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Journal articles on the topic 'Complex Function of One Variable'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

Chambers, Ll G., Robert E. Greene, and Steven G. Krantz. "Function Theory of One Complex Variable." Mathematical Gazette 82, no. 494 (1998): 347. http://dx.doi.org/10.2307/3620457.

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2

Hayman, W. K., Yusaku Komatu, Kiyoshi Niino, and Chung-Chun Yang. "Analytic Function Theory of One Complex Variable." Mathematical Gazette 74, no. 470 (1990): 413. http://dx.doi.org/10.2307/3618181.

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3

Whitley, R. J., and T. V. Hromadka. "Approximating harmonic functions onRn with one function of a single complex variable." Numerical Methods for Partial Differential Equations 21, no. 5 (2005): 905–17. http://dx.doi.org/10.1002/num.20067.

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Yusephus, Decupertino Sumanto, Hariyanto Susilo, and Adilla Jazmeen. "Analysis of the Mean Value Theorem and Rolle's Theorem in Holomorphic Function." International Journal of Mathematics and Computer Research 13, no. 06 (2025): 5316–26. https://doi.org/10.5281/zenodo.15598612.

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The Mean Value Theorem and Rolle’s Theorem are one of the fundamental concepts in real analytical mathematics related to the derivative value of functions. This research examines both theorems on holomorphic functions in the complex plane. Holomorphic functions are also known as analytic functions, which are complex functions of one variable that have derivatives at every point in their domain. The results of the analysis show that there are fundamental differences in the application of the two theorems to holomorphic functions which can be seen in terms of  the separation real and

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Dellnitz, Michael, Oliver Schütze, and Qinghua Zheng. "Locating all the zeros of an analytic function in one complex variable." Journal of Computational and Applied Mathematics 138, no. 2 (2002): 325–33. http://dx.doi.org/10.1016/s0377-0427(01)00371-5.

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VİJAY and A. K. B. CHAND. "Zipper Fractal Functions with Variable Scalings." Advances in the Theory of Nonlinear Analysis and its Application 6, no. 4 (2022): 481–501. http://dx.doi.org/10.31197/atnaa.1149689.

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Zipper fractal interpolation function (ZFIF) is a generalization of fractal interpolation function through an improved version of iterated function system by using a binary parameter called a signature. The signature allows the horizontal scalings to be negative. ZFIFs have a complex geometric structure, and they can be non-differentiable on a dense subset of an interval I. In this paper, we construct k-times continuously differentiable ZFIFs with variable scaling functions on I. Some properties like the positivity, monotonicity, and convexity of a zipper fractal

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Koo, Ja Kyung. "On holomorphic differentials of some algebraic function field of one variable over C." Bulletin of the Australian Mathematical Society 43, no. 3 (1991): 399–405. http://dx.doi.org/10.1017/s0004972700029245.

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Dzagnidze, O. "Allied Integrals, Functions, and Series for the Unit Sphere." gmj 5, no. 3 (1998): 213–32. http://dx.doi.org/10.1515/gmj.1998.213.

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Abstract Among the functions defined on the two-dimensional unit sphere we distinguish functions generalizing the conjugate integral, the conjugate function, and the conjugate series which depend on one variable. We establish the properties of these functions whose structures essentially differ from those of integrals, functions, and series based on the theory of analytic functions of two complex variables.

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HU, PEI-CHU, and CHUNG-CHUN YANG. "THE TUMURA–CLUNIE THEOREM IN SEVERAL COMPLEX VARIABLES." Bulletin of the Australian Mathematical Society 90, no. 3 (2014): 444–56. http://dx.doi.org/10.1017/s0004972714000446.

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AbstractIt is a well-known result that if a nonconstant meromorphic function $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}f$ on $\mathbb{C}$ and its $l$th derivative $f^{(l)}$ have no zeros for some $l\geq 2$, then $f$ is of the form $f(z)=\exp (Az+B)$ or $f(z)=(Az+B)^{-n}$ for some constants $A$, $B$. We extend this result to meromorphic functions of several variables, by first extending the classic Tumura–Clunie theorem for m

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Zhou, Jun, and Zhaoxia Duan. "Partial and Local Argument Properties of Holomorphic and Meromorphic Complex Functions in Several Variables." Mathematical Problems in Engineering 2019 (August 6, 2019): 1–10. http://dx.doi.org/10.1155/2019/7971495.

