In this Note a mathematical formulation of a monotonically decreasing functional with respect to time (the Hfunctional) is derived for physical systems described by the diffusion equation. This returns a condition which is equivalent to the second law of thermodynamics. The H-theorem is certainly the most debated (and probably the most important) part of Boltzmann’s scientific heritage [1,2]. A...

We present a model, in which some nodes (called interconnecting nodes) in two networks merge and play the roles in both the networks. The model analytic and simulation discussions show a monotonically increasing dependence of interconnecting node topological position difference and a monotonically decreasing dependence of the interconnecting node number on function difference of both networks. ...

An n-person bargaining situation is two-sided when participants of bargaining are divided into two groups and their preferences over bargained outcomes are exactly opposite to each other. This is so when the issue on the bargaining table is represented by a one dimensional set and people’s preferences are monotonically increasing in one group and monotonically decreasing in the other group. In ...

Some impurities cannot integrate into isolated kinks because they completely block the growth of to which adsorb. For this class impurity, we derive an equation for amount that incorporates a crystal during elementary step by assuming such impurity if and only it gets captured between kink antikink. We show concentration in increases monotonically with mother phase, but can vary non-monotonical...

The reaction path is an important concept of theoretical chemistry. We employ the definitions of the intrinsic reaction coordinate (IRC), the gradient extremal (GE), and the Newton trajectory (NT). The usual imagination in chemistry is that a minimum energy path is in a convex region of the potential energy surface. We describe different schemes of convexity to handle the situation. It comes ou...

A score sequence of a tournament is a monotonically non-decreasing sequence of the out-degrees of its vertices. We develop two algorithms that generates all score sequences, each of which appears to use only a constant amount of computation per sequence produced. A degree sequence of a graph is a monotonically non-increasing sequence of the degrees of its vertices. We develop an algorithm that ...

We report on some aspects of our efforts to establish properties of the extremely faint galaxy population by applying our photometric redshift technique to the HDF and HDF–S WFPC2 and NICMOS fields. We find that cosmological surface brightness dimming effects play a dominant role in setting what is observed at redshifts z > 2, that the comoving number density of high intrinsic surface brightnes...

Aligned carbon nanotube (CNT) array adhesion strength evolves with CNT process time, decreasing and then increasing during growth annealing, as captured by models relating diameter, effective modulus, CNT–substrate work of adhesion.

Piezoresistive strain gauges allow for electronic readout of mechanical deformations with high fidelity. As piezoresistive are aggressively being scaled down applications in nanotechnology, it has become critical to investigate their physical attributes at different limits. Here, we describe an experimental approach studying the gauge factor a gold thin-film nanoresistor as function frequency. ...

background: due to difficulty of obtaining a 24h urine (especially in children), a random urine calcium sample is recommended to detect of hypercalciuria. however, recent studies have shown that the urinary calcium/creatinine ratio varies with age and geographic areas. so, the aim of this study was determining the normal value of urinary calcium to creatinine ratio in healthy adolescent’s child...