A ring which is a sum of two PI subrings is always a PI ring

We prove that a ring which is a sum of two PI subrings is a PI ring as well. This answers a question of K. I. Beidar and A. V. Mikhalev that has been open since 1995.     

A primitive ring which is a sum of two Wedderburn radical subrings

We give an example of a primitive ring which is a sum of two Wedderburn radical subrings. This answers an open question and simplifies the proof of the known theorem that there exists a ring which is not nil but is a sum of two locally nilpotent subrings.

     

Discrete gauge invariant approximations of a time dependent Ginzburg-Landau model of superconductivity

We present here a mathematical analysis of a nonstandard difference method for the numerical solution of the time dependent Ginzburg-Landau models of superconductivity. This type of method has been widely used in numerical simulations of the behavior of superconducting materials. We also illustrate some of their nice properties such as the gauge invariance being retained in discrete approximations and the discrete order parameter having physically consistent pointwise bound.

     

Heavy-traffic analysis of the sojourn time in a three node Jackson network with overtaking

We consider a Jackson network consisting of three first-in-first-out (FIFO)M/M/1 queues. When customers leave the first queue they can be routed to either the second or third queue. Thus, a customer that traverses the network by going from the first to the second to the third queue, can be overtaken by another customer that is routed from the first queue directly to the third. We study the distribution of the sojourn time of a customer through the three node network, in the heavy traffic limit. A three term heavy traffic asymptotic approximation to the sojourn time density is derived. The leading term shows that the nodes decouple in the heavy traffic limit. The next two terms, however, do show the dependence of the sojourn times at the individual nodes and give quantitative measures of the effects of overtaking.     

Conditions under which the least compactification of a regular continuous frame is perfect

We characterize those regular continuous frames for which the least compactification is a perfect compactification. Perfect compactifications are those compactifications of frames for which the right adjoint of the compactification map preserves disjoint binary joins. Essential to our characterization is the construction of the frame analog of the two-point compactification of a locally compact Hausdorff space, and the concept of remainder in a frame compactification. Indeed, one of the characterizations is that the remainder of the regular continuous frame in each of its compactifications is compact and connected.     

V-uniform ergodicity of a continuous time asymmetric power GARCH(1,1) model

A continuous time asymmetric power GARCH(1,1) model is presented and the V-uniform ergodicity and β-mixing property of the process with exponential decay rate are proved. The V-uniform ergodicity of the COGARCH(1,1) model is obtained as a special case.     

Linear sufficiency and linear admissibility in a continuous time Gauss–Markov model

This paper considers the problem of estimation in a linear model when a stochastic process instead of a random vector is observed. Estimators obtained as integrals of the observed process are studied. Characterizations of linear sufficiency and admissibility similar to those given in the classical linear model are obtained in this context. Moreover, a definition of generalized ridge estimators in continuous time is introduced and also a characterization of such estimators is given.     

Periodic solutions of a nonautonomous periodic model of population with continuous and discrete time

In this paper, we employ the Mawhin's continuation theorem to study the existence of positive periodic solutions of the nonautonomous periodic model of population with continuous and discrete time. It is interesting that the conditions to guarantee the existence of positive periodic solutions of discrete time model are similar to those for the corresponding continuous time model.     

A mathematical study of a muscle contraction model in which the fibre is a continuum of elements

In the framework of the sliding-filament theory of muscle contraction, we introduce and study a model which assumes the muscle fibre to be a continuum of elastic and contractile elements. Using the contracting mapping principle, we prove existence and uniqueness of the solution of the nonlinear and nonlocal hyperbolic equation related to the model.     

Dynamic information handling in continuous time Boolean Network model of gene interactions

Growing information and knowledge on gene regulatory networks, which are typical hybrid systems, has led a significant interest in modeling those networks. An important direction of gene network modeling is studying the abstract network models to understand the behavior of a class of systems. Boolean Networks has emerged as an important model class on this direction. Limitations of traditional Boolean Networks led the researchers to propose several generalizations. In this work, one such class, the Continuous Time Boolean Networks (CTBN’s), is studied. CTBN’s are constructed by allowing the Boolean variables evolve in continuous time and involve a biologically-motivated refractory period. In particular, we analyze the basic circuits and subsystems of the class of CTBN’s. We demonstrate the existence of various qualitative dynamic behavior including stable, multistable, neutrally stable, quasiperiodic and chaotic behaviors. We show that those models are capable of demonstrating highly adjustable features like maintenance of continuous protein concentrations. Finally, we discuss the relation between qualitative dynamic features and information handling.     

Discrete spectrum of a model operator in Fock space

We consider a model describing a “truncated” operator (truncated with respect to the number of particles) acting in the direct sum of zero-, one-, and two-particle subspaces of a Fock space. Under some natural conditions on the parameters specifying the model, we prove that the discrete spectrum is finite. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 518–527, September, 2007.     

The model of security market when the security price is a continuous semimartingale

In this paper, we set the stock price model in security market when the price process is a continuous semartingale, and find a unigue solution of price process model.     

一类噬菌体死亡率受到噪声干扰的随机噬菌体-细菌模型研究

考虑了一类噬菌体死亡率受到白噪声干扰的随机噬菌体-细菌模型.主要研究了边界平衡点的随机渐近稳定性和随机模型的解围绕相应确定性模型正平衡点的振荡行为,并通过数值仿真验证了所得理论结果的正确性.     

Absolutely continuous spectrum of a nondissipative operator and a functional model. II

The second part of the paper (the first is published in J. Sov. Math.,16, No. 3 (1981)), is devoted to the study of nondissipative operators in Hilbert space, which are nearly self-adjoint. In the model representation, generalizing the familiar model of B. S. Nagy-C. Foias for dissipative operators, formulas are obtained for spectral projectors on a segment of the absolutely continuous spectrum and conditions for their boundedness are studied. Questions of linear similarity for a generally nondissipative operator and its parts to self-adjoint and dissipative operators are considered. New proofs are found for the similarity theorems of L. A. Sakhnovich and Davis-Foias. Some of the results are new even in the dissipative case which is not excluded.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 73, pp. 118–135, 1977.In conclusion the author expresses gratitude to B. S. Pavlov for interest in the work and helpful discussions.