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The study describes a general argument analysis technique for holomorphic and meromorphic complex functions in several variables, or simply n-variable complex functions with n≥2. Argument analytic relationships for n-variable complex functions with significance similar to the argument principle for one-variable ones are retrieved partially and locally. More precisely, argument analysis in n-variable complex functions is carried out one-by-one in terms of each and all variables, namely, partially, so that argument-principle-like relations are established in poly-disc neighborhoods of the variab

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11

Wang, Xiling. "Transition from complex numbers to complex function and series." Highlights in Science, Engineering and Technology 38 (March 16, 2023): 107–12. http://dx.doi.org/10.54097/hset.v38i.5771.

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Complex analysis, traditionally known as the theory of functions of a complex variable, is a branch of mathematical analysis that investigates functions of complex numbers. If n is odd, there is only one order n root, and if n is even, there are only two order n roots. Things change in complex numbers, though. Keep in mind that complex numbers have closed algebra. As a result, there exist n roots of order n always.Dating back to the 16th century when Italian mathematicians Girolamo Cardano and Raphael Bombelli first observed complex numbers when they were trying to solve a certain algebra and

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12

Deng, Yajie, Chao Liu, Miaojuan Peng, and Yumin Cheng. "The Interpolating Complex Variable Element-Free Galerkin Method for Temperature Field Problems." International Journal of Applied Mechanics 07, no. 02 (2015): 1550017. http://dx.doi.org/10.1142/s1758825115500179.

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In this paper, an interpolating complex variable moving least-squares (ICVMLS) method is presented. In the ICVMLS method, the trial function of a two-dimensional problem is formed with a one-dimensional basis function, and the shape function of the ICVMLS method satisfies the property of Kronecker δ function. The ICVMLS method has greater computational efficiency than the moving least-squares (MLS) approximation. Then combining the ICVMLS method with the Galerkin weak form of temperature field problems, an interpolating complex variable element-free Galerkin (ICVEFG) method is proposed. In the

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Meana, Jorge Jiménez. "Asymptotic developments of analytic functions in cones." Asymptotic Analysis 26, no. 3-4 (2001): 239–56. https://doi.org/10.3233/asy-2001-446.

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In this paper we give a definition of asymptotic development of an analytic function of several complex variables. So far, there existed two different definitions which are joined by the definition given in this paper. This definition generalizes, in a natural sense, the one given for one variable. The generalization is made by changing the object polysector by a conoidal domain which is more general because all the polysectors are conoidal domains but not all the conoidal domains are polysectors. It is given a characterization of the analytic functions that admit asymptotic developments in a

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Almutairi, Ohud Bulayhan, and Muhammad Amer Latif. "Two-variable Trapezoidal Types Inequalites in Banach Spaces." European Journal of Pure and Applied Mathematics 18, no. 1 (2025): 5613. https://doi.org/10.29020/nybg.ejpam.v18i1.5613.

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This study presents weighted trapezoidal-type inequalities for the product of two functions. While one function takes its values in the Banach spaces, the other takes values in the complex plane. We employed the technique of integration by parts for Bochner integrals for functions of two variables, along with principles of analysis for functions taking values in the productof Banach spaces, to report our findings. In addition to the extension of previous studies on functions of a single variable, our work generalizes results reported in Dragomir for two functions whose product of their variabl

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Khirivskyi, Roman, Liudmyla Petryshyn, Tymofii Pasichnyk, Oksana Brukh, Iryna Bernatska, and Lesia Kucher. "Assessment and Forecast of the Efficiency of Use of the Financial Resources of Amalgamated Territorial Communities in the Context of European Integration." European Journal of Sustainable Development 9, no. 3 (2020): 607. http://dx.doi.org/10.14207/ejsd.2020.v9n3p607.

