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Journal articles on the topic 'Generalized complex Lamé coefficients'

Author: Grafiati

Published: 9 November 2024

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1

Joshi, Nalini, and Andrew Pickering. "Generalized Halphen systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, no. 6 (December 2006): 1287–301. http://dx.doi.org/10.1017/s0308210500004984.

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Towards the end of the nineteenth century, Halphen studied a remarkable sequence of higher-order linear equations with doubly periodic coefficients, generalizations of a certain Lamé equation, having the property that quotients of solutions are single valued. Here we consider further generalizations where, instead of the Weierstrass ℘-function, the coefficients depend on the first Painlevé transcendent. Using these equations, we obtain new higher-order systems of nonlinear equations having the Painlevé property. We also give new results on the interpretation of the Painlevé tests with regard to the representations of solutions, general and particular, afforded by various branches, and to understanding the corresponding pattern of compatibility conditions.

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2

Khomasuridze, N. "Representation of Solutions of Some Boundary Value Problems of Elasticity by a Sum of the Solutions of Other Boundary Value Problems." gmj 10, no. 2 (June 2003): 257–70. http://dx.doi.org/10.1515/gmj.2003.257.

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Abstract Basic static boundary value problems of elasticity are considered for a semi-infinite curvilinear prism Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < ∞} in generalized cylindrical coordinates ρ, α, 𝑧 with Lamé coefficients ℎ ρ = ℎ α = ℎ(ρ, α), ℎ𝑧 = 1. It is proved that the solution of some boundary value problems of elasticity can be reduced to the sum of solutions of other boundary value problems of elasticity. Besides its cognitive significance, this fact also enables one to solve some non-classical elasticity problems.

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3

XIA, BINGXING, and VIET HA HOANG. "BEST N-TERM GPC APPROXIMATIONS FOR A CLASS OF STOCHASTIC LINEAR ELASTICITY EQUATIONS." Mathematical Models and Methods in Applied Sciences 24, no. 03 (December 29, 2013): 513–52. http://dx.doi.org/10.1142/s0218202513500589.

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We consider a class of stochastic linear elasticity problems whose elastic moduli depend linearly on a countable set of random variables. The stochastic equation is studied via a deterministic parametric problem on an infinite-dimensional parameter space. We first study the best N-term approximation of the generalized polynomial chaos (gpc) expansion of the solution to the displacement formula by considering a Galerkin projection onto the space obtained by truncating the gpc expansion. We provide sufficient conditions on the coefficients of the elastic moduli's expansion so that a rate of convergence for this approximation holds. We then consider two classes of stochastic and parametric mixed elasticity problems. The first one is the Hellinger–Reissner formula for approximating directly the gpc expansion of the stress. For isotropic problems, the multiplying constant of the best N-term convergence rate for the displacement formula grows with the ratio of the Lamé constants. We thus consider stochastic and parametric mixed problems for nearly incompressible isotropic materials whose best N-term approximation rate is uniform with respect to the ratio of the Lamé constants.

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4

Peherstorfer, F. "Explicit generalized zolotarev polynomials with complex coefficients." Constructive Approximation 13, no. 2 (June 1997): 261–69. http://dx.doi.org/10.1007/bf02678468.

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5

Peherstorfer, F. "Explicit Generalized Zolotarev Polynomials with Complex Coefficients." Constructive Approximation 13, no. 2 (July 1, 1997): 261–69. http://dx.doi.org/10.1007/s003659900042.

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6

Ramachandran, C., T. Soupramanien, and J. Sokół. "On a Generalization of Bounded Univalent Function of Complex Order." Journal of Computational and Theoretical Nanoscience 15, no. 2 (February 1, 2018): 601–5. http://dx.doi.org/10.1166/jctn.2018.7130.

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In this paper, we introduce a new class of analytic functions of complex order involving a family of generalized differential operators and we discuss the sufficient conditions, estimation of coefficients. The motivation of this paper is to generalize the Coefficient Estimates obtained by Attiya, and Aouf et al. by making use of the generalized differential operator Dnλ, μ.

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7

Deniz, Erhan, Jay M. Jahangiri, Samaneh G. Hamidi, and Sibel K. Kına. "Faber polynomial coefficients for generalized bi-subordinate functions of complex order." Journal of Mathematical Inequalities, no. 3 (2018): 645–53. http://dx.doi.org/10.7153/jmi-2018-12-49.

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8

Zhang, Sheng, Lijie Zhang, and Bo Xu. "Rational Waves and Complex Dynamics: Analytical Insights into a Generalized Nonlinear Schrödinger Equation with Distributed Coefficients." Complexity 2019 (March 21, 2019): 1–17. http://dx.doi.org/10.1155/2019/3206503.

