear algebra, and then a linear ordinary differential equation example. We then investigate the effectiveness of the bound using a non-linear coupled fluid-temperature problem. One of the bounds derived is very sharp for most linear functionals considered, allowing us to predict very accurately when to terminate our block Gauss-Seidel iteration. © 2011 John Wiley & Sons, Ltd.
Quantum Gauss-Jordan Elimination and Simulation of Accounting Principles on Quantum Computers
Diep, Do Ngoc; Giang, Do Hoang; Van Minh, Nguyen
2017-06-01
The paper is devoted to a version of Quantum Gauss-Jordan Elimination and its applications. In the first part, we construct the Quantum Gauss-Jordan Elimination (QGJE) Algorithm and estimate the complexity of computation of Reduced Row Echelon Form (RREF) of N × N matrices. The main result asserts that QGJE has computation time is of order 2 N/2. The second part is devoted to a new idea of simulation of accounting by quantum computing. We first expose the actual accounting principles in a pure mathematics language. Then, we simulate the accounting principles on quantum computers. We show that, all accounting actions are exhousted by the described basic actions. The main problems of accounting are reduced to some system of linear equations in the economic model of Leontief. In this simulation, we use our constructed Quantum Gauss-Jordan Elimination to solve the problems and the complexity of quantum computing is a square root order faster than the complexity in classical computing.
Steganalysis of content-adaptive JPEG steganography based on Gauss partial derivative filter bank
Zhang, Yi; Liu, Fenlin; Yang, Chunfang; Luo, Xiangyang; Song, Xiaofeng; Lu, Jicang
2017-01-01
A steganalysis feature extraction method based on Gauss partial derivative filter bank is proposed in this paper to improve the detection performance for content-adaptive JPEG steganography. Considering that the embedding changes of content-adaptive steganographic schemes are performed in the texture and edge regions, the proposed method generates filtered images comprising rich texture and edge information using Gauss partial derivative filter bank, and histograms of absolute values of filtered subimages are extracted as steganalysis features. Gauss partial derivative filter bank can represent texture and edge information in multiple orientations with less computation load than conventional methods and prevent redundancy in different filtered images. These two properties are beneficial in the extraction of low-complexity sensitive features. The results of experiments conducted on three selected modern JPEG steganographic schemes-uniform embedding distortion, JPEG universal wavelet relative distortion, and side-informed UNIWARD-indicate that the proposed feature set is superior to the prior art feature sets-discrete cosine transform residual, phase aware rich model, and Gabor filter residual.
State space orderings for Gauss-Seidel in Markov chains revisited
Energy Technology Data Exchange (ETDEWEB)
Dayar, T. [Bilkent Univ., Ankara (Turkey)
1996-12-31
Symmetric state space orderings of a Markov chain may be used to reduce the magnitude of the subdominant eigenvalue of the (Gauss-Seidel) iteration matrix. Orderings that maximize the elemental mass or the number of nonzero elements in the dominant term of the Gauss-Seidel splitting (that is, the term approximating the coefficient matrix) do not necessarily converge faster. An ordering of a Markov chain that satisfies Property-R is semi-convergent. On the other hand, there are semi-convergent symmetric state space orderings that do not satisfy Property-R. For a given ordering, a simple approach for checking Property-R is shown. An algorithm that orders the states of a Markov chain so as to increase the likelihood of satisfying Property-R is presented. The computational complexity of the ordering algorithm is less than that of a single Gauss-Seidel iteration (for sparse matrices). In doing all this, the aim is to gain an insight for faster converging orderings. Results from a variety of applications improve the confidence in the algorithm.
Development of a Double-Gauss Lens Based Setup for Optoacoustic Applications.
Choi, Hojong; Ryu, Jae-Myung; Yeom, Jung-Yeol
2017-03-03
In optoacoustic (photoacoustic) systems, different echo signal intensities such as amplitudes, center frequencies, and bandwidths need to be compensated by utilizing variable gain or time-gain compensation amplifiers. However, such electronic components can increase system complexities and signal noise levels. In this paper, we introduce a double-Gauss lens to generate a large field of view with uniform light intensity due to the low chromatic aberrations of the lens, thus obtaining uniform echo signal intensities across the field of view of the optoacoustic system. In order to validate the uniformity of the echo signal intensities in the system, an in-house transducer was placed at various positions above a tissue sample and echo signals were measured and compared with each other. The custom designed double-Gauss lens demonstrated negligible light intensity variation (±1.5%) across the illumination field of view (~2 cm diameter). When the transducer was used to measure echo signal from an eye of a bigeye tuna within a range of ±1 cm, the peak-to-peak amplitude, center frequency, and their -6 dB bandwidth variations were less than 2 mV, 1 MHz, and 6%, respectively. The custom designed double-Gauss lens can provide uniform light beam across a wide area while generating insignificant echo signal variations, and thus can lower the burden of the receiving electronics or signal processing in the optoacoustic system.
Propagation Dynamics of Nonspreading Cosine-Gauss Water-Wave Pulses.
Fu, Shenhe; Tsur, Yuval; Zhou, Jianying; Shemer, Lev; Arie, Ady
2015-12-18
Linear gravity water waves are highly dispersive; therefore, the spreading of initially short wave trains characterizes water surface waves, and is a universal property of a dispersive medium. Only if there is sufficient nonlinearity does this envelope admit solitary solutions which do not spread and remain in fixed forms. Here, in contrast to the nonlinear localized wave packets, we present both theoretically and experimentally a new type of linearly nondispersive water wave, having a cosine-Gauss envelope, as well as its higher-order Hermite cosine-Gauss variations. We show that these waves preserve their width despite the inherent dispersion while propagating in an 18-m wave tank, accompanied by a slowly varying carrier-envelope phase. These wave packets exhibit self-healing; i.e., they are restored after bypassing an obstacle. We further demonstrate that these nondispersive waves are robust to weakly nonlinear perturbations. In the strong nonlinear regime, symmetry breaking of these waves is observed, but their cosine-Gauss shapes are still approximately preserved during propagation.
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] ...
Isospin sum rules for inclusive cross-sections
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.
7 CFR 42.132 - Determining cumulative sum values.
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...
Notes on sum-tests and independence tests
Bauwens, B.; Terwijn, S.A.
2011-01-01
We study statistical sum-tests and independence tests, in particular for computably enumerable semimeasures on a discrete domain. Among other things, we prove that for universal semimeasures every Sigma0/1-sum-test is bounded, but unbounded Pi0/1-sum-tests exist, and we study to what extent the
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
Extremal extensions for the sum of nonnegative selfadjoint relations
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
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 ...
Direct and reverse inclusions for strongly multiple summing operators
Indian Academy of Sciences (India)
Pellegrino and Santos [10] raise the question whether there are true inclusion results for the class of strongly multiple summing operators. The main purpose of this paper is to show that the results proven in [16] for multiple summing operators can be adapted to obtain similar results for strongly multiple summing operators ...
A comparative application of Jacobi and Gauss Seidel's numerical ...
African Journals Online (AJOL)
In PageRank calculation the Jacobi matrix is given by d T (damping factor times transition matrix), a sparse matrix. The solution of the iteration is x, if the limit exists. The convergence is guaranteed, if the absolute value of the largest eigen value of ƒv1ƒ{ Mƒw is less than one. In case of PageRank calculation this is fulfilled for ...
Fractional Sums and Differences with Binomial Coefficients
Directory of Open Access Journals (Sweden)
Thabet Abdeljawad
2013-01-01
Full Text Available In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives. The second approach is by iterating the derivative and then defining a fractional order by making use of the binomial theorem to obtain Grünwald-Letnikov fractional derivatives. In this paper we formulate the delta and nabla discrete versions for left and right fractional integrals and derivatives representing the second approach. Then, we use the discrete version of the Q-operator and some discrete fractional dual identities to prove that the presented fractional differences and sums coincide with the discrete Riemann ones describing the first approach.
Holography and ARPES sum-rules
Gursoy, Umut; Stoof, Henk; Vandoren, Stefan
2012-01-01
We study correlation functions of elementary fermions in strongly interacting field theories using the AdS/CFT correspondence. This correspondence generically associates bulk fields to composite operators in field theory. We modify the holographic prescription in order to obtain correlators that correspond to fermonic single-particle excitations by introducing a dynamical fermionic source localized on a UV brane in a holographic background. We work out the conditions when these correlators obey the zeroth frequency sum-rule satisfied by angle-resolved photo-emission spectroscopy (ARPES) and are thus directly relevant to the AdS/CMT correspondence. To illustrate our techniques, we study field theories at zero chemical potential with an arbitrary dynamical exponent z, i.e., the Lifshitz invariant conformal field theories, including the usual relativistic case z=1.
Sum of Bernoulli Mixtures: Beyond Conditional Independence
Directory of Open Access Journals (Sweden)
Taehan Bae
2014-01-01
Full Text Available We consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the threshold tending to one. The large-sample distribution of the empirical frequency and its use in approximating the risk measures, value at risk and conditional tail expectation, are presented for a new class of models which we call double mixtures. Several illustrative examples with a Beta mixing distribution, are given. As well, some data from the area of credit risk are fit with the models, and comparisons are made between the new models and also the classical Beta-binomial model.
Polynomial Formula for Sums of Powers of Integers
Indian Academy of Sciences (India)
IAS Admin
jk. A well-known story in the history of mathematics is that the great German mathematician Carl Friedrich Gauss, while in elementary school, noted that for k = 1, S1,n ≡. 1+2+...+n is, when written in reverse order, equal to n+(n−1)+ ...+1. And when they are added one gets. 2S1,n = (1+n)+(2+(n−1))+(3+(n−2))+...+(n+1) =.
Test elements of direct sums and free products of free Lie algebras
Indian Academy of Sciences (India)
Abstract. We give a characterization of test elements of a direct sum of free Lie algebras in terms of test elements of the factors. In addition, we construct certain types of test elements and we prove that in a free product of free Lie algebras, product of the homogeneous test elements of the factors is also a test element.
Test elements of direct sums and free products of free Lie algebras
Indian Academy of Sciences (India)
We give a characterization of test elements of a direct sum of free Lie algebras in terms of test elements of the factors. In addition, we construct certain types of test elements and we prove that in a free product of free Lie algebras, product of the homogeneous test elements of the factors is also a test element.
Energy Technology Data Exchange (ETDEWEB)
Ernazarov, K.K. [RUDN University, Institute of Gravitation and Cosmology, Moscow (Russian Federation); Ivashchuk, V.D. [RUDN University, Institute of Gravitation and Cosmology, Moscow (Russian Federation); VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation)
2017-06-15
We consider a D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term Λ. We restrict the metrics to diagonal cosmological ones and find for certain Λ a class of solutions with exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters H > 0, h{sub 1} and h{sub 2}, corresponding to factor spaces of dimensions m > 2, k{sub 1} > 1 and k{sub 2} > 1, respectively, with k{sub 1} ≠ k{sub 2} and D = 1 + m + k{sub 1} + k{sub 2}. Any of these solutions describes an exponential expansion of 3d subspace with Hubble parameter H and zero variation of the effective gravitational constant G. We prove the stability of these solutions in a class of cosmological solutions with diagonal metrics. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Ernazarov, K.K. [RUDN University, Institute of Gravitation and Cosmology, Moscow (Russian Federation); Ivashchuk, V.D. [RUDN University, Institute of Gravitation and Cosmology, Moscow (Russian Federation); Center for Gravitation and Fundamental Metrology, VNIIMS, Moscow (Russian Federation)
2017-02-15
A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term Λ is considered. By assuming diagonal cosmological metrics, we find, for a certain fine-tuned Λ, a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters H > 0 and h < 0, corresponding to factor spaces of dimensions m > 3 and l > 1, respectively, with (m,l) ≠ (6,6), (7,4), (9,3) and D = 1+m+l. Any of these solutions describes an exponential expansion of three-dimensional subspace with Hubble parameter H and zero variation of the effective gravitational constant G. We prove the stability of these solutions in a class of cosmological solutions with diagonal metrics. (orig.)
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)
SEU System Analysis: Not Just the Sum of All Parts
Berg, Melanie D.; Label, Kenneth
2014-01-01
Single event upset (SEU) analysis of complex systems is challenging. Currently, system SEU analysis is performed by component level partitioning and then either: the most dominant SEU cross-sections (SEUs) are used in system error rate calculations; or the partition SEUs are summed to eventually obtain a system error rate. In many cases, system error rates are overestimated because these methods generally overlook system level derating factors. The problem with overestimating is that it can cause overdesign and consequently negatively affect the following: cost, schedule, functionality, and validation/verification. The scope of this presentation is to discuss the risks involved with our current scheme of SEU analysis for complex systems; and to provide alternative methods for improvement.
Dual-consistency study for Green-Gauss gradient schemes in an unstructured Navier-Stokes method
Stück, Arthur
2017-12-01
A multi-pass reconstruction method for the discrete-adjoint residual is presented that computes the adjoint of the viscous fluxes based on Green-Gauss gradients in an unstructured finite-volume RANS method. The intermediate discrete-adjoint multipliers of the multi-pass reconstruction are the dual viscous stresses containing the dual Green-Gauss gradients. Since the latter are explicitly evaluated on the fly, meaningful discrete-adjoint operators can be identified and compared against their primal counterparts. Numerical experiments are carried out for a 1D diffusion problem, 2D and 3D RANS cases on a sequence of grids to verify the consistency of the dual Green-Gauss gradients. They are compared against a rediscretisation of the adjoint Green-Gauss gradients known from the continuous-adjoint approach. In that sense, the multi-pass residual reconstruction method provides a deeper insight into the effective dual discretisation, an important part of which is the dual Green-Gauss gradient.
Konoplya, R. A.; Zhidenko, A.
2017-09-01
Here we shall show that there is no other instability for the Einstein-Gauss-Bonnet-anti-de Sitter (AdS) black holes, than the eikonal one and consider the features of the quasinormal spectrum in the stability sector in detail. The obtained quasinormal spectrum consists from the two essentially different types of modes: perturbative and non-perturbative in the Gauss-Bonnet coupling α. The sound and hydrodynamic modes of the perturbative branch can be expressed through their Schwazrschild-AdS limits by adding a linear in α correction to the damping rates: ω≈Re ω SAdS -Im ω SAdS(1- α·(( D+1)( D-4) /2 R 2)) i, where R is the AdS radius. The non-perturbative branch of modes consists of purely imaginary modes, whose damping rates unboundedly increase when α goes to zero. When the black hole radius is much larger than the anti-de Sitter radius R, the regime of the black hole with planar horizon (black brane) is reproduced. If the Gauss-Bonnet coupling α (or used in holography λGB) is not small enough, then the black holes and branes suffer from the instability, so that the holographic interpretation of perturbation of such black holes becomes questionable, as, for example, the claimed viscosity bound violation in the higher derivative gravity. For example, D = 5 black brane is unstable at |λGB| > 1 /8 and has anomalously large relaxation time when approaching the threshold of instability.
Parallelization of Lower-Upper Symmetric Gauss-Seidel Method for Chemically Reacting Flow
Yoon, Seokkwan; Jost, Gabriele; Chang, Sherry
2005-01-01
Development of technologies for exploration of the solar system has revived an interest in computational simulation of chemically reacting flows since planetary probe vehicles exhibit non-equilibrium phenomena during the atmospheric entry of a planet or a moon as well as the reentry to the Earth. Stability in combustion is essential for new propulsion systems. Numerical solution of real-gas flows often increases computational work by an order-of-magnitude compared to perfect gas flow partly because of the increased complexity of equations to solve. Recently, as part of Project Columbia, NASA has integrated a cluster of interconnected SGI Altix systems to provide a ten-fold increase in current supercomputing capacity that includes an SGI Origin system. Both the new and existing machines are based on cache coherent non-uniform memory access architecture. Lower-Upper Symmetric Gauss-Seidel (LU-SGS) relaxation method has been implemented into both perfect and real gas flow codes including Real-Gas Aerodynamic Simulator (RGAS). However, the vectorized RGAS code runs inefficiently on cache-based shared-memory machines such as SGI system. Parallelization of a Gauss-Seidel method is nontrivial due to its sequential nature. The LU-SGS method has been vectorized on an oblique plane in INS3D-LU code that has been one of the base codes for NAS Parallel benchmarks. The oblique plane has been called a hyperplane by computer scientists. It is straightforward to parallelize a Gauss-Seidel method by partitioning the hyperplanes once they are formed. Another way of parallelization is to schedule processors like a pipeline using software. Both hyperplane and pipeline methods have been implemented using openMP directives. The present paper reports the performance of the parallelized RGAS code on SGI Origin and Altix systems.