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The task of forecasting in economics is fulfilled by developing a variety of econometric models. The complexity of actual relations between the economic indices requires improvement of the existing and creation of new methods of modeling. That diversity is limited by the current set of elementary mathematical functions, whereas some of them cannot be applied in economics. At the beginning of the 21st century, it was proposed to use the functions of complex variable in economics. Due to their properties, which differ from the functions of real variables, they describe relations between the econ

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Chen, Bofan. "Fundamental theorems in Complex analysis." Journal of Physics: Conference Series 2381, no. 1 (2022): 012056. http://dx.doi.org/10.1088/1742-6596/2381/1/012056.

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Abstract This article will first introduce the conception of complex numbers and then deal with some famous results in complex numbers. In the beginning, we prove the Cauchy-Goursat theorem and calculate the integral along a closed path in a domain on which the given function is analytic. We want to check the relation between a function being analytic, having primitive, and its integral along a closed path equals zero. In conclusion, for a given analytic function on a simply connected domain, integral along any closed path is zero. Using this conclusion, we can prove the residue theorem and th

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17

Howison, S. D. "Complex variable methods in Hele–Shaw moving boundary problems." European Journal of Applied Mathematics 3, no. 3 (1992): 209–24. http://dx.doi.org/10.1017/s0956792500000802.

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We discuss the one-phase Hele–Shaw problem in two space dimensions. We review exact solutions in the zero-surface-tension case, giving a unified account of the Schwarz function and conformal mapping approaches. We discuss the extension of the former method to the cases in which surface tension or ‘kinetic undercooling’ terms apply on the moving boundary, and we give some conjectures on the resulting singularity structure. Finally, we give a new interpretation of the linear stability analysis of the zero-surface-tension problem, and we suggest a possible regularization of ill-posed problems by

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18

Matz, Florian, and Thomas-C. Jagau. "Molecular Auger decay rates from complex-variable coupled-cluster theory." Journal of Chemical Physics 156, no. 11 (2022): 114117. http://dx.doi.org/10.1063/5.0075646.

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The emission of an Auger electron is the predominant relaxation mechanism of core-vacant states in molecules composed of light nuclei. In this non-radiative decay process, one valence electron fills the core vacancy, while a second valence electron is emitted into the ionization continuum. Because of this coupling to the continuum, core-vacant states represent electronic resonances that can be tackled with standard quantum-chemical methods only if they are approximated as bound states, meaning that Auger decay is neglected. Here, we present an approach to compute Auger decay rates of core-vaca

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19

ROMÁN, P., and J. TIRAO. "SPHERICAL FUNCTIONS, THE COMPLEX HYPERBOLIC PLANE AND THE HYPERGEOMETRIC OPERATOR." International Journal of Mathematics 17, no. 10 (2006): 1151–73. http://dx.doi.org/10.1142/s0129167x06003886.

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In this paper, we determine all irreducible spherical functions Φ of any K-type associated to the dual Hermitian symmetric pairs (G, K) = ( SU (3), U (2)) and ( SU (2,1), U (2)). This is accomplished by associating to Φ a vector valued function H = H(u) of a real variable u, analytic at u = 0, which is a simultaneous eigenfunction of two second order differential operators with matrix coefficients. One of them comes from the Casimir operator of G and we prove that it is conjugated to a hypergeometric operator, allowing us to express the function H in terms of a matrix valued hypergeometric fun

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20

Trishin, V., and N. Trishina. "The Lorentz group and linear fractional transformations of the complex plane." Bulletin of State University of Education. Series: Physics and Mathematics, no. 3 (January 28, 2024): 57–69. https://doi.org/10.18384/2949-5067-2023-3-57-69.

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Aim. Demonstration of the relationship between the linear-fractional function, analyzed by students of technical universities in the course of complex function theory, and the Lorentz group, which students study in the course of theoretical physics. Methodology. Demonstration of the relationship between the fractional linear function, which is analyzed by students of technical universities in the course "Theory of Function of Complex Variable (TFCV)", and the Lorentz group, which students study in the course of theoretical physics. Results. The one-to-one correspondence between the classes of

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Kumar, Deepak, Janak Raj Sharma, and Ioannis K. Argyros. "Optimal One-Point Iterative Function Free from Derivatives for Multiple Roots." Mathematics 8, no. 5 (2020): 709. http://dx.doi.org/10.3390/math8050709.

