We establish the physical origins of chemical transferability from the perspective of the nearsightedness of electronic matter. To do this, we explicitly evaluate the response of electron density to a change in the system, at constant chemical potential, by computing the softness kernel, [Formula: see text] The softness kernel is nearsighted, indicating that under constant-chemical-potential co...

Lanthanum substituted lead zirconate titanate (PLZT) nanocrystallite with stichometry formula Pb0.90La0.10 (Zr0.52Ti0.48) O3 have been synthesized by sol gel process. The effect of nanocrystallite on dielectric, ferroelectric and piezoelectric properties of La substituted PZT was studied. The average crystallite size of the PLZT powder was 21nm.Variation of dielectric constant with temperature ...

In the article, we prove that the double inequality [Formula: see text] holds for all [Formula: see text], we present the best possible constants λ and μ such that [Formula: see text] for all [Formula: see text], and we find the value of [Formula: see text] in the interval [Formula: see text] such that [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text], ...

Kemeny’s constant of a simple connected graph G is the expected length random walk from i to any given vertex $$j \ne i$$ . We provide method for computing 1-separable graphs via effective resistance methods electrical network theory. Using this formula, we furnish proof that path on n vertices maximizes class undirected trees vertices. Applying again, simplify existing expressions barbell and ...

In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are two non-zero polynomials, [Formula: see text] is a polynomial and [Formula: see text]. In addition, we investigate the non-existence of entire solutions of finite order of the differ...