In this paper, we study the ratios of order statistics based on samples drawn from uniform distribution and establish some limit properties such as the almost sure central limit theorem, the large deviation principle, the Marcinkiewicz-Zygmund law of large numbers and complete convergence.

The µ-limit set of a cellular automaton is a subshift whose forbidden patterns are exactly those, whose probabilities tend to zero as time tends to infinity. In this article, for a given subshift in a large class of subshifts, we propose the construction of a cellular automaton which realizes this subshift as µ-limit set where µ is the uniform Bernoulli measure.

Points P1; : : : ; Pn in the unit square de ne a convex n-chain if they are below y = x and, together with P0 = (0; 0) and Pn+1 = (1; 1), they are in convex position. Under uniform probability, we prove an almost sure limit theorem for these chains that uses only probabilistic arguments, and which strengthens similar limit shape statements established by other authors. An interesting feature is...

Points P1, . . . , Pn in the unit square define a convex n-chain if they are below y = x and, together with P0 = (0, 0) and Pn+1 = (1, 1), they are in convex position. Under uniform probability, we prove an almost sure limit theorem for these chains that uses only probabilistic arguments, and which strengthens similar limit shape statements established by other authors. An interesting feature i...

We show that every continuous action of a finite group on smooth three-manifold is uniform limit actions.

Placing column lap-splice in the locations of possible nonlinear deformation may adversely affect the structures response to strong ground motions. Localization of damage in splice zone may change the structural response and prevent the load redistribution and development of a uniform pattern of nonlinear excursions among the various members. Validated by existing laboratory experiments, this s...

In multi-processor database systems there are processor initialization and inter-communication overheads that diverge real systems from the ideal linear behaviour as the number of processors increases. Main-memory database systems suffer more since the database processing cost is small compared to disk-based database systems and thus comparable to the processor initialization cost. The usual un...

Continuous random variables are widely used to mathematically describe random phenomenon in engineering and physical sciences. In this paper, we present a higherorder logic formalization of the Standard Uniform random variable as the limit value of the sequence of its discrete approximations. We then show the correctness of this specification by proving the corresponding probability distributio...

In multi-processor database systems there are processor initialization and inter-communication overheads that diverge real systems from the ideal linear behaviour as the number of processors increases. Main-memory database systems suffer more since the database processing cost is small compared to disk-based database systems and thus comparable to the processor initialization cost. The usual un...

In this paper, we investigate the uniform regularity for the isentropic compressible Navier-Stokes system with general Navier-slip boundary conditions (1.6) and the inviscid limit to the compressible Euler system. It is shown that there exists a unique strong solution of the compressible Navier-Stokes equations with general Navier-slip boundary conditions in an interval of time which is uniform...