Energetics and optical properties of 6-dimensional rotating black hole in pure Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Abdujabbarov, Ahmadjon; Ahmedov, Bobomurat; Atamurotov, Farruh; Dadhich, Naresh; Stuchlik, Zdenek
2015-01-01
We study physical processes around a rotating black hole in pure Gauss-Bonnet (GB) gravity. In pure GB gravity, the gravitational potential has a slower fall-off as compared to the corresponding Einstein potential in the same dimension. It is therefore expected that the energetics of a pure GB black hole would be weaker, and our analysis bears out that the efficiency of energy extraction by the Penroseprocess is increased to 25.8 % and the particle acceleration is increased to 55.28 %; the optical shadow of the black hole is decreased. These are in principle distinguishing observable features of a pure GB black hole. (orig.)
GPU-accelerated Modeling and Element-free Reverse-time Migration with Gauss Points Partition
Zhen, Z.; Jia, X.
2014-12-01
Element-free method (EFM) has been applied to seismic modeling and migration. Compared with finite element method (FEM) and finite difference method (FDM), it is much cheaper and more flexible because only the information of the nodes and the boundary of the study area are required in computation. In the EFM, the number of Gauss points should be consistent with the number of model nodes; otherwise the accuracy of the intermediate coefficient matrices would be harmed. Thus when we increase the nodes of velocity model in order to obtain higher resolution, we find that the size of the computer's memory will be a bottleneck. The original EFM can deal with at most 81×81 nodes in the case of 2G memory, as tested by Jia and Hu (2006). In order to solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition (GPP), and utilize the GPUs to improve the computation efficiency. Considering the characteristics of the Gaussian points, the GPP method doesn't influence the propagation of seismic wave in the velocity model. To overcome the time-consuming computation of the stiffness matrix (K) and the mass matrix (M), we also use the GPUs in our computation program. We employ the compressed sparse row (CSR) format to compress the intermediate sparse matrices and try to simplify the operations by solving the linear equations with the CULA Sparse's Conjugate Gradient (CG) solver instead of the linear sparse solver 'PARDISO'. It is observed that our strategy can significantly reduce the computational time of K and Mcompared with the algorithm based on CPU. The model tested is Marmousi model. The length of the model is 7425m and the depth is 2990m. We discretize the model with 595x298 nodes, 300x300 Gauss cells and 3x3 Gauss points in each cell. In contrast to the computational time of the conventional EFM, the GPUs-GPP approach can substantially improve the efficiency. The speedup ratio of time consumption of computing K, M is 120 and the
International Nuclear Information System (INIS)
Watanabe, Shuichi; Kudo, Hiroyuki; Saito, Tsuneo
1993-01-01
In this paper, we propose a new reconstruction algorithm based on MAP (maximum a posteriori probability) estimation principle for emission tomography. To improve noise suppression properties of the conventional ML-EM (maximum likelihood expectation maximization) algorithm, direct three-dimensional reconstruction that utilizes intensity correlations between adjacent transaxial slices is introduced. Moreover, to avoid oversmoothing of edges, a priori knowledge of RI (radioisotope) distribution is represented by using a doubly-stochastic image model called the compound Gauss-Markov random field. The a posteriori probability is maximized by using the iterative GEM (generalized EM) algorithm. Computer simulation results are shown to demonstrate validity of the proposed algorithm. (author)
Decentralized Gauss-Newton method for nonlinear least squares on wide area network
Liu, Lanchao; Ling, Qing; Han, Zhu
2014-10-01
This paper presents a decentralized approach of Gauss-Newton (GN) method for nonlinear least squares (NLLS) on wide area network (WAN). In a multi-agent system, a centralized GN for NLLS requires the global GN Hessian matrix available at a central computing unit, which may incur large communication overhead. In the proposed decentralized alternative, each agent only needs local GN Hessian matrix to update iterates with the cooperation of neighbors. The detail formulation of decentralized NLLS on WAN is given, and the iteration at each agent is defined. The convergence property of the decentralized approach is analyzed, and numerical results validate the effectiveness of the proposed algorithm.
Phantom-like behavior of a DGP-inspired Scalar-Gauss-Bonnet gravity
International Nuclear Information System (INIS)
Nozari, Kourosh; Azizi, Tahereh; Setare, M.R.
2009-01-01
We study the phantom-like behavior of a DGP-inspired braneworld scenario where curvature correction on the brane is taken into account. We include a possible modification of the induced gravity on the brane by incorporating higher order curvature terms of Gauss-Bonnet type. We investigate the cosmological implications of the model and we show that the normal branch of the scenario self-accelerates in this modified scenario without introducing any dark energy component. Also, a phantom-like behavior can be realized in this model without introducing any phantom field that suffers from serious difficulties such as violation of the null energy condition
Kink-antikink, trapping bags and five-dimensional Gauss-Bonnet gravity
Giovannini, Massimo
2006-01-01
Five-dimensional Gauss-Bonnet gravity, with one warped extra-dimension, allows classes of solutions where two scalar fields combine either in a kink-antikink system or in a trapping bag configuration. While the kink-antikink system can be interpreted as a pair of gravitating domain walls with opposite topological charges, the trapping bag solution consists of a domain wall supplemented by a non-topological defect. In both classes of solutions, for large absolute values of the bulk coordinate (i.e. far from the core of the defects), the geometry is given by five-dimensional anti-de Sitter space.
Kink-antikink, trapping bags and five-dimensional Gauss-Bonnet gravity
Giovannini, Massimo
2006-01-01
Five-dimensional Gauss-Bonnet gravity, with one warped extra-dimension, allows classes of solutions where two scalar fields combine either in a kink-antikink system or in a trapping bag configuration. While the kink-antikink system can be interpreted as a pair of gravitating domain walls with opposite topological charges, the trapping bag solution consists of a domain wall supplemented by a non-topological defect. In both classes of solutions, for large absolute values of the bulk coordinate ...
Dataset for petroleum based stock markets and GAUSS codes for SAMEM.
Khalifa, Ahmed A A; Bertuccelli, Pietro; Otranto, Edoardo
2017-02-01
This article includes a unique data set of a balanced daily (Monday, Tuesday and Wednesday) for oil and natural gas volatility and the oil rich economies' stock markets for Saudi Arabia, Qatar, Kuwait, Abu Dhabi, Dubai, Bahrain and Oman, using daily data over the period spanning Oct. 18, 2006-July 30, 2015. Additionally, we have included unique GAUSS codes for estimating the spillover asymmetric multiplicative error model (SAMEM) with application to Petroleum-Based Stock Market. The data, the model and the codes have many applications in business and social science.
Li, Yun; Sun, Shu Li; Hao, Gang
2017-09-28
We addressed the fusion estimation problem for nonlinear multisensory systems. Based on the Gauss-Hermite approximation and weighted least square criterion, an augmented high-dimension measurement from all sensors was compressed into a lower dimension. By combining the low-dimension measurement function with the particle filter (PF), a weighted measurement fusion PF (WMF-PF) is presented. The accuracy of WMF-PF appears good and has a lower computational cost when compared to centralized fusion PF (CF-PF). An example is given to show the effectiveness of the proposed algorithms.
A Stable Clock Error Model Using Coupled First and Second Order Gauss-Markov Processes
Carpenter, Russell; Lee, Taesul
2008-01-01
Long data outages may occur in applications of global navigation satellite system technology to orbit determination for missions that spend significant fractions of their orbits above the navigation satellite constellation(s). Current clock error models based on the random walk idealization may not be suitable in these circumstances, since the covariance of the clock errors may become large enough to overflow flight computer arithmetic. A model that is stable, but which approximates the existing models over short time horizons is desirable. A coupled first- and second-order Gauss-Markov process is such a model.
The solution of the Navier-Stokes equations using Gauss-Seidel line relaxation
Maccormack, Robert W.; Candler, Graham V.
1989-01-01
The Navier-Stokes equations in an implicit flux-split difference formulation are solved numerically using a Gauss-Seidel line-relaxation procedure. Particular attention is given to the selection of flux-vector splitting method and flux splitting in boundary layers. Results for sample problems involving (1) turbulent supersonic flow over a cone and (2) the viscous hypersonic flow of a chemically reacting gas in thermal nonequilibrium past a blunted cone are presented in extensive graphs and briefly characterized. The present flux-split procedures are shown to provide accurate shear-layer calculations.
Compound Poisson Approximations for Sums of Random Variables
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...
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)
On the general Dedekind sums and its reciprocity formula
Indian Academy of Sciences (India)
Introduction. For a positive integer q and an arbitrary integer h, the Dedekind sums S(h, q) is defined as: S(h, q) = ... we obtain an interesting reciprocity formula for the general Dedekind sums S(h, 1, 3,q). That is, we ..... [3] Conrey J B, Fransen Eric, Klein Robert and Scott Clayton, Mean values of Dedekind sums,. J. Number ...
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
Extended M1 sum rule for mixed-symmetry states
International Nuclear Information System (INIS)
Smirnova, N.A.; Pietralla, N.; Leviatan, A.; Ginocchio, J.N.; Fransen, C.
2002-01-01
A generalized M1 sum rule for orbital magnetic dipole strength from excited symmetric states to mixed-symmetry states is derived within the interacting boson model of even-even nuclei. The applicability of the sum rule is investigated for the U(5)-SO(6) transition region. By applying the sum rule to the recent extensive data on mixed-symmetry states in 94Mo one obtains valuable structure information in a largely parameter-independent way
International Nuclear Information System (INIS)
Elizalde, E.; Makarenko, A.N.; Obukhov, V.V.; Osetrin, K.E.; Filippov, A.E.
2007-01-01
Six-dimensional Einstein-Gauss-Bonnet gravity (with a linear Gauss-Bonnet term) is investigated. This theory is inspired by basic features of results coming from string and M-theory. Dynamical compactification is carried out and it is seen that a four-dimensional accelerating FRW universe is recovered, when the two-dimensional internal space radius shrinks. A non-perturbative structure of the corresponding theory is identified which has either three or one stable fixed points, depending on the Gauss-Bonnet coupling being positive or negative. A much richer structure than in the case of the perturbative regime of the dynamical compactification recently studied by Andrew, Bolen, and Middleton is exhibited
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)
Zero Modes of Gauss Constraint in Gaugeless Reduction of Yang-Mills Theory
International Nuclear Information System (INIS)
Khvedelidze, A.; Pervushin, V.
1994-01-01
The physical variables for pure Yang-Mills theory in four-dimensional Minkowski space-time are constructed without using a gauge-fixing condition by the explicit resolving of the non-Abelian Gauss constraint and by the Bogolyubov transformation that diagonalizes the kinetic term in reduced action (action on constraint shell). As a result, the reduced action is expressed in terms of gauge invariant field variables including an additional global (only time-dependent) one, describing zero mode dynamics of the Gauss constraint. This additional variable reflects the symmetry group of topologically nontrivial transformations remaining after the reduction. (It gives also the characteristic of the Gribov ambiguity from the point of view of the gauge fixing method). The perturbation theory in terms of quasiparticles with the new stable vacuum, which is defined through the zero mode configuration, is proposed. It was shown that the averaging of Green's functions for quasiparticles over the global variable describes the mechanism of color confinement. 21 refs
Algorithm implementation and testing to ensure consistency of Gauss's law in OSIRIS
Miller, Kyle; Elias, Paul; Fonseca, Ricardo; Winjum, Benjamin; Tsung, Frank; Decyk, Viktor; Mori, Warren
2017-10-01
Electromagnetic particle-in-cell (PIC) simulations compute the trajectories of particles as they interact via fields calculated by numerically solving Maxwell's equations on a grid using currents (and charge densities) from the particles. Within PICKSC, UCLA maintains a variety of open-source and open-access codes. These include OSIRIS-developed in partnership with IST-and UPIC-EMMA. Standard OSIRIS uses a rigorous charge-conserving current deposit to ensure the consistency of Gauss's law together with a finite-difference (FD) solution to Maxwell's equations. It also contains options for spectral (FFT) and hybrid (FFT and FD) field solvers, as well as a customized, higher-order FD field solver to help mitigate the numerical Cerenkov instability. The standard charge conserving current deposit is only valid for second-order accurate FD solvers. Another option for maintaining the consistency of Gauss's law is the Boris correction, where a ``direct'' current deposit is used and the electric field is corrected through the use of a Poisson solve. The Boris correction-with both exact and iterative multigrid Poisson solves-has been implemented into OSIRIS. Preliminary analyses of timing and fluctuations levels will be presented, including the effects of different particle orders. Work supported by NSF and DOE.
Competing s-wave orders from Einstein-Gauss-Bonnet gravity
Li, Zhi-Hong; Fu, Yun-Chang; Nie, Zhang-Yu
2018-01-01
In this paper, the holographic superconductor model with two s-wave orders from 4 + 1 dimensional Einstein-Gauss-Bonnet gravity is explored in the probe limit. At different values of the Gauss-Bonnet coefficient α, we study the influence of tuning the mass and charge parameters of the bulk scalar field on the free energy curve of condensed solution with signal s-wave order, and compare the difference of tuning the two different parameters while the changes of the critical temperature are the same. Based on the above results, it is indicated that the two free energy curves of different s-wave orders can have one or two intersection points, where two typical phase transition behaviors of the s + s coexistent phase, including the reentrant phase transition near the Chern-Simons limit α = 0.25, can be found. We also give an explanation to the nontrivial behavior of the Tc- α curves near the Chern-Simons limit, which might be heuristic to understand the origin of the reentrant behavior near the Chern-Simons limit.
Black holes in Einstein-Gauss-Bonnet gravity with a string cloud background
International Nuclear Information System (INIS)
Herscovich, Estanislao; Richarte, Martin G.
2010-01-01
We obtain a black hole solution in the Einstein-Gauss-Bonnet theory for the string cloud model in a five-dimensional spacetime. We analyze the event horizons and naked singularities. Later, we compute the Hawking temperature T H , the specific heat C, the entropy S, and the Helmholtz free energy F of the black hole. The entropy was computed using the Wald formulation. In addition, the quantum correction to the Wald's entropy is considered for the string cloud source. We mainly explore the thermodynamical global and local stability of the system with vanishing or non-vanishing cosmological constant. The global thermodynamic phase structure indicates that the Hawking-Page transition is achieved for this model. Further, we observe that there exist stable black holes with small radii and that these regions are enlarged when choosing small values of the string cloud density and of the Gauss-Bonnet parameter. Besides, the rate of evaporation for these black holes are studied, determining whether the evaporation time is finite or not. Then, we concentrate on the dynamical stability of the system, studying the effective potential for s-waves propagating on the string cloud background.
Calculation of photoionization differential cross sections using complex Gauss-type orbitals.
Matsuzaki, Rei; Yabushita, Satoshi
2017-09-05
Accurate theoretical calculation of photoelectron angular distributions for general molecules is becoming an important tool to image various chemical reactions in real time. We show in this article that not only photoionization total cross sections but also photoelectron angular distributions can be accurately calculated using complex Gauss-type orbital (cGTO) basis functions. Our method can be easily combined with existing quantum chemistry techniques including electron correlation effects, and applied to various molecules. The so-called two-potential formula is applied to represent the transition dipole moment from an initial bound state to a final continuum state in the molecular coordinate frame. The two required continuum functions, the zeroth-order final continuum state and the first-order wave function induced by the photon field, have been variationally obtained using the complex basis function method with a mixture of appropriate cGTOs and conventional real Gauss-type orbitals (GTOs) to represent the continuum orbitals as well as the remaining bound orbitals. The complex orbital exponents of the cGTOs are optimized by fitting to the outgoing Coulomb functions. The efficiency of the current method is demonstrated through the calculations of the asymmetry parameters and molecular-frame photoelectron angular distributions of H2+ and H2 . In the calculations of H2 , the static exchange and random phase approximations are employed, and the dependence of the results on the basis functions is discussed. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
International Nuclear Information System (INIS)
Mueller, A.
