In this paper, we propose an order statistics−based unbiased homomorphic system to reduce multiplicative noise. The design of such a system is based on the probability density function (PDF) of the noise. First, we generalize the order statistics−based nonlinear filter called the sampled function weighted order (SFWO) filter proposed in [1] to reduce additive noise, to the case when the additiv...

In the present work we study set of multiplicative convex functions. particular, focus on properties injectiveness and discontinuity. We will show that a non constant function is at most 2-injective, construct functions which are discontinuous infinitely many points.

Multiplicative linear secret sharing is a fundamental notion in the area of secure multiparty computation (MPC) and, since recently, in the area of two-party cryptography as well. In a nutshell, this notion guarantees that “the product of two secrets is obtained as a linear function of the vector consisting of the coordinate-wise product of two respective share-vectors”. This paper focuses on t...

for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

We study a typing scheme derived from a semantic situation where a single category possesses several closed structures, corresponding to different varieties of function type. In this scheme typing contexts are trees built from two (or more) binary combining operations, or in short, bunches. Bunched typing and its logical counterpart, bunched implications, have arisen in joint work of the author...

We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold: First, we establish new regularity results based on averaging techniques. Second, we prove the existence and uniqueness of solutions in a full L1 setting requiring no growth assumptions on the nonline...