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In this paper, we first present a complex multirational exp-function ansatz for constructing explicit solitary wave solutions, N-wave solutions, and rouge wave solutions of nonlinear partial differential equations (PDEs) with complex coefficients. To illustrate the effectiveness of the complex multirational exp-function ansatz, we then consider a generalized nonlinear Schrödinger (gNLS) equation with distributed coefficients. As a result, some explicit rational exp-function solutions are obtained, including solitary wave solutions, N-wave solutions, and rouge wave solutions. Finally, we simulate some spatial structures and dynamical evolutions of the modules of the obtained solutions for more insights into these complex rational waves. It is shown that the complex multirational exp-function ansatz can be used for explicit solitary wave solutions, N-wave solutions, and rouge wave solutions of some other nonlinear PDEs with complex coefficients.

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9

Polosin, V. G. "Shape measures of generalized beta distributions." Journal of Physics: Conference Series 2094, no. 2 (November 1, 2021): 022009. http://dx.doi.org/10.1088/1742-6596/2094/2/022009.

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Abstract This paper presents shape measures for generalized beta distributions that unit many subfamilies of distributions. For the study of complex systems, the information entropy of the whole family of the generalized beta distribution is obtained. The paper uses the interval of entropy uncertainty as an estimate of the entropy uncertainty for probable models, which are given in units of an observable random variable. The entropy uncertainty interval was used to construct the entropy coefficient of unbiased subfamilies of the generalized beta distribution. Particular entropy coefficients are given for frequently used subfamilies of beta distribution, that greatly facilitates the use of coefficients as independent information measures in determining the shape of models. The paper contains the most general formulas for probabilistic measures of the distributions shape also.

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10

Teshaev, Muhsin, Ismoil Safarov, Dilshoda Ibragimova, Doniyor Rayimov, and Sharif Akhmedov. "Stationary response of the system “Cylindrical shell – viscoelastic filler” to the effect of a moving load." Journal of Physics: Conference Series 2697, no. 1 (February 1, 2024): 012004. http://dx.doi.org/10.1088/1742-6596/2697/1/012004.

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Abstract The paper considers the stationary response of the system “cylindrical shell - viscoelastic filler” to the action of a moving load. The filler and the shell were assumed to be viscoelastic. Using the principle of analogy of viscoelastic and elastic problems (elastic-viscoelastic analogy), a stationary solution of the action of mobile loads on a shell with a viscoelastic filler is obtained. It is shown that this principle makes it possible to generalize the class of problems obtained for the case of viscoelastic media. Since the viscoelastic filler has damping properties, the inversion integrals have no singularities on the real axis, and the elements of the determinants in integrals become complex since in this problem in the image space, the Lame coefficients are complex and depend on the speed of the load movement, as well as the Fourier transform parameter. Numerical results are obtained, and an analysis is made.

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11

Hsu, Chi-Yun. "Fourier coefficients of the overconvergent generalized eigenform associated to a CM form." International Journal of Number Theory 16, no. 06 (February 11, 2020): 1185–97. http://dx.doi.org/10.1142/s1793042120500608.

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Let [Formula: see text] be a modular form with complex multiplication. If [Formula: see text] has critical slope, then Coleman’s classicality theorem implies that there is a [Formula: see text]-adic overconvergent generalized Hecke eigenform with the same Hecke eigenvalues as [Formula: see text]. We give a formula for the Fourier coefficients of this generalized Hecke eigenform. We also investigate the dimension of the generalized Hecke eigenspace of [Formula: see text]-adic overconvergent forms containing [Formula: see text].

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12

Zernov, V., A. V. Pichugin, and J. Kaplunov. "Eigenvalue of a semi-infinite elastic strip." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2068 (January 24, 2006): 1255–70. http://dx.doi.org/10.1098/rspa.2005.1615.

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A semi-infinite elastic strip, subjected to traction free boundary conditions, is studied in the context of in-plane stationary vibrations. By using normal (Rayleigh–Lamb) mode expansion the problem of existence of the strip eigenmode is reformulated in terms of the linear dependence within infinite system of normal modes. The concept of Gram's determinant is used to introduce a generalized criterion of linear dependence, which is valid for infinite systems of modes and complex frequencies. Using this criterion, it is demonstrated numerically that in addition to the edge resonance for the Poisson ratio ν =0, there exists another value of ν ≈0.22475 associated with an undamped resonance. This resonance is best explained physically by the orthogonality between the edge mode and the first Lamé mode. A semi-analytical proof for the existence of the edge resonance is then presented for both described cases with the help of the augmented scattering matrix formalism.

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13

Wazwaz, Abdul-Majid. "New solutions for two integrable cases of a generalized fifth-order nonlinear equation." Modern Physics Letters B 29, no. 14 (May 29, 2015): 1550065. http://dx.doi.org/10.1142/s0217984915500657.

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Multiple-complexiton solutions for a new generalized fifth-order nonlinear integrable equation are constructed with the help of the Hirota's method and the simplified Hirota's method. By extending the real parameters into complex parameters, nonsingular complexiton solutions are obtained for two specific coefficients of the new generalized equation.