1985-01-01
The advantage of the Gauss-function-based models doubtlessly consists in their proven propagation parameter sets and empirical stack plume rise formulas and in their easy matchability and handability. However, grid models based on trace matter transport equation are more convincing concerning their fundamental principle. Grid models of the MODIS type are to acquire a practical applicability comparable to Gauss models by developing techniques allowing to consider the vertical self-movement of the plumes in grid models and to secure improved diffusion co-efficient determination. (orig./PW) [de
Arrizón, Victor; Ruiz, Ulises; Aguirre-Olivas, Dilia; Sánchez-de-la-Llave, David; Ostrovsky, Andrey S
2014-03-01
We compare two phase optical elements that are employed to generate approximate Bessel-Gauss beams of arbitrary order. These elements are the helical axicon (HA) and the kinoform of the desired Bessel-Gauss beam. The HA generates a Bessel beam (BB) by free propagation, and the kinoform is employed in a Fourier spatial filtering optical setup. As the main result, it is obtained that the error in the BBs generated with the kinoform is smaller than the error in the beams obtained with the HA. On the other hand, it is obtained that the efficiencies of the methods are approximately 1.0 (HA) and 0.7 (kinoform).
Application of sum rule to the dispersion model of hydrogenated amorphous silicon
Czech Academy of Sciences Publication Activity Database
Franta, D.; Nečas, D.; Zajíčková, L.; Ohlídal, I.; Stuchlík, Jiří; Chvostová, Dagmar
2013-01-01
Roč. 539, JUL (2013), s. 233-244 ISSN 0040-6090 Institutional support: RVO:68378271 Keywords : optical constants * ellipsometry * spectrophotometry * a-Si:H * Urbach tail * localized states * sum rule Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.867, year: 2013
Sum-of-squares based observer design for polynomial systems with a known fixed time delay
Czech Academy of Sciences Publication Activity Database
Rehák, Branislav
2015-01-01
Roč. 51, č. 5 (2015), s. 858-873 ISSN 0023-5954 R&D Projects: GA ČR GA13-02149S Institutional support: RVO:67985556 Keywords : sum-of-squares polynomial * observer * polynomial system Subject RIV: BC - Control Systems Theory Impact factor: 0.628, year: 2015 http://www.kybernetika.cz/content/2015/5/856
The nucleon axial isoscalar coupling constant and the Bjorken sum rule
International Nuclear Information System (INIS)
Belyaev, V.M.; Ioffe, B.L.; Kogan, Ya.I.
1984-01-01
The nucleon coupling constant with the axial isoscalar current entering the Bjorken sum rule for the deep inelastic scattering of polarized electrons on a polarized target is calculated in nonperturbative QCD. The result, gsub(A)sup(s) approximately 0.5, is about a factor of two smaller as compared to that of the SU(6) symmetric quark model
A practical comparison of methods to assess sum-of-products
International Nuclear Information System (INIS)
Rauzy, A.; Chatelet, E.; Dutuit, Y.; Berenguer, C.
2003-01-01
Many methods have been proposed in the literature to assess the probability of a sum-of-products. This problem has been shown computationally hard (namely no. P-hard). Therefore, algorithms can be compared only from a practical point of view. In this article, we propose first an efficient implementation of the pivotal decomposition method. This kind of algorithms is widely used in the Artificial Intelligence framework. It is unfortunately almost never considered in the reliability engineering framework, but as a pedagogical tool. We report experimental results that show that this method is in general much more efficient than classical methods that rewrite the sum-of-products under study into an equivalent sum of disjoint products. Then, we derive from our method a factorization algorithm to be used as a preprocessing method for binary decision diagrams. We show by means of experimental results that this latter approach outperforms the formers
Finding Sums for an Infinite Class of Alternating Series
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…
Some multiple summing operators defined by the determinant of a ...
African Journals Online (AJOL)
We give some new examples of multilinear Hilbert-Schmidt and multiple summing operators, involving the determinant of a n × n -square matrix of scalars. We also determine the exact value of the Hilbert-Schmidt and multiple summing norms and we show that both of them are related to the permanent of a certain matrix.
Vector-meson-baryon coupling constants in QCD sum rules
Erkol, G.; Timmermans, R.G.E.; Rijken, T.A.
2006-01-01
The external-field quantum chromodynamics (QCD) sum rules method is used to evaluate the coupling constants of the vector mesons rho and omega to the nucleon and the Lambda,Sigma, and Xi baryons. It is shown that these coupling constants as calculated from QCD sum rules are consistent with
Scalar-meson-baryon coupling constants in QCD sum rules
Erkol, G; Timmermans, RGE; Oka, M; Rijken, TA; Rijken, Th.A.
The external-field QCD sum rules method is used to evaluate the coupling constants of the light isoscalar-scalar meson ("sigma" or epsilon) to the Lambda,Sigma, and Xi baryons. It is shown that these coupling constants as calculated from QCD sum rules are consistent with SU(3) flavor relations,
Scalar-meson baryon coupling constants in QCD sum rules
Erkol, G.; Timmermans, R.G.E.; Oka, M.; Rijken, T.A.
2006-01-01
The external-field QCD sum rules method is used to evaluate the coupling constants of the light isoscalar-scalar meson (``sigma'' or ε) to the Lambda,Sigma, and Xi baryons. It is shown that these coupling constants as calculated from QCD sum rules are consistent with SU(3) flavor relations, which
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.)
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.
Effectiveness evaluation of contingency sum as a risk management ...
African Journals Online (AJOL)
Construction managers in a bid to effectively manage risks prone projects have adopted several methods, one of which is contingency sum. This study aims at evaluating the effectiveness of contingency sum as a risk management tool for construction projects in Niger Delta region of Nigeria. The objectives are to establish ...
Efficient yellow beam generation by intracavity sum frequency ...
Indian Academy of Sciences (India)
2014-02-06
: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 ...
28 CFR 523.16 - Lump sum awards.
2010-07-01
... Judicial Administration BUREAU OF PRISONS, DEPARTMENT OF JUSTICE INMATE ADMISSION, CLASSIFICATION, AND TRANSFER COMPUTATION OF SENTENCE Extra Good Time § 523.16 Lump sum awards. Any staff member may recommend to the Warden the approval of an inmate for a lump sum award of extra good time. Such recommendations...
College Sports: The Mystery of the Zero-Sum Game
Getz, Malcolm; Siegfried, John J.
2012-01-01
In recent years, when a university may earn well over $10 million per year from fees for sports-broadcast rights, half of the teams still lose. Collegiate athletic competition is a zero sum game: The number of winners equals the number of losers. So why do universities spend growing sums of scarce resources on an activity when the odds of winning…
An electrophysiological signature of summed similarity in visual working memory
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
Root and critical point behaviors of certain sums of polynomials
Indian Academy of Sciences (India)
Seon-Hong Kim
2018-04-24
Apr 24, 2018 ... Introduction. There is an extensive literature concerning roots of sums of polynomials. Many authors. [5–7] 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?' ...
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.
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...
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.)
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 ...
Sum formula for SL2 over imaginary quadratic number fields
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
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.)
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.
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.
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.
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;…
African Journals Online (AJOL)
was analysed using logistic regression with the Health Belief Model (HBM) as an explanatory tool. The outcome variable for this study is ..... It therefore offers a useful framework for analysing the factors influencing condom ..... Controlling for all other variables in the model, women with primary education are significantly less ...
Is there a relation between the 2D Causal Set action and the Lorentzian Gauss-Bonnet theorem?
Benincasa, Dionigi M. T.
2011-07-01
We investigate the relation between the two dimensional Causal Set action, Script S, and the Lorentzian Gauss-Bonnet theorem (LGBT). We give compelling reasons why the answer to the title's question is no. In support of this point of view we calculate the causal set inspired action of causal intervals in some two dimensional spacetimes: Minkowski, the flat cylinder and the flat trousers.
Is there a relation between the 2D Causal Set action and the Lorentzian Gauss-Bonnet theorem?
International Nuclear Information System (INIS)
Benincasa, Dionigi M T
2011-01-01
We investigate the relation between the two dimensional Causal Set action, S, and the Lorentzian Gauss-Bonnet theorem (LGBT). We give compelling reasons why the answer to the title's question is no. In support of this point of view we calculate the causal set inspired action of causal intervals in some two dimensional spacetimes: Minkowski, the flat cylinder and the flat trousers.
Energy Technology Data Exchange (ETDEWEB)
Grozdanov, Sašo [Instituut-Lorentz for Theoretical Physics, Leiden University, Niels Bohrweg 2, Leiden 2333 CA (Netherlands); Starinets, Andrei O. [Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP (United Kingdom)
2017-03-30
Gauss-Bonnet holographic fluid is a useful theoretical laboratory to study the effects of curvature-squared terms in the dual gravity action on transport coefficients, quasinormal spectra and the analytic structure of thermal correlators at strong coupling. To understand the behavior and possible pathologies of the Gauss-Bonnet fluid in 3+1 dimensions, we compute (analytically and non-perturbatively in the Gauss-Bonnet coupling) its second-order transport coefficients, the retarded two- and three-point correlation functions of the energy-momentum tensor in the hydrodynamic regime as well as the relevant quasinormal spectrum. The Haack-Yarom universal relation among the second-order transport coefficients is violated at second order in the Gauss-Bonnet coupling. In the zero-viscosity limit, the holographic fluid still produces entropy, while the momentum diffusion and the sound attenuation are suppressed at all orders in the hydrodynamic expansion. By adding higher-derivative electromagnetic field terms to the action, we also compute corrections to charge diffusion and identify the non-perturbative parameter regime in which the charge diffusion constant vanishes.
Yoon, Seokkwan; Kwak, Dochan
1991-01-01
A numerical method based on the pseudocompressibility concept is developed for solving the three-dimensional incompressible Navier-Stokes equations using the lower-upper symmetric-Gauss-Seidel implicit scheme. Very high efficiency is achieved in a new flow solver, INS3D-LU code, by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.
Jiang, Chen; Liu, Xiaozhou; Liu, Jiehui; Mao, Yiwei; Marston, Philip L
2017-04-01
By means of series expansion theory, the incident quasi-Bessel-Gauss beam is expanded using spherical harmonic functions, and the beam coefficients of the quasi-Bessel-Gauss beam are calculated. According to the theory, the acoustic radiation force function, which is the radiation force per unit energy on a unit cross-sectional surface on a sphere made of diverse materials and immersed in an ideal fluid along the propagation axis of zero-order quasi-Bessel-Gauss progressive and standing beams, is investigated. The acoustic radiation force function is calculated as a function of the spherical radius parameter ka and the half-cone angle β with different beam widths in a progressive and standing zero-order Bessel-Gauss beam. Simulation results indicate that the acoustic radiation forces with different waist radii demonstrate remarkably different features from those found in previous studies. The results are expected to be useful in potential applications such as acoustic tweezers. Copyright Â© 2016 Elsevier B.V. All rights reserved.
ON THE GAUSS MAP OF RULED SURFACES OF TYPE II IN 3-DIMENSIONAL PSEUDO-GALILEAN SPACE
Directory of Open Access Journals (Sweden)
Alper Osman Öğrenmis
2013-02-01
Full Text Available In this paper, ruled surfaces of type II in a three-dimensional Pseudo-Galilean space are given. By studying its Gauss map and Laplacian operator, we obtain a classification of ruled surfaces of type II in a three-dimensional Pseudo-Galilean space.
International Nuclear Information System (INIS)
Zhou, Guoquan
2011-01-01
Based on the propagation equation of higher-order intensity moments, analytical propagation expressions for the kurtosis parameters of a Lorentz–Gauss beam through a paraxial and real ABCD optical system have been derived. The kurtosis parameters of a Lorentz–Gauss beam through a paraxial and real ABCD optical system depend on two parameters. One parameter is related to the ratio of the beam width of the Lorentz part to the waist of the Gaussian part. The other parameter is the ratio of the transfer matrix element B to the product of the transfer matrix element A and the diffraction-free range of the Lorentz part. As special cases of the general formula, the kurtosis parameters of the Gaussian and the Lorentz beams are also presented and are consistent with the well-known results. The properties of the kurtosis parameters of a Lorentz–Gauss beam are illustrated with numerical examples. This research is beneficial to the practical applications of Lorentz–Gauss beams
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.
Zero-sum bias: perceived competition despite unlimited resources.
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.
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.)
Gauss-Newton method for image reconstruction in diffuse optical tomography
International Nuclear Information System (INIS)
Schweiger, Martin; Arridge, Simon R; Nissilae, Ilkka
2005-01-01
We present a regularized Gauss-Newton method for solving the inverse problem of parameter reconstruction from boundary data in frequency-domain diffuse optical tomography. To avoid the explicit formation and inversion of the Hessian which is often prohibitively expensive in terms of memory resources and runtime for large-scale problems, we propose to solve the normal equation at each Newton step by means of an iterative Krylov method, which accesses the Hessian only in the form of matrix-vector products. This allows us to represent the Hessian implicitly by the Jacobian and regularization term. Further we introduce transformation strategies for data and parameter space to improve the reconstruction performance. We present simultaneous reconstructions of absorption and scattering distributions using this method for a simulated test case and experimental phantom data
Nonsingular solutions and instabilities in Einstein-scalar-Gauss-Bonnet cosmology
Sberna, Laura; Pani, Paolo
2017-12-01
It is generically believed that higher-order curvature corrections to the Einstein-Hilbert action might cure the curvature singularities that plague general relativity. Here we consider Einstein-scalar-Gauss-Bonnet gravity, the only four-dimensional, ghost-free theory with quadratic curvature terms. For any choice of the coupling function and of the scalar potential, we show that the theory does not allow for bouncing solutions in the flat and open Friedmann universe. For the case of a closed universe, using a reverse-engineering method, we explicitly provide a bouncing solution which is nevertheless linearly unstable in the scalar gravitational sector. Moreover, we show that the expanding, singularity-free, early-time cosmologies allowed in the theory are unstable. These results rely only on analyticity and finiteness of cosmological variables at early times.
GigaGauss solenoidal magnetic field inside bubbles excited in under-dense plasma
Lécz, Zs.; Konoplev, I. V.; Seryi, A.; Andreev, A.
2016-10-01
This paper proposes a novel and effective method for generating GigaGauss level, solenoidal quasi-static magnetic fields in under-dense plasma using screw-shaped high intensity laser pulses. This method produces large solenoidal fields that move with the driving laser pulse and are collinear with the accelerated electrons. This is in contrast with already known techniques which rely on interactions with over-dense or solid targets and generates radial or toroidal magnetic field localized at the stationary target. The solenoidal field is quasi-stationary in the reference frame of the laser pulse and can be used for guiding electron beams. It can also provide synchrotron radiation beam emittance cooling for laser-plasma accelerated electron and positron beams, opening up novel opportunities for designs of the light sources, free electron lasers, and high energy colliders based on laser plasma acceleration.
Near-infrared reflectance analysis by Gauss-Jordan linear algebra
International Nuclear Information System (INIS)
Honigs, D.E.; Freelin, J.M.; Hieftje, G.M.; Hirschfeld, T.B.
