Nambudiripad, K B M
2014-01-01
After presenting the theory in engineers' language without the unfriendly abstraction of pure mathematics, several illustrative examples are discussed in great detail to see how the various functions of the Bessel family enter into the solution of technically important problems. Axisymmetric vibrations of a circular membrane, oscillations of a uniform chain, heat transfer in circular fins, buckling of columns of varying cross-section, vibrations of a circular plate and current density in a conductor of circular cross-section are considered. The problems are formulated purely from physical considerations (using, for example, Newton's law of motion, Fourier's law of heat conduction electromagnetic field equations, etc.) Infinite series expansions, recurrence relations, manipulation of expressions involving Bessel functions, orthogonality and expansion in Fourier-Bessel series are also covered in some detail. Some important topics such as asymptotic expansions, generating function and Sturm-Lioville theory are r...
Luke, Yudell L
2014-01-01
Integrals of Bessel Functions concerns definite and indefinite integrals, the evaluation of which is necessary to numerous applied problems. A massive compendium of useful information, this volume represents a resource for applied mathematicians in many areas of academia and industry as well as an excellent text for advanced undergraduates and graduate students of mathematics.Starting with an extensive introductory chapter on basic formulas, the treatment advances to indefinite integrals, examining them in terms of Lommel and Bessel functions. Subsequent chapters explore airy functions, incomp
Computation of hyperspherical Bessel functions
Tram, Thomas
2013-01-01
In this paper we present a fast and accurate numerical algorithm for the computation of hyperspherical Bessel functions of high order and real arguments. For the hyperspherical Bessel functions of closed type, no stable algorithm existed so far due to the lack of a backwards recurrence. All our algorithms are written in C and are publicly available, see the conclusion for web page.
Extension of Oppenheim's Problem to Bessel Functions
Directory of Open Access Journals (Sweden)
Zhu Ling
2007-01-01
Full Text Available Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we deduce the hyperbolic analogue of these trigonometric inequalities, and we extend these inequalities to modified Bessel functions.
Trigonometric Approximations for Some Bessel Functions
Muhammad Taher Abuelma'atti
1999-01-01
Formulas are obtained for approximating the tabulated Bessel functions Jn(x), n = 0–9 in terms of trigonometric functions. These formulas can be easily integrated and differentiated and are convenient for personal computers and pocket calculators.
Bessel functions for root systems via the trigonometric setting
DEFF Research Database (Denmark)
Ørsted, Bent; Said, S.B.
2005-01-01
In this paper, we study generalized Bessel functions related to root systems and give explicit formulas in several cases.......In this paper, we study generalized Bessel functions related to root systems and give explicit formulas in several cases....
Monotonicity and bounds on Bessel functions
Directory of Open Access Journals (Sweden)
Larry Landau
2000-07-01
Full Text Available survey my recent results on monotonicity with respect to order of general Bessel functions, which follow from a new identity and lead to best possible uniform bounds. Application may be made to the "spreading of the wave packet" for a free quantum particle on a lattice and to estimates for perturbative expansions.
Special Relativity via Modified Bessel Functions
Lavenda, B. H.
2000-10-01
The recursive formulas of modified Bessel functions give the relativistic expressions for energy and momentum. Modified Bessel functions are solutions to a continuous time, one-dimensional discrete jump process. The jump process is analyzed from two inertial frames with a relative constant velocity; the average distance of a particle along the chain corresponds to the distance between two observers in the two inertial frames. The recursion relations of modified Bessel functions are compared to the 'k calculus' which uses the radial Doppler effect to derive relativistic kinematics. The Doppler effect predicts that the frequency is a decreasing function of the velocity, and the Planck frequency, which increases with velocity, does not transform like the frequency of a clock. The Lorentz transformation can be interpreted as energy and momentum conservation relations through the addition formula for hyperbolic cosine and sine, respectively. The addition formula for the hyperbolic tangent gives the well-known relativistic formula for the addition of velocities. In the non-relativistic and ultra-relativistic limits the distributions of the particle's position are Gaussian and Poisson, respectively.
Bessel Function Model for Corneal Topography
Okrasiński, Wojciech
2011-01-01
In this paper we consider a new nonlinear mathematical model for corneal topography formulated as two-point boudary value problem. We derive it from first physical principles and provide some mathematical analysis. The existence and uniqeness theorems are proved as well as various estimates on exact solution. At the end we fit the simplified model based on Modified Bessel Function of the First Kind with the real corneal data consisting of matrix of 123x123 points and obtain an error of order of 1%.
Evaluation of a Family of Bessel Function Integrals
Birrell, Jeremiah
2015-01-01
We investigate a family of integrals involving modified Bessel functions that arise in the context of neutrino scattering. Recursive formulas are derived for evaluating these integrals and their asymptotic expansions are computed. We prove in certain cases that the asymptotic expansion yields the exact result after a finite number of terms. In each of these cases we derive a formula that bounds the order at which the expansion terminates. The method of calculation developed in this paper is applicable to similar families of integrals that involve Bessel or modified Bessel functions.
Bessel functions in mass action modeling of memories and remembrances
Energy Technology Data Exchange (ETDEWEB)
Freeman, Walter J. [Department of Molecular and Cell Biology, University of California, Berkeley, CA 94720-3206 (United States); Capolupo, Antonio [Dipartimento di Fisica, E.R. Caianiello Universitá di Salerno, and INFN Gruppo collegato di Salerno, Fisciano 84084 (Italy); Kozma, Robert [Department of Mathematics, Memphis University, Memphis, TN 38152 (United States); Olivares del Campo, Andrés [The Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BZ (United Kingdom); Vitiello, Giuseppe, E-mail: vitiello@sa.infn.it [Dipartimento di Fisica, E.R. Caianiello Universitá di Salerno, and INFN Gruppo collegato di Salerno, Fisciano 84084 (Italy)
2015-10-02
Data from experimental observations of a class of neurological processes (Freeman K-sets) present functional distribution reproducing Bessel function behavior. We model such processes with couples of damped/amplified oscillators which provide time dependent representation of Bessel equation. The root loci of poles and zeros conform to solutions of K-sets. Some light is shed on the problem of filling the gap between the cellular level dynamics and the brain functional activity. Breakdown of time-reversal symmetry is related with the cortex thermodynamic features. This provides a possible mechanism to deduce lifetime of recorded memory. - Highlights: • We consider data from observations of impulse responses of cortex to electric shocks. • These data are fitted by Bessel functions which may be represented by couples of damped/amplified oscillators. • We study the data by using couples of damped/amplified oscillators. • We discuss lifetime and other properties of the considered brain processes.
An integral estimate of Bessel function and its application
Institute of Scientific and Technical Information of China (English)
DING Yong; LI Ran
2008-01-01
In this paper the authors give a new integral estimate of the Bessel function, which parameterized Marcinkiewicz integral μΩρ with variable kernels is of type (2, 2), where the kernel function Ω does not have any smoothness on the unit sphere in Rn.
Further properties of the zeros of Bessel functions
Directory of Open Access Journals (Sweden)
Carla Giordano
1987-11-01
Full Text Available New monotonicity and convexity properties for the zeros cνk (k=1,2,... of the Bessel functions are proved. New inequalities for cνk are also given. These inequalities are useful for small values of ν.
An integral estimate of Bessel function and its application
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper the authors give a new integral estimate of the Bessel function,which is an extension of Calder(?)n-Zygmund’s result.As an application of this result,we prove that the parameterized Marcinkiewicz integralμ_Ω~p with variable kernels is of type (2,2),where the kernel functionΩdoes not have any smoothness on the unit sphere in R~n.
K-Bessel functions associated to a 3-rank Jordan algebra
Directory of Open Access Journals (Sweden)
Hacen Dib
2005-01-01
Full Text Available Using the Bessel-Muirhead system, we can express the K-Bessel function defined on a Jordan algebra as a linear combination of the J-solutions. We determine explicitly the coefficients when the rank of this Jordan algebra is three after a reduction to the rank two. The main tools are some algebraic identities developed for this occasion.
On a new class of integrals involving Bessel functions of the first kind
Directory of Open Access Journals (Sweden)
P. Agarwal
2014-06-01
Full Text Available In recent years, several integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas containing the Bessel function $J_\
Indian Academy of Sciences (India)
A K Chattopadhyay; C V S Rao
2003-07-01
Here we describe the superiority of Bessel function as base function for radial expansion over Zernicke polynomial in the tomographic reconstruction technique. The causes for the superiority have been described in detail. The superiority has been shown both with simulated data for Kadomtsev’s model for saw-tooth oscillation and real experimental x-ray data from W7-AS Stellarator.
Expansion of Infinite Series Containing Modified Bessel Functions of the Second Kind
Fucci, Guglielmo
2014-01-01
The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the parameters in the argument of the modified Bessel function of the second kind is small compared to the others. We apply the results obtained for the asymptotic expansion to specific problems that arise in the ambit of quantum field theory.
Algorithm 831: modified Bessel functions of imaginary order and positive argument
Gil, A.; Segura, J.; Temme, N.M.
2004-01-01
77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions Kia (x), Lia (x) and their derivatives for real a and positive x; these functions are independent solutions of the differential equation x2w'' + xw' + (a2
On the Computation and Applications of Bessel Functions with Pure Imaginary Indices
Matyshev, A A
2009-01-01
Bessel functions with pure imaginary index (order) play an important role in corpuscular optics where they govern the dynamics of charged particles in isotrajectory quadrupoles. Recently they were found to be of great importance in semiconductor material characterization as they are manifested in the strain state of crystalline material. A new algorithm which can be used for the computation of the normal and modifed Bessel functions with pure imaginary index is proposed. The developed algorithm is very fast to compute and for small arguments converges after a few iterations.
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; WANG Yong
2006-01-01
In Phys. Lett. A 313 (2003) 343 we have found that the self-reciprocal Hankel transformation (HT) is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations' transformation in quantum mechanics.
Remarks on the paper: "Bounds for functions involving ratios of modified Bessel functions"
Segura, Javier
2011-01-01
A recent paper by C.G. Kokologiannaki published in J. Math. Anal. Appl. \\cite{Kolo:2012:BFI} gives some properties for ratios of modified Bessel functions and, in particular, some bounds. These bounds are said to improve the range of some inequalities in \\cite{Segura:2011:BRM} or to be sharper. Unfortunately, Kokologiannaki made some mistakes in the comparison and no improvement or extension is made over the results in \\cite{Segura:2011:BRM}. We explain the errors in these comments and show that the bounds given in \\cite{Kolo:2012:BFI} are already contained in \\cite{Segura:2011:BRM}.
Multi-point quasi-rational approximants for the modified Bessel function I1(x)
Martin, P.; Olivares, J.; Cortés-Vega, L.; Sotomayor, A.
2016-08-01
Approximants for the modified Bessel function I1(x) has been found using the multi-point quasi-rational technique. The approximations here determined has good accuracy for any positive value of the variable, and it seems to be adequate for most of the works where this function are used. Furthermore, the approximants are simple to calculate numerically in a direct way or using any usual MAPLE or MATLAB software.
Institute of Scientific and Technical Information of China (English)
Huo TANG; Erhan DENIZ
2014-01-01
In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z(Bcκ+1f(z))′=κBcκf(z)−(κ−1)Bcκ+1f(z), where b, c, p ∈ C and κ = p+(b+1)/2 ∈ C\\Z−0 (Z−0 = {0,−1,−2, · · ·}). The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.
Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions
Farrell, Orin J
2013-01-01
Nearly 200 problems, each with a detailed, worked-out solution, deal with the properties and applications of the gamma and beta functions, Legendre polynomials, and Bessel functions. The first two chapters examine gamma and beta functions, including applications to certain geometrical and physical problems such as heat-flow in a straight wire. The following two chapters treat Legendre polynomials, addressing applications to specific series expansions, steady-state heat-flow temperature distribution, gravitational potential of a circular lamina, and application of Gauss's mechanical quadrature
On infinite series concerning zeros of Bessel functions of the first kind
Giusti, Andrea; Mainardi, Francesco
2016-06-01
A relevant result independently obtained by Rayleigh and Sneddon on an identity on series involving the zeros of Bessel functions of the first kind is derived by an alternative method based on Laplace transforms. Our method leads to a Bernstein function of time, expressed by Dirichlet series, that allows us to recover the Rayleigh-Sneddon sum. We also consider another method arriving at the same result based on a relevant formula by Calogero. Moreover, we also provide an electrical example in which this sum results to be extremely useful in order to recover the analytical expression for the response of the system to a certain external input.
On determinants of modified Bessel functions and entire solutions of double confluent Heun equations
Buchstaber, V. M.; Glutsyuk, A. A.
2016-12-01
We investigate the question on existence of entire solutions of well-known linear differential equations that are linearizations of nonlinear equations modeling the Josephson effect in superconductivity. We consider the modified Bessel functions I j (x) of the first kind, which are Laurent series coefficients of the analytic function family {{\\text{e}}\\frac{x{2}≤ft(z+\\frac{1}{z}\\right)}} . For every l≥slant 1 we study the family parametrized by k,n\\in {{{Z}}l} , {{k}1}>\\cdots >{{k}l} , {{n}1}>\\cdots >{{n}l} of (l× l) -matrix functions formed by the modified Bessel functions of the first kind {{a}ij}(x)={{I}{{kj}-{{n}i}}}(x) , i,j=1,\\ldots,l . We show that their determinants f k, n (x) are positive for every l≥slant 1 , k,n\\in {{{Z}}l} as above and x > 0. The above determinants are closely related to a sequence (indexed by l) of families of double confluent Heun equations, which are linear second order differential equations with two irregular singularities, at zero and at infinity. Buchstaber and Tertychnyi have constructed their holomorphic solutions on {C} for an explicit class of parameter values and conjectured that they do not exist for other parameter values. They have reduced their conjecture to the second conjecture saying that if an appropriate second similar equation has a polynomial solution, then the first one has no entire solution. They have proved the latter statement under the additional assumption (third conjecture) that {{f}k,n}(x)\
Keldysh theory re-examined: Application of the generalized Bessel functions
Bauer, J H
2015-01-01
A derivation of the ionization rate for the hydrogen-like ion in the strong linearly polarized laser field is presented. This derivation utilizes the famous Keldysh probability amplitude in the length gauge (in the dipole approximation) and without Coulomb effects in the final state of the ionized electron. No further approximations are being made, because the amplitude has been expanded in the double Fourier series in a time domain (with the help of the generalized Bessel functions). Thus, our theory has no other limitations characteristic of the original Keldysh theory. We compare our "exact" theory with the original Keldysh one, studying photoionization energy spectra and total ionization rates. We show breakdown of the original Keldysh theory for higher frequencies. In the barrier-suppresion regime the "exact" Keldysh theory gives results closer to well-known numerical or other analytical results.
On q-analogues of the Mangontarum transform for certain q-Bessel functions and some application
Directory of Open Access Journals (Sweden)
S.K.Q. Al-Omari
2016-10-01
Full Text Available Several q-analogues of certain integral transforms have been recently investigated by many authors in the recent past. In this paper, we introduce certain analogues of the so-called q-Mangontarum transform and implement the proposed variants to given classes of q-Bessel functions. The results of this paper are new and complement the previously known results of Mangontarum (2014. Some results related to q-Laplace transforms are also obtained.
The Bessel Numbers and Bessel Matrices
Institute of Scientific and Technical Information of China (English)
Sheng Liang YANG; Zhan Ke QIAO
2011-01-01
In this paper,using exponential Riordan arrays,we investigate the Bessel numbers and Bessel matrices.By exploring links between the Bessel matrices,the Stirling matrices and the degenerate Stirling matrices,we show that the Bessel numbers are special case of the degenerate Stirling numbers,and derive explicit formulas for the Bessel numbers in terms of the Stirling numbers and binomial coefficients.
Revisiting the orthogonality of Bessel functions of the first kind on an infinite interval
Ponce de Leon, J.
2015-01-01
The rigorous proof of the orthogonality integral \\int 0∞ ρ {{J}ν }(kρ ){{J}ν }(k\\prime ρ ) dρ =\\frac{δ (k-k\\prime )}{k}, for ν ≥slant -1, is laborious and requires the use of mathematical techniques that, probably, are unfamiliar to most physics students, even at the graduate level. In physics, we are used to the argument that it may be proved by the use of Hankel transforms. However, the logic of the matter is the opposite, i.e., the existence of the inverse Hankel transform is a consequence of the orthogonality integral. The goal of this work is to prove this integral without circular reasoning. In this paper, using elementary properties of Bessel functions, we give a simple analytical derivation of this integral for the case where ν is an integer, zero, or half-integer not less than -1/2. Then, using the asymptotic behaviour of {{J}ν }(x), we extend the result to any ν ≥slant -1. This work is of a pedagogical nature. Therefore, to add educational value to the discussion, we do not skip the details of the calculations.
On hyperbolic Bessel processes and beyond
Wisniewolski, Maciej
2011-01-01
We investigate distributions of hyperbolic Bessel processes. We find links between the hyperbolic cosinus of the hyperbolic Bessel processes and the functionals of geometric Brownian motion. We present an explicit formula of Laplace transform of hyperbolic cosinus of hyperbolic Bessel processes and some interesting different probabilistic representations of this Laplace transform. We express the one-dimensional distribution of hyperbolic Bessel process in terms of other, known and independent processes. We present some applications including a new proof of Bougerol's identity and it's generalization. We characterize the distribution of the process being hyperbolic sinus of hyperbolic Bessel processes.
Energy Technology Data Exchange (ETDEWEB)
Avakian, Harut [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Gamberg, Leonard [Pennsylvania State Univ., University Park, PA (United States); Rossi, Patrizia [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Prokudin, Alexei [Pennsylvania State Univ., University Park, PA (United States)
2016-05-01
We review the concept of Bessel weighted asymmetries for semi-inclusive deep inelastic scattering and focus on the cross section in Fourier space, conjugate to the outgoing hadron’s transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. The procedure is applied to studies of the double longitudinal spin asymmetry in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized parton model. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Monte Carlo extraction compared to input model calculations, which is due to the limitations imposed by the energy and momentum conservation at the given energy and hard scale Q2. We find that the Bessel weighting technique provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics due to experimental acceptances and resolutions with different TMD model inputs.
Institute of Scientific and Technical Information of China (English)
Zhu Kai-Cheng; Li Shao-Xin; Tang Ying; Zheng Xiao-Juan; Tang Hui-Qin
2012-01-01
A new kind of quantum non-Gaussian state with a vortex structure,termed a Bessel-Gaussian vortex state,is constructed,which is an eigenstate of the sum of squared annihilation operators a2 + b2.The Wigner function of the quantum vortex state is derived and exhibits negativity which is an indication of nonclassicality.It is also found that a quantized vortex state is always in entanglement.And a scheme for generating such quantized vortex states is proposed.
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.
Ebaid, Abdelhalim; Al-Blowy, Ahmed B.
2016-05-01
In this article, a simple approach is suggested to calculate the approximate dates of opposition and conjunction of Earth and Mars since their opposition on August 28, 2003 (at perihelion of Mars). The goal of this article has been achieved via using accurate analytical solution to Kepler's equation in terms of Bessel function. The periodicity property of this solution and its particular values at specified times are discussed through some lemmas. The mathematical conditions of opposition and conjunction of the two planets are formulated. Moreover, the intervals of opposition and conjunction have been determined using the graphs of some defined functions. The calculations reveal that there are nine possible oppositions and conjunctions for Earth and Mars during 20 years started on August 28, 2003. The dates of such oppositions and conjunctions were approximately determined and listed in Tables. It is found that our calculations differ few days from the published real dates of Earth-Mars oppositions due to the neglected effects of the gravitational attraction of other planets in the Solar system on the motion of two planets. The period of 20 years can be extended for any number of years by following the suggested analysis. Furthermore, the current approach may be extended to study the opposition and conjunction of the Earth and any outer planet.
General description of circularly symmetric Bessel beams of arbitrary order
Wang, Jia Jie; Wriedt, Thomas; Lock, James A.; Mädler, Lutz
2016-11-01
A general description of circularly symmetric Bessel beams of arbitrary order is derived in this paper. This is achieved by analyzing the relationship between different descriptions of polarized Bessel beams obtained using different approaches. It is shown that a class of circularly symmetric Davis Bessel beams derived using the Hertz vector potentials possesses the same general functional dependence as the aplanatic Bessel beams generated using the angular spectrum representation (ASR). This result bridges the gap between different descriptions of Bessel beams and leads to a general description of circularly symmetric Bessel beams, such that the Davis Bessel beams and the aplanatic Bessel beams are merely the two simplest cases of an infinite number of possible circularly symmetric Bessel beams. Additionally, magnitude profiles of the electric and magnetic fields, the energy density and the Poynting vector are displayed for Bessel beams in both paraxial and nonparaxial cases. The results presented in this paper provide a fresh perspective on the description of Bessel beams and cast some insights into the light scattering and light-matter interactions problems in practice.
Marginal phase correction of truncated Bessel beams
Sedukhin
2000-06-01
Approximate analytic expressions are obtained for evaluating the axial intensity and the central-lobe diameter of J0 Bessel beams transmitted through a finite-aperture phase filter. A reasonable quality factor governing the axial-intensity behavior of a phase-undistorted truncated Bessel beam is found to be the inverse square root of the Fresnel number defined, for a given aperture, from the axial point of geometrical shadow. Additional drastic reduction of axial-intensity oscillations is accomplished by using marginal phase correction of the beam instead of the well-known amplitude apodization. A procedure for analytically calculating an optimal monotonic slowly varying correction phase function is described.
On fractional Bessel equation and the description of corneal topography
Okrasiński, Wojciech
2012-01-01
In this note we apply a modified fractional Bessel differential equation to the problem of describing corneal topography. We find the solution in terms of the power series. This solution has an interesting behavior at infinity which is a generalization of the classical results for modified Bessel function of order 0. Our model fits the real corneal geometry data with an error of order of a few per cent.
Single Bessel tractor-beam tweezers
Mitri, F G
2014-01-01
The tractor behavior of a zero-order Bessel acoustic beam acting on a fluid sphere, and emanating from a finite circular aperture (as opposed to waves of infinite extent) is demonstrated theoretically. Conditions for an attractive force acting in opposite direction of the radiating waves, determined by the choice of the beam's half-cone angle, the size of the radiator, and its distance from a fluid sphere, are established and discussed. Numerical predictions for the radiation force function, which is the radiation force per unit energy density and cross-sectional surface, are provided using a partial-wave expansion method stemming from the acoustic scattering. The results suggest a simple and reliable analysis for the design of Bessel beam acoustical tweezers and tractor beam devices.
Müller, Angelina; Wallrabe, Ulrike
2016-01-01
We present a ring aperture with independently switchable segments for the three-dimensional control of quasi propagation invariant beams. We demonstrate that our liquid crystal design concept preserves coherence and generates the Bessel beam structure.
Auluck, S K H
2010-01-01
Spectral decomposition of dynamical equations using curl-eigenfunctions has been extensively used in fluid and plasma dynamics problems using their orthogonality and completeness properties for both linear and non-linear cases. Coefficients of such expansions are integrals over products of Bessel functions in problems involving cylindrical geometry. In this paper, certain identities involving products of two and three general solutions of Bessel's equation have been derived. Some of these identities have been useful in the study of Turner relaxation of annular magnetized plasma [S.K.H. Auluck, Phys. Plasmas, 16, 122504, 2009], where quadratic integral quantities such as helicity and total energy were expressed as algebraic functions of the arbitrary constants of the general solution of Bessel's equation, allowing their determination by a minimization procedure. Identities involving products of three solutions enable expanding a product of two solutions in a Fourier-Bessel series of single Bessel functions fac...
Maximal inequalities for bessel processes
Directory of Open Access Journals (Sweden)
Graversen SE
1998-01-01
Full Text Available It is proved that the uniform law of large numbers (over a random parameter set for the -dimensional ( Bessel process started at 0 is valid: for all stopping times for . The rate obtained (on the right-hand side is shown to be the best possible. The following inequality is gained as a consequence: for all stopping times for , where the constant satisfies as . This answers a question raised in [4]. The method of proof relies upon representing the Bessel process as a time changed geometric Brownian motion. The main emphasis of the paper is on the method of proof and on the simplicity of solution.
Transport of intensity phase imaging using Bessel sources
Petruccelli, Jonathan C.; Chakraborty, Tonmoy
2016-05-01
Propagation-based phase contrast using the transport of intensity equation (TIE) allows rapid, deterministic phase retrieval from defocused images. For weakly attenuating objects, phase can be retrieved from a single image. However, the TIE suffers from significant low frequency artifacts due to enhancement of noise during phase retrieval. We demonstrate that by patterning the illumination source as approximately a modified Bessel function of the 2nd kind of zero order, quantitative phase can be imaged directly at the detector within a spatial frequency band. Outside of that band, Bessel sources still improve low frequency performance in phase retrieval.
Higher-order chaotic oscillator using active bessel filter
DEFF Research Database (Denmark)
Lindberg, Erik; Mykolaitis, Gytis; Bumelien, Skaidra;
2010-01-01
A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel filter is described. The Bessel unit plays the role of "three-in-one": a delay line, an amplifier and a filter. Results of hardware experiments and numerical simulation are presented. Depending on the pa...... on the parameters of the nonlinear unit the oscillator operates either in a one-scroll or two-scroll mode. Two positive Lyapunov exponents, found at larger values of the negative slopes of the nonlinear function, characterize the oscillations as hyperchaotic....
On the product and ratio of Bessel random variables
Directory of Open Access Journals (Sweden)
Saralees Nadarajah
2005-01-01
Full Text Available The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Bessel function random variables. An application of the results is provided by tabulating the associated percentage points.
Heat kernel analysis for Bessel operators on symmetric cones
DEFF Research Database (Denmark)
Möllers, Jan
2014-01-01
. The heat kernel is explicitly given in terms of a multivariable $I$-Bessel function on $Ω$. Its corresponding heat kernel transform defines a continuous linear operator between $L^p$-spaces. The unitary image of the $L^2$-space under the heat kernel transform is characterized as a weighted Bergmann space...
On the Diamond Bessel Heat Kernel
Directory of Open Access Journals (Sweden)
Wanchak Satsanit
2011-01-01
Full Text Available We study the heat equation in n dimensional by Diamond Bessel operator. We find the solution by method of convolution and Fourier transform in distribution theory and also obtain an interesting kernel related to the spectrum and the kernel which is called Bessel heat kernel.
Optical tractor Bessel polarized beams
Mitri, F. G.; Li, R. X.; Guo, L. X.; Ding, C. Y.
2017-01-01
Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization. The angular spectrum decomposition method (ASDM) is used to derive the non-paraxial electromagnetic (EM) field components of the Bessel beams. The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections. The analysis has no limitation to a particular range of frequencies such that the Rayleigh, Mie or geometrical optics regimes can all be considered effectively using the present rigorous formalism. The focus of this investigation is to identify some of the tractor beam conditions so as to achieve retrograde motion of a dielectric sphere located arbitrarily in space. Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively. As the sphere shifts off the beam's axis, the axial pulling (tractor) force is weakened. Moreover, the transverse radiation force cross-section field changes with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on the choice of ka and the half-cone angle α0. These results are particularly important in the development of emergent technologies for the photophoretic assembly of optically-engineered (meta)materials with designed properties using optical tractor (vortex) beams, particle manipulation, levitation and positioning, and other applications.
Fiber microaxicons fabricated by a polishing technique for the generation of Bessel-like beams.
Grosjean, Thierry; Saleh, Said Sadat; Suarez, Miguel Angel; Ibrahim, Idriss Abdoulkader; Piquerey, Vincent; Charraut, Daniel; Sandoz, Patrick
2007-11-20
We report a simple method for generating microaxicons at the extremity of commercial optical fibers. The proposed solution, based on a polishing technique, can readily produce any desired microaxicon cone angle and is independent of the nature of the fiber. An optical study of microaxicon performance, in terms of confinement ability and length of the generated Bessel-like beams, is presented as a function of the microaxicon angle. This study, made possible by the experimental acquisition of the 3D light distribution of the Bessel-like beams, reveals the relationship between the Bessel-like beam confinement zone and the beam length. Finally, the effect of diffraction of the Bessel-like beams, induced by the limited lateral extent of the incident fiber mode, is studied and discussed.
Cylindrically polarized Bessel-Gauss beams
Madhi, Daena; Aiello, Andrea
2014-01-01
We present a study of radially and azimuthally polarized Bessel-Gauss beams in both the paraxial and nonparaxial regimes. We discuss the validity of the paraxial approximation and the form of the nonparaxial corrections for Bessel-Gauss beams. We show that, independently from the ratio between the Bessel aperture cone angle $\\vartheta_0$ and the Gauss beam divergence $\\theta_0$, the nonparaxial corrections are always very small and therefore negligible. Explicit expressions for the nonparaxial vector electric field components are also reported.
Laser micromachining of transparent glass using ultrafast Bessel beams
Zambon, Véronique; McCarthy, Nathalie; Piché, Michel
2009-06-01
We fabricated optical waveguides in fused silica by focusing femtosecond laser pulses with an axicon. With this technique, we also produced microholes by using chemical etching. The axicon, which is a conical lens, generates an optical beam with a transverse intensity profile that follows a zero-order Bessel function. Bessel beams produced by axicon focusing have a narrow focal line of a few micron width which is invariant along a long distance (>1 cm). By focusing femtosecond pulses with an axicon into fused silica, we induced permanent modifications over the extented focal line of the axicon without scanning axially the glass sample. The waveguides so fabricated exhibit low losses and no detectable birefringence due their excellent circular symmetry. By translating the glass sample during the inscription process, we have fabricated planar waveguides. Microfluidic channels were obtained by soaking the exposed samples into a HF solution.
Structural disorder correlation examined using the Fourier-Bessel technique
Gauthier, Robert C.
2015-11-01
The presence of structural disorder in a photonic crystal is examined through the rotational symmetry extracted from a Fourier-Bessel approach to solving Maxwell's wave equation in cylindrical space. A dielectric correlation function is proposed that relates the original structure to the disordered structure and when normalized it can be used to quantify the level of any disorder mechanism present. It is shown that the presence of disorder causes a mixing of localized and extended states and that the mixing can be directly attributed to "off diagonal" elements of the eigen-matrix and rotational symmetry breaking within the structure. The properties of disorder in an ordered structure are used to identify locations of local order in disordered structures. The Fourier-Bessel analysis of a disordered structure confirms the presence of localized light states at these sites.
Fourier-Bessel rotational invariant eigenimages.
Zhao, Zhizhen; Singer, Amit
2013-05-01
We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two-dimensional images and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by expanding each image, originally given on a Cartesian grid, in the Fourier-Bessel basis for the disk. Because the images are essentially band limited in the Fourier domain, we use a sampling criterion to truncate the Fourier-Bessel expansion such that the maximum amount of information is preserved without the effect of aliasing. The constructed covariance matrix is invariant to rotation and reflection and has a special block diagonal structure. PCA is efficiently done for each block separately. This Fourier-Bessel-based PCA detects more meaningful eigenimages and has improved denoising capability compared to traditional PCA for a finite number of noisy images.
Bessel beams with spatial oscillating polarization
Fu, Shiyao; Zhang, Shikun; Gao, Chunqing
2016-08-01
Bessel beams are widely used in optical metrology mainly because of their large Rayleigh range (focal length). Radial/azimuthal polarization of such beams is of interest in the fields of material processing, plasma absorption or communication. In this paper an experimental set-up is presented, which generates a Bessel-type vector beam with a spatial polarization, oscillating along the optical axis, when propagating in free space. A first holographic axicon (HA) HA1 produces a normal, linearly polarized Bessel beam, which by a second HA2 is converted into the spatial oscillating polarized beam. The theory is briefly discussed, the set-up and the experimental results are presented in detail.
Microwave bessel beams generation using guided modes
Salem, Mohamed
2011-06-01
A novel method is devised for Bessel beams generation in the microwave regime. The beam is decomposed in terms of a number of guided transverse electric modes of a metallic waveguide. Modal expansion coefficients are computed from the modal power orthogonality relation. Excitation is achieved by means of a number of inserted coaxial loop antennas, whose currents are calculated from the excitation coefficients of the guided modes. The efficiency of the method is evaluated and its feasibility is discussed. Obtained results can be utilized to practically realize microwave Bessel beam launchers. © 2006 IEEE.
Elliptic integral evaluations of Bessel moments
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Glasser, M.L.
2008-01-06
We record what is known about the closed forms for variousBessel function moments arising in quantum field theory, condensed mattertheory and other parts of mathematical physics. More generally, wedevelop formulae for integrals of products of six or fewer Besselfunctions. In consequence, we are able to discover and prove closed formsfor c(n,k) := Int_0 inf tk K_0 n(t) dt, with integers n = 1, 2, 3, 4 andk greater than or equal to 0, obtaining new results for the even momentsc3,2k and c4,2k . We also derive new closed forms for the odd momentss(n,2k+1) := Int_0 inf t(2k+1) I_0(t) K_0n(t) dt,with n = 3, 4 and fort(n,2k+1) := Int_0 inf t(2k+1) I_02(t) K_0(n-2) dt, with n = 5, relatingthe latter to Green functions on hexagonal, diamond and cubic lattices.We conjecture the values of s(5,2k+1), make substantial progress on theevaluation of c(5,2k+1), s(6,2k+1) and t(6,2k+1) and report more limitedprogress regarding c(5,2k), c(6,2k+1) and c(6,2k). In the process, weobtain 8 conjectural evaluations, each of which has been checked to 1200decimal places. One of these lies deep in 4-dimensional quantum fieldtheory and two are probably provable by delicate combinatorics. Thereremains a hard core of five conjectures whose proofs would be mostinstructive, to mathematicians and physicists alike.
REMARKS ON SUB-FRACTIONAL BESSEL PROCESSES
Institute of Scientific and Technical Information of China (English)
Shen Guangjun; Chen Chao; Yan Litan
2011-01-01
Let S={(S1t,… Sdt)}t≥o denote a d-dimensional sub-fractional Brownian motion with index H ≥ 1/2.In this paper we study some properties of the process X of the form Xt:=d-Σi=(j)toSis/RsdSiSs,d≥ 1,where Rt =（/）(St／1)2 +..+ (Std)2 is the sub-fractional Bessel process.
Nonparaxial accelerating Bessel-like beams
Chremmos, Ioannis D
2013-01-01
A new class of nonparaxial accelerating optical waves is introduced. These are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space. The concept expands on our previous proposal of paraxial accelerating Bessel-like beams to include beams with subwavelength lobes and/or large trajectory angles. Such waves are produced when the phase at the input plane is engineered so that the interfering ray cones are made to focus along the prespecified path. When the angle of these cones is fixed, the beams possess a diffraction-free Bessel profile on planes that stay normal to their trajectory, which can be considered as a generalized definition of diffractionless propagation in the nonparaxial regime. The analytical procedure leading to these results is based on a ray optics interpretation of Rayleigh-Sommerfeld diffraction and is presented in detail. The evolution of the proposed waves is demonstrated through a series of numerical...
Bessel's improved Kater pendulum in the teaching lab
Candela, D.; Martini, K. M.; Krotkov, R. V.; Langley, K. H.
2001-06-01
We describe a Bessel pendulum for use in the teaching laboratory, and measurements of the local acceleration of gravity made with it to an accuracy of better than one part in 104. The Bessel pendulum is a reversible pendulum that eliminates atmospheric corrections that apply to the more familiar Kater pendulum. The physical principles underlying the Kater pendulum as well as Bessel's refinement are reviewed, and construction details are given for a realization of the pendulum.
Study of Gaussian and Bessel beam propagation using a new analytic approach
Dartora, C. A.; Nobrega, K. Z.
2012-03-01
The main feature of Bessel beams realized in practice is their ability to resist diffractive effects over distances exceeding the usual diffraction length. The theory and experimental demonstration of such waves can be traced back to the seminal work of Durnin and co-workers already in 1987. Despite that fact, to the best of our knowledge, the study of propagation of apertured Bessel beams found no solution in closed analytic form and it often leads to the numerical evaluation of diffraction integrals, which can be very awkward. In the context of paraxial optics, wave propagation in lossless media is described by an equation similar to the non-relativistic Schrödinger equation of quantum mechanics, but replacing the time t in quantum mechanics by the longitudinal coordinate z. Thus, the same mathematical methods can be employed in both cases. Using Bessel functions of the first kind as basis functions in a Hilbert space, here we present a new approach where it is possible to expand the optical wave field in a series, allowing to obtain analytic expressions for the propagation of any given initial field distribution. To demonstrate the robustness of the method two cases were taken into account: Gaussian and zeroth-order Bessel beam propagation.
BESSEL FILTER AND CHAOS: THREE-IN-ONE ACTION
DEFF Research Database (Denmark)
Tamaševicius, Arunas; Mykolaitis, Gytis; Bumeliene, Skaidra;
2006-01-01
Low-pass active Bessel filters are proposed to be used in a chaotic oscillator. The Bessel unit plays the role of three-in-one: the delay line, the amplifier, and the filter. Results of Spice simulations and hardware experiments are presented.......Low-pass active Bessel filters are proposed to be used in a chaotic oscillator. The Bessel unit plays the role of three-in-one: the delay line, the amplifier, and the filter. Results of Spice simulations and hardware experiments are presented....
Near-Field Acoustic Resonance Scattering of a Finite Bessel Beam by an Elastic Sphere
Mitri, F G
2014-01-01
The near-field acoustic scattering from a sphere centered on the axis of a finite Bessel acoustic beam is derived stemming from the Rayleigh-Sommerfeld diffraction surface integral and the addition theorems for the spherical wave and Legendre functions. The beam emerges from a finite circular disk vibrating according to one of its radial modes corresponding to the fundamental solution of a Bessel beam J0. The incident pressure field's expression is derived analytically as a partial-wave series expansion taking into account the finite size and the distance from the center of the disk transducer. Initially, the scattered pressure by a rigid sphere is evaluated, and backscattering pressure moduli plots as well as 3-D directivity patterns for an elastic PMMA sphere centered on a finite Bessel beam with appropriate tuning of its half-cone angle, reveal possible resonance suppression of the sphere only in the zone near the Bessel transducer. Moreover, the analysis is extended to derive the mean spatial incident and...
Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid
Mitri, F. G.
2015-12-01
Partial-wave series representation of the acoustic scattering field of high-order Bessel vortex beams by rigid oblate and prolate spheroids using the modal matching method is developed. The method, which is applicable to slightly elongated objects at low-to-moderate frequencies, requires solving a system of linear equations which depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated partial-wave series expansions (PWSEs), and satisfying the Neumann boundary condition for a rigid immovable surface in the least-squares sense. This original semi-analytical approach developed for Bessel vortex beams is demonstrated for finite oblate and prolate spheroids, where the mathematical functions describing the spheroidal geometry are written in a form involving single angular (polar) integrals that are numerically computed. The transverse (θ = π / 2) and 3D scattering directivity patterns are evaluated in the far-field for both prolate and oblate spheroids, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid) not exceeding 3:1, the half-cone angle β and order m of the Bessel vortex beam, as well as the dimensionless size parameter kr0. Periodic oscillations in the magnitude plots of the far-field scattering form function are observed, which result from the interference of the reflected waves with the circumferential (Franz') waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3D directivity patterns illustrate the far-field scattering from the spheroid, that vanishes in the forward (θ = 0) and backward (θ = π) directions. Particular applications in underwater acoustics and scattering, acoustic levitation and the detection of submerged elongated objects using Bessel vortex waves to name a few, would benefit from the results of the present investigation.
Efficient Generation of Truncated Bessel Beams using Cylindrical Waveguides
Ilchenko, Vladimir S.; Mohageg, Makan; Savchenkov, Anatoliy A.; Matsko, Andrey B.; Maleki, Lute
2007-01-01
In this paper we address efficient conversion between a Gaussian beam (a truncated plane wave) and a truncated Bessel beam of agiven order, using cylindrical optical waveguides and whispering gallery mode resonators. Utilizing a generator based on waveguides combined with whispering gallery mode resonators, we have realized Bessel beams of the order of 200 with a conversion efficiency exceeding 10 %.
