In this study, as a new approach to the concept of asymptotical equivalence in Wijsman sense for double set sequences, concepts which are called invariant statistical order ? and lacunary (0<??1) sequences introduced explained with examples. addition, existence some relations between these furthermore, relationships previously studied investigated.

• Let Ak denote the set of methods that observe a sequence of data pairs Y t = (F (θ, X ), F (τ , X )), 1 ≤ t ≤ k, and return an estimate θ̂(k) ∈ Θ. • Let FG denote the class of functions we want to optimize, where for each (F, P ) ∈ FG the subgradient g(θ;X) satisfies EP [‖g(θ;X)‖2∗] ≤ G. • For each A ∈ Ak and (F, P ) ∈ FG, consider the optimization gap: k(A, F, P,Θ) := f (θ̂(k))− inf θ∈Θ f (θ) ...

Consider a semigroup action on a set. We derive conditions, in terms of the induced action of the semigroup on {0, 1}-valued probability charges, which ensure that all invariant probability charges are strongly continuous.

A striking feature of the T cell receptor (TCR) beta chain structure is the large FG loop that protrudes freely into the solvent on the external face of the Cbeta domain. We have already shown that a transgene-encoded Vbeta8.2(+) TCR beta chain lacking the complete Cbeta FG loop supports normal development and function of conventional alpha/beta T cells. Thus, the FG loop is not absolutely nece...

 In this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. In fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. Some examples are provided to verify the effectiveness and applicability of our results.

Trafficking of nucleic acids and large proteins through nuclear pore complexes (NPCs) requires interactions with NPC proteins that harbor FG (phenylalanine-glycine) repeat domains. Specialized transport receptors that recognize cargo and bind FG domains facilitate these interactions. Whether different transport receptors utilize preferential FG domains in intact NPCs is not fully resolved. In t...

Fuzzy relation inequalities based on max-F composition are discussed, where F is a binary aggregation on [0,1]. For a fixed fuzzy relation inequalities system $ A circ^{F}textbf{x}leqtextbf{b}$, we characterize all matrices $ A^{'} $ For which the solution set of the system $ A^{' } circ^{F}textbf{x}leqtextbf{b}$ is the same as the original solution set. Similarly, for a fixed matrix $ A $, the...