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We suggest a derivative-free optimal method of second order which is a new version of a modification of Newton’s method for achieving the multiple zeros of nonlinear single variable functions. Iterative methods without derivatives for multiple zeros are not easy to obtain, and hence such methods are rare in literature. Inspired by this fact, we worked on a family of optimal second order derivative-free methods for multiple zeros that require only two function evaluations per iteration. The stability of the methods was validated through complex geometry by drawing basins of attraction. Moreover

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22

Solé, Laura, Daniel Sastre, Magalí Colomer-Molera, et al. "Functional Consequences of the Variable Stoichiometry of the Kv1.3-KCNE4 Complex." Cells 9, no. 5 (2020): 1128. http://dx.doi.org/10.3390/cells9051128.

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The voltage-gated potassium channel Kv1.3 plays a crucial role during the immune response. The channel forms oligomeric complexes by associating with several modulatory subunits. KCNE4, one of the five members of the KCNE family, binds to Kv1.3, altering channel activity and membrane expression. The association of KCNEs with Kv channels is the subject of numerous studies, and the stoichiometry of such associations has led to an ongoing debate. The number of KCNE4 subunits that can interact and modulate Kv1.3 is unknown. KCNE4 transfers important elements to the Kv1.3 channelosome that negative

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23

PENG, MIAOJUAN, PEI LIU, and YUMIN CHENG. "THE COMPLEX VARIABLE ELEMENT-FREE GALERKIN (CVEFG) METHOD FOR TWO-DIMENSIONAL ELASTICITY PROBLEMS." International Journal of Applied Mechanics 01, no. 02 (2009): 367–85. http://dx.doi.org/10.1142/s1758825109000162.

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Based on element-free Galerkin (EFG) method and the complex variable moving least-squares (CVMLS) approximation, the complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems is presented in this paper. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than in the trial function of moving least-squares (MLS) approximation, and we can thus select fewer nodes in the meshless method that is form

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Dayani, Zahra, Fatemeh Parastesh, Fahimeh Nazarimehr, et al. "Optimal time-varying coupling function can enhance synchronization in complex networks." Chaos: An Interdisciplinary Journal of Nonlinear Science 33, no. 3 (2023): 033139. http://dx.doi.org/10.1063/5.0142891.

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In this paper, we propose a time-varying coupling function that results in enhanced synchronization in complex networks of oscillators. The stability of synchronization can be analyzed by applying the master stability approach, which considers the largest Lyapunov exponent of the linearized variational equations as a function of the network eigenvalues as the master stability function. Here, it is assumed that the oscillators have diffusive single-variable coupling. All possible single-variable couplings are studied for each time interval, and the one with the smallest local Lyapunov exponent

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Svetunkov, Sergey G. "Short-Term Economic Forecasting by Complex-Valued Autoregressions." Economics of Contemporary Russia, no. 4 (December 29, 2021): 35–48. http://dx.doi.org/10.33293/1609-1442-2021-4(95)-35-48.

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One of the directions that can expand the instrumental base for modeling the economy is complex-valued economics – a section of economic and mathematical modeling devoted to the use of models and methods of the theory of the function of a complex variable in economics. The article discusses the possibility of short-term economic forecasting using autoregressive models of complex variables. A classification of possible modifications of complex-valued autoregressive models is given, and the main properties of each of the classes of these models are shown. One of the varieties of these complex-v

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Kumar, Akshay, and H. K. Rangavittal. "Genetic Algorithm Parameter Effect on 3D Truss Optimization with Discrete Variable." Advanced Journal of Graduate Research 5, no. 1 (2018): 61–70. http://dx.doi.org/10.21467/ajgr.5.1.61-70.

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The Genetic Algorithm is one of the advanced optimization techniques frequently used for solving complex problems in the research field, and there are plenty of parameters which affect the outcome of the GA. In this study, a 25-bar truss with the nonlinear constraint is chosen with the objective to minimize the mass and variables being the discrete area. For the same, GA parameter like Selection Function, Population Size, Crossover Function, and Creation Function are varied to find the best combination with minimum function evaluation. It is found that the Uniform selection gives the best resu

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Mohanty, P. M., M. Acharya, and B. P. Acharya. "Numerical evaluation of integrals of analytic functions of more than one complex variable." Applied Mathematical Sciences 8 (2014): 8655–60. http://dx.doi.org/10.12988/ams.2014.49717.