Second-harmonic generation with Bessel beams
Shatrovoy, Oleg
We present the results of a numerical simulation tool for modeling the second-harmonic generation (SHG) interaction experienced by a diffracting beam. This code is used to study the simultaneous frequency and spatial profile conversion of a truncated Bessel beam that closely resembles a higher-order mode (HOM) of an optical fiber. SHG with Bessel beams has been investigated in the past and was determined have limited value because it is less efficient than SHG with a Gaussian beam in the undepleted pump regime. This thesis considers, for the first time to the best of our knowledge, whether most of the power from a Bessel-like beam could be converted into a second-harmonic beam (full depletion), as is the case with a Gaussian beam. We study this problem because using HOMs for fiber lasers and amplifiers allows reduced optical intensities, which mitigates nonlinearities, and is one possible way to increase the available output powers of fiber laser systems. The chief disadvantage of using HOM fiber amplifiers is the spatial profile of the output, but this can be transformed as part of the SHG interaction, most notably to a quasi-Gaussian profile when the phase mismatch meets the noncollinear criteria. We predict, based on numerical simulation, that noncollinear SHG (NC-SHG) can simultaneously perform highly efficient (90%) wavelength conversion from 1064 nm to 532 nm, as well as concurrent mode transformation from a truncated Bessel beam to a Gaussian-like beam (94% overlap with a Gaussian) at modest input powers (250 W, peak power or continuous-wave operation). These simulated results reveal two attractive features -- the feasibility of efficiently converting HOMs of fibers into Gaussian-like beams, and the ability to simultaneously perform frequency conversion. Combining the high powers that are possible with HOM fiber amplifiers with access to non-traditional wavelengths may offer significant advantages over the state of the art for many important applications
Kaiser-Bessel Basis for the Particle-Mesh Interpolation
Gao, Xingyu; Wang, Han
2016-01-01
In this work, we introduce the Kaiser-Bessel interpolation basis for the particle-mesh interpolation in the fast Ewald method. A reliable a priori error estimate is developed to measure the accuracy of the force computation, and is shown to be effective in optimizing the shape parameter of the Kaiser-Bessel basis in terms of accuracy. By comparing the optimized Kaiser-Bessel basis with the traditional B-spline basis, we demonstrate that the former is more accurate than the latter in part of the working parameter space, saying a relatively small real space cutoff, a relatively small reciprocal space mesh and a relatively large truncation of basis. In some cases, the Kaiser-Bessel basis is found to be more than one order of magnitude more accurate. Therefore, it is worth trying the Kaiser-Bessel basis in the simulations where the computational accuracy of the electrostatic interaction is critical.
Nanolithography using Bessel Beams of Extreme Ultraviolet Wavelength
Fan, Daniel; Wang, Li; Ekinci, Yasin
2016-08-01
Bessel beams are nondiffracting light beams with large depth-of-focus and self-healing properties, making them suitable as a serial beam writing tool over surfaces with arbitrary topography. This property breaks the inherent resolution vs. depth-of-focus tradeoff of photolithography. One approach for their formation is to use circularly symmetric diffraction gratings. Such a ring grating was designed and fabricated for the extreme ultraviolet (EUV) wavelength of 13.5 nm, a candidate wavelength for future industrial lithography. Exposure of the aerial images showed that a Bessel beam with an approximately 1 mm long z-invariant central core of 223 nm diameter had been achieved, in good agreement with theory. Arbitrary patterns were written using the Bessel spot, demonstrating possible future application of Bessel beams for serial beam writing. Lithographic marks of ~30 nm size were also observed using a high resolution Bessel beam.
Institute of Scientific and Technical Information of China (English)
O.B. Awojoyogbe; O.M. Dada
2013-01-01
Bloch方程是NMR/MRI计算、模拟和实验的基础，但通常在不加特定的绝热和非绝热条件的前提下获得Bloch流动方程的解析解是非常困难的。流动方程的一般解析解可以为理解NMR/MRI的基本概念提供额外的信息，而又不需要通常的指数方程。作者的目的是通过贝塞尔函数及其特性得到与时间无关的NMR流动方程的解析解。在不需要主观添加弥散项的前提下利用贝塞尔函数及其特性从NMR流动方程中获得了Stejskal-Tanner公式。这证实了弥散是Bloch流动方程的内在属性并可以通过如贝塞尔函数的适当数学函数提取出来。从解析解得到的非高斯行为的弥散信号在如脑白质的各项异性组织环境中是非常有意义的。发现弥散系数是与T1和T2弛豫参数直接相关的，因此通过对大量已有的贝塞尔函数进行合适利用可以在四个分离的缓存内采集MRI信号(实部和虚部，相位和绝对值)。能够利用MRI监测药物对于不同组织尤其是脑部功能活动的效果。%Bloch NMR equations are fundamental to all NMR/MRI computations, simulations and experiments. It has been very difficult to solve the Bloch NMR flow equations analytically without imposing specific adiabatic and non adiabatic conditions. General analytical solutions of the flow equations can easily provide additional information to understand the basic concept of NMR/MRI without the usual exponential functions. The goal of this report is to present analytical solutions to the time independent NMR lfow equation using the Bessel functions and properties. We derived the Stejskal-Tanner formula from the NMR lfow equations using the Bessel functions and properties without the need to arbitrarily add the diffusion term. This confirms that diffusion is an intrinsic property embedded in the Bloch NMR flow equation and can be extracted by the use of appropriate mathematical functions such as Bessel functions and
Spatial-temporal dynamics of broadband terahertz Bessel beam propagation
Semenova, V. A.; Kulya, M. S.; Bespalov, V. G.
2016-08-01
The unique properties of narrowband and broadband terahertz Bessel beams have led to a number of their applications in different fields, for example, for the depth of focusing and resolution enhancement in terahertz imaging. However, broadband terahertz Bessel beams can probably be also used for the diffraction minimization in the short-range broadband terahertz communications. For this purpose, the study of spatial-temporal dynamics of the broadband terahertz Bessel beams is needed. Here we present a simulation-based study of the propagating in non-dispersive medium broadband Bessel beams generated by a conical axicon lens. The algorithm based on scalar diffraction theory was used to obtain the spatial amplitude and phase distributions of the Bessel beam in the frequency range from 0.1 to 3 THz at the distances 10-200 mm from the axicon. Bessel beam field is studied for the different spectral components of the initial pulse. The simulation results show that for the given parameters of the axicon lens one can obtain the Gauss-Bessel beam generation in the spectral range from 0.1 to 3 THz. The length of non-diffraction propagation for a different spectral components was measured, and it was shown that for all spectral components of the initial pulse this length is about 130 mm.
Behavior of obliquely incident vector Bessel beams at planar interfaces
Salem, Mohamed
2013-01-01
We investigate the behavior of full-vector electromagnetic Bessel beams obliquely incident at an interface between two electrically different media. We employ a Fourier transform domain representation of Bessel beams to determine their behavior upon reflection and transmission. This transform, which is geometric in nature, consists of elliptical support curves with complex weighting associated with them. The behavior of the scattered field at an interface is highly complex, owing to its full-vector nature; nevertheless, this behavior has a straightforward representation in the transform domain geometry. The analysis shows that the reflected field forms a different vector Bessel beam, but in general, the transmitted field cannot be represented as a Bessel beam. Nevertheless, using this approach, we demonstrate a method to propagate a Bessel beam in the refractive medium by launching a non- Bessel beam at the interface. Several interesting phenomena related to the behavior of Bessel beams are illustrated, such as polarized reflection at Brewster\\'s angle incidence, and the Goos-Hänchen and Imbert-Federov shifts in the case of total reflection. © 2013 Optical Society of America.
Melchert, O; Roth, B
2016-01-01
We discuss efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform (dFBT) as numerical tools to assist in the 2D polar convolution of two radially symmetric functions, relevant, e.g., to applications in computational biophotonics. In our survey of the numerical procedure we account for the circumstance that the objective function might result from a more complex measurement process and is, in the worst case, known on a finite sequence of coordinate values, only. We contrast the performance of the resulting algorithms with a procedure based on a straight forward numerical quadrature of the underlying integral transform and asses its efficienty for two benchmark Fourier-Bessel pairs. An application to the problem of finite-size beam-shape convolution in polar coordinates, relevant in the context of tissue optics and optoacoustics, is used to illustrate the versatility and computational efficiency of the numerical procedure.
Acoustic Bessel-like beam formation by an axisymmetric grating
Jiménez, N.; Romero-García, V.; Picó, R.; Cebrecos, A.; Sánchez-Morcillo, V. J.; Garcia-Raffi, L. M.; Sánchez-Pérez, J. V.; Staliunas, K.
2014-04-01
We report Bessel-like beam formation of acoustic waves by means of an axisymmetric grating of rigid tori. The results show that the generated beam pattern is similar to that of Bessel beams, characterized by elongated non-diffracting focal spots. A multiple foci structure is observed, due to the finite size of the lens. The dependence of the focal distance on the frequency is also discussed, on the basis of an extended grating theory. Experimental validation of acoustic Bessel-like beam formation is also reported for sound waves. The results can be generalized to wave beams of different nature, as optical or matter waves.
Comments on "Slowing of Bessel light beam group velocity"
Saari, Peeter
2016-01-01
In a recent article [R. R. Alfano and D. A. Nolan, Opt. Commun. 361 (2016) 25] the group velocity reduction below the speed of light in the case of certain Bessel beam pulses has been considered and an idea of its application for a natural optical buffer presented. However, the authors treat the problem as if only one type of Bessel pulse existed, no matter how it is generated. The deficiencies of the article stem from not being familiar with an extensive literature on Bessel pulses, in particular, with a couple of papers published much earlier in the J. Opt. Soc. Am. A, which have studied exactly the same problem more thoroughly.
Higher-order harmonics of general limited diffraction Bessel beams
Ding, De-Sheng; Huang, Jin-Huang
2016-12-01
In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).
Millijoule femtosecond micro-Bessel beams for ultra-high aspect ratio machining.
Mitra, Sambit; Chanal, Margaux; Clady, Raphaël; Mouskeftaras, Alexandros; Grojo, David
2015-08-20
We report on a functional experimental design for Bessel beam generation capable of handling high-energy ultrashort pulses (up to 1.2 mJ per pulse of 50 fs duration). This allows us to deliver intensities exceeding the breakdown threshold for air or any dielectric along controlled micro-filaments with lengths exceeding 4 mm. It represents an unprecedented upscaling in comparison to recent femtosecond Bessel beam micromachining experiments. We produce void microchannels through glass substrates to demonstrate that aspect ratios exceeding 1200∶1 can be achieved by using single high-intensity pulses. This demonstration must lead to new methodologies for deep-drilling and high-speed cutting applications.
Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid
Mitri, F G
2015-01-01
Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (\\theta = \\pi) in the near-field and the backscattering form function in the far-field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam \\beta, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) due to the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigati...
Second-Harmonic Generation of Bessel Beams in Lossy Media
Institute of Scientific and Technical Information of China (English)
丁德胜; 许坚毅; 王耀俊
2002-01-01
We present a further analysis for the second-harmonic generation of Bessel beams in lossy media. The emphasis is put on the effect of absorption to the radial pattern of the second-harmonic beam. It is shown that within the absorption length of the second harmonic, the Bessel second-harmonic beam approaches limited diffraction in the radial direction and behaves as in the case of lossless media.
Long-distance Bessel beam propagation through Kolmogorov turbulence.
Birch, Philip; Ituen, Iniabasi; Young, Rupert; Chatwin, Chris
2015-11-01
Free-space optical communication has the potential to transmit information with both high speed and security. However, since it is unguided it suffers from losses due to atmospheric turbulence and diffraction. To overcome the diffraction limits the long-distance propagation of Bessel beams is considered and compared against Gaussian beam properties. Bessel beams are shown to have a number of benefits over Gaussian beams when propagating through atmospheric turbulence.
Generation and application of bessel beams in electron microscopy
Energy Technology Data Exchange (ETDEWEB)
Grillo, Vincenzo, E-mail: vincenzo.grillo@cnr.it [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); CNR-IMEM, Parco Area delle Scienze 37/A, I-43124 Parma (Italy); Harris, Jérémie [Department of Physics, University of Ottawa, 25 Templeton St., Ottawa, Ontario, Canada K1N 6N5 (Canada); Gazzadi, Gian Carlo [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); Balboni, Roberto [CNR-IMM Bologna, Via P. Gobetti 101, 40129 Bologna (Italy); Mafakheri, Erfan [Dipartimento di Fisica Informatica e Matematica, Università di Modena e Reggio Emilia, via G Campi 213/a, I-41125 Modena (Italy); Dennis, Mark R. [H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL (United Kingdom); Frabboni, Stefano [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); Dipartimento di Fisica Informatica e Matematica, Università di Modena e Reggio Emilia, via G Campi 213/a, I-41125 Modena (Italy); Boyd, Robert W.; Karimi, Ebrahim [Department of Physics, University of Ottawa, 25 Templeton St., Ottawa, Ontario, Canada K1N 6N5 (Canada)
2016-07-15
We report a systematic treatment of the holographic generation of electron Bessel beams, with a view to applications in electron microscopy. We describe in detail the theory underlying hologram patterning, as well as the actual electron-optical configuration used experimentally. We show that by optimizing our nanofabrication recipe, electron Bessel beams can be generated with relative efficiencies reaching 37±3%. We also demonstrate by tuning various hologram parameters that electron Bessel beams can be produced with many visible rings, making them ideal for interferometric applications, or in more highly localized forms with fewer rings, more suitable for imaging. We describe the settings required to tune beam localization in this way, and explore beam and hologram configurations that allow the convergences and topological charges of electron Bessel beams to be controlled. We also characterize the phase structure of the Bessel beams generated with our technique, using a simulation procedure that accounts for imperfections in the hologram manufacturing process. - Highlights: • Bessel beams with different convergence, topological charge, visible fringes are demonstrated. • The relation between the Fresnel hologram and the probe shape is explained by detailed calculations and experiments. • Among the holograms here presented the highest relative efficiency is 37%, the best result ever reached for blazed holograms.
Wireless Links in the Radiative Near Field via Bessel Beams
Heebl, Jason D.; Ettorre, Mauro; Grbic, Anthony
2016-09-01
The generation of propagating Bessel beams is typically limited to optical frequencies with bulky experimental setups. Recent works have demonstrated Bessel-beam generation at microwave and millimeter-wave frequencies utilizing low-profile, planar, leaky-wave antennas. These studies have assumed a single leaky mode in the antenna. In this work, the rigorous analysis of a planar Bessel-beam launcher supporting multiple modes is presented. By employing the mode-matching technique, a complete electromagnetic solution of the structure, its supported modes, and radiated fields is obtained. Additionally, a coupled system of two planar Bessel launchers is analyzed, and it is shown that the system can both transmit and receive Bessel beams. The energy-transfer characteristics of the coupled system are analyzed and discussed. An analysis of the coupled system's even and odd modes of operation show that efficient power transfer is possible, and that an odd mode is preferred since it yields higher field confinement and power-transfer efficiency.
Indian Academy of Sciences (India)
Hüseyin Yildirim; M Zeki Sarikaya; Sermin Öztürk
2004-11-01
In this article, the operator $\\Diamond^k_B$ is introduced and named as the Bessel diamond operator iterated times and is defined by $$\\Diamond^k_B=[(B_{x_1}+B_{x_2}+\\cdots +B_{x_p})^2-(B_{x_{p+1}}+\\cdots +B_{x_{p+q}})^2]^k,$$ where $p + q = n, B_{x_i} = \\frac{^2}{ x^2_i}+\\frac{2_i}{x_i}\\frac{}{ x_i}$, where $2_i = 2_i + 1, _i > - \\frac{1}{2} [8], x_i > 0, i = 1, 2,\\ldots ,n, k$ is a non-negative integer and is the dimension of $\\mathbb{R}^+_n$. In this work we study the elementary solution of the Bessel diamond operator and the elementary solution of the operator $\\Diamond^k_B$ is called the Bessel diamond kernel of Riesz. Then, we study the Fourier–Bessel transform of the elementary solution and also the Fourier–Bessel transform of their convolution.
Bessel beam fluorescence lifetime tomography of live embryos (Conference Presentation)
Xu, Dongli; Peng, Leilei
2016-03-01
Optical tomography allows isotropic 3D imaging of embryos. Scanning-laser optical tomography (SLOT) has superior light collecting efficiency than wide-field optical tomography, making it ideal for fluorescence imaging of live embryos. We previously reported an imaging system that combines SLOT with a novel Fourier-multiplexed fluorescence lifetime imaging (FmFLIM) technique named FmFLIM-SLOT. FmFLIM-SLOT performs multiplexed FLIM-FRET readout of multiple FRET sensors in live embryos. Here we report a recent effort on improving the spatial resolution of the FmFLIM-SLOT system in order to image complex biochemical processes in live embryos at the cellular level. Optical tomography has to compromise between resolution and the depth of view. In SLOT, the commonly-used focused Gaussian beam diverges quickly from the focal plane, making it impossible to achieve high resolution imaging in a large volume specimen. We thus introduce Bessel beam laser-scanning tomography, which illuminates the sample with a spatial-light-modulator-generated Bessel beam that has an extended focal depth. The Bessel beam is scanned across the whole specimen. Fluorescence projection images are acquired at equal angular intervals as the sample rotates. Reconstruction artifacts due to annular-rings of the Bessel beam are removed by a modified 3D filtered back projection algorithm. Furthermore, in combination of Fourier-multiplexing fluorescence lifetime imaging (FmFLIM) method, the Bessel FmFLIM-SLOT system is capable of perform 3D lifetime imaging of live embryos at cellular resolution. The system is applied to in-vivo imaging of transgenic Zebrafish embryos. Results prove that Bessel FmFLIM-SLOT is a promising imaging method in development biology research.
Practical realization of a microwave Bessel beam launcher
Manzhura, Oksana
2011-08-01
An experimental setup is realized to practically generate Bessel beams in the microwave regime. The setup, which consists of a series of circular loop antennas inserted coaxially inside a circular metallic waveguide, excites the waveguide\\'s transverse-electric modes such that their superposition forms a Bessel beam at the open-end of the waveguide. The excitation currents are calculated from the needed excitation coefficients of each guided mode, which, in turn, are calculated from the modal decomposition of the beam. The efficiency of the setup is evaluated and the obtained experimental results are compared to the theoretical estimates. © 2011 IEEE.
Two-photon flow cytometer with laser scanning Bessel beams
Wang, Yongdong; Ding, Yu; Ray, Supriyo; Paez, Aurelio; Xiao, Chuan; Li, Chunqiang
2016-03-01
Flow cytometry is an important technique in biomedical discovery for cell counting, cell sorting and biomarker detection. In vivo flow cytometers, based on one-photon or two-photon excited fluorescence, have been developed for more than a decade. One drawback of laser beam scanning two-photon flow cytometer is that the two-photon excitation volume is fairly small due to the short Rayleigh range of a focused Gaussian beam. Hence, the sampling volume is much smaller than one-photon flow cytometry, which makes it challenging to count or detect rare circulating cells in vivo. Bessel beams have narrow intensity profiles with an effective spot size (FWHM) as small as several wavelengths, making them comparable to Gaussian beams. More significantly, the theoretical depth of field (propagation distance without diffraction) can be infinite, making it an ideal solution as a light source for scanning beam flow cytometry. The trade-off of using Bessel beams rather than a Gaussian beam is the fact that Bessel beams have small concentric side rings that contribute to background noise. Two-photon excitation can reduce this noise, as the excitation efficiency is proportional to intensity squared. Therefore, we developed a two-photon flow cytometer using scanned Bessel beams to form a light sheet that intersects the micro fluidic channel.
Polarization properties of linearly polarized parabolic scaling Bessel beams
Guo, Mengwen; Zhao, Daomu
2016-10-01
The intensity profiles for the dominant polarization, cross polarization, and longitudinal components of modified parabolic scaling Bessel beams with linear polarization are investigated theoretically. The transverse intensity distributions of the three electric components are intimately connected to the topological charge. In particular, the intensity patterns of the cross polarization and longitudinal components near the apodization plane reflect the sign of the topological charge.
Elliptic Bessel processes and elliptic Dyson models realized as temporally inhomogeneous processes
Katori, Makoto
2016-10-01
The Bessel process with parameter D > 1 and the Dyson model of interacting Brownian motions with coupling constant β > 0 are extended to the processes in which the drift term and the interaction terms are given by the logarithmic derivatives of Jacobi's theta functions. They are called the elliptic Bessel process, eBES(D), and the elliptic Dyson model, eDYS(β), respectively. Both are realized on the circumference of a circle [0, 2πr) with radius r > 0 as temporally inhomogeneous processes defined in a finite time interval [0, t∗), t∗ < ∞. Transformations of them to Schrödinger-type equations with time-dependent potentials lead us to proving that eBES(D) and eDYS(β) can be constructed as the time-dependent Girsanov transformations of Brownian motions. In the special cases where D = 3 and β = 2, observables of the processes are defined and the processes are represented for them using the Brownian paths winding round a circle and pinned at time t∗. We show that eDYS(2) has the determinantal martingale representation for any observable. Then it is proved that eDYS(2) is determinantal for all observables for any finite initial configuration without multiple points. Determinantal processes are stochastic integrable systems in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single continuous function called the spatio-temporal correlation kernel.
Hitting time for Bessel processes - walk on moving spheres algorithm
Deaconu, Madalina
2011-01-01
In this article we investigate the hitting time of some given boundaries for Bessel processes. The main motivation is coming from mathematical finance when dealing with volatility models but the results can also be used in optimal control problems. The aim is here to construct a new and efficient algorithm in order to approach this hitting time. As an application we will consider the hitting time of a given level for the Cox-Ingersoll-Ross process. The main tools we use are on one side an adaptation of the method of images to this particular situation and on the other side the connection existing between Cox-Ingersoll-Ross processes and Bessel processes.
Controllable light capsules employing modified Bessel-Gauss beams
Gong, Lei; Zhao, Qian; Ren, Yuxuan; Qiu, Xingze; Zhong, Mincheng; Li, Yinmei
2016-01-01
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 rou...
Fabrication of microchannels in fused silica using femtosecond Bessel beams
Energy Technology Data Exchange (ETDEWEB)
Yashunin, D. A., E-mail: yashuninda@yandex.ru [Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov Str., Nizhny Novgorod 603950 (Russian Federation); Nizhny Novgorod State Technical University, 24 Minin St., Nizhny Novgorod 603950 (Russian Federation); Malkov, Yu. A. [Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov Str., Nizhny Novgorod 603950 (Russian Federation); Mochalov, L. A.; Stepanov, A. N. [Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov Str., Nizhny Novgorod 603950 (Russian Federation); Nizhny Novgorod State Technical University, 24 Minin St., Nizhny Novgorod 603950 (Russian Federation); Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., Nizhny Novgorod 603950 (Russian Federation)
2015-09-07
Extended birefringent waveguiding microchannels up to 15 mm long were created inside fused silica by single-pulse irradiation with femtosecond Bessel beams. The birefringent refractive index change of 2–4 × 10{sup −4} is attributed to residual mechanical stress. The microchannels were chemically etched in KOH solution to produce 15 mm long microcapillaries with smooth walls and a high aspect ratio of 1:250. Bessel beams provide higher speed of material processing compared to conventional multipulse femtosecond laser micromachining techniques and permit simple control of the optical axis direction of the birefringent waveguides, which is important for practical applications [Corrielli et al., “Rotated waveplates in integrated waveguide optics,” Nat. Commun. 5, 4249 (2014)].
Yuan, Yangsheng; Lei, Ting; Li, Zhaohui; Li, Yangjin; Gao, Shecheng; Xie, Zhenwei; Yuan, Xiaocong
2017-02-01
Optical beam wander is one of the most important issues for free-space optical (FSO) communication. We theoretically derive a beam wander model for Bessel beams propagating in turbulent atmosphere. The calculated beam wander of high order Bessel beams with different turbulence strengths are consistent with experimental measurements. Both theoretical and experimental results reveal that high order Bessel beams are less influenced by the turbulent atmosphere. We also demonstrate the Bessel beams based orbital angular momentum (OAM) multiplexing/demultiplexing in FSO communication with atmospheric turbulence. Under the same atmospheric turbulence condition, the bit error rates of transmitted signals carried by high order Bessel beams show smaller values and fluctuations, which indicates that the high order Bessel beams have an advantage of mitigating the beam wander in OAM multiplexing FSO communication.
On a nonorthogonal polynomial sequence associated with Bessel operator
Loureiro, Ana F; Yakubovich, S
2011-01-01
By means of the Bessel operator a polynomial sequence is constructed to which several properties are given. Among them, its explicit expression, the connection with the Euler numbers, its integral representation via the Kontorovich-Lebedev transform. Despite its non-orthogonality, it is possible to associate to the canonical element of its dual sequence a positive-definite measure as long as certain stronger constraints are imposed.
Extensions of Bessel sequences to dual pairs of frames
DEFF Research Database (Denmark)
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2013-01-01
Tight frames in Hilbert spaces have been studied intensively for the past years. In this paper we demonstrate that it often is an advantage to use pairs of dual frames rather than tight frames. We show that in any separable Hilbert space, any pairs of Bessel sequences can be extended to a pair of...... be extended to a pair of dual frames. © 2012 Elsevier Inc. All rights reserved....
Role of free carriers excited by ultrafast Bessel beams for submicron structuring applications
Velpula, Praveen Kumar; Bhuyan, Manoj Kumar; Mauclair, Cyril; Colombier, Jean-Philippe; Stoian, Razvan
2014-07-01
Ultrafast Bessel beams are ideal sources for high aspect ratio submicron structuring applications because of their nondiffracting nature and higher stability in nonlinear propagation. We report here on the interaction of ultrafast Bessel beams at various laser energies and pulse durations with transparent materials (fused silica) and define their impact on photoinscription regimes, i.e., formation of positive and negative refractive index structures. The laser pulse duration was observed to be key in deciding the type of the structures via excitation efficiency. To understand the relevant mechanisms for forming these different structures, the free carrier behavior as a function of laser pulse duration and energy was studied by capturing instantaneous excitation profiles using time-resolved microscopy. Time-resolved imaging and simulation studies reveal that low carrier densities are generated for ultrashort pulses, leading to soft positive index alterations via presumably nonthermally induced structural transitions involving defects. On the other hand, the high free carrier density generation in the case of longer pulse durations leads to hydrodynamic expansion, resulting in high aspect ratio submicron-size wide voids. Delayed ionization, carrier defocusing, and lower nonlinear effects are responsible for the confinement of energy, resulting in efficient energy deposition on-axis.
Helicon waves in uniform plasmas. IV. Bessel beams, Gendrin beams, and helicons
Urrutia, J. M.; Stenzel, R. L.
2016-05-01
Electromagnetic waves in the low frequency whistler mode regime are investigated experimentally and by digital data superposition. The radiation from a novel circular antenna array is shown to produce highly collimated helicon beams in a uniform unbounded plasma. The differences to Bessel beams in free space are remarked upon. Low divergence beams arise from the parallel group velocity of whistlers with phase velocity either along the guide field or at the Gendrin angle. Waves with angular momentum are produced by phasing the array in the circular direction. The differences in the field topologies for positive and negative modes numbers are shown. It is also shown that in uniform plasmas, the radial amplitude profile of the waves depends on the antenna field topology. Thus, there are no helicon "eigenmodes" with radial Bessel function profiles in uniform plasmas. It is pointed out that phase measurements in helicon devices indicate radial wave propagation which is inconsistent with helicon eigenmode theory based on paraxial wave propagation. Trivelpiece-Gould modes also exist in uniform unbounded plasmas.
Elliptic Bessel processes and elliptic Dyson models realized as temporally inhomogeneous processes
Katori, Makoto
2016-01-01
The Bessel process with parameter $D>1$ and the Dyson model of interacting Brownian motions with coupling constant $\\beta >0$ are extended to the processes, in which the drift term and the interaction terms are given by the logarithmic derivatives of Jacobi's theta functions. They are called the elliptic Bessel process, eBES$^{(D)}$, and the elliptic Dyson model, eDYS$^{(\\beta)}$, respectively. Both are realized on the circumference of a circle $[0, 2 \\pi r)$ with radius $r >0$ as temporally inhomogeneous processes defined in a finite time interval $[0, t_*), t_* < \\infty$. Transformations of them to Schr\\"odinger-type equations with time-dependent potentials lead us to proving that eBES$^{(D)}$ and eDYS$^{(\\beta)}$ can be constructed as the time-dependent Girsanov transformations of Brownian motions. In the special cases where $D=3$ and $\\beta=2$, observables of the processes are defined and the processes are represented for them using the Brownian paths winding round a circle and pinned at time $t_*$. We...
Adaptive Bessel-autocorrelation of ultrashort pulses with phase-only spatial light modulators
Huferath-von Luepke, Silke; Bock, Martin; Grunwald, Ruediger
2009-06-01
Recently, we proposed a new approach of a noncollinear correlation technique for ultrashort-pulsed coherent optical signals which was referred to as Bessel-autocorrelator (BAC). The BAC-principle combines the advantages of Bessellike nondiffracting beams like stable propagation, angular robustness and self-reconstruction with the principle of temporal autocorrelation. In comparison to other phase-sensitive measuring techniques, autocorrelation is most straightforward and time-effective because of non-iterative data processing. The analysis of nonlinearly converted fringe patterns of pulsed Bessel-like beams reveals their temporal signature from details of fringe envelopes. By splitting the beams with axicon arrays into multiple sub-beams, transversal resolution is approximated. Here we report on adaptive implementations of BACs with improved phase resolution realized by phase-only liquid-crystal-on-silicon spatial light modulators (LCoS-SLMs). Programming microaxicon phase functions in gray value maps enables for a flexible variation of phase and geometry. Experiments on the diagnostics of few-cycle pulses emitted by a mode-locked Ti:sapphire laser oscillator at wavelengths around 800 nm with 2D-BAC and angular tuned BAC were performed. All-optical phase shift BAC and fringe free BAC approaches are discussed.
Efficient Coupler for a Bessel Beam Dispersive Element
Savchenkov, Anatoliy; Iltchenko, Vladimir; Matsko, Andrey; Le, Thanh; Yu, nan; Maleki, Lute
2008-01-01
A document discusses overcoming efficient optical coupling to high orbital momentum modes by slightly bending the taper dispersive element. This little shape distortion is not enough to scramble the modes, but it allows the use of regular, free-beam prism coupling, fiber coupling, or planar fiber on-chip coupling with, ultimately, 100 percent efficiency. The Bessel-beam waveguide is bent near the contact with the coupler, or a curved coupler is used. In this case, every Bessel-beam mode can be successfully coupled to a collimated Gaussian beam. Recently developed Bessel-beam waveguides allow long optical delay and very high dispersion. Delay values may vary from nanoseconds to microseconds, and dispersion promises to be at 100 s/nm. Optical setup consisted of a red laser, an anamorphic prism pair, two prism couplers, and a bent, single-mode fiber attached to prisms. The coupling rate increased substantially and corresponded to the value determined by the anamorphic prism pair.
Seipt, D; Surzhykov, A; Fritzsche, S
2016-01-01
The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultra-violet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target (atoms) with regard to the beam axis. In addition, analogue to the circular dichroism in typical two-color ATI experiments with circularly polarized light, we define and discuss seven different dichroism signals for such vortex Bessel beams that arise from the various combinations of the orbital and spin angular momenta of the two light fields. For localized targets, it is found that these dichroism signals strongly depend on the size and position of t...
Deniz, Coşkun
2017-01-01
Common recipe for the lengthening pendulum (LP) involves some change of variables to give a relationship with the Bessel's equation. In this work, conventional semiclassical JWKB solution (named after Jeffreys, Wentzel, Kramers and Brillouin) of the LP is being obtained by first transforming the related Bessel's equation into the normal form `via the suggested change of independent variable'. JWKB approximation of the first-order Bessel functions ( ν=1) of both types along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders ( ν=0 and 2) by the recursion relations. The required initial values are also being studied and a quantization rule regarding the experimental LP parameters is being determined. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is slow, JWKB solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined by the JWKB applicability criterion given in the literature. As a result, the semiclassical JWKB method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully.
Terahertz imaging system based on bessel beams via 3D printed axicons at 100GHz
Liu, Changming; Wei, Xuli; Zhang, Zhongqi; Wang, Kejia; Yang, Zhenggang; Liu, Jinsong
2014-11-01
Terahertz (THz) imaging technology shows great advantage in nondestructive detection (NDT), since many optical opaque materials are transparent to THz waves. In this paper, we design and fabricate dielectric axicons to generate zeroth order-Bessel beams by 3D printing technology. We further present an all-electric THz imaging system using the generated Bessel beams in 100GHz. Resolution targets made of printed circuit board are imaged, and the results clearly show the extended depth of focus of Bessel beam, indicating the promise of Bessel beam for the THz NDT.
From amorphous speckle pattern to reconfigurable Bessel beam via wavefront shaping
Di Battista, Diego; Leonetti, Marco; Zacharakis, Giannis
2015-01-01
Bessel beams are non-diffracting light structures, which can be produced with simple tabletop optical elements such as axicon lenses or ring spatial filters and coherent laser beams. One of their main characteristic is that Bessel beams maintain their spatial characteristics after meters of propagation. In this paper we demonstrate a system and method for generating Bessel beams from amorphous speckle patterns, exploiting adaptive optimization by a spatial light modulator. These speckles are generated by light modes transmitted through a scattering curtain and selected by a ring shaped filter. With the proposed strategy it is possible to produce at user defined positions, reconfigurable, non-diffracting Bessel beams through a disordered medium.
Electromagnetic scattering of a vector Bessel beam in the presence of an impedance cone
Salem, Mohamed
2013-07-01
The electromagnetic field scattering of a vector Bessel beam in the presence of an infinite circular cone with an impedance boundary on its surface is considered. The impinging field is normal to the tip of the cone and is expanded in terms of vector spherical wave functions; a Kontorovich-Lebedev (KL) transform is employed to expand the scattered fields. The problem is reduced to a singular integral equation with a variable coefficient of the non-convolution type. The singularities of the spectral function are deduced and representations for the field at the tip of the cone as well as other regions are given together with the conditions of validity of these representations. © 2013 IEEE.
S^{2}-imaging of Bessel-like Beams
DEFF Research Database (Denmark)
Ingerslev, Kasper; Israelsen, Stine Møller; Rottwitt, Karsten
Bessel-like beams generated in a double cladding fiber are characterized for the first time using S2-imaging. The wavelength independence across the beam is examined numerically.......Bessel-like beams generated in a double cladding fiber are characterized for the first time using S2-imaging. The wavelength independence across the beam is examined numerically....
Herz-type Sobolev and Bessel potential spaces and their applications
Institute of Scientific and Technical Information of China (English)
陆善镇; 杨大春
1997-01-01
The Herz-type Sobolev spaces are introduced and the Sobolev theorem is established. The Herz-type Bessel potential spaces and the relation between the Herz-type Sobolev spaces and Bessel potential spaces are discussed. As applications of these theories, some regularity results of nonlinear quantities appearing in the compensated compactness theory on Herz-type Hardy spaces are given.
Bessel equation as an operator identity's matrix element in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Fan Hongyi; Li Chao
2004-05-17
We study the well-known Bessel equation itself in the framework of quantum mechanics. We show that the Bessel equation is a spontaneous result of an operator identity's matrix element in some definite entangled state representations, which is a fresh look. Application of this operator formalism in the Hankel transform of Laplace equation is presented.
Partially coherent n onpar axial modified Bessel-Gauss beams
Institute of Scientific and Technical Information of China (English)
Gao Zeng-Hui; Lü Bai-Da
2006-01-01
The concept of partially coherent nonparaxial modified Bessel-Gauss (MBG) beams is proposed. Based on the generalized Rayleigh-Sommerfeld diffraction integral, the analytical propagation equations of nonparaxial MBG beams in free space are derived and analysed, and some special cases are discussed. In particular, under the paraxial approximation our results reduce to the corresponding paraxial ones. Numerical calculation examples are given to illustrate the dependence of intensity and spectral degree of coherence on the beam order m,ξ and f parameters, and to compare the difference between the paraxial and nonparaxial results.
Reformulation of the Fourier-Bessel steady state mode solver
Gauthier, Robert C.
2016-09-01
The Fourier-Bessel resonator state mode solver is reformulated using Maxwell's field coupled curl equations. The matrix generating expressions are greatly simplified as well as a reduction in the number of pre-computed tables making the technique simpler to implement on a desktop computer. The reformulation maintains the theoretical equivalence of the permittivity and permeability and as such structures containing both electric and magnetic properties can be examined. Computation examples are presented for a surface nanoscale axial photonic resonator and hybrid { ε , μ } quasi-crystal resonator.
Non-diffracting chirped Bessel waves in optical antiguides
Chremmos, Ioannis
2015-01-01
Chirped Bessel waves are introduced as stable (non-diffracting) solutions of the paraxial wave equation in optical antiguides with a power-law radial variation in their index of refraction. Through numerical simulations, we investigate the propagation of apodized (finite-energy) versions of such waves, with or without vorticity, in antiguides with practical parameters. The new waves exhibit a remarkable resistance against the defocusing effect of the unstable index potentials, outperforming standard Gaussians with the same full width at half maximum. The chirped profile persists even under conditions of eccentric launching or antiguide bending and is also capable of self-healing like standard diffraction-free beams in free space.
Evolution properties of Bessel-Gaussian Schell-model beams in non-Kolmogorov turbulence.
Wang, Xiaoyang; Yao, Mingwu; Qiu, Zhiliang; Yi, Xiang; Liu, Zengji
2015-05-18
The analytical expressions for the spectral degree of coherence, the effective radius of curvature and the propagation factor of the Bessel-Gaussian Schell-model (BGSM) beam in turbulent atmosphere are derived based on the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function (WDF). The evolution properties of BGSM beams propagating in non-Kolmogorov turbulence are investigated by a set of numerical examples. It is demonstrated that the spectral degree of coherence of the BGSM beam evolves into Gaussian profile twice with the increasing of the propagation distance. The turbulence-induced degradation can be remarkably reduced by using the BGSM beam with the proper source parameters. The effects that the generalized refractive-index structure constant, outer and inner scales, and the spectral index of spatial power spectrum of atmospheric turbulence have on the evolution properties of BGSM beams are also discussed in detail.
Energy Technology Data Exchange (ETDEWEB)
Wetzel, Benjamin, E-mail: benjamin.wetzel@femto-st.fr; Xie, Chen; Lacourt, Pierre-Ambroise; Dudley, John M.; Courvoisier, Francois [Département d' Optique P.M. Duffieux, Institut FEMTO-ST, UMR–6174 CNRS, Université de Franche-Comté, 25030 Besançon (France)
2013-12-09
We report the fabrication of micro and nano-disks in single layer chemical vapor deposition graphene on glass substrate using femtosecond laser ablation with vortex Bessel beams. The fabricated graphene disks with diameters ranging from 650 nm to 4 μm were characterized by spatially resolved micro-Raman spectroscopy. The variation of ablation threshold was investigated as a function of the number of pulses showing an incubation effect. A very high degree of size control of the fabricated graphene disks is enabled using a sequence of femtosecond pulses with different vortex orders.
Generation of Bessel Beams at mm- and Sub mm-wavelengths by Binary Optical Elements
Yu, Y. Z.; Dou, W. B.
2008-07-01
In this paper, binary optical elements (BOE’s) are designed for generating Bessel beams at mm- and sub mm- wavelengths. The design tool is to combine a genetic algorithm (GA) for global optimization with a two-dimension finite-difference time-domain (2-D FDTD) method for rigorous electromagnetic computation. The design process for converting a normally incident Gaussian beam into a Bessel beam is described in detail. Numerical results demonstrate that the designed BOE’s can not only successfully produce arbitrary order Bessel beams, but also have higher diffraction efficiencies when compared with amplitude holograms.
Multiaxial Cyclic Thermoplasticity Analysis with Besseling's Subvolume Method
Mcknight, R. L.
1983-01-01
A modification was formulated to Besseling's Subvolume Method to allow it to use multilinear stress-strain curves which are temperature dependent to perform cyclic thermoplasticity analyses. This method automotically reproduces certain aspects of real material behavior important in the analysis of Aircraft Gas Turbine Engine (AGTE) components. These include the Bauschinger effect, cross-hardening, and memory. This constitutive equation was implemented in a finite element computer program called CYANIDE. Subsequently, classical time dependent plasticity (creep) was added to the program. Since its inception, this program was assessed against laboratory and component testing and engine experience. The ability of this program to simulate AGTE material response characteristics was verified by this experience and its utility in providing data for life analyses was demonstrated. In this area of life analysis, the multiaxial thermoplasticity capabilities of the method have proved a match for the actual AGTE life experience.
Nonparaxial shape-preserving Airy beams with Bessel signature
Zapata-Rodriguez, Carlos J
2014-01-01
Spatially accelerating beams that are solutions to the Maxwell equations may propagate along incomplete circular trajectories, after which diffraction broadening takes over and the beams spread out. Taking these truncated Bessel wave fields to the paraxial limit, some authors sustained that it is recovered the known Airy beams (AiBs). Based on the angular spectrum representation of optical fields, we demonstrated that the paraxial approximation rigorously leads to off-axis focused beams instead of finite-energy AiBs. The latter will arise under the umbrella of a nonparaxial approach following elliptical trajectories in place of parabolas. Deviations from full-wave simulations appear more severely in beam positioning rather than its local profile.
Photoacoustic transformation of Bessel light beams in magnetoactive superlattices
Energy Technology Data Exchange (ETDEWEB)
Mityurich, G. S., E-mail: George-mityurich@mail.ru [Belarusian Trade and Economics University of Consumer Cooperatives (Belarus); Chernenok, E. V.; Sviridova, V. V.; Serdyukov, A. N. [Gomel State University (Belarus)
2015-03-15
Photoacoustic transformation of the TE mode of a Bessel light beam (BLB) has been studied for piezoelectric detection in short-period superlattices formed by magnetoactive crystals of bismuth germanate (Bi{sub 12}GeO{sub 20}) and bismuth silicate (Bi{sub 12}SiO{sub 20}) types. It is shown that the resulting signal amplitude can be controlled using optical schemes of BLB formation with a tunable cone angle. A resonant increase in the signal amplitude has been found in the megahertz range of modulation frequencies and its dependences on the BLB modulation frequency, geometric sizes of the two-layer structure and piezoelectric transducer, radial coordinate of the polarization BLB mode, and dissipative superlattice parameters are analyzed.
