Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

We consider the number of zeros of the integral $I(h) = oint_{Gamma_h} omega$ of real polynomial form $omega$ of degree not greater than $n$ over a family of vanishing cycles on curves $Gamma_h:$ $y^2+3x^2-x^6=h$, where the integral is considered as a function of the parameter $h$. We prove that the number of zeros of $I(h)$, for $0 < h < 2$, is bounded above by $2[frac{n-1}{2}]+1$.

Masking is a well-known countermeasure to protect block cipher implementations against side-channel attacks. The principle is to randomly split every sensitive intermediate variable occurring in the computation into d + 1 shares, where d is called the masking order and plays the role of a security parameter. Although widely used in practice, masking is often considered as an empirical solution ...

We consider the problem of constructing efficient locally decodable codes in the presence of a computationally bounded adversary. Assuming the existence of one-way functions, we construct efficient locally decodable codes with positive information rate and low (almost optimal) query complexity which can correctly decode any given bit of the message from constant channel error rate ρ. This compa...

We study the computational complexity of finding stable outcomes in hedonic games, which are a class of coalition formation games. We restrict our attention to a nontrivial subclass of such games, which are guaranteed to possess stable outcomes, i.e., the set of symmetric additively-separable hedonic games. These games are specified by an undirected edge-weighted graph: nodes are players, an ou...

‎This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset $K$ of a reflexive Banach space $X$. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when $K$ is compact convex subsets. Fina...

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

Abstract The time-optimal path following (OPF) problem is to find a time evolution along prescribed in task space with shortest duration. Numerical solution algorithms rely on an algorithm-specific (usually equidistant) sampling of the parameter. This does not account for dynamics joint space, that is, actual motion robot, however. Moreover, well-known large velocities are obtained when approac...

All NP-complete problems can be solved in exponential time by enumerating the space of possible solutions. In the area of moderatelyexponential algorithms, we seek for exact algorithms for NP-complete problems that are faster than the naive ones. Surprisingly, often such results exist and their development leads to a good insight into a considered problem. In the rst part of this dissertation w...