The Limit Distribution of Stochastic Evolution Equations Driven by-Stable Non-Gaussian Noise

We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.

Corresponding Prime Number Distribution Equation

The conjecture of twin prime numbers is a mathematical problem. Proving the twin prime conjecture using traditional modern number theory is extremely profound and complex. We propose an elementary research method for corresponding prime number, proved that the conjecture of twin prime numbers and obtain the corresponding prime distribution equation. According to the distribution rate of corresponding prime numbers, the distribution pattern of twin prime numbers was proved the distribution rate theorem. This is the distribution rate of prime numbers corresponding to composite numbers, which approaches the distribution rate of prime numbers corresponding to integers. Based on the corresponding prime distribution equation, obtain the twin prime inequality function. Then, the formula for calculating twin prime numbers was discussed. There is also the Hardy Littlewood conjecture. This provides a practical and feasible approach for studying the distribution of twin prime numbers.

On numerical stationary distribution of overdamped Langevin equation in harmonic system

Efficient numerical algorithm for stochastic differential equation has been an important object in the research of statistical physics and mathematics for a long time.In this work we study the highly accurate numerical algorithm for the overdamped Langevin equation.In particular,our interest is in the behaviour of the numerical schemes for solving the overdamped Langevin equation in the harmonic system.Based on the large friction limit of the underdamped Langevin dynamic scheme,three algorithms for overdamped Langevin equation are obtained.We derive the explicit expression of the stationary distribution of each algorithm by analysing the discrete time trajectory for both one-dimensional case and multi-dimensional case.The accuracy of the stationary distribution of each algorithm is illustrated by comparing with the exact Boltzmann distribution.Our results demonstrate that the“BAOA-limit”algorithm generates an accurate distribution of the harmonic system in a canonical ensemble,within a stable range of time interval.The other algorithms do not produce the exact distribution of the harmonic system.

Random Attractors for Stochastic Reaction-Diffusion Equations with Distribution Derivatives on Unbounded Domains

In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears spatially distributed temporal white noise. The stochastic reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform estimates far-field values of solutions. The results are new and appear to be optimal.

New Criteria for Oscillation of Vector Parabolic Equations with Continuous Distribution Arguments

The oscillations of a class of vector parabolic partial differential equations with continuous distribution arguments are studied.By employing the concept of H-oscillation and the method of reducing dimension with inner product,the multi-dimensional oscillation problems are changed into the problems of which one-dimensional functional differential inequalities have not eventually positive solution.Some new sufficient conditions for the H-oscillation of all solutions of the equations are obtained under Dirichlet boundary condition,where H is a unit vector of RM.

CAUCHY PROBLEM FOR LINEARIZED NON-CUTOFF BOLTZMANN EQUATION WITH DISTRIBUTION INITIAL DATUM

In this article, we study the Cauchy problem for the linearized spatially homogeneous non-cutoff Boltzamnn equation with Maxwellian molecules. By using the spectral decomposition, we solve the Cauchy problem with initial datum in the sense of distribution, which contains the dual space of a Gelfand-Shilov class. We also prove that this solution belongs to the Gelfand-Shilov space for any positive time.

Some dynamical property of the Tsallis distribution from a Fokker-Planck equation

This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian white noise, it shows that the current form of Tsallis distribution cannot describe any nonequilibrium dynamics of the system, and it only stands for a simple isothermal situation of the system governed by a potential field. So the form of Tsallis distribution and many existing applications using the Tsallis distribution need to be reconsidered.

THE DISTRIBUTION OF ZEROES OF SOLUTIONSOF NEUTRAL EQUATIONS

The purpose of ibis paper is to study the distribution of zerocs of solutions of theneutral delay differential equations. An estimate is estublished for the distween betweenadjacenlt zeroes of the solutions of such equations under less restritive hypotheses on the variable coefficients.The results obtained improve and extend scme known resultsin the literature.