Generation of Bessel Surface Plasmon Polaritons in a Finite-Thickness Metal Film
Directory of Open Access Journals (Sweden)
S. N. Kurilkina
2013-01-01
Full Text Available A theory of generation of low- and high-index Bessel surface plasmon polaritons and their superposition in a metal film of a finite thickness is developed. Correct analytical expressions are obtained for the field of two families of Bessel surface plasmon polariton modes formed inside and outside the metal layer. The intensity distribution near the boundary of the layer has been calculated and analyzed. A scheme for the experimental realization of a superposition of Bessel surface plasmon polaritons is suggested. Our study demonstrates that it is feasible to use the superposition of Bessel surface plasmon polaritons as a virtual tip for near-field optical microscopy with a nanoscale resolution.
Broadband description of the copper cable transfer function
Waal, D.C.H.
2007-01-01
This report is describes the characteristics of two different copper cables, namely the coax cable and the twisted pair cable. By using the Maxwell equations we can describe the coax cable and the twisted pair cable with the Bessel functions. By these Bessel functions we can simulate the two seconda
Comparison between Bessel and Gaussian beam propagation for in-depth optogenetic stimulation
Tejeda, Hector; Li, Ting; Mohanty, Samarendra
2013-03-01
Optogenetics technology has opened new landscapes for neuroscience research. Due to its non-diffracting and selfhealing nature, Bessel beam has potential to improve in-depth optogenetic stimulation. A detailed understanding of Bessel beam propagation, as well as its superiority over commonly used Gaussian beam, is essential for delivery and control of light irradiation for optogenetics and other light stimulation approaches. We developed an algorithm for modeling Bessel beam propagation and then compared both beam propagations in two-layered mice brain under variance of multiple variables (i.e., wavelength, numerical aperture, and beam size). These simulations show that Bessel beam is significantly advantageous over Gaussian beam for in-depth optogenetic stimulation, leading to development of lessinvasive probes. While experimental measurements using single-photon Bessel-Gauss beam generated by axicon-tip fiber did not show improved stimulation-depth, near-infrared Bessel beam generated using free-space optics and an axicon led to better penetration than near-infrared Gaussian beam.
Formation of high-order acoustic Bessel beams by spiral diffraction gratings
Jiménez, Noé; Sánchez-Morcillo, Víctor; Romero-García, Vicent; García-Raffi, Lluis M; Staliunas, Kestutis
2016-01-01
The formation of high-order Bessel beams by a passive acoustic device consisting of an Archimedes' spiral diffraction grating is theoretically, numerically and experimentally reported in this work. These beams are propagation-invariant solutions of the Helmholtz equation and are characterized by an azimuthal variation of the phase along its annular spectrum producing an acoustic vortex in the near field. In our system, the scattering of plane acoustic waves by the spiral grating leads to the formation of the acoustic vortex with zero pressure on-axis and the angular phase dislocations characterized by the spiral geometry. The order of the generated Bessel beam and, as a consequence, the size of the generated vortex can be fixed by the number of arms in the spiral diffraction grating. The obtained results allow to obtain Bessel beams with controllable vorticity by a passive device, which has potential applications in low-cost acoustic tweezers and acoustic radiation force devices.
Fourier-Bessel Field Calculation and Tuning of a CW Annular Array
DEFF Research Database (Denmark)
Fox, Paul D.; Cheng, Jiqi; Lu, Jian-yu
2002-01-01
A 1-D Fourier-Bessel series method for computing and tuning the linear lossless field of flat continuous wave (CW) annular arrays is given and discussed with both numerical simulation and experimental verification. The technique provides a new method for modelling and manipulating the propagated...... field by linking the quantized surface pressure profile to a set of limited diffraction Bessel beams propagating into the medium. In the limit, these become a known set of nondiffracting Bessel beams satisfying the lossless linear wave equation, which allow us to derive a linear matrix formulation...... for the field in terms of the ring pressures on the transducer surface. Tuning (beamforming) of the field then follows by formulating a least squares design with respect to the transducer ring pressures. Results are presented in the context of a 10-ring annular array operating at 2.5 MHz in water....
Formation of high-order acoustic Bessel beams by spiral diffraction gratings
Jiménez, Noé; Picó, R.; Sánchez-Morcillo, V.; Romero-García, V.; García-Raffi, L. M.; Staliunas, K.
2016-11-01
The formation of high-order Bessel beams by a passive acoustic device consisting of an Archimedes' spiral diffraction grating is theoretically, numerically, and experimentally reported in this paper. These beams are propagation-invariant solutions of the Helmholtz equation and are characterized by an azimuthal variation of the phase along its annular spectrum producing an acoustic vortex in the near field. In our system, the scattering of plane acoustic waves by the spiral grating leads to the formation of the acoustic vortex with zero pressure on axis and the angular phase dislocations characterized by the spiral geometry. The order of the generated Bessel beam and, as a consequence, the size of the generated vortex can be fixed by the number of arms in the spiral diffraction grating. The obtained results allow for obtaining Bessel beams with controllable vorticity by a passive device, which has potential applications in low-cost acoustic tweezers and acoustic radiation force devices.
Bessel beams in tunable acoustic gradient index lenses and optical trap assisted nanolithography
McLeod, Euan
2009-12-01
Bessel beams are laser beams whose shape gives them nondiffracting and self-healing properties. They find use in applications requiring a narrow laser beam with a high depth of field. The first part of this thesis presents the study of a new adaptive optical element capable of generating rapidly tunable Bessel beams: the tunable acoustic gradient index (TAG) lens. This device uses piezoelectrically-generated acoustic waves to modulate a fluid's density and refractive index, leading to electrically controllable lensing behavior. Both modeling and experiment are used to explain the observed multiscale Bessel beams. Because the TAG lens operates at frequencies of hundreds of kilohertz, the effective Bessel beam cone angle continuously varies at timescales on the order of microseconds or smaller-orders of magnitude faster than other existing technologies. In addition, the TAG lens may be driven with a Fourier superposition of multiple frequencies, which could enable the generation of arbitrary patterns. The second part of this thesis presents the application of Bessel beams in a new probe-based direct-write optical nanolithography method called optical trap assisted nanolithography (OTAN). When compared to alternative techniques, OTAN makes probe placement and parallelization easier. The method uses Bessel beam optical tweezers to trap dielectric microspheres in close proximity to a surface. These microspheres are then illuminated with pulses from a second laser beam, whose fluence is enhanced directly below the microsphere by focusing and near-field effects to a level great enough to modify the substrate. This technique is used to produce 100 nm features, which are less than lambda/3, and whose sizes agree well with finite-difference time-domain models of the experiment. A demonstration is given of how the technique can be parallelized by trapping multiple microspheres with multiple beams and exposing all spheres in unison with a single pulsed beam. Finally, modeling
非偏振贝塞尔高斯光束的球散射%Scattering of Unpolarized Bessel-Gauss Beams by a Sphere
Institute of Scientific and Technical Information of China (English)
马秀波; 李恩邦
2012-01-01
The Bessel beams are often used for investigating the scattering properties of the non-diffracting beams, but the Bessel beams cannot be realized physically. As the pseudo-nondiffracting beams and the exact solution to the paraxial Helmholz equation, the Bessel-Gauss beams can be generated directly from the laser resonator and possess finite spatial width. The dimensionless scattering function is derived for the Bessel-Gauss beams scattered by a sphere by means of Fourier-transform, the plane wave expansion and the vector spherical wave expansion. By numerical simulation and comparison with that of the Bessel beam and the Gauss beam, it can be found that only the scattering intensity is influenced as the spherical scatterer is shifted off the beam axis, the directions where the scattering extreme points exist almost keep no changes. The scattering is dominant in the direction of the conical angle for the Bessel-Gauss beam and the Bessel beam, but for the Gauss beam the forward scattering is always dominant.%无衍射光束球散射性质的研究目前一般采用贝塞尔光束,但是贝塞尔光束在物理上是不可实现的.贝塞尔高斯光束作为近似无衍射光束,是亥姆霍兹方程在傍轴条件下的解,并且可以用激光振荡器直接产生,但其光束宽是有限的.应用傅里叶变换,平面波谱展开和球面矢量波函数展开法,推导了非偏振贝塞尔高斯光束的球散射远场的无量纲散射函数.通过数值模拟,对非偏振的贝塞尔高斯光束与贝塞尔光束,高斯光束的球散射远场进行了比较,比较发现:当球散射体偏离光轴时,非偏振贝塞尔高斯光束跟贝塞尔光束散射远场的差异主要是散射强度的差异,但是散射极点所在的方向基本保持不变；贝塞尔高斯光束和贝塞尔光束的散射在光束圆锥角方向上比较显著,但高斯光束的前向散射比较显著.
Extension of filament propagation in water with Bessel-Gaussian beams
Directory of Open Access Journals (Sweden)
G. Kaya
2016-03-01
Full Text Available We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.
Optical induction of Bessel-like lattices in methyl-red doped liquid crystal cells
Mantashyan, Paytsar; Drampyan, Rafael; Beeckman, Jeroen; Willekens, Oliver; Neyts, Kristiaan
2015-03-01
The optical induction of annular photonic lattices by a traveling Bessel beam has been investigated in Methyl-red (MR) doped nematic liquid crystal (LC). Non-diffracting Bessel beams were formed by an axicon. The induced Bessel-like lattice had a ~15 μm period in the radial direction. The lattice was tested by measuring the forward diffracted power of the recording Bessel beam. The dependency on the angle between the polarization of the laser beam and the director of the LC and on the axial position of the LC cell had been investigated. A diffraction efficiency of 14% had been obtained. Investigations have been performed for different MR dye doping concentrations. An erasure time of the lattice of 60 s has been determined by a 532 nm probe Gaussian beam of 2 mW in a LC cell with MR dye concentration of 1.15 wt%. The induced periodically varying refractive index in the LC medium is analogous to microstructured fibers and allows the study of light localization and soliton behavior in highly nonlinear waveguide arrays.
Chillara, Vamshi Krishna; Pantea, Cristian; Sinha, Dipen N.
2017-02-01
We present a very simple approach to generate a collimated ultrasonic beam that exploits the natural Bessel-like vibration pattern of the radial modes of a piezoelectric disc with lateral clamping. This eliminates the need for the conventional annular Bessel pattern of the electrodes with individual electrode excitation on the piezo-disc, thus simplifying the transducer design. Numerical and experimental studies are carried out to investigate the Bessel-like vibration patterns of these radial modes showing an excellent agreement between these two studies. Measured ultrasonic beam-profiles in water from the radial modes confirm the profile to be a Bessel beam. Collimated beam generation from radial modes is investigated using a coupled electromechanical finite-element model. It is found that clamping the lateral edges of piezoelectric transducers results in a high-degree of collimation with practically no side-lobes similar to a parametric array beam. Ultrasonic beam-profile measurements in water with both free and clamped piezoelectric transducer are presented. The collimated beam generation using the present technique of using the laterally clamped radial modes finds significant applications in low-frequency imaging through highly attenuating materials.
Variational derivatives in locally Lagrangian field theories and Noether-Bessel-Hagen currents
Cattafi, Francesco; Palese, Marcella; Winterroth, Ekkehart
2016-01-01
The variational Lie derivative of classes of forms in the Krupka's variational sequence is defined as a variational Cartan formula at any degree, in particular for degrees lesser than the dimension of the basis manifold. As an example of application, we determine the condition for a Noether-Bessel-H
Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on Cn
Institute of Scientific and Technical Information of China (English)
CHANG; Der-Chen; GRIENER; Peter; TIE; Jingzhi
2006-01-01
Given a principal value convolution on the Heisenberg group Hn = Cn × R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.
Walde, Marie; Jost, Aurélie; Wicker, Kai; Heintzmann, Rainer
2017-01-01
Bessel illumination is an established method in optical imaging and manipulation to achieve an extended depth of field without compromising the lateral resolution. When broadband or multicolour imaging is required, wavelength-dependent changes in the radial profile of the Bessel illumination can complicate further image processing and analysis. We present a solution for engineering a multicolour Bessel beam that is easy to implement and promises to be particularly useful for broadband imaging applications. A phase-only spatial light modulator (SLM) in the image plane and an iterative Fourier Transformation algorithm (IFTA) are used to create an annular light distribution in the back focal plane of a lens. The 2D Fourier transformation of such a light ring yields a Bessel beam with a constant radial profile for different wavelength.
G-Frame Representation and Invertibility of G-Bessel Multipliers
Institute of Scientific and Technical Information of China (English)
A.ABDOLLAHI; E.RAHIMI
2013-01-01
In this paper we show that every g-frame for an infinite dimensional Hilbert space H can be written as a sum of three g-orthonormal bases for H.Also,we prove that every gframe can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis.Further,we show each g-Bessel multiplier is a Bessel multiplier and investigate the inversion of g-frame multipliers.Finally,we introduce the concept of controlled g-frames and weighted g-frames and show that the sequence induced by each controlled g-frame (resp.,weighted g-frame) is a controlled frame (resp.,weighted frame).
Laser controlled deposition of metal microstructures via nondiffracting Bessel beam illumination
Drampyan, Rafael; Leonov, Nikita; Vartanyan, Tigran
2016-04-01
The technique of the laser controlled deposition of sodium and rubidium deposits on the sapphire substrate is presented. The metals were deposited on the clean sapphire substrate from the vapor phase contained in the evacuated and sealed cell. We use an axicon to produce a non-diffracting Bessel beam out of the beam got from the cw diode laser with 200 mW power at the wavelength of 532 nm. After 30 minutes of the laser-controlled deposition the substrates were examined in the optical microscope. The obtained metal deposits form the sharp-cut circles with the pitch of 10 μm, coincident with the tens of dark rings of the Bessel beam. Reduction of the laser power leads to the build up of the continuous metal film over the whole substrate.
Generation of J0-Bessel-Gauss Beam by an heterogeneous refractive index map
Alerigi, Damian P San Roman; Benslimane, Ahmed; Zhang, Yaping; Alsunaidi, Mohammad; Ooi, Boon S; 10.1364/JOSAA.29.001252
2012-01-01
In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of such device by solving the inverse electromagnetic problem. The computed conversion e?ficiency is 90%. The theoretical results, obtained from the beam conversion efi?ciency, self-regeneration, and propagation through an opaque obstruction; demonstrate that a 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 ?rst demonstration of such beam transformation by means of a 2D index-mapping which is fully integrable in silicon photonics based planar lightwave circuits (PLC). The concept device is signi?cant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and non-linear beam diode lasers.
Milione, Giovanni; Nguyen, Thien An; Chakraborty, Ougni; Karimi, Ebrahim; Forbes, Andrew; Alfano, Robert R
2014-01-01
We experimentally measured the self-healing of the spatially inhomogeneous states of polarization of radial and azimuthal polarized vector Bessel beams. Radial and azimuthal polarized vector Bessel beams were generated via a digital version of Durnin's method, using a spatial light modulator in concert with a liquid crystal $q$-plate. As a proof of principle, their intensities and spatially inhomogeneous states of polarization were measured using Stokes polarimetry as they propagated through two disparate obstructions. It was found, similar to their intensities, the spatially inhomogeneous states of polarization of a radial and azimuthal polarized vector Bessel beams self-heal. Similar to scalar Bessel beams, the self-healing of vector Bessel beams can be understood via geometric optics, i.e., the interference of the unobstructed conical rays in the shadow region of the obstruction. The self-healing of vector Bessel beams may have applications in, for example, optical trapping.
Goos-Haenchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam
Aiello, Andrea
2010-01-01
Goos-Haenchen and Imbert-Fedorov shifts are diffractive corrections to geometrical optics that have been extensively studied for a Gaussian beam that is reflected or transmitted by a dielectric interface. Propagating in free space before and after reflection or transmission, such a Gaussian beam spreads due to diffraction. We address here the question how the Goos-Haenchen and Imbert-Fedorov shifts behave for a ``nondiffracting'' Bessel beam.
Goos-Hänchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam.
Aiello, Andrea; Woerdman, J P
2011-02-15
Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts are diffractive corrections to geometric optics that have been extensively studied for a Gaussian beam that is reflected or transmitted by a dielectric interface. Propagating in free space before and after reflection or transmission, such a Gaussian beam spreads due to diffraction. We address here the question of how the GH and IF shifts behave for a "nondiffracting" Bessel beam.
Design of Bessel low-pass filter using DGS for RF/microwave applications
Kumar, Ashwani; Verma, A. K.
2016-09-01
A synthesis method to design a defected ground structures (DGS)-based Bessel low-pass filter (LPF) using a triangular and an open-square (OS)-type DGS is reported. For the five-pole Bessel LPF at fc = 2.5 GHz, we get 10.6 dB/GHz selectivity using the triangular DGS; while the OS-type DGS provides 39 dB/GHz selectivity. For these two filters, the 10 dB impedance matching BW is 76% and 84%, respectively. It is a much wider BW that is obtained for a lumped element Bessel LPF. The maximum group delay (GD) variation within the pass band is 25pS and 28pS, respectively. The 20 dB rejection BW can be increased from 5.8 GHz to 18.8 GHz with increase in the order of filter from 5 to 11. We have also presented the design of a compact five-pole DGS-based elliptic filter with selectivity 38.2 dB/GHz and 17.8 dB return loss. Results on the DGS-based elliptic filter, Butterworth and Chebyshev filters are also presented. The experimental results are compared against the recently reported LPFs. Our reported filters perform better with respect to selectivity and group delay variation. The flatter GD and high selectivity, along with a wide 10 dB impedance matching BW, make the DGS Bessel filter a candidate for high-speed data communication, front end of a wideband communication system and efficiency improvement of a power amplifier.
Bessel-X waves: superluminal propagation and the Minkowski space-time
Mugnai, D.
2006-01-01
Superluminal behavior has been extensively studied in recent years, especially with regard to the topic of superluminality in the propagation of a signal. Particular interest has been devoted to Bessel-X waves propagation, since some experimental results showed that these waves have both phase and group velocities greater that light velocity c. However, because of the lack of an exact definition of signal velocity, no definite answer about the signal propagation (or velocity of information) h...
Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series
2014-10-16
Double Fourier harmonic balance method for nonlinear oscillators by means of Bessel series T.C. Lipscombe∗1 and C.E. Mungan†2 1Catholic University of...harmonic balance method consists in expanding the displacement of an oscillator as a Fourier cosine series in time. A key modification is proposed here, in...which the conservative force is additionally expanded as a Fourier sine series in space. As a result, the steady-state oscillation frequency can be
Mitri, F G
2016-01-01
The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and prolate spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure st...
Off-axial acoustic radiation force of pressor and tractor Bessel beams on a sphere
Silva, Glauber T; Lobo, Tiago P; Mitri, Farid G
2012-01-01
Acoustic Bessel beams are known to produce an axial radiation force on a sphere centered on the beam axis (on-axial configuration) that exhibits both "pressor" and "tractor" behaviors. The pressor and the tractor forces are oriented along the beam's direction of propagation and opposite to it, respectively. The behavior of the acoustic radiation force generated by Bessel beams when the sphere lies outside the beam's axis (off-axial configuration) is unknown. Using the 3D radiation force formulas given in terms of the partial wave expansion coefficients for the incident and scattered waves, both axial and transverse components of the force exerted on a silicone-oil sphere are obtained for a zero- and a first-order Bessel vortex beam. As the sphere departs from the beam's axis, the tractor force becomes weaker. Moreover, the behavior of the transverse radiation force field may vary with the sphere's size factor $ka$ (where $k$ is the wavenumber and $a$ is the sphere radius). Both stable and unstable equilibrium...
Dynamics of submicron aerosol droplets in a robust optical trap formed by multiple Bessel beams
Energy Technology Data Exchange (ETDEWEB)
Thanopulos, Ioannis [Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, ETH Zurich, CH-8093 Zurich (Switzerland); Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Athens 11635 (Greece); Luckhaus, David; Signorell, Ruth, E-mail: rsignorell@ethz.ch [Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, ETH Zurich, CH-8093 Zurich (Switzerland); Preston, Thomas C. [School of Chemistry, University of Bristol, Cantock' s Close, Clifton, Bristol BS8 1TS (United Kingdom)
2014-04-21
In this paper, we model the three-dimensional escape dynamics of single submicron-sized aerosol droplets in optical multiple Bessel beam traps. Trapping in counter-propagating Bessel beams (CPBBs) is compared with a newly proposed quadruple Bessel beam (QBB) trap, which consists of two perpendicularly arranged CPBB traps. Calculations are performed for perfectly and imperfectly aligned traps. Mie-theory and finite-difference time-domain methods are used to calculate the optical forces. The droplet escape kinetics are obtained from the solution of the Langevin equation using a Verlet algorithm. Provided the traps are perfectly aligned, the calculations indicate very long lifetimes for droplets trapped either in the CPBB or in the QBB trap. However, minor misalignments that are hard to control experimentally already severely diminish the stability of the CPBB trap. By contrast, such minor misalignments hardly affect the extended droplet lifetimes in a QBB trap. The QBB trap is found to be a stable, robust optical trap, which should enable the experimental investigation of submicron droplets with radii down to 100 nm. Optical binding between two droplets and its potential role in preventing coagulation when loading a CPBB trap is briefly addressed.
Efficient second-harmonic imaging of collagen in histological slides using Bessel beam excitation
Vuillemin, Nelly; Mahou, Pierre; Débarre, Delphine; Gacoin, Thierry; Tharaux, Pierre-Louis; Schanne-Klein, Marie-Claire; Supatto, Willy; Beaurepaire, Emmanuel
2016-07-01
Second-harmonic generation (SHG) is the most specific label-free indicator of collagen accumulation in widespread pathologies such as fibrosis, and SHG-based measurements hold important potential for biomedical analyses. However, efficient collagen SHG scoring in histological slides is hampered by the limited depth-of-field of usual nonlinear microscopes relying on focused Gaussian beam excitation. In this work we analyze theoretically and experimentally the use of Bessel beam excitation to address this issue. Focused Bessel beams can provide an axially extended excitation volume for nonlinear microscopy while preserving lateral resolution. We show that shaping the focal volume has consequences on signal level and scattering directionality in the case of coherent signals (such as SHG) which significantly differ from the case of incoherent signals (two-photon excited fluorescence, 2PEF). We demonstrate extended-depth SHG-2PEF imaging of fibrotic mouse kidney histological slides. Finally, we show that Bessel beam excitation combined with spatial filtering of the harmonic light in wave vector space can be used to probe collagen accumulation more efficiently than the usual Gaussian excitation scheme. These results open the way to SHG-based histological diagnoses.
Riaud, Antoine; Baudoin, Michael; Matar, Olivier Bou
2015-01-01
Despite their self-reconstruction properties in heterogeneous media, Bessel beams are known to degenerate when they are refracted from an isotropic to an anisotropic medium. In this paper, we study the converse situation wherein an anisotropic Bessel beam is refracted into an isotropic medium. It is shown that these anisotropic Bessel beams also degenerate, leading to confined vortical waves that may serve as localized particle trap for acoustical tweezers. The linear nature of this degeneration allows the 3D control of this trap position by wavefront correction. Theory is confronted to experiments performed in the field of acoustics. A swirling surface acoustic wave is synthesized at the surface of a piezoelectric crystal by a MEMS integrated system and radiated inside a miniature liquid vessel. The wavefront correction is operated with inverse filter technique. This work opens perspectives for contactless on-chip manipulation devices.
Columnar deformation of human red blood cell by highly localized fiber optic Bessel beam stretcher.
Lee, Sungrae; Joo, Boram; Jeon, Pyo Jin; Im, Seongil; Oh, Kyunghwan
2015-11-01
A single human red blood cell was optically stretched along two counter-propagating fiber-optic Bessel-like beams in an integrated lab-on-a-chip structure. The beam enabled highly localized stretching of RBC, and it induced a nonlinear mechanical deformation to finally reach an irreversible columnar shape that has not been reported. We characterized and systematically quantified this optically induced mechanical deformation by the geometrical aspect ratio of stretched RBC and the irreversible stretching time. The proposed RBC mechanism can realize a versatile and compact opto-mechanical platform for optical diagnosis of biological substances in the single cell level.
Generalized Fourier-grid R-matrix theory: a discrete Fourier-Riccati-Bessel transform approach
Energy Technology Data Exchange (ETDEWEB)
Layton, E.G. (Joint Inst. for Lab. Astrophysics, Boulder, CO (United States)); Stade, E. (Colorado Univ., Boulder, CO (United States). Dept. of Mathematics)
1993-08-28
We present the latest developments in the Fourier-grid R-matrix theory of scattering. These developments are based on the generalized Fourier-grid formalism and use a new type of extended discrete Fourier transform: the discrete Fourier-Riccati-Bessel transform. We apply this new R-matrix approach to problems of potential scattering, to demonstrate how this method reduces computational effort by incorporating centrifugal effects into the representation. As this technique is quite new, we have hopes to broaden the formalism to many types of problems. (author).
Application of nondiffracting Bessel beams for shaping of surface metal microstructures
Drampyan, Rafael; Leonov, Nikita; Vartanyan, Tigran
2016-08-01
A novel method of laser-controlled shaping of metal microstructures based on the processes of metal atoms adsorption on the surface of crystalline substrate and simultaneous control of photostimulated desorption of atoms by spatially modulated nondiffracting laser beam illumination is presented. The experiments were performed for sodium atoms deposition to the sapphire substrate, which was illuminated by Bessel beam at 532 nm wavelength and 2 W/cm2 intensity. Experiments showed that the optical pattern was well reproduced in the sodium deposits thus creating the annularly microstructured metal film with few tens nanometre thickness.
Generation of J_0-Bessel-Gauss beam by a heterogeneous refractive index map
San-Román-Alerigi, Damián P.
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.
Negative optical spin torque wrench of a nondiffracting non-paraxial fractional Bessel vortex beam
Mitri, F G
2016-01-01
An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge and the beam's half-cone angle. When the beam order is zero, the axial spin torque component vanishes. However, when the beam order becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable to induce a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, the design of optically-engineered metamateri...
Stöger-Pollach, Michael; Schachinger, Thomas; Biedermann, Kati; Beyer, Volkhard
2017-02-01
In this experimental work we present novel methods to increase the spatial resolution of valence electron energy loss spectrometry (VEELS) investigations below the limit given by the inelastic delocalization. For this purpose we analyse a layer stack consisting of silicon/silicon-oxide/silicon-nitride/silicon-oxide/silicon (SONOS) with varying layer thickness down to the 2nm level. Using a combination of a conical illumination and energy filtered transmission electron microscopy we are able to identify the layers by using low energy losses. Employing Bessel beams we demonstrate that VEELS can be performed in dark-field conditions while simultaneously the Bessel beam increases the spatial resolution of the elastic image due to less sensitivity to the spherical aberration of the condenser lens system. The dark-field conditions also guarantee that only electrons are collected that have neither undergone an energy loss being due to the Cˇerenkov effect, nor due to the excitation of transition radiation or light guiding modes. We consequently are able to measure the optical properties of a 2.5nm thin oxide being sandwiched by the silicon substrate and a silicon-nitride layer.
Tailoring femtosecond 1.5-μm Bessel beams for manufacturing high-aspect-ratio through-silicon vias
He, Fei; Yu, Junjie; Tan, Yuanxin; Chu, Wei; Zhou, Changhe; Cheng, Ya; Sugioka, Koji
2017-01-01
Three-dimensional integrated circuits (3D ICs) are an attractive replacement for conventional 2D ICs as high-performance, low-power-consumption, and small-footprint microelectronic devices. However, one of the major remaining challenges is the manufacture of high-aspect-ratio through-silicon vias (TSVs), which is a crucial technology for the assembly of 3D Si ICs. Here, we present the fabrication of high-quality TSVs using a femtosecond (fs) 1.5-μm Bessel beam. To eliminate the severe ablation caused by the sidelobes of a conventional Bessel beam, a fs Bessel beam is tailored using a specially designed binary phase plate. We demonstrate that the tailored fs Bessel beam can be used to fabricate a 2D array of approximately ∅10-μm TSVs on a 100-μm-thick Si substrate without any sidelobe damage, suggesting potential application in the 3D assembly of 3D Si ICs. PMID:28098250
Flammer, Carson
2005-01-01
Intended to facilitate the use and calculation of spheroidal wave functions, this applications-oriented text features a detailed and unified account of the properties of these functions. Addressed to applied mathematicians, mathematical physicists, and mathematical engineers, it presents tables that provide a convenient means for handling wave problems in spheroidal coordinates.Topics include separation of the scalar wave equation in spheroidal coordinates, angle and radial functions, integral representations and relations, and expansions in spherical Bessel function products. Additional subje
Probing the energy flow in Bessel light beams using atomic photoionization
Surzhykov, A.; Seipt, D.; Fritzsche, S.
2016-09-01
The growing interest in twisted light beams also requires a better understanding of their complex internal structure. Particular attention is currently being given to the energy circulation in these beams as usually described by the Poynting vector field. In the present study we propose to use the photoionization of alkali-metal atoms as a probe process to measure (and visualize) the energy flow in twisted light fields. Such measurements are possible since the angular distribution of photoelectrons, emitted from a small atomic target, appears sensitive to and is determined by the local direction of the Poynting vector. To illustrate the feasibility of the proposed method, detailed calculations were performed for the ionization of sodium atoms by nondiffractive Bessel beams.
High-speed laser-assisted cutting of strong transparent materials using picosecond Bessel beams
Bhuyan, M. K.; Jedrkiewicz, O.; Sabonis, V.; Mikutis, M.; Recchia, S.; Aprea, A.; Bollani, M.; Trapani, P. Di
2015-08-01
We report single-pass cutting of strong transparent glass materials of 700 μm thickness with a speed up to 270 mm/s using single-shot nanostructuring technique exploiting picosecond, zero-order Bessel beams at laser wavelength of 1030 nm. Particularly, we present results of a systematic study of cutting of tempered glass which has high resistance to thermal and mechanical shocks due to the inhomogeneous material properties along its thickness, and homogeneous glass that identify a unique focusing geometry and a finite pitch dependency, for which cutting with high quality and high reproducibility can be achieved. These results represent a significant advancement in the field of high-speed cutting of technologically important transparent materials.
Fahrbach, Florian O.; Rohrbach, Alexander
2012-01-01
Laser beams that can self-reconstruct their initial beam profile even in the presence of massive phase perturbations are able to propagate deeper into inhomogeneous media. This ability has crucial advantages for light sheet-based microscopy in thick media, such as cell clusters, embryos, skin or brain tissue or plants, as well as scattering synthetic materials. A ring system around the central intensity maximum of a Bessel beam enables its self-reconstruction, but at the same time illuminates out-of-focus regions and deteriorates image contrast. Here we present a detection method that minimizes the negative effect of the ring system. The beam's propagation stability along one straight line enables the use of a confocal line principle, resulting in a significant increase in image contrast. The axial resolution could be improved by nearly 100% relative to the standard light-sheet techniques using scanned Gaussian beams, while demonstrating self-reconstruction also for high propagation depths.
Super-resolution deep imaging with hollow Bessel beam STED microscopy
Yu, Wentao; Dong, Dashan; Yang, Xusan; Xiao, Yunfeng; Gong, Qihuang; Xi, Peng; Shi, Kebin
2015-01-01
Stimulated emission depletion (STED) microscopy has become a powerful imaging and localized excitation method beating the diffraction barrier for improved lateral spatial resolution in cellular imaging, lithography, etc. Due to specimen-induced aberrations and scattering distortion, it has been a great challenge for STED to maintain consistent lateral resolution deeply inside the specimens. Here we report on a deep imaging STED microscopy by using Gaussian beam for excitation and hollow Bessel beam for depletion (GB-STED). The proposed scheme shows the improved imaging depth up to ~155{\\mu}m in solid agarose sample, ~115{\\mu}m in PDMS and ~100{\\mu}m in phantom of gray matter in brain tissue with consistent super resolution, while the standard STED microscopy shown a significantly reduced lateral resolution at the same imaging depth. The results indicate the excellent imaging penetration capability of GB-STED, making it a promising tool for deep 3D imaging optical nanoscopy and laser fabrication.
Laser-plasma interactions with a Fourier-Bessel Particle-in-Cell method
Andriyash, Igor A; Lifschitz, Agustin
2016-01-01
A new spectral particle-in-cell (PIC) method for plasma modeling is presented and discussed. In the proposed scheme, the Fourier-Bessel transform is used to translate the Maxwell equations to the quasi-cylindrical spectral domain. In this domain, the equations are solved analytically in time, and the spatial derivatives are approximated with high accuracy. In contrast to the finite-difference time domain (FDTD) methods that are commonly used in PIC, the developed method does not produce numerical dispersion, and does not involve grid staggering for the electric and magnetic fields. These features are especially valuable in modeling the wakefield acceleration of particles in plasmas. The proposed algorithm is implemented in the code PLARES-PIC, and the test simulations of laser plasma interactions are compared to the ones done with the quasi-cylindrical FDTD PIC code CALDER-CIRC.
Auñon, J M
2014-01-01
In this work we address, first, the optical force on a magnetodielectric particle on a flat dielectric surface due to an evanescent Bessel beam and, second, the effects on the force of multiple scattering with the substrate. For the first question we find analytical solutions showing that due to the interference of the excited electric and magnetic particle dipoles, the vertical force unusually pushes the object out from the plane. The incident wavelength rules whether the illumination constitutes, or not, an optical trap. As for the second problem, we make a 2D study with a single evanescent plane wave, and we present the Kerker conditions, (so far established for spheres), for magnetodielectric cylinders; showing that in $p$-polarization those are practically reproduced and are associated to minima of the horizontal and vertical forces.
Wave-optics description of self-healing mechanism in Bessel beams.
Aiello, Andrea; Agarwal, Girish S
2014-12-15
Bessel beams' great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work, we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mechanism can be entirely explained in terms of the propagation of plane waves with radial wave vectors lying on a ring.
Optical torque on a magneto-dielectric Rayleigh absorptive sphere by a vector Bessel (vortex) beam
Li, Renxian; Yang, Ruiping; Ding, Chunying; Mitri, F. G.
2017-04-01
The optical torque exerted on an absorptive megneto-dielectric sphere by an axicon-generated vector Bessel (vortex) beam with selected polarizations is investigated in the framework of the dipole approximation. The total optical torque is expressed as the sum of orbital and spin torques. The axial orbital torque component is calculated from the z-component of the cross-product of the vector position r and the optical force exerted on the sphere F. Depending on the beam characteristics (such as the half-cone angle and polarization type) and the physical properties of the sphere, it is shown here that the axial orbital torque vanishes before reversing sign, indicating a counter-intuitive orbital motion in opposite handedness of the angular momentum carried by the incident waves. Moreover, analytical formulas for the spin torque, which is divided into spin torques induced by electric and magnetic dipoles, are derived. The corresponding components of both the optical spin and orbital torques are numerically calculated, and the effects of polarization, the order of the beam, and half-cone angle are discussed in detail. The left-handed (i.e., negative) optical torque is discussed, and the conditions for generating optical spin and orbital torque sign reversal are numerically investigated. The transverse optical spin torque has a vortex-like character, whose direction depends on the polarization, the half-cone angle, and the order of the beam. Numerical results also show that the vortex direction depends on the radial position of the particle in the transverse plane. This means that a sphere may rotate with different directions when it moves radially. Potential applications are in particle manipulation and rotation, single beam optical tweezers, and other emergent technologies using vector Bessel beams on a small magneto-dielectric (nano) particle.
Pump-probe imaging of the fs-ps-ns dynamics during femtosecond laser Bessel beam drilling in PMMA.
Yu, Yanwu; Jiang, Lan; Cao, Qiang; Xia, Bo; Wang, Qingsong; Lu, Yongfeng
2015-12-14
A pump-probe shadowgraph imaging technique was used to reveal the femtosecond-picosecond-nanosecond multitimescale fundamentals of high-quality, high-aspect-ratio (up to 287:1) microhole drilling in poly-methyl-meth-acrylate (PMMA) by a single-shot femtosecond laser Bessel beam. The propagation of Bessel beam in PMMA (at 1.98 × 10⁸ m/s) and it induced cylindrical pressure wave expansion (at 3000-3950 m/s in radius) were observed during drilling processes. Also, it was unexpectedly found that the expansion of the cylindrical pressure wave in PMMA showed a linear relation with time and was insensitive to the laser energy fluctuation, quite different from the case in air. It was assumed that the energy insensitivity was due to the anisotropy of wave expansion in PMMA and the ambient air.
Zhao, Ming; Zhang, Han; Li, Yu; Ashok, Amit; Liang, Rongguang; Zhou, Weibin; Peng, Leilei
2014-05-01
In vivo fluorescent cellular imaging of deep internal organs is highly challenging, because the excitation needs to penetrate through strong scattering tissue and the emission signal is degraded significantly by photon diffusion induced by tissue-scattering. We report that by combining two-photon Bessel light-sheet microscopy with nonlinear structured illumination microscopy (SIM), live samples up to 600 microns wide can be imaged by light-sheet microscopy with 500 microns penetration depth, and diffused background in deep tissue light-sheet imaging can be reduced to obtain clear images at cellular resolution in depth beyond 200 microns. We demonstrate in vivo two-color imaging of pronephric glomeruli and vasculature of zebrafish kidney, whose cellular structures located at the center of the fish body are revealed in high clarity by two-color two-photon Bessel light-sheet SIM.
Murukeshan, V. M.; Jesmond, Hong Xun J.; Shinoj, V. K.; Baskaran, M.; Tin, Aung
2015-07-01
Primary angle closure glaucoma is a major form of disease that causes blindness in Asia and worldwide. In glaucoma, irregularities in the ocular aqueous outflow system cause an elevation in intraocular pressure (IOP) with subsequent death of retinal ganglion cells, resulting in loss of vision. High resolution visualization of the iridocorneal angle region has great diagnostic value in understanding the disease condition which enables monitoring of surgical interventions that decrease IOP. None of the current diagnostic techniques such as goniophotography, ultrasound biomicroscopy (UBM), anterior segment optical coherence tomography (AS-OCT) and RetCam™ can image with molecular specificity and required spatial resolution that can delineate the trabecular meshwork structures. This paper in this context proposes new concepts and methodology using Bessel beams based illumination and imaging for such diagnostic ocular imaging applications. The salient features using Bessel beams instead of the conventional Gaussian beam, and the optimization challenges in configuring the probe system will be illustrated with porcine eye samples.
Yang, Ruiping; Li, Renxian; Qin, Shitong; Ding, Chunying; Mitri, F. G.
2017-02-01
The effect of polarization on the optical spin torque (OST) exerted on an absorptive Rayleigh dielectric sphere by a vector Bessel beam is investigated using the dipole approximation method, with particular emphasis on the polarization of the plane wave component forming the beam. On the basis of the mathematical descriptions for the electric fields, which are derived using the angular spectrum decomposition method in plane waves, analytical formulas of the OST are established. The OSTs are numerically calculated, and the effects of polarization, beam-order, and half-cone angle are discussed in detail. Numerical results show that by choosing an appropriate polarization, order and half-cone angle, the transverse OST will manifest vortex-like behaviors, and the sphere will experience negative axial OSTs, i.e. OST sign reversal. Important applications in particle manipulation, rotation and handling using optical Bessel polarized beams would benefit from the results of the present investigation.
Mitri, F G
2016-09-01
Energy and angular momentum flux density characteristics of an optical nondiffracting nonparaxial vector Bessel vortex beam of fractional order are examined based on the dual-field method for the generation of symmetric electric and magnetic fields. Should some conditions determined by the polarization state, the half-cone angle as well as the beam-order (or topological charge) be met, the axial energy and angular momentum flux densities vanish (representing Poynting singularities), before they become negative. These negative counterintuitive properties suggest retrograde (negative) propagation as well as a rotation reversal of the angular momentum with respect to the beam handedness. These characteristics of nondiffracting nonparaxial Bessel fractional vortex beams of progressive waves open new capabilities in optical tractor beam tweezers, optical spanners, invisibility cloaks, optically engineered metamaterials, and other applications.
Bounds for the radii of univalence of some special functions
Aktaş, Ibrahim; Baricz, Árpád; Yağmur, Nihat
2016-01-01
Tight lower and upper bounds for the radius of univalence of some normalized Bessel, Struve and Lommel functions of the first kind are obtained via Euler-Rayleigh inequalities. It is shown also that the radius of univalence of the Struve functions is greater than the corresponding radius of univalence of Bessel functions. Moreover, by using the idea of Kreyszig and Todd, and Wilf it is proved that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of ...
Inequalities for Humbert functions
Directory of Open Access Journals (Sweden)
Ayman Shehata
2014-04-01
Full Text Available This paper is motivated by an open problem of Luke’s theorem. We consider the problem of developing a unified point of view on the theory of inequalities of Humbert functions and of their general ratios are obtained. Some particular cases and refinements are given. Finally, we obtain some important results involving inequalities of Bessel and Whittaker’s functions as applications.
