We address two properties for Abelian topological groups: “every closed subgroup is dually closed” and “every closed subgroup is dually embedded.” We exhibit a pair of topological groups such that each has both of the properties and the product has neither, which refutes a remark of N. Noble. These examples are the additive group of integers topologized with respect to a convergent sequence as ...

Let (Ω,F ,P) be a probability space and S = {S1, . . . , SK} a discrete-topological space that consists of K real d-by-d matrices, where K and d both ≥ 2. In this paper, we study the pointwise stabilizability of a discrete-time, time-homogeneous, stationary (p, P)-Markovian jump linear system Ξ = (ξn) n=1 where ξn : Ω → S. Precisely, Ξ is called “pointwise convergent”, if to any initial state x...

Let (Ω,F ,P) be a probability space and S = {S1, . . . , SK} a discrete-topological space that consists of K real d-by-d matrices, where K and d both ≥ 2. In this paper, we study the pointwise stabilizability of a discrete-time, time-homogeneous, stationary (p, P)-Markovian jump linear system Ξ = (ξn) n=1 where ξn : Ω → S. Precisely, Ξ is called “pointwise convergent”, if to any initial state x...

in this paper we introduce strongly $left[  v_{2},lambda_{2},m,pright]-$summable double vsequence spaces via orlicz function and examine someproperties of the resulting these spaces. also we give natural relationshipbetween these spaces and $s_{lambda_{2}}-$statistical convergence.

The synthesis of the alleged natural product pochonin J is presented. Key steps of this convergent synthesis include a chemoselective Wacker oxidation, and an Evans' anti-reduction of the resulting ketone. Upon ozonolysis, this intermediate undergoes a 6-exo-trig cyclization to give a hemiketal intermediate, the key oxocarbenium precursor. The construction of the α-C-glycoside subunit is highli...

The noncanonical wnt/planar cell polarity (PCP) pathway [1] regulates the mediolaterally (planarly) polarized cell protrusive activity and intercalation that drives the convergent extension movements of vertebrate gastrulation [2], yet the underlying mechanism is unknown. We report that perturbing expression of Xenopus PCP genes, Strabismus (Xstbm), Frizzled (Xfz7), and Prickle (Xpk), disrupts ...

Using forcing we produce a model of ZFC + CH (with 2 arbitrarily large) and, in this model, we obtain a characterization of the Abelian groups G (necessarily of size at most 2) which admit: (i) a hereditarily separable group topology, (ii) a group topology making G into an S-space, (iii) a hereditarily separable group topology that is either precompact, or pseudocompact, or countably compact (a...

With the market competition increasing, in order to shorten product development cycle and reduce the development costs, product design is changed from the traditional serial-type process to the parallel, collaborative development process. Food product collaborative design of Feature modeling refers to the number of the design team through the division of labor and cooperation has completed a pr...