American Journal of Computational Mathematics

Journal Information
ISSN / EISSN : 2161-1203 / 2161-1211
Published by: Scientific Research Publishing, Inc. (10.4236)
Total articles ≅ 396
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Latest articles in this journal

Gastón Vergara-Hermosilla
American Journal of Computational Mathematics, Volume 11, pp 31-41; doi:10.4236/ajcm.2021.111003

Abstract:
In this work we develop necessary and sufficient conditions for describing the family of anti-Hurwitz polynomials, introduced by Vergara-Hermosilla et al. in [1]. Specifically, we studied a dual version of the Theorem of Routh-Hurwitz and present explicit criteria for polynomials of low order and derivatives. Another contribution of this work is establishing a dual version of the Hermite-Biehler Theorem. To this aim, we give extensions of the boundary crossing Theorems and a zero exclusion principle for anti-Hurwitz polynomials.
Haiduke Sarafian
American Journal of Computational Mathematics, Volume 11, pp 71-82; doi:10.4236/ajcm.2021.112007

Abstract:
We consider the motion of a massive point-like projectile thrown with initial velocity with respect to horizontal in a two-dimensional vertical plane under the influence of gravity in a viscose media. Two different velocity-dependent resistive media models are considered—linear and quadratic. With an objective to utilizing a Computer Algebra System (CAS), specifically Mathematica [1] numerically we solve the corresponding equations of motions. For a set of compatible parameters characterizing viscose forces graphically we display comparing the trajectories explicitly showing the impact of the models. Utilizing the model-dependent trajectory equations numerically we evaluate their associated arc-lengths. What distinguishes our approach vs. the existing body of work is the notion of the “reverse engineering”. Meaning, utilizing our numeric data we establish their corresponding analytic counter parts. Ultimately, utilizing both outputs numerically and analytically we determine the matching initial projectile angles maximizing their respective arc-lengths.
Bin Li
American Journal of Computational Mathematics, Volume 11, pp 175-188; doi:10.4236/ajcm.2021.112012

Abstract:
The main purpose of verifiable secret sharing scheme is to solve the honesty problem of participants. In this paper, the concept of nonzero k-submatrix and theresidual vector of system of hyperplane intersecting line equations is proposed. Based on certain projective transformations in projective space, a verifiable (t, n)-threshold secret sharing scheme is designed by using the structure of solutions of linear equations and the difficulty of solving discrete logarithm problems. The results show that this scheme can verify the correctness of the subkey provided by each participant before the reconstruction of the master key, and can effectively identify the fraudster. The fraudster can only cheat by guessing and the probability of success is only 1/p. The design of the scheme is exquisite and the calculation complexity is small. Each participant only needs to hold a subkey, which is convenient for management and use. The analysis shows that the scheme in this paper meets the security requirements and rules of secret sharing, and it is a computationally secure and effective scheme with good practical value.
Yuelong Tang
American Journal of Computational Mathematics, Volume 11, pp 53-63; doi:10.4236/ajcm.2021.111005

Abstract:
In this paper, we consider a fully discrete finite element approximation for time fractional optimal control problems. The state and adjoint state are approximated by triangular linear fi nite elements in space and L1 scheme in time. The control is obtained by the variational discretization technique. The main purpose of this work is to derive the convergence and superconvergence. A numerical example is presented to validate our theoretical results.
Yoshihiro Tanaka, Mitsuru Togashi
American Journal of Computational Mathematics, Volume 11, pp 23-30; doi:10.4236/ajcm.2021.111002

Abstract:
There are a few studies that focus on solution methods for finding a Nash equilibrium of zero-sum games. We discuss the use of Karmarkar’s interior point method to solve the Nash equilibrium problems of a zero-sum game, and prove that it is theoretically a polynomial time algorithm. We implement the Karmarkar method, and a preliminary computational result shows that it performs well for zero-sum games. We also mention an affine scaling method that would help us compute Nash equilibria of general zero-sum games effectively.
Haiduke Sarafian
American Journal of Computational Mathematics, Volume 11, pp 42-52; doi:10.4236/ajcm.2021.111004

Abstract:
In search of nonlinear oscillations, we envision a 3D elliptic curva-ture-dependent nonuniform charge distribution to creating an electric field along the symmetry axis causing a massive point-like charged particle placed on the symmetry axis to oscillate in a delayed/hesitant nonlinear mode. The charge distribution is a 3D twisted line creating nontrivial electric field causing an unexpected oscillation that is non-orthodox defying the common sense. Calculation of this research flavored investigation is entirely based on utilities accompanied with Computer Algebra Systems (CAS) especially Mathematic [1]. The characteristics of the delayed oscillations in addition to embodying classic graphics displaying the time-dependent kinematic quantities are augmented including various phase diagrams signifying the nonlinear oscillations. The output of our investigation is compared to nonlinear non-delayed oscillations revealing fresh insight. For comprehensive understanding of the hesitant oscillator a simulation program is crafted clarifying visually the scenario on hand.
Xiaojie Zheng
American Journal of Computational Mathematics, Volume 11, pp 83-93; doi:10.4236/ajcm.2021.112008

Abstract:
In theorem LP [1], Liu proves the theorem when N = 2, but it can’t be ex-tended to the general case in his proof. So we consider the condition that the families of holomorphic curves share eleven hyperplanes, and we get the theorem 1.1.
Abdul Mannan, R. Rahman, Halima Akter, Nazmun Nahar, Samiran Mondal
American Journal of Computational Mathematics, Volume 11, pp 157-174; doi:10.4236/ajcm.2021.112011

Abstract:
This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed point theory is a beautiful mixture of Mathematical analysis to explain some conditions in which maps give excellent solutions. Here later many mathematicians used this fixed point theory to establish their results, see for instance, Picard-Lindel of Theorem, The Picard theorem, Implicit function theorem etc. Also, we developed ideas that many of known fixed point theorems can easily be derived from the Banach theorem. It extends some recent works on the extension of Banach contraction principle to metric space with norm spaces.
Haiduke Sarafian
American Journal of Computational Mathematics, Volume 11, pp 64-69; doi:10.4236/ajcm.2021.111006

Abstract:
It is customary to apply Newton’s cooling as the standard model investigating the temperature profile of a hot substance exposed to a cool ambient. The rate of change of temperature in Newton’s model is simplistically related to linear-temperature difference of the two e.g. [1]. In our research flavored investigation, we consider a fresh model, cooling that depends to the difference of temperature-squared conducive to similar results. Utilizing a Computer Algebra System (CAS), especially Mathematica [2] we show the equivalency of the two.
Vardges Melkonian
American Journal of Computational Mathematics, Volume 11, pp 1-22; doi:10.4236/ajcm.2021.111001

Abstract:
In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of company employees as an effective way to curb the spread, and use integer programming techniques to model it. The goal of the model is to maximize the number of direct interactions between employees who are essential for company’s work subject to the constraint that all employees should be partitioned into components of no more than a certain size implied by the regulations. Then we further develop the basic model to take into account different restrictions and provisions. We also give heuristics for solving the problem. Our computational results include sensitivity analysis on some of the models and analysis of the heuristic performance.
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