Implementation of Bessel's method for solar eclipses prediction in the WRF-ARW model
Montornes, Alex; Codina, Bernat; Zack, John W.; Sola, Yolanda
2016-05-01
Solar eclipses are predictable astronomical events that abruptly reduce the incoming solar radiation into the Earth's atmosphere, which frequently results in non-negligible changes in meteorological fields. The meteorological impacts of these events have been analyzed in many studies since the late 1960s. The recent growth in the solar energy industry has greatly increased the interest in providing more detail in the modeling of solar radiation variations in numerical weather prediction (NWP) models for the use in solar resource assessment and forecasting applications. The significant impact of the recent partial and total solar eclipses that occurred in the USA (23 October 2014) and Europe (20 March 2015) on solar power generation have provided additional motivation and interest for including these astronomical events in the current solar parameterizations.Although some studies added solar eclipse episodes within NWP codes in the 1990s and 2000s, they used eclipse parameterizations designed for a particular case study. In contrast to these earlier implementations, this paper documents a new package for the Weather Research and Forecasting-Advanced Research WRF (WRF-ARW) model that can simulate any partial, total or hybrid solar eclipse for the period 1950 to 2050 and is also extensible to a longer period. The algorithm analytically computes the trajectory of the Moon's shadow and the degree of obscuration of the solar disk at each grid point of the domain based on Bessel's method and the Five Millennium Catalog of Solar Eclipses provided by NASA, with a negligible computational time. Then, the incoming radiation is modified accordingly at each grid point of the domain.This contribution is divided in three parts. First, the implementation of Bessel's method is validated for solar eclipses in the period 1950-2050, by comparing the shadow trajectory with values provided by NASA. Latitude and longitude are determined with a bias lower than 5 x 10-3 degrees (i
Bessel processes and hyperbolic Brownian motions stopped at different random times
D'Ovidio, Mirko
2010-01-01
Iterated Bessel processes R^\\gamma(t), t>0, \\gamma>0 and their counterparts on hyperbolic spaces, i.e. hyperbolic Brownian motions B^{hp}(t), t>0 are examined and their probability laws derived. The higher-order partial differential equations governing the distributions of I_R(t)=_1R^\\gamma(_2R^\\gamma(t)), t>0 and J_R(t) =_1R^\\gamma(|_2R^\\gamma(t)|^2), t>0 are obtained and discussed. Processes of the form R^\\gamma(T_t), t>0, B^{hp}(T_t), t>0 where T_t=\\inf{s: B(s)=t} are examined and numerous probability laws derived, including the Student law, the arcsin laws (also their asymmetric versions), the Lamperti distribution of the ratio of independent positively skewed stable random variables and others. For the process R^{\\gamma}(T^\\mu_t), t>0 (where T^\\mu_t = \\inf{s: B^\\mu(s)=t} and B^\\mu is a Brownian motion with drift \\mu) the explicit probability law and the governing equation are obtained. For the hyperbolic Brownian motions on the Poincar\\'e half-spaces H^+_2, H^+_3 we study B^{hp}(T_t), t>0 and the corresp...
Radiation forces on a three-level atom in the high-order Bessel beams
Institute of Scientific and Technical Information of China (English)
Wang Zheng-Ling; Yin Jian-Ping
2008-01-01
The general expressions of the average dissipative and dipole forces acting on a A-configuration three-level atom in an arbitrary light field are derived by means of the optical Bloch equations based on the atomic density matrix elements, and the general properties of the average dissipative and dipole forces on a three-level atom in the linearly-polarized high-order Bessel beams (HBBs) are analysed. We find a resonant property (with two resonant peaks) of the dissipative force and a non-resonant property (with two pairs of non-resonant peaks) of the dipole force on the three-level atom, which are completely different from those on the two-level atom. Meanwhile we find a saturation effect of the average dissipative force in the HBB, which comes from the saturation of the upper-level population. Our study shows that the general expressions of the average dissipative and dipole forces on the three-level atom will be simplified to those of the two-level atom under the approximation of large detuning. Finally, we study the axial and azimuthal Doppler cooling of atoms in 1D optical molasses composed of two counter-propagating HBBs and discuss the azimuthal influence of the HBB on the Doppler cooling limit. We also find that the Doppler limit of atoms in the molasses HBB is slightly below the conventional Doppler limit of hг/(2кB) due to the orbital angular momentum lh of the HBB.
Perturbation approach to resonator state solution using the Fourier-Bessel numerical solver
Gauthier, Robert C.
2017-02-01
The Fourier-Bessel (FFB) numerical solver is a useful tool for obtaining the steady states of resonator structures that conform to a cylindrical symmetry. Recently the FFB solver has been greatly simplified by reconfiguring the matrix generating expressions using Maxwell's curl expressions rather than the standard wave equations. This presentation provides a numerical framework suitable for the application on non-degenerate perturbation theory within the theoretical structure of the reconfigured FFB computation environment. It is shown that the resonator structure's perturbation contribution can be isolated as a separate matrix which dictates the shift in resonator state properties. Two distinct application examples are provide; the first has the perturbation possess the same rotational symmetry as the original structure and preserves azimuthal mode order families; the second perturbation has a symmetry different than the original structure and promotes a mixing between azimuthal mode order families. The perturbation extension promises to amplify the potential usefulness of the FFB technique when theoretically considering photonic sensors such as whispering-gallery mode, photonic crystal hole infiltration and a host of others in which the measurand undergoes small changes in its optical properties.
Spin-orbit photonic interaction engineering of Bessel beams (Conference Presentation)
Aleksanyan, Artur; Brasselet, Etienne
2016-09-01
Interaction between the polarization and spatial degrees of freedom of a light field has become a powerful tool to tailor the amplitude and phase of light beams. This usually implies the use of space-variant photonic elements involving sophisticated fabrication technologies. Here we report on the optical spin-orbit engineering of the intensity, phase, and polarization structure of Bessel light beams using a homogeneous birefringent axicon. Various kinds of spatially modulated free-space light fields are predicted depending on the nature of the incident light field impinging on the birefringent axicon. In particular, we present the generation of bottle beam arrays, hollow beams with periodic modulation of the core size, and hollow needle beams with periodic modulation of the orbital angular momentum. An experimental attempt is also reported. The proposed structured light fields may find applications in long-distance optical manipulation endowed with self-healing features, periodic atomic waveguides, contactless handling of high aspect ratio micro-objects, and optical shearing of matter.
Chaudhry, M A
1998-01-01
Two representations of the extended gamma functions find a transformation relation between two Fox's $H$-functions. These results are used to solve Fox's $H$-function in terms of Meijer's $G$-function for certain values of the parameters. A closed form representation of the kernel of the Bessel type integral transform is also proved.
Institute of Scientific and Technical Information of China (English)
程传福; 刘曼; 滕树云; 宋洪胜; 陈建平; 徐至展
2003-01-01
A method for the extracting the correlation functions of random surfaces is proposed by using the image speckle intensity. Theoretically, we analyse the integral expression of average intensity of the image speckles, and compare it with the pair of Fourier-Bessel-transform-and-the-inversion of the exponential function of the height-height correlation function of the random surfaces. Then the algorithm is proposed numerically to complement the lacking Bessel function factor in the expression of the average speckle intensity, which changes the intensity data into the pair of the Fourier-Bessel-transform. Experimentally, we measure the average image speckle intensities versus the radius of the filtering aperture in the 4 f system and extract the height-height correlation function by using the proposed algorithm. The results of the practical measurements for three surface samples and the comparison with those by atomic force microscopy validate the feasibility of this method.
Special functions for scientists and engineers
Bell, W W
2004-01-01
Clear and comprehensive, this text provides undergraduates with a straightforward guide to special functions. It is equally suitable as a reference volume for professionals, and readers need no higher level of mathematical knowledge beyond elementary calculus. Topics include the solution of second-order differential equations in terms of power series; gamma and beta functions; Legendre polynomials and functions; Bessel functions; Hermite, Laguerre, and Chebyshev polynomials; Gegenbauer and Jacobi polynomials; and hypergeometric and other special functions. Three appendices offer convenient t
Theory and experiment of Fourier-Bessel field calculation and tuning of a pulsed wave annular array
DEFF Research Database (Denmark)
Fox, Paul D.; Jiqi, Cheng; Jian-yu, Lu
2003-01-01
A one-dimensional (1D) Fourier-Bessel series method for computing and tuning (beamforming) the linear lossless field of flat pulsed wave annular arrays is developed and supported with both numerical simulation and experimental verification. The technique represents a new method for modeling....... Tuning of the field then also follows by formulating a least-squares design for the transducer surface pressure with respect to a given desired field in space and time. Simulated and experimental results for both field computation and tuning are presented in the context of a 10-ring annular array...
Wang, Zhe; Zhang, Qingbin; Wang, Shaoyi; Lu, Peixiang
2011-01-01
The generation of isolated attosecond pulses with high efficiency and high beam quality is essential for attosec- ond spectroscopy. We numerically investigate the supercontinuum generation in a neutral rare-gas medium driven by a two-color Bessel-Gauss beam. The results show that an efficient smooth supercontinuum in the plateau is obtained after propagation, and the spatial profile of the generated attosecond pulse is Gaussian-like with the divergence angle of 0.1 degree in the far field. This bright source with high beam quality is beneficial for detecting and controlling the microscopic processes on attosecond time scale.
Solid-state Q-switch laser generating pulsed Bessel beam%全固态调Q激光器产生脉冲Bessel光束
Institute of Scientific and Technical Information of China (English)
王涛; 杜团结; 庄凤江; 吴逢铁
2014-01-01
使用连续式输出的砷化镓半导体激光器泵浦的掺钕钒酸钇激光器作为光源，被动式通过轴棱锥产生Bessel光束。在激光谐振腔内加入Cr4+：YAG晶体调Q产生脉冲Bessel光束。理论模拟了1064 nm波长光束经过轴棱锥之后的三维传播图和截面光强分布。通过实验得到了1064 nm波长脉冲Bessel光束的脉冲宽度和脉冲重复率，并计算得到了单脉冲Bessel光束的能量和峰值功率。利用光束分析仪记录了1064 nm波长Bessel光束的截面光强分布，并测量了中心光斑的直径，得到的数据与理论计算基本吻合。%The laser diode pumped Nd:YVO4 laser was used as light source, Bessel beam was generated by passively passing through axicon. The pulsed Bessel beam was generated by putting the Cr4+:YAG in the laser resonator. The propagation and cross- section distribution of 1 064 nm Bessel beam were simulated. In experiment, the pulse width and pulse repetition rate of 1 064 nm pulse Bessel beam were obtained, the energy and the peak power of pulsed Bessel beam were calculated. The cross- section intensity distribution of Bessel beam was recorded by the laser beam analysis and the diameter of centre spot was measured. The experimental results agrees well with the simulation.
Rahmat-Samii, Y.; Galindo-Israel, V.
1981-01-01
It is pointed out that the computation of the Fresnel fields for large aperture antennas is significant for many applications. The present investigation is concerned with an approach for the effective utilization of the coefficients of the Jacobi-Bessel series for the far-field to obtain an analytically continuous representation of the antenna field which is valid from the Fresnel region into the far field. Attention is given to exact formulations and closed form solutions, Fresnel and Fresnel small angle approximations, aspects of field expansion, the accuracy of the Fresnel and Fresnel small angle approximations, and the Jacobi-Bessel expansion applied to the Fresnel small angle approximation.
Negative optical spin torque wrench of a non-diffracting non-paraxial fractional Bessel vortex beam
Mitri, F. G.
2016-10-01
An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge α and the half-cone angle of the beam. When α is zero, the axial spin torque component vanishes. However, when α becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable of inducing a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, and the design of optically-engineered metamaterials to name a few areas.
Analysis for the Potential Function of the Digital Microstructure Image of Porous Media
Institute of Scientific and Technical Information of China (English)
XUYou-Sheng; LINJi; LIHua-Mei; WUPeng-Min
2003-01-01
Making use of the full information obtained in our previous discussions, a new analytical solutions for the potential function of the digital microstructure image of porous media is reported in this paper. It is demonstrated that the distribution of potential function depends on the zeroth order Bessel function. All these will be helpful for analyzing the similar subjects in porous media.
Analysis for the Potential Function of the Digital Microstructure Image of Porous Media
Institute of Scientific and Technical Information of China (English)
XU You-Sheng; LIN Ji; LI Hua-Mei; WU Feng-Min
2003-01-01
Making use of the full information obtained in our previous discussions, a new analytical solutions for thepotential function of the digital microstructure image of porous media is reported in this paper. It is demonstrated that the distribution of potential function depends on the zeroth order Bessel function. All these will be helpful for analyzingthe similar subjects in porous media.
Institute of Scientific and Technical Information of China (English)
于永江; 陈建农; 闫金良; 王菲菲
2011-01-01
Longitudinally polarized subwavelength beams have found many applications such as particle acceleration, single molecule dipole detection, second harmonic generation imaging, longitudinally polarization confocal microscopy. We present a radially modulated Bessel-Gaussian beam model which produces longitudinally polarized beams with high purity after being focused by high numerical aperture objective. Based on the vector diffraction theory, the electric field intensity distribution, magnetic field intensity distribution and energy flux density near the focal plane are numerically simulated.The result shows that the full-width at half-maximum is as small as 0.4λ. The method does not require a physical annulus or annular phase filter and it features high energy efficiency, high resolution, thus improving application performances.%亚波长尺寸纵向偏振光束在粒子加速,单个分子偶极矩测量,二次谐波成像和纵向偏振共焦显微镜等方面有非常广泛的应用.本文提出径向调制的Bessel-Gaussian光束模型,经高数值孔径显微物镜聚焦可以获得高纯度的纵向偏振光束.利用矢量衍射理论数值模拟了焦点附近光强分布、磁场分布和能流密度空间分布.结果表明光斑半高全宽度可以达到0.4λ.该方法无需环形孔径或环形相位滤波器,光能利用率高,分辨率好,达到改进各种应用的效果.
Ambrosio, Leonardo A; Hernández-Figueroa, Hugo E
2011-08-01
When impinged by an arbitrary laser beam, lossless and homogeneous negative refractive index (NRI) spherical particles refract and reflect light in an unusual way, giving rise to different scattered and internal fields when compared to their equivalent positive refractive index particles. In the generalized Lorenz-Mie theory, the scattered fields are dependent upon the Mie scattering coefficients, whose values must reflect the metamaterial behavior of an NRI scatterer, thus leading to new optical properties such as force and torque. In this way, this work is devoted to the analysis of both radial and longitudinal optical forces exerted on lossless and simple NRI particles by zero-order Bessel beams, revealing how the force profiles are changed whenever the refractive index becomes negative.
Li, Ye; Zhang, Yixin; Wang, Donglin; Shan, Lei; Xia, Mingchao; Zhao, Yuanhang
2016-05-01
The effects of strong turbulence on the orbital angular momentum (OAM) states of infrared and non-diffraction beam propagation in a terrestrial atmosphere are investigated. A new probability density model for OAM states of Bessel-Gaussian-Schell beam in the paraxial and strong turbulent channel is modeled based on the modified Rytov approximation. We find that the normalization energy weight of signal OAM modes at each OAM level is approximate equivalence in strong turbulence regime, one can constitute multiple mode channels by choosing OAM modes with large energy level difference between modes to reduce mode interference, and one can utilize BGS beam with OAM modes increasing the channel capacity of optical communications.
Wang, Zhi-Bin; Zhang, Rui; Wang, Yao-Li; Huang, Yan-Fei; Chen, You-Hua; Wang, Li-Fu; Yang, Qiang
2014-02-01
As the existing photoelastic-modulator(PEM) modulating frequency in the tens of kHz to hundreds of kHz between, leading to frequency of modulated interference signal is higher, so ordinary array detector cannot effectively caprure interference signal..A new beat frequency modulation method based on dual-photoelastic-modulator (Dual-PEM) and Fourier-Bessel transform is proposed as an key component of dual-photoelastic-modulator-based imaging spectrometer (Dual-PEM-IS) combined with charge coupled device (CCD). The dual-PEM are operated as an electro-optic circular retardance modulator, Operating the PEMs at slightly different resonant frequencies w1 and w2 respectively, generates a differential signal at a much lower heterodyne frequency that modulates the incident light. This method not only retains the advantages of the existing PEM, but also the frequency of modulated photocurrent decreased by 2-3 orders of magnitude (10-500 Hz) and can be detected by common array detector, and the incident light spectra can be obtained by Fourier-Bessel transform of low frequency component in the modulated signal. The method makes the PEM has the dual capability of imaging and spectral measurement. The basic principle is introduced, the basic equations is derived, and the feasibility is verified through the corresponding numerical simulation and experiment. This method has' potential applications in imaging spectrometer technology, and analysis of the effect of deviation of the optical path difference. This work provides the necessary theoretical basis for remote sensing of new Dual-PEM-IS and for engineering implementation of spectra inversion.
1981-05-01
involving modified Bessel function and Fox’s H- function," Rivista di Matematica della Universita di Parma. Italie, (3) 2, 109-113 (1973). function...Ciencias Matematicas , A(2) 14, 105-111 (1971-72). 100. Dahiya, R. S., "ultiple integrals and the transformations involving H- functions and Tchebichef...transform," R di Matematica della Universita di Parma. Italie, 5, 159- 164 (1964). 117. Gupta, R. K., and S. D. Sharma, "Some infinite integrals involv- ing
Kim, Jongki; Jeong, Yoonseob; Lee, Sejin; Ha, Woosung; Shin, Jeon-Soo; Oh, Kyunghwan
2012-02-15
Highly efficient Bessel-like beam generation was achieved based on a new all-fiber method that implements Fourier transformation of a micro annular aperture along a concatenated composite optical fiber. The beam showed unique characteristics of tilted washboard optical potential in the transverse plane and sustained a nondiffracting length over 400 μm along the axial direction. Optical trapping of multiple dielectric particles and living Jurkat cells were successfully demonstrated along the axial direction of the beam in the water.
Swain, Prasad Kumar; Goswami, Nabamita; Saha, Ardhendu
2017-01-01
A new theoretical approach towards the composite effect of spatial and angular Goos-Hanchen (GH) shift and Imbert-Fedorov (IF) shift for the Gaussian beam, Laguerre-Gaussian beam and Bessel beam with long range surface plasmon (LRSP) resonance is observed, designed and simulated through the variation of incident angle at a wavelength of 1550 nm where the four layered Kreschmann-Rather geometry comprises a ZnSe prism, a liquid crystal layer of E44 and two metal layers of silver. To the best of our knowledge several articles have been devoted, separately considering the Gaussian beam, Laguerre-Gaussian beam and Bessel beam without considering the effect of spatial and angular GH shift and IF shift whereas the exact output beam position can only be identified with the composite effect of these shifts. The investigation of these spatial and angular shifts for Gaussian beam and different orders of Laguerre-Gaussian beam are calculated and represented where these lateral shifts increase with the increment of the modes and further these lateral shifts for Bessel beam have also been analyzed. With this new approach various avenues expedite the way of futuristic applications in the field of fine tuning in optical switching with the accurate beam position using different beams.
Gil, A.; Segura, J.; Temme, N.M.
2004-01-01
We describe a variety of methods to compute the functions Kia (x), Lia (x) and their derivatives for real a and positive x. These functions are numerically satisfactory independent solutions of the differential equation x2w'' + xw' + (a2
On bounds of certain classes of special functions
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C. M. Joshi
2001-03-01
Full Text Available Inequalities of the ratios of Whittaker function, which include in its fold inequalities of a large class of special functions, are obtained. In the sequel inequalities of the ratios of Bessel functions of 2nd kind and inequalities of the ratios $ J_v(x / Y_v(x $ are also derived. Finally, we point out some correction which appear in the paper of Joshi and Bissu (J. Aust. Math. Soc., Ser. A. 50(1991, 333-342.
The functions of mathematical physics
Hochstadt, Harry
2012-01-01
A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics.In the 18th and 19th centuries, the theorists who devoted themselves to this field - pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel - were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating
Bessel-weighted asymmetries in semi-inclusive deep inelastic scattering
Boer, D.; Gamberg, L.; Musch, B. U.; Prokudin, A.
2011-01-01
The concept of weighted asymmetries is revisited for semi-inclusive deep inelastic scattering. We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation f
Generalised partition functions: inferences on phase space distributions
Treumann, Rudolf A.; Baumjohann, Wolfgang
2016-06-01
It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs-Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1/|q - 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel-Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs-Boltzmann partition function is fundamental not only to Gibbs-Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.
热光源产生贝塞尔光束的理论与实验%Theory and Experiment of Bessel Beam Generated by Thermal Light Source
Institute of Scientific and Technical Information of China (English)
程治明; 吴逢铁; 郑维涛; 张前安; 范丹丹
2012-01-01
Bessel-like beam is generated by using thermal light source. The incident condition for the light waves with multi-wavelength passing through axicon simultaneously is analyzed and simulated. The results show that Bessel beam can be generated behind the axicon, but the contrast of the cross section light intensity drops because of the incoherent superposition of the multi-wavelength light waves. In our experiment, halogen light cup is used as thermal light source for generating Bessel beam. A set of optical system is designed to improve the spatial coherence of the light waves, and the Besse!-!ike beam is generated after the light waves passing the axicon. Comparing the experimental result with the numerical simulation, it is found that Bessel beam obtained from experiment is basically in accord with the numerical calculation. Besides the maximum diffraction-free distance is shorter in the experiment, which is analyzed at the end of the paper.%利用热光源获得了近似贝塞尔光束.对多波长光波同时入射轴棱锥的情形进行分析和数值模拟,结果显示轴棱锥后会形成近似贝塞尔光束,但受光场非相干叠加的影响截面光强对比度降低.实验采用卤素灯杯作为产生贝塞尔光束的热光源,针对热光源相干性差的特点设计出一套光学系统,提高光波的空间相干性,再使光波平行透过轴棱锥得到了近似贝塞尔光束.将实验结果与数值计算对比,发现实验所得贝塞尔光束的特性与理论基本吻合,但最大无衍射距离较理论计算所得的短,并对此进行了分析.
Spatially induced Airy-Bessel light bullets%空间诱导产生艾里-贝塞尔光弹研究
Institute of Scientific and Technical Information of China (English)
任志君; 吴琼; 周卫东; 吴根柱; 施逸乐
2012-01-01
利用波动方程，研究了脉冲贝塞尔光束在自由空间传输时的空间诱导群速度色散（SIGVD）效应．结果表明，三阶SIGVD能使脉冲贝塞尔光束的时域逐渐演化为艾里分布．由于艾里一贝塞尔光弹是一种新奇的时、空都不扩展的局域波包，能在光与物质相互作用的很多应用领域发挥作用．因此，本文提出了通过色散管理技术补偿二阶SIGVD，利用三阶SIGVD在自由空间产生艾里．贝塞尔光弹的方案．为分析这种光弹的时空传输特性，数值模拟了它在色散介质中的传输情况．结果表明，这种光弹能在色散介质中保持空域不衍射、时域不色散的稳定传输．%Based on wave equation, we theoretically study the effect of spatially induced group velocity dispersion （SIGVD） of pulsed Bessel light beam propagation in free space. The results show that the third-order SIGVD can make pulsed Bessel beam gradually evolve into temporally Airy distribution. Airy-Bessel wave packet is such an exotic localized optical wave packet that it can possibly serve versatile tool in the research of light-matter interactions and has extensive applications. Hence we demonstrate the realization scheme of Airy-Bessel light bullets in free space by compensating the second-order SIGVD through utilizing dispersion management technique. To analyze the spatiotemporal propagation properties, we numerically simulate this light bullet propagation in a dispersion medium. The results show that it can retain spatial diffraction-free and temporal dispersion-free propagation in medium.
Bessel-Modal Method for Finite-Height Two-Dimensional Photonic Crystal
Institute of Scientific and Technical Information of China (English)
SHI Jun-Feng; HUANG Sheng-Ye; WANG Dong-Sheng
2005-01-01
@@ By applying the dyadic Green function, the dispersion relation of two-dimensional photonic crystal can be ex pressed as the cylindrical wave expansions of eigenmodes. With the aid of Green's theorem, the plane-wavecoefficients of eigenmodes are reconstructed and employed to formulate the scattering matrix of finite-height twodimensional photonic crystal. These operations make the convergence rate very rapid, and reduce the dimension of the scattering matrix. As a demonstration, we present the transmission and electromagnetic field distributions for an InGaAsIn photonic crystal, and investigate their convergence.
Excursions and local limit theorems for Bessel-like random walks
Alexander, Kenneth S
2009-01-01
We consider reflecting random walks on the nonnegative integers with drift of order 1/x at height x. We establish explicit asymptotics for various probabilities associated to such walks, including the distribution of the hitting time of 0 and first return time to 0, and the probability of being at a given height k at time n (uniformly in a large range of k.) In particular, for drift of form -\\delta/2x + o(1/x) with \\delta > -1, we show that the probability of a first return to 0 at time n is asymptotically n^{-c}\\phi(n), where c = (3+\\delta)/2 and \\phi is a slowly varying function given explicitly in terms of the o(1/x) terms.
Directory of Open Access Journals (Sweden)
Nader Ali Makboul Hassan
2014-01-01
Full Text Available This paper is an attempt to stress the usefulness of the multi-variable special functions. In this paper, we derive certain generating relations involving 2-indices 5-variables 5-parameters Tricomi functions (2I5V5PTF by using a Lie-algebraic method. Further, we derive certain new and known generating relations involving other forms of Tricomi and Bessel functions as applications.
Ahmed, Nisar; Zhao, Zhe; Li, Long; Huang, Hao; Lavery, Martin P J; Liao, Peicheng; Yan, Yan; Wang, Zhe; Xie, Guodong; Ren, Yongxiong; Almaiman, Ahmed; Willner, Asher J; Ashrafi, Solyman; Molisch, Andreas F; Tur, Moshe; Willner, Alan E
2016-03-01
We experimentally investigate the potential of using 'self-healing' Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively.
2014-08-04
trigonometric functions of large arguments. 11. Conclusions We have shown that the solutions of a large class of second order differential equations can be...nonoscillatory phase functions . In addition, we describe numerical experiments which illustrate com- putational implications of this fact. For example, many...special functions of interest — such as the Bessel functions Jν and Yν — can be evaluated accurately using a number of operations which is Op1q in
On Parameter Differentiation for Integral Representations of Associated Legendre Functions
Cohl, Howard S.
2011-05-01
For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-half-integer degrees, for general complex-orders, and derivatives with respect to the order are evaluated at integer-orders, for general complex-degrees. We also discuss the properties of the complex function f: C\\{-1,1}→C given by f(z)=z/((z+1)1/2(z-1)1/2).
On parameter differentiation for integral representations of associated Legendre functions
Cohl, Howard S
2011-01-01
For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-half-integer degrees, for general complex-orders, and derivatives with respect to the order are evaluated at integer-orders, for general complex-degrees. We also discuss the properties of the complex function $f:\\C\\setminus\\{-1,1\\}\\to\\C$ given by $f(z)=z/\\sqrt{(z+1)(z-1)}$.
Directory of Open Access Journals (Sweden)
Bäcker, Rolf
2006-12-01
Full Text Available
The present paper is devoted to the German musicologist Heinrich Besseler and his relation with the Instituto Español de Musicología through Miquel Querol and Higini Anglès, which can be regarded as a paradigm for the participation of Spanish musicology in the international network of institutions and individuals devoted to the discipline. Relying on documentation conserved in the Department of Musicology at the Institució Milà i Fontanals, the present contribution expects to cast some light on Besseler and the IEM, whose collaboration led to a study that was presented on internacional level at the IV Congreso of the Internacional Musicological Society.
El presente artículo centra su interés en el musicólogo alemán Heinrich Besseler, y su relación con el Instituto Español de Musicología a través de Miquel Querol y Higini Anglès, relación de algún modo paradigmática para la participación de la musicología española de la época en la red internacional de instituciones y personas dedicadas a la disciplina. Basándose en la documentación guardada en el Departamento de Musicología de la Institució Milà i Fontanals, la presente contribución pretende arrojar alguna luz sobre Besseler y el IEM, cuya colaboración se concretó en un estudio presentado a escala internacional en el IV Congreso de la Sociedad International de Musicología.
Institute of Scientific and Technical Information of China (English)
邵先喜; 尹传存
2001-01-01
对暂留Bessel过程X，令I(t)=infs>tX(s)及ξ(t)＝inf{u≥t：X(u)＝I(t)}， 本文求出了I(t)，ξ(t)及Xt的联合分布.%For a transient Bessel process X let I(t) ＝ inf>tX(s) and ε(t) ＝ inf{u >t: X(u) ＝ I(t)}. In this note we compute the joint distribution of I(t),ε(t) and Xt.
Sarkadi, L.
2017-03-01
The program MTRXCOUL [1] calculates the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ ψf∗ (r) | R - r | - 1ψi(r) d r. Bound-free transitions are considered, and non-relativistic hydrogenic wave functions are used. In this revised version a bug discovered in the F3Y CPC Program Library (PL) subprogram [2] is fixed. Furthermore, the COULCC CPC PL subprogram [3] applied for the calculations of the radial wave functions of the free states and the Bessel functions is replaced by the CPC PL subprogram DCOUL [4].
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
A novel energy analyzer with a simple-structured Bessel-box has been successfully developed and incorporated into ionization gauges and quadrupole mass spectrometers (QMS) to improve their measurement of the total and partial pressures,respectively.We found that the energy analyzer may not only effectively separate the gas phase ions and electron stimulated desorption (ESD) ions produced in the ionizer,but also screen the ion collector from irradiation of the soft X-rays and VUVphotons generated in the ionizer.The screening effects considerably better the trace impurity detection limit of the QMS down to a few tens ppb in the pressure range of 10-3 Pa.The modified ionization gauge is capable of measuring pressure ranging from 10-11 to 10-6 Pa in the pulse counting mode and its upper limit may extends to 10-3 Pa in DC ion current mode with typical sensitivities factor of(6.7±0.2)×10-3 Pa-1 for N2 and (2.3±0.2)×10-3 Pa-1 for H2,respectively.No ESD ions was observed in the simple-looking spectrum obtained with the modified QMS.We also found that the energy spectra of fragment ions depend strongly on species of parent ions.
贝塞尔高斯光束通过硬边光阑的衍射损耗%Losses of Bessel-Gaussian Beams Propagating through a Hard-Edge Aperture
Institute of Scientific and Technical Information of China (English)
王莉
2001-01-01
The losses Bessel-Gaussian beams, a kind of non-diffracting beam,propagating through a hard aperture are studied, and a general formula is derived. As an example of applications, numerical calculation is performed to calculate the losses of Bessel-Gaussian beams propagating through a circular aperture. The obtained results are analyzed and discussed. The proposed method can also be applied to calculation of the losses of other types of laser beams propagating through a hard-edge aperture.%对无衍射光束——贝塞尔高斯光束通过硬边光阑时的功率损耗作了研究，给出了普适的损耗公式。作为应用举例，对零阶贝塞尔高斯光束通过圆孔硬边光阑时的衍射损耗作了详细的计算。对计算结果进行了分析和讨论。该方法还可用于其它光束通过硬边光阑的衍射损耗计算。
Generalized fractional integration of the \\overline{H}-function
Directory of Open Access Journals (Sweden)
Praveen Agarwal
2012-11-01
Full Text Available A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera. In the present paper, we study and develop the generalized fractional integral operators given by Saigo. First, we establish two Theorems that give the images of the product of H-function and a general class of polynomials inSaigo operators. On account of the general nature of the Saigo operators, H-function and a general class of polynomials a large number of new and known Images involving Riemann-Liouville and Erdélyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric function, generalized Wright-Bessel function, the polylogarithm and Mittag-Leffler functions follow as special cases of our main findings.
Directory of Open Access Journals (Sweden)
Fedoua Gandia
2014-07-01
Full Text Available The study was carried out to investigate the effects of inhaled Mg alone and associated with F in the treatment of bronchial hyperresponsiveness. 43 male Wistar rats were randomly divided into four groups and exposed to inhaled NaCl 0.9%, MeCh, MgSO4 and MgF2. Pulmonary changes were assessed by means of functional tests and quantitative histological examination of lungs and trachea. Results revealed that delivery of inhaled Mg associated with F led to a significant decrease of total lung resistance better than inhaled Mg alone (p < 0.05. Histological examinations illustrated that inhaled Mg associated with F markedly suppressed muscular hypertrophy (p = 0.034 and bronchoconstriction (p = 0.006 in MeCh treated rats better than inhaled Mg alone. No histological changes were found in the trachea. This study showed that inhaled Mg associated with F attenuated the main principle of the central components of changes in MeCh provoked experimental asthma better than inhaled Mg alone, potentially providing a new therapeutic approach against asthma.
Computer routines for probability distributions, random numbers, and related functions
Kirby, W.H.
1980-01-01
Use of previously codes and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main programs. The probability distributions provided include the beta, chisquare, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F tests. Other mathematical functions include the Bessel function I (subzero), gamma and log-gamma functions, error functions and exponential integral. Auxiliary services include sorting and printer plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)
Methods of theme presentation "The Fourier transform of impulse functions"
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Faniya Ahmetova
2016-09-01
Full Text Available The paper considers the Fourier transform of impulse functions, which is the mathematical basis of the tasks associated with the theory of reception and signal conversion in optoelectronic system. The method of calculating of two functions convolution, its Fourier image and the image of the Fourier-Bessel axisymmetric functions are demonstrated in details. A table, which summarizes the analytical expression for the shifted impulse functions and records their Fourier transforms, is provided. A wide range of examples of solving tasks, containing the graphic illustration, is analyzed. A structured approach to the presentation of the material, which combines basic theoretical information and analysis of typical tasks, will help second-year students of optoelectronic specialty in their independent work and homework.
On Parameter Differentiation for Integral Representations of Associated Legendre Functions
Directory of Open Access Journals (Sweden)
Howard S. Cohl
2011-05-01
Full Text Available For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-half-integer degrees, for general complex-orders, and derivatives with respect to the order are evaluated at integer-orders, for general complex-degrees. We also discuss the properties of the complex function f: C{−1,1}→C given by f(z=z/((z+1^{1/2}(z−1^{1/2}.
Efficient and accurate computation of electric field dyadic Green's function in layered media
Cho, Min Hyung
2016-01-01
Concise and explicit formulas for dyadic Green's functions, representing the electric and magnetic fields due to a dipole source placed in layered media, are derived in this paper. First, the electric and magnetic fields in the spectral domain for the half space are expressed using Fresnel reflection and transmission coefficients. Each component of electric field in the spectral domain constitutes the spectral Green's function in layered media. The Green's function in the spatial domain is then recovered involving Sommerfeld integrals for each component in the spectral domain. By using Bessel identities, the number of Sommerfeld integrals are reduced, resulting in much simpler and more efficient formulas for numerical implementation compared with previous results. This approach is extended to the three-layer Green's function. In addition, the singular part of the Green's function is naturally separated out so that integral equation methods developed for free space Green's functions can be used with minimal mo...
Problems of the theory of the consolidation solved in the special functions
Dasibekov, Azhibek; Abzhapbarov, Azimkhan; Duisebayeva, Peruza; Polatbek, Aigul
2016-08-01
The soil, which deformation modulus is continuously increased with depth is called continuously heterogeneous. In this paper, this heterogeneity is presented in the form of: E =Em(α+β z ) m (α >0 ,Em>0 ,α +βz>0 ), wher Em, α, β, m are experimental parameters. On the basis of this dependence the consolidation problems of elastic and elastically creeping inhomogeneous soils are solved in relation to the restricted area of the consolidation. These solutions make it possible to calculate the values of the pore pressure, the amount of the main stresses and vertical displacements of upper surface points of the condensed inhomogeneous soil mass. In these solutions for highly compressed water-saturated clay soils is also taken into account that at the initial time the part of loading, instantly enclosed load q to the soil which is equal in value of the structural strength of the compression pstr, is immediately perceived by a matrix. In addition, Darcy's law is broken, i.e. the initial gradient of pressure is considered. The resulting calculation formulas are presented as a combination of Bessel functions of the first and second kinds. Taking into account that currently one can define any values of the Bessel functions, it is possible to calculate the pressure in the pore fluids and predict the speed of sediments of the compacting mass.
Analytical fits to the synchrotron functions
Institute of Scientific and Technical Information of China (English)
Mourad Fouka; Saad Ouichaoui
2013-01-01
Accurate fitting formulae to the synchrotron function,F(x),and its complementary function,G(x),are performed and presented.The corresponding relative errors are less than 0.26％ and 0.035％ for F(x) and G(x),respectively.To this end we have,first,fitted the modified Bessel functions,K5/3(x) and K2/3(x).For all the fitted functions,the general fit expression is the same,and is based on the well known asymptotic forms for low and large values of x for each function.It consists of multiplying each asymptotic form by a function that tends to unity or zero for low and large values of x.Simple formulae are suggested in this paper,depending on adjustable parameters.The latter have been determined by adopting the Levenberg-Marquardt algorithm.The proposed formulae should be of great utility and simplicity for computing spectral powers and the degree of polarization for synchrotron radiation,both for laboratory and astrophysical applications.
Analytical Fits to the Synchrotron Functions
Fouka, M
2013-01-01
Accurate fitting formulae to the synchrotron function, $F(x)$, and its complementary function, $G(x)$, are performed and presented. The corresponding relative errors are less than $0.26\\%$ and $0.035\\%$ for $F(x) $ and $G(x)$, respectively. To this aim we have, first, fitted the modified Bessel functions, $K_{5/3}(x)$ and $K_{2/3}(x)$. For all the fitted functions, the general fit expression is the same, and is based on the well known asymptotic forms for low and large $x$-values for each function. It consists of multiplying each asymptotic form by a function that tends to unity or zero for low and large $x$-values. Simple formulae are suggested in this paper, depending on adjustable parameters. The latter have been determined by adopting the Levenberg-Marquardt algorithm. The proposed formulae should be of great utility and simplicity for computing spectral powers and the degree of polarization for the synchrotron radiation, both for laboratory and astrophysical applications.
Institute of Scientific and Technical Information of China (English)
陈斐楠; 陈晶晶; 赵琦; 陈延如; 王勇清; 辛煜
2012-01-01
利用广义惠更斯菲涅耳原理计算高阶贝塞尔高斯光束(BGB)在非柯尔莫哥诺夫湍流模型下传输的横向光强分布特性.该模型中,湍流对相位干扰的大小与距离和幂律有关.在远距离处,幂律对干扰大小的影响较为明显.通过Matlab进行数值计算的结果表明,远距离处(10 kmn)的各阶BGB光束光强分布形式均有很大展宽,同时它们随幂律的变化也相对于短距离时更为剧烈.高阶BGB光束受到湍流干扰的影响要小于低阶光束.对于同阶光束来说,横向参数越大的光源在湍流中传输的展宽现象也越为明显.%Extended Huygens-Fresnel principle is used to analyze the optical intensity transverse distribution of higher-order Bessel Gaussian beam (BGB) propagation through non-Kolmogorov (NoK) atmosphere turbulence model. In NoK turbulence model, the distance and power law effect the strength at phase perturbed by turbulence. So the result by numerical integral shows that the intensity distribution of BGB beam gets more severe changes at large distance. The higher order beam is less effected by turbulence than lower order beam. The lager transverse parameter of the source can get more spreads when it propagates through turbulence.
TORSIONAL IMPACT RESPONSE OF A PENNY-SHAPED CRACK IN A FUNCTIONAL GRADED STRIP
Institute of Scientific and Technical Information of China (English)
冯文杰; 李向国; 王守东
2004-01-01
The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered. The shear modulus is assumed to be functionally graded such that the reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering behavior of Bessel function. Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived. And it is shown that, as crack igated are the effects of material nonhomogeneity and strip's highness on the dynamic fracture behavior.at the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus, and that the ting of the strip' s highness.
Indefinite integrals of products of some exponential and trigonometric functions
Rostafinski, W. A.
1972-01-01
Two integrals have been developed which are needed to solve certain problems of mathematical physics related to the Bessel and Euler equations. Integrals of this type have known application in problems using cylindrical coordinates.
Expansion of Arbitrary Electromagnetic Fields in Terms of Vector Spherical Wave Functions
Moreira, W L; Garbos, M K; Euser, T G; Russell, P St J; Cesar, C L
2010-01-01
Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of an electromagnetic plane-wave, generalizing his analysis to the case of an arbitrary incident wave has proved elusive. This is due to the presence of certain radially-dependent terms in the equation for the beam-shape coefficients of the expansion of the electromagnetic fields in terms of vector spherical wave functions. Here we show for the first time how these terms can be canceled out, allowing analytical expressions for the beam shape coefficients to be found for a completely arbitrary incident field. We give several examples of how this new method, which is well suited to numerical calculation, can be used. Analytical expressions are found for Bessel beams and the modes of rectangular and cylindrical metallic waveguides. The results are highly relevant for speeding up calculation of the radiation forces acting on small spherical particles placed in an arbitrary electromagnetic field, fo...
Energy Technology Data Exchange (ETDEWEB)
Cvetic, G. [Universidad Tecnica Federico Santa Maria, Valparaiso (Chile). Dept. of Physics; Illarionov, A.Yu. [International School for Advanced Studies SISSA, Trieste (Italy); Kniehl, B.A.; Kotikov, A.V. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik
2009-06-15
Using the leading-twist approximation of the Wilson operator product expansion with ''frozen'' and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F{sub 2} and its slope {partial_derivative}lnF{sub 2}/{partial_derivative}ln(1/x) at small values of x, obtained for a at initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of deep-inelastic scattering at DESY HERA. (orig.)
