We consider the first Dirichlet eigenvalue of diffusion operators on the half line. A criterion for the equivalence of the first Dirichlet eigenvalue with respect to the maximum domain and that to the minimum domain is presented. We also describle the relationships between the first Dirichlet eigenvalue of transient diffusion operators and the standard Muckenhoupt’s conditions for the dual weig...

in this paper, we present some inequalities for the co-pi index involving the some topological indices, the number of vertices and edges, and the maximum degree. after that, we give a result for trees. in addition, we give some inequalities for the largest eigenvalue of the co-pi matrix of g.

Tensile stress–strain and stress relaxation properties of 1100 equivalent weight Nafion have been measured from 23 to 120 C at 0–100% relative humidity. At room temperature, the elastic modulus of Nafion decreases with water activity. At 90 C, the elastic modulus goes through a maximum at a water activity of 0.3. At temperatures 90 C, hydrated membranes are stiffer than dry membranes. Stressrel...

For a functionally graded (FG) circular cylinder loaded by uniform pressures on the inner and the outer surfaces and Young’s modulus varying in the radial direction, we find lower and upper bounds for Young’s modulus of the energetically equivalent homogeneous cylinder. That is, the strain energies of the FG and the homogeneous cylinders are equal to each other. For a typical power law variatio...

In last years, many modulus sets in the Residue Number System (RNS) for increasing Dynamic Range (DR) and parallelism are presented. Hence, for reach these purposes a new 5-Moduli Set for even n, and its efficient reverse converter design are introduced in this paper. This modulus set contains pair-wise relatively prime, and it offers the maximum feasible DR. New CRT-I and MRC are used to obtai...

If a body with a stiffer surface layer is loaded in compression, a surface wrinkling instability may be developed. A bifurcation analysis is presented for determining the critical load for the onset of wrinkling and the associated wavelength for materials in which the elastic modulus is an arbitrary function of depth. The analysis leads to an eigenvalue problem involving a pair of linear ordina...

A numerical method is proposed to calculate damping properties for sound-proof structures involving elastic body, viscoelastic body, and porous media. For elastic and viscoelastic body displacement is modeled using conventional finite elements including complex modulus of elasticity. Both effective density and bulk modulus have complex quantities to represent damped sound fields in the porous m...

We generate a series of pseudopotentials to examine the relationship between pseudoatomic properties and solid-state results. We find that lattice constants and bulk moduli are quite sensitive to eigenvalue, total-energy difference and tail norm errors, and clear correlations emerge. These trends motivate our identification of two criteria for accurate transition metal pseudopotentials. We find...

A connected ρ-regular graph G has largest eigenvalue ρ in modulus. G is called Ramanujan if it has at least 3 vertices and the second largest modulus of its eigenvalues is at most 2 √ ρ− 1. In 2010 Droll classified all Ramanujan unitary Cayley graphs. These graphs of type ICG(n, {1}) form a subset of the class of integral circulant graphs ICG(n,D), which can be characterised by their order n an...