1983-01-01
Near-infrared reflectance analysis is an analytical technique that uses the near-infrared diffuse reflectance of a sample at several discrete wavelengths to predict the concentration of one or more of the chemical species in that sample. However, because near-infrared bands from solid samples are both abundant and broad, the reflectance at a given wavelength usually contains contributions from several sample components, requiring extensive calculations on overlapped bands. In the present study, these calculations have been performed using an approach similar to that employed in multi-component spectrophotometry, but with Gauss-Jordan linear algebra serving as the computational vehicle. Using this approach, correlations for percent protein in wheat flour and percent benzene in hydrocarbons have been obtained and are evaluated. The advantages of a linear-algebra approach over the common one employing stepwise regression are explored
Mixed LS-TLS Estimation Based on Nonlinear Gauss-Helmert Model
Directory of Open Access Journals (Sweden)
FANG Xing
2016-03-01
Full Text Available For the case of design matrix in EIV(errors-in-variables model containing both fixed elements and random elements, this paper proposes a mixed LS-TLS(least squares-total least squares algorithm and deduces the precision estimator by reformulating an EIV model as a nonlinear Gauss-Helmert model, in which random elements are extracted to the random model of adjustment. This algorithm can be applied to the general design matrix including simultaneously fixed columns, fixed elements and random elements. The example illustrates that the solution of mixed LS-TLS equal the solution of structured or weighted TLS algorithms which can solve mixed LS-TLS problem. Additionally, the solution of mixed LS-TLS statistically superior to solution of LS or TLS.
Fast large-scale clustering of protein structures using Gauss integrals
DEFF Research Database (Denmark)
Harder, Tim; Borg, Mikael; Boomsma, Wouter
2011-01-01
-workers – and subsequently performing K-means clustering. Conclusions: Compared to current methods, Pleiades dramatically improves on the time needed to perform clustering, and can cluster a signicantly larger number of structures, while providing state-ofthe- art results. The number of low energy structures generated...... trajectories. Results: We present Pleiades, a novel approach to clustering protein structures with a rigorous mathematical underpinning. The method approximates clustering based on the root mean square deviation by rst mapping structures to Gauss integral vectors – which were introduced by Røgen and co......Motivation: Clustering protein structures is an important task in structural bioinformatics. De novo structure prediction, for example, often involves a clustering step for nding the best prediction. Other applications include assigning proteins to fold families and analyzing molecular dynamics...
Dilaton field released under collision of dilatonic black holes with Gauss-Bonnet term
Energy Technology Data Exchange (ETDEWEB)
Gwak, Bogeun [Sejong University, Department of Physics and Astronomy, Seoul (Korea, Republic of); Ro, Daeho [POSTECH, Asia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk (Korea, Republic of)
2017-08-15
We investigate the upper limit of the gravitational radiation released upon the collision of two dilatonic black holes by analyzing the Gauss-Bonnet term. Dilatonic black holes have a dilaton hair coupled with this term. Using the laws of thermodynamics, the upper limit of the radiation is obtained, which reflected the effects of the dilaton hair. The amount of radiation released is greater than that emitted by a Schwarzschild black hole due to the contribution from the dilaton hair. In the collision, most of the dilaton hair can be released through radiation, where the energy radiated by the dilaton hair is maximized when the horizon of one black hole is minimized for a fixed second black hole. (orig.)
Handling of the Generation of Primary Events in Gauss, the LHCb Simulation Framework
Corti, G; Brambach, T; Brook, N H; Gauvin, N; Harrison, K; Harrison, P; He, J; Ilten, P J; Jones, C R; Lieng, M H; Manca, G; Miglioranzi, S; Robbe, P; Vagnoni, V; Whitehead, M; Wishahi, J
2010-01-01
The LHCb simulation application, Gauss, consists of two independent phases, the generation of the primary event and the tracking of particles produced in the experimental setup. For the LHCb experimental program it is particularly important to model B meson decays: the EvtGen code developed in CLEO and BaBar has been chosen and customized for non coherent B production as occuring in pp collisions at the LHC. The initial proton-proton collision is provided by a different generator engine, currently Pythia 6 for massive production of signal and generic pp collisions events. Beam gas events, background events originating from proton halo, cosmics and calibration events for different detectors can be generated in addition to pp collisions. Different generator packages are available in the physics community or specifically developed in LHCb, and are used for the different purposes. Running conditions affecting the events generated such as the size of the luminous region, the number of collisions occuring in a bunc...
Yao, Hainan; Wang, Fei; Cai, Yangjian
2018-01-01
Two-index Bessel beams (TIBBs) was introduced by Ornigotti and Aiello (2014) theoretically. In this paper, we propose a simple experimental scheme for generation of two-index Bessel-Gauss beams (TIBGBs), as an extension of the TIBBs. The scheme is based on manipulating the amplitude and phase in the Fourier plane with the use of a spatial light modulator and a spiral phase plate. Furthermore, we experimentally report the generation of the several examples of the TIBGBs based on the proposed optical system. The focusing properties of the TIBGB with indices p = 1 and l = 2 passing through a single lens are investigated both theoretically and experimentally. The experimental results agree well with theoretical predictions.
New perspective for black hole thermodynamics in Gauss-Bonnet-Born-Infeld massive gravity
Energy Technology Data Exchange (ETDEWEB)
Hendi, Seyed Hossein [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM),Maragha (Iran, Islamic Republic of); Li, Gu-Qiang; Mo, Jie-Xiong [Lingnan Normal University, Institute of Theoretical Physics, Zhanjiang, Guangdong (China); Panahiyan, Shahram [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Shahid Beheshti University, Physics Department, Tehran (Iran, Islamic Republic of); Panah, Behzad Eslam [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of)
2016-10-15
Following an earlier study regarding Einstein-Gauss-Bonnet-massive black holes in the presence of a Born-Infeld nonlinear electromagnetic field (Hendi, arXiv:1510.00108, 2016), we study thermodynamical structure and critical behavior of these black holes through various methods in this paper. Geometrical thermodynamics is employed to give a picture regarding the phase transition of these black holes. Next, a new method is used to derive critical pressure and radius of the horizon of these black holes. In addition, Maxwell equal area law is employed to study the Van der Waals like behavior of these black holes. Moreover, the critical exponents are calculated and by using Ehrenfest equations, the type of phase transition is determined. (orig.)
Quantum dynamics of electronic transitions with Gauss-Hermite wave packets.
Borrelli, Raffaele; Peluso, Andrea
2016-03-21
A new methodology based on the superposition of time-dependent Gauss-Hermite wave packets is developed to describe the wave function of a system in which several interacting electronic states are coupled to a bath of harmonic oscillators. The equations of motion for the wave function parameters are obtained by employing the Dirac-Frenkel time-dependent variational principle. The methodology is applied to study the quantum dynamical behaviour of model systems with two interacting electronic states characterized by a relatively large reorganization energy and a range of energy biases. The favourable scaling properties make it a promising tool for the study of the dynamics of chemico-physical processes in molecular systems.
Role of beam waist in Laguerre-Gauss expansion of vortex beams.
Vallone, Giuseppe
2017-03-15
Laguerre-Gauss (LG) modes represent an orthonormal basis set of solutions of the paraxial wave equation. LG modes are characterized by two integer parameters n and ℓ that are related to the radial and azimuthal profile of the beam. The physical dimension of the mode is instead determined by the beam waist parameter w0: only LG modes with the same w0 satisfy the orthogonality relation. Here, we derive the scalar product between two LG modes with different beam waists and show how this result can be exploited to derive different expansions of a generic beam in terms of LG modes. In particular, we apply our results to the recently introduced circular beams by deriving a previously unknown expansion. We finally show how the waist parameter must be chosen in order to optimize such expansion.
Sha, Xiaopeng; Wang, Pu; Shan, Peng; Li, Huiguang; Li, Zhiquan
2017-10-01
For the microvision system, a new autofocus evaluation function based on the Robert function is proposed by increasing the threshold value. Compared with the traditional evaluation function, the new focus function reduces the local extreme value and increases the steepness of the focusing curve. According to the characteristics of the focusing evaluation function, the focus curve can be divided into two stages: the gentle area and the steep area. In the gentle area, there will be set a large step-length to realize the fast search. In the steep area, the data will be fitted by Gauss method, and on the basis of the fitting results, the motor of microvision system was directly driven to achieve the focal plane and this method has been improved in real-time and accuracy. © 2017 Wiley Periodicals, Inc.
Experimental demonstration of higher-order Laguerre-Gauss mode interferometry
International Nuclear Information System (INIS)
Fulda, Paul; Kokeyama, Keiko; Chelkowski, Simon; Freise, Andreas
2010-01-01
The compatibility of higher-order Laguerre-Gauss (LG) modes with interferometric technologies commonly used in gravitational wave detectors is investigated. In this paper, we present the first experimental results concerning the performance of the LG 33 mode in optical resonators. We show that the Pound-Drever-Hall error signal for a LG 33 mode in a linear optical resonator is identical to that of the more commonly used LG 00 mode, and demonstrate the feedback control of the resonator with a LG 33 mode. We succeeded to increase the mode purity of a LG 33 mode generated using a spatial-light modulator from 51% to 99% upon transmission through a linear optical resonator. We further report the experimental verification that a triangular optical resonator does not transmit helical LG modes.
Shear spectral sum rule in a nonconformal gravity dual
Springer, Todd; Gale, Charles; Jeon, Sangyong; Lee, Su Houng
2010-11-01
A sum rule which relates a stress-energy tensor correlator to thermodynamic functions is examined within the context of a simple nonconformal gravity dual. Such a sum rule was previously derived using AdS/CFT for conformal N=4 supersymmetric Yang-Mills theory, but we show that it does not generalize to the nonconformal theory under consideration. We provide a generalized sum rule and numerically verify its validity. A useful by-product of the calculation is the computation of the spectral density in a strongly coupled nonconformal theory. Qualitative features of the spectral densities and implications for lattice measurements of transport coefficients are discussed.
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
Durbin, Timothy J.
1983-01-01
The Gauss optimization technique can be used to identify the parameters of a model of a groundwater system for which the parameter identification problem is formulated as a least squares comparison between the response of the prototype and the response of the model. Unavoidable uncertainty in the true stress on the prototype and in the true response of the prototype to that stress will introduce errors into the parameter identification problem. A method for evaluating errors in the predictions of future water levels due to errors in recharge estimates was demonstrated. The method involves a Monte Carlo simulation of the parameter identification problem and of the prediction problem. The steps in the method are: (1) to prescribe the distribution of the recharge estimates; (2) to use this distribution to generate random sets of recharge estimates; (3) to use the Gauss optimization technique to identify the corresponding set of parameter estimates for each set of recharge estimates; (4) to make the corresponding set of hydraulic head predictions for each set of parameter estimates; and (5) to examine the distribution of hydraulic head predictions and to draw appropriate conclusions. Similarly, the method can be used independently or simultaneously to estimate the effect on hydraulic head predictions of errors in the measured water levels that are used in the parameter identification problem. The fit of the model to the data that are used to identify parameters is not a good indicator of these errors. A Monte Carlo simulation of the parameter identification problem can be used, however, to evaluate the effects on water level predictions of errors in the recharge (and pumpage) data used in the parameter identification problem. (Lantz-PTT)
[A Hyperspectral Imagery Anomaly Detection Algorithm Based on Gauss-Markov Model].
Gao, Kun; Liu, Ying; Wang, Li-jing; Zhu, Zhen-yu; Cheng, Hao-bo
2015-10-01
With the development of spectral imaging technology, hyperspectral anomaly detection is getting more and more widely used in remote sensing imagery processing. The traditional RX anomaly detection algorithm neglects spatial correlation of images. Besides, it does not validly reduce the data dimension, which costs too much processing time and shows low validity on hyperspectral data. The hyperspectral images follow Gauss-Markov Random Field (GMRF) in space and spectral dimensions. The inverse matrix of covariance matrix is able to be directly calculated by building the Gauss-Markov parameters, which avoids the huge calculation of hyperspectral data. This paper proposes an improved RX anomaly detection algorithm based on three-dimensional GMRF. The hyperspectral imagery data is simulated with GMRF model, and the GMRF parameters are estimated with the Approximated Maximum Likelihood method. The detection operator is constructed with GMRF estimation parameters. The detecting pixel is considered as the centre in a local optimization window, which calls GMRF detecting window. The abnormal degree is calculated with mean vector and covariance inverse matrix, and the mean vector and covariance inverse matrix are calculated within the window. The image is detected pixel by pixel with the moving of GMRF window. The traditional RX detection algorithm, the regional hypothesis detection algorithm based on GMRF and the algorithm proposed in this paper are simulated with AVIRIS hyperspectral data. Simulation results show that the proposed anomaly detection method is able to improve the detection efficiency and reduce false alarm rate. We get the operation time statistics of the three algorithms in the same computer environment. The results show that the proposed algorithm improves the operation time by 45.2%, which shows good computing efficiency.
Calculation of “LS-curves” for coincidence summing corrections in gamma ray spectrometry
Vidmar, Tim; Korun, Matjaž
2006-01-01
When coincidence summing correction factors for extended samples are calculated in gamma-ray spectrometry from full-energy-peak and total efficiencies, their variation over the sample volume needs to be considered. In other words, the correction factors cannot be computed as if the sample were a point source. A method developed by Blaauw and Gelsema takes the variation of the efficiencies over the sample volume into account. It introduces the so-called LS-curve in the calibration procedure and only requires the preparation of a single standard for each sample geometry. We propose to replace the standard preparation by calculation and we show that the LS-curves resulting from our method yield coincidence summing correction factors that are consistent with the LS values obtained from experimental data.
The Gauge-Invariant Angular Momentum Sum-Rule for the Proton
Shore, G.M.
2000-01-01
We give a gauge-invariant treatment of the angular momentum sum-rule for the proton in terms of matrix elements of three gauge-invariant, local composite operators. These matrix elements are decomposed into three independent form factors, one of which is the flavour singlet axial charge. We further show that the axial charge cancels out of the sum-rule, so that it is unaffacted by the axial anomaly. The three form factors are then related to the four proton spin components in the parton model, namely quark and gluon intrinsic spin and orbital angular momentum. The renormalisation of the three operators is determined to one loop from which the scale dependence and mixing of the spin components is derived under the constraint that the quark spin be scale-independent. We also show how the three form factors can be measured in experiments.
A Cube as (Almost) a Sum of Two Cubes
Indian Academy of Sciences (India)
Admin
2012-09-07
Fermat's Last The- orem). The number 1728 (= 123) comes close to being the sum of two cubes, but falls short by 1. An entry in Srinivasa Ramanujan's Lost Note- book gives a remarkable identity which provides infinitely many ...
A Pascal-like triangle from finding power sums
Chen, Zhibo
2014-08-01
A Pascal-like triangle is constructed so that power sums can be conveniently obtained by college (or high school) students with no need for memorizing complicated formulas or performing difficult calculations.
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
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.
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- ...
Convolutional Codes with Maximum Column Sum Rank for Network Streaming
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...
Sum rules for effective resistances in infinite graphs
Markowsky, Greg; Palacios, José Luis
2017-04-01
Extending work of Foster, Doyle, and others, we show how the Foster theorems, a family of results concerning effective resistances on finite graphs, can in certain cases be extended to infinite graphs. A family of sum rules is then obtained, which allows one to easily calculate the sum of the resistances over all paths of a given length. The results are illustrated with some of the most common grids in the plane, including the square, triangular, and hexagonal grids.
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
Magnetic Dipole Sum Rules for Odd-Mass Nuclei
Energy Technology Data Exchange (ETDEWEB)
Ginocchio, J.N.; Leviatan, A. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Leviatan, A. [Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel); Ginocchio, J.N.; Leviatan, A. [European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT), I-38050 Villazano, Trento (Italy)
1997-08-01
Sum rules for the total- and scissors-mode M1 strength in odd-A nuclei are derived within the single-j interacting boson-fermion model. We discuss the physical content and geometric interpretation of these sum rules and apply them to {sup 167}Er and {sup 161}Dy. We find consistency with the former measurements but not with the latter. {copyright} {ital 1997 } {ital The American Physical Society}
Magnetic Dipole Sum Rules for Odd-Mass Nuclei
International Nuclear Information System (INIS)
Ginocchio, J.N.; Leviatan, A.; Leviatan, A.; Ginocchio, J.N.; Leviatan, A.
1997-01-01
Sum rules for the total- and scissors-mode M1 strength in odd-A nuclei are derived within the single-j interacting boson-fermion model. We discuss the physical content and geometric interpretation of these sum rules and apply them to 167 Er and 161 Dy. We find consistency with the former measurements but not with the latter. copyright 1997 The American Physical Society
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
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:.