Directory of Open Access Journals (Sweden)
Cristian Hernando Acevedo
2015-01-01
Full Text Available La carga topológica de una onda electromagnética CT, está relacionada con su distribucion espacial en el frente de onda. Ondas electromagnéticas con un factor acimutal exp(il en su fase, tienen CT entera (l=m o no entera (l=M. Estas ondas electromagnéticas con un valor definido de carga topológica pueden ser producidas en el régimen visible utilizando máscaras tenedor holográficas generadas por computador. En este artículo se estudia mediante simulaciones numéricas la red triangular formada en el régimen de intensidad de Fraunhofer de haces Bessel-Gauss con CT entera y no entera que han difractado sobre una rendija en forma triangular para determinar su signo y su magnitud. También se presentan los resultados experimentales de la intensidad en campo lejano obtenidos al difractar una onda luminosa Bessel-Gauss con CT entera y no entera a través de una rendija triangular equilátera. Argumentos cualitativos parciales han sido expuestos para explicar el fenómeno de difracción de estos haces con carga topológica. Aquí se presentan argumentos cualitativos y cuantitativos que permiten explicar todos los resultados de la difracción por una abertura triangular de haces con carga topológica obtenidos ya sea por simulación numérica o mediante su realización experimental.
Hypergeometric type functions and their symmetries
2013-01-01
We give a systematic and unified discussion of various classes of hypergeometric type equations: the hypergeometric equation, the confluent equation, the F_1 equation (equivalent to the Bessel equation), the Gegenbauer equation and the Hermite equation. In particular, we discuss recurrence relations of their solutions, their integral representations and discrete symmetries.
Explicit solutions of fractional diffusion equations via Generalized Gamma Convolution
D'Ovidio, Mirko
2010-01-01
In this paper we deal with Mellin convolution of generalized Gamma densities which brings to integrals of modified Bessel functions of the second kind. Such convolutions allow us to write explicitly the solutions of the time-fractional diffusion equations involving the adjoint operators of a square Bessel process and a Bessel process.
On computation and use of Fourier coefficients for associated Legendre functions
Gruber, Christian; Abrykosov, Oleh
2016-06-01
The computation of spherical harmonic series in very high resolution is known to be delicate in terms of performance and numerical stability. A major problem is to keep results inside a numerical range of the used data type during calculations as under-/overflow arises. Extended data types are currently not desirable since the arithmetic complexity will grow exponentially with higher resolution levels. If the associated Legendre functions are computed in the spectral domain, then regular grid transformations can be applied to be highly efficient and convenient for derived quantities as well. In this article, we compare three recursive computations of the associated Legendre functions as trigonometric series, thereby ensuring a defined numerical range for each constituent wave number, separately. The results to a high degree and order show the numerical strength of the proposed method. First, the evaluation of Fourier coefficients of the associated Legendre functions has been done with respect to the floating-point precision requirements. Secondly, the numerical accuracy in the cases of standard double and long double precision arithmetic is demonstrated. Following Bessel's inequality the obtained accuracy estimates of the Fourier coefficients are directly transferable to the associated Legendre functions themselves and to derived functionals as well. Therefore, they can provide an essential insight to modern geodetic applications that depend on efficient spherical harmonic analysis and synthesis beyond [5~× ~5] arcmin resolution.
Multiple zeta functions and double wrapping in planar N=4 SYM
Leurent, Sébastien
2013-01-01
Using the FiNLIE solution of the AdS/CFT Y-system, we compute the anomalous dimension of the Konishi operator in planar N=4 SYM up to eight loops, i.e. up to the leading double wrapping order. At this order a non reducible Euler-Zagier sum, zeta(1,2,8), appears for the first time. We find that at all orders in perturbation, every spectral-dependent quantity of the Y-system is expressed through multiple Hurwitz zeta functions, hence we provide a Mathematica package to manipulate these functions, including the particular case of Euler-Zagier sums. Furthermore, we conjecture that only Euler-Zagier sums can appear in the answer for the anomalous dimension at any order in perturbation theory. We also resum the leading transcendentality terms of the anomalous dimension at all orders, obtaining a simple result in terms of Bessel functions. Finally, we demonstrate that exact Bethe equations should be related to an absence of poles condition that becomes especially nontrivial at double wrapping.
Interpolation by Hankel Translates of a Basis Function: Inversion Formulas and Polynomial Bounds
Directory of Open Access Journals (Sweden)
Cristian Arteaga
2014-01-01
Full Text Available For μ≥−1/2, the authors have developed elsewhere a scheme for interpolation by Hankel translates of a basis function Φ in certain spaces of continuous functions Yn (n∈ℕ depending on a weight w. The functions Φ and w are connected through the distributional identity t4n(hμ′Φ(t=1/w(t, where hμ′ denotes the generalized Hankel transform of order μ. In this paper, we use the projection operators associated with an appropriate direct sum decomposition of the Zemanian space ℋμ in order to derive explicit representations of the derivatives SμmΦ and their Hankel transforms, the former ones being valid when m∈ℤ+ is restricted to a suitable interval for which SμmΦ is continuous. Here, Sμm denotes the mth iterate of the Bessel differential operator Sμ if m∈ℕ, while Sμ0 is the identity operator. These formulas, which can be regarded as inverses of generalizations of the equation (hμ′Φ(t=1/t4nw(t, will allow us to get some polynomial bounds for such derivatives. Corresponding results are obtained for the members of the interpolation space Yn.
Interpolation by Hankel translates of a basis function: inversion formulas and polynomial bounds.
Arteaga, Cristian; Marrero, Isabel
2014-01-01
For μ≥-1/2, the authors have developed elsewhere a scheme for interpolation by Hankel translates of a basis function Φ in certain spaces of continuous functions Yn(n∈ℕ) depending on a weight w. The functions Φ and w are connected through the distributional identity t4n(hμ'Φ)(t)=1/w(t), where hμ' denotes the generalized Hankel transform of order μ. In this paper, we use the projection operators associated with an appropriate direct sum decomposition of the Zemanian space ℋμ in order to derive explicit representations of the derivatives SμmΦ and their Hankel transforms, the former ones being valid when m∈ℤ+ is restricted to a suitable interval for which SμmΦ is continuous. Here, Sμm denotes the mth iterate of the Bessel differential operator Sμ if m∈ℕ, while Sμ0 is the identity operator. These formulas, which can be regarded as inverses of generalizations of the equation (hμ'Φ)(t)=1/t4nw(t), will allow us to get some polynomial bounds for such derivatives. Corresponding results are obtained for the members of the interpolation space Y n .
A spectral scheme for Kohn–Sham density functional theory of clusters
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Amartya S., E-mail: baner041@umn.edu; Elliott, Ryan S., E-mail: relliott@umn.edu; James, Richard D., E-mail: james@umn.edu
2015-04-15
Starting from the observation that one of the most successful methods for solving the Kohn–Sham equations for periodic systems – the plane-wave method – is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn–Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn–Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.
Discussion on Cylindrical Function Teaching%关于柱函数的教学探讨
Institute of Scientific and Technical Information of China (English)
侯慎勇; 赵博
2015-01-01
Cylindrical function is an important content of methods of mathematical physics. It includes Bessel function, Neumann function and Hankel function. Since these functions have complex expressions, lot of properties and the complicated process of calculation, students feel difficult to master them. In particular, the integral of cylindrical function by Lomel integral is more difficult than it in higher mathematics, which is usually the integral of same kind cylindrical function. However, the integral of different kind cylindrical function will appears in the teaching process of coaxial resonator and coaxial waveguide. Hence, this integral will be studied in teaching process.%柱函数是数学物理方法中的一个重要内容，它包括贝赛尔函数、诺伊曼函数和汉克尔函数。这些函数表达复杂、性质众多、计算过程繁琐，学生在学习过程中感到很困惑。特别是柱函数积分计算比微积分中的积分要困难得多，通常使用洛梅尔积分教学计算。它的特点是只涉及同类柱函数乘积的积分。而在同轴谐振腔和同轴波导教学中，我们经常要涉及不同种类柱函数乘积的积分。因此，对这类积分进行研究，得到一般公式并应用于教学。
HEXADECAPOLE INTERACTING BOSON APPROXIMATION STRUCTURE FUNCTIONS IN NEODYMIUM ISOTOPES
PERRINO, R; BLASI, N; BORDEWIJK, JA; DELEO, R; HARAKEH, MN; DEJAGER, CW; MICHELETTI, S; PIGNANELLI, M; SANDOR, RKJ; DEVRIES, H; VANDERWERF, SY; WESSELING, J
1993-01-01
Low-lying hexadecapole states in stable even-even neodymium isotopes have been investigated by means of inelastic electron scattering. Transition charge densities were extracted in a Fourier-Bessel analysis of the form factors. The analysis of the experimental results within the interacting sdg-boso
Ahn, Chi Young; Jeon, Kiwan; Park, Won-Kwang
2015-06-01
This study analyzes the well-known MUltiple SIgnal Classification (MUSIC) algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered field data collected within the so-called multi-static response matrix in limited-view inverse scattering problems. The mathematical theories of MUSIC are partially discovered, e.g., in the full-view problem, for an unknown target of dielectric contrast or a perfectly conducting crack with the Dirichlet boundary condition (Transverse Magnetic-TM polarization) and so on. Hence, we perform further research to analyze the MUSIC-type imaging functional and to certify some well-known but theoretically unexplained phenomena. For this purpose, we establish a relationship between the MUSIC imaging functional and an infinite series of Bessel functions of integer order of the first kind. This relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve. Various results of numerical simulation are presented in order to support the identified structure of MUSIC. Although a priori information of the target is needed, we suggest a least condition of range of incident and observation directions to apply MUSIC in the limited-view problem.
Directory of Open Access Journals (Sweden)
Zhen Qu
2016-01-01
Full Text Available Subsurface damage could affect the service life of structures. In nuclear engineering, nondestructive evaluation and detection of the evaluation of the subsurface damage region are of great importance to ensure the safety of nuclear installations. In this paper, we propose the use of circumferential horizontal shear (SH waves to detect mechanical properties of subsurface regions of damage on cylindrical structures. The regions of surface damage are considered to be functionally graded material (FGM and the cylinder is considered to be a layered structure. The Bessel functions and the power series technique are employed to solve the governing equations. By analyzing the SH waves in the 12Cr-ODS ferritic steel cylinder, which is frequently applied in the nuclear installations, we discuss the relationship between the phase velocities of SH waves in the cylinder with subsurface layers of damage and the mechanical properties of the subsurface damaged regions. The results show that the subsurface damage could lead to decrease of the SH waves’ phase velocity. The gradient parameters, which represent the degree of subsurface damage, can be evaluated by the variation of the SH waves’ phase velocity. Research results of this study can provide theoretical guidance in nondestructive evaluation for use in the analysis of the reliability and durability of nuclear installations.
Power-Scalable Blue-Green Bessel Beams
2016-02-23
conversion at 1 μm with large mode area fibers,” Optics Letters , vol. 39, p. 743, 2014. 5) M. Laurila, R. Barankov, M. Jørgensen, T. Alkeskjold, J...J. Demas, M.D.W. Grogan, T. Alkeskjold, S. Ramachandran, “Sensing with optical vortices in photonic crystal fibers,” Optics Letters , vol. 37, p... Letters , vol. 37, p. 3327, 2012. 9) R.A. Barankov, K. Wei, B. Samson and S. Ramachandran, “Resonant Bend Loss in Leakage Channel Fibers,” Optics Letters
Sun, Ying
2011-01-01
This article proposes an informative exploratory tool, the functional boxplot, for visualizing functional data, as well as its generalization, the enhanced functional boxplot. Based on the center outward ordering induced by band depth for functional data, the descriptive statistics of a functional boxplot are: the envelope of the 50% central region, the median curve, and the maximum non-outlying envelope. In addition, outliers can be detected in a functional boxplot by the 1.5 times the 50% central region empirical rule, analogous to the rule for classical boxplots. The construction of a functional boxplot is illustrated on a series of sea surface temperatures related to the El Niño phenomenon and its outlier detection performance is explored by simulations. As applications, the functional boxplot and enhanced functional boxplot are demonstrated on children growth data and spatio-temporal U.S. precipitation data for nine climatic regions, respectively. This article has supplementary material online. © 2011 American Statistical Association.
DEFF Research Database (Denmark)
Vargas-Zúñiga, Gabriela; Sessler, Jonathan; Bähring, Steffen
2016-01-01
as the extraction and transport of anionic species and ion pairs including cesium halide and sulfate salts. It is divided into seven sections. The first section describes the synthetic methods employed to functionalized calix[4]pyrrole. The second section focuses on functionalized calix[4]pyrroles that display...... enhanced anion binding properties compared to the non-functionalized parent system, octamethylcalix[4]pyrrole. The use of functionalized calix[4]pyrroles containing a fluorescent group or functionalized calix[4]pyrroles as building blocks for the preparation of stimulus-responsive materials is discussed...... and the eventual development of therapeutics that function via the transport of anions across cell membranes, are discussed....
Markushevich, A I
1966-01-01
Entire Functions focuses on complex numbers and the algebraic operations on them and the basic principles of mathematical analysis.The book first elaborates on the concept of an entire function, including the natural generalization of the concept of a polynomial and power series. The text then takes a look at the maximum absolute value and the order of an entire function, as well as calculations for the coefficients of power series representing a given function, use of integrals, and complex numbers. The publication elaborates on the zeros of an entire function and the fundamen
DEFF Research Database (Denmark)
Della Pia, Eduardo Antonio; Hansen, Randi Westh; Zoonens, Manuela
2014-01-01
Amphipols are amphipathic polymers that stabilize membrane proteins isolated from their native membrane. They have been functionalized with various chemical groups in the past years for protein labeling and protein immobilization. This large toolbox of functionalized amphipols combined with their......Amphipols are amphipathic polymers that stabilize membrane proteins isolated from their native membrane. They have been functionalized with various chemical groups in the past years for protein labeling and protein immobilization. This large toolbox of functionalized amphipols combined...... surfaces for various applications in synthetic biology. This review summarizes the properties of functionalized amphipols suitable for synthetic biology approaches....
DEFF Research Database (Denmark)
Campi, Stefano; Gardner, Richard; Gronchi, Paolo;
2012-01-01
Variants of the brightness function of a convex body K in n-dimensional Euclidean are investigated. The Lambertian lightness function L(K; v , w ) gives the total reflected light resulting from illumination by a light source at infinity in the direction w that is visible when looking...... in the direction v . The partial brightness function R( K ; v , w ) gives the area of the projection orthogonal to v of the portion of the surface of K that is both illuminated by a light source from the direction w and visible when looking in the direction v . A class of functions called lightness functions...... is introduced that includes L(K;.) and R(K;.) as special cases. Much of the theory of the brightness function like uniqueness, stability, and the existence and properties of convex bodies of maximal and minimal volume with finitely many function values equal to those of a given convex body, is extended...
Analytical structure and properties of Coulomb wave functions for real and complex energies
Humblet, J.
1984-07-01
The radical Coulomb wave functions are analysed in their dependence on the energy E considered as a complex parameter. Repulsive and attractive fields are both considered. First turning to the function Φl ∝ r- l-1 Fl introduced by Briet, slightly modifying its definition, and assuming that the angular momentum is also a complex parameter, for which the notation L is used, it is proved that ΦL is an entire function of both E and L. From an expansion of the regular Whittaker function given by Buchholz, the Taylor expansion of ΦL in powers of E and a simple recurrence relation for its coefficients are easily obtained. The expansion of the regular function Fl is readily obtained from that of ΦL for L = l, but the irregular function Gl contains Φl and ∂Φ L/∂L for L = l and - l-1. Having proved that the expansion obtained for ΦL in powers of E can also be regarded as a uniformly convergent series of entire functions of L, the derivative ∂Φ L/∂L can be obtained by term-by-term derivation. This method for obtaining the expansion of Gl is straightforward and leads to a final result involving essentially: (i) the conventional function h(η) = 1/2ψ(1 + iη) + 1/2ψ(1 - iη) - ln η which is singular at η = ∞, i.e., at k = 0; (ii) two entire functions of E, namely Φl and Ψl; the terms of the expansion of the latter in powers of E contain only Bessel functions multiplied by Bernoulli numbers and coefficients easily obtained from a simple recurrence relation. As an application of the above results, the last sections contain: (i) an alternate from of Gl expansion useful in numerical computations; (ii) the definition and expansion of two linearly independent solutions of the Coulomb equation which are entire in E; (iii) the expansion and threshold properties of the outgoing and incoming solutions, Ol and Il, corresponding to those we have obtained for Fl and Gl.
Institute of Scientific and Technical Information of China (English)
王雷
2008-01-01
<正>A power function of degree n is a function of the form f(x)=ax~n.For large n,it appears that the graph coincide with the x-axis near the origin,but it does not;the graph actually touches the x—axis only at the origin.
Burns, Daniel; Wang, Zuoqin
2008-01-01
In this article we discuss the role of stability functions in geometric invariant theory and apply stability function techniques to problems in toric geometry. In particular we show how one can use these techniques to recover results of Burns-Guillemin-Uribe and Shiffman-Tate-Zelditch on asymptotic properties of sections of holomorphic line bundles over toric varieties.
On the solving of one type of problems of mathematical physics
Chebakova, V. J.; Gerasimov, A. V.; Kirpichnikov, A. P.
2016-11-01
A relationship between generalized hypergeometric functions of a special type and modified Bessel functions has been established. Using this relationship the solution of inhomogeneous differential equations of Bessel type containing even degrees of an independent variable in the right-hand part can be expressed in a form convenient for engineering and technical applications.
CARDINAL FUNCTIONS AND INTEGRAL FUNCTIONS
MIRCEA E. ŞELARIU; FLORENTIN SMARANDACHE; MARIAN NIŢU
2015-01-01
This paper presents the correspondences of the eccentric mathematics of cardinal and integral functions and centric mathematics, or ordinary mathematics. Centric functions will also be presented in the introductory section, because they are, although widely used in undulatory physics, little known.
An improved algorithm and a Fortran 90 module for computing the conical function P-1/2+iτm(x)
Gil, Amparo; Segura, Javier; Temme, Nico M.
2012-03-01
In this paper we describe an algorithm and a Fortran 90 module ( Conical) for the computation of the conical function P-1/2 >+iτm(x) for x>-1, m⩾0, τ>0. These functions appear in the solution of Dirichlet problems for domains bounded by cones; because of this, they are involved in a large number of applications in engineering and physics. In the Fortran 90 module, the admissible parameter ranges for computing the conical functions in standard IEEE double precision arithmetic are restricted to (x,m,τ)∈(-1,1)×[0,40]×[0,100] and (x,m,τ)∈(1,100)×[0,100]×[0,100]. Based on tests of the three-term recurrence relation satisfied by these functions and direct comparison with Maple, we claim a relative accuracy close to 10 in the full parameter range, although a mild loss of accuracy can be found at some points of the oscillatory region of the conical functions. The relative accuracy increases to 10-10 in the region of the monotonic regime of the functions where integral representations are computed ( -1xIEEE double precision arithmetic are restricted to (x,m,τ)∈(-1,1)×[0,40]×[0,100] and (x,m,τ)∈(1,100)×[0,100]×[0,100]. Additional comments: The module Conical uses a Fortran 90 version of the routine dkia (developed by the authors) for computing the modified Bessel functions K(x) and its derivative. This routine is included in the distribution file and is also available at http://toms.calgo.org. Running time: Depending on the parameter range: when numerical quadrature is used (for x<0), the algorithm is 10-20 times slower than the computations made using asymptotic expansions + recurrence relations.
DEFF Research Database (Denmark)
Danvy, Olivier
1998-01-01
A string-formatting function such as printf in C seemingly requires dependent types, because its control string determines the rest of its arguments. We show how changing the representation of the control string makes it possible to program printf in ML (which does not allow dependent types......). The result is well typed and perceptibly more efficient than the corresponding library functions in Standard ML of New Jersey and in Caml....
DEFF Research Database (Denmark)
Danvy, Olivier
2000-01-01
A string-formatting function such as printf in C seemingly requires dependent types, because its control string determines the rest of its arguments. Examples: formula here We show how changing the representation of the control string makes it possible to program printf in ML (which does not allow...... dependent types). The result is well typed and perceptibly more efficient than the corresponding library functions in Standard ML of New Jersey and in Caml....
Directory of Open Access Journals (Sweden)
J. A. Chatfield
1978-01-01
Full Text Available Suppose N is a Banach space of norm |•| and R is the set of real numbers. All integrals used are of the subdivision-refinement type. The main theorem [Theorem 3] gives a representation of TH where H is a function from R×R to N such that H(p+,p+, H(p,p+, H(p−,p−, and H(p−,p each exist for each p and T is a bounded linear operator on the space of all such functions H. In particular we show that TH=(I∫abfHdα+∑i=1∞[H(xi−1,xi−1+−H(xi−1+,xi−1+]β(xi−1+∑i=1∞[H(xi−,xi−H(xi−,xi−]Θ(xi−1,xiwhere each of α, β, and Θ depend only on T, α is of bounded variation, β and Θ are 0 except at a countable number of points, fH is a function from R to N depending on H and {xi}i=1∞ denotes the points P in [a,b]. for which [H(p,p+−H(p+,p+]≠0 or [H(p−,p−H(p−,p−]≠0. We also define an interior interval function integral and give a relationship between it and the standard interval function integral.
Institute of Scientific and Technical Information of China (English)
王雷
2008-01-01
<正>Polynomial functions are among the sim- plest expressions in algebra.They are easy to evaluate:only addition and repeated multipli- cation are required.Because of this,they are often used to approximate other more compli-
Kleibeuker, JH; Thijs, JC
2004-01-01
Purpose of review Functional dyspepsia is a common disorder, most of the time of unknown etiology and with variable pathophysiology. Therapy has been and still is largely empirical. Data from recent studies provide new clues for targeted therapy based on knowledge of etiology and pathophysiologic me
Institute of Scientific and Technical Information of China (English)
K.H.DTZ
2007-01-01
1 Results The lecture will address aspects of functional organometallics related to the development of novel organometallic materials.In chromium complexes of fused arenes-regio-and diastereoselectively accessible by chromium-templated benzannulation of arylcarbenes by alkynes[1]-a haptotropic migration of the chromium fragment along the π-face of fused arenes is controlled by both thermodynamics and the substitution pattern of the arene and the metal coligand sphere,and can be applied towards an organo...
Guasp, J.; Pastor, I.; Álvarez-Estrada, R. F.; Castejón, F.
2015-02-01
Analytical results obtained recently of the ab-initio classical incoherent Thomson Scattering (TS) spectrum from a single-electron (Alvarez-Estrada et al 2012 Phys. Plasmas 19 062302) have been numerically implemented in a paralelized code to efficiently compute the TS emission from a given electron distribution function, irrespective of its characteristics and/or the intensity of the incoming radiation. These analytical results display certain differences, when compared with other authors, in the general case of incoming linearly and circularly polarized radiation and electrons with arbitrary initial directions. We regard such discrepancies and the ubiquitous interest in TS as motivations for this work. Here, we implement some analytical advances (like generalized Bessel functions for incoming linearly polarized radiation) in TS. The bulk of this work reports on the efficient computation of TS spectra (based upon our analytical approach), for an electron population having an essentially arbitrary distribution function and for both incoming linearly and circularly polarized radiation. A detailed comparison between the present approach and a previous Monte Carlo one (Pastor et al 2011 Nuclear Fusion 51 043011), dealing with the ab-initio computation of TS spectra, is reported. Both approaches are shown to fully agree with each other. As key computational improvements, the analytical technique yields a × 30 to × 100 gain in computation time and is a very flexible tool to compute the scattered spectrum and eventually the scattered electromagnetic fields in the time domain. The latter are computed explicitly here for the first time, as far as we know. Scaling laws for the power integrated over frequency versus initial kinetic energy are studied for the case of isotropic and monoenergetic electron distribution functions and their potential application as diagnostic tools for high-energy populations is briefly discussed. Finally, we discuss the application of these
Institute of Scientific and Technical Information of China (English)
2005-01-01
2005200 The effect of body position changes on lung function, lung CT imaging and pathology in an oleic acid induced acute lung injury model. JI Xin-ping (戢新平), et al. Dept Emergency, 1st Affili Hosp, China Med Univ, Shenyang 110001. Chin J Tuberc Respir Dis, 2005;28(1) :33-36. Objective: To study the effect of body position changes on lung mechanics, oxygenation, CT images and pathology in an oleic acid-induced acute lung injury (ALl) model. Methods: The study groups con-
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A V
2015-01-01
The eikonal approximation for moderately small scattering amplitudes is considered. With the purpose of using for their numerical estimations, the formulas are derived which contain no Bessel functions, and, hence, no rapidly oscillating integrands. To obtain these formulas, the improper integrals of the first kind which contain products of the Bessel functions J_0(z) are studied. The expression with four functions J_0(z) is generalized. The expressions for the integrals with the product of five and six Bessel functions J_0(z) are also found. The known formula for the improper integral with two functions J_nu(z) is generalized for non-integer nu.
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A. V.
2016-08-01
We consider the eikonal approximation for moderately small scattering amplitudes. To find numerical estimates of these approximations, we derive formulas that contain no Bessel functions and consequently no rapidly oscillating integrands. To obtain these formulas, we study improper integrals of the first kind containing products of the Bessel functions J0(z). We generalize the expression with four functions J0(z) and also find expressions for the integrals with the product of five and six Bessel functions. We generalize a known formula for the improper integral with two functions Jυ (az) to the case with noninteger υ and complex a.
Asadchy, V S; Vehmas, J; Tretyakov, S A
2014-01-01
Conventional mirrors obey Snell's reflection law: a plane wave is reflected as a plane wave, at the same angle. To engineer spatial distributions of fields reflected from a mirror, one can either shape the reflector (for example, creating a parabolic reflector) or position some phase-correcting elements on top of a mirror surface (for example, designing a reflectarray antenna). Here we show, both theoretically and experimentally, that full-power reflection with general control over reflected wave phase is possible with a single-layer array of deeply sub-wavelength inclusions. These proposed artificial surfaces, metamirrors, provide various functions of shaped or nonuniform reflectors without utilizing any mirror. This can be achieved only if the forward and backward scattering of the inclusions in the array can be engineered independently, and we prove that it is possible using electrically and magnetically polarizable inclusions. The proposed sub-wavelength inclusions possess desired reflecting properties at...
Diffraction of light by a nanowire
Krzyżanowska, Katarzyna
2013-01-01
A general scattering problem of a plane electromagnetic wave on an infinite cylindrical rod is formulated and solved in a form of Bessel functions series expansion. The conductivity account via Ohm law directly in Maxwell equation leads to complex wavenumber and hence the complex arguments of Bessel functions inside the cylinder. The general formula for averaged by period Pointing vector is derived. For numerical calculations asymptotics of Bessel functions are used. Dependence of scattered wave intensity as function of angle and frequency is presented for different values of the rod radius.
Functions of bounded variation
Lind, Martin
2006-01-01
The paper begins with a short survey of monotone functions. The functions of bounded variation are introduced and some basic properties of these functions are given. Finally the jump function of a function of bounded variation is defined.
Relations between Lipschitz functions and convex functions
Institute of Scientific and Technical Information of China (English)
RUAN Yingbin
2005-01-01
We discuss the relationship between Lipschitz functions and convex functions.By these relations, we give a sufficient condition for the set of points where Lipschitz functions on a Hilbert space is Frechet differentiable to be residual.
Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups
DEFF Research Database (Denmark)
Hilgert, Joachim; Kobayashi, Toshiyuki; Möllers, Jan;
2012-01-01
For any Hermitian Lie group G of tube type we construct a Fock model of its minimal representation. The Fock space is defined on the minimal nilpotent K_C-orbit X in p_C and the L^2-inner product involves a K-Bessel function as density. Here K is a maximal compact subgroup of G, and g_C=k_C+p_C i...... intertwines the Schroedinger and Fock model. Its kernel involves the same I-Bessel function. Using the Segal--Bargmann transform we also determine the integral kernel of the unitary inversion operator in the Schroedinger model which is given by a J-Bessel function....
Gaussian Functions, Γ-Functions and Wavelets
Institute of Scientific and Technical Information of China (English)
蔡涛; 许天周
2003-01-01
The relations between Gaussian function and Γ-function is revealed first at one-dimensional situation. Then, the Fourier transformation of n-dimensional Gaussian function is deduced by a lemma. Following the train of thought in one-dimensional situation, the relation between n-dimensional Gaussian function and Γ-function is given. By these, the possibility of arbitrary derivative of an n-dimensional Gaussian function being a mother wavelet is indicated. The result will take some enlightening role in exploring the internal relations between Gaussian function and Γ-function as well as in finding high-dimensional mother wavelets.
On quasinearly subharmonic functions
Dovgoshey, O.; Riihentaus, J.
2016-01-01
We recall the definition of quasinearly subharmonic functions, point out that this function class includes, among others, subharmonic functions, quasisubharmonic functions, nearly subharmonic functions and essentially almost subharmonic functions. It is shown that the sum of two quasinearly subharmonic functions may not be quasinearly subharmonic. Moreover, we characterize the harmonicity via quasinearly subharmonicity.
Bayesian function-on-function regression for multilevel functional data.
Meyer, Mark J; Coull, Brent A; Versace, Francesco; Cinciripini, Paul; Morris, Jeffrey S
2015-09-01
Medical and public health research increasingly involves the collection of complex and high dimensional data. In particular, functional data-where the unit of observation is a curve or set of curves that are finely sampled over a grid-is frequently obtained. Moreover, researchers often sample multiple curves per person resulting in repeated functional measures. A common question is how to analyze the relationship between two functional variables. We propose a general function-on-function regression model for repeatedly sampled functional data on a fine grid, presenting a simple model as well as a more extensive mixed model framework, and introducing various functional Bayesian inferential procedures that account for multiple testing. We examine these models via simulation and a data analysis with data from a study that used event-related potentials to examine how the brain processes various types of images.
Stochastic properties of lower ionosphere as earthquake precursor
Šlégr, Jan; Váňová, Kamila
2017-01-01
Lower portion of the ionosphere known as the D-layer has properties of Gaussian random plane affecting very low frequency waves. This is manifested by stochastic properties of reflected VLF waves as their auto-correlation function (ACF) in time is the Bessel function of the first kind and zero order. In this paper, we show that the properties of this Bessel function are connected with the seismic activity in the area near the great circle path of VLF waves.
Modelling distribution functions and fragmentation functions
Rodrigues, J; Mulders, P J
1995-01-01
We present examples for the calculation of the distribution and fragmentation functions using the representation in terms of non-local matrix elements of quark field operators. As specific examples, we use a simple spectator model to estimate the leading twist quark distribution functions and the fragmentation functions for a quark into a nucleon or a pion.
An improved Hardy type inequality on Heisenberg group
Directory of Open Access Journals (Sweden)
Xiao Ying-Xiong
2011-01-01
Full Text Available Abstract Motivated by the work of Ghoussoub and Moradifam, we prove some improved Hardy inequalities on the Heisenberg group ℍ n via Bessel function. Mathematics Subject Classification (2000: Primary 26D10
Introduction to linear algebra and differential equations
Dettman, John W
1986-01-01
Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index.
Institute of Scientific and Technical Information of China (English)
华建文; 刘立人; 王宁
1997-01-01
A recipe to construct the exact dual self-Fourier-Fresnel-transform functions is shown, where the Dirac comb function and transformable even periodic function are used. The mathematical proof and examples are given Then this kind of self-transform function is extended to the feasible optical dual self-transform functions.
Kargın, Levent; Kurt, Veli
2015-01-01
In this study, obtaining the matrix analog of the Euler's reflection formula for the classical gamma function we expand the domain of the gamma matrix function and give a infinite product expansion of sinπxP. Furthermore we define Riemann zeta matrix function and evaluate some other matrix integrals. We prove a functional equation for Riemann zeta matrix function.
Functionality and homogeneity.
2011-01-01
Functionality and homogeneity are two of the five Sustainable Safety principles. The functionality principle aims for roads to have but one exclusive function and distinguishes between traffic function (flow) and access function (residence). The homogeneity principle aims at differences in mass, spe
Properties of Bourbaki's Function
McCollum, James
2010-01-01
We examine Bourbaki's function, an easily-constructed continuous but nowhere-differentiable function, and explore properties including functional identities, the antiderivative, and the Hausdorff dimension of the graph.
... be limited. Home Visit Global Sites Search Help? Platelet Function Tests Share this page: Was this page helpful? ... their patients by ordering one or more platelet function tests. Platelet function testing may include one or more of ...
Congenital platelet function defects
... storage pool disorder; Glanzmann's thrombasthenia; Bernard-Soulier syndrome; Platelet function defects - congenital ... Congenital platelet function defects are bleeding disorders that ... function, even though there are normal platelet numbers. Most ...
Independent trapping and manipulation of microparticles using dexterous acoustic tweezers
Courtney, Charles R. P.; Demore, Christine E. M.; Wu, Hongxiao; Grinenko, Alon; Wilcox, Paul D.; Cochran, Sandy; Drinkwater, Bruce W.
2014-01-01
An electronically controlled acoustic tweezer was used to demonstrate two acoustic manipulation phenomena: superposition of Bessel functions to allow independent manipulation of multiple particles and the use of higher-order Bessel functions to trap particles in larger regions than is possible with first-order traps. The acoustic tweezers consist of a circular 64-element ultrasonic array operating at 2.35 MHz which generates ultrasonic pressure fields in a millimeter-scale fluid-filled chambe...
Random functions and turbulence
Panchev, S
1971-01-01
International Series of Monographs in Natural Philosophy, Volume 32: Random Functions and Turbulence focuses on the use of random functions as mathematical methods. The manuscript first offers information on the elements of the theory of random functions. Topics include determination of statistical moments by characteristic functions; functional transformations of random variables; multidimensional random variables with spherical symmetry; and random variables and distribution functions. The book then discusses random processes and random fields, including stationarity and ergodicity of random
Functional Maximum Autocorrelation Factors
DEFF Research Database (Denmark)
Larsen, Rasmus; Nielsen, Allan Aasbjerg
2005-01-01
Purpose. We aim at data where samples of an underlying function are observed in a spatial or temporal layout. Examples of underlying functions are reflectance spectra and biological shapes. We apply functional models based on smoothing splines and generalize the functional PCA in\\verb+~+\\$\\backsl......Purpose. We aim at data where samples of an underlying function are observed in a spatial or temporal layout. Examples of underlying functions are reflectance spectra and biological shapes. We apply functional models based on smoothing splines and generalize the functional PCA in...
Acquired platelet function defect
Acquired qualitative platelet disorders; Acquired disorders of platelet function ... blood clotting. Disorders that can cause problems in platelet function include: Idiopathic thrombocytopenic purpura Chronic myelogenous leukemia Multiple ...
Functional microorganisms for functional food quality.
Gobbetti, M; Cagno, R Di; De Angelis, M
2010-09-01
Functional microorganisms and health benefits represent a binomial with great potential for fermented functional foods. The health benefits of fermented functional foods are expressed either directly through the interactions of ingested live microorganisms with the host (probiotic effect) or indirectly as the result of the ingestion of microbial metabolites synthesized during fermentation (biogenic effect). Since the importance of high viability for probiotic effect, two major options are currently pursued for improving it--to enhance bacterial stress response and to use alternative products for incorporating probiotics (e.g., ice cream, cheeses, cereals, fruit juices, vegetables, and soy beans). Further, it seems that quorum sensing signal molecules released by probiotics may interact with human epithelial cells from intestine thus modulating several physiological functions. Under optimal processing conditions, functional microorganisms contribute to food functionality through their enzyme portfolio and the release of metabolites. Overproduction of free amino acids and vitamins are two classical examples. Besides, bioactive compounds (e.g., peptides, γ-amino butyric acid, and conjugated linoleic acid) may be released during food processing above the physiological threshold and they may exert various in vivo health benefits. Functional microorganisms are even more used in novel strategies for decreasing phenomenon of food intolerance (e.g., gluten intolerance) and allergy. By a critical approach, this review will aim at showing the potential of functional microorganisms for the quality of functional foods.
Rough function model and rough membership function
Institute of Scientific and Technical Information of China (English)
Wang Yun; Guan Yanyong; Huang Zhiqin
2008-01-01
Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower (upper) approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.
Entire functions sharing one small function
Institute of Scientific and Technical Information of China (English)
LI Yun-tong; CAO Yao
2007-01-01
The uniqueness problem of entire functions sharing one small function was studied. By Picard's Theorem, we proved that for two transcendental entire functions f (z) and g(z), a positive integer n≥9, and a(z) (not identically eaqual to zero) being a common small function related to f (z) and g(z), if f n(z)(f(z)-1)f'(z) and gn(z)(g'z)-1)g'(z) share a(z) CM, where CM is counting multiplicity, then g(z)≡f (z). This is an extended version of Fang and Hong's theorem [ Fang ML, Hong W, A unicity theorem for entire functions concerning differential polynomials, Journal of Indian Pure Applied Mathematics, 2001, 32 (9): 1343-1348].
Hepatic (Liver) Function Panel
... 1- to 2-Year-Old Blood Test: Hepatic (Liver) Function Panel KidsHealth > For Parents > Blood Test: Hepatic (Liver) Function Panel Print A A A What's in ... Is The hepatic function panel, also known as liver function tests, is a group of seven tests ...
Institute of Scientific and Technical Information of China (English)
丁夏畦; 罗佩珠
2004-01-01
In this paper the authors introduce some new ideas on generalized numbers and generalized weak functions. They prove that the product of any two weak functions is a generalized weak function. So in particular they solve the problem of the multiplication of two generalized functions.
DEFF Research Database (Denmark)
Bysted, Tommy Kristensen; Hamila, R.; Gabbouj, M.;
1998-01-01
A new correlation function called the Teager correlation function is introduced in this paper. The connection between this function, the Teager energy operator and the conventional correlation function is established. Two applications are presented. The first is the minimization of the Teager err...... norm and the second one is the use of the instantaneous Teager correlation function for simultaneous estimation of TDOA and FDOA (Time and Frequency Difference of Arrivals)....
Relations between Lipschitz functions and convex functions
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Zajicek, J., On the differentation of convex functions in finite and infinite dimensional spaces, Czech J. Math.,1979, 29: 340-348.[2]Hu, T. C., Klee, V. L., Larman, D. G., Optimization of globally convex functions, SIAM J. Control Optim., 1989,27: 1026-1047.[3]Cepedello Boiso, M., Approximation of Lipschitz functions by △-convex functions in Banach spaces, Israel J.Math., 1998, 106: 269-284.[4]Asplund, E., Frechet differentiability of convex functions, Acta Math., 1968, 121: 31-47.[5]Johnson, J. A., Lipschitz spaces, Pacific J. Math, 1974, 51: 177-186.[6]Stromberg, T., The operation of infimal convolution, Dissert. Math., (Rozprawy Mat.), 1996, 325: 58.[7]Kadison, R. V., Ringrose, J. R., Fundamentals of the theory of operator algebras, volume Ⅰ: Elementary Theory,Graduate Studies in Math., vol. 15, Amer. Math. Soc., 1997.[8]Phelps, R. R., Convex functions,monotone operators and differentiability, Lect. Notes in Math., vol. 1364,Springer-Verlag, 1977.[9]Lindenstrauss, J., On operators which attain their norm, Israel J. Math., 1963, 1: 139-148.[10]Press, D., Gateaux differentiable functions are somewhere Frechet differentiable, Rend. Circ. Mat. Palermo,1984, 33: 122-133.[11]Press, D., Differentiability of Lipschitz functions on Banach spaces, J. Funct. Anal., 1990, 91:312-345.[12]Lindenstrauss, J., Press, D., On Frechet differentiability of Lipschitz maps between Banach spaces, Annals of Math., 2003, 157: 257-288.[13]Press, D., Gateaux differentiable Lipschitz functions need not be Frechet differentiable on a residual set, Supplemento Rend. Circ. Mat. Palermo, Serie Ⅱ, 1982, 2: 217-222.
Sampling functions for geophysics
Giacaglia, G. E. O.; Lunquist, C. A.
1972-01-01
A set of spherical sampling functions is defined such that they are related to spherical-harmonic functions in the same way that the sampling functions of information theory are related to sine and cosine functions. An orderly distribution of (N + 1) squared sampling points on a sphere is given, for which the (N + 1) squared spherical sampling functions span the same linear manifold as do the spherical-harmonic functions through degree N. The transformations between the spherical sampling functions and the spherical-harmonic functions are given by recurrence relations. The spherical sampling functions of two arguments are extended to three arguments and to nonspherical reference surfaces. Typical applications of this formalism to geophysical topics are sketched.
Filter function synthesis by Gegenbauer generating function
Directory of Open Access Journals (Sweden)
Pavlović Vlastimir D.
2006-01-01
Full Text Available Low-pass all-pole transfer functions with non-monotonic amplitude characteristic in the pass-band and at least (n -1 flatness conditions for ω = 0 are considered in this paper. A new class of filters in explicit form with one free parameter is obtained by applying generating functions of Gegenbauer polynomials. This class of filters has good selectivity and good shape of amplitude characteristics in the pass-band. The amplitude characteristics of these transfer functions have gain in the upper part of pass-band with respect to the gain for ω = 0. This way we have greater margin of attenuation in the upper part of the pass-band. This means a greater tolerance of elements or for elements with given tolerances, greater ambient temperature changes. The appropriate choice of the free parameter enables us to generate filter functions obtained with Chebyshev polynomials of the first and second kind and Legendre polynomials.
