Modeling the motion of a bright spot in jets from black holes M87* and SgrA*

General Relativity and Gravitation - In previous work, we established theoretical results concerning the effect of matter shells surrounding a gravitational wave (GW) source, and we now apply these...     

About Global Solvability of a Multidimensional Inverse Problem for an Equation with Memory

Siberian Mathematical Journal - Under study is the multidimensional inverse problem of determining the convolutional kernel of the integral term in an integro-differential wave equation....     

Fractional derivative method for describing solitons on the surface of deep water

Theoretical and Mathematical Physics - The fractional derivative method is used to take wave dispersion into account in the wave equation when describing the propagation of gravitational soliton...     

Exponential Stability for Time-changed Stochastic Differential Equations

Acta Mathematicae Applicatae Sinica, English Series - So far there have been few results presented on the exponential stability for time-changed stochastic differential equations. The main aim of...     

多元统计分析中一类矩阵迹函数最小化问题的有效算法

研究来源于多元统计分析中的一类矩阵迹函数最小化问题$\min c+ tr(AX)+\sum\limits_{j=1}^{m}tr(B_j X C_jX^{T}),\ \ {\rm s. t.} \ X^TX=I_p,$其中$c$为常数, $A\in R^{p\times n}\ (n\geq p)$, $B_j\in R^{n\times n}, C_j\in R^{p\times p}$为给定系数矩阵. 数值实验表明已有的Majorization算法虽可行, 但收敛速度缓慢且精度不高. 本文从黎曼流形的角度重新研究该问题, 基于Stiefel流形的几何性质, 构造一类黎曼非单调共轭梯度迭代求解算法, 并给出算法收敛性分析.数值实验和数值比较验证所提出的算法对于问题模型是高效可行的.     

Estimation of the Sorption Activity of Silver Nanoparticles on Biodegradable Fibers of Natural and Artificial Origin

Russian Physics Journal - The specific features of the sorption activity of silver nanoparticles (AgNPs) on biodegradable polymers of natural (collagen) and artificial (polyamide 6.6) origin have...     

Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements

Integrated information theory (IIT) provides a mathematical framework to characterize the cause-effect structure of a physical system and its amount of integrated information (Φ). An accompanying Python software package (“PyPhi”) was recently introduced to implement this framework for the causal analysis of discrete dynamical systems of binary elements. Here, we present an update to PyPhi that extends its applicability to systems constituted of discrete, but multi-valued elements. This allows us to analyze and compare general causal properties of random networks made up of binary, ternary, quaternary, and mixed nodes. Moreover, we apply the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2) and discuss commonly used binarization methods in light of their capacity to preserve the causal structure of the original system with multi-valued elements.     

Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Upper Bounds for the Expected Maxima of Independent Random Variables Given Known First Four Moments

Mathematical Notes - The paper is devoted to the study of conditional bounds for the expectation of the maximum of independent identically distributed standardized random variables for which the...     

Approximation Properties of the Vallée-Poussin Means of Partial Sums of a Special Series in Laguerre Polynomials

Mathematical Notes - We consider the problem of the approximation of functions, continuous on the semiaxis $$[0,\infty)$$ and for which the derivatives $$f^{(\nu)}(0)$$ , $$\nu=0,\dots,r-1$$ exist...