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14

Xu, Xiao-Chuan. "Inverse spectral problems for the generalized Robin–Regge problem with complex coefficients." Journal of Geometry and Physics 159 (January 2021): 103936. http://dx.doi.org/10.1016/j.geomphys.2020.103936.

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15

Placidi, Luca, and Emilio Barchiesi. "Energy approach to brittle fracture in strain-gradient modelling." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2210 (February 2018): 20170878. http://dx.doi.org/10.1098/rspa.2017.0878.

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In this paper, we exploit some results in the theory of irreversible phenomena to address the study of quasi-static brittle fracture propagation in a two-dimensional isotropic continuum. The elastic strain energy density of the body has been assumed to be geometrically nonlinear and to depend on the strain gradient. Such generalized continua often arise in the description of microstructured media. These materials possess an intrinsic length scale, which determines the size of internal boundary layers. In particular, the non-locality conferred by this internal length scale avoids the concentration of deformations, which is usually observed when dealing with local models and which leads to mesh dependency. A scalar Lagrangian damage field, ranging from zero to one, is introduced to describe the internal state of structural degradation of the material. Standard Lamé and second-gradient elastic coefficients are all assumed to decrease as damage increases and to be locally zero if the value attained by damage is one. This last situation is associated with crack formation and/or propagation. Numerical solutions of the model are provided in the case of an obliquely notched rectangular specimen subjected to monotonous tensile and shear loading tests, and brittle fracture propagation is discussed.

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16

Alibrahim, Ali Hamzah, and Saptarshi Das. "Fourier Series Related to p-Trigonometric Functions." Axioms 13, no. 9 (September 4, 2024): 600. http://dx.doi.org/10.3390/axioms13090600.

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In this paper, we introduce the concept of generalized Fourier series, generated by the p-trigonometric functions, namely cosp and sinp, recently introduced related to the generalized complex numbers systems. The aim of this study is to represent a periodic signal as a sum of p-sine and p-cosine functions. In order to achieve this, we first present the integrals of the product of the same or different family of p-trigonometric functions over the full period of these functions to understand the orthogonality properties. Next, we use these integrals to derive the coefficients of the generalized p-Fourier series along with a few examples. The generalized Fourier series can be used to expand an arbitrary forcing function in the solution of a non-homogeneous linear ordinary differential equation (ODE) with constant coefficients.

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17

Bouzzit, Aziz, Loïc Martinez, Andres Arciniegas, Stéphane Serfaty, and Nicolas Wilkie-Chancellier. "Ellipsometry of surface acoustic waves using 3D vibrometry for viscoelastic material characterization by the estimation of complex Lamé coefficients versus the frequency." Applied Acoustics 228 (January 2025): 110312. http://dx.doi.org/10.1016/j.apacoust.2024.110312.

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18

Donno, Giuseppe De. "Generalized Vandermonde determinants for reversing Taylor's formula and application to hypoellipticity." Tamkang Journal of Mathematics 38, no. 2 (June 30, 2007): 183–89. http://dx.doi.org/10.5556/j.tkjm.38.2007.89.

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The problem of the hypoellipticity of the linear partial differential operators with constant coefficients was completely solved by H"{o}r-man-der in [5]. He listed many equivalent algebraic conditions on the polynomial symbol of the operator, each necessary and sufficient for hypoellipticity. In this paper we employ two Mitchell's Theorems (1881) regarding a type of Generalized Vandermonde Determinants, for inverting Taylor's formula of polynomials in several variables with complex coefficients. We obtain then a more direct and easy proof of an equivalence for the mentioned H"{o}r-man-der's hypoellipticity conditions.

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19

Zahreddine, Ziad. "The generalized Routh array and a further simplification of the extended Routh array." Tamkang Journal of Mathematics 32, no. 2 (June 30, 2001): 131–36. http://dx.doi.org/10.5556/j.tkjm.32.2001.355.

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The well-known Routh Array settles the problem of stability of systems of differential equations with rral coefficients. The Extended Routh Array (ERA) is the complex counterpart of the Routh Array and it settles the stability of these systems when the coefficients are complex. Since its construction, the ERA remained more of a theoretical achievement, than a practical tool to test the stability of linear systems. Some attempts were made to overcome the complexity of the ERA. The Modified Extended Routh Array (MERA) was then introduced and it reduced the burden of computations, but still it involved lots of divisions and many operations with complex numbers. In the present work, we use the interlacing property to propose an equivalent criterion to both ERA and MERA, we call the Generalized Routh Array (GRA). The new array has advantages over both ERA and MERA in the sense that neither division algorithm, nor operations of complex numbers are involved. An example is given to illustrate the feasibility of the new test.

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20

Singh, Gurmeet, Gagandeep Singh, and Gurcharanjit Singh. "A GENERALIZED SUBCLASS OF ALPHA CONVEX BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER." Jnanabha 50, no. 01 (2020): 65–71. http://dx.doi.org/10.58250/jnanabha.2020.50108.