DEFF Research Database (Denmark)
Markvorsen, Steen
2007-01-01
We consider a specific function of two variables whose graph surface resembles a blue lagoon. The function has a saddle point $p$, but when the function is restricted to any given straight line through $p$ it has a {\\em{strict local minimum}} along that line at $p$.......We consider a specific function of two variables whose graph surface resembles a blue lagoon. The function has a saddle point $p$, but when the function is restricted to any given straight line through $p$ it has a {\\em{strict local minimum}} along that line at $p$....
Functionalized boron nitride nanotubes
Sainsbury, Toby; Ikuno, Takashi; Zettl, Alexander K
2014-04-22
A plasma treatment has been used to modify the surface of BNNTs. In one example, the surface of the BNNT has been modified using ammonia plasma to include amine functional groups. Amine functionalization allows BNNTs to be soluble in chloroform, which had not been possible previously. Further functionalization of amine-functionalized BNNTs with thiol-terminated organic molecules has also been demonstrated. Gold nanoparticles have been self-assembled at the surface of both amine- and thiol-functionalized boron nitride Nanotubes (BNNTs) in solution. This approach constitutes a basis for the preparation of highly functionalized BNNTs and for their utilization as nanoscale templates for assembly and integration with other nanoscale materials.
Grabisch, Michel
2008-01-01
We extend the notion of belief function to the case where the underlying structure is no more the Boolean lattice of subsets of some universal set, but any lattice, which we will endow with a minimal set of properties according to our needs. We show that all classical constructions and definitions (e.g., mass allocation, commonality function, plausibility functions, necessity measures with nested focal elements, possibility distributions, Dempster rule of combination, decomposition w.r.t. simple support functions, etc.) remain valid in this general setting. Moreover, our proof of decomposition of belief functions into simple support functions is much simpler and general than the original one by Shafer.
DEFF Research Database (Denmark)
Thomsen, Søren Steffen
2009-01-01
Cryptographic hash functions are commonly used in many different areas of cryptography: in digital signatures and in public-key cryptography, for password protection and message authentication, in key derivation functions, in pseudo-random number generators, etc. Recently, cryptographic hash...... functions have received a huge amount of attention due to new attacks on widely used hash functions. This PhD thesis, having the title "Cryptographic Hash Functions", contains both a general description of cryptographic hash functions, including their applications and expected properties as well as some...
Scaled density functional theory correlation functionals.
Ghouri, Mohammed M; Singh, Saurabh; Ramachandran, B
2007-10-18
We show that a simple one-parameter scaling of the dynamical correlation energy estimated by the density functional theory (DFT) correlation functionals helps increase the overall accuracy for several local and nonlocal functionals. The approach taken here has been described as the "scaled dynamical correlation" (SDC) method [Ramachandran, J. Phys. Chem. A 2006, 110, 396], and its justification is the same as that of the scaled external correlation (SEC) method of Brown and Truhlar. We examine five local and five nonlocal (hybrid) DFT functionals, the latter group including three functionals developed specifically for kinetics by the Truhlar group. The optimum scale factors are obtained by use of a set of 98 data values consisting of molecules, ions, and transition states. The optimum scale factors, found with a linear regression relationship, are found to differ from unity with a high degree of correlation in nearly every case, indicating that the deviation of calculated results from the experimental values are systematic and proportional to the dynamic correlation energy. As a consequence, the SDC scaling of dynamical correlation decreases the mean errors (signed and unsigned) by significant amounts in an overwhelming majority of cases. These results indicate that there are gains to be realized from further parametrization of several popular exchange-correlation functionals.
Sun, Ying
2012-08-03
This article proposes functional median polish, an extension of univariate median polish, for one-way and two-way functional analysis of variance (ANOVA). The functional median polish estimates the functional grand effect and functional main factor effects based on functional medians in an additive functional ANOVA model assuming no interaction among factors. A functional rank test is used to assess whether the functional main factor effects are significant. The robustness of the functional median polish is demonstrated by comparing its performance with the traditional functional ANOVA fitted by means under different outlier models in simulation studies. The functional median polish is illustrated on various applications in climate science, including one-way and two-way ANOVA when functional data are either curves or images. Specifically, Canadian temperature data, U. S. precipitation observations and outputs of global and regional climate models are considered, which can facilitate the research on the close link between local climate and the occurrence or severity of some diseases and other threats to human health. © 2012 International Biometric Society.
Functionalized diamond nanoparticles
Beaujuge, Pierre M.
2014-10-21
A diamond nanoparticle can be functionalized with a substituted dienophile under ambient conditions, and in the absence of catalysts or additional reagents. The functionalization is thought to proceed through an addition reaction.
Lott, Steven
2015-01-01
This book is for developers who want to use Python to write programs that lean heavily on functional programming design patterns. You should be comfortable with Python programming, but no knowledge of functional programming paradigms is needed.
DEFF Research Database (Denmark)
Gardner, Richard J.; Kiderlen, Markus
A structural theory of operations between real-valued (or extended-real-valued) functions on a nonempty subset A of Rn is initiated. It is shown, for example, that any operation ∗ on a cone of functions containing the constant functions, which is pointwise, positively homogeneous, monotonic......, and associative, must be one of 40 explicitly given types. In particular, this is the case for operations between pairs of arbitrary, or continuous, or differentiable functions. The term pointwise means that (f ∗g)(x) = F(f(x), g(x)), for all x ∈ A and some function F of two variables. Several results in the same...... spirit are obtained for operations between convex functions or between support functions. For example, it is shown that ordinary addition is the unique pointwise operation between convex functions satisfying the identity property, i.e., f ∗ 0 = 0 ∗ f = f, for all convex f, while other results classify Lp...
... food, store energy, and remove poisons. Liver function tests are blood tests that check to see how well your liver ... hepatitis and cirrhosis. You may have liver function tests as part of a regular checkup. Or you ...
Pseudolinear functions and optimization
Mishra, Shashi Kant
2015-01-01
Pseudolinear Functions and Optimization is the first book to focus exclusively on pseudolinear functions, a class of generalized convex functions. It discusses the properties, characterizations, and applications of pseudolinear functions in nonlinear optimization problems.The book describes the characterizations of solution sets of various optimization problems. It examines multiobjective pseudolinear, multiobjective fractional pseudolinear, static minmax pseudolinear, and static minmax fractional pseudolinear optimization problems and their results. The authors extend these results to locally
Distributed processing; distributed functions?
Fox, Peter T.; FRISTON, KARL J
2012-01-01
After more than twenty years busily mapping the human brain, what have we learned from neuroimaging? This review (coda) considers this question from the point of view of structure–function relationships and the two cornerstones of functional neuroimaging; functional segregation and integration. Despite remarkable advances and insights into the brain’s functional architecture, the earliest and simplest challenge in human brain mapping remains unresolved: We do not have a principled way to map ...
Energy Technology Data Exchange (ETDEWEB)
Korshunov, A D [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
2003-10-31
Monotone Boolean functions are an important object in discrete mathematics and mathematical cybernetics. Topics related to these functions have been actively studied for several decades. Many results have been obtained, and many papers published. However, until now there has been no sufficiently complete monograph or survey of results of investigations concerning monotone Boolean functions. The object of this survey is to present the main results on monotone Boolean functions obtained during the last 50 years.
2015-01-01
This work aims at the exposition of two different results we have obtained in Functional Data Analysis. The first is a variable selection method in Functional Regression which is an adaptation of the well known Lasso technique. The second is a brand new Random Walk test for Functional Time Series. Being the results afferent to different areas of Functional Data Analysis, as well as of general Statistics, the introduction will be divided in three parts. Firstly we expose the fundament...
Feldman, Carol Fleisher
1977-01-01
Author advocates the view that meaning is necessarily dependent upon the communicative function of language and examines the objections, particularly those of Noam Chomsky, to this view. Argues that while Chomsky disagrees with the idea that communication is the essential function of language, he implicitly agrees that it has a function.…
Diplomacy and diplomatic functions
2011-01-01
Through the main lines of this study we try to introduce specific approaches of diplomacy, diplomatic mission, diplomatic visits and diplomatic functions. Functions of diplomacy: representation, negotiation, information, diplomatic protection, international cooperation, consular function have been developed and analyzed more in depth
Bates, Elizabeth; MacWhinney, Brian
A defense of functionalism in linguistics, and more specifically the competition model of linguistic performance, examines six misconceptions about the functionalist approach. Functionalism is defined as the belief that the forms of natural languages are created, governed, constrained, acquired, and used for communicative functions. Functionalism…
Degenerate Euler zeta function
Kim, Taekyun
2015-01-01
Recently, T. Kim considered Euler zeta function which interpolates Euler polynomials at negative integer (see [3]). In this paper, we study degenerate Euler zeta function which is holomorphic function on complex s-plane associated with degenerate Euler polynomials at negative integers.
Shabat, A. B.
2016-12-01
We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.
Expanding Pseudorandom Functions
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Nielsen, Jesper Buus
2002-01-01
Given any weak pseudorandom function, we present a general and efficient technique transforming such a function to a new weak pseudorandom function with an arbitrary length output. This implies, among other things, an encryption mode for block ciphers. The mode is as efficient as known (and widely...
Clinical functional MRI. Presurgical functional neuroimaging
Energy Technology Data Exchange (ETDEWEB)
Stippich, C. (ed.) [Heidelberg Univ. (Germany). Div. of Neuroradiology
2007-07-01
Functional magnetic resonance imaging (fMRI) permits noninvasive imaging of the ''human brain at work'' under physiological conditions. This is the first textbook on clinical fMRI. It is devoted to preoperative fMRI in patients with brain tumors and epilepsies, which are the most well-established clinical applications. By localizing and lateralizing specific brain functions, as well as epileptogenic zones, fMRI facilitates the selection of a safe treatment and the planning and performance of function-preserving neurosurgery. State of the art fMRI procedures are presented, with detailed consideration of the physiological and methodological background, imaging and data processing, normal and pathological findings, diagnostic possibilities and limitations, and other related techniques. All chapters are written by recognized experts in their fields, and the book is designed to be of value to beginners, trained clinicians and experts alike. (orig.)
Hall, Joanne L; Donovan, Diane
2012-01-01
In 1980 Alltop produced a family of cubic phase sequences that nearly meet the Welch bound for maximum non-peak correlation magnitude. This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography. Alltop's construction used a function that is not planar, but whose difference function is planar. In this paper we show that Alltop type functions cannot exist in fields of characteristic 3 and that for a known class of planar functions, $x^3$ is the only Alltop type function.
DEFF Research Database (Denmark)
Rosenstand, Claus Andreas Foss; Laursen, Per Kyed
2013-01-01
How does one manage functional power relations between leading functions in vision driven digital media creation, and this from idea to master during the creation cycle? Functional power is informal, and it is understood as roles, e.g. project manager, that provide opportunities to contribute...... to the product quality. The area of interest is the vision driven digital media industry in general; however, the point of departure is the game industry due to its aesthetic complexity. The article's contribution to the area is a power graph, which shows the functional power of the leading functions according...
Introduction to functional equations
Sahoo, Prasanna K
2011-01-01
Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections hig
The Cosmological Mass Function
Monaco, P
1997-01-01
This thesis aims to review the cosmological mass function problem, both from the theoretical and the observational point of view, and to present a new mass function theory, based on realistic approximations for the dynamics of gravitational collapse. Chapter 1 gives a general introduction on gravitational dynamics in cosmological models. Chapter 2 gives a complete review of the mass function theory. Chapters 3 and 4 present the ``dynamical'' mass function theory, based on truncated Lagrangian dynamics and on the excursion set approach. Chapter 5 reviews the observational state-of-the-art and the main applications of the mass function theories described before. Finally, Chapter 6 gives conclusions and future prospects.
Approximation of several dimensional functions by trigonometric polynomials
Institute of Scientific and Technical Information of China (English)
CHENG Minde; CHEN Yonghe
2006-01-01
Let f(x,y) be a periodic function defined on the region D 0≤x≤2π, 0≤y≤2πwith period 2π for each variable.If f(x,y) ∈ CP(D),i.e.,f(x,y) has continuous partial derivatives of order p on D,then we denote by ωα,β(ρ) the modulus of continuity of the function(a)pf(x,y)/(a)xα(a)yβ (α,β≥0,α+β=p)and writeωp(ρ)=max ωα,β(ρ) α,β≥0,α+β=pFor p=0,we write simply C(D) and ω(p) instead of C0(D) and ω0(ρ).Let T(x,y) be a trigonometrical polynomial written in the complex form T(x,y) = ΣCm,nei(mx+ny).We consider R=max(m2+n2)1/2 as the degree of T(x,y),and write TR(x,y)for the trigonometrical polynomial of degree≤R.Our main purpose is to find the trigonometrical polynomial TR(x,y) for a given f(x,y) of a certain class of functions such that max xy|f(x,y)-TR(x,y)|attains the same order of accuracy as the best approximation of f(x,y).Let the Fourier series of f(x,y)∈C(D) be f(x,y)～∞Σ-∞ Cm,n ei(mx+ny),and let Av(x,y)=Σm2+n2=v Cm,n ei(mx+ny).Our results are as follows:Theorem 1 Let f(x,y)∈CP(D) (p=0,1) andSδR(x,y;f)=Σv=R2 (1-v/R2)δAv(x,y) (δ＞1/2).ThenSδR(x,y;f)-f(x,y)=0[1/Rp ωp(1/R)](p=0,1)holds uniformly on D.If we consider the circular mean of the Riesz sum SδR(x,y)≡SδR(x,y;f):μt[SδR(x,y)]=1/2π∫2π0 SδR(x+t cosθ,y+t sinθ)dθ,then we have the following:Theorem 2 If f(x,y)∈CP(D) andωp(ρ)=O(pα) (0＜α≤1;p=0,1),thenμλ0/R[SδR(x,y)-f(x,y)=O(1/Rp+α) (p=0,1;δ≥0)holds uniformly on D,where λ0 is a positive root of the Bessel function Jo(x).It should be noted that eitherSδR(x,y;f)-f(x,y)=o(1/R2)orμλ0/R[SδR(x,y)]-f(x,y)=o(1/R2)implies that f (x,y)≡const.Now we consider the following trigonometrical polynomialSκR(x,y;f)=Σ(1-νk/2/Rk)δAν(x,y)(k ∈Z+).Then we haveTheorem 3 If f(x,y)∈CP(D),then uniformly on D,S(k)R(x,y;f)-f(x,y)={O[1/Rpωp(1/R)],p=0,1,...,k-1 for k even,O[1/Rpωp(1/R)InR],p=k-1 for k odd.Theorems 1 and 2 include the results of Chandrasekharan and Minakshisundaram,and Theorem 3 is a
Transfer function combinations
Zhou, Liang
2012-10-01
Direct volume rendering has been an active area of research for over two decades. Transfer function design remains a difficult task since current methods, such as traditional 1D and 2D transfer functions, are not always effective for all data sets. Various 1D or 2D transfer function spaces have been proposed to improve classification exploiting different aspects, such as using the gradient magnitude for boundary location and statistical, occlusion, or size metrics. In this paper, we present a novel transfer function method which can provide more specificity for data classification by combining different transfer function spaces. In this work, a 2D transfer function can be combined with 1D transfer functions which improve the classification. Specifically, we use the traditional 2D scalar/gradient magnitude, 2D statistical, and 2D occlusion spectrum transfer functions and combine these with occlusion and/or size-based transfer functions to provide better specificity. We demonstrate the usefulness of the new method by comparing to the following previous techniques: 2D gradient magnitude, 2D occlusion spectrum, 2D statistical transfer functions and 2D size based transfer functions. © 2012 Elsevier Ltd.
Multistate nested canalizing functions
Adeyeye, J O; Laubenbacher, R; Li, Y
2013-01-01
The concept of a nested canalizing Boolean function has been studied over the course of the last decade in the context of understanding the regulatory logic of molecular interaction networks, such as gene regulatory networks. Such functions appear preferentially in published models of such networks. Recently, this concept has been generalized to include multi-state functions, and a recursive formula has been derived for their number, as a function of the number of variables. This paper carries out a detailed analysis of the class of nested canalizing functions over an arbitrary finite field. Furthermore, the paper generalizes the concept further, and derives a closed formula for the number of such generalized functions. The paper also derives a closed formula for the number of equivalence classes under permutation of variables. This is motivated by the fact that two nested canalizing functions that differ by a permutation of the variables share many important properties with each other. The paper contributes ...
DEFF Research Database (Denmark)
Gauravaram, Praveen; Knudsen, Lars Ramkilde
2010-01-01
standard which will be referred to as SHA-3. This chapter studies hash functions. Several approaches to design hash functions are discussed. An overview of the generic attacks and short-cut attacks on the iterated hash functions is provided. Important hash function applications are described. Several hash......Cryptographic hash functions are an important tool of cryptography and play a fundamental role in efficient and secure information processing. A hash function processes an arbitrary finite length input message to a fixed length output referred to as the hash value. As a security requirement, a hash...... value should not serve as an image for two distinct input messages and it should be difficult to find the input message from a given hash value. Secure hash functions serve data integrity, non-repudiation and authenticity of the source in conjunction with the digital signature schemes. Keyed hash...
ALGEBROIDAL FUNCTION AND ITS DERIVED FUNCTION IN UNIT CIRCULAR DISC
Institute of Scientific and Technical Information of China (English)
Huo Yingying; Sun Daochun
2009-01-01
In this article, the authors define the derived function of an algeboidal function in the unit disc, prove it is an algabriodal function, and study the order of algebroidal function and that of its derived function in unit circular disc.
Directory of Open Access Journals (Sweden)
Anatoliy Klimyk
2007-02-01
Full Text Available In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space $E_n$ are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl group, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. These functions are closely related to irreducible characters of a compact semisimple Lie group $G$ of rank $n$. Up to a sign, values of antisymmetric orbit functions are repeated on copies of the fundamental domain $F$ of the affine Weyl group (determined by the initial Weyl group in the entire Euclidean space $E_n$. Antisymmetric orbit functions are solutions of the corresponding Laplace equation in $E_n$, vanishing on the boundary of the fundamental domain $F$. Antisymmetric orbit functions determine a so-called antisymmetrized Fourier transform which is closely related to expansions of central functions in characters of irreducible representations of the group $G$. They also determine a transform on a finite set of points of $F$ (the discrete antisymmetric orbit function transform. Symmetric and antisymmetric multivariate exponential, sine and cosine discrete transforms are given.
On a link between a species survival time in an evolution model and the Bessel distributions
Guiol, Herve; Schinazi, Rinaldo B
2011-01-01
We consider a stochastic model for species evolution. A new species is born at rate lambda and a species dies at rate mu. A random number, sampled from a given distribution F, is associated with each new species at the time of birth. Every time there is a death event, the species that is killed is the one with the smallest fitness. We consider the (random) survival time of a species with a given fitness f. We show that the survival time distribution depends crucially on whether ff_c where f_c is a critical fitness that is computed explicitly.
The VLBA Calibrator Search for the BeSSeL Survey
Immer, K; Reid, M J; Bartkiewicz, A; Choi, Y K; Menten, K M; Moscadelli, L; Sanna, A; Wu, Y W; Xu, Y; Zhang, B; Zheng, X W
2011-01-01
We present the results of a survey of radio continuum sources near the Galactic plane using the Very Long Baseline Array (VLBA). Our observations are designed to identify compact extragalactic sources of milliarcsecond size that can be used for parallax measurements in the Bar and Spiral Structure Legacy Survey. We selected point sources from the NVSS and CORNISH catalogs with flux densities above 30 mJy and within $1.5\\degr$ of known maser targets. Of the 1529 sources observed, 199 were detected. For sources detected on 3 or more baselines, we determined accurate positions and evaluated their quality as potential calibrators. Most of the 1330 sources that were not detected with the VLBA are probably of extragalactic origin.
Directory of Open Access Journals (Sweden)
Nicy Sebastian
2015-08-01
Full Text Available The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral, one can list out almost all of the extended densities for the pathway parameter q < 1 and q → 1. Here, we bring out the idea of thicker- or thinner-tailed models associated with a gamma-type distribution as a limiting case of the pathway operator. Applications of this extended gamma model in statistical mechanics, input-output models, solar spectral irradiance modeling, etc., are established.
Counting with symmetric functions
Mendes, Anthony
2015-01-01
This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enu...
Elliptic hypergeometric functions
Spiridonov, V P
2016-01-01
This is author's Habilitation Thesis (Dr. Sci. dissertation) submitted at the beginning of September 2004. It is written in Russian and is posted due to the continuing requests for the manuscript. The content: 1. Introduction, 2. Nonlinear chains with the discrete time and their self-similar solutions, 3. General theory of theta hypergeometric series, 4. Theta hypergeometric integrals, 5. Biorthogonal functions, 6. Elliptic hypergeometric functions with |q|=1, 7. Conclusion, 8. References. It contains an outline of a general heuristic scheme for building univariate special functions through self-similar reductions of spectral transformation chains, which allowed construction of the differential-difference q-Painleve equations, as well as of the most general known set of elliptic biorthogonal functions comprising all classical orthogonal polynomials and biorthogonal rational functions. One of the key results of the thesis consists in the discovery of genuinely transcendental elliptic hypergeometric functions d...
Engel, J
2006-01-01
The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to functionals of the localized intrinsic density of a self-bound system such as a nucleus. After defining the intrinsic-density functional, we modify the usual Kohn-Sham procedure slightly to evaluate the mean-field approximation to the functional, and carefully describe the construction of the leading corrections for a system of fermions in one dimension with a spin-degeneracy equal to the number of particles N. Despite the fact that the corrections are complicated and nonlocal, we are able to construct a local Skyrme-like intrinsic-density functional that, while different from the exact functional, shares with it a minimum value equal to the exact ground-state energy at the exact ground-state intrinsic density, to next-to-leading order in 1/N. We briefly discuss implications for real Skyrme functionals.
DEFF Research Database (Denmark)
Yazdani, Hossein; Ortiz-Arroyo, Daniel; Kwasnicka, Halina
2016-01-01
In data science, there are important parameters that affect the accuracy of the algorithms used. Some of these parameters are: the type of data objects, the membership assignments, and distance or similarity functions. This paper discusses similarity functions as fundamental elements in membership...... assignments. The paper introduces Weighted Feature Distance (WFD), and Prioritized Weighted Feature Distance (PWFD), two new distance functions that take into account the diversity in feature spaces. WFD functions perform better in supervised and unsupervised methods by comparing data objects on their feature...... spaces, in addition to their similarity in the vector space. Prioritized Weighted Feature Distance (PWFD) works similarly as WFD, but provides the ability to give priorities to desirable features. The accuracy of the proposed functions are compared with other similarity functions on several data sets...
1991-01-01
Researchers at the Balance Function Laboratory and Clinic at the Minneapolis (MN) Neuroscience Institute on the Abbot Northwestern Hospital Campus are using a rotational chair (technically a "sinusoidal harmonic acceleration system") originally developed by NASA to investigate vestibular (inner ear) function in weightlessness to diagnose and treat patients with balance function disorders. Manufactured by ICS Medical Corporation, Schaumberg, IL, the chair system turns a patient and monitors his or her responses to rotational stimulation.
Directory of Open Access Journals (Sweden)
Samo Drobne
2012-12-01
Full Text Available In the paper, we suggest an approach to evaluate the number and composition of functional regions. Suggested approach is based on basic characteristics of functional regions, that are (1 more intensive intra-regional than the inter-regional interactions and (2 internal social and economic heterogeneity. Those characteristics are measured by factors estimated in spatial interaction model. The approach to evaluate functional regions was applied to Slovenia for three time periods.
Pisani, Pablo
2015-01-01
We present a pedagogical exposition of some applications of functional methods in quantum field theory: we use heat-kernel and zeta-function techniques to study the Casimir effect, the pair production in strong electric fields, quantum fields at finite temperature and beta-functions for a self-interacting scalar field, QED and pure Yang-Mills theories. The more recent application to the UV/IR mixing phenomenon in noncommutative theories is also discussed in this framework.
DEFF Research Database (Denmark)
Rumessen, J J; Gudmand-Høyer, E
1988-01-01
Twenty-five patients with functional bowel disease were given fructose, sorbitol, fructose-sorbitol mixtures, and sucrose. The occurrence of malabsorption was evaluated by means of hydrogen breath tests and the gastrointestinal symptoms, if any, were recorded. One patient could not be evaluated...... with functional bowel disease. The findings may have direct influence on the dietary guidance given to a major group of patients with functional bowel disease and may make it possible to define separate entities in this disease complex....
Canteaut, Anne; Videau, Marion
2005-01-01
http://www.ieee.org/; We present an extensive study of symmetric Boolean functions, especially of their cryptographic properties. Our main result establishes the link between the periodicity of the simplified value vector of a symmetric Boolean function and its degree. Besides the reduction of the amount of memory required for representing a symmetric function, this property has some consequences from a cryptographic point of view. For instance, it leads to a new general bound on the order of...
Artin, Emil
2015-01-01
This brief monograph on the gamma function was designed by the author to fill what he perceived as a gap in the literature of mathematics, which often treated the gamma function in a manner he described as both sketchy and overly complicated. Author Emil Artin, one of the twentieth century's leading mathematicians, wrote in his Preface to this book, ""I feel that this monograph will help to show that the gamma function can be thought of as one of the elementary functions, and that all of its basic properties can be established using elementary methods of the calculus."" Generations of teachers
Institute of Scientific and Technical Information of China (English)
Ding Yi
2009-01-01
In this article, the author derives a functional equation η(s)=［(π/4)s-1/2√2/πг(1-s)sin(πs/2)]η(1-s) of the analytic function η(s) which is defined by η(s)=1-s-3-s-5-s+7-s…for complex variable s with Re s>1, and is defined by analytic continuation for other values of s. The author proves (1) by Ramanujan identity (see [1], [3]). Her method provides a new derivation of the functional equation of Riemann zeta function by using Poisson summation formula.
Quantum Iterated Function Systems
Lozinski, A; Slomczynski, W; Lozinski, Artur; Zyczkowski, Karol; Slomczynski, Wojciech
2003-01-01
Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on the initial point. In an analogous way, we define quantum iterated functions system (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting a QIFS consists of completely positive maps acting in the space of density operators. We present exemplary classical IFSs, the invariant measure of which exhibits fractal structure, and study properties of the corresponding QIFSs and their invariant state.
DEFF Research Database (Denmark)
Raket, Lars Lau
-effect formulations, where the observed functional signal is assumed to consist of both fixed and random functional effects. This thesis takes the initial steps toward the development of likelihood-based methodology for functional objects. We first consider analysis of functional data defined on high......-dimensional Euclidean spaces under the effect of additive spatially correlated effects, and then move on to consider how to include data alignment in the statistical model as a nonlinear effect under additive correlated noise. In both cases, we will give directions on how to generalize the methodology to more complex...
Functional foods in pediatrics.
Van den Driessche, M; Veereman-Wauters, G
2002-01-01
The philosophy that food can be health promoting beyond its nutritional value is gaining acceptance. Known disease preventive aspects of nutrition have led to a new science, the 'functional food science'. Functional foods, first introduced in Japan, have no universally accepted definition but can be described as foods or food ingredients that may provide health benefits and prevent diseases. Currently, there is a growing interest in these products. However, not all regulatory issues have been settled yet. Five categories of foods can be classified as functional foods: dietary fibers, vitamins and minerals, bioactive substances, fatty acids and pro-, pre- and symbiotics. The latter are currently the main focus of research. Functional foods can be applied in pediatrics: during pregnancy, nutrition is 'functional' since it has prenatal influences on the intra-uterine development of the baby, after birth, 'functional' human milk supports adequate growth of infants and pro- and prebiotics can modulate the flora composition and as such confer certain health advantages. Functional foods have also been studied in pediatric diseases. The severity of necrotising enterocolitis (NEC), diarrhea, irritable bowel syndrome, intestinal allergy and lactose intolerance may be reduced by using functional foods. Functional foods have proven to be valuable contributors to the improvement of health and the prevention of diseases in pediatric populations.
DEFF Research Database (Denmark)
Törpel, Bettina
2006-01-01
The objective of this paper is the design of computer supported joint action spaces. It is argued against a view of functionality as residing in computer applications. In such a view the creation of functionality is equivalent to the creation of computer applications. Functionality, in the view...... advocated in this paper, emerges in the specific dynamic interplay of actors, objectives, structures, practices and means. In this view, functionality is the result of creating, harnessing and inhabiting computer supported joint action spaces. The successful creation and further development of a computer...
Functional Nausea in Children.
Kovacic, Katja; Di Lorenzo, Carlo
2016-03-01
Chronic nausea is a highly prevalent, bothersome, and difficult-to-treat symptom among adolescents. When chronic nausea presents as the predominant symptom and is not associated with any underlying disease, it may be considered a functional gastrointestinal disorder and named "functional nausea." The clinical features of functional nausea and its association with comorbid conditions provide clues to the underlying pathophysiological mechanisms. These may include gastrointestinal motor and sensory disturbances, autonomic imbalance, altered central nervous system pathways, or a combination of these. This review summarizes the current knowledge on mechanisms and treatment strategies for chronic, functional nausea in children.
DEFF Research Database (Denmark)
Lind, Morten
2011-01-01
Multilevel Flow Modeling (MFM) has been proposed as a tool for representing goals and functions of complex industrial plants and suggested as a basis for reasoning about control situations. Lind presents an introduction to MFM but do not describe how control functions are used in the modeling....... The purpose of the present paper is to serve as a companion paper to this introduction by explaining the basic principles used in MFM for representation of control functions. A theoretical foundation for modeling control functions is presented and modeling examples are given for illustration....
Perceptual Audio Hashing Functions
Directory of Open Access Journals (Sweden)
Emin Anarım
2005-07-01
Full Text Available Perceptual hash functions provide a tool for fast and reliable identification of content. We present new audio hash functions based on summarization of the time-frequency spectral characteristics of an audio document. The proposed hash functions are based on the periodicity series of the fundamental frequency and on singular-value description of the cepstral frequencies. They are found, on one hand, to perform very satisfactorily in identification and verification tests, and on the other hand, to be very resilient to a large variety of attacks. Moreover, we address the issue of security of hashes and propose a keying technique, and thereby a key-dependent hash function.
Knopp, Konrad
1996-01-01
This is a one-volume edition of Parts I and II of the classic five-volume set The Theory of Functions prepared by renowned mathematician Konrad Knopp. Concise, easy to follow, yet complete and rigorous, the work includes full demonstrations and detailed proofs.Part I stresses the general foundation of the theory of functions, providing the student with background for further books on a more advanced level.Part II places major emphasis on special functions and characteristic, important types of functions, selected from single-valued and multiple-valued classes.
Luten, J.B.
2009-01-01
This book reviews the research on seafood and health, the use and quality aspects of marine lipids and seafood proteins as ingredients in functional foods and consumer acceptance of (marine) functional food. The first chapter covers novel merging areas where seafood may prevent disease and improve h
Thyroid function in pregnancy☆
Leung, Angela M.
2012-01-01
Iodine is required for the production of thyroid hormones. Normal thyroid function during pregnancy is important for both the mother and developing fetus. This review discusses the changes in thyroid physiology that occur during pregnancy, the significance of thyroid function tests and thyroid antibody titers assessed during pregnancy, and the potential obstetric complications associated with maternal hypothyroidism.
Construction of Resilient Functions
Institute of Scientific and Technical Information of China (English)
ZHANG Jie; WEN Qiao-yan
2005-01-01
Based on the relationship between nonlinearity and resiliency of a multi-output function, we present a method for constructing nonintersecting linear codes from packing design. Through these linear codes, we obtain n-variable, moutput, t-resilient functions with very high nonlinearity.Their nonlinearities are currently the best results for most of cases.
Khimshiashvili, G.; Siersma, D.
2001-01-01
We describe the structure of minimal round functions on closed surfaces and three-folds. The minimal possible number of critical loops is determined and typical non-equisingular round function germs are interpreted in the spirit of isolated line singularities. We also discuss a version of Lusternik-
Institute of Scientific and Technical Information of China (English)
HAN You-fa; YAN Xin-ming; LV Li-li
2012-01-01
In this paper,we discuss the properties of the colored Jones function of knots.Particularly,we calculate the colored Jones function of some knots(31,41,51,52).Furthermore,one can compute the Kashaev's invariants and study some properties of the Kashaev's conjecture.
Functional and cognitive grammars
Institute of Scientific and Technical Information of China (English)
Anna Siewierska
2011-01-01
This paper presents a comprehensive review of the functional approach and cognitive approach to the nature of language and its relation to other aspects of human cognition. The paper starts with a brief discussion of the origins and the core tenets of the two approaches in Section 1. Section 2 discusses the similarities and differences between the three full-fledged structural functional grammars subsumed in the functional approach： Halliday＇s Systemic Functional Grammar （SFG）, Dik＇s Functional Grammar （FG）, and Van Valin＇s Role and Reference Grammar （RRG）. Section 3 deals with the major features of the three cognitive frameworks： Langacker＇s Cognitive Grammar （CG）, Goldberg＇s Cognitive Construction Grammar （CCG）, and Croft＇s Radical Construction Grammar （RCG）. Section 4 compares the two approaches and attempts to provide a unified functional-cognitive grammar. In the last section, the author concludes the paper with remarks on the unidirectional shift from functional grammar to cognitive grammar that may indicate a reinterpretation of the traditional relationship between functional and cognitive models of grammar.
Distribution Functions of Copulas
Institute of Scientific and Technical Information of China (English)
LI Yong-hong; He Ping
2007-01-01
A general method was proposed to evaluate the distribution function of 〈C1|C2〉 . Some examples were presented to validate the application of the method. Then the sufficient and necessary condition for that the distribution function ofis uniform was proved.
Pick, Luboš; John, Oldrich; Fucík, Svatopluk
2012-01-01
This is the first part of the second revised and extended edition of a well established monograph. It is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces to study other topics such as partial differential equations. Volum
DEFF Research Database (Denmark)
Yazdani, Hossein; Ortiz-Arroyo, Daniel; Kwasnicka, Halina
2016-01-01
In data science, there are important parameters that affect the accuracy of the algorithms used. Some of these parameters are: the type of data objects, the membership assignments, and distance or similarity functions. This paper discusses similarity functions as fundamental elements in membership...
Institute of Scientific and Technical Information of China (English)
王雷
2008-01-01
<正>EXAMPLE 1 Determining Wheth- er a Relation Represents a Function. Determining whether the following relation represent functions. (a)For this relation, the domain represents the employee of Saraxvs Pre -Owner Car Mart and the range repre- sents their base salary.
Ranu, H; Wilde, M.; Madden, B
2011-01-01
Pulmonary function tests are valuable investigations in the management of patients with suspected or previously diagnosed respiratory disease. They aid diagnosis, help monitor response to treatment and can guide decisions regarding further treatment and intervention. The interpretation of pulmonary functions tests requires knowledge of respiratory physiology. In this review we describe investigations routinely used and discuss their clinical implications.
Fundamentals of Functional Analysis
Kutateladze, S S; Slovák, Jan
2001-01-01
A concise guide to basic sections of modern functional analysis. Included are such topics as the principles of Banach and Hilbert spaces, the theory of multinormed and uniform spaces, the Riesz-Dunford holomorphic functional calculus, the Fredholm index theory, convex analysis and duality theory for locally convex spaces with applications to the Schwartz spaces of distributions and Radon measures.
Functional Magnetic Resonance Imaging
Voos, Avery; Pelphrey, Kevin
2013-01-01
Functional magnetic resonance imaging (fMRI), with its excellent spatial resolution and ability to visualize networks of neuroanatomical structures involved in complex information processing, has become the dominant technique for the study of brain function and its development. The accessibility of in-vivo pediatric brain-imaging techniques…
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A new characterization of univalent Bloch functions is given by investigating the growth order of an essentially increasing function. Our contribution can be considered as a slight improvement of the well-known Pommerenke's result and its all generalizations, and the proof presented in this paper is independently developed.
Monadic Functional Reactive Programming
Ploeg, A.J. van der; Shan, C
2013-01-01
Functional Reactive Programming (FRP) is a way to program reactive systems in functional style, eliminating many of the problems that arise from imperative techniques. In this paper, we present an alternative FRP formulation that is based on the notion of a reactive computation: a monadic computatio
A Functional HAZOP Methodology
DEFF Research Database (Denmark)
Liin, Netta; Lind, Morten; Jensen, Niels;
2010-01-01
A HAZOP methodology is presented where a functional plant model assists in a goal oriented decomposition of the plant purpose into the means of achieving the purpose. This approach leads to nodes with simple functions from which the selection of process and deviation variables follow directly....... The functional HAZOP methodology lends itself directly for implementation into a computer aided reasoning tool to perform root cause and consequence analysis. Such a tool can facilitate finding causes and/or consequences far away from the site of the deviation. A functional HAZOP assistant is proposed...... and investigated in a HAZOP study of an industrial scale Indirect Vapor Recompression Distillation pilot Plant (IVaRDiP) at DTU-Chemical and Biochemical Engineering. The study shows that the functional HAZOP methodology provides a very efficient paradigm for facilitating HAZOP studies and for enabling reasoning...
Submodular functions and optimization
Fujishige, Satoru
2005-01-01
It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics. Key features: - Self-contained exposition of the theory of submodular ...
Implementing function spreadsheets
DEFF Research Database (Denmark)
Sestoft, Peter
2008-01-01
A large amount of end-user development is done with spreadsheets. The spreadsheet metaphor is attractive because it is visual and accommodates interactive experimentation, but as observed by Peyton Jones, Blackwell and Burnett, the spreadsheet metaphor does not admit even the most basic abstraction......: that of turning an expression into a named function. Hence they proposed a way to define a function in terms of a worksheet with designated input and output cells; we shall call it a function sheet. The goal of our work is to develop implementations of function sheets and study their application to realistic...... examples. Therefore, we are also developing a simple yet comprehensive spreadsheet core implementation for experimentation with this technology. Here we report briefly on our experiments with function sheets as well as other uses of our spreadsheet core implementation....
Wu, Xiang-Yao; Yang, Jing-Hai; Liu, Xiao-Jing; Ba, Nuo; Wu, Yi-Heng; Wang, Qing-Cai; Li, Jing-Wu
2010-01-01
In the paper, we present a new kind of function photonic crystals, which refractive index is a function of space position. Unlike conventional PCs, which structure grow from two materials, A and B, with different dielectric constants $\\epsilon_{A}$ and $\\epsilon_{B}$. By Fermat principle, we give the motion equations of light in one-dimensional, two-dimensional and three-dimensional function photonic crystals. For one-dimensional function photonic crystals, we study the dispersion relation, band gap structure and transmissivity, and compare them with conventional photonic crystals. By choosing various refractive index distribution function $n(z)$, we can obtain more width or more narrow band gap structure than conventional photonic crystals.
properties and luminosity functions
Directory of Open Access Journals (Sweden)
Hektor Monteiro
2007-01-01
Full Text Available In this article, we present an investigation of a sample of 1072 stars extracted from the Villanova Catalog of Spectroscopically Identified White Dwarfs (2005 on-line version, studying their distribution in the Galaxy, their physical properties and their luminosity functions. The distances and physical properties of the white dwarfs are determined through interpolation of their (B-V or (b-y colors in model grids. The solar position relative to the Galactic plane, luminosity function, as well as separate functions for each white dwarf spectral type are derived and discussed. We show that the binary fraction does not vary significantly as a function of distance from the Galactic disk out to 100 pc. We propose that the formation rates of DA and non-DAs have changed over time and/or that DAs evolve into non-DA types. The luminosity functions for DAs and DBs have peaks possibly related to a star burst event.
Ramsay, J O
1997-01-01
Scientists today collect samples of curves and other functional observations. This monograph presents many ideas and techniques for such data. Included are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modelling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drwan from growth analysis, meterology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology while keeping the mathematical level widely accessible. It is designed to appeal to students, to applied data analysts, and to experienced researc...
DEFF Research Database (Denmark)
Sørensen, A S; Hansen, H; Høgenhaven, H;
1988-01-01
served as controls: 15 patients with a non-neurological but relapsing disorder, psoriasis, and 15 healthy volunteers. Compared with the group of healthy volunteers, a decreased adaptive level of ego functioning was found in the epilepsy groups, regardless of seizure types and EEG findings, and......, to a lesser extent, compared with the psoriasis group. Areas of ego functioning most affected were "reality testing", "cognitive functioning", "integrative functioning" and "regulation and control of drives". Patients with more than one type of seizure were the most affected, as were patients who were younger...... than 15 years when the disease began. The number of anticonvulsants administered did not influence the results. No difference on adaptive level of ego functioning was found between the group with primary generalized epilepsy and the group with temporal lobe epilepsy. Similarly, the temporal lobe...
Minguzzi, E.