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Murdock, C. C., Krijn P. Paaijmans, Andrew S. Bell, et al. "Complex effects of temperature on mosquito immune function." Proceedings of the Royal Society B: Biological Sciences 279, no. 1741 (2012): 3357–66. http://dx.doi.org/10.1098/rspb.2012.0638.

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Over the last 20 years, ecological immunology has provided much insight into how environmental factors shape host immunity and host–parasite interactions. Currently, the application of this thinking to the study of mosquito immunology has been limited. Mechanistic investigations are nearly always conducted under one set of conditions, yet vectors and parasites associate in a variable world. We highlight how environmental temperature shapes cellular and humoral immune responses (melanization, phagocytosis and transcription of immune genes) in the malaria vector, Anopheles stephensi. Nitric oxid

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Makarchuk, O. "ASYMPTOTIC BEHAVIOR OF THE CHARACTERISTIC FUNCTION OF ONE DISTRIBUTION OF THE JESSEN-WINTNER TYPE." Bukovinian Mathematical Journal 11, no. 2 (2023): 173–82. http://dx.doi.org/10.31861/bmj2023.02.17.

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The paper considers a random variable, which is the sum of a pointwise convergent random power series with independent discretely distributed terms that take on integer values. The corresponding random variable is a random variable represented by an s-fraction with a redundant set of digits and is included in the set of distributions of the Jessen-Wintner type. The Lebesgue distribution function of a random variable represented by an s-fraction with a redundant set of digits contains only a discrete or absolutely continuous or singular component. Emphasis in the paper is on the study of the as

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Alhazmi, Sharifah E., M. A. Abdou, and M. Basseem. "The stresses components in position and time of weakened plate with two holes conformally mapped into a unit circle by a conformal mapping with complex constant coefficients." AIMS Mathematics 8, no. 5 (2023): 11095–112. http://dx.doi.org/10.3934/math.2023562.

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<abstract> <p>In this paper, an infinite elastic plate weakened by two holes are considered and the complex variable method is used to derive a closed form of Gaursat functions for the first and second fundamental problems with variant time. The holes, in all previous works, are conformally mapped outside the unit circle without time. Here, the two holes are conformally mapped into the unit circle $ \varpi $ in the effect of time by the generalized rational mapping function with complex constant coefficients. By using this conformal mapping function, the fundamental problems transf

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31

Bondar, V. S., D. R. Abashev, and D. Yu Fomin. "COMPARATIVE ANALYSIS OF PLASTICITY THEORIES UNDER COMPLEX LOADING." Problems of Strength and Plasticity 84, no. 4 (2022): 493–510. http://dx.doi.org/10.32326/1814-9146-2022-84-4-493-510.

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Variants of theories of plastic flow under combined hardening, widely used in practical calculations of structures, are considered. A comparative analysis of the variants of theories under complex loading along plane and spatial deformation trajectories is carried out, covering a wide range of trajectories from multi-link polylines to curved trajectories of variable curvature and torsion. Trajectories from medium to large curvature and torsion are considered. The analysis of the research results is carried out in the vector space of A.A. Ilyushin. The plane trajectories of deformations in the

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Shamoyan, R. F., and E. B. Tomashevskaya. "On Bergman type projections in bounded strongly pseudoconvex domains." ADYGHE INTERNATIONAL SCIENTIFIC JOURNAL 23, no. 2 (2023): 18–26. http://dx.doi.org/10.47928/1726-9946-2023-23-2-18-26.

