Search results for: Bessel functions

Authors: Vernie C. Convicto, Henry P. Aringa, Wilson I. Barredo

Abstract:

This study presents a conformational model of the helical structures of globular protein particularly ferritin in the framework of white noise path integral formulation by using Associated Legendre functions, Bessel and convolution of Bessel and trigonometric functions as modulating functions. The model incorporates chirality features of proteins and their helix-turn-helix sequence structural motif.

Keywords: Globular protein, modulating function, white noise, winding probability.

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Authors: Vitalice K. Oduol, C. Ardil

Abstract:

The transient analysis of a queuing system with fixed-size batch Poisson arrivals and a single server with exponential service times is presented. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. These functions are shown to be a generalization of the modified Bessel functions of the first kind, with the batch size B as the generalizing parameter. Results for the case of single-packet arrivals are obtained first. The similarities between the two families of functions are then used to obtain results for the general case of batch arrival queue with a batch size larger than one.

Keywords: batch arrivals, generalized Bessel functions, queuetransient analysis, time-varying probabilities.

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Authors: R. K. Saxena, Ravi Saxena

Abstract:

In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

Keywords: Fox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

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Authors: Anupma Bansal

Abstract:

We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.

Keywords: Klein-Gordon-Schödinger Equation, Lie Classical Method, Exact Solutions

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Authors: Saeed Sarabadan, Mehran Nikarya, Kouroah Parand

Abstract:

The magnetohydrodynamic (MHD) Falkner-Skan equations appear in study of laminar boundary layers flow over a wedge in presence of a transverse magnetic field. The partial differential equations of boundary layer problems in presence of a transverse magnetic field are reduced to MHD Falkner-Skan equation by similarity solution methods. This is a nonlinear ordinary differential equation. In this paper, we solve this equation via spectral collocation method based on Bessel functions of the first kind. In this approach, we reduce the solution of the nonlinear MHD Falkner-Skan equation to a solution of a nonlinear algebraic equations system. Then, the resulting system is solved by Newton method. We discuss obtained solution by studying the behavior of boundary layer flow in terms of skin friction, velocity, various amounts of magnetic field and angle of wedge. Finally, the results are compared with other methods mentioned in literature. We can conclude that the presented method has better accuracy than others.

Keywords: MHD Falkner-Skan, nonlinear ODE, spectral collocation method, Bessel functions, skin friction, velocity.

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Authors: Vitalice K. Oduol

Abstract:

The paper considers a single-server queue with fixedsize batch Poisson arrivals and exponential service times, a model that is useful for a buffer that accepts messages arriving as fixed size batches of packets and releases them one packet at time. Transient performance measures for queues have long been recognized as being complementary to the steady-state analysis. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. The paper exploits practical modelling to obtain a solution to the integral equation encountered in the analysis. Results obtained indicate that under heavy load conditions, there is significant disparity in the statistics between the transient and steady state values.

Keywords: batch arrivals, modelling, single-server queue, time-varying probabilities, transient analysis.

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Authors: Valentina Koliskina

Abstract:

Change in impedance of an encircling coil is obtained in the present paper for the case where the electric conductivity and magnetic permeability of a metal cylindrical tube depend on the radial coordinate. The system of equations for the vector potential is solved by means of the Fourier cosine transform. The solution is expressed in terms of improper integral containing modified Bessel functions of complex order.

Keywords: Eddy currents, magnetic permeability, Besselfunctions

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Authors: İnci M. Erhan

Abstract:

A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid.

Keywords: Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics

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Authors: Leonardo A. Ambrosio, Carlos. H. Silva Santos, Ivan E. L. Rodrigues, Ayumi K. de Campos, Leandro A. Machado

Abstract:

In this work, we propose an algorithm developed under Python language for the modeling of ordinary scalar Bessel beams and their discrete superpositions and subsequent calculation of optical forces exerted over dielectric spherical particles. The mathematical formalism, based on the generalized Lorenz-Mie theory, is implemented in Python for its large number of free mathematical (as SciPy and NumPy), data visualization (Matplotlib and PyJamas) and multiprocessing libraries. We also propose an approach, provided by a synchronized Software as Service (SaaS) in cloud computing, to develop a user interface embedded on a mobile application, thus providing users with the necessary means to easily introduce desired unknowns and parameters and see the graphical outcomes of the simulations right at their mobile devices. Initially proposed as a free Android-based application, such an App enables data post-processing in cloud-based architectures and visualization of results, figures and numerical tables.