2010-09-01
Every time function on spacetime gives a (continuous) total preordering of the spacetime events which respects the notion of causal precedence. The problem of the existence of a (semi-)time function on spacetime and the problem of recovering the causal structure starting from the set of time functions are studied. It is pointed out that these problems have an analog in the field of microeconomics known as utility theory. In a chronological spacetime the semi-time functions correspond to the utilities for the chronological relation, while in a K-causal (stably causal) spacetime the time functions correspond to the utilities for the K + relation (Seifert’s relation). By exploiting this analogy, we are able to import some mathematical results, most notably Peleg’s and Levin’s theorems, to the spacetime framework. As a consequence, we prove that a K-causal (i.e. stably causal) spacetime admits a time function and that the time or temporal functions can be used to recover the K + (or Seifert) relation which indeed turns out to be the intersection of the time or temporal orderings. This result tells us in which circumstances it is possible to recover the chronological or causal relation starting from the set of time or temporal functions allowed by the spacetime. Moreover, it is proved that a chronological spacetime in which the closure of the causal relation is transitive (for instance a reflective spacetime) admits a semi-time function. Along the way a new proof avoiding smoothing techniques is given that the existence of a time function implies stable causality, and a new short proof of the equivalence between K-causality and stable causality is given which takes advantage of Levin’s theorem and smoothing techniques.
Balcan, Maria-Florina
2010-01-01
There has recently been significant interest in the machine learning community on understanding and using submodular functions. Despite this recent interest, little is known about submodular functions from a learning theory perspective. Motivated by applications such as pricing goods in economics, this paper considers PAC-style learning of submodular functions in a distributional setting. A problem instance consists of a distribution on {0,1}^n and a real-valued function on {0,1}^n that is non-negative, monotone and submodular. We are given poly(n) samples from this distribution, along with the values of the function at those sample points. The task is to approximate the value of the function to within a multiplicative factor at subsequent sample points drawn from the same distribution, with sufficiently high probability. We prove several results for this problem. (1) If the function is Lipschitz and the distribution is a product distribution, such as the uniform distribution, then a good approximation is pos...
Minguzzi, E
2009-01-01
Every time function on spacetime gives a (continuous) total preordering of the spacetime events which respects the notion of causal precedence. The problem of the existence of a (semi-)time function on spacetime and the problem of recovering the causal structure starting from the set of time functions are studied. It is pointed out that these problems have an analog in the field of microeconomics known as utility theory. In a chronological spacetime the semi-time functions correspond to the utilities for the chronological relation, while in a K-causal (stably causal) spacetime the time functions correspond to the utilities for the K^+ relation (Seifert's relation). By exploiting this analogy, we are able to import some mathematical results, most notably Peleg's and Levin's theorems, to the spacetime framework. As a consequence, we prove that a K-causal (i.e. stably causal) spacetime admits a time function and that the time or temporal functions can be used to recover the K^+ (or Seifert) relation which indeed...
Unification of Filled Function and Tunnelling Function in Global Optimization
Institute of Scientific and Technical Information of China (English)
Wei Wang; Yong-jian Yang; Lian-sheng Zhang
2007-01-01
In this paper, two auxiliary functions for global optimization are proposed. These two auxiliary functions possess all characters of tunnelling functions and filled functions under certain general assumptions.Thus, they can be considered as the unification of filled function and tunnelling function. Moreover, the process of tunneling or filling for global optimization can be unified as the minimization of such auxiliary functions.Result of numerical experiments shows that such two auxiliary functions are effective.
Mathai, AM
2009-01-01
The two main topics emphasized in this book, special functions and fractional calculus, are currently under fast development in theory and application to many problems in statistics, physics, and engineering, particularly in condensed matter physics, plasma physics, and astrophysics. The book begins by setting forth definitions, contours, existence conditions, and particular cases of the H-function. The authors then deal with Laplace, Fourier, Hankel, and other transforms. As these relations are explored, fractional calculus and its relations to H-functions emerge with important results on fra
Quantum iterated function systems.
Łoziński, Artur; Zyczkowski, Karol; Słomczyński, Wojciech
2003-10-01
An iterated function system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum IFS (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting, a QIFS consists of completely positive maps acting in the space of density operators. This formalism is designed to describe certain problems of nonunitary quantum dynamics. We present exemplary classical IFSs, the invariant measure of which exhibits fractal structure, and study properties of the corresponding QIFSs and their invariant states.
Directory of Open Access Journals (Sweden)
Carlos A. Berenstein
1980-01-01
Full Text Available We show that any mean-periodic function f can be represented in terms of exponential-polynomial solutions of the same convolution equation f satisfies, i.e., u∗f=0(μ∈E′(ℝn. This extends to n-variables the work of L. Schwartz on mean-periodicity and also extends L. Ehrenpreis' work on partial differential equations with constant coefficients to arbitrary convolutors. We also answer a number of open questions about mean-periodic functions of one variable. The basic ingredient is our work on interpolation by entire functions in one and several complex variables.
Correlation Functions and Spin
Tyc, T
2000-01-01
The k-electron correlation function of a free chaotic electron beam is derived with the spin degree of freedom taken into account. It is shown that it can be expressed with the help of correlation functions for a polarized electron beam of all orders up to k and the degree of spin polarization. The form of the correlation function suggests that if the electron beam is not highly polarized, observing multi-particle correlations should be difficult. The result can be applied also to chaotic photon beams, the degree of spin polarization being replaced by the degree of polarization.
DEFF Research Database (Denmark)
Sørensen, A S; Hansen, H; Høgenhaven, H;
1988-01-01
Two groups of epilepsy patients (28 patients with temporal lobe epilepsy and 15 patients with primary generalized epilepsy) entered a study of personality traits related to epilepsy, based on a modification of Bellak's semistructured interview for assessment of ego strength. Two groups of subjects......, to a lesser extent, compared with the psoriasis group. Areas of ego functioning most affected were "reality testing", "cognitive functioning", "integrative functioning" and "regulation and control of drives". Patients with more than one type of seizure were the most affected, as were patients who were younger...
Choice probability generating functions
DEFF Research Database (Denmark)
Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel
2010-01-01
This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with specific properties, and that every function with these specific properties is consistent with a RUM. The choice...... probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized by logarithmic mixtures of their associated CPGF. The paper relates CPGF to multivariate extreme value distributions, and reviews and extends methods for constructing generating functions for applications...
Catalytic Functions of Standards
K. Blind (Knut)
2009-01-01
textabstractThe three different areas and the examples have illustrated several catalytic functions of standards for innovation. First, the standardisation process reduces the time to market of inventions, research results and innovative technologies. Second, standards themselves promote the diffusi
DEFF Research Database (Denmark)
Knudsen, Lars Ramkilde; Rechberger, Christian; Thomsen, Søren Steffen
2007-01-01
In this paper we propose the Grindahl hash functions, which are based on components of the Rijndael algorithm. To make collision search sufficiently difficult, this design has the important feature that no low-weight characteristics form collisions, and at the same time it limits access to the st......In this paper we propose the Grindahl hash functions, which are based on components of the Rijndael algorithm. To make collision search sufficiently difficult, this design has the important feature that no low-weight characteristics form collisions, and at the same time it limits access...... to the state. We propose two concrete hash functions, Grindahl-256 and Grindahl-512 with claimed security levels with respect to collision, preimage and second preimage attacks of 2^128 and 2^256, respectively. Both proposals have lower memory requirements than other hash functions at comparable speeds...
Campos, Cédric M.; Epstein, Marcelo; De León, Manuel
2007-01-01
The notions of uniformity and homogeneity of elastic materials are reviewed in terms of Lie groupoids and frame bundles. This framework is also extended to consider the case Functionally Graded Media, which allows us to obtain some homogeneity conditions.
... Spread the Word Shop AAP Find a Pediatrician Family Life Medical Home Family Dynamics Adoption & Foster Care ... Español Text Size Email Print Share Normal Functioning Family Page Content Article Body Is there any way ...
The methods used seem to be new, and the author feels that further work in this direction may eventually yield a proof of the conjecture in the case when one of the functions is of bounded variation . (Author)
Pair Correlation Function Integrals
DEFF Research Database (Denmark)
Wedberg, Nils Hejle Rasmus Ingemar; O'Connell, John P.; Peters, Günther H.J.;
2011-01-01
numerical tests complementing previous results. Pure molecular fluids are here studied in the isothermal-isobaric ensemble with isothermal compressibilities evaluated from the total correlation function integrals and compared with values derived from volume fluctuations. For systems where the radial......We describe a method for extending radial distribution functions obtained from molecular simulations of pure and mixed molecular fluids to arbitrary distances. The method allows total correlation function integrals to be reliably calculated from simulations of relatively small systems. The long......, and J. Abildskov, Mol. Simul. 36, 1243 (2010); Fluid Phase Equilib. 302, 32 (2011)], but describe here its theoretical basis more thoroughly and derive long-distance approximations for the direct correlation functions. We describe the numerical implementation of the method in detail, and report...
The Protostellar Luminosity Function
Offner, Stella
2011-01-01
The protostellar luminosity function (PLF) is the present-day luminosity function of the protostars in a region of star formation. It is determined using the protostellar mass function (PMF) in combination with a stellar evolutionary model that provides the luminosity as a function of instantaneous and final stellar mass. As in McKee & Offner (2010), we consider three main accretion models: the Isothermal Sphere model, the Turbulent Core model, and an approximation of the Competitive Accretion model. We also consider the effect of an accretion rate that tapers off linearly in time and an accelerating star formation rate. For each model, we characterize the luminosity distribution using the mean, median, maximum, ratio of the median to the mean, standard deviation of the logarithm of the luminosity, and the fraction of very low luminosity objects. We compare the models with bolometric luminosities observed in local star forming regions and find that models with an approximately constant accretion time, suc...
Fundamentals of functional analysis
Farenick, Douglas
2016-01-01
This book provides a unique path for graduate or advanced undergraduate students to begin studying the rich subject of functional analysis with fewer prerequisites than is normally required. The text begins with a self-contained and highly efficient introduction to topology and measure theory, which focuses on the essential notions required for the study of functional analysis, and which are often buried within full-length overviews of the subjects. This is particularly useful for those in applied mathematics, engineering, or physics who need to have a firm grasp of functional analysis, but not necessarily some of the more abstruse aspects of topology and measure theory normally encountered. The reader is assumed to only have knowledge of basic real analysis, complex analysis, and algebra. The latter part of the text provides an outstanding treatment of Banach space theory and operator theory, covering topics not usually found together in other books on functional analysis. Written in a clear, concise manner,...
Lectures on Functional Analysis
Kurepa, Svetozar; Kraljević, Hrvoje
1987-01-01
This volume consists of a long monographic paper by J. Hoffmann-Jorgensen and a number of shorter research papers and survey articles covering different aspects of functional analysis and its application to probability theory and differential equations.
1991-01-01
The concepts of source and quantum action principle are used to produce the phonon Green's function appropriate for an initial phonon vacuum state. An application to the Mossbauer effect is presented.
[Vascular endothelial Barrier Function].
Ivanov, A N; Puchinyan, D M; Norkin, I A
2015-01-01
Endothelium is an important regulator of selective permeability of the vascular wall for different molecules and cells. This review summarizes current data on endothelial barrier function. Endothelial glycocalyx structure, its function and role in the molecular transport and leukocytes migration across the endothelial barrier are discussed. The mechanisms of transcellular transport of macromolecules and cell migration through endothelial cells are reviewed. Special section of this article addresses the structure and function of tight and adherens endothelial junction, as well as their importance for the regulation of paracellular transport across the endothelial barrier. Particular attention is paid to the signaling mechanism of endothelial barrier function regulation and the factors that influence on the vascular permeability.
On Network Functional Compression
Feizi, Soheil
2010-01-01
In this paper, we consider different aspects of the network functional compression problem where computation of a function (or, some functions) of sources located at certain nodes in a network is desired at receiver(s). The rate region of this problem has been considered in the literature under certain restrictive assumptions, particularly in terms of the network topology, the functions and the characteristics of the sources. In this paper, we present results that significantly relax these assumptions. Firstly, we consider this problem for an arbitrary tree network and asymptotically lossless computation. We show that, for depth one trees with correlated sources, or for general trees with independent sources, a modularized coding scheme based on graph colorings and Slepian-Wolf compression performs arbitrarily closely to rate lower bounds. For a general tree network with independent sources, optimal computation to be performed at intermediate nodes is derived. We introduce a necessary and sufficient condition...
Kellerstein, M; Verbaarschot, J J M
2016-01-01
The behavior of quenched Dirac spectra of two-dimensional lattice QCD is consistent with spontaneous chiral symmetry breaking which is forbidden according to the Coleman-Mermin-Wagner theorem. One possible resolution of this paradox is that, because of the bosonic determinant in the partially quenched partition function, the conditions of this theorem are violated allowing for spontaneous symmetry breaking in two dimensions or less. This goes back to work by Niedermaier and Seiler on nonamenable symmetries of the hyperbolic spin chain and earlier work by two of the auhtors on bosonic partition functions at nonzero chemical potential. In this talk we discuss chiral symmetry breaking for the bosonic partition function of QCD at nonzero isospin chemical potential and a bosonic random matrix theory at imaginary chemical potential and compare the results with the fermionic counterpart. In both cases the chiral symmetry group of the bosonic partition function is noncompact.
Bioprinting: Functional droplet networks
Durmus, Naside Gozde; Tasoglu, Savas; Demirci, Utkan
2013-06-01
Tissue-mimicking printed networks of droplets separated by lipid bilayers that can be functionalized with membrane proteins are able to spontaneously fold and transmit electrical currents along predefined paths.
ON BANDLIMITED SCALING FUNCTION
Institute of Scientific and Technical Information of China (English)
Wei Chen; Qiao Yang; Wei-jun Jiang; Si-long Peng
2002-01-01
This paper discuss band-limited scaling function, especially on the interval band case and three interval bands case, its relationship to oversampling property and weakly translation invariance are also studied. At the end, we propose an open problem.
Holographic Three point Functions
DEFF Research Database (Denmark)
Bissi, Agnese
In this thesis it is addressed the problem of the computation of three point correlation functions within the AdS=CFT correspondence. In the context of the AdS 5=CFT4 correspondence we present three computations. First we compare the results of tree level three point functions of two giant...... gravitons and a point like graviton and its dual counterpart, namely two Schur polynomials and a single trace chiral primary. Secondly we compute the one loop correction to planar, non extremal three point functions of two heavy and one light operators, both from the gauge and string side in the Frolov......-Tseytlin regime. Finally we generalize the scalar product of two states belonging to the SO(6) sector of N = 4 SYM with implications on the construction of three point functions of 3 non-BPS operators from the gauge theory side. On the other hand in the AdS4=CFT3 correspondence we compare the computations...
Directory of Open Access Journals (Sweden)
N. Carella
2013-09-01
Full Text Available A new unconditional inequality of the totient function is contributed to the literature. This result is associated with various unsolved problems about the distribution of prime numbers.
Characterisation of Functional Surfaces
DEFF Research Database (Denmark)
Lonardo, P.M.; De Chiffre, Leonardo; Bruzzone, A.A.
2004-01-01
Characterisation of surfaces is of fundamental importance to control the manufacturing process and the functional performance of the part. Many applications concern contact and tribology problems, which include friction, wear and lubrication. This paper presents the techniques and instruments for...
Center for Functional Nanomaterials
Federal Laboratory Consortium — The Center for Functional Nanomaterials (CFN) explores the unique properties of materials and processes at the nanoscale. The CFN is a user-oriented research center...
Functional Task Test: Data Review
Cromwell, Ronita
2014-01-01
After space flight there are changes in multiple physiological systems including: Cardiovascular function; Sensorimotor function; and Muscle function. How do changes in these physiological system impact astronaut functional performance?
Roy D Sleator
2012-01-01
An overwhelming array of structural variants has evolved from a comparatively small number of protein structural domains; which has in turn facilitated an expanse of functional derivatives. Herein, I review the primary mechanisms which have contributed to the vastness of our existing, and expanding, protein repertoires. Protein function prediction strategies, both sequence and structure based, are also discussed and their associated strengths and weaknesses assessed.
Griffel, DH
2002-01-01
A stimulating introductory text, this volume examines many important applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Detailed enough to impart a thorough understanding, the text is also sufficiently straightforward for those unfamiliar with abstract analysis. Its four-part treatment begins with distribution theory and discussions of Green's functions. Essentially independent of the preceding material, the second and third parts deal with Banach spaces, Hilbert space, spectral theory, and variational techniques. The final part outlines the
Green's functions with applications
Duffy, Dean G
2015-01-01
This second edition systematically leads readers through the process of developing Green's functions for ordinary and partial differential equations. In addition to exploring the classical problems involving the wave, heat, and Helmholtz equations, the book includes special sections on leaky modes, water waves, and absolute/convective instability. The book helps readers develop an intuition about the behavior of Green's functions, and considers the questions of the computational efficiency and possible methods for accelerating the process.
Function, anticipation, representation
Bickhard, Mark. H.
2001-06-01
Function emerges in certain kinds of far-from-equilibrium systems. One important kind of function is that of interactive anticipation, an adaptedness to temporal complexity. Interactive anticipation is the locus of the emergence of normative representational content, and, thus, of representation in general: interactive anticipation is the naturalistic core of the evolution of cognition. Higher forms of such anticipation are involved in the subsequent macro-evolutionary sequence of learning, emotions, and reflexive consciousness.
Energy Technology Data Exchange (ETDEWEB)
McGraw, John T [Placitas, NM; Zimmer, Peter C [Albuquerque, NM; Ackermann, Mark R [Albuquerque, NM
2012-01-24
Methods and apparatus for a structure function monitor provide for generation of parameters characterizing a refractive medium. In an embodiment, a structure function monitor acquires images of a pupil plane and an image plane and, from these images, retrieves the phase over an aperture, unwraps the retrieved phase, and analyzes the unwrapped retrieved phase. In an embodiment, analysis yields atmospheric parameters measured at spatial scales from zero to the diameter of a telescope used to collect light from a source.
LDF (Lag Dependence Functions)
DEFF Research Database (Denmark)
2000-01-01
LDF (Lag Dependence Functions) is an S-PLUS library for identification of non-linear dependencies in univariate time series. The methods can be considered generalizations of the tools applicable for linear time series.......LDF (Lag Dependence Functions) is an S-PLUS library for identification of non-linear dependencies in univariate time series. The methods can be considered generalizations of the tools applicable for linear time series....
Mahamood, Rasheedat Modupe
2017-01-01
This book presents the concept of functionally graded materials as well as their use and different fabrication processes. The authors describe the use of additive manufacturing technology for the production of very complex parts directly from the three dimension computer aided design of the part by adding material layer after layer. A case study is also presented in the book on the experimental analysis of functionally graded material using laser metal deposition process.
Directory of Open Access Journals (Sweden)
W. L. Fouché
1983-03-01
Full Text Available In this article we discuss some aspects of nonlinear functional analysis. It included reviews of Banach’s contraction theorem, Schauder’s fixed point theorem, globalising techniques and applications of homotopy theory to nonlinear functional analysis. The author emphasises that fundamentally new ideas are required in order to achieve a better understanding of phenomena which contain both nonlinear and definite infinite dimensional features.
Purely Functional Structured Programming
Obua, Steven
2010-01-01
The idea of functional programming has played a big role in shaping today's landscape of mainstream programming languages. Another concept that dominates the current programming style is Dijkstra's structured programming. Both concepts have been successfully married, for example in the programming language Scala. This paper proposes how the same can be achieved for structured programming and PURELY functional programming via the notion of LINEAR SCOPE. One advantage of this proposal is that m...
Partly occupied Wannier functions
DEFF Research Database (Denmark)
Thygesen, Kristian Sommer; Hansen, Lars Bruno; Jacobsen, Karsten Wedel
2005-01-01
We introduce a scheme for constructing partly occupied, maximally localized Wannier functions (WFs) for both molecular and periodic systems. Compared to the traditional occupied WFs the partly occupied WFs possess improved symmetry and localization properties achieved through a bonding-antibondin......We introduce a scheme for constructing partly occupied, maximally localized Wannier functions (WFs) for both molecular and periodic systems. Compared to the traditional occupied WFs the partly occupied WFs possess improved symmetry and localization properties achieved through a bonding...
Production Functions Behaving Badly
DEFF Research Database (Denmark)
Fredholm, Thomas
This paper reconsiders Anwar Shaikh's critique of the neoclassical theory of growth and distribution based on its use of aggregate production functions. This is done by reconstructing and extending Franklin M. Fisher's 1971 computer simulations, which Shaikh used to support his critique. Together...... with other recent extensions to Shaikh's seminal work, my results support and strengthen the evidence against the use of aggregate production functions....
Functions & Features of Idioms
Institute of Scientific and Technical Information of China (English)
周来纳
2015-01-01
Idioms, or conventionalized multiword expressions, often but not always non-literal, are hardly marginal in English, though they have been relatively neglected in lexical studies of the language. This neglect is especially evident in respect of the functions of idioms. The aim of this article, accordingly, is to account for the functions of idioms by analyzing what they do with the features of idioms.
Handbook of functional equations functional inequalities
2014-01-01
As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemann–Stieltjes integral, means and related functional inequalities, Weighted G...
Directory of Open Access Journals (Sweden)
Parvin Raji
2012-12-01
Full Text Available Background and Aim: All activities of daily living need to balance control in static and dynamic movements. In recent years, a numerous increase can be seen in the functional balance assessment tools. Functional balance tests emphasize on static and dynamic balance, balance in weight transfer, the equilibrium response to the imbalances, and functional mobility. These standardized and available tests assess performance and require minimal or no equipment and short time to run. Functional balance is prerequisite for the most static and dynamic activities in daily life and needs sufficient interaction between sensory and motor systems. According to the critical role of balance in everyday life, and wide application of functional balance tests in the diagnosis and assessment of patients, a review of the functional balance tests was performed.Methods: The Google Scholar, PubMed, Science Direct, Scopus, Magiran, Iran Medex, and IranDoc databases were reviewed and the reliable and valid tests which were mostly used by Iranian researchers were assessed.Conclusion: It seems that Berg balance scale (BBS have been studied by Iranian and foreign researches more than the other tests. This test has high reliability and validity in elderly and in the most neurological disorders.
Functional neuroimaging of sleep.
Nofzinger, Eric A
2005-03-01
Sleep and sleep disorders have traditionally been viewed from a polysomnographic perspective. Although these methods provide information on the timing of various stages of sleep and wakefulness, they do not provide information regarding function in brain structures that have been implicated in the generation of sleep and that may be abnormal in different sleep disorders. Functional neuroimaging methods provide information regarding changes in brain function across the sleep-wake cycle that provides information for models of sleep dysregulation in a variety of sleep disorders. Early studies show reliable increases in function in limbic and anterior paralimbic cortex in rapid eye movement (REM) sleep and decreases in function in higher-order cortical regions in known thalamocortical networks during non-REM sleep. Although most of the early work in this area has been devoted to the study of normal sleep mechanisms, a collection of studies in diverse sleep disorders such as sleep deprivation, depression, insomnia, dyssomnias, narcolepsy, and sleep apnea suggest that functional neuroimaging methods have the potential to clarify the pathophysiology of sleep disorders and to guide treatment strategies.
Directory of Open Access Journals (Sweden)
Pankaj Talwar
2015-01-01
Full Text Available With absolute normal semen analysis parameters it may not be necessary to shift to specialized tests early but in cases with borderline parameters or with history of fertilization failure in past it becomes necessary to do a battery of tests to evaluate different parameters of spermatozoa. Various sperm function tests are proposed and endorsed by different researchers in addition to the routine evaluation of fertility. These tests detect function of a certain part of spermatozoon and give insight on the events in fertilization of the oocyte. The sperms need to get nutrition from the seminal plasma in the form of fructose and citrate (this can be assessed by fructose qualitative and quantitative estimation, citrate estimation. They should be protected from the bad effects of pus cells and reactive oxygen species (ROS (leukocyte detection test, ROS estimation. Their number should be in sufficient in terms of (count, structure normal to be able to fertilize eggs (semen morphology. Sperms should have intact and functioning membrane to survive harsh environment of vagina and uterine fluids (vitality and hypo-osmotic swelling test, should have good mitochondrial function to be able to provide energy (mitochondrial activity index test. They should also have satisfactory acrosome function to be able to burrow a hole in zona pellucida (acrosome intactness test, zona penetration test. Finally, they should have properly packed DNA in the nucleus to be able to transfer the male genes (nuclear chromatic decondensation test to the oocyte during fertilization.
Functional integration over geometries
Mottola, E
1995-01-01
The geometric construction of the functional integral over coset spaces {\\cal M}/{\\cal G} is reviewed. The inner product on the cotangent space of infinitesimal deformations of \\cal M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber \\cal G, the functional measure on the coset space {\\cal M}/{\\cal G} is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev-Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where \\cal G is the group of coordinate reparametrizations of spacetime, the continuum functional integral over geometries, {\\it i.e.} metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the me...
Space race functional responses.
Sjödin, Henrik; Brännström, Åke; Englund, Göran
2015-02-22
We derive functional responses under the assumption that predators and prey are engaged in a space race in which prey avoid patches with many predators and predators avoid patches with few or no prey. The resulting functional response models have a simple structure and include functions describing how the emigration of prey and predators depend on interspecific densities. As such, they provide a link between dispersal behaviours and community dynamics. The derived functional response is general but is here modelled in accordance with empirically documented emigration responses. We find that the prey emigration response to predators has stabilizing effects similar to that of the DeAngelis-Beddington functional response, and that the predator emigration response to prey has destabilizing effects similar to that of the Holling type II response. A stability criterion describing the net effect of the two emigration responses on a Lotka-Volterra predator-prey system is presented. The winner of the space race (i.e. whether predators or prey are favoured) is determined by the relationship between the slopes of the species' emigration responses. It is predicted that predators win the space race in poor habitats, where predator and prey densities are low, and that prey are more successful in richer habitats.
Directory of Open Access Journals (Sweden)
Samson Z Assefa
2015-08-01
Full Text Available Sleep is a ubiquitous component of animal life including birds and mammals. The exact function of sleep has been one of the mysteries of biology. A considerable number of theories have been put forward to explain the reason(s for the necessity of sleep. To date, while a great deal is known about what happens when animals sleep, there is no definitive comprehensive explanation as to the reason that sleep is an inevitable part of animal functioning. It is well known that sleep is a homeostatically regulated body process, and that prolonged sleep deprivation is fatal in animals. In this paper, we present some of the theories as to the functions of sleep and provide a review of some hypotheses as to the overall physiologic function of sleep. To better understand the purpose for sleeping, we review the effects of sleep deprivation on physical, neurocognitive and psychic function. A better understanding of the purpose for sleeping will be a great advance in our understanding of the nature of the animal kingdom, including our own.
Functional imaging and endoscopy
Institute of Scientific and Technical Information of China (English)
Jian-Guo Zhang; Hai-Feng Liu
2011-01-01
The emergence of endoscopy for the diagnosis of gastrointestinal diseases and the treatment of gastrointestinal diseases has brought great changes.The mere observation of anatomy with the imaging mode using modern endoscopy has played a significant role in this regard.However,increasing numbers of endoscopies have exposed additional deficiencies and defects such as anatomically similar diseases.Endoscopy can be used to examine lesions that are difficult to identify and diagnose.Early disease detection requires that substantive changes in biological function should be observed,but in the absence of marked morphological changes,endoscopic detection and diagnosis are difficult.Disease detection requires not only anatomic but also functional imaging to achieve a comprehensive interpretation and understanding.Therefore,we must ask if endoscopic examination can be integrated with both anatomic imaging and functional imaging.In recent years,as molecular biology and medical imaging technology have further developed,more functional imaging methods have emerged.This paper is a review of the literature related to endoscopic optical imaging methods in the hopes of initiating integration of functional imaging and anatomical imaging to yield a new and more effective type of endoscopy.
Learning View Generalization Functions
Breuel, Thomas M
2007-01-01
Learning object models from views in 3D visual object recognition is usually formulated either as a function approximation problem of a function describing the view-manifold of an object, or as that of learning a class-conditional density. This paper describes an alternative framework for learning in visual object recognition, that of learning the view-generalization function. Using the view-generalization function, an observer can perform Bayes-optimal 3D object recognition given one or more 2D training views directly, without the need for a separate model acquisition step. The paper shows that view generalization functions can be computationally practical by restating two widely-used methods, the eigenspace and linear combination of views approaches, in a view generalization framework. The paper relates the approach to recent methods for object recognition based on non-uniform blurring. The paper presents results both on simulated 3D ``paperclip'' objects and real-world images from the COIL-100 database sho...
Algal functional annotation tool
Energy Technology Data Exchange (ETDEWEB)
Lopez, D. [UCLA; Casero, D. [UCLA; Cokus, S. J. [UCLA; Merchant, S. S. [UCLA; Pellegrini, M. [UCLA
2012-07-01
The Algal Functional Annotation Tool is a web-based comprehensive analysis suite integrating annotation data from several pathway, ontology, and protein family databases. The current version provides annotation for the model alga Chlamydomonas reinhardtii, and in the future will include additional genomes. The site allows users to interpret large gene lists by identifying associated functional terms, and their enrichment. Additionally, expression data for several experimental conditions were compiled and analyzed to provide an expression-based enrichment search. A tool to search for functionally-related genes based on gene expression across these conditions is also provided. Other features include dynamic visualization of genes on KEGG pathway maps and batch gene identifier conversion.
Functional Programming Using F#
DEFF Research Database (Denmark)
Hansen, Michael Reichhardt; Rischel, Hans
This comprehensive introduction to the principles of functional programming using F# shows how to apply basic theoretical concepts to produce succinct and elegant programs. It demonstrates the role of functional programming in a wide spectrum of applications including databases and systems....... Coverage also includes advanced features in the .NET library, the imperative features of F# and topics such as text processing, sequences, computation expressions and asynchronous computation. With a broad spectrum of examples and exercises, the book is perfect for courses in functional programming...... and for self-study. Enhancing its use as a text is an accompanying website with downloadable programs, lecture slides, a mini-projects and links to further F# sources....
Ghrelin and Functional Dyspepsia
Directory of Open Access Journals (Sweden)
Takashi Akamizu
2010-01-01
Full Text Available The majority of patients with dyspepsia have no identifiable cause of their disease, leading to a diagnosis of functional dyspepsia (FD. While a number of different factors affect gut activity, components of the nervous and endocrine systems are essential for normal gut function. Communication between the brain and gut occurs via direct neural connections or endocrine signaling events. Ghrelin, a peptide produced by the stomach, affects gastric motility/emptying and secretion, suggesting it may play a pathophysiological role in FD. It is also possible that the functional abnormalities in FD may affect ghrelin production in the stomach. Plasma ghrelin levels are reported to be altered in FD, correlating with FD symptom score. Furthermore, some patients with FD suffer from anorexia with body-weight loss. As ghrelin increases gastric emptying and promotes feeding, ghrelin therapy may be a new approach to the treatment of FD.
Axler, Sheldon; Ramey, Wade
2013-01-01
This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by e-mail - supplements the text for readers who wish to explore harmonic function theory on a computer.
[Functional mitral regurgitation].
Sade, Leyla Elif
2009-07-01
Functional mitral regurgitation (FMR) is the mitral regurgitation that occurs due to myocardial disease in the presence of normal mitral valve leaflets. This scenario has the different characteristics than the organic mitral regurgitation. Functional mitral regurgitation is a disease of the ventricle and occurs by the deformation of the mitral valve leaflets. This morbid entity is frequent and has bad prognosis. Functional mitral regurgitation is the result of complex pathophysiologic process including left ventricular local and global remodeling, mitral annular and papillary muscle dysfunction, and left ventricular dysfunction. The dynamic behavior of FMR complicates the quantification of the regurgitation. Exercise stress echocardiography is of particular importance in the evaluation of the hemodynamic burden of FMR. Particular pathophysiological properties of the FMR necessitate different therapeutic approaches than the current ones for classical mitral regurgitation.
DEFF Research Database (Denmark)
Nielsen, Line A.; Zois, Nora Elisabeth; Pedersen, Henrik D.
2007-01-01
Background: Clinical studies investigating platelet function in dogs have had conflicting results that may be caused by normal physiologic variation in platelet response to agonists. Objectives: The objective of this study was to investigate platelet function in clinically healthy dogs of 4...... different breeds by whole-blood aggregometry and with a point-of-care platelet function analyzer (PFA-100), and to evaluate the effect of acetylsalicylic acid (ASA) administration on the results from both methods. Methods: Forty-five clinically healthy dogs (12 Cavalier King Charles Spaniels [CKCS], 12...... applied. However, the importance of these breed differences remains to be investigated. The PFA-100 method with Col + Epi as agonists, and ADP-induced platelet aggregation appear to be sensitive to ASA in dogs....
Protein Functionalized Nanodiamond Arrays
Directory of Open Access Journals (Sweden)
Liu YL
2010-01-01
Full Text Available Abstract Various nanoscale elements are currently being explored for bio-applications, such as in bio-images, bio-detection, and bio-sensors. Among them, nanodiamonds possess remarkable features such as low bio-cytotoxicity, good optical property in fluorescent and Raman spectra, and good photostability for bio-applications. In this work, we devise techniques to position functionalized nanodiamonds on self-assembled monolayer (SAMs arrays adsorbed on silicon and ITO substrates surface using electron beam lithography techniques. The nanodiamond arrays were functionalized with lysozyme to target a certain biomolecule or protein specifically. The optical properties of the nanodiamond-protein complex arrays were characterized by a high throughput confocal microscope. The synthesized nanodiamond-lysozyme complex arrays were found to still retain their functionality in interacting with E. coli.
Quantal density functional theory
Sahni, Viraht
2016-01-01
This book deals with quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The treated time-independent QDFT constitutes a special case. In the 2nd edition, the theory is extended to include the presence of external magnetostatic fields. The theory is a description of matter based on the ‘quantal Newtonian’ first and second laws which is in terms of “classical” fields that pervade all space, and their quantal sources. The fields, which are explicitly defined, are separately representative of electron correlations due to the Pauli exclusion principle, Coulomb repulsion, correlation-kinetic, correlation-current-density, and correlation-magnetic effects. The book further describes Schrödinger theory from the new physical perspective of fields and quantal sources. It also describes traditional Hohenberg-Kohn-Sham DFT, and explains via QDFT the physics underlying the various energy functionals and functional derivatives o...
Spaces of continuous functions
Groenewegen, G L M
2016-01-01
The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other hand we discuss a number of classical results according to which an algebra or a vector lattice can be represented as a C(X). Various applications of these theorems are given. Some attention is devoted to related theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem. The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory.
Generating functions for symmetric and shifted symmetric functions
Jing, Naihuan; Rozhkovskaya, Natasha
2016-01-01
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to treat various families of symmetric functions and their shifted analogues.
Clocks and cardiovascular function
McLoughlin, Sarah C.; Haines, Philip; FitzGerald, Garret A.
2016-01-01
Circadian clocks in central and peripheral tissues enable the temporal synchronization and organization of molecular and physiological processes of rhythmic animals, allowing optimum functioning of cells and organisms at the most appropriate time of day. Disruption of circadian rhythms, from external or internal forces, leads to widespread biological disruption and is postulated to underlie many human conditions, such as the incidence and timing of cardiovascular disease. Here, we describe in vivo and in vitro methodology relevant to studying the role of circadian rhythms in cardiovascular function and dysfunction PMID:25707279
Lieber, Michael
1989-06-01
It is something of a miracle that the nonrelativistic Schrodinger equation with a Coulomb potential can be solved for the wavefunction in exact analytic form. Even more miraculous is the result of Schwinger which enables the Green's function to be solved in closed form, for this is in effect, an infinite sum of wavefunction products. In the relativistic case too the wavefunction can be found in closed form, but as yet no such result for the Green's function has been found. This lecture provides a brief overview of the situation with an emphasis on the ``hidden symmetry'' which underlies the nonrelativisitic problem and its degenerate form which carries over to the relativistic case.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
@@ Genomics is a biology term appeared ten years ago, used to describe the researches of genomic mapping, sequencing, and structure analysis, etc. Genomics, the first journal for publishing papers on genomics research was born in 1986. In the past decade, the concept of genomics has been widely accepted by scientists who are engaging in biology research. Meanwhile, the research scope of genomics has been extended continuously, from simple gene mapping and sequencing to function genomics study. To reflect the change, genomics is divided into two parts now, the structure genomics and the function genomics.
Rarefied elliptic hypergeometric functions
Spiridonov, V P
2016-01-01
We prove exact evaluation formulae for two multiple rarefied elliptic beta integrals related to the simplest lens space. These integrals generalize the multiple type I and II van Diejen-Spiridonov integrals attached to the root system $C_n$. Symmetries of the rarefied elliptic analogue of the Euler-Gauss hypergeometric function are described and the corresponding generalization of the hypergeometric equation is constructed. An extension of the latter function to the root system $C_n$ and applications to some eigenvalue problems are briefly discussed.
Magnetosome production and functionalization
DEFF Research Database (Denmark)
Anyaogu, Diana Chinyere; Zhuang, Shiwen; Mortensen, Uffe Hasbro
as a model organism used to produce magnetosmes and is known to require a low dissolved oxygen (DO) concentration and iron during cultivation for magnetosome production. However, the relationship between these parameters and fermentation behavior is not well understood. We will present a study where we...... investigate how the addition of iron impacts the physiology of the MSR-1 cells and the expression of key genes involved in the production of mangetosomes. Furthermore, utilization of magnetosomes for applications as immunoassays requires the functionalization of the magnetsomes. Functionalization...
Sarason, Donald
2007-01-01
Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Co
A stabilized pairing functional
Erler, J; Reinhard, P --G
2008-01-01
We propose a modified pairing functional for nuclear structure calculations which avoids the abrupt phase transition between pairing and non-pairing states. The intended application is the description of nuclear collective motion where the smoothing of the transition is compulsory to remove singularities. The stabilized pairing functional allows a thoroughly variational formulation, unlike the Lipkin-Nogami (LN) scheme which is often used for the purpose of smoothing. First applications to nuclear ground states and collective excitations prove the reliability and efficiency of the proposed stabilized pairing.
Chromatin Structure and Function
Wolffe, Alan P
1999-01-01
The Third Edition of Chromatin: Structure and Function brings the reader up-to-date with the remarkable progress in chromatin research over the past three years. It has been extensively rewritten to cover new material on chromatin remodeling, histone modification, nuclear compartmentalization, DNA methylation, and transcriptional co-activators and co-repressors. The book is written in a clear and concise fashion, with 60 new illustrations. Chromatin: Structure and Function provides the reader with a concise and coherent account of the nature, structure, and assembly of chromatin and its active
GADRAS Detector Response Function.
Energy Technology Data Exchange (ETDEWEB)
Mitchell, Dean J.; Harding, Lee; Thoreson, Gregory G; Horne, Steven M.
2014-11-01
The Gamma Detector Response and Analysis Software (GADRAS) applies a Detector Response Function (DRF) to compute the output of gamma-ray and neutron detectors when they are exposed to radiation sources. The DRF is fundamental to the ability to perform forward calculations (i.e., computation of the response of a detector to a known source), as well as the ability to analyze spectra to deduce the types and quantities of radioactive material to which the detectors are exposed. This document describes how gamma-ray spectra are computed and the significance of response function parameters that define characteristics of particular detectors.
Stability of Trigonometric Functional Equations in Generalized Functions
Directory of Open Access Journals (Sweden)
Jeongwook Chang
2010-01-01
Full Text Available We consider the Hyers-Ulam stability of a class of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.
Executive functions in synesthesia
R. Rouw; J. van Driel; K. Knip; K.R. Ridderinkhof
2013-01-01
In grapheme-color synesthesia, a number or letter can evoke two different and possibly conflicting (real and synesthetic) color sensations at the same time. In this study, we investigate the relationship between synesthesia and executive control functions. First, no general skill differences were ob
Objectification and Semiotic Function
Santi, George
2011-01-01
The objective of this paper is to study students' difficulties when they have to ascribe the same meaning to different representations of the same mathematical object. We address two theoretical tools that are at the core of Radford's cultural semiotic and Godino's onto-semiotic approaches: objectification and the semiotic function. The analysis…
Choice probability generating functions
DEFF Research Database (Denmark)
Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel
2013-01-01
This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice prob...
Educational Production Functions.
Polachek, Solomon W.; And Others
1978-01-01
A constant partial elasticity of substitution production function for academic achievement is presented and estimated with nonlinear maximum likelihood methods. We find that ability and time devoted to various aspects of the learning process are the most important determinants of students' accomplishments. (Author/CTM)
functional-differential inequalities
Directory of Open Access Journals (Sweden)
Ludwik Byszewski
1995-01-01
Full Text Available A theorem about a system of strong impulsive degenerate nonlinear parabolic functional-differential inequalities in an arbitrary parabolic set is proved. As a consequence of the theorem, some theorems about impulsive degenerate nonlinear parabolic differential inequalities and the uniqueness of a classical solution of an impulsive degenerate nonlinear parabolic differential problem are established.
Thrombocyte and thrombocyte function
Institute of Scientific and Technical Information of China (English)
1997-01-01
970384 The mechanism of preserving platelet func-tion by aprotinin during cardiopulmonary bypass.YANG Tianyu(杨天宇), et al. Anesthesiol &Cardiòpulmon Bypass Lab, Cardiovasc Instit & FuwaiHosp, CAMS & PUMC, Beijing, 100037. Chin Cir J1996; 11(12): 739-742.
Directory of Open Access Journals (Sweden)
Ramesh Kalindri
2014-06-01
Full Text Available Currently, software engineers are increasingly turning to the option of automating functional tests, but not always have successful in this endeavor. Reasons range from low planning until over cost in the process. Some principles that can guide teams in automating these tests are described in this article.
Hantush Well Function Revisited
Veling, E.J.M.; Maas, C.
