this paper addresses the problem of testing simple hypotheses about the mean of a bivariate normal distribution with identity covariance matrix against restricted alternatives. the lrts and their power functions for such types of hypotheses are derived. furthermore, through some elementary calculus, it is shown that the power function of the lrt satisfies certain monotonicity and symmetry prope...

For the study of some typical problems in finance and economics, Žitković introduced convex compactness gave many remarkable applications. Recently, motivated by random optimization variational inequalities, Guo, et al. L0-convex compactness, developed related theory normed modules further applied it to backward stochastic equations. In this paper, we extensively L0-convexly compact sets locall...

In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuz...

We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in t...

In this paper, under a suitable regularity condition, we establish that a broad class of conic convex polynomial optimization problems, called conic sum-of-squares convex polynomial programs, exhibits exact conic programming relaxation, which can be solved by various numerical methods such as interior point methods. By considering a general convex cone-program, we give unified results that appl...

In this paper, by using C-sequentially sign property for bifunctions, we provide sufficient conditions that ensure the existence of solutions of some vector equilibrium problems in Hausdorff topological vector spaces which ordered by a cone. The conditions which we consider are not imposed on the whole domain of the operators involved, but just on a locally segment-dense subset of the domain.

Coconvex sets (complements in a convex cone of convex subsets coinciding with the cone far enough from its apex) appear in singularity theory (as Newton diagrams) and in commutative algebra. Such invariants of coconvex sets as volumes, mixed volumes, number of integer points, etc., play an important role. This paper aims at extending various results from the theory of convex bodies to the cocon...

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...