In this paper we study two different cases of inhomogeneous EOS the form p_d = \omega(t)\rho_d+w_1 f(H, t) . We derive energy density dark fluid and matter component for both cases. Further calculate evolution density, gravitational constant cosmological constant. also explore finite time singularity thermodynamic stability conditions EOS. Finally, discuss thermodynamics with derivation interna...

Truth Diagrams, TDs, are a new diagrammatic notation for propositional logic. TDs provide: (1) representations of logical states of affairs and relations; (2) operators on such relations; (3) a test of the validity of derivations. A proof of one of de Morgan’s laws is given as an illustration of TDs. Truth Diagrams (TDs) were invented as part of a programme of research on the Representational E...

In a simple model of Maxwell’s demon endowed with a Turing-type memory tape, we present an operational derivation of the Maxwell-Boltzmann distribution in the equilibrium statistical mechanics. It is based solely on the combined gas law of the elementary thermodynamics for the model of the memory. Equilibrium is defined in terms of the stability of thermodynamic work F against noise, where F is...

We derive an upper bound on the mass difference between the Ξ and Θ+ pentaquarks which are the manifestly exotic members of the SU(3)f antidecuplet. The derivation is based on simple assumptions about SU(3)f symmetry breaking and uses the standard quantum mechanical variational method. The resulting rather robust bound is more than 20 MeV below the experimentally reported Ξ − Θ+ mass difference...

The derivation of counterexamples to L1 estimates can be reduced to a geometric decomposition procedure along rank-one lines in matrix space. We illustrate this concept in two concrete applications. Firstly, we recover a celebrated, and rather complex, counterexample by Ornstein, proving the failure of Korn’s inequality, and of the corresponding geometrically nonlinear rigidity result, in L1. S...

A categorial semantics for Lexical-khmctional Grammar provides a means for semantic interpretation of sentences of natural language that is appropriately constrained both syntactically and semantically. The f-structure of LFG provides a cross-lingnistically uniform format for representing syntactic information; constraining a derivation with respect to the f-structure rather than a phrase struc...

The predicative lexicographic path order (PLPO for short), a syntactic restriction of the lexicographic path order, is presented. As well as lexicographic path orders, several non-trivial primitive recursive equations, e.g., primitive recursion with parameter substitution, unnested multiple recursion, or simple nested recursion, can be oriented with PLPOs. It can be shown that PLPOs however onl...

The diffusive coarsening of 2D soap froths is governed by von Neumann's law. A statistical version of this law for dry 3D foams has long been conjectured. A new derivation, based on a theorem by Minkowski, yields an explicit analytical von Neumann's law in 3D which is in very good agreement with detailed simulations and experiments. The average growth rate of a bubble with F faces is shown to b...

We discuss the dependence of superpotential terms in 4D F-theory on moduli parameters. Two cases are studied: the dependence on world-filling 3-brane positions and the dependence on 2-form VEVs. In the first case there is a zero when the 3-brane hits the divisor responsible for the superpotential. In the second case, which has been extensively discussed by Witten in 3D M-theory, there is a zero...