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In this present investigation a subclass of alpha convex bi-univalent functions of complex order in the open unit disc U = {z :| z |< 1}, defined by Salagean operator and quasi- subordination is discussed. The estimates on the initial coefficients |a 2 | and |a 3 | for the functions in this subclass are studied. The results obtained in this paper would generalise those already proved by various authors.

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21

Golubkov, A. A., and V. A. Makarov. "Inverse spectral problem for a generalized Sturm-Liouville equation with complex-valued coefficients." Differential Equations 47, no. 10 (October 2011): 1514–19. http://dx.doi.org/10.1134/s0012266111100156.

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22

Murugusundaramoorthy, G., and N. Magesh. "Certain Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/178605.

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Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the classTSml(α,β,γ). In particular, we obtain integral means inequalities for the functionfthat belongs to the classTSml(α,β,γ)in the unit disc.

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23

Dubey, Anil Kumar, Manjula Tripathi, and Ravi Prakash Dubey. "Various Fixed Point Theorems in Complex Valued b-Metric Spaces." International Journal of Engineering Mathematics 2016 (November 3, 2016): 1–7. http://dx.doi.org/10.1155/2016/7072606.

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We prove some common fixed point results for a pair of mappings which satisfy generalized contractive conditions with rational expressions having point-dependent control functions as coefficients in complex valued b-metric spaces. The results of this paper generalize and extend the several known results in complex valued b-metric spaces. Finally, examples are provided to verify the effectiveness and to usability of our main results.

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24

Campos, L. M. B. C. "On generalizations of the series of Taylor, Lagrange, Laurent and Teixeira." International Journal of Mathematics and Mathematical Sciences 13, no. 4 (1990): 687–708. http://dx.doi.org/10.1155/s0161171290000941.

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The classical theorems of Taylor, Lagrange, Laurent and Teixeira, are extended from the representation of a complex functionF(z), to its derivativeF(ν)(z)of complex orderν, understood as either a Liouville (1832) or a Rieman (1847) differintegration (Campos 1984, 1985); these results are distinct from, and alternative to, other extensions of Taylor's series using differintegrations (Osler 1972, Lavoie & Osler & Tremblay 1976). We consider a complex functionF(z), which is analytic (has an isolated singularity) atζ, and expand its derivative of complex orderF(ν)(z), in an ascending (ascending-descending) series of powers of an auxiliary functionf(z), yielding the generalized Teixeira (Lagrange) series, which includes, forf(z)=z−ζ, the generalized Taylor (Laurent) series. The generalized series involve non-integral powers and/or coefficients evaluated by fractional derivatives or integrals, except in the caseν=0, when the classical theorems of Taylor (1715), Lagrange (1770), Laurent (1843) and Teixeira (1900) are regained. As an application, these generalized series can be used to generate special functions with complex parameters (Campos 1986), e.g., the Hermite and Bessel types.

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25

Ibrahim, Rabha W., Rafida M. Elobaid, and Suzan J. Obaiys. "A Class of Quantum Briot–Bouquet Differential Equations with Complex Coefficients." Mathematics 8, no. 5 (May 14, 2020): 794. http://dx.doi.org/10.3390/math8050794.

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Quantum inequalities (QI) are local restraints on the magnitude and range of formulas. Quantum inequalities have been established to have a different range of applications. In this paper, we aim to introduce a study of QI in a complex domain. The idea basically, comes from employing the notion of subordination. We shall formulate a new q-differential operator (generalized of Dunkl operator of the first type) and employ it to define the classes of QI. Moreover, we employ the q-Dunkl operator to extend the class of Briot–Bouquet differential equations. We investigate the upper solution and exam the oscillation solution under some analytic functions.

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26

Bezyazichny, V. F., T. V. Shehovtseva, and E. V. Shehovtseva. "THE GENERALIZED CRITERION OF THE PARTS FOR THEIR MANUFACTURE." Spravochnik. Inzhenernyi zhurnal, no. 308 (November 2022): 18–27. http://dx.doi.org/10.14489/hb.supp.2022.11.pp.018-027.

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The CNC machines application is justified by the range rational selection of the mechanisms manufactured parts in the group organization of the specialized processing areas. It has been established that on the CNC machines it is the most effective to manufacture complex profile parts with a large number of machined surfaces. The generalized criterion of the part design manufacturability, taking into account weight coefficients for each indicator, has been developed.

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27

Bród, Dorota, Anetta Szynal-Liana, and Iwona Włoch. "On a new one-parameter generalization of dual-complex Jacobsthal numbers." Acta Universitatis Sapientiae, Mathematica 13, no. 1 (August 1, 2021): 127–44. http://dx.doi.org/10.2478/ausm-2021-0007.

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Abstract In this paper we define dual-complex numbers with generalized Jacobsthal coefficients. We introduce one-parameter generalization of dual-complex Jacobsthal numbers - dual-complex r-Jacobsthal numbers. We investigate some algebraic properties of introduced numbers, among others Binet type formula, Catalan, Cassini, d’Ocagne and Honsberger type identities. Moreover, we present the generating function, summation formula and matrix generator for these numbers. The results are generalization of the properties for the dual-complex Jacobsthal numbers.

