We establish inequalities for the eigenvalues of Schrödinger operators on compact submanifolds (possibly with nonempty boundary) of Euclidean spaces, of spheres, and of real, complex and quaternionic projective spaces, which are related to inequalities for the Laplacian on Euclidean domains due to Payne, Pólya, and Weinberger and to Yang, but which depend in an explicit way on the mean curvatur...

Using local Ward identities and a new correlation inequality, we prove that the mean field transition temperature is an upper bound on the true transition temperature in multicomponent Heisenberg-type classical ferromagnets. (49' = 1 i=1 Given a translation-invariant function J(c~-t3) on Z v x Z ~, we consider for A c Z ~ the Hamiltonian D c~,B~A i = 1 cEA and form the partition function with a...

We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by BialynickiBirula [1] and Zozor et al. [2]. Those inequalities can be considered as generalizations of the Heisenberg uncertainty principle, since they measure the mutual uncertainty of a wave function and its Fourier transform through their associat...

It is a consensus in signal processing that the Gaussian kernel and its partial derivatives enable the development of robust algorithms for feature detection. Fourier analysis and convolution theory have central role in such development. In this paper we collect theoretical elements to follow this avenue but using the q-Gaussian kernel that is a nonextensive generalization of the Gaussian one. ...

In this paper we consider the question of sampling for spaces entire functions exponential type in several variables. The novelty resides growth condition impose, that is, their restriction to a hypersurface is square integrable with respect natural measure. boundary $b\mathcal U$ Siegel upper half-space $\mathcal and it fundamental can be identified Heisenberg group $\mathbb H_n$. We C^{n+1}$ ...

Abstract The concepts of concurrence, 3-steerability, and Clauser–Horne–Shimony–Holt (CHSH) inequality are employed to investigate the environmental impacts on quantum correlations two-spin-1/2 Heisenberg XYZ chain model. In particular, effects a homogeneous magnetic field, symmetric cross interaction, dipole–dipole interaction entanglement, degree steerability, non-locality discussed. Results ...

‎in this paper‎, ‎we study translation invariant surfaces in the‎ ‎3-dimensional heisenberg group $rm nil_3$‎. ‎in particular‎, ‎we‎ ‎completely classify translation invariant surfaces in $rm nil_3$‎ ‎whose position vector $x$ satisfies the equation $delta x = ax$‎, ‎where $delta$ is the laplacian operator of the surface and $a$‎ ‎is a $3 times 3$-real matrix‎.

Abstract—In this article, a new method is proposed for the measuring of well-being inequality through a model composed of superimposing satisfaction waves. The displacement of households’ satisfactory state (i.e. satisfaction) is defined in a satisfaction string. The duration of the satisfactory state for a given period is measured in order to determine the relationship between utility and tota...

Abstract We present a new secondary school teaching method of quantum uncertainties two-state systems. Intending to be material teachable in schools, only systems described by real numbers can considered. An elementary argumentation based on statistics leads the identification uncertainty physical quantity such with standard deviation two random variables. provide qualitative picture state-depe...

We prove that the $L_4$ norm of vertical perimeter any measurable subset $3$-dimensional Heisenberg group $\mathbb{H}$ is at most a universal constant multiple (Heisenberg) subset. show this isoperimetric-type inequality optimal in sense there are sets for which it fails to hold with replaced by $L_q$ $q<4$. This contrast $5$-dimensional setting, where above result holds $L_2$ norm. The proof...