In this paper, we study the Casimir effect of a scalar field with Dirichlet boundary condition in some certain topologies. By numerical analysis we show that Casimir energy is a shape-dependent quantity. We also obtain the phase transition in different topologies in which the Casimir force changes from attractive to repulsive or vice versa.  eararqr

By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.

The problem of unbounded uniaxial chiral omega media in the presence of both static electric and magnetic point charges is investigated. For this purpose scalar electric and magnetic potentials in these media are introduced. Using these potentials, the corresponding electric and magnetic fields are determined. The similar problem of static electric and magnetic current sources with the goal of ...

Let E be a B-complete (B -complete) locally convex algebra and $ the topological direct sum of countably many copies of the scalar field with a jointly continuous algebra multiplication. It has been shown that E is also B-complete (B -complete) for componentwise multiplication on E . B-and Br-completeness of E , the unitization of E, and also of E x for other multiplications on E ...

In this paper an exact and complete analysis of average design complexities of Lloyd-Max's scalar quantizers, scalar compandors and scalar quantizers designed using the hybrid model is carried out. The average design complexity depends on arithmetic complexity, memory complexity and implementation complexity. It is demonstrated that for a fixed number of quantizaton levels N, scalar compandors ...