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 ...
Li, Yang; Zhang, Qingbin; Hong, Weiyi; Wang, Shaoyi; Wang, Zhe; Lu, Peixiang
2012-07-02
Single attosecond pulse generation with polarization gating Bessel-Gauss beam in relatively strongly-ionized media is investigated. The results show that Bessel-Gauss beam has the ability to suppress the spatial plasma dispersion effects caused by high density of free electrons, thus the laser field can maintain its spatial profile through highly-ionized medium. This indicates the use of Bessel-Gauss beam has advantages over Gaussian beam in high harmonic generation under high ionization conditions. In our scheme, significant improvement of spatiotemporal properties of harmonics is achieved and an isolated attosecond pulse with high beam quality is filtered out using polarization gating.
Use of sum-peak and coincidence counting methods for activity standardization of {sup 22}Na
Energy Technology Data Exchange (ETDEWEB)
Oliveira, E.M. de, E-mail: estela@ird.gov.br [Laboratorio Nacional de Metrologia das Radiacoes Ionizantes (LNMRI/IRD/CNEN), Av. Salvador Allende, s/n, Recreio, CEP 22780-160 Rio de Janeiro (Brazil); Iwahara, A.; Poledna, R. [Laboratorio Nacional de Metrologia das Radiacoes Ionizantes (LNMRI/IRD/CNEN), Av. Salvador Allende, s/n, Recreio, CEP 22780-160 Rio de Janeiro (Brazil); Silva, M.A.L. da [Coordenacao Geral de Instalacoes Nucleares/Comissao Nacional de Energia Nuclear, R. Gal. Severiano, 90 - Botafogo, CEP 22290-901 Rio de Janeiro (Brazil); Tauhata, L. [Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro (FAPERJ), Av. Erasmo Braga, 118-6 Degree-Sign andar, CEP 20020-000 Centro, Rio de Janeiro (Brazil); Delgado, J.U. [Laboratorio Nacional de Metrologia das Radiacoes Ionizantes (LNMRI/IRD/CNEN), Av. Salvador Allende, s/n, Recreio, CEP 22780-160 Rio de Janeiro (Brazil); Lopes, R.T. [Laboratorio de Instrumentacao Nuclear (LIN/PEN/COPPE/UFRJ), Caixa Postal 68509, CEP 21945-970 Rio de Janeiro (Brazil)
2012-09-21
A solution containing the positron emitter {sup 22}Na has been absolutely standardized using the 4{pi}{beta}-{gamma} coincidence counting method and the sum-peak spectrometry counting method. In the 4{pi}{beta}-{gamma} coincidence method two ways for the activity concentration measurements were used: gating on the 1275 keV photopeak and on the 1786 keV sum-peak where the knowledge of the {beta}{sup +}-branching ratio is required. In the sum-peak method the measurements were carried out using three experimental arrangements: the first composed by a well type 5 in. Multiplication-Sign 5 in. NaI(Tl) scintillation crystal, the second by a 3 in. Multiplication-Sign 3 in. NaI(Tl) scintillation crystal placed on the top of the first, resulting in a 4{pi} counting geometry and the third arrangement is a high purity coaxial germanium detector. The results that are obtained by these two methods are compatible within the standard uncertainty values with a coverage factor of k=2 ({approx}95% of the confidence level). This means that the sum-peak counting with its more simple experimental setup than the complex coincidence 4{pi}{beta}-{gamma} counting system gives consistent results for the activity standardization of {sup 22}Na with smaller uncertainties. Besides, the time period involved to attain the result of the standardization was quite shorter than the coincidence measurements used in this work.
Directory of Open Access Journals (Sweden)
S. N. Mamedbekov
2014-01-01
Full Text Available This paper considers the dynamics of the abscissa and ordinate points in the far zone meridian six degree conformal Gauss-Kruger projection. Performed calculations and graphical representation of the classic formulas of conformal projection.
Dynamic properties of one-component strongly coupled plasmas: The sum-rule approach
International Nuclear Information System (INIS)
Arkhipov, Yu. V.; Askaruly, A.; Davletov, A. E.; Ballester, D.; Tkachenko, I. M.; Zwicknagel, G.
2010-01-01
The dynamic characteristics of strongly coupled one-component plasmas are studied within the moment approach. Our results on the dynamic structure factor and the dynamic local-field correction satisfy the sum rules and other exact relations automatically. A quantitative agreement is obtained with numerous simulation data on the plasma dynamic properties, including the dispersion and decay of collective modes. Our approach allows us to correct and complement the results previously found with other treatments.
Calculation of electromagnetic rhoπ formfactor from QCD sum rules
International Nuclear Information System (INIS)
Eletskij, V.L.; Kogan, Ya.I.
1982-01-01
Electromagnetic rhoπγ form factor at intermediate momentum transfer, 0.7 GeV 2 2 2 , is calculated using QCD sum rules for the vertex function of two vector and one axial-vector currents. In this region the results obtained are consistent within 25% accuracy with the vector meson dominance model predictions and can be regarded as its theoretical ustification
$B \\rightarrow \\pi$ and $B \\rightarrow K$ transitions from QCD Sum Rules on the Light-Cone
Ball, P
1998-01-01
I calculate the form factors describing semileptonic and penguin induced decays of B mesons into light pseudoscalar mesons. The form factors are calculated from QCD sum rules on the light-cone including contributions up to twist 4, radiative corrections to the leading twist contribution and SU(3) breaking effects. The theoretical uncertainty is estimated to be $\\sim$ (10-15)%.
Contração de Lorentz, lei de Gauss e lei de Ampère
Directory of Open Access Journals (Sweden)
Ortiz Olivia
2003-01-01
Full Text Available Mostramos como obter a expressão para a contração de Lorentz dos comprimentos, a partir das leis de Gauss e Ampère, sem qualquer conhecimento da teoria da relatividade especial de Einstein. Mostramos em seguida que tal resultado é consistente com a transformação relativística dos campos elétrico e magnético.
Taipe, Donny
2017-01-01
This article sustains the transfer of the national standard of mass (KP1) of INACAL to two reference standards ‘Weight 1’, ‘Weight 2’ and also KP2 (as witnessed mass standard and with known error). The dissemination was done using the Gauss Markov method by Generalized Least Squares. The uncertainty calculation was performed using Univariate Gaussian Distribution and Multivariate Gaussian Distribution; the latter was developed with the Monte Carlo method using a programming language called 'R...
Is there a relation between the 2D Causal Set action and the Lorentzian Gauss-Bonnet theorem?
Energy Technology Data Exchange (ETDEWEB)
Benincasa, Dionigi M T, E-mail: db1808@ic.ac.uk [Theoretical Physics Group, Blackett Laboratory, Imperial College, Prince Consort Rd., London SW7 2AZ (United Kingdom)
2011-07-08
We investigate the relation between the two dimensional Causal Set action, S, and the Lorentzian Gauss-Bonnet theorem (LGBT). We give compelling reasons why the answer to the title's question is no. In support of this point of view we calculate the causal set inspired action of causal intervals in some two dimensional spacetimes: Minkowski, the flat cylinder and the flat trousers.
A sum-over-paths impulse-response moment-extraction algorithm for RLCM IC-interconnect networks
Le Coz, Y. L.; Krishna, D.; Petranovic, D. M.
2007-08-01
We have created a new impulse-response (IR) moment-extraction algorithm for RLCM circuit networks. It employs a Feynman sum-over-paths postulate. Our approach begins with generation of s-domain nodal-voltage equations. We then perform a Taylor-series expansion of the circuit transfer function. These expansions yield transition diagrams involving mathematical coupling constants, or weight factors, in integral powers of complex frequency s. Our sum-over-paths postulate supports stochastic evaluation of path sums within the circuit transition diagram to any desired order of s. The specific order of s in the sum corresponds, as well, to the order of IR moment we seek to extract. In developing the algorithm, importantly, we maintain computational efficiency and full parallelism. Initial verification studies of uncoupled and coupled RLCM lines furnished promising results: less than 10% 1- σ error for m1 or m2 moment, after 10 K sampled path-sum terms. In addition, we observed excellent convergence to exact, analytical moment values with increasing number of samples. Our sum-over-paths postulate, in fact, implies generality for arbitrary RLCM-interconnect network topologies, beyond those specific examples presented in this work. We believe, in conclusion, that this type of IR-moment extraction algorithm may find useful application in a massively coupled electrical system, such as a high-end digital-IC interconnect network.
A sum-over-paths impulse-response moment-extraction algorithm for RLC IC-interconnect networks
Le Coz, Y. L.; Krishna, D.; Hariharan, G.; Petranovic, D. M.
2005-10-01
We have created a new impulse-response (IR) moment-extraction algorithm for RLC circuit networks. It employs a Feynman sum-over-paths postulate. Our approach begins with generation of s-domain nodal-voltage equations. We then perform a Taylor-series expansion of the circuit transfer function. These expansions yield transition diagrams involving mathematical coupling constants, or weight factors, in integral powers of complex frequency s. Our sum-over-paths postulate supports stochastic evaluation of path sums within the circuit transition diagram to any desired order of s. The specific order of s in the sum corresponds, as well, to the order of IR moment we seek to extract. In developing the algorithm, importantly, we maintain computational efficiency and full parallelism. Initial verification studies of uncoupled and coupled RLC lines furnished promising results: 5% and 10% approximate 1- σ error for first- and second-order IR moments, respectively, after only 100 sampled path-sum terms. In addition, we observed excellent convergence to exact, analytical moment values with increasing number of samples. Our sum-over-paths postulate, in fact, implies generality for arbitrary RLC-interconnect networks, beyond those specific examples presented in this work. We believe, in conclusion, that this type of IR-moment extraction algorithm may find useful application in a massively coupled electrical system, such as that encountered in high-end digital-IC interconnects.
A sum-over-paths impulse-response moment-extraction algorithm for RC IC-interconnect networks
Le Coz, Y. L.; Krishna, D.; Petranovic, D. M.; Loh, W. M.; Bendix, P.
2004-12-01
We have created a new impulse-response (IR) moment-extraction algorithm for RC circuit networks. It employs a Feynman sum-over-paths postulate. Our approach begins with generation of s-domain nodal-voltage equations. We then perform a Taylor-series expansion of the circuit transfer function. These expansions yield transition diagrams involving mathematical coupling constants, or weight factors, in integral powers of complex frequency s. Our sum-over-paths postulate supports stochastic evaluation of path sums within the circuit transition diagram to any desired order of s. The specific order of s in the sum corresponds, as well, to the order of IR moment we seek to extract. In developing the algorithm, importantly, we maintain computational efficiency and full parallelism. Initial verification studies of uncoupled and coupled RC lines furnished promising results: 5% and 15% approximate 1-σ error for first- and second-order IR moments, respectively, after only 100 sampled path-sum terms. In addition, we observed excellent convergence to exact, analytical moment values with increasing number of samples. Our sum-over-paths postulate, in fact, implies generality for arbitrary RC-interconnect networks, beyond those specific examples presented in this work. We believe, in conclusion, that this type of IR moment-extraction algorithm may find useful application in a massively coupled electrical system, such as that encountered in high-end digital-IC interconnects.
International Nuclear Information System (INIS)
Zhou Yi-Min; Zhou Guo-Quan
2013-01-01
An orthonormal beam family of super Lorentz—Gauss (SLG) beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG 00 , SLG 01 , SLG 10 , and SLG 11 beams. The SLG 00 beam is just the Lorentz—Gauss beam. Based on the Collins integral formula and the Hermite—Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function (WDF) of an SLG 11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG 11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG 11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLG 11 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG 11 beam in free space are also examined. This research reveals the propagation properties of an SLG 11 beam from another perspective. The WDFs of SLG 01 and SLG 10 beams can be easily obtained by using the WDFs of Lorentz—Gauss beam and the SLG 11 beam. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
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.
Limit theorems for multi-indexed sums of random variables
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 ...
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)
Closed-form summations of Dowker's and related trigonometric sums
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’.
Learning curve for fetoscopic laser surgery using cumulative sum analysis.
Peeters, Suzanne H P; Van Zwet, Erik W; Oepkes, Dick; Lopriore, Enrico; Klumper, Frans J; Middeldorp, Johanna M
2014-07-01
To identify a learning curve and monitor operator performance for fetoscopic laser surgery for twin-to-twin transfusion syndrome using cumulative sum analysis. Retrospective cohort study. National tertiary referral center for invasive fetal therapy. A total of 340 consecutive monochorionic pregnancies with twin-to-twin transfusion syndrome treated with fetoscopic laser coagulation between August 2000 and December 2010. A learning curve was generated using learning curve cumulative sum analysis and cumulative sum methodology to assess changes in double survival across the case sequence. Laser surgery was initially performed by two operators, joined by a third and fourth operator after 1 and 2 years, respectively. Individual operator performance, double perinatal survival at 4 weeks. Overall survival of both twins occurred in 59% (201/340), median gestational age at birth was 32.0 weeks. Cumulative sum graphs showed that level of competence for double survival for the operators was reached after 26, 25, 26, and 35 procedures, respectively. Two operators kept their competence level and continued to improve after completing the initial learning process; two others went out of control at one point in time, according to the cumulative sum boundaries. A difference in learning effect was associated with number of procedures performed annually and previous experience with other ultrasound-guided invasive procedures. This study shows that all operators reached a level of competence after at least 25 fetoscopic laser procedures and confirms the value of using the cumulative sum method both for learning curve assessment and for ongoing quality control. © 2014 Nordic Federation of Societies of Obstetrics and Gynecology.
Multi-instantons, three-dimensional gauge theory, and the Gauss-Bonnet-Chern theorem
International Nuclear Information System (INIS)
Dorey, N.; Mattis, M.P.
1997-01-01
We calculate multi-instanton effects in a three-dimensional gauge theory with N=8 supersymmetry and gauge group SU(2). The k-instanton contribution to an eight-fermion correlator is found to be proportional to the Gauss-Bonnet-Chern integral of the Gaussian curvature over the centered moduli space of charge-k BPS monopoles, M k . For k=2 the integral can be evaluated using the explicit metric on M 2 found by Atiyah and Hitchin. In this case the integral is equal to the Euler character of the manifold. More generally the integral is the volume contribution to the index of the Euler operator on M k , which may differ from the Euler character by a boundary term. We conjecture that the boundary terms vanish and evaluate the multi-instanton contributions using recent results for the cohomology of M k . We comment briefly on the implications of our result for a recently proposed test of M(atrix) theory. (orig.)
Pre-scaled two-parameter Gauss-Newton image reconstruction to reduce property recovery imbalance
International Nuclear Information System (INIS)
Meaney, Paul M.; Yagnamurthy, Navin K.; Paulsen, Keith D.
2002-01-01
Gauss-Newton image reconstruction in microwave imaging can be formulated in terms of a single complex quantity, the wave number squared (k 2 ), with the understanding that the relative permittivity and conductivity images can be extracted afterwards through a simple constitutive relationship. However, this approach ignores the fact that the magnitude of the average real and imaginary components can be considerably out of balance depending on the operating frequency and tissue characteristics which can inadvertently imbalance the process in favour of one parameter over the other. In an effort to achieve property recovery which is balanced, we introduce a pre-scaling procedure at the property update stage of the reconstruction. Utilization of this concept in conjunction with our two-step regularization process for both simulation and phantom experiments demonstrates that the penalty term weighting parameters for the optimal mean-squared property errors for the two recovered distributions (relative permittivity and conductivity) together with that yielding the lowest least-squared electric field error coincide only when the scaling is applied. The scheme provides a means for simultaneous optimization of the two permittivity and conductivity images. (author)
Time-domain incomplete Gauss-Newton full-waveform inversion of Gulf of Mexico data
AlTheyab, Abdullah
2013-09-22
We apply the incomplete Gauss-Newton full-waveform inversion (TDIGN-FWI) to Gulf of Mexico (GOM) data in the space-time domain. In our application, iterative least-squares reverse-time migration (LSRTM) is used to estimate the model update at each non-linear iteration, and the number of LSRTM iterations is progressively increased after each non-linear iteration. With this method, model updating along deep reflection wavepaths are automatically enhanced, which in turn improves imaging below the reach of diving-waves. The forward and adjoint operators are implemented in the space-time domain to simultaneously invert the data over a range of frequencies. A multiscale approach is used where higher frequencies are down-weighted significantly at early iterations, and gradually included in the inversion. Synthetic data results demonstrate the effectiveness of reconstructing both the high- and low-wavenumber features in the model without relying on diving waves in the inversion. Results with Gulf of Mexico field data show a significantly improved migration image in both the shallow and deep sections.
