the mechanical properties and microstructural developments of 321 stainless steel during thermomechanicalprocess were investigated. the repetitive cold rolling and subsequent annealing wereconducted to achieve nanocrystalline structure in an aisi 321 stainless steel. heavily cold rolling at−20°c was conducted to form martensite in metastable austenitic steel. the process was followed byannealin...

If two symmetric convex bodies K and L both have nicely bounded sections, then the intersection of random rotations of K and L is also nicely bounded. For L being a subspace, this main result immediately yields the unexpected “existence vs. prevalence” phenomenon: If K has one nicely bounded section, then most sections of K are nicely bounded. The main result represents a new connection between...

Let V be a real linear space. The functor ConvexComb(V ) yielding a set is defined by: (Def. 1) For every set L holds L ∈ ConvexComb(V ) iff L is a convex combination of V . Let V be a real linear space and let M be a non empty subset of V . The functor ConvexComb(M) yielding a set is defined as follows: (Def. 2) For every set L holds L ∈ ConvexComb(M) iff L is a convex combination of M . We no...

There are many notions of discrete convexity of polyominoes (namely hvconvex [1], Q-convex [2], L-convex polyominoes [5]) and each one has been deeply studied. One natural notion of convexity on the discrete plane leads to the definition of the class of hv-convex polyominoes, that is polyominoes with consecutive cells in rows and columns. In [1] and [6], it has been shown how to reconstruct in ...

In this brief article we characterize the relatively compact subsets of A for the topology σ(A,R) (see below), by the weak compact subsets of L . The spaces R endowed with the weak topology induced by A, was recently employed to create the convex risk theory of random processes. The weak compact sets of A are important to characterize the so-called Lebesgue property of convex risk measures, to ...

Abstract. We study some properties of the randomized series and their applications to the geometric structure of Banach spaces. For n ≥ 2 and 1 < p < ∞, it is shown that l ∞ is representable in a Banach space X if and only if it is representable in the Lebesgue-Bochner Lp(X). New criteria for various convexity properties in Banach spaces are also studied. It is proved that a Banach lattice E is...

In this paper, we consider a type of cone-constrained convex program in finitedimensional space, and are interested in characterization of the solution set of this convex program with the help of the Lagrange multiplier. We establish necessary conditions for a feasible point being an optimal solution. Moreover, some necessary conditions and sufficient conditions are established which simplifies...

In this paper we establish a one-to-one correspondence between lawinvariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L.

In this paper we establish a one-to-one correspondence between lawinvariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L.