We investigate quantitative properties of BCI and BCK logics. The first part of the paper compares the number of formulas provable in BCI versus BCK logics. We consider formulas built on implication and a fixed set of k variables. We investigate the proportion between the number of such formulas of a given length n provable in BCI logic against the number of formulas of length n provable in ric...

Using Monte Carlo simulations, we have studied aging phenomena in three-dimensional Gaussian Ising spin-glass model focusing on quasi-equilibrium behavior of the spin autocorrelation functions. Weak violation of the time translational invariance in the quasiequilibrium regime is analyzed in terms of effective stiffness for droplet excitations in the presence of domain walls. The simulated resul...

Let M be a commutative cancellative atomic monoid. We use unions of sets of lengths in M to construct the V-Delta set of M . We first derive some basic properties of V-Delta sets and then show how they offer a method to investigate the asymptotic behavior of the sizes of unions of sets of lengths. A central focus of number theory is the study of number theoretic functions and their asymptotic b...

This paper aims to propose a significant way of remote access and real time monitoring of a particular geographic area by integrating wireless sensor clouds with existing Telecom infrastructure and applications built around them through a gateway. This utility is very potent for environment monitoring in harsh and inaccessible places like mines, nuclear reactors, etc. We demonstrate a scaled do...

In this section we study the relation between throughput and queue-length distributions in discrete-time closed cyclic networks when the number of customers and the number of nodes grows unboundedly. To state our findings more precisely: For each positive integer N , consider a cyclic network with n(N) nodes and k(N) customers. We suppose that there are only finitely many types of nodes. That i...

‎this paper deals with the singular sturm-liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of sturm-liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...

‎This paper deals with the singular Sturm-Liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎Using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of Sturm-Liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...

Timing is often seen as the most important property of systems after function, and safety-critical systems are no exception. In this paper, we consider how timing is typically treated in safety assurance and, in particular, the safety arguments being proposed by industry and academia. A critique of these arguments is performed based on how systems are generally developed and how evidence is gat...