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In our note we prove the boundedness of Bergman type projections in two different spaces of analytic functions with mixed norm in general bounded strongly pseudoconvex domains with smooth boundary.The first class of analytic functions was studied previously by many authors,the second function space hovewer is completely new. Our proofs are based on standard known estimates of function space theory in bounded strongly pseudoconvex domains with smooth boundary and on some known estimates of Bergman kernel in such type domains. These estimates are also well- known in the unit disk.This allows us

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Goncharov, Valery I., Vadim A. Onufriev, and Ekaterina S. Perebeynosova. "The Device for Control Objects Identification: Getting Temporal Dynamic Characteristics." Advanced Materials Research 1006-1007 (August 2014): 631–38. http://dx.doi.org/10.4028/www.scientific.net/amr.1006-1007.631.

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The authors consider the problem of numerical inversion of Laplace transform using its values of the Laplace-image defined on the positive real half-axis of the complex plane. The main distinction of the proposed path associated with the method of forming these values. This path is based on a special case of the direct formula of the Laplace transform, when complex variable degenerates into a real variable. As a result, they continue getting image-function, but these functions have an important feature for numerical problems – they have a real argument. The presence of a continuous-time functi

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CHENG, YUMIN, JIANFEI WANG, and RONGXIN LI. "THE COMPLEX VARIABLE ELEMENT-FREE GALERKIN (CVEFG) METHOD FOR TWO-DIMENSIONAL ELASTODYNAMICS PROBLEMS." International Journal of Applied Mechanics 04, no. 04 (2012): 1250042. http://dx.doi.org/10.1142/s1758825112500421.

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The complex variable moving least-squares (CVMLS) approximation is discussed in this paper, and the mathematical and physical meaning of the complex functional in the CVMLS approximation is presented. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. Then combining the CVMLS approximation and the Galerkin weak form, we investigate the complex variable element-free Galerkin (CVEFG) method for two-dimensional elastodynamics problems. The penalty method is used to apply the essential boundary conditions, and the implicit

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Dubnitskiy, Valeriy, Anatolii Kobylin, Oleg Kobylin, Yuriy Kushneruk, and Iurii Sheviakov. "Calculation of the value of the functions of the complex variable with by an interval argument, we will design in the hyperbolic form." Advanced Information Systems 6, no. 3 (2022): 83–91. http://dx.doi.org/10.20998/2522-9052.2022.3.11.

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Information about the interval numbers presented in the classical form, the CENTER-RADIUS system and in the hyperbolic form is given. Rules for the transition from one of the forms of representation of interval numbers to others are proposed. Information is given on complex interval numbers, the real and imaginary parts of which are presented in hyperbolic form. The rules for performing basic arithmetic operations with these numbers and the calculation of interval values of power, exponential, logarithmic functions, direct and inverse trigonometric functions, direct and inverse hyperbolic func

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Pan, Xuhan. "Some Fundamental Results from Complex Analysis." Theoretical and Natural Science 1, no. 1 (2022): 10–19. http://dx.doi.org/10.54254/tns.2022003.

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This paper is going to introduce the most basic theory of analytic functions of one complex variable. It begins at the discussion of meaning of complex number and the historical development from the formula of cubic equation to the square root of negative number. In the middle section, which is divided in to four small parts. First part states the expression of complex number z, algebraic properties, and the relationship of each single complex number with whole complex plane. Second part concerns about several elementary functions of complex number. Next part relates to the derivative of compl

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Pan, Xuhan. "Some Fundamental Results from Complex Analysis." Theoretical and Natural Science 2, no. 1 (2023): 204–13. http://dx.doi.org/10.54254/2753-8818/2/20220084.

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This paper is going to introduce the most basic theory of analytic functions of one complex variable. It begins at the discussion of meaning of complex number and the historical development from the formula of cubic equation to the square root of negative number. In the middle section, which is divided in to four small parts. First part states the expression of complex number z, algebraic properties, and the relationship of each single complex number with whole complex plane. Second part concerns about several elementary functions of complex number. Next part relates to the derivative of compl

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Withers, W. Douglas. "Differentiability with respect to parameters of average values in probabilistic contracting dynamical systems." Ergodic Theory and Dynamical Systems 10, no. 3 (1990): 599–610. http://dx.doi.org/10.1017/s0143385700005769.