Keywords: Bessel Beams and Frozen Waves, Generalized Lorenz-Mie Theory, Numerical Methods, Optical Forces.

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Authors: Yu Lou, Chunming Tang, Yanfeng Qi, Maozhi Xu

Abstract:

This paper considers the bent and hyper-bent properties of a class of Boolean functions. For one case, we present a detailed description for them to be hyper-bent functions, and give a necessary condition for them to be bent functions for another case.

Keywords: Boolean functions, bent functions, hyper-bent functions, character sums.

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Authors: Amrita Tripathi, Neeru Adlakha

Abstract:

Calcium [Ca2+] dynamics is studied as a potential form of neuron excitability that can control many irregular processes like metabolism, secretion etc. Ca2+ ion enters presynaptic terminal and increases the synaptic strength and thus triggers the neurotransmitter release. The modeling and analysis of calcium dynamics in neuron cell becomes necessary for deeper understanding of the processes involved. A mathematical model has been developed for cylindrical shaped neuron cell by incorporating physiological parameters like buffer, diffusion coefficient, and association rate. Appropriate initial and boundary conditions have been framed. The closed form solution has been developed in terms of modified Bessel function. A computer program has been developed in MATLAB 7.11 for the whole approach.

Keywords: Laplace Transform, Modified Bessel function, reaction diffusion equation, diffusion coefficient, excess buffer, calcium influx

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Authors: Hakan Bostancı, Metin Öztürk

Abstract:

In this paper, a necessary and sufficient coefficient are given for functions in a class of complex valued meromorphic harmonic univalent functions of the form f = h + g using Salagean operator. Furthermore, distortion theorems, extreme points, convolution condition and convex combinations for this family of meromorphic harmonic functions are obtained.

Keywords: Harmonic mappings, Meromorphic functions, Salagean operator.

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Authors: Fatimah A. Alshaikh

Abstract:

This paper is concerned with propagation of thermoelastic longitudinal vibrations of an infinite circular cylinder, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Three displacement potential functions are introduced to uncouple the equations of motion. The frequency equation, by using the traction free boundary conditions, is given in the form of a determinant involving Bessel functions. The roots of the frequency equation give the value of the characteristic circular frequency as function of the wave number. These roots, which correspond to various modes, are numerically computed and presented graphically for different values of the thermal relaxation times. It is found that the influences of the thermal relaxation times on the amplitudes of the elastic and thermal waves are remarkable. Also, it is shown in this study that the propagation of thermoelastic longitudinal vibrations based on the generalized thermoelasticity can differ significantly compared with the results under the classical formulation. A comparison of the results for the case with no thermal effects shows well agreement with some of the corresponding earlier results.

Keywords: Wave propagation, longitudinal vibrations, circular cylinder, generalized thermoelasticity, Thermal relaxation times.

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Authors: Muna Tabuni

Abstract:

The paper contains an investigation of zeros Of Bargmann analytic representation. A brief introduction to Harmonic oscillator formalism is given. The Bargmann analytic representation has been studied. The zeros of Bargmann analytic function are considered. The Q or Husimi functions are introduced. The The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros μn are discussed. Various examples have been given.

Keywords: Bargmann functions, Husimi functions, zeros.

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Authors: Manoj Singh, Mumtaz Ahmad Khan, Abdul Hakim Khan

Abstract:

The object of the present paper is to investigate several general families of bilinear and bilateral generating functions with different argument for the Gauss’ hypergeometric polynomials.

Keywords: Appell’s functions, Gauss hypergeometric functions, Heat polynomials, Kampe’ de Fe’riet function, Laguerre polynomials, Lauricella’s function, Saran’s functions.

