in this paper we focus on a special class of commutative local‎ ‎rings called spap-rings and study the relationship between this‎ ‎class and other classes of rings‎. ‎we characterize the structure of‎ ‎modules and especially‎, ‎the prime submodules of free modules over‎ ‎an spap-ring and derive some basic properties‎. ‎then we answer the‎ ‎question of lam and reyes about strongly oka ideals fam...

We introduce the class of “right almost V-rings” which is properly between the classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-rin...

In this work, we approach the minimization of a continuously differentiable convex function under linear equality constraints by second-order dynamical system with asymptotically vanishing damping term. The is formulated in terms augmented Lagrangian associated to problem. We show fast convergence primal-dual gap, feasibility measure, and objective value along generated trajectories. case has L...

We devise and analyze two hybrid high-order (HHO) methods for the numerical approximation of biharmonic problem. The support polyhedral meshes, rely on primal formulation problem, deliver $O(h^{k+1})$ $H^2$-error estimates when using polynomials order $k\ge0$ to approximate normal derivative mesh (inter)faces. Both HHO hinge a stabilization in spirit Lehrenfeld Schöberl second-order PDEs. cell ...

We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primal-dual schema and the local ratio technique. Recently, primal-dual algorithms were devised by first constructing a local ratio algorithm, and then transforming it into a primal-dual algorithm. This was done in the case of the 2-approximation algorithms for the f...

In this paper, we give a recursive formula for optimal dual barrier functions on homogeneous cones. This is done in a way similar to the primal construction of Güler and Tunçel [1] by means of the dual Siegel cone construction of Rothaus [2]. We use invariance of the primal barrier function with respect to a transitive subgroup of automorphisms and the properties of the duality mapping, which i...

Knot theory is one of the hottest topics in contemporary mathematics, right there at the interface between a range of exciting research fronts in pure mathematics, with seminal contributions made by leading string theorist Edward Witten. We shall see more of how it fits the higher-dimensional outlook in later chapters. Here, I want to take the time to consider the peculiar constellation of circ...