The principal methods for the definition of thermodynamic entropy are discussed with special reference to those developed by Carathéodory, the Keenan School, Lieb and Yngvason, and the present authors. An improvement of the latter method is then presented. Seven basic axioms are employed: three Postulates, which are considered as having a quite general validity, and four Assumptions, which iden...

The TRUTH of our existence has not been detected by science so far. Why does theoretical physics know nothing about the essence of space, matter, energy and time? How can we come to the true knowledge about our existence? Let us look at the reason of critical situation in contemporary theoretical physics and show how critical logical thinking and reasoning can open the door to the truth. I am s...

We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite element mesh. The method modifies a given partition of unity such that optimal convergence is achieved independent of oscillation or discontinuities of the diffus...

A deterministic compartmental model for the transmission dynamics of onchocerciasis with nonlinear incidence functions in two interacting populations is studied. The qualitatively analyzed to investigate its local asymptotic behavior respect disease-free and endemic equilibria. It shown, using Routh-Hurwitz criteria, that equilibrium locally asymptotically stable when associated basic reproduct...

duns scouts the famous theologian of thirteen century under the influence of avecina’s doctorine of “nature” on the basis of hierarchy of the unity presents a hypothesis and describes the unconditioned nature as minor unity and individual entities as numerical unity. as an celeberating hypothesis of“distinct forms” it accounts with the haeccity as the criterion of individuality of external enti...

UNITY is a simple programming logic to reason about distributed systems. It is especially attractive because of its elegant axiomatical style. Since its power is limited, people introduce variants to extends it with various new functionalities. However, in the axiomatical style it is easy to make a mistake: a seemingly very logical new inference rule may turn out to be unsound. Formal verificat...

The main result of this paper gives necessary and sufficient conditions for the ^-primary part S(K)P of the Schur group S (K) to be induced from S (F)p for any subfield F of K where K is contained in Q (εn), under the restriction that εp2 is not in K if p > 2 and n is odd if p~2, where εn is a primitive nth root of unity. Moreover we completely answer the question: "When is SiQiεn + ε-)) induce...

Let F be the cyclotomic field of fifth roots of unity. We computationally investigate modularity of elliptic curves over F .

In this paper we used the finite Fourier transformation to obtain the polar decomposition of the q-deformed boson algebra with q a root of unity. Since the q-deformed boson algebra was known [1,2], much work has been accomplished in this direction [3-8]. It is well known that this algebra has an infinite dimensional representation when the deformation parameter q is real, while it has a finite ...