Related papers: Sturm Oscillation and Comparison Theorems
In this paper, we present a new approachment for Sturm-Liouville problem having special potentials. We acquire the representations of solutions and asymptotic formulas for solutions with regard to initial conditions. Also, a few…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
We study the phenomenon of turbulence from the point of view of statistical physics. We discuss what makes the turbulent states different from the thermodynamic equilibrium and give the turbulent analog of the partition function. Then,…
We first give a combinatorial proof of Stanley's shuffle theorem by using the insertion lemma of Haglund, Loehr and Remmel. Based on this combinatorial construction, we establish several refinements of Stanley's shuffle theorem.
This paper establishes a converse comparison theorem for real-valued decoupled forward backward stochastic differential equations with jumps.
An introduction to Chiral Perturbation Theory is given including a discussion of power counting, the Wess-Zumino term, the values of the coupling constants and the inclusion of the effects of other resonances.
A review of chiral perturbation theory and that of recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.
In this paper we discuss mechanical systems with inequality constraints. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate…
This is a survey of the spectral theory of tensors.
The present work proposes a theory of isotropic and homogeneous turbulence for incompressible fluids, which assumes that the turbulence is due to the bifurcations associated to the velocity field. The theory is formulated using a…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
Oscillation theory locates the spectrum of a differential equation by counting the zeros of its solutions. We present a version of this theory for canonical systems $Ju'=-zHu$ and then use it to discuss semibounded operators from this point…
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
The Lifshitz theory and its modifications are discussed with respect to the Nernst heat theorem and the experimental data of several recent experiments. An analysis of all available information leads to the conclusion that some concepts of…
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and…
This review article is the second part of the project ``Selected Topics of Social Physics". The first part has been devoted to equilibrium systems. The present part considers nonequilibrium systems. The style of the paper combines the…
A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very…
In this paper, we give a new approach for the study of Weyl-type theorems. Precisely we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued…
We compare, for the static potential and at short distances, perturbation theory with the results of lattice simulations. We show that a renormalon-dominance picture explains why in the literature sometimes agreement, and another…
Quantum analogues of the transient fluctuation theorem(TFT) and steady-state fluctuation theorem(SSFT) are investigated for a harmonic oscillator linearly coupled with a harmonic reservoir. The probability distribution for the work done…