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AbstractWe consider a dynamical system consisting of a compact subset of RN or CN with several contracting maps chosen with prescribed probabilities, which may depend on position. We show that if the maps and the probabilities are Cl+α functions of the spatial variable and an external parameter, then the average value of a Cl+α function is a differentiate function of the parameter. One implication of this theorem is that for certain families of complex functions dependent on a parameter the reciprocal of the dimension of an invariant measure on the Julia set is a harmonic function of the param

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Liu, Guan Ting, and Li Ying Yang. "Interaction among n Parallel Dislocations in One-Dimensional Hexagonal Quasicrystals." Applied Mechanics and Materials 775 (July 2015): 133–37. http://dx.doi.org/10.4028/www.scientific.net/amm.775.133.

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By means of analytic function theory, the problems of interaction amongparallel dislocations in one-dimensional hexagonal quasicrystals are investigated. The interaction force of parallel dislocations in the material is obtained in forms of complex variable function firstly, which is the versions of well-known Peach-Koehler formula in one-dimensional hexagonal quasicrystals on parallel dislocations. These results are development of the corresponding parts of quasicrystals. Meanwhile, in this paper, we firstly give the equivalent action point of parallel dislocations in one-dimensional hexagona

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TAKATAMA, Isao. "211 From irrotational-potential flow to rotational-nonpotential one(Part 1) : Study based on function of a complex variable." Proceedings of Conference of Hokuriku-Shinetsu Branch 2007.44 (2007): 63–64. http://dx.doi.org/10.1299/jsmehs.2007.44.63.

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Rouba, Ya A., K. A. Smatrytski, and Ya V. Dirvuk. "On one interpolating rational process of Fejer – Hermite." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 3 (2020): 263–74. http://dx.doi.org/10.29235/1561-2430-2020-56-3-263-274.

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In this paper, a new approach to the definition of the interpolating rational process of Fejer – Hermite with first-type Chebyshev – Markov nodes on a segment is studied and some of its approximating properties are described. In the introduction a brief analysis of the results on the topic of the research is carried out. Herein, the methods of the construction of interpolating processes, in particular, Fejer – Hermite processes, in the polynomial and rational approximation are analysed. A new method to determine the interpolating rational Fejer – Hermite process is proposed. One of the main re

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ALMIRA, J. M., and KH F. ABU-HELAIEL. "On Montel’s theorem in several variables." Carpathian Journal of Mathematics 31, no. 1 (2015): 1–10. http://dx.doi.org/10.37193/cjm.2015.01.01.

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Recently, the first author of this paper, used the structure of finite dimensional translation invariant subspaces of C(R, C) to give a new proof of classical Montel’s theorem, about continuous solutions of Frechet’s functional equation ∆m h f = 0, for real functions (and complex functions) of one real variable. In this paper we use similar ideas to prove a Montel’s type theorem for the case of complex valued functions defined over the discrete group Z d. Furthermore, we also state and demonstrate an improved version of Montel’s Theorem for complex functions of several real variables and compl

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MARSHALL, DELMAR, and J. C. SPROTT. "SIMPLE CONSERVATIVE, AUTONOMOUS, SECOND-ORDER CHAOTIC COMPLEX VARIABLE SYSTEMS." International Journal of Bifurcation and Chaos 20, no. 03 (2010): 697–702. http://dx.doi.org/10.1142/s0218127410025983.

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It is shown that, for analytic functions f, systems of the form [Formula: see text] and [Formula: see text] cannot produce chaos; and that systems of the form [Formula: see text] and [Formula: see text] are conservative. Eight simple chaotic systems of the form [Formula: see text] with quadratic and cubic polynomial f(z, z*) are given. Lyapunov spectra are calculated, and the systems' phase space trajectories are displayed. For each system, a Hamiltonian is given, if one exists.

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GHILONI, RICCARDO, VALTER MORETTI, and ALESSANDRO PEROTTI. "CONTINUOUS SLICE FUNCTIONAL CALCULUS IN QUATERNIONIC HILBERT SPACES." Reviews in Mathematical Physics 25, no. 04 (2013): 1350006. http://dx.doi.org/10.1142/s0129055x13500062.

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The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable.