A Note on Finding Geodesic Equation of Two Parameters Gamma Distribution

Engineers commonly use the gamma distribution to describe the life span or metal fatigue of a manufactured item. In this paper, we focus on finding a geodesic equation of the two parameters gamma distribution. To find this equation, we applied both the well-known Darboux Theorem and a pair of differential equations taken from Struik [1]. The solution proposed in this note could be used as a general solution of the geodesic equation of gamma distribution. It would be interesting if we compare our results with Lauritzen’s [2].

On Finding Geodesic Equation of Normal Distribution and Gaussian Curvature

In this paper, we apply two different algorithms to find the geodesic equation of the normal distribution. The first algorithm consists of solving a triply partial differential equation where these equations originated from the normal distribution. While the second algorithm applies the well-known Darboux Theory. These two algorithms draw the same geodesic equation. Finally, we applied Baltzer R.’s finding to compute the Gaussian Curvature.

On Finding Geodesic Equation of Two Parameters Logistic Distribution

In this paper, we used two different algorithms to solve some partial differential equations, where these equations originated from the well-known two parameters of logistic distributions. The first method was the classical one that involved solving a triply of partial differential equations. The second approach was the well-known Darboux Theory. We found that the geodesic equations are a pair of isotropic curves or minimal curves. As expected, the two methods reached the same result.

Oscillation of Solutions for a Class of Nonlinear Neutral Partial Differential Equations with Continuous Distribution Delay

In this paper, some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and Dirichlet＇s boundary value conditions.

Distribution of Zeros of Solutions of Advanced Differential Equations with One Advanced Variable

The distribution of zeros of solutions of the advanced differential equations with an advanced variable x′（t）-P（t）x（τ（t））=0,t≥t0 is studied, where P（t）∈C（[t0,∞）,R^＋）,τ：[t0,∞）→R^＋ are continuously differentiable and strictly increasing,τ（t）≥t and limt→∞τ（t）=∞.The estimate for the distance between adjacent zeros of the oscillatory solution of the above equation is obtained.

The Matching Conditions for the Distribution Functions of Boltzmann Equation in Nonequilibrium Transport

Based on the equation of motion in nonequilibrium Green function formalism, the matching conditions for the distribution functions of Boltzmann equation at interfaces of metallic multilayers are investigated in the nonequlibrium transport procedure. We also explore the matching conditions when the current-induced spin accumulation is accounted for, the contribution of coulomb interaction due to accumulated electrons is included. In order to study the matching conditions in the position space, we generalize the tunneling Hamiltonian to the formalism in position space, the matching conditions in this case is then obtained, which is convenient for us to match the usual distribution function of Boltzmann equation.

VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS

In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.

Simulation of gas-solid adsorption process considering particle-size distribution

The particle-size distribution of adsorbents usually plays an important role on the adsorption performance. In this study, population balance equation(PBE) is utilized in the simulation of an adsorption process to model the time-dependent adsorption amount distribution on adsorbent particles of a certain size distribution. Different adsorption kinetics model can be used to build the adsorption rate function in PBE according to specific adsorption processes. Two adsorption processes, including formaldehyde on activated carbon and CO_(2)/N_(2)/CH_(4) mixture on 4A zeolite are simulated as case studies, and the effect of particle-size distribution of adsorbent is analyzed. The simulation results proved that the influence of particle-size distribution is significant. The proposed model can help consider the influence of particlesize distribution of adsorbents on adsorption processes to improve the prediction accuracy of the performance of adsorbents.

Construction and Weight Distributions of Binary Linear Codes Based on Deep Holes

Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.

DISTRIBUTED PARAMETER NEURAL NETWORKS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS

Novel distributed parameter neural networks are proposed for solving partial differential equations, and their dynamic performances are studied in Hilbert space. The locally connected neural networks are obtained by separating distributed parameter neural networks. Two simulations are also given. Both theoretical and computed results illustrate that the distributed parameter neural networks are effective and efficient for solving partial differential equation problems.

Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.

Periodic Solutions for a Class of Neutral Functional Differential Equations with Distributed and Discrete Delays

Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with distributed and discrete delays are obtained. Moreover,we construct an example to illustrate the feasibility of our results.