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28

Vijaya, K., G. Murugusundaramoorthy, and M. Kasthuri. "Pascu-Type Harmonic Functions with Positive Coefficients Involving Salagean Operator." International Journal of Analysis 2014 (April 6, 2014): 1–10. http://dx.doi.org/10.1155/2014/793709.

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Making use of a Salagean operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc. Among the results presented in this paper including the coeffcient bounds, distortion inequality, and covering property, extreme points, certain inclusion results, convolution properties, and partial sums for this generalized class of functions are discussed.

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29

RAO, M. VENU GOPALA, and S. VATHSAL. "Bi-ComForWaRD: BIVARIATE COMPLEX FOURIER-WAVELET REGULARIZED DECONVOLUTION FOR MEDICAL IMAGING." International Journal of Computational Intelligence and Applications 08, no. 02 (June 2009): 85–95. http://dx.doi.org/10.1142/s1469026809002540.

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In this paper, we propose a new hybrid Bivariate Complex Fourier Wavelet Regularized Deconvolution (Bi-ComForWaRD) that is an extension to the ComForWaRD algorithm, for medical imaging. This new algorithm is a two-step process, a global blur compensation using generalized Wiener filter and followed by a denoising algorithm using local adaptive Bivariate shrinkage function. It is a low-complexity denoising algorithm using the joint statistics of the wavelet coefficients and considers the statistical dependencies between the coefficients. And also, the performance of this system will be demonstrated on both the orthogonal wavelet transform and the dual-tree complex wavelet transform (DT-CWT) and some comparisons with the best available wavelet-based image denoising results will be given in order to illustrate the effectiveness of the system.

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30

ODŽAK, ALMASA, and LEJLA SMAJLOVIĆ. "ON INTERPOLATION FUNCTIONS FOR GENERALIZED Li COEFFICIENTS IN THE SELBERG CLASS." International Journal of Number Theory 07, no. 03 (May 2011): 771–92. http://dx.doi.org/10.1142/s1793042111004356.

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We prove that there exists an entire complex function of order one and finite exponential type that interpolates the Li coefficients λF(n) attached to a function F in the class [Formula: see text] that contains both the Selberg class of functions and (unconditionally) the class of all automorphic L-functions attached to irreducible, cuspidal, unitary representations of GL n(ℚ). We also prove that the interpolation function is (essentially) unique, under generalized Riemann hypothesis. Furthermore, we obtain entire functions of order one and finite exponential type that interpolate both archimedean and non-archimedean contribution to λF(n) and show that those functions can be interpreted as zeta functions built, respectively, over trivial zeros and all zeros of a function [Formula: see text].

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Cho, MoonJung, John L. Eltinge, Julie Gershunskaya, and Larry Huff. "Evaluation of Generalized Variance Functions in the Analysis of Complex Survey Data." Journal of Official Statistics 30, no. 1 (March 1, 2014): 63–90. http://dx.doi.org/10.2478/jos-2014-0004.

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Abstract Two sets of diagnostics are presented to evaluate the properties of generalized variance functions (GVFs) for a given sample survey. The first set uses test statistics for the coefficients of multiple regression forms of GVF models. The second set uses smoothed estimators of the mean squared error (MSE) of GVF-based variance estimators. The smooth version of the MSE estimator can provide a useful measure of the performance of a GVF estimator, relative to the variance of a standard design-based variance estimator. Some of the proposed methods are applied to sample data from the Current Employment Statistics survey.

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32

Ibrahim, Rabha W., Rafida M. Elobaid, and Suzan J. Obaiys. "Generalized Briot-Bouquet Differential Equation Based on New Differential Operator with Complex Connections." Axioms 9, no. 2 (April 21, 2020): 42. http://dx.doi.org/10.3390/axioms9020042.

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A class of Briot–Bouquet differential equations is a magnificent part of investigating the geometric behaviors of analytic functions, using the subordination and superordination concepts. In this work, we aim to formulate a new differential operator with complex connections (coefficients) in the open unit disk and generalize a class of Briot–Bouquet differential equations (BBDEs). We study and generalize new classes of analytic functions based on the new differential operator. Consequently, we define a linear operator with applications.

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33

Ruan, Dehao, and Yao Lu. "Generalized exponential stability of stochastic Hopfield neural networks with variable coefficients and infinite delay." AIMS Mathematics 9, no. 8 (2024): 22910–26. http://dx.doi.org/10.3934/math.20241114.