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Hernández, Jordy Alexander, Efrén Fernández, and Hugo Torres. "Electric Vehicle NiMH Battery State of Charge Estimation Using Artificial Neural Networks of Backpropagation and Radial Basis." World Electric Vehicle Journal 14, no. 11 (2023): 312. http://dx.doi.org/10.3390/wevj14110312.

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The state of charge of a battery depends on many magnitudes, but only voltage and intensity are included in mathematical equations because other variables are complex to integrate into. The contribution of this work was to obtain a model to determine the state of charge with these complex variables. This method was developed considering four models, the multilayer feed-forward backpropagation models of two and three input variables used supervised training, with the variable-learning-rate backpropagation training function, five and seven neurons in the hidden layer, respectively, achieving an

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Neumerzhitskaia, N., S. Uglich, and T. Volosatova. "Sufficient conditions for the uniqueness of the maxima of the optimization problem in the framework of a stochastic model with priorities depending on one random variable." E3S Web of Conferences 224 (2020): 01014. http://dx.doi.org/10.1051/e3sconf/202022401014.

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An objective function arising in the optimization problem of a quasilinear complex system with dependent priorities is considered. In the case of three priorities based on the results of one experiment, sufficient conditions are obtained for all stationary points of the objective function under consideration to be local maximum points.

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Mahmoud, Emad E., and Fatimah S. Abood. "A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization." Complexity 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/3848953.

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Another chaotic nonlinear Lü model with complex factors is covered here. We can build this riotous complex system when we add a complex nonlinear term to the third condition of the complex Lü system and think of it as if every one of the factors is mind boggling or complex. This system in real adaptation is a 6-dimensional continuous autonomous chaotic system. Different types of chaotic complex Lü system are developed. Also, another sort of synchronization is presented by us which is simple for anybody to ponder for the chaotic complex nonlinear system. This sort might be called a complex anti

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Şahin, Hasan, and İsmet Yildiz. "Determination of some properties of starlike and close-to-convex functions according to subordinate conditions with convexity of a certain analytic function." Ukrains’kyi Matematychnyi Zhurnal 75, no. 7 (2023): 995–1008. http://dx.doi.org/10.37863/umzh.v75i7.7214.

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UDC 517.5 Investigation of the theory of complex functions is one of the most fascinating aspects of theory of complex analytic functions of one variable. It has a huge impact on all areas of mathematics. Many mathematical concepts are explained when viewed through the theory of complex functions. Let f ( z ) ∈ A , f ( z ) = z + ∑ n ≥ 2 ∞ a n z n , be an analytic function in the open unit disc normalized by f ( 0 ) = 0 and f ' ( 0 ) = 1. For close-to-convex and starlike functions, new and different conditions are obtained by using subordination properties, where r is a positive integer of orde

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Bandura, A. I., T. M. Salo, and O. B. Skaskiv. "Composition of entire function and analytic functions in the unit ball with a vanished gradient." Matematychni Studii 62, no. 2 (2024): 132–40. https://doi.org/10.30970/ms.62.2.132-140.

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The composition $H(z)=f(\Phi(z))$ is studied,where $f$ is an entire function of a single complex variable and $\Phi$ is an analytic function in the $n$-dimensional unit ball with a vanished gradient.We found conditions by the function $\Phi$ providing boundedness of the $\mathbf{L}$-index in joint variables for the function $H$, if the function $f$ has bounded $l$-index for some positive continuous function $l$and $\mathbf{L}(z)= l(\Phi(z))(\max\{1,|\Phi_{z_1}'(z)|\},\ldots, \max\{1,|\Phi_{z_n}'(z)|\}),$ $z\in\mathbb{B}^n.$ Such a constructed function $\mathbf{L}$ allows us to consider a funct

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Iguchi, Kazumoto. "How Does Lagrange's Theorem Solve Thermodynamics of a Multispecies Quasiparticle Gas with Mutual Fractional Exclusion Statistics?" Modern Physics Letters B 12, no. 05 (1998): 163–71. http://dx.doi.org/10.1142/s0217984998000226.

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Lagrange's theorem for one complex variable functions is generalized to that for multi-complex variable functions, and applied to obtaining thermodynamics and generalized cluster expansions for a multispecies quasiparticle gas with mutual fractional exclusion statistics.

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