scholarly journals Trace class properties of the non homogeneous linear Vlasov–Poisson equation in dimension 1+1

2021 ◽  
Author(s):  
Bruno Després
Keyword(s):  
Poisson Equation ◽  
Trace Class ◽  
Homogeneous Linear

scholarly journals Quantum Orlicz Spaces in Information Geometry

2004 ◽  
Vol 11 (04) ◽  
pp. 359-375 ◽  
Author(s):  
R. F. Streater
Keyword(s):  
Quantum Information ◽  
Tangent Space ◽  
Selfadjoint Operator ◽  
Affine Connection ◽  
Orlicz Spaces ◽  
Trace Class ◽  
Information Geometry ◽  
Young Function ◽  
Affine Structure ◽  
Cotangent Space

Let H0 be a selfadjoint operator such that Tr e−βH0 is of trace class for some β < 1, and let χɛ denote the set of ɛ-bounded forms, i.e., ∥(H0+C)−1/2−ɛX(H0+C)−1/2+ɛ∥ < C for some C > 0. Let χ := Span ∪ɛ∈(0,1/2]χɛ. Let [Formula: see text] denote the underlying set of the quantum information manifold of states of the form ρx = e−H0−X−ψx, X ∈ χ. We show that if Tr e−H0 = 1. 1. the map Φ, [Formula: see text] is a quantum Young function defined on χ 2. The Orlicz space defined by Φ is the tangent space of [Formula: see text] at ρ0; its affine structure is defined by the (+1)-connection of Amari 3. The subset of a ‘hood of ρ0, consisting of p-nearby states (those [Formula: see text] obeying C−1ρ1+p ≤ σ ≤ Cρ1 − p for some C > 1) admits a flat affine connection known as the (−1) connection, and the span of this set is part of the cotangent space of [Formula: see text] 4. These dual structures extend to the completions in the Luxemburg norms.

Lattice-BGK Methods for Simulating Incompressible Fluid Flows

1997 ◽  
Vol 08 (04) ◽  
pp. 793-803 ◽  
Author(s):  
Yu Chen ◽  
Hirotada Ohashi
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Poisson Equation ◽  
General Model ◽  
Incompressible Flows ◽  
Fluid Flows ◽  
Incompressible Limit ◽  
Numerical Example ◽  
Incompressible Fluid Flows

The lattice-Bhatnagar-Gross-Krook (BGK) method has been used to simulate fluid flow in the nearly incompressible limit. But for the completely incompressible flows, two special approaches should be applied to the general model, for the steady and unsteady cases, respectively. Introduced by Zou et al.,1 the method for steady incompressible flows will be described briefly in this paper. For the unsteady case, we will show, using a simple numerical example, the need to solve a Poisson equation for pressure.

scholarly journals Existence and Concentration Behavior of Solutions of the Critical Schrödinger–Poisson Equation in R3

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 464
Author(s):  
Jichao Wang ◽  
Ting Yu
Keyword(s):  
Poisson Equation ◽  
Existence Result ◽  
Critical Growth ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Number Of Solutions ◽  
Concentration Behavior ◽  
The Relationship ◽  
Concentration Phenomenon

In this paper, we study the singularly perturbed problem for the Schrödinger–Poisson equation with critical growth. When the perturbed coefficient is small, we establish the relationship between the number of solutions and the profiles of the coefficients. Furthermore, without any restriction on the perturbed coefficient, we obtain a different concentration phenomenon. Besides, we obtain an existence result.

Research on the application of 3D reconstruction technology in traditional handicraft design

2021 ◽  
pp. 002072092110052
Author(s):  
GuoLong Zhang
Keyword(s):  
Poisson Equation ◽  
Optimization Algorithm ◽  
Three Dimensional ◽  
Reconstruction Algorithm ◽  
Social Production ◽  
Design Constraint ◽  
Reconstruction Process ◽  
Key Steps ◽  
Shielding Design ◽  
Reconstruction Model

The use of computer technology for three-dimensional (3 D) reconstruction is one of the important development directions of social production. The purpose is to find a new method that can be used in traditional handicraft design, and to explore the application of 3 D reconstruction technology in it. Based on the description and analysis of 3 D reconstruction technology, the 3 D reconstruction algorithm based on Poisson equation is analyzed, and the key steps and problems of the method are clarified. Then, by introducing the shielding design constraint, a 3 D reconstruction algorithm based on shielded Poisson equation is proposed. Finally, the performance of two algorithms is compared by reconstructing the 3 D image of rabbit. The results show that: when the depth value of the algorithm is 11, the surface of the rabbit image obtained by the proposed optimization algorithm is smoother, and the details are more delicate and fluent; under different depth values, with the increase of the depth value, the number of vertices and faces of the two algorithms increase, and the optimal depth values of 3 D reconstruction are more than 8. However, the proposed optimization algorithm has more vertices, and performs better in the reconstruction process; the larger the depth value is, the more time and memory are consumed in 3 D reconstruction, so it is necessary to select the appropriate depth value; the shielding parameters of the algorithm have a great impact on the fineness of the reconstruction model. The larger the parameter is, the higher the fineness is. In a word, the proposed 3 D reconstruction algorithm based on shielded Poisson equation has better practicability and superiority.

scholarly journals Note on some representations of general solutions to homogeneous linear difference equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Stevo Stević ◽  
Bratislav Iričanin ◽  
Witold Kosmala ◽  
Zdeněk Šmarda
Keyword(s):  
General Solution ◽  
Difference Equation ◽  
Difference Equations ◽  
Fibonacci Sequence ◽  
Linear Difference Equation ◽  
Linear Difference Equations ◽  
Second Order Difference Equation ◽  
Constant Coefficients ◽  
Order Difference Equation ◽  
Homogeneous Linear

Abstract It is known that every solution to the second-order difference equation $x_{n}=x_{n-1}+x_{n-2}=0$ x n = x n − 1 + x n − 2 = 0 , $n\ge 2$ n ≥ 2 , can be written in the following form $x_{n}=x_{0}f_{n-1}+x_{1}f_{n}$ x n = x 0 f n − 1 + x 1 f n , where $f_{n}$ f n is the Fibonacci sequence. Here we find all the homogeneous linear difference equations with constant coefficients of any order whose general solution have a representation of a related form. We also present an interesting elementary procedure for finding a representation of general solution to any homogeneous linear difference equation with constant coefficients in terms of the coefficients of the equation, initial values, and an extension of the Fibonacci sequence. This is done for the case when all the roots of the characteristic polynomial associated with the equation are mutually different, and then it is shown that such obtained representation also holds in other cases. It is also shown that during application of the procedure the extension of the Fibonacci sequence appears naturally.

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