Abstract: In this note, we derive existence and uniqueness results for backward stochastic Volterra integral equations with time delayed generators under non-Lipschitz condition. PubDate: Mon, 03 Jun 2019 12:37:24 +000

Abstract: In this article we will study the Riemann Stieltjes Laplace integral of vectorial functions in Fréchet spaces. Particularly we will prove a isometric theorem and a generation theorem for integrated semigroups on Fréchet spaces. PubDate: Mon, 03 Jun 2019 08:39:04 +000

Abstract: Journal of Mathematics Research wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.Many authors, regardless of whether Journal of Mathematics Research publishes their work, appreciate the helpful feedback provided by the reviewers.Reviewers for Volume 11, Number 3 Abdessadek Saib, University of Tebessa, AlgeriaArman Aghili, University of Guilan, IranCinzia Bisi, Ferrara University, ItalyGabriela Ciuperca, University Lyon 1, FranceGener Santiago Subia, NUeva Ecija University of Science and Technology, PhilippinesKong Liang, University of Illinois at Springfield, USAKuldeep Narain Mathur, University Utara Malaysia, MalaysiaMaria Alessandra Ragusa, University of Catania, ItalyRami Ahmad El, Athens Institute for Education and Research, GreeceRovshan Bandaliyev, National Academy of Sciences of Azerbaijan, AzerbaijanSanjib Kumar Datta, University of Kalyani, IndiaShenghua Ni, Vanderbilt University Medical Center, USASreedhara Rao Gunakala, The University of The West Indies, Trinidad and TobagoXiaofei Zhao, Texas A&M University, United StatesYaqin Feng, Ohio University, USAYifan Wang, University of Houston, USA Sophia WangOn behalf of,The Editorial Board of Journal of Mathematics ResearchCanadian Center of Science and Education PubDate: Mon, 03 Jun 2019 08:25:03 +000

Abstract: The entropy approach to a description of quantum processes, represented like the Markov chain, is elaborated. It is supposed that at an atomic scale the law of the conservation of entropy holds. From this principle issues the simple explanation of the different behavior of bosons and fermions in experiments with scattering particles, proved by Pauli. Introducing in consideration Markov’ chain, applied to a motion of particles, made possible to write an equation, determining the change of their states. This pure logical result, completed by physical laws, brought to a new equation, generalizing Schrödinger one. It includes electric and magnetic fields as well as the spin of particles. Analysis of its solution for a case of only electric field, led to the formula of tunnel effect. Consideration of the motion of a particle in magnetic field gave the fundamental expression of Lorentz force without any mention of electrodynamics. Addition of an angular momentum in the reasoning by including Hamiltonian, allowed deducing the result, which coincides with the spherically symmetric Schrödinger equation for hydrogen atom. In general case there is the system of equations. If the atom is put in a weak magnetic field, without a possibility of flipping, the classical formulas of Bohr radius orbits and Rydberg energy obtained. The property of intrinsic quantization of electron spin ħ/2 is explained easily as a solution of the proposed system. These equations do not repeat the known arguments only, but can predict the new phenomena. They describe the effect of spin depolarization of electrons in a strong magnetic field, earlier considered been related to vacuum polarization. The obtained solution gives its magnetic induction equal about 1012 Gs, that corresponds well with experimental data. PubDate: Thu, 30 May 2019 10:03:17 +000

Abstract: We propose an original mathematical model according to a Bayesian approach explaining uncertainty from a point of view connected with vector spaces. A parameter space can be represented by means of random quantities by accepting the principles of the theory of concordance into the domain of subjective probability. We observe that metric properties of the notion of $\alpha$-product mathematically fulfill the ones of a coherent prevision of a bivariate random quantity. We introduce fundamental metric expressions connected with transformed random quantities representing changes of origin. We obtain a posterior probability law by applying the Bayes' theorem into a geometric context connected with a two-dimensional parameter space. PubDate: Thu, 30 May 2019 09:50:37 +000

Abstract: The Brent-McMillan algorithm is the fastest known procedure for the high-precision computation of Euler’s constant γ and is based on the modified Bessel functions I_0(2x) and K_0(2x). An error estimate for this algorithm relies on the optimally truncated asymptotic expansion for the product I_0(2x)K_0(2x) when x assumes large positive integer values. An asymptotic expansion for this optimal error term is derived by exploiting the techniques developed in hyperasymptotics, thereby enabling more precise information on the error term than recently obtained bounds and estimates. PubDate: Wed, 22 May 2019 02:59:42 +000

Abstract: This paper has completed main fields of making dialectical logic pure mathematically, it is involved both atomic proposition and 1-order predicate function for dialectical logic, and by state-dual, true-valued function vector, state-contradiction law into basic logic law. In addition, also defines true-valued function for logic operators so that more easy to represent atomic proposition. Some examples are given and shown that Boolean algebra, as a special case of dialectical logic, is how to operate hybridize-able with dialectical logic. PubDate: Mon, 13 May 2019 09:24:25 +000

Abstract: A class of stochastic dynamical systems with strong damped stochastic higher order Kirchhoff equation solutions with white noise is studied. Firstly, the equation is transformed into a stochastic equation with random variables as parameters and without noise by using Ornstein-Uhlenbeck process. Secondly, the bounded stochastic absorption set is obtained by estimating the solution of the equation. Finally, the stochastic dynamical system is obtained by using the isomorphic mapping method and the compact embedding theorem. It is progressively compact, thus proving the existence of random attractors. PubDate: Thu, 09 May 2019 03:05:26 +000

Abstract: In this article we will consider third order homogeneous diﬀerential equations: L(y)=y'''+a_1y'+a_0y(a_0,a_1 ∈k) whose Galois group G（L） is imprimitive. This case is characterised by the fact that the third symmetric power equation L ^ⓢ3(y)=0 has an exponential solution whose square is rational (Singer & Ulmer 1993). If L(y)=0 has a Liouvillian solution z whose logarithmic derivative u=z'/z is algebraic over a differential field (k,') ,we will give an algorithm to find the relation between a_0, a_1 , the semi-invariant S=Y_1Y_2Y_3 which is unique up to multiplication by a constant, the coefficients C_0, C_1 of the minimal polynomial P(u) of u and their derivatives. The aim of this work is to diminutize the number of constants C_m stated in the algorithm of Singer & Ulmer (Singer & Ulmer 1993 Algorithm p. 31) whose determination is not easy to do, and we will achieve this by using Groebner Basis. PubDate: Thu, 09 May 2019 02:57:19 +000