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<p>This paper centers on stochastic Hopfield neural networks with variable coefficients and infinite delay. First, we propose an integral inequality that improves and extends some existing works. Second, by employing some inequalities and stochastic analysis techniques, some sufficient conditions for ensuring $ p $th moment generalized exponential stability are established. Our results do not necessitate the construction of a complex Lyapunov function or rely on the assumption of bounded variable coefficients, and our results expand some existing works. At last, to illustrate the efficacy of our result, we present several simulation examples.</p>

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Şentürk, Gülsüm Yeliz, and Nurten Gürses. "Dual quaternion theory over HGC numbers." Journal of Discrete Mathematical Sciences & Cryptography 27, no. 1 (2024): 117–42. http://dx.doi.org/10.47974/jdmsc-1611.

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Knowing the applications of quaternions in various fields, such as robotics, navigation, computer visualization and animation, in this study, we give the theory of dual quaternions considering Hyperbolic-Generalized Complex (HGC) numbers as coefficients via generalized complex and hyperbolic numbers. We account for how HGC number theory can extend dual quaternions to HGC dual quaternions. Some related theoretical results with HGC Fibonacci/Lucas numbers are established, including their dual quaternions. Given HGC Fibonacci/Lucas numbers, their special matrix correspondences have been identified and these are carried out to HGC Fibonacci/Lucas dual quaternions. Furthermore, we provide a more accurate way to quickly calculate HGC Fibonacci numbers and associate this with HGC generalized Fibonacci numbers. For implementation, we produce an algorithm in Maple. Lastly, we put the theory into practice.

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35

Vijaya, Kaliappan, and Gangadharan Murugusundaramoorthy. "Bi-Starlike Function of Complex Order Involving Mathieu-Type Series Associated with Telephone Numbers." Symmetry 15, no. 3 (March 3, 2023): 638. http://dx.doi.org/10.3390/sym15030638.

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For the first time, we attempted to define two new sub-classes of bi-univalent functions in the open unit disc of the complex order involving Mathieu-type series, associated with generalized telephone numbers. The initial coefficients of functions in these classes were obtained. Moreover, we also determined the Fekete–Szegö inequalities for function in these and several related corollaries.

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36

Zhang, Ru, Shengyao Zhang, Yucheng Xu, Lianying Zhou, Futi Liu, and Xunqian Xu. "Modeling of a Magnetoelectric Laminate Ring Using Generalized Hamilton’s Principle." Materials 12, no. 9 (May 3, 2019): 1442. http://dx.doi.org/10.3390/ma12091442.

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The mathematical modeling of the magnetoelectric (ME) effect in ME laminates has been established for some simple structures. However, these methods, which are based on the differential equation approach, are difficult to use in other complex structures (e.g., ring structures). In this work, a new established approach based on the generalized Hamilton’s principle is used to analyze the ME effect in an ME laminated ring. Analytical expressions for ME voltage coefficients are derived. A comparison with the conventional method indicates that this approach is more convenient when the modeling analysis is performed on complex structures. Further, experimental data are also obtained to compare with the theoretical calculations in order to validate the new approach.

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Bart, Anneke, and Kevin P. Scannell. "The Generalized Cuspidal Cohomology Problem." Canadian Journal of Mathematics 58, no. 4 (August 1, 2006): 673–90. http://dx.doi.org/10.4153/cjm-2006-028-1.

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AbstractLet Γ ⊂ SO(3, 1) be a lattice. The well known bending deformations, introduced by Thurston and Apanasov, can be used to construct non-trivial curves of representations of Γ into SO(4, 1) when Γ\ℍ3 contains an embedded totally geodesic surface. A tangent vector to such a curve is given by a non-zero group cohomology class in H1(Γ, ℍ41). Our main result generalizes this construction of cohomology to the context of “branched” totally geodesic surfaces. We also consider a natural generalization of the famous cuspidal cohomology problem for the Bianchi groups (to coefficients in non-trivial representations), and perform calculations in a finite range. These calculations lead directly to an interesting example of a link complement in S3 which is not infinitesimally rigid in SO(4, 1). The first order deformations of this link complement are supported on a piecewise totally geodesic 2-complex.

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Singh, Shailendra, and S. Saha Ray. "New analytical solutions and integrability for the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system arising in the study of fluid dynamics via auto-Backlund transformation approach." Physica Scripta 98, no. 8 (July 27, 2023): 085243. http://dx.doi.org/10.1088/1402-4896/ace6dc.

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Abstract Recognising the non-uniformity of boundaries and the inhomogeneities of media, nonlinear evolution equations with variable coefficients may display more realistic scenarios dealing with time-varying environments and inhomogeneous media. In this work, the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system that occurs in the domain of fluid dynamics is investigated. Painlevé analysis technique is used to demonstrate the integrability of the above mentioned system. The governing equations are revealed to be integrable in the Painlevé sense under no specific criterion on the variable-coefficients. To derive numerous analytical solutions, the auto-Bäcklund transformation (ABT) method is taken into account. Consequently, three different analytical solutions are found using the ABT technique, which include linear, exponential, rational, and complex solutions. All the solutions are displayed as 3D plots in which variable coefficients and parameters are varied to produce the desired results. These graphs depict the many aspects of the proposed coupled system in the various forms of periodic waves and complex periodic wave surfaces.

