An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

This paper generalizes the idea of strongly associative hyperoperation introduced in [7]  to the class of hyperrings. We introduce and investigate hyperrings of type 1, type 2 and SDIS. Moreover, we study some examples of these hyperrings and give a new kind of hyperrings called  totally hyperrings. Totally hyperrings give us a characterization of Krasner hyperrings. Also, we investigate these ...

—This paper studies the frequency estimation of twodimensional (2-D) harmonics in presence of multiplicative and additive noise. We construct a cyclic covariance matrix using a class of cyclic covariance of the 2-D harmonics. Exploiting the shift-invariance structure of the signal subspace, we extend ESPRIT to estimate the frequency pairs of 2-D harmonics in multiplicative and additive noise. ...

We prove a lower bound of 5 2 n 2 ? 3n for the multiplicative complexity of n n{matrix multiplication over arbitrary elds. More general, we show that for any nite dimensional semisimple algebra A with unity, the multiplicative complexity of the multiplication in A is bounded from below by 5 2 dim A ? 3(n1 + + nt) if the decomposition of A = A1 At into simple algebras A = D n n contains only non...

A directed graph $G=(V,E)$ is strongly biconnected if $G$ connected and its underlying biconnected. called $2$-vertex-strongly $|V|\geq 3$ the induced subgraph on $V\setminus\left\lbrace w\right\rbrace $ for every vertex $w\in V$. In this paper we study following problem. Given a $G=(V,E)$, compute an edge subset $E^{2sb} \subseteq E$ of minimum size such that $(V,E^{2sb})$

In this work we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic perturbations. For the linear case, robustness and existence exponential dichotomies random dynamical systems. Next, establish a result on persistence hyperbolic equilibria nonlinear equations. We show that each perturbation an semilinear problem with equilibrium there e...

In this article, we extend the theory of multiplicative chaos for positive definite functions in R of the form f(x) = λ ln T |x| + g(x) where g is a continuous and bounded function. The construction is simpler and more general than the one defined by Kahane in 1985. As main application, we give a rigorous mathematical meaning to the Kolmogorov-Obukhov model of energy dissipation in a turbulent ...