Comparing two electrical impedance tomography algorithms: Gauss-Newton and topology optimization
Motta-Mello, L. A.; Lima, C. R.; Aya, J. C.; Pai, C. N.; Moura, F. S.; Silva, E. C. N.; Gonzalez-Lima, R.
2006-03-01
Electrical Impedance Tomography (EIT) seeks to recover the impedance distribution within a body using boundary data. More specifically, given the measured potentials, the model of the body - an elliptic partial differential equation - and the boundary conditions, this technique solves a non-linear inverse problem for the unknown impedance. In this work, an algorithm called Topology Optimization Method (TOM) is applied to EIT and compared to the Gauss-Newton Method (GNM). The Topology Optimization has solved some non-linear inverse problems and some of its procedures were not investigated for EIT, for instance, the use of Sequential Linear Programming. Assuming a pure resistive medium, the static resistivity distribution of a phantom was estimated using a 2-D finite element model. While the first method (GNM) essentially solves several algebraic systems, the second (TOM) solves several linear programming problems. Results using experimental data are shown and the quality of the images obtained, time and memory used are compared for both algorithms. We intend to use these methods, in future works, for the visualization of a human lung subjected to mechanical ventilation.
Gauss-Bonnet assisted braneworld inflation in light of BICEP2 and Planck data
Neupane, Ishwaree P
2014-01-01
Motivated by the idea that quantum gravity corrections usually suppress the power of the scalar primordial spectrum (E-mode) more than the power of the tensor primordial spectrum (B-mode), in this paper we construct a concrete gravitational theory in five-dimensions for which $V(\\phi)\\propto \\phi^n$-type inflation ($n\\ge 1$) generates an appropriate tensor-to-scalar ratio that may be compatible with the BICEP2 and Planck data together. The true nature of gravity is five-dimensional and described by the action $S = \\int d^5{x} \\sqrt{|g|} M^3 (- 6\\lambda M^2 + R + \\alpha M^{-2} {\\cal R}^2)$ where $M$ is the five-dimensional Planck mass and ${\\cal R}^2=R^2-4 R_{ab} R^{ab} + R_{abcd} R^{abcd}$ is the Gauss-Bonnet (GB) term. The five-dimensional "bulk" spacetime is anti-de Sitter ($\\lambda<0$) for which inflation ends naturally. The effects of ${\\cal R}^2$ term on the magnitudes of scalar and tensor fluctuations and spectral indices are shown to be important at the energy scale of inflation. For GB-assisted $m^...
Subluminal group velocity and dispersion of Laguerre Gauss beams in free space
Bareza, Nestor D.; Hermosa, Nathaniel
2016-05-01
That the speed of light in free space c is constant has been a pillar of modern physics since the derivation of Maxwell and in Einstein’s postulate in special relativity. This has been a basic assumption in light’s various applications. However, a physical beam of light has a finite extent such that even in free space it is by nature dispersive. The field confinement changes its wavevector, hence, altering the light’s group velocity vg. Here, we report the subluminal vg and consequently the dispersion in free space of Laguerre-Gauss (LG) beam, a beam known to carry orbital angular momentum. The vg of LG beam, calculated in the paraxial regime, is observed to be inversely proportional to the beam’s divergence θ0, the orbital order ℓ and the radial order p. LG beams of higher orders travel relatively slower than that of lower orders. As a consequence, LG beams of different orders separate in the temporal domain along propagation. This is an added effect to the dispersion due to field confinement. Our results are useful for treating information embedded in LG beams from astronomical sources and/or data transmission in free space.
Incompressible Navier-Stokes equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell theories
International Nuclear Information System (INIS)
Niu Chao; Tian Yu; Wu Xiaoning; Ling Yi
2012-01-01
The dual fluid description for a general cutoff surface at radius r=r c outside the horizon in the charged AdS black brane bulk space-time is investigated, first in the Einstein-Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter ε, the coupled Einstein-Maxwell equations are solved up to O(ε 2 ). The incompressible Navier-Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density η/s is independent of both the cutoff r c and the black brane charge. Then, we extend our discussion to the Gauss-Bonnet-Maxwell case, where the incompressible Navier-Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio η/s is independent of the cutoff r c but dependent on the charge density of the black brane.
Gauss-Bonnet coupling constant as a free thermodynamical variable and the associated criticality
International Nuclear Information System (INIS)
Xu, Wei; Xu, Hao; Zhao, Liu
2014-01-01
The thermodynamic phase space of Gauss-Bonnet (GB) AdS black holes is extended, taking the inverse of the GB coupling constant as a new thermodynamic pressure P GB . We studied the critical behavior associated with P GB in the extended thermodynamic phase space at fixed cosmological constant and electric charge. The result shows that when the black holes are neutral, the associated critical points can only exist in five dimensional GB-AdS black holes with spherical topology, and the corresponding critical exponents are identical to those for the Van der Waals system. For charged GB-AdS black holes, it is shown that there can be only one critical point in five dimensions (for black holes with either spherical or hyperbolic topologies), which also requires the electric charge to be bounded within some appropriate range; while in d < 5 dimensions, there can be up to two different critical points at the same electric charge, and the phase transition can occur only at temperatures which are not in between the two critical values. (orig.)
Asgharzadeh, M. F.; Hashemi, H.; von Frese, R. RB
2018-01-01
Forward modeling is the basis of gravitational anomaly inversion that is widely applied to map subsurface mass variations. This study uses numerical least-squares Gauss-Legendre quadrature (GLQ) integration to evaluate the gravitational potential, anomaly and gradient components of the vertical cylindrical prism element. These results, in turn, may be integrated to accurately model the complete gravitational effects of fluid bearing rock formations and other vertical cylinder-like geological bodies with arbitrary variations in shape and density. Comparing the GLQ gravitational effects of uniform density, vertical circular cylinders against the effects calculated by a number of other methods illustrates the veracity of the GLQ modeling method and the accuracy limitations of the other methods. Geological examples include modeling the gravitational effects of a formation washout to help map azimuthal variations of the formation's bulk densities around the borehole wall. As another application, the gravitational effects of a seismically and gravimetrically imaged salt dome within the Laurentian Basin are evaluated for the velocity, density and geometric properties of the Basin's sedimentary formations.
Generalized spheroidal spacetimes in 5-D Einstein-Maxwell-Gauss-Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Hansraj, Sudan [University of KwaZulu Natal, Astrophysics and Cosmology Research Unit, Durban (South Africa)
2017-08-15
The field equations for static EGBM gravity are obtained and transformed to an equivalent form through a coordinate redefinition. A form for one of the metric potentials that generalizes the spheroidal ansatz of Vaidya-Tikekar superdense stars and additionally prescribing the electric field intensity yields viable solutions. Some special cases of the general solution are considered and analogous classes in the Einstein framework are studied. In particular the Finch-Skea ansatz is examined in detail and found to satisfy the elementary physical requirements. These include positivity of pressure and density, the existence of a pressure free hypersurface marking the boundary, continuity with the exterior metric, a subluminal sound speed as well as the energy conditions. Moreover, the solution possesses no coordinate singularities. It is found that the impact of the Gauss-Bonnet term is to correct undesirable features in the pressure profile and sound speed index when compared to the equivalent Einstein gravity model. Furthermore graphical analyses suggest that higher densities are achievable for the same radial values when compared to the 5-dimensional Einstein case. The case of a constant gravitational potential, isothermal distribution as well as an incompressible fluid are studied. All exact solutions derived exhibit an equation of state explicitly. (orig.)
Subluminal group velocity and dispersion of Laguerre Gauss beams in free space.
Bareza, Nestor D; Hermosa, Nathaniel
2016-05-27
That the speed of light in free space c is constant has been a pillar of modern physics since the derivation of Maxwell and in Einstein's postulate in special relativity. This has been a basic assumption in light's various applications. However, a physical beam of light has a finite extent such that even in free space it is by nature dispersive. The field confinement changes its wavevector, hence, altering the light's group velocity vg. Here, we report the subluminal vg and consequently the dispersion in free space of Laguerre-Gauss (LG) beam, a beam known to carry orbital angular momentum. The vg of LG beam, calculated in the paraxial regime, is observed to be inversely proportional to the beam's divergence θ0, the orbital order ℓ and the radial order p. LG beams of higher orders travel relatively slower than that of lower orders. As a consequence, LG beams of different orders separate in the temporal domain along propagation. This is an added effect to the dispersion due to field confinement. Our results are useful for treating information embedded in LG beams from astronomical sources and/or data transmission in free space.
Linked Gauss-Diffusion processes for modeling a finite-size neuronal network.
Carfora, M F; Pirozzi, E
2017-11-01
A Leaky Integrate-and-Fire (LIF) model with stochastic current-based linkages is considered to describe the firing activity of neurons interacting in a (2×2)-size feed-forward network. In the subthreshold regime and under the assumption that no more than one spike is exchanged between coupled neurons, the stochastic evolution of the neuronal membrane voltage is subject to random jumps due to interactions in the network. Linked Gauss-Diffusion processes are proposed to describe this dynamics and to provide estimates of the firing probability density of each neuron. To this end, an iterated integral equation-based approach is applied to evaluate numerically the first passage time density of such processes through the firing threshold. Asymptotic approximations of the firing densities of surrounding neurons are used to obtain closed-form expressions for the mean of the involved processes and to simplify the numerical procedure. An extension of the model to an (N×N)-size network is also given. Histograms of firing times obtained by simulations of the LIF dynamics and numerical firings estimates are compared. Copyright © 2017 Elsevier B.V. All rights reserved.
On terahertz pulsed broadband Gauss-Bessel beam free-space propagation.
Kulya, Maksim S; Semenova, Varvara A; Bespalov, Victor G; Petrov, Nikolay V
2018-01-23
Terahertz pulse time-domain holography is the ultimate technique allowing the evaluating a propagation of pulse broadband terahertz wavefronts and analyze their spatial, temporal and spectral evolution. We have numerically analyzed pulsed broadband terahertz Gauss-Bessel beam's both spatio-temporal and spatio-spectral evolution in the non-paraxial approach. We have characterized two-dimensional spatio-temporal beam behavior and demonstrated all stages of pulse reshaping during the propagation, including X-shape pulse forming. The reshaping is also illustrated by the energy transfer dynamics, where the pulse energy flows from leading edge to trailing edge. This behavior illustrates strong spatio-temporal coupling effect when spatio-temporal distribution of Bessel beam's wavefront depends on propagation distance. The spatio-temporal and spatio-spectral profiles for different spectral components clearly illustrate the model where the Bessel beam's wavefront at the exit from the axicon can be divided into radial segments for which the wave vectors intersect. Phase velocity via propagation distance is estimated and compared with existing experimantal results. Results of the phase velocity calculation depend strongly on distance increment value, thus demonstrating superluminal or subluminal behavior.
Adaptive 6-DoF Haptic Contact Stiffness Using the Gauss Map.
Xu, Hongyi; Barbic, Jernej
2016-04-25
The penalty method is a popular approach to resolving contact in haptic rendering. In simulations involving complex distributed contact, there are, however, many simultaneous individual contacts. These contacts have normals pointing in several directions, many of which may be parallel, causing the stiffness effectively to add up in a temporally highly-varying and unpredictable way. Consequently, penalty-based simulation suffers from stability problems. Previous methods tackled this problem using implicit integration, or simply by scaling the stiffness down globally by the number of contacts. Although this provides some control over the net stiffness, it leads to large penetrations, as small contacts are effectively ignored when compared to larger contacts. We propose an adaptive stiffness method that employs the Gauss map of the normal distribution to ensure a spatially uniform and controllable stiffness in all the contact directions. Combined with virtual coupling saturation, the penetration can be kept shallow all the while haptic simulation remains stable, even for large-scale complex geometry with complex distributed 6-DoF contact scenarios. Our method is fast and can be applied to any penalty-based formulation between rigid objects. While used primarily for rigid objects, we also apply our method to reduced deformable objects. We demonstrate the effectiveness of our approach on several challenging 6-DoF haptic rendering scenarios, such as car engine and landing gear virtual assembly.
Kurtosis parameters of super Lorentz—Gauss beams through a paraxial and real ABCD optical system
International Nuclear Information System (INIS)
Zhou Guo-Quan
2011-01-01
Based on the propagation equation of higher-order intensity moments, analytical propagation expressions for the kurtosis parameters of a super Lorentz—Gauss (SLG) SLG 01 beam through a paraxial and real ABCD optical system are derived. By replacing the parameters in the expressions of the kurtosis parameters of the SLG 01 beam, the kurtosis parameters of the SLG 10 and SLG 11 beams through a paraxial and real ABCD optical system can be easily obtained. The kurtosis parameters of an SLG 01 beam through a paraxial and real ABCD optical system depend on two ratios. One is the ratio of the transfer matrix element B to the product of the transfer matrix element A and the diffraction-free range of the super-Lorentzian part. The other is the ratio of the width parameter of the super-Lorentzian part to the waist of the Gaussian part. As a numerical example, the properties of the kurtosis parameters of an SLG 01 beam propagating in free space are illustrated. The influences of different parameters on the kurtosis parameters of an SLG 01 beam are analysed in detail. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Examining resonant inelastic spontaneous scattering of classical Laguerre-Gauss beams from molecules
Rury, Aaron S.
2013-04-01
This paper treats theoretically the spontaneous resonant inelastic scattering of Laguerre-Gauss (LG) beams from the vibrations of complex polyatomic molecules within the semiclassical framework. We develop an interaction Hamiltonian that accounts for the position of the molecule within the excitation beam to derive the effective differential scattering cross section of a classical LG beam from a molecule using the frequency-domain third-order nonlinear optical response function. To gain physical insight, we utilize a model vibronic molecule to study the changes to this scattering process. For specific molecular parameters including vibrational frequency and relative displacement of the involved electronic states, this investigation shows that an incident LG beam asymmetrically enhances one of two participating excitation transitions causing modulation of the interference present in the scattering process. This modulation allows a pathway to coherent control of resonant inelastic scattering from complex, polyatomic molecules. We discuss the possible application of this control to the resonant x-ray inelastic scattering (RIXS) of small polyatomic molecules central to applications ranging from single-molecule electronics to solar energy science.
Generalised extreme value statistics and sum of correlated variables
Bertin, Eric; Clusel, Maxime
2006-01-01
To appear in J.Phys.A; We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and (generally) correlated random variables with a sum distributed according to one of the three (k-dependent) asymptotic distributions of extreme value statistics, namely the Gumbel, Frechet and Weibull distributions. These classes, as well as t...
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
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, and sup......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...
Operator-sum representation for bosonic Gaussian channels
International Nuclear Information System (INIS)
Ivan, J. Solomon; Sabapathy, Krishna Kumar; Simon, R.