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Adel, Mohamed, Khaled Aldwoah, Farrie Alharbi, and Mohamed S. Osman. "Dynamic Properties of Non-Autonomous Femtosecond Waves Modeled by the Generalized Derivative NLSE with Variable Coefficients." Crystals 12, no. 11 (November 13, 2022): 1627. http://dx.doi.org/10.3390/cryst12111627.

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The primary purpose of this study is to analyze non-autonomous femtosecond waves with various geometrical configurations correlated to the generalized derivative nonlinear Shrödinger equation (NLSE) with variable coefficients. Numerous academic publications, especially in nonlinear optics, material science, semiconductor, chemical engineering, and many other fields, have looked into this model since it is closer to real-world situations and has more complex wave structures than models with constant coefficients. It can serve as a reflection for the slowly altering inhomogeneities, non-uniformities, and forces acting on boundaries. New complex wave solutions in two different categories are proposed: implicit and elliptic (or periodic or hyperbolic) forms are obtained for this model via the unified method. Indeed, the innovative wave solutions that were achieved and reported here are helpful for investigating optical communication applications as well as the transmission characteristics of light pulses.

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Shilin, Andrei P. "Hypersingular Integro-Differential Equation Containing Polynomials and Their Derivatives in Coefficients." Mathematics 11, no. 24 (December 12, 2023): 4940. http://dx.doi.org/10.3390/math11244940.

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A new linear integro-differential equation is considered on a closed curve located on the complex plane. The integrals in the equation are understood in the sense of a finite part, according to Hadamard. The order of the equation can be higher than one. The coefficients of the equation have a special structure. A characteristic of the coefficients is that they contain two arbitrary polynomials and their derivatives. Solvability conditions are explicitly stated. Whenever they are satisfied, an exact analytical solution is given. Generalized Sokhotsky formulas, the theory of Riemann boundary value problems, methods for solving linear differential equations, and the properties of analytic functions of a complex variable are used. An example is given.

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Peng, Li-Juan. "Dynamics investigation on a Kadomtsev–Petviashvili equation with variable coefficients." Open Physics 20, no. 1 (January 1, 2022): 1041–47. http://dx.doi.org/10.1515/phys-2022-0207.

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Abstract In this work, we investigate a generalized Kadomtsev–Petviashvili equation with variable coefficients and self-consistent sources in plasma and fluid mechanics. The multiple rogue wave solutions, including 1-, 3-, and 6-order rogue waves, are presented by three different functions under a nonlinear transformation. Based on the Hirota bilinear method and a more complex assumption, new lump solutions are constructed, which have not been seen in other literature. The dynamic properties of the obtained results are illustrated graphically.

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PRASAD, K. S., C. ESWARAN, and A. ANTONIOU. "NEW FIRST-ORDER COMPLEX DIGITAL-FILTER SECTIONS AND THEIR APPLICATION FOR THE REALIZATION OF IIR FILTERS." Journal of Circuits, Systems and Computers 03, no. 03 (September 1993): 757–71. http://dx.doi.org/10.1142/s0218126693000459.

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New first-order complex digital-filter sections are realized using the concept of the generalized-immittance converter. These sections are then employed for the realization of infinite impulse response digital filters with real coefficients. The filters obtained with the proposed sections have sensitivity and roundoff noise properties that are comparable to those of other structures of this class reported earlier.

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Guo, Long-Chuan, and Xiang-Kun Fang. "Bounded Analysis and Practical Tracking Control of Complex Stochastic Nonlinear Systems with Unknown Control Coefficients." Complexity 2020 (February 13, 2020): 1–8. http://dx.doi.org/10.1155/2020/1502065.

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This paper mainly focuses on the output practical tracking controller design for a class of complex stochastic nonlinear systems with unknown control coefficients. In the existing research results, most of the complex systems are controlled in a certain direction, which leads to the disconnection between theoretical results and practical applications. The authors introduce unknown control coefficients, and the values of the upper and lower bounds of the control coefficients are generalized by constants to allow arbitrary values to be arbitrarily large or arbitrarily small. In the control design program, the design problem of the controller is transformed into a parameter construction problem by introducing appropriate coordinate transformation. Moreover, we construct an output feedback practical tracking controller based on the dynamic and static phase combined by Ito stochastic differential theory and selection of appropriate design parameters, ensuring that the system tracking error can be made arbitrarily small after some large enough time. Finally, a simulation example is provided to illustrate the efficiency of the theoretical results.

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You, Guo Qiang, and Ying Bai Xie. "Pretension Optimization Method for Complex Cablenet System." Applied Mechanics and Materials 574 (July 2014): 143–46. http://dx.doi.org/10.4028/www.scientific.net/amm.574.143.

