In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that $ell^1(S)$ is  a symmetric $ell^1(E)$-module amenable if and only if $S$ is amenable, where $S$ is an inverse semigroup with subsemigr...

let $rin textbf{c}^{mtimes m}$ and $sin textbf{c}^{ntimes n}$ be nontrivial involution matrices; i.e., $r=r^{-1}neq pm~i$ and $s=s^{-1}neq pm~i$. an $mtimes n$ complex matrix $a$ is said to be an $(r, s)$-symmetric ($(r, s)$-skew symmetric) matrix if $ras =a$ ($ ras =-a$). the $(r, s)$-symmetric and $(r, s)$-skew symmetric matrices have a number of special properties and widely used in engi...

The generalized degrees of freedom (GDoF) of the two user symmetric multiple input multiple output (MIMO) interference channel (IC) are characterized as a function of the channel strength levels and the level of channel state information at the transmitters (CSIT). In this symmetric setting, each transmitter is equipped with M antennas, each receiver is equipped with N antennas, and both cross ...

Consider a symmetric differentiated duopoly model in which firms have private market data about the uncertain demand. We analyze two types of duopoly information equilibrium, Cournot and Bertrand, which emerge, respectively, from quantity and price competition, and show that the incentives for information sharing and its welfare consequences depend crucially on the type of competition, the natu...

Consider a market where producers submit supply functions to a procurement auction — e.g. an electric power auction — under uncertainty, before demand has been realized. In the Supply Function Equilibrium (SFE), every firm commits to the supply function maximizing his expected profit given the supply functions of the competitors. The presence of multiple equilibria is one basic weakness of SFE....

We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on R which may be written as P (x) exp(Ax, x), with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f(x)f̂(y). We also give the best constant in uncertainty principles of Gelf’and Shilov type. We then obtain sim...

We analyze Cournot competition under demand uncertainty. We show that under rather general assumptions, the game has no asymmetric equilibria but multiple symmetric equilibria. Multiplicity is caused by the requirement of nonnegative prices and remains an issue also for simple demand specifications, such as the linear case. We then show that uniqueness of equilibrium is guaranteed if uncertaint...

This paper introduces a measure of uncertainty in the determination of the Shapley value, illustrates it with examples, and studies some of its properties. The introduced measure of uncertainty quantifies random variations in a player’s marginal contribution during the bargaining process. The measure is symmetric with respect to exchangeable substitutions in the players, equal to zero for dummy...

The rigorous uncertainty estimation in Electromagnetic Compatibility (EMC) testing is a complex task that has been addressed through a simplified approach that typically assumes that all the contributions are uncorrelated and symmetric, and combine them in a linear or linearized model using the error propagation law. These assumptions may affect the reliability of test results, and therefore, i...

Let G be a noncompact semisimple Lie group with finite centre. $$X=G/K$$ the associated Riemannian symmetric space and assume that X is of rank one. The generalized spectral projections to Laplace-Beltrami operator are given by $$P_{\lambda }f =f*\Phi _{\lambda }$$ , where $$\Phi elementary spherical functions on X. In this paper, we prove an Ingham type uncertainty principle for }f$$ . Moreove...