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

Abstract:

The effects of large vibration amplitudes on the first axisymetric mode shape of thin isotropic annular plates having both edges clamped are examined in this paper. The theoretical model based on Hamilton’s principle and spectral analysis by using a basis of Bessel’s functions is adapted اhere to the case of annular plates. The model effectively reduces the large amplitude free vibration problem to the solution of a set of non-linear algebraic equations.

The governing non-linear eigenvalue problem has been linearised in the neighborhood of each resonance and a new one-step iterative technique has been proposed as a simple alternative method of solution to determine the basic function contributions to the non-linear mode shape considered.

Numerical results are given for the first non-linear mode shape for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency, the membrane and bending stress distributions are given. By comparison with the iterative method of solution, it was found that the present procedure is efficient for a wide range of vibration amplitudes, up to at least 1.8 times the plate thickness,

Keywords: Non-linear vibrations, Annular plates, Large vibration amplitudes.

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Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

Abstract:

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f^-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: Analytic functions, bi-univalent functions, Hohlov operator, subordination.

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Authors: Chahid K. Ghaddar

Abstract:

The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: Calculus functions, nonlinear systems, differential algebraic equations, solvers, spreadsheet.

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Authors: Hesam Mahzoon

Abstract:

By using the two existing operators, we have defined an operator, which is an extension for them. In this paper, first the operator is introduced. Then, using this operator, the subclasses of multivalent functions are defined. These subclasses of multivalent functions are utilized in order to obtain coefficient inequalities, extreme points, and integral means inequalities for functions belonging to these classes.

Keywords: Coefficient inequalities, extreme points, integral means, multivalent functions, Al-Oboudi operator, and Sãlãgean operator.

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Authors: Jaewook Shin, Aesoon Park

Abstract:

MBMS is a unidirectional point-to-multipoint bearer service in which data are transmitted from a single source entity to multiple recipients. For a mobile to support the MBMS, MBMS client functions as well as MBMS radio protocols should be designed and implemented. In this paper, we analyze the MBMS client functions and describe the implementation of them in our mobile test-bed. User operations and signaling flows between protocol entities to control the MBMS functions are designed in detail. Service announcement utilizing the file download MBMS service and four MBMS user services are demonstrated in the test-bed to verify the MBMS client functions.

Keywords: BM-SC, Broadcast, MBMS, Mobile, Multicast.

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Authors: Anita S. Gangal, P. K. Kalra, D. S. Chauhan

Abstract:

The backpropagation algorithm in general employs quadratic error function. In fact, most of the problems that involve minimization employ the Quadratic error function. With alternative error functions the performance of the optimization scheme can be improved. The new error functions help in suppressing the ill-effects of the outliers and have shown good performance to noise. In this paper we have tried to evaluate and compare the relative performance of complex valued neural network using different error functions. During first simulation for complex XOR gate it is observed that some error functions like Absolute error, Cauchy error function can replace Quadratic error function. In the second simulation it is observed that for some error functions the performance of the complex valued neural network depends on the architecture of the network whereas with few other error functions convergence speed of the network is independent of architecture of the neural network.

Keywords: Complex backpropagation algorithm, complex errorfunctions, complex valued neural network, split activation function.

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Authors: Sheena Mathew, K. Poulose Jacob

Abstract:

This paper describes the results of an extensive study and comparison of popular hash functions SHA-1, SHA-256, RIPEMD-160 and RIPEMD-320 with JERIM-320, a 320-bit hash function. The compression functions of hash functions like SHA-1 and SHA-256 are designed using serial successive iteration whereas those like RIPEMD-160 and RIPEMD-320 are designed using two parallel lines of message processing. JERIM-320 uses four parallel lines of message processing resulting in higher level of security than other hash functions at comparable speed and memory requirement. The performance evaluation of these methods has been done by using practical implementation and also by using step computation methods. JERIM-320 proves to be secure and ensures the integrity of messages at a higher degree. The focus of this work is to establish JERIM-320 as an alternative of the present day hash functions for the fast growing internet applications.