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Based on balance matrix analysis method and considered the evenness of pretension distribution as objective function, a pretension optimization method is proposed for complex cablenet system of large span structure. In this method, the whole cablenet system is firstly divided into several groups according to its axial symmetry to simplify its balance matrix, and then balance matrix analysis method is used to analyze balance matrix of grouped cablenet system. Next, the corresponding optimum mathematic model for grouped cablenet system can be established with pretension solutions coefficients as design variables and evenness of pretension distribution as objective function. Finally, generalized reduced gradient algorithm is used to solve the optimum mathematic model of an example, and the result is satisfactory.

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Promyslova, A. S. "Solving the generalized Sturm-Liouville problem with complex coefficients by the method of accelerated convergence." Moscow University Mechanics Bulletin 63, no. 2 (April 2008): 47–49. http://dx.doi.org/10.3103/s0027133008020052.

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Oluwayemi, Matthew Olanrewaju, Esther O. Davids, and Adriana Cătaş. "On Geometric Properties of a Certain Analytic Function with Negative Coefficients." Fractal and Fractional 6, no. 3 (March 21, 2022): 172. http://dx.doi.org/10.3390/fractalfract6030172.

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Various function theorists have successfully defined and investigated different kinds of analytic functions. The applications of such functions have played significant roles in geometry function theory as a field of complex analysis. In this work, therefore, a certain subclass of univalent analytic functions of the form f(z)=z−∑m=2t[ω(2+β)+cγ−σ]Cm[mσ−cω(2+β)+cγ]Knzm−∑k=t+1∞akzk is defined using a generalized differential operator. Furthermore, some geometric properties for the class were established.

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Shilin, Andrei P. "Hypersingular integro-differential equations with power factors in coefficients." Journal of the Belarusian State University. Mathematics and Informatics, no. 3 (November 29, 2019): 48–56. http://dx.doi.org/10.33581/2520-6508-2019-3-48-56.

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The linear hypersingular integro-differential equation of arbitrary order on a closed curve located on the complex plane is considered. A scheme is proposed to study this equation in the case when its coefficients have some particular structure. This scheme providers for the use of generalized Sokhotsky formulas, the solution of the Riemann boundary value problem and the solution in the class of analytical functions of linear differential equations. According to this scheme, the equations are explicitly solved, the coefficients of which contain power factors, so that along with the Riemann problem the arising differential equations are constructively solved. Solvability conditions, solution formulas, examples are given.

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Ja'afar Mohamad Jawad, Anwar J., Mahmood J. Abu-Al Shaeer, and Marko D. Petkovi_c. "New Soliton Solutions of the (2+1)-Dimensional System Davey-Stewartson Equation." International Journal of Engineering & Technology 7, no. 4.1 (September 12, 2018): 37. http://dx.doi.org/10.14419/ijet.v7i4.1.19489.

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In this paper, we derive several soliton solutions of the generalized Davey-Stewartson equation with the complex coefficients. First we use the travelling wave transformation to reduce the initial system to ODE. The equivalent ODE is then solved, giving several classes of solutions, depending on the values of the parameters. Finally, the Extended Tanh-Coth method and Modified simple equation method.

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Jovovic, Ivana. "Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system." Applicable Analysis and Discrete Mathematics, no. 00 (2020): 24. http://dx.doi.org/10.2298/aadm190627024j.

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In this paper we consider total reduction of the nonhomogeneous linear system of operator equations with constant coefficients and commuting operators. The totally reduced system obtained in this manner is completely decoupled. All equations of the system differ only in the variables and in the nonhomogeneous terms. The homogeneous parts are obtained using the generalized characteristic polynomial of the system matrix. We also indicate how this technique may be used to examine differential transcendence of the solution of the linear system of the differential equations with constant coefficients over the complex field and meromorphic free terms.

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WANG, XIONG, JUAN CHEN, JUN-AN LU, and GUANRONG CHEN. "A SIMPLE YET COMPLEX ONE-PARAMETER FAMILY OF GENERALIZED LORENZ-LIKE SYSTEMS." International Journal of Bifurcation and Chaos 22, no. 05 (May 2012): 1250116. http://dx.doi.org/10.1142/s0218127412501167.

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This paper reports the finding of a simple one-parameter family of three-dimensional quadratic autonomous chaotic systems. By tuning the only parameter, this system can continuously generate a variety of cascading Lorenz-like attractors, which appears to be richer than the unified chaotic system that contains the Lorenz and the Chen systems as its two extremes. Although this new family of chaotic systems has very rich and complex dynamics, it has a very simple algebraic structure with only two quadratic terms (same as the Lorenz and the Chen systems) and all nonzero coefficients in the linear part being -1 except one -0.1 (thus, simpler than the Lorenz and Chen systems). Surprisingly, although this new system belongs to the Lorenz-type of systems in the classification of the generalized Lorenz canonical form, it can generate not only Lorenz-like attractors but also Chen-like attractors. This suggests that there may exist some other unknown yet more essential algebraic characteristics for describing general three-dimensional quadratic autonomous chaotic systems.

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