Recently, there have been many results which show that the global dimension of certain rings can be computed using a proper subclass of the cyclic modules, e.g., the simple modules. In this paper we view calculating global dimensions in this fashion as a property of a ring and show that this is a property which transfers to the ring's idealizer and subidealizer ring.

Some structural properties as well as a general three-dimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of functions if some conditions are fulfilled.

The Skorokhod oblique reflection problem is studied in the case ofn-dimensional convex polyhedral domains. The natural sufficient condition on the reflection directions is found, which together with the Lipschitz condition on the coefficients gives the existence and uniqueness of the solution. The continuity of the corresponding solution mapping is established. This property enables one to construct in a direct way the reflected (in a convex polyhedral domain) diffusion processes possessing the nice properties.

Asymptotic distribution of the mean square deviation of the Gasser–Müller estimate of the regression curve is investigated. The testing of hypotheses on regression function is considered. The asymptotic behaviour of the power of the proposed criteria under contiguous alternatives is studed.

We consider the quantifier-free set theoryMLSUn containing the symbolsU, \,=,∈,Un. Un(p) is interpreted as the union of all members of the setp. It is proved that there exists an algorithm which for any formulaQ of theMLSUn theory containing at most one occurrence of the symbolUn decides whetherQ is true or not using the spacecn³ log₂n (n is the lenhth ofQ).

New oscillation and nonoscillation criteria are established for the equation $$u'' + p(t)u = 0,$$ ,where p :]1,+∞[→ R is the locally integrable function. These criteria generalize and complement the well known criteria of E. Hille, Z. Nehari, A. Wintner, and P. Hartman.