2011-01-01
Operator-sum or Kraus representations for single-mode bosonic Gaussian channels are developed, and several of their consequences explored. The fact that the two-mode metaplectic operators acting as unitary purification of these channels do not, in their canonical form, mix the position and momentum variables is exploited to present a procedure which applies uniformly to all families in the Holevo classification. In this procedure the Kraus operators of every quantum-limited Gaussian channel can be simply read off from the matrix elements of a corresponding metaplectic operator. Kraus operators are employed to bring out, in the Fock basis, the manner in which the antilinear, unphysical matrix transposition map when accompanied by injection of a threshold classical noise becomes a physical channel, denoted D(κ) in the Holevo classification. The matrix transposition channels D(κ), D(κ -1 ) turn out to be a dual pair in the sense that their Kraus operators are related by the adjoint operation. The amplifier channel with amplification factor κ and the beam-splitter channel with attenuation factor κ -1 turn out to be mutually dual in the same sense. The action of the quantum-limited attenuator and amplifier channels as simply scaling maps on suitable quasiprobabilities in phase space is examined in the Kraus picture. Consideration of cumulants is used to examine the issue of fixed points. The semigroup property of the amplifier and attenuator families leads in both cases to a Zeno-like effect arising as a consequence of interrupted evolution. In the cases of entanglement-breaking channels a description in terms of rank 1 Kraus operators is shown to emerge quite simply. In contradistinction, it is shown that there is not even one finite rank operator in the entire linear span of Kraus operators of the quantum-limited amplifier or attenuator families, an assertion far stronger than the statement that these are not entanglement breaking channels. A characterization of
A Cube as (Almost) a Sum of Two Cubes
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 17; Issue 9. A Cube as (Almost) a Sum of Two Cubes - A Remarkable Identity of S Ramanujan. C S Yogananda. General Article Volume 17 Issue 9 September 2012 pp 847-854 ...
Program summing up of the bubble chamber experiment
International Nuclear Information System (INIS)
Balgansurehn, Ya.; Glagolev, V.V.; Zaikina, A.G.; Ivanov, V.G.; Pervushov, V.V.; Pestova, G.D.
1986-01-01
During the creation of a high-automated system for film data mathematical processing a rather simple and efficient system for maintaining the bookkeeping of ''history'' information has been developed. It permitted to automate practically completely the process of summing up the bubble chamber experiment
Adhikari SD Zero-sum problems with subgroup weights 259 ...
Indian Academy of Sciences (India)
AUTHOR INDEX. Adhikari S D. Zero-sum problems with subgroup weights. 259. Alaeiyan Mehdi. Semisymmetric cubic graphs of order. 16p2. 19. Alexandru V. On the Iwasawa algebra associated to a normal element of Cp. 45. Alzer Horst. Integral inequalities for self-reciprocal polynomials. 131. Ambily A A see Adhikari S D.
Asymptotic distribution of products of sums of independent random ...
Indian Academy of Sciences (India)
the product of the partial sums of i.i.d. positive random variables as follows. Theorem GR. Let (Xn)n≥1 be a ..... ful suggestions, which have resulted in an improved presentation of the paper. This work is supported by Henan Province Foundation and Frontier Technology Research Plan. (112300410205). References.
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 ...
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.
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.
Summing of the asymptotic series in the quantum field theory
International Nuclear Information System (INIS)
Krasnikov, N.V.; Rubakov, V.A.; Tokarev, V.F.
1979-01-01
It is suggested to sum up the asymptotic series of the perturbation theory in the gphi 4 model by the method which stems naturally from the representation of the Green functions in terms of the continual integral. In this method the Green functions are analytical in the coupling constant in the region Re g >= 0. The method suggested is equivalent to the Borel one
Relaxing the zero-sum assumption in neutral biodiversity theory
Haegeman, Bart; Etienne, Rampal S.
2008-01-01
The zero-sum assumption is one of the ingredients of the standard neutral model of biodiversity by Hubbell. It states that the community is saturated all the time, which in this model means that the total number of individuals in the community is constant over time, and therefore introduces a
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
Lump Sum Moving Cost and Aggregate Office Space Use
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
Proximinal subspaces of finite codimension in direct sum spaces
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
d(x, A)}. Proximinal subspaces of finite codimension have been studied by various authors (see. [1–4, 7–10]). In this paper we obtain a necessary and sufficient condition for proximinality of subspaces of finite codimension inc0-direct sum of Banach spaces in terms of the proxim- inality of the corresponding subspaces of ...
Dominated operators, absolutely summing operators and the strict ...
African Journals Online (AJOL)
b(X;E) be the space of all E-valued bounded continuous functions on X, equipped with the strict topology β. We study dominated and absolutely summing operators T : Cb(X;E) → F. We derive that if X is a locally compact Hausdorff space and E ...
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 )= (.
Some inequalities for sums of nonnegative definite matrices in quaternions
Directory of Open Access Journals (Sweden)
Styan George PH
2005-01-01
Full Text Available Some matrix versions of the Cauchy-Schwarz and Frucht-Kantorovich inequalities are established over the quaternionic algebra. As applications, a group of inequalities for sums of Hermitian nonnegative definite matrices over the quaternionic algebra are derived.
Complete moment convergence of weighted sums for processes ...
Indian Academy of Sciences (India)
[15] extended Theorem C to moving average processes of AANA sequence. The purpose of this paper is to further study the limit properties of weighted sums for sequences of identically distributed AANA random variables and to obtain complete moment convergence by using the Rosenthal type moment inequality.
Large-Nc quantum chromodynamics and harmonic sums
Indian Academy of Sciences (India)
2012-06-08
Jun 8, 2012 ... Abstract. In the large-Nc 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 phenomeno- logical applications. This has led us to consider a class of analytic number theory functions as toy models of ...
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 ...
A Solution to Weighted Sums of Squares as a Square
Withers, Christopher S.; Nadarajah, Saralees
2012-01-01
For n = 1, 2, ... , we give a solution (x[subscript 1], ... , x[subscript n], N) to the Diophantine integer equation [image omitted]. Our solution has N of the form n!, in contrast to other solutions in the literature that are extensions of Euler's solution for N, a sum of squares. More generally, for given n and given integer weights m[subscript…
Sum Rules, Classical and Quantum - A Pedagogical Approach
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.
Nucleon-sigma coupling constant in QCD sum rules
Erkol, G; Timmermans, RGE; Rijken, TA; Rijken, A.M.
The external-field QCD sum rules method is used to evaluate the coupling constant of the light isoscalar-scalar meson ("sigma" or epsilon) to the nucleon. The contributions that come from the excited nucleon states and the response of the continuum threshold to the external field are calculated. The
ADORAVA - A computer code to sum random variables
International Nuclear Information System (INIS)
Fleming, P.V.; Oliveira, L.F.S. de; Senna, V.; Salles, M.R.
1985-06-01
The ADORAVA computer code was carried out aiming to determine the moments of random variable sum distribution when moments are known. The ADORAVA computer code was developed to be applied in probabilistic safety analysis, more specifically for uncertainty propagation in fault trees. The description of ADORAVA algorithm, input, examples and the output of compiled code are presented. (M.C.K.) [pt
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 ...
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.
On the generality of the mass sum rule
International Nuclear Information System (INIS)
Polchinski, J.; Wise, M.B.
1983-01-01
The sum rule, μsub(i)(-1)sup(2Jsub(i))(2Jsub(i)+1)msub(i) 2 =2μsub(a)Dsup(a)TrQsup(a), is studied to first order in supersymmetry breaking, treating the other interactions exactly. It is found to hold for spontaneous breaking and many types of explicit breaking. (orig.)
Partial sums of arithmetical functions with absolutely convergent ...
Indian Academy of Sciences (India)
, Chennai 600 113, India. E-mail: biswajyoti@imsc.res.in. MS received 9 May 2015; revised 9 July 2015. Abstract. For an arithmetical function f with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the sum. ∑.
Improved light quark masses from pseudoscalar sum rules
Directory of Open Access Journals (Sweden)
Stephan Narison
2014-11-01
Full Text Available Using ratios of the inverse Laplace transform sum rules within stability criteria for the subtraction point μ in addition to the ones of the usual τ spectral sum rule variable and continuum threshold tc, we extract the π(1300 and K(1460 decay constants to order αs4 of perturbative QCD by including power corrections up to dimension-six condensates, tachyonic gluon mass for an estimate of large order PT terms, instanton and finite width corrections. Using these inputs with enlarged generous errors, we extract, in a model-independent and conservative ways, the sum of the scale-independent renormalization group invariant (RGI quark masses (mˆu+mˆq:q≡d,s and the corresponding running masses (m¯u+m¯q evaluated at 2 GeV. By giving the value of the ratio mu/md, we deduce the running quark masses m¯u,d,s and condensate 〈u¯u¯〉 and the scale-independent mass ratios: 2ms/(mu+md and ms/md. Using the positivity of the QCD continuum contribution to the spectral function, we also deduce, from the inverse Laplace transform sum rules, for the first time to order αs4, new lower bounds on the RGI masses which are translated into the running masses at 2 GeV and into upper bounds on the running quark condensate 〈u¯u¯〉. Our results summarized in Table 3 and compared with our previous results and with recent lattice averages suggest that precise phenomenological determinations of the sum of light quark masses require improved experimental measurements of the π(1.3 and K(1.46 hadronic widths and/or decay constants which are the dominant sources of errors in the analysis.
The generation of arbitrary order, non-classical, Gauss-type quadrature for transport applications
International Nuclear Information System (INIS)
Spence, Peter J.
2015-01-01
A method is presented, based upon the Stieltjes method (1884), for the determination of non-classical Gauss-type quadrature rules, and the associated sets of abscissae and weights. The method is then used to generate a number of quadrature sets, to arbitrary order, which are primarily aimed at deterministic transport calculations. The quadrature rules and sets detailed include arbitrary order reproductions of those presented by Abu-Shumays in [4,8] (known as the QR sets, but labelled QRA here), in addition to a number of new rules and associated sets; these are generated in a similar way, and we label them the QRS quadrature sets. The method presented here shifts the inherent difficulty (encountered by Abu-Shumays) associated with solving the non-linear moment equations, particular to the required quadrature rule, to one of the determination of non-classical weight functions and the subsequent calculation of various associated inner products. Once a quadrature rule has been written in a standard form, with an associated weight function having been identified, the calculation of the required inner products is achieved using specific variable transformations, in addition to the use of rapid, highly accurate quadrature suited to this purpose. The associated non-classical Gauss quadrature sets can then be determined, and this can be done to any order very rapidly. In this paper, instead of listing weights and abscissae for the different quadrature sets detailed (of which there are a number), the MATLAB code written to generate them is included as Appendix D. The accuracy and efficacy (in a transport setting) of the quadrature sets presented is not tested in this paper (although the accuracy of the QRA quadrature sets has been studied in [12,13]), but comparisons to tabulated results listed in [8] are made. When comparisons are made with one of the azimuthal QRA sets detailed in [8], the inherent difficulty in the method of generation, used there, becomes apparent
Small dark energy and stable vacuum from Dilaton-Gauss-Bonnet coupling in TMT
Energy Technology Data Exchange (ETDEWEB)
Guendelman, Eduardo I. [Ben-Gurion University of the Negev, Department of Physics, Beer-Sheva (Israel); Nishino, Hitoshi; Rajpoot, Subhash [California State University at Long Beach, Long Beach, CA (United States)
2017-04-15
In two measures theories (TMT), in addition to the Riemannian measure of integration, being the square root of the determinant of the metric, we introduce a metric-independent density Φ in four dimensions defined in terms of scalars φ{sub a} by Φ = ε{sup μνρσ} ε{sub abcd}(∂{sub μ}φ{sub a})(∂{sub ν}φ{sub b})(∂{sub ρ}φ{sub c})(∂{sub σ}φ{sub d}). With the help of a dilaton field φ we construct theories that are globally scale invariant. In particular, by introducing couplings of the dilaton φ to the Gauss-Bonnet (GB) topological density √(-g)φ (R{sub μνρσ}{sup 2} - 4R{sub μν}{sup 2} + R{sup 2}) we obtain a theory that is scale invariant up to a total divergence. Integration of the φ{sub a} field equation leads to an integration constant that breaks the global scale symmetry. We discuss the stabilizing effects of the coupling of the dilaton to the GB-topological density on the vacua with a very small cosmological constant and the resolution of the 'TMT Vacuum-Manifold Problem' which exists in the zero cosmological-constant vacuum limit. This problem generically arises from an effective potential that is a perfect square, and it gives rise to a vacuum manifold instead of a unique vacuum solution in the presence of many different scalars, like the dilaton, the Higgs, etc. In the non-zero cosmological-constant case this problem disappears. Furthermore, the GB coupling to the dilaton eliminates flat directions in the effective potential, and it totally lifts the vacuum-manifold degeneracy. (orig.)
Light deflection and Gauss-Bonnet theorem: definition of total deflection angle and its applications
Arakida, Hideyoshi
2018-05-01
In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild-de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle α of the light ray by constructing a quadrilateral Σ^4 on the optical reference geometry M^opt determined by the optical metric \\bar{g}_{ij}. On the basis of the definition of the total deflection angle α and the Gauss-Bonnet theorem, we derive two formulas to calculate the total deflection angle α ; (1) the angular formula that uses four angles determined on the optical reference geometry M^opt or the curved (r, φ ) subspace M^sub being a slice of constant time t and (2) the integral formula on the optical reference geometry M^opt which is the areal integral of the Gaussian curvature K in the area of a quadrilateral Σ ^4 and the line integral of the geodesic curvature κ _g along the curve C_{Γ}. As the curve C_{Γ}, we introduce the unperturbed reference line that is the null geodesic Γ on the background spacetime such as the Minkowski or the de Sitter spacetime, and is obtained by projecting Γ vertically onto the curved (r, φ ) subspace M^sub. We demonstrate that the two formulas give the same total deflection angle α for the Schwarzschild and the Schwarzschild-de Sitter spacetime. In particular, in the Schwarzschild case, the result coincides with Epstein-Shapiro's formula when the source S and the receiver R of the light ray are located at infinity. In addition, in the Schwarzschild-de Sitter case, there appear order O(Lambda;m) terms in addition to the Schwarzschild-like part, while order O(Λ) terms disappear.
Xiong, Xiao-Gen; Yanai, Takeshi
2017-07-11
The Projector Augmented Wave (PAW) method developed by Blöchl is well recognized as an efficient, accurate pseudopotential approach in solid-state density functional theory (DFT) calculations with the plane-wave basis. Here we present an approach to incorporate the PAW method into the Gauss-type function (GTF) based DFT implementation, which is widely used for molecular quantum chemistry calculations. The nodal and high-exponent GTF components of valence molecular orbitals (MOs) are removed or pseudized by the ultrasoft PAW treatment, while there is elaborate transparency to construct an accurate and well-controlled pseudopotential from all-electron atomic description and to reconstruct an all-electron form of valence MOs from the pseudo MOs. The smoothness of the pseudo MOs should benefit the efficiency of GTF-based DFT calculations in terms of elimination of high-exponent primitive GTFs and reduction of grid points in the numerical quadrature. The processes of the PAW method are divided into basis-independent and -dependent parts. The former is carried out using the previously developed PAW libraries libpaw and atompaw. The present scheme is implemented by incorporating libpaw into the conventional GTF-based DFT solver. The details of the formulations and implementations of GTF-related PAW procedures are presented. The test calculations are shown for illustrating the performance. With the near-complete GTF basis at the cc-pVQZ level, the total energies obtained using our PAW method with suited frozen core treatments converge to those with the conventional all-electron GTF-based method with a rather small absolute error.
Mang, Andreas; Ruthotto, Lars
2017-01-01
We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity field. This allows us to use fast Gauss-Newton based methods. We present quickly converging iterative linear solvers using spectral preconditioners that render the overall optimization efficient and scalable. Our method is embedded into the image registration framework FAIR and, thus, supports the most commonly used similarity measures and regularization functionals. We demonstrate the potential of our new approach using several synthetic and real world test problems with up to 14.7 million degrees of freedom.
Maris, Virginie
An existing 3-D magnetotelluric (MT) inversion program written for a single processor personal computer (PC) has been modified and parallelized using OpenMP, in order to run the program efficiently on a multicore workstation. The program uses the Gauss-Newton inversion algorithm based on a staggered-grid finite-difference forward problem, requiring explicit calculation of the Frechet derivatives. The most time-consuming tasks are calculating the derivatives and determining the model parameters at each iteration. Forward modeling and derivative calculations are parallelized by assigning the calculations for each frequency to separate threads, which execute concurrently. Model parameters are obtained by factoring the Hessian using the LDLT method, implemented using a block-cyclic algorithm and compact storage. MT data from 102 tensor stations over the East Flank of the Coso Geothermal Field, California are inverted. Less than three days are required to invert the dataset for ˜ 55,000 inversion parameters on a 2.66 GHz 8-CPU PC with 16 GB of RAM. Inversion results, recovered from a halfspace rather than initial 2-D inversions, qualitatively resemble models from massively parallel 3-D inversion by other researchers and overall, exhibit an improved fit. A steeply west-dipping conductor under the western East Flank is tentatively correlated with a zone of high-temperature ionic fluids based on known well production and lost circulation intervals. Beneath the Main Field, vertical and north-trending shallow conductors are correlated with geothermal producing intervals as well.
