scholarly journals Rate of convergence toward Hartree dynamics with singular interaction potential

2018 ◽  
Vol 59 (3) ◽  
pp. 031902 ◽  
Author(s):  
Li Chen ◽  
Ji Oon Lee ◽  
Jinyeop Lee
Keyword(s):  
Rate Of Convergence ◽  
Interaction Potential ◽  
Singular Interaction

Products of 2 × 2 stochastic matrices with random entries

1986 ◽  
Vol 23 (04) ◽  
pp. 1019-1024
Author(s):  
Walter Van Assche
Keyword(s):  
Rate Of Convergence ◽  
Beta Distribution ◽  
Stopping Time ◽  
Stochastic Matrices

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

A Factorization of Least-Squares Projection Schemes for Ill-Posed Problems

2020 ◽  
Vol 20 (4) ◽  
pp. 783-798
Author(s):  
Shukai Du ◽  
Nailin Du
Keyword(s):  
Least Squares ◽  
Rate Of Convergence ◽  
Convergence Conditions ◽  
Principal Angles ◽  
Factorization Formula ◽  
Ill Posed

AbstractWe give a factorization formula to least-squares projection schemes, from which new convergence conditions together with formulas estimating the rate of convergence can be derived. We prove that the convergence of the method (including the rate of convergence) can be completely determined by the principal angles between {T^{\dagger}T(X_{n})} and {T^{*}T(X_{n})}, and the principal angles between {X_{n}\cap(\mathcal{N}(T)\cap X_{n})^{\perp}} and {(\mathcal{N}(T)+X_{n})\cap\mathcal{N}(T)^{\perp}}. At the end, we consider several specific cases and examples to further illustrate our theorems.

scholarly journals Self-exciting multifractional processes

2021 ◽  
Vol 58 (1) ◽  
pp. 22-41
Author(s):  
Fabian A. Harang ◽  
Marc Lagunas-Merino ◽  
Salvador Ortiz-Latorre
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Rate Of Convergence ◽  
Existence And Uniqueness ◽  
Volterra Equation ◽  
The Self ◽  
The Past ◽  
Stochastic Volterra Equation ◽  
Multifractional Brownian Motion ◽  
Self Organizing

AbstractWe propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a multifractional Brownian motion, where the Hurst function is dependent on the past of the process. We define this by means of a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as giving bounds on the p-order moments, for all $p\geq1$. We show convergence of an Euler–Maruyama scheme for the process, and also give the rate of convergence, which is dependent on the self-exciting dynamics of the process. Moreover, we discuss various applications of this process, and give examples of different functions to model self-exciting behavior.

scholarly journals Clinical Pharmacokinetic Drug Interaction Potential of MenoAct851 in Adult, Female Healthy Volunteers

2021 ◽  
Vol 94 ◽  
pp. 100619
Author(s):  
Vijayakumar Thangavel Mahalingam ◽  
Ilango Kaliappan ◽  
Satish Kumar Rajappan Chandra ◽  
Melvin George ◽  
Mohan Kumar Ramasamy ◽  
...  
Keyword(s):  
Drug Interaction ◽  
Healthy Volunteers ◽  
Clinical Pharmacokinetic ◽  
Adult Female ◽  
Interaction Potential ◽  
Pharmacokinetic Drug Interaction ◽  
Pharmacokinetic Drug

scholarly journals Deformation of the Fermi surface of a spinless two-dimensional electron gas in presence of an anisotropic Coulomb interaction potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Orion Ciftja
Keyword(s):  
Fermi Surface ◽  
Coulomb Interaction ◽  
Interaction Potential ◽  
Fermi Liquid ◽  
Energy State ◽  
Electron Gas ◽  
Two Dimensional ◽  
Dimensional Electron ◽  
Two Dimensional Electron Gas ◽  
Dimensional Electron Gas

AbstractWe consider the stability of the circular Fermi surface of a two-dimensional electron gas system against an elliptical deformation induced by an anisotropic Coulomb interaction potential. We use the jellium approximation for the neutralizing background and treat the electrons as fully spin-polarized (spinless) particles with a constant isotropic (effective) mass. The anisotropic Coulomb interaction potential considered in this work is inspired from studies of two-dimensional electron gas systems in the quantum Hall regime. We use a Hartree–Fock procedure to obtain analytical results for two special Fermi liquid quantum electronic phases. The first one corresponds to a system with circular Fermi surface while the second one corresponds to a liquid anisotropic phase with a specific elliptical deformation of the Fermi surface that gives rise to the lowest possible potential energy of the system. The results obtained suggest that, for the most general situations, neither of these two Fermi liquid phases represent the lowest energy state of the system within the framework of the family of states considered in this work. The lowest energy phase is one with an optimal elliptical deformation whose specific value is determined by a complex interplay of many factors including the density of the system.

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