Keywords: Cryptography, Hash function, JERIM-320, Messageintegrity

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Authors: Manoj Singh, Mumtaz Ahmad Khan, Abdul Hakim Khan

Abstract:

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral.

Keywords: Fractional Derivatives and Integrals, Hypergeometric functions.

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Authors: Changqing Yang, Jianhua Hou, Beibo Qin

Abstract:

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Keywords: Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.

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Authors: Ε. Giovanis

Abstract:

In this paper we present, propose and examine additional membership functions for the Smoothing Transition Autoregressive (STAR) models. More specifically, we present the tangent hyperbolic, Gaussian and Generalized bell functions. Because Smoothing Transition Autoregressive (STAR) models follow fuzzy logic approach, more fuzzy membership functions should be tested. Furthermore, fuzzy rules can be incorporated or other training or computational methods can be applied as the error backpropagation or genetic algorithm instead to nonlinear squares. We examine two macroeconomic variables of US economy, the inflation rate and the 6-monthly treasury bills interest rates.

Keywords: Forecast , Fuzzy membership functions, Smoothingtransition, Time-series

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Authors: Muna Tabuni

Abstract:

The paper contains an investigation of winding numbers of paths of zeros of analytic theta functions. We have considered briefly an analytic representation of finite quantum systems ZN. The analytic functions on a torus have exactly N zeros. The brief introduction to the zeros of analytic functions and there time evolution is given. We have discussed the periodic finite quantum systems. We have introduced the winding numbers in general. We consider the winding numbers of the zeros of analytic theta functions.

Keywords: Winding numbers, period, paths of zeros.

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Authors: B. M. Mohan, Sanjeeb Kumar Kar

Abstract:

In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included.

Keywords: Linear quadratic Gaussian control, linear quadratic estimator, linear quadratic regulator, time-invariant systems, orthogonal functions, block-pulse functions, shifted legendre polynomials.

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Authors: M. Habchi, S. M. Mesli, M. Kotbi

Abstract:

A structural study of an aqueous electrolyte whose experimental results are available. It is a solution of LiCl-6H2O type at glassy state (120K) contrasted with pure water at room temperature by means of Partial Distribution Functions (PDF) issue from neutron scattering technique. Based on these partial functions, the Reverse Monte Carlo method (RMC) computes radial and angular correlation functions which allow exploring a number of structural features of the system. The obtained curves include some artifacts. To remedy this, we propose to introduce a screened potential as an additional constraint. Obtained results show a good matching between experimental and computed functions and a significant improvement in PDFs curves with potential constraint. It suggests an efficient fit of pair distribution functions curves.

Keywords: RMC simulation; Screened potential; partial and pair distribution functions; glassy and liquid state

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Authors: Nabila Charkaoui

Abstract:

Interest in Human Consciousness has been revived in the late 20th century from different scientific disciplines. Consciousness studies involve both its understanding and its application. In this paper, a computational model of the minimum consciousness functions necessary in my point of view for Artificial Intelligence applications is presented with the aim of improving the way computations will be made in the future. In section I, human consciousness is briefly described according to the scope of this paper. In section II, a minimum set of consciousness functions is defined - based on the literature reviewed - to be modelled, and then a computational model of these functions is presented in section III. In section IV, an analysis of the model is carried out to describe its functioning in detail.

Keywords: Consciousness, perception, attention.

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Authors: Kriuk Boris, Kriuk Fedor

Abstract:

This paper presents a comparative study of fundamental similarity functions for Siamese networks in semantic textual similarity (STS) tasks. We evaluate various similarity functions using the STS Benchmark dataset, analyzing their performance and stability. Additionally, we present a multi-objective approach for optimal threshold selection. Our findings provide insights into the effectiveness of different similarity functions and offer a straightforward method for threshold selection optimization, contributing to the advancement of Siamese network architectures in STS applications.

Keywords: Siamese networks, Semantic textual similarity, Similarity functions, STS Benchmark dataset, Threshold selection.

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