Matrix Rings with Summand Intersection Property

A ring R has right SIP (SSP) if the intersection (sum) of two direct summands of R is also a direct summand. We show that the right SIP (SSP) is the Morita invariant property. We also prove that the trivial extension of R by M has SIP if and only if R has SIP and (1 – e)Me = 0 for every idempotent e in R. Moreover, we give necessary and sufficient conditions for the generalized upper triangular matrix rings to have SIP.     

On the level density of random band matrices

Translated from Matematicheskie Zametki, Vol. 50, No. 6, pp. 31–42, December, 1991.     

Entanglement of qutrits

For two types of qutrits specified by the dynamical symmetry SU(3) and SU(2), we consider the difference in entanglement caused by the lack of quantum observables in the latter case. In particular, we show that the SU(2) qutrits can have specific separable entanglement caused by quantum correlations of intrinsic degrees of freedom in a single party without interparty correlations.     

Ordering of structural vacancies in vanadium monoxide of substoichiometric composition

The order-disorder phase transition in vanadium monoxide of substoichiometric compositions VO_y has been studied for the first time in situ by the Faraday method with a pendulum magnetic balance of the Domenically type. A minimum is found on the temperature dependence of the magnetic susceptibility of vanadium monoxide of different compositions at a temperature of about 700 K. X-ray diffraction analysis performed before and after measuring the magnetic susceptibility confirmed the change in the structure of vanadium monoxide and the possibility of atom-vacancy processes upon cooling and heating of the samples.     

Schemes of effective magnetic AND and XOR logic elements

Schemes and calculated characteristics of effective logic elements with two inputs for classical ground-state computations are reported. These elements have a high threshold (0.48) and perform a desired logical operation in a wide range of input signals.     

Areal objects and the problem of the λ term in the theory of gravitation

The following areal objects are considered: an ether thread contracting two material points and a multidimensional ether fibre in the pseudo-Euclidean world of events. An ether space-time model with an arbitrarily determined Riemannian metric is constructed and the problem of the λ term in Einstein equations is discussed in this regard.     

Asymptotic analysis of a large closed queueing network with discriminatory processor sharing

In this paper the steady-state behavior of a closed queueing network with multiple classes and large populations is investigated. One of the two nodes of the network simply introduces random delays and the discipline in the other node is discriminatory processor sharing. The network is not product-form, so not even the steady-state behavior is known. We assume that the usage is moderately heavy, and obtain two-term asymptotic approximations to the mean number of jobs, and the mean sojourn time, of each class of jobs in the processor node. We also obtain the leading term in the asymptotic approximation to the joint distribution of the number of jobs in the processor node, which is a zero-mean multivariate Gaussian distribution around a line through the origin.     

Cluster sets of subharmonic functions and associated measures in a cone

A study is conducted of the relationship between the asymptotic behavior of a subharmonic function of finite order in a cone and the distribution of the measure associated with it.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 2, pp. 247–261, Febraury, 1991.