Related papers: Further results on the Craig-Sakamoto equation
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
The paper investigates a pivotal condition for the Bobkov-Tanaka type spectrum for double-phase operators. This condition is satisfied if either the weight $w$ driving the double-phase operator is strictly positive in the whole domain or…
In this article we consider a convex feasible set described by inequality constraints that are continuous and not necessarily Lipschitz or convex. We show that if the Slater constraint qualification and a non-degeneracy condition are…
We derive the Thermodynamic Bethe Ansatz (TBA) equations for the Schr\"odinger equation with an arbitrary polynomial potential and a regular singular (simple and double pole) term. The TBA equations provide a non-trivial generalization of…
Sufficient conditions for the well-posedness of the initial value problem for the scalar wave equation are obtained in space-times with hypersurface singularities
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…
We obtain a local two weight $Tb$ theorem with an energy side condition for higher dimensional fractional Calder\'{o}n-Zygmund operators. The proof follows the general outline of the proof for the corresponding one-dimensional $Tb$ theorem…
This paper presents the general form and essential properties of the q-optimal measure following the approach of Delbaen and Schachermayer (1996) and proves its existence under mild conditions. Most importantly, it states a necessary and…
The purpose of this note is to announce the results of our investigation into the role played by the continuous spectrum in the development of the Selberg trace formula vis-\`a-vis a pair $(G,\Gamma)$. For the sake of simplicity, we shall…
We demonstrate the separability of the Hamilton-Jacobi and scalar field equations in general higher dimensional Kerr-NUT-AdS spacetimes. No restriction on the parameters characterizing these metrics is imposed.
In this paper we give alternate proofs of some well-known matrix inequalities. In particular, we show that under certain conditions the inequality holds \begin{align}\sum \limits_{\lambda_i\in \mathrm{Spec}(ab^{T})}\mathrm{min}\{\log…
We derive a formula for the signature of the symmetrized Stokes matrix $\cal{S}+\cal{S}^\mathrm{T}$ for the $tt^*$-Toda equation. As a corollary, we verify a conjecture of Cecotti and Vafa regarding when $\cal{S}+\cal{S}^\mathrm{T}$ is…
We consider the equation $u_t = \mbox{Div}(a[u]\nabla u - u\nabla a[u])$, $-\Delta a = u$. This model has attracted some attention in the recents years and several results are available in the literature. We review recent results on…
For nonautonomous linear differential equations with nonuniform hyperbolicity, we introduce a definition for nonuniform dichotomy spectrum, which can be seen as a generalization of Sacker-Sell spectrum. We prove a spectral theorem and use…
Under integral restrictions on dilatations, it is proved existence theorems for the degenerate Beltrami equations with two characteristics and, in particular, to the Beltrami equations of the second type that play a great role in many…
We provide proofs of some assumptions recently made by F. O. Minotti to conclude on the possibility that an additional scalar field minimally coupled to gravity may help to reconcile a Brans-Dicke coupling constant $\omega$ of the order…
A description of the essential spectrum is given for a general class of linear advective PDE with pseudodifferential bounded perturbation. We prove that every point in the Sacker-Sell spectrum of the corresponding bicharacteristic-amplitude…
The most general scalar potential of two real scalar fields and a Higgs boson is a quartic homogeneous polynomial about 3 variables, which defines a 4th order 3 dimensional symmetric tensor. Hence, the boundedness from below of such a…
We will revise one of the methods given in the literature to determine the necessary and sufficient conditions that the parameters must satisfy to have a stable scalar potential in the general two-Higgs doublet model. We will give a…
We consider matrix Riccati inequality arising in the theory of absolute stability, $H_\infty$ control problem, $LQ$ problem, and optimal estimation problem. In the case of sign definite frequency domain function, the solvability of Riccati…