Crowther, Michael J; Look, Maxime P; Riley, Richard D
2014-09-28
Multilevel mixed effects survival models are used in the analysis of clustered survival data, such as repeated events, multicenter clinical trials, and individual participant data (IPD) meta-analyses, to investigate heterogeneity in baseline risk and covariate effects. In this paper, we extend parametric frailty models including the exponential, Weibull and Gompertz proportional hazards (PH) models and the log logistic, log normal, and generalized gamma accelerated failure time models to allow any number of normally distributed random effects. Furthermore, we extend the flexible parametric survival model of Royston and Parmar, modeled on the log-cumulative hazard scale using restricted cubic splines, to include random effects while also allowing for non-PH (time-dependent effects). Maximum likelihood is used to estimate the models utilizing adaptive or nonadaptive Gauss-Hermite quadrature. The methods are evaluated through simulation studies representing clinically plausible scenarios of a multicenter trial and IPD meta-analysis, showing good performance of the estimation method. The flexible parametric mixed effects model is illustrated using a dataset of patients with kidney disease and repeated times to infection and an IPD meta-analysis of prognostic factor studies in patients with breast cancer. User-friendly Stata software is provided to implement the methods. Copyright © 2014 John Wiley & Sons, Ltd.
International Nuclear Information System (INIS)
Rosa, Massimiliano; Warsa, James S.; Perks, Michael
2011-01-01
We have implemented a cell-wise, block-Gauss-Seidel (bGS) iterative algorithm, for the solution of the S n transport equations on the Roadrunner hybrid, parallel computer architecture. A compute node of this massively parallel machine comprises AMD Opteron cores that are linked to a Cell Broadband Engine™ (Cell/B.E.) 1 . LAPACK routines have been ported to the Cell/B.E. in order to make use of its parallel Synergistic Processing Elements (SPEs). The bGS algorithm is based on the LU factorization and solution of a linear system that couples the fluxes for all S n angles and energy groups on a mesh cell. For every cell of a mesh that has been parallel decomposed on the higher-level Opteron processors, a linear system is transferred to the Cell/B.E. and the parallel LAPACK routines are used to compute a solution, which is then transferred back to the Opteron, where the rest of the computations for the S n transport problem take place. Compared to standard parallel machines, a hundred-fold speedup of the bGS was observed on the hybrid Roadrunner architecture. Numerical experiments with strong and weak parallel scaling demonstrate the bGS method is viable and compares favorably to full parallel sweeps (FPS) on two-dimensional, unstructured meshes when it is applied to optically thick, multi-material problems. As expected, however, it is not as efficient as FPS in optically thin problems. (author)
Uncanny Sums and Products May Prompt “Wise Choices”: Semantic Misalignment and Numerical Judgments
Directory of Open Access Journals (Sweden)
Ethan C. Brown
2016-08-01
Full Text Available Automatized arithmetic can interfere with numerical judgments, and semantic misalignment may diminish this interference. We gave 92 adults two numerical priming tasks that involved semantic misalignment. We found that misalignment either facilitated or reversed arithmetic interference effects, depending on misalignment type. On our number matching task, digit pairs (as primes for sums appeared with nouns that were either categorically aligned and concrete (e.g., pigs, goats, categorically misaligned and concrete (e.g., eels, webs, or categorically misaligned concrete and intangible (e.g., goats, tactics. Next, participants were asked whether a target digit matched either member of the previously presented digit pair. Participants were slower to reject sum vs. neutral targets on aligned/concrete and misaligned/concrete trials, but unexpectedly slower to reject neutral versus sum targets on misaligned/concrete-intangible trials. Our sentence verification task also elicited unexpected facilitation effects. Participants read a cue sentence that contained two digits, then evaluated whether a subsequent target statement was true or false. When target statements included the product of the two preceding digits, this inhibited accepting correct targets and facilitated rejecting incorrect targets, although only when semantic context did not support arithmetic. These novel findings identify a potentially facilitative role of arithmetic in semantically misaligned contexts and highlight the complex role of contextual factors in numerical processing.
The spin-dependent structure function of the proton g(1)(p) and a test of the Bjorken sum rule
Czech Academy of Sciences Publication Activity Database
Alekseev, M.; Alexakhin, V. Yu.; Alexandrov, Yu.; Alexeev, G. D.; Amoroso, A.; Austregisilio, A.; Badelek, B.; Balestra, F.; Ball, J.; Barth, J.; Baum, G.; Bedfer, Y.; Bernhard, J.; Bertini, R.; Bettinelli, M.; Birsa, R.; Bisplinghoff, J.; Bordalo, P.; Bradamante, F.; Bravar, A.; Bressan, A.; Brona, G.; Burtin, E.; Bussa, M.; Chaberny, D.; Chiosso, M.; Chung, S.U.; Cicuttin, A.; Colantoni, M.; Cotic, D.; Crespo, M.; Dalla Torre, S.; Das, S.; Dasgupta, S. S.; Denisov, O.; Dhara, L.; Diaz, V.; Donskov, S.; Doshita, N.; Duic, V.; Dünnweber, W.; Efremov, A.V.; El Alaoui, A.; Eversheim, P.; Eyrich, W.; Faessler, M.; Ferrero, A.; Filin, A.; Finger, M.; Finger jr., M.; Fischer, H.; Franco, C.; Friedrich, J.; Garfagnini, R.; Gautheron, F.; Gavrichtchouk, O.; Gazda, R.; Gerassimov, S.; Geyer, R.; Giorgi, M.; Gnesi, I.; Gobbo, B.; Goertz, S.; Grabmüller, S.; Grasso, A.; Grube, B.; Gushterski, R.; Guskov, A.; Haas, F.; von Harrach, D.; Hasegawa, T.; Heinsius, F.; Hermann, R.; Herrmann, F.; Hess, C.; Hinterberger, F.; Horikawa, N.; Höppner, Ch.; d'Hose, N.; Ilgner, C.; Ishimoto, S.; Ivanov, O.; Ivanshin, Yu.; Iwata, T.; Jahn, R.; Jasinski, P.; Jegou, G.; Joosten, R.; Kabuss, E.; Käfer, W.; Kang, D.; Ketzer, B.; Khaustov, G.; Khokhlov, Y.; Kisselev, Y.; Klein, F.; Klimaszewski, K.; Koblitz, S.; Koivuniemi, J.; Kolosov, V.; Kondo, K.; Königsmann, K.; Konopka, R.; Konorov, I.; Konstantinov, V.; Korzenev, A.; Kotzinian, A.; Kouznetsov, O.; Kowalik, K.; Krämer, M.; Kral, A.; Kroumchtein, Z.; Kuhn, R.; Kunne, F.; Kurek, K.; Lauser, L.; Le Goff, J.; Lednev, A.; Lehmann, A.; Levorato, S.; Lichtenstadt, J.; Liska, T.; Maggiora, A.; Maggiora, M.; Magnon, A.; Mallot, G.; Mann, A.; Marchand, C.; Marroncle, J.; Martin, A.; Marzec, J.; Massmann, F.; Matsuda, T.; Meyer, W.; Michigami, T.; Mikhailov, Y.; Moinester, M.; Mutter, A.; Nagaytsev, A.; Nagel, T.; Nassalski, J.; Negrini, S.; Nerling, F.; Neubert, S.; Neyret, D.; Nikolaenko, V.; Nunes, A.S.; Olshevsky, A.; Ostrick, M.; Padee, A.; Panknin, R.; Panzieri, D.; Parsamyan, B.; Paul, S.; Pawlukiewicz-Kaminska, B.; Perevalova, E.; Pesaro, G.; Peshekhonov, D.; Piragino, G.; Platchkov, S.; Pochodzalla, J.; Polak, J.; Polyakov, V.; Pontecorvo, G.; Pretz, J.; Quintans, C.; Rajotte, J.; Ramos, S.; Rapatsky, V.; Reicherz, G.; Richter, A.; Robinet, F.; Rocco, E.; Rondio, E.; Ryabchikov, D.; Samoylenko, V.; Sandacz, A.; Santos, H.; Sapozhnikov, M.; Sarkar, S.; Savin, I.; Sbrizzai, G.; Schiavon, P.; Schill, C.; Schlütter, T.; Schmitt, L.; Schopferer, S.; Schröder, W.; Shevchenko, O.; Siebert, H.; Silva, L.; Sinha, L.; Sissakian, A.; Slunecka, M.; Smirnov, G.; Sosio, S.; Sozzi, F.; Srnka, Aleš; Stolarski, M.; Sulc, M.; Sulej, R.; Takekawa, S.; Tessaro, S.; Tessarotto, F.; Teufel, A.; Tkatchev, L.; Uhl, S.; Uman, I.; Virius, M.; Vlassov, N.; Vossen, A.; Weitzel, Q.; Windmolders, R.; Wislicki, W.; Wollny, H.; Zaremba, K.; Zavertyaev, M.; Zemlyanichkina, E.; Ziembicki, M.; Zhao, J.; Zhuravlev, N.; Zvyagin, A.
2010-01-01
Roč. 690, č. 5 (2010), s. 466-472 ISSN 0370-2693 R&D Projects: GA MŠk ME 492 Institutional research plan: CEZ:AV0Z20650511 Keywords : deep inelastic scattering * structure function * QCD analysis * Bjorken sum rule Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 5.255, year: 2010
Borel sum rules for octet baryons in nuclear medium
Energy Technology Data Exchange (ETDEWEB)
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 [Pi][sup R]([omega], q[sup 2]) in the energy [omega]. Then, [Pi][sup R]([omega], q[sup 2]) is split into even and odd parts of [omega] 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, , induce attraction to the octet baryons in the medium in contrast to the results of previous works. It is also found that [delta]M[sub N] > [delta]M[sub [Lambda
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.
One-Loop BPS amplitudes as BPS-state sums
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.
Summability calculus a comprehensive theory of fractional finite sums
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...
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
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 efficient as the tail probability of interest decreases to zero. The first estimator, based on importance sampling, involves a scaling of the whole covariance matrix and can be shown to be asymptotically optimal. A further study, based on the Cross-Entropy algorithm, is also performed in order to adaptively...... 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...
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.
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.)
Madhava, Gregory, Leibnitz, and Sums of Two Squares
Indian Academy of Sciences (India)
IAS Admin
If n is a prime number of the type 1 (mod 4), then n can be written as a sum of two squares in ... Jacobi used elliptic functions and `q-series' to prove his identity (see [4] for details), so his was certainly .... D Hilbert, and S Cohn-Vossen, Geometry and the Imagination, New York,. Chelsea, pp.27–39,1999. [3]. S A Shirali ...
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)
Counting Your Way to the Sum of Squares Formula
Indian Academy of Sciences (India)
IAS Admin
number of two-element subsets of Sn; this number is (n+1. 2 ). It follows readily from the above that. 12 + 22 + 32 + ··· + n2 = 2 · ( n + 1. 3 )+ ( n + 1. 2 ) . (2). 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 ...
Minimum perimeter-sum partitions in the plane
DEFF Research Database (Denmark)
Abrahamsen, Mikkel; de Berg, Mark; Buchin, Kevin
2017-01-01
Let P be a set of n points in the plane. We consider the problem of partitioning P into two subsets P1 and P2 such that the sum of the perimeters of CH(P1) and CH(P2) is minimized, where CH(Pi) denotes the convex hull of Pi. The problem was first studied by Mitchell and Wynters in 1991 who gave...
Volume sums of polar Blaschke–Minkowski homomorphisms
Indian Academy of Sciences (India)
usual Minkowski sum and V1(K, L) denotes the mixed volume of the convex bodies K and L defined by .... The convex body. (K1,...,Kn−1) contains the origin in its interior, as was shown in [30]. If K is a convex body that contains the origin in its interior, the polar body of K is defined by .... We will use Ku to denote the image.
Asymptotic distribution of products of sums of independent random ...
Indian Academy of Sciences (India)
Yanling Wang et al. Recently, Gonchigdanzan and Rempała [3] discussed an almost sure limit theorem for the product of the partial sums of i.i.d. positive random variables as follows. Theorem GR. Let (Xn)n≥1 be a sequence of i.i.d. positive square integrable random variables with EX1 = μ > 0, Var X1 = σ2. Denote γ = σ/μ ...
On the functional limits for partial sums under stable law
Gonchigdanzan, K.; Kosiński, K.M.
2009-01-01
For the partial sums (S,) of independent random variables we define a stochastic process s(n)(t) := (1/d(n)) Sigma(k <=[nt])(S-k/k - mu) and prove that (1/log N) Sigma(n <= N)(1/n)I {S-n(t) <= x} -> G(t)(x) a.s. if and only if (1/log N) Sigma(n <= N)(1/n)P(s(n)(t) <= x) -> G(t)(x), for some sequence
Sum rules for zeros of polynomials and generalized Lucas polynomials
Ricci, Paolo Emilio
1993-10-01
A representation formula in terms of generalized Lucas polynomials of the second kind [see formula (4.3)], for the sum rules Js(i) introduced by Case [J. Math. Phys. 21, 702 (1980)] and studied by Dehesa et al. [J. Math. Phys. 26, 1547 (1985); 26, 2729 (1985)] in order to obtain information about the zeros' distribution of eigenfunctions of a class of ordinary polynomial differential operators, is derived.
Heavy-meson decay constants from QCD sum rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2010-12-01
We sketch a recent sum-rule extraction of the decay constants of the heavy pseudoscalar mesons D, Ds, B, and Bs from the two-point correlator of heavy-light pseudoscalar currents [1]. Our main emphasis lies on the control over all the uncertainties in the decay constants, related both to the input QCD parameters and to the limited accuracy of the method of sum rules. Gaining this control has become possible by application of our new procedure of extracting hadron observables based on a dual threshold depending on the Borel parameter. For the charmed-meson decay constants, we find fD = (206.2±7.3(OPE)±5.1syst)) MeV, fDs = (245.3±15.7(OPE)±4.5(syst)) MeV. For the beauty mesons, the decay constants turn out to be extremely sensitive to the precise value of the MS¯ mass of the b-quark, accent="true">m¯b(accent="true">m¯b). By requiring our sum-rule estimate to match the average of the lattice determinations of fB, we extract the rather accurate value accent="true">m¯b(accent="true">m¯b) = (4.245±0.025) GeV Feeding this parameter value into our sum-rule formalismleads to the beauty-meson decay constants fB = (193.4±12.3(OPE)±4.3(syst)) MeV, fBs = (232.5±18.6(OPE)±2.4syst)) MeV.
Fields generated by sums and products of singular moduli
Faye, Bernadette; Riffaut, Antonin
2017-01-01
We show that the field $\\mathbb{Q}(x,y)$, generated by two singular moduli~$x$ and~$y$, is generated by their sum ${x+y}$, unless~$x$ and~$y$ are conjugate over~$\\mathbb{Q}$, in which case ${x+y}$ generates a subfield of degree at most~$2$. We obtain a similar result for the product of two singular moduli.
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
Sum rules for strangeness exchange reactions with nuclei
International Nuclear Information System (INIS)
Fiebig, H.R.
1983-01-01
Within the framework of a constituent quark model we derive energy-weighted sum rules for strangeness exchange (analog) and spin-strangeness exchange (generalized Gamow-Teller) reactions in the limit of small momentum transfer. The target nucleus is treated as a system of non-communicating 3-quark clusters. We also calculate the branching between the SU(3) octet and decouplet channels and we consider double strangeness exchange reactions. (orig.)
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
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.
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.