2010-01-01
In this paper we comment on some recent numerical and analytical work to evaluate the Hantush Well Function. We correct an expression found in a Comment by Nadarajah (J. of Hydrology, vol. 338, p. 152-153 (2007)) to a paper by Prodanoff et al. (J. of Hydrology, vol. 318, p. 173-183 (2006)). We subse
Brants, T; Krenn, B; Brants, Thorsten; Skut, Wojciech; Krenn, Brigitte
1997-01-01
This paper addresses issues in automated treebank construction. We show how standard part-of-speech tagging techniques extend to the more general problem of structural annotation, especially for determining grammatical functions and syntactic categories. Annotation is viewed as an interactive process where manual and automatic processing alternate. Efficiency and accuracy results are presented. We also discuss further automation steps.
Functional ingredients from microalgae
Buono, S.; Langellotti, A.L.; Martello, A.; Rinna, F.; Fogliano, V.
2014-01-01
A wide variety of natural sources are under investigation to evaluate their possible use for new functional ingredient formulation. Some records attested the traditional and ancient use of wild harvested microalgae as human food but their cultivation for different purposes started about 40 years ago
Laboratory Density Functionals
Giraud, B G
2007-01-01
We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory frame. This result is useful for the practical definition of density functionals.
Empirical microeconomics action functionals
Baaquie, Belal E.; Du, Xin; Tanputraman, Winson
2015-06-01
A statistical generalization of microeconomics has been made in Baaquie (2013), where the market price of every traded commodity, at each instant of time, is considered to be an independent random variable. The dynamics of commodity market prices is modeled by an action functional-and the focus of this paper is to empirically determine the action functionals for different commodities. The correlation functions of the model are defined using a Feynman path integral. The model is calibrated using the unequal time correlation of the market commodity prices as well as their cubic and quartic moments using a perturbation expansion. The consistency of the perturbation expansion is verified by a numerical evaluation of the path integral. Nine commodities drawn from the energy, metal and grain sectors are studied and their market behavior is described by the model to an accuracy of over 90% using only six parameters. The paper empirically establishes the existence of the action functional for commodity prices that was postulated to exist in Baaquie (2013).
Deimling, Klaus
1985-01-01
topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical languag...
Holographic Three point Functions
DEFF Research Database (Denmark)
Martirosyan, Ara
The main subject of this thesis is the computation of structure constants appearing in the three-point functions for certain type of states/operators in the context of the AdS/CFT correspondence, which is one of the important parts of the dynamical problem in the dual theories of the correspondence...
Choice Probability Generating Functions
DEFF Research Database (Denmark)
Fosgerau, Mogens; McFadden, Daniel L; Bierlaire, Michel
This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice...
Enzyme design: Functional Frankensteins
Makhlynets, Olga V.; Korendovych, Ivan V.
2016-09-01
An artificial esterase with no known natural structural analogues has been formed via the homo-heptameric self-assembly of a designed peptide. This esterase represents the first report of a functional catalytic triad rationally engineered into a de novo protein framework.
Bayes Multiple Decision Functions
Wu, Wensong
2011-01-01
This paper deals with the problem of simultaneously making many (M) binary decisions based on one realization of a random data matrix X. M is typically large and X will usually have M rows associated with each of the M decisions to make, but for each row the data may be low dimensional. A Bayesian decision-theoretic approach for this problem is implemented with the overall loss function being a cost-weighted linear combination of Type I and Type II loss functions. The class of loss functions considered allows for the use of the false discovery rate (FDR), false nondiscovery rate (FNR), and missed discovery rate (MDR) in assessing the decision. Through this Bayesian paradigm, the Bayes multiple decision function (BMDF) is derived and an efficient algorithm to obtain the optimal Bayes action is described. In contrast to many works in the literature where the rows of the matrix X are assumed to be stochastically independent, we allow in this paper a dependent data structure with the associations obtained through...
Automatic Functional Harmonic Analysis
de Haas, W.B.; Magalhães, J.P.; Wiering, F.; Veltkamp, R.C.
2013-01-01
Music scholars have been studying tonal harmony intensively for centuries, yielding numerous theories and models. Unfortunately, a large number of these theories are formulated in a rather informal fashion and lack mathematical precision. In this article we present HarmTrace, a functional model of W
Predicatively computable functions on sets
Arai, Toshiyasu
2012-01-01
Inspired from a joint work by A. Beckmann, S. Buss and S. Friedman, we propose a class of set-theoretic functions, predicatively computable functions. Each function in this class is polynomial time computable when we restrict to finite binary strings. Moreover a fragment of set theory is given in which \\Sigma_1-definable functions are exactly the functions in the class.
Completely monotonic functions related to logarithmic derivatives of entire functions
DEFF Research Database (Denmark)
Pedersen, Henrik Laurberg
2011-01-01
The logarithmic derivative l(x) of an entire function of genus p and having only non-positive zeros is represented in terms of a Stieltjes function. As a consequence, (-1)p(xml(x))(m+p) is a completely monotonic function for all m ≥ 0. This generalizes earlier results on complete monotonicity...... of functions related to Euler's psi-function. Applications to Barnes' multiple gamma functions are given....
EXECUTIVE FUNCTIONING IN SCHIZOPHRENIA
Directory of Open Access Journals (Sweden)
Gricel eOrellana
2013-06-01
Full Text Available The executive function (EF is a set of abilities, which allows us to invoke voluntary control of our behavioral responses. These functions enable human beings to develop and carry out plans, make up analogies, obey social rules, solve problems, adapt to unexpected circumstances, do many tasks simultaneously and locate episodes in time and place. EF includes divided attention and sustained attention, working memory, set-shifting, flexibility, planning and the regulation of goal directed behavior and can be defined as a brain function underlying the human faculty to act or think not only in reaction to external events but also in relation with internal goals and states. EF is mostly associated with dorsolateral prefrontal cortex (PFC. Besides EF, PFC is involved in self-regulation of behavior, i.e. the ability to regulate behavior according to internal goals and constraints, particularly in less structured situations. Self-regulation of behavior is subtended by ventral medial /orbital PFC. Impairment of EF is one of the most commonly observed deficits in schizophrenia through the various disease stages. Impairment in tasks measuring conceptualization, planning, cognitive flexibility, verbal fluency, ability to solve complex problems and working memory occur in schizophrenia. Disorders detected by executive tests are consistent with evidence from functional neuroimaging, which have shown PFC dysfunction in patients while performing these kinds of tasks. Schizophrenics also exhibit deficit in odor identifying, decision-making and self-regulation of behavior suggesting dysfunction of the orbital PFC. However, impairment in executive tests is explained by dysfunction of prefronto-striato-thalamic, prefronto-parietal and prefronto-temporal neural networks mainly. Disorders in executive functions may be considered central facts with respect to schizophrenia and it has been suggested that negative symptoms may be explained by that executive dysfunction.
Partition density functional theory
Nafziger, Jonathan
Partition density functional theory (PDFT) is a method for dividing a molecular electronic structure calculation into fragment calculations. The molecular density and energy corresponding to Kohn Sham density-functional theory (KS-DFT) may be exactly recovered from these fragments. Each fragment acts as an isolated system except for the influence of a global one-body 'partition' potential which deforms the fragment densities. In this work, the developments of PDFT are put into the context of other fragment-based density functional methods. We developed three numerical implementations of PDFT: One within the NWChem computational chemistry package using basis sets, and the other two developed from scratch using real-space grids. It is shown that all three of these programs can exactly reproduce a KS-DFT calculation via fragment calculations. The first of our in-house codes handles non-interacting electrons in arbitrary one-dimensional potentials with any number of fragments. This code is used to explore how the exact partition potential changes for different partitionings of the same system and also to study features which determine which systems yield non-integer PDFT occupations and which systems are locked into integer PDFT occupations. The second in-house code, CADMium, performs real-space calculations of diatomic molecules. Features of the exact partition potential are studied for a variety of cases and an analytical formula determining singularities in the partition potential is derived. We introduce an approximation for the non-additive kinetic energy and show how this quantity can be computed exactly. Finally a PDFT functional is developed to address the issues of static correlation and delocalization errors in approximations within DFT. The functional is applied to the dissociation of H2 + and H2.
THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION
Institute of Scientific and Technical Information of China (English)
刘海峰; 周炜星; 王辅臣; 龚欣; 于遵宏
2002-01-01
Some properties of the wavelet transform of trigonometric function, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with this equation agrees well with the function.
Uniqueness property for quasiharmonic functions
Directory of Open Access Journals (Sweden)
Sevdiyor A. Imomkulov
2014-10-01
Full Text Available In this paper we consider a class of continuous functions, called quasiaharmonic functions, admitting best approximations by harmonic polynomials. In this class we prove a uniqueness theorem by analogy with the analytic functions.
Functional magnetic microspheres
Yen, Shiao-Ping S. (Inventor); Rembaum, Alan (Inventor); Landel, Robert F. (Inventor)
1981-01-01
Functional magnetic particles are formed by dissolving a mucopolysaccharide such as chitosan in acidified aqueous solution containing a mixture of ferrous chloride and ferric chloride. As the pH of the solution is raised magnetite is formed in situ in the solution by raising the pH. The dissolved chitosan is a polyelectrolyte and forms micelles surrounding the granules at pH of 8-9. The chitosan precipitates on the granules to form microspheres containing the magnetic granules. On addition of the microspheres to waste aqueous streams containing dissolved ions, the hydroxyl and amine functionality of the chitosan forms chelates binding heavy metal cations such as lead, copper, and mercury and the chelates in turn bind anions such as nitrate, fluoride, phosphate and borate.
Functional Biomimetic Architectures
Levine, Paul M.
N-substituted glycine oligomers, or 'peptoids,' are a class of sequence--specific foldamers composed of tertiary amide linkages, engendering proteolytic stability and enhanced cellular permeability. Peptoids are notable for their facile synthesis, sequence diversity, and ability to fold into distinct secondary structures. In an effort to establish new functional peptoid architectures, we utilize the copper-catalyzed azide-alkyne [3+2] cycloaddition (CuAAC) reaction to generate peptidomimetic assemblies bearing bioactive ligands that specifically target and modulate Androgen Receptor (AR) activity, a major therapeutic target for prostate cancer. Additionally, we explore chemical ligation protocols to generate semi-synthetic hybrid biomacromolecules capable of exhibiting novel structures and functions not accessible to fully biosynthesized proteins.
Functionalization of Carbon Nanotubes
Khare, Bishun N. (Inventor); Meyyappan, Meyya (Inventor)
2009-01-01
Method and system for functionalizing a collection of carbon nanotubes (CNTs). A selected precursor gas (e.g., H2 or F2 or CnHm) is irradiated to provide a cold plasma of selected target species particles, such as atomic H or F, in a first chamber. The target species particles are d irected toward an array of CNTs located in a second chamber while suppressing transport of ultraviolet radiation to the second chamber. A CNT array is functionalized with the target species particles, at or below room temperature, to a point of saturation, in an exposure time interval no longer than about 30 sec. *Discrimination against non-target species is provided by (i) use of a target species having a lifetime that is much greater than a lifetime of a non-target species and/or (2) use of an applied magnetic field to discriminate between charged particle trajectories for target species and for non-target species.
Vestnorden. A functional region?
Directory of Open Access Journals (Sweden)
Grétar Þór Eyþórsson
2013-06-01
Full Text Available This article discusses the issue of what kind of a region Vestnorden is. The need for such a discussion arises from the challenges posed by globalisation for the idea and construction of the West Nordic space, and the need to observe how this regional unit counters these processes. The article is based on an analytical framework which presupposes that a functional region has to consist of four elements. First, whether the space has its own institutions for decision making; second, how far there is economic complementarities among the involved nations and territories; third, to what degree they have common economic interests; and finally, to what extent social, cultural and historical ties exist between the territories involved. The article argues that there is an urgent need to discuss and reorient the institutional functionality of Vestnorden as a regional unit.
DEFF Research Database (Denmark)
Bech-Larsen, Tino; Scholderer, Joachim
2007-01-01
reading of the main principles of the harmonized regulation COM/2003/0424, this situation is about to change. This article reviews the regulatory aspects, the results of consumer research and the marketing strategies regarding the use of health claims for functional foods in Europe, and it comments......The fact that the European markets for functional foods generally are less developed, compared to the US and the Japanese markets, has often been attributed to a restrictive and inconsistent health claim legislation in and between the European countries. With the European Parliament's second...... on the lack of correspondence between the new regulation and the marketing experiences and research as regard consumer reactions to health claims....
Directory of Open Access Journals (Sweden)
VEZURE OANA SABINA
2011-09-01
Full Text Available The emergence of public finances is due to objective causes needs and determined their main function being to obtain the financial resources it needs for the State to exercise its powers and on the way to intervene in the economy and society general. Public finances are necessary, subjectively and objectively, as it contributes to accomplishing the tasks and functions of the state, which could not be realized without financial leverage. Public finances are inextricably linked to the existence of the state, and public sector's role in the economy. Thus, they express "social relations, economic arising in the establishment and use of public funds between the state, on the one hand, and members of society on the other hand, to meet the needs of general interest of society" [1]. Thus, the role of public finance is to meet the needs of general interest or collective needs.
Subtypes of functional dyspepsia
Institute of Scientific and Technical Information of China (English)
Georgina Baker; Robert J Fraser; Graeme Young
2006-01-01
Functional dyspepsia is a common clinical condition characterised by chronic or recurrent upper abdominal pain or discomfort commonly associated with a variety of associated gastrointestinal symptoms and a normal endoscopy. To standardise research-based approaches,an initial categorisation of into sub groups was agreed to, based on clusters of symptoms. However the early expectation that these subgroups would be associated with distinct pathophysiologies amenable to specific therapy has not been realised. A classification based on the most troublesome symptom has been suggested but the utility of this is also unclear. More recent data suggest that some of the pathophysiologic dysfunctions may be associated with specific symptoms and so provide a better tool for grouping patients. But this approach remains incomplete as current insights into the pathogenesis are still too limited for this to be satisfactory. In conclusion, no classification provides for an adequate treatment-based approach to the syndrome of functional dyspepsia. As a consequence treatment remains largely empiric.
DEFF Research Database (Denmark)
2016-01-01
Renowned experts present the latest knowledge Although a very fragile structure, the skin barrier is probably one of the most important organs of the body. Inward/out it is responsible for body integrity and outward/in for keeping microbes, chemicals, and allergens from penetrating the skin. Since...... the role of barrier integrity in atopic dermatitis and the relationship to filaggrin mutations was discovered a decade ago, research focus has been on the skin barrier, and numerous new publications have become available. This book is an interdisciplinary update offering a wide range of information...... on the subject. It covers new basic research on skin markers, including results on filaggrin and on methods for the assessment of the barrier function. Biological variation and aspects of skin barrier function restoration are discussed as well. Further sections are dedicated to clinical implications of skin...
Nuclear Parton Distribution Functions
Energy Technology Data Exchange (ETDEWEB)
I. Schienbein, J.Y. Yu, C. Keppel, J.G. Morfin, F. Olness, J.F. Owens
2009-06-01
We study nuclear effects of charged current deep inelastic neutrino-iron scattering in the framework of a {chi}{sup 2} analysis of parton distribution functions (PDFs). We extract a set of iron PDFs which are used to compute x{sub Bj}-dependent and Q{sup 2}-dependent nuclear correction factors for iron structure functions which are required in global analyses of free nucleon PDFs. We compare our results with nuclear correction factors from neutrino-nucleus scattering models and correction factors for charged-lepton--iron scattering. We find that, except for very high x{sub Bj}, our correction factors differ in both shape and magnitude from the correction factors of the models and charged-lepton scattering.
DEFF Research Database (Denmark)
Larsen, S H; Wagner, G; Heitmann, B L
2007-01-01
OBJECTIVE: To review the literature on the relationship between obesity and sexual function. METHOD: A search in the medical literature from 1966 and onwards was carried out through Medline and Embase for publications on obesity, in combination with Medical Subject Heading words related to sexual...... function and dysfunction. COMMENTS: Four prospective and seven cross-sectional studies were found describing association between obesity and erectile dysfunction (ED). One cross-sectional study was found describing obesity and female sexual dysfunction (FSD). The prospective studies on ED all demonstrated...... activity among both men and women after weight loss intervention. CONCLUSION: Support for the assumption that obesity is associated with ED was found in both prospective and cross-sectional studies. FSD was not adequately described in the literature and prospective studies are needed here. Results from...
Physically Functional Materials
Berg, Rolf Henrik; Hvilsted, Søren; Ramanujam, P.S.
2002-01-01
The invention relates to novel monodisperse or polydisperse compounds, in general named DNO (diamino acid Nalpha-substituted oligopeptides), preferably low molecular weight polypeptides, e.g., based on ornithine, lysine, diaminobutyric acid, diaminopropionic acid, aminoethylglycine or other amino acids or peptides having azobenzenes or other physicially functional groups, e.g., photoresponsive groups, as side chains. These compounds may be synthesized using solid phase peptide synthesis techn...
Haque, S Shajidul
2016-01-01
We propose a simple and generic holographic $c$-function that is defined purely from geometry by using the non-affine expansion for null congruences. We examined the proposal for BPS black solutions in $\\mathcal{N}=2$ gauged supergravity that interpolate between two different dimensional AdS spacetimes and also for domain wall solutions. Moreover, we commented on the relation of this geometric proposal with the one from the holographic entanglement entropy.
Generalised twisted partition functions
Petkova, V B
2001-01-01
We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D Conformal Field Theory (CFT). A consistency equation, which gives a classification of twists, is written and solved in particular cases. This generalises old results on twisted torus boundary conditions, gives a physical interpretation of Ocneanu's algebraic construction, and might offer a new route to the study of properties of CFT.
Design of Functional Metalloproteins
Lu, Yi; Yeung, Natasha; Sieracki, Nathan; Marshall, Nicholas M.
2009-01-01
Metalloproteins catalyze some of the most difficult and yet important functions in Nature, such as photosynthesis and water oxidation. An ultimate test of our knowledge of how metalloproteins work is by designing novel metalloproteins. Such design can not only reveal hidden structural features that may be missing from studies of native metalloproteins and their variants, but also result in new metalloenzymes for biotechnological and pharmaceutical applications. While it is much more challengi...
Which impulse response function?
2011-01-01
This paper compares standard and local projection techniques in the production of impulse response functions both theoretically and empirically. Through careful selection of a structural decomposition, the comparison continues to an application of US data to the textbook ISLM model. It is argued that local projection techniques offer a remedy to the bias of the conventional method especially at horizons longer than the vector autoregression's lag length. The application highlights that the te...
Analyzing Pseudophosphatase Function.
Hinton, Shantá D
2016-01-01
Pseudophosphatases regulate signal transduction cascades, but their mechanisms of action remain enigmatic. Reflecting this mystery, the prototypical pseudophosphatase STYX (phospho-serine-threonine/tyrosine-binding protein) was named with allusion to the river of the dead in Greek mythology to emphasize that these molecules are "dead" phosphatases. Although proteins with STYX domains do not catalyze dephosphorylation, this in no way precludes their having other functions as integral elements of signaling networks. Thus, understanding their roles in signaling pathways may mark them as potential novel drug targets. This chapter outlines common strategies used to characterize the functions of pseudophosphatases, using as an example MK-STYX [mitogen-activated protein kinase (MAPK) phospho-serine-threonine/tyrosine binding], which has been linked to tumorigenesis, apoptosis, and neuronal differentiation. We start with the importance of "restoring" (when possible) phosphatase activity in a pseudophosphatase so that the active mutant may be used as a comparison control throughout immunoprecipitation and mass spectrometry analyses. To this end, we provide protocols for site-directed mutagenesis, mammalian cell transfection, co-immunoprecipitation, phosphatase activity assays, and immunoblotting that we have used to investigate MK-STYX and the active mutant MK-STYXactive. We also highlight the importance of utilizing RNA interference (RNAi) "knockdown" technology to determine a cellular phenotype in various cell lines. Therefore, we outline our protocols for introducing short hairpin RNA (shRNA) expression plasmids into mammalians cells and quantifying knockdown of gene expression with real-time quantitative PCR (qPCR). A combination of cellular, molecular, biochemical, and proteomic techniques has served as powerful tools in identifying novel functions of the pseudophosphatase MK-STYX. Likewise, the information provided here should be a helpful guide to elucidating the
LENUS (Irish Health Repository)
Lang, E E
2010-06-01
Vestibular symptoms of vertigo, dizziness and dysequilibrium are common complaints which can be disabling both physically and psychologically. Routine examination of the ear nose and throat and neurological system are often normal in these patients. An accurate history and thorough clinical examination can provide a diagnosis in the majority of patients. However, in a subgroup of patients, vestibular function testing may be invaluable in arriving at a correct diagnosis and ultimately in the optimal treatment of these patients.
Heart function and hemodynamics
Institute of Scientific and Technical Information of China (English)
1993-01-01
930054 Clinical assessment of left ventricularfunction by equilibrium radionuclide ventriculo-graphy before and after mitral valve replace-ment.CHU Yinping(褚银平),et al.2nd Hosp,Shanxi Med Coll,Taiyuan.Chin Cir J 1992;7(5):457-458.Equilibrium radionuclide ventriculographywas used to estimate the left ventricular(LV)function in control subjects(Group 1;n=8)and in 24 patients of mitral valvular diseasesChina Medical Abstracts(Internal Medicine)
Oden, J Tinsley
2010-01-01
The textbook is designed to drive a crash course for beginning graduate students majoring in something besides mathematics, introducing mathematical foundations that lead to classical results in functional analysis. More specifically, Oden and Demkowicz want to prepare students to learn the variational theory of partial differential equations, distributions, and Sobolev spaces and numerical analysis with an emphasis on finite element methods. The 1996 first edition has been used in a rather intensive two-semester course. -Book News, June 2010
Notes on the ellipsoidal function
Liang, Chang-Hong
2017-01-01
This book focuses on the ellipsoidal function, which serves as an evolution and extension of the circular function (trigonometric function) and elliptic function. It presents an in-depth discussion of the ellipsoidal function (algebra) theory and the conformal mapping (geometry) theory of the ellipsoid function, demonstrating the outstanding performance of the ellipsoid function response filter. Applications of the ellipsoidal function include the capacitance of ellipsoidal conductors and the surface area of ellipsoids, which in turn correspond to ellipsoidal integrals of the first kind and the second kind, respectively. The book offers a valuable reference guide for undergraduates, graduate students and researchers in the related fields. .
Remarks on Shintani's zeta function
Wakayama, Masato
2005-01-01
We introduce a zeta function attached to a representation of a group. We show that the multi-dimensional zeta function due to Shintani [Sh 1], which is a generalization of the multiple Hurwitz zeta function, can be obtained in this framework. We also construct a gamma function from the zeta function attached to a representation via zeta regularization. We study then a $q$-analogue of the Shintani zeta function and the corresponding gamma function. A sine function defined via the reflection fo...
Posttraumatic functional movement disorders.
Ganos, C; Edwards, M J; Bhatia, K P
2017-01-01
Traumatic injury to the nervous system may account for a range of neurologic symptoms. Trauma location and severity are important determinants of the resulting symptoms. In severe head injury with structural brain abnormalities, the occurrence of trauma-induced movement disorders, most commonly hyperkinesias such as tremor and dystonia, is well recognized and its diagnosis straightforward. However, the association of minor traumatic events, which do not lead to significant persistent structural brain damage, with the onset of movement disorders is more contentious. The lack of clear clinical-neuroanatomic (or symptom lesion) correlations in these cases, the variable timing between traumatic event and symptom onset, but also the presence of unusual clinical features in a number of such patients, which overlap with signs encountered in patients with functional neurologic disorders, contribute to this controversy. The purpose of this chapter is to provide an overview of the movement disorders, most notably dystonia, that have been associated with peripheral trauma and focus on their unusual characteristics, as well as their overlap with functional neurologic disorders. We will then provide details on pathophysiologic views that relate minor peripheral injuries to the development of movement disorders and compare them to knowledge from primary organic and functional movement disorders. Finally, we will comment on the appropriate management of these disorders.
Functions of multivector variables.
Chappell, James M; Iqbal, Azhar; Gunn, Lachlan J; Abbott, Derek
2015-01-01
As is well known, the common elementary functions defined over the real numbers can be generalized to act not only over the complex number field but also over the skew (non-commuting) field of the quaternions. In this paper, we detail a number of elementary functions extended to act over the skew field of Clifford multivectors, in both two and three dimensions. Complex numbers, quaternions and Cartesian vectors can be described by the various components within a Clifford multivector and from our results we are able to demonstrate new inter-relationships between these algebraic systems. One key relationship that we discover is that a complex number raised to a vector power produces a quaternion thus combining these systems within a single equation. We also find a single formula that produces the square root, amplitude and inverse of a multivector over one, two and three dimensions. Finally, comparing the functions over different dimension we observe that Cl(R(3)) provides a particularly versatile algebraic framework.
Functions of multivector variables.
Directory of Open Access Journals (Sweden)
James M Chappell
Full Text Available As is well known, the common elementary functions defined over the real numbers can be generalized to act not only over the complex number field but also over the skew (non-commuting field of the quaternions. In this paper, we detail a number of elementary functions extended to act over the skew field of Clifford multivectors, in both two and three dimensions. Complex numbers, quaternions and Cartesian vectors can be described by the various components within a Clifford multivector and from our results we are able to demonstrate new inter-relationships between these algebraic systems. One key relationship that we discover is that a complex number raised to a vector power produces a quaternion thus combining these systems within a single equation. We also find a single formula that produces the square root, amplitude and inverse of a multivector over one, two and three dimensions. Finally, comparing the functions over different dimension we observe that Cl(R(3 provides a particularly versatile algebraic framework.
[Functional hypothalamic amenorrhea].
Stárka, Luboslav; Dušková, Michaela
2015-10-01
Functional hypothalamic amenorrhea (FHA) besides pregnancy and syndrome of polycystic ovary is one of the most common causes of secondary amenorrhea. FHA results from the aberrations in pulsatile gonadotropin-releasing hormone (GnRH) secretion, which in turn causes impairment of the gonadotropins (follicle-stimulating hormone and luteinizing hormone). FHA is a form of the defence of organism in situations where life functions are more important than reproductive function. FHA is reversible; it can be normalized after ceasing the stress situation. There are three types of FHA: weight loss related, stress-related, and exercise-related amenorrhea. The final consequences are complex hormonal changes manifested by profound hypoestrogenism. Additionally, these patients present mild hypercortisolemia, low serum insulin levels, low insulin-like growth factor 1 (IGF-1) and low total triiodothyronine. Women health in this disorder is disturbed in several aspects including the skeletal system, cardiovascular system, and mental problems. Patients manifest a decrease in bone mass density, which is related to an increase in fracture risk. Therefore, osteopenia and osteoporosis are the main long-term complications of FHA. Cardiovascular complications include endothelial dysfunction and abnormal changes in the lipid profile. FHA patients present significantly higher depression and anxiety and also sexual problems compared to healthy subjects.
Vitale, J J; Broitman, S A
1981-09-01
There is in vitro and in vivo evidence to suggest that dietary lipids play a role in modulating immune function. A review of the current literature on the interrelationships among dietary lipids, blood cholesterol levels, immunosuppression, and tumorigenesis makes for a very strong argument that (a) immunosuppression may be causally related to lymphoproliferative disorders, as well as to tumorigenesis and (b) diets high in polyunsaturated fat, relative to diets high in saturated fat, are more immunosuppressive and are better promotors of tumorigenesis. The effects of dietary fat on immune function seem to be mediated though its component parts, the unsaturated fatty acids, specially linoleic, linolenic, and arachidonic. It is not clear how these components affect immune function. Several studies suggest that one effect is mediated by altering the lipid component of the cell membrane and thus its fluidity; the more fluid the membrane, the less responsive it is. Thus, fluidity of both immune cells and those to be destroyed or protected may be affected. The effects of saturated as well as unsaturated fatty acids may be mediated by modulating serum lipoprotein levels, prostaglandin metabolism, and cholesterol concentrations and metabolism.
Composing decoherence functionals
Boes, Paul
2016-01-01
Quantum Measure Theory (QMT) is a generalization of quantum theory where physical predictions are computed from a matrix known as decoherence functional (DF). Previous works have noted that, in its original formulation, QMT exhibits a problem with composability, since the composition of two decoherence functionals is, in general, not a valid decoherence functional. This does not occur when the DFs in question happen to be positive semidefinite (a condition known as strong positivity). In this paper, we study the concept of composability of DFs and its consequences for QMT. First, using the notion of composability, we settle an old problem in QMT regarding the definition of decoherent histories. Then we show that the problem of composability is much deeper than originally envisaged, since, for any $n$, there exists a DF that can co-exist with $n-1$ copies of itself, but not with $n$. Finally, we prove that the set of strongly positive DFs cannot be enlarged while remaining closed under composition. Furthermore...
Functional neuropeptidomics in invertebrates.
De Haes, Wouter; Van Sinay, Elien; Detienne, Giel; Temmerman, Liesbet; Schoofs, Liliane; Boonen, Kurt
2015-07-01
Neuropeptides are key messengers in almost all physiological processes. They originate from larger precursors and are extensively processed to become bioactive. Neuropeptidomics aims to comprehensively identify the collection of neuropeptides in an organism, organ, tissue or cell. The neuropeptidome of several invertebrates is thoroughly explored since they are important model organisms (and models for human diseases), disease vectors and pest species. The charting of the neuropeptidome is the first step towards understanding peptidergic signaling. This review will first discuss the latest developments in exploring the neuropeptidome. The physiological roles and modes of action of neuropeptides can be explored in two ways, which are largely orthogonal and therefore complementary. The first way consists of inferring the functions of neuropeptides by a forward approach where neuropeptide profiles are compared under different physiological conditions. Second is the reverse approach were neuropeptide collections are used to screen for receptor-binding. This is followed by localization studies and functional tests. This review will focus on how these different functional screening methods contributed to the field of invertebrate neuropeptidomics and expanded our knowledge of peptidergic signaling. This article is part of a Special Issue entitled: Neuroproteomics: Applications in Neuroscience and Neurology.
Functionalized Amorphous Aluminosilicates
Mesgar, Milad
Alkali treated aluminosilicate (geopolymer) was functionalized by surfactant to increase the hydrophobicity for making Pickering emulsion for the first part of this work. In the first part of this study, alkali treated metakaolin was functionalized with cetyltrimethylammonium bromide ((C16H33)N(CH 3)3Br, CTAB). The electrostatic interaction between this quaternary ammonium and the surface of the aluminosilicate which has negative charge has taken place. The particles then were used to prepare Pickering emulsion. The resulting stable dispersions, obtained very fast at very simple conditions with low ratio of aluminosilicate to liquid phase. In the second part, the interaction between geopolymer and glycerol was studied to see the covalent grafting of the geopolymer for making geopolymer composite. The composite material would be the basis material to be used as support catalyst, thin coating reagent and flame retardant material and so on, Variety of techniques, Thermogravimetric (TGA), Particle-induced X-ray emission (PIXE), FTIR, Solid state NMR, Powder X-ray diffraction (PXRD), BET surface area, Elemental analysis (CHN), TEM, SEM and Optical microscopy were used to characterize the functionalized geopolymer.
Directory of Open Access Journals (Sweden)
John W. Erdman
2015-10-01
Full Text Available Lutein is one of the most prevalent carotenoids in nature and in the human diet. Together with zeaxanthin, it is highly concentrated as macular pigment in the foveal retina of primates, attenuating blue light exposure, providing protection from photo-oxidation and enhancing visual performance. Recently, interest in lutein has expanded beyond the retina to its possible contributions to brain development and function. Only primates accumulate lutein within the brain, but little is known about its distribution or physiological role. Our team has begun to utilize the rhesus macaque (Macaca mulatta model to study the uptake and bio-localization of lutein in the brain. Our overall goal has been to assess the association of lutein localization with brain function. In this review, we will first cover the evolution of the non-human primate model for lutein and brain studies, discuss prior association studies of lutein with retina and brain function, and review approaches that can be used to localize brain lutein. We also describe our approach to the biosynthesis of 13C-lutein, which will allow investigation of lutein flux, localization, metabolism and pharmacokinetics. Lastly, we describe potential future research opportunities.
Hexagonalization of Correlation Functions
Fleury, Thiago
2016-01-01
We propose a nonperturbative framework to study general correlation functions of single-trace operators in $\\mathcal{N}=4$ supersymmetric Yang-Mills theory at large $N$. The basic strategy is to decompose them into fundamental building blocks called the hexagon form factors, which were introduced earlier to study structure constants using integrability. The decomposition is akin to a triangulation of a Riemann surface, and we thus call it hexagonalization. We propose a set of rules to glue the hexagons together based on symmetry, which naturally incorporate the dependence on the conformal and the R-symmetry cross ratios. Our method is conceptually different from the conventional operator product expansion and automatically takes into account multi-trace operators exchanged in OPE channels. To illustrate the idea in simple set-ups, we compute four-point functions of BPS operators of arbitrary lengths and correlation functions of one Konishi operator and three short BPS operators, all at one loop. In all cases,...
A CLASS OF FUNCTIONAL EQUATION AND FRACTAL INTERPOLATION FUNCTIONS
Institute of Scientific and Technical Information of China (English)
ShaZhen
1999-01-01
A new class of functional equation in C0(I) is investigated. It is proved that some class of FIF satisfies the functional equation. Another functional equation is constructed. Theirsolutions can approximate FIF arbitrarily. And a new approximate estimate between FIF andinterpolated function is given.
[Functional pathophysiology of consciousness].
Jellinger, Kurt A
2009-01-01
Consciousness (Latin conscientia "moral conscience"), according to the English philosopher John Locke (1632-1704) [103], is the awareness of all that occurs in the mind of a person, whereas the American philosopher John Searle (2000) defined it as "inner qualitative, subjective states and processes of awareness". In modern science it is defined as a continuous state of full awareness of the Self and one's relationship to the external and internal environment, describing the degree of wakefulness in which an organism recognizes stimuli. This widely discussed biological term for complex neuronal processes that allow an individuum to recognize itself and its environment and to act accordingly, has been and still is the subject of much research in philosophy and natural/neuroscience. Its definition is often used for awareness and recognition, too. While the Egyptians in the papyrus Edwin Smith already recognized the brain as the seat of consciousness, René Descartes (1644 [36]) believed its special structure should be "a small gland in the middle", but the anatomical structures and physiological processes involved in consciousness were elucidated only in the middle of the 20th century. Neuronal substrates include several functional networks that are hierarchically organized and cooperate functionally. The lowest level is the mesencephalic formatio reticularis and its projections to the thalamus that were identified als ascending reticular system (ARAS) by the classical experiments of Moruzzi and Magoun, whereas later analyses of patients with impaired consciousness provided further insights. The mesencephalic ARAS as motor of the function of higher structures projects 1. via the reticular thalamus diffusely to the cortex, 2. via hypothalamus to the basal forebrain and limbic system, and 3. to the medial raphe of the brainstem and locus coeruleus and their diffuse cortical projections. The reticular system is stimulated directly and indirectly via numerous collaterals
Collision-resistant hash function based on composition of functions
Ndoundam, Rene
2011-01-01
cryptographic hash function is a deterministic procedure that compresses an arbitrary block of numerical data and returns a fixed-size bit string. There exist many hash functions: MD5, HAVAL, SHA, ... It was reported that these hash functions are not longer secure. Our work is focused in the construction of a new hash function based on composition of functions. The construction used the NP-completeness of Three-dimensional contingency tables and the relaxation of the constraint that a hash function should also be a compression function.
Log-supermodular functions, functional clones and counting CSPs
Bulatov, Andrei A; Goldberg, Leslie Ann; Jerrum, Mark
2011-01-01
Motivated by a desire to understand the computational complexity of counting constraint satisfaction problems (counting CSPs), particularly the complexity of approximation, we study functional clones of functions on the Boolean domain, which are analogous to the familiar relational clones constituting Post's lattice. One of these clones is the collection of log-supermodular (lsm) functions, which turns out to play a significant role in classifying counting CSPs. In our study, we assume that non-negative unary functions (weights) are available. Given this, we prove that there are no functional clones lying strictly between the clone of lsm functions and the total clone (containing all functions). Thus, any counting CSP that contains a single non-lsm function is computationally as hard as any problem in #P. Furthermore, any non-trivial functional clone (in a sense that will be made precise below) contains the binary function "implies". As a consequence, all non-trivial counting CSPs (with non-negative unary wei...
Effects of periodic modulation on the nonlinear Landau-Zener tunneling
Institute of Scientific and Technical Information of China (English)
Wu Li-Hua; Duan Wen-Shan
2009-01-01
We study the Landau-Zener tunneling of a nonlinear two-level system by applying a periodic modulation on its energy bias. We find that the two levels are splitting at the zero points of the zero order Bessel function for high-frequency modulation. Moreover, we obtain the effective coupling constant between two levels at the zero points of the zero order Bessel function by calculating the final tunneling probability at these points. It seems that the effective coupling constant can be regarded as the approximation of the higher order Bessel function at these points. For the low-frequency modulation, we find that the final tunneling probability is a function of the interaction strength. For the weak inter-level coupling case, we find that the final tunneling probability is more disordered as the interaction strength becomes larger.
Gelfand, I M; Shnol, E E
2002-01-01
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu
DEFF Research Database (Denmark)
Sinden, Richard R.; E. Pearson, Christopher; N. Potaman, Vladimir
1998-01-01
This chapter discusses the structure and function of DNA. DNA occupies a critical role in cells, because it is the source of all intrinsic genetic information. Chemically, DNA is a very stable molecule, a characteristic important for a macromolecule that may have to persist in an intact form...... for a long period of time before its information is accessed by the cell. Although DNA plays a critical role as an informational storage molecule, it is by no means as unexciting as a computer tape or disk drive. The structure of the DNA described by Watson and Crick in 1953 is a right handed helix of two...
Matrix string partition function
Kostov, Ivan K; Kostov, Ivan K.; Vanhove, Pierre
1998-01-01
We evaluate quasiclassically the Ramond partition function of Euclidean D=10 U(N) super Yang-Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasiclassical expressions reproduce exactly the recently obtained expression for the partition of the completely reduced SYM theory, including the overall numerical factor. This is an evidence that our quasiclassical calculation might be exact.
Functional properties of vinegar.
Budak, Nilgün H; Aykin, Elif; Seydim, Atif C; Greene, Annel K; Guzel-Seydim, Zeynep B
2014-05-01
A variety of natural vinegar products are found in civilizations around the world. A review of research on these fermented products indicates numerous reports of health benefits derived by consumption of vinegar components. Therapeutic effects of vinegar arising from consuming the inherent bioactive components including acetic acid, gallic acid, catechin, ephicatechin, chlorogenic acid, caffeic acid, p-coumaric acid, and ferulic acid cause antioxidative, antidiabetic, antimicrobial, antitumor, antiobesity, antihypertensive, and cholesterol-lowering responses. The aims of this article are to discuss vinegar history, production, varieties, acetic acid bacteria, and functional properties of vinegars.
Directory of Open Access Journals (Sweden)
A. Calver
1997-01-01
Full Text Available This paper explores the establishment of transfer functions for describing the annual oscillation of unconfined aquifer water levels in response to effective precipitation. A simple saturated zone representation is developed to accompany the unsaturated zone mechanism. Practical examples are drawn from a sample of sites from the chalk and the Permo-Triassic sandstones of England and Wales. Modelled water levels are in many cases good. The technique is most appropriate within the usual range of fluctuation of aquifer water level, with no great change in influence of abstractions, and when it is acceptable to approximate the complexity of unsaturated zone processes in practical analysis.
DEFF Research Database (Denmark)
Bang, Anne Louise
2007-01-01
to the establishment of an initial framework for the project it has a focus on how to explore costumers and users emotional experiences with fabrics. The three year research project is based on experimental design research and the textile designer's competences and knowledge. During the research project exploring...... sensing of fabrics in function. It is proposed that tactile and visual sensing of fabrics is a way to investigate and express emotional utility values. The further purpose is to use experiments with repertory grid models as part of the mapping of the entire research project and also as a basis...
Design of functional metalloproteins.
Lu, Yi; Yeung, Natasha; Sieracki, Nathan; Marshall, Nicholas M
2009-08-13
Metalloproteins catalyse some of the most complex and important processes in nature, such as photosynthesis and water oxidation. An ultimate test of our knowledge of how metalloproteins work is to design new metalloproteins. Doing so not only can reveal hidden structural features that may be missing from studies of native metalloproteins and their variants, but also can result in new metalloenzymes for biotechnological and pharmaceutical applications. Although it is much more challenging to design metalloproteins than non-metalloproteins, much progress has been made in this area, particularly in functional design, owing to recent advances in areas such as computational and structural biology.
Aumasson, Jean-Philippe; Phan, Raphael; Henzen, Luca
2014-01-01
This is a comprehensive description of the cryptographic hash function BLAKE, one of the five final contenders in the NIST SHA3 competition, and of BLAKE2, an improved version popular among developers. It describes how BLAKE was designed and why BLAKE2 was developed, and it offers guidelines on implementing and using BLAKE, with a focus on software implementation. In the first two chapters, the authors offer a short introduction to cryptographic hashing, the SHA3 competition, and BLAKE. They review applications of cryptographic hashing, they describe some basic notions such as security de