and Applied Analysis 3 x ν αx, t ν x, t/|α| for each α/ 0, xi ν x, t ν y, s ≥ ν x y, t s , xii ν x, · : 0,∞ → 0, 1 is continuous, xiii limt→∞ν x, t 0 and limt→ 0ν x, t 1. In this case μ, ν is called an intuitionistic fuzzy norm. Example 1.4 cf. 37 . Let X, ‖·‖ be a normed space, a∗b ab, and a b min a b, 1 for all a, b ∈ 0, 1 . For all x ∈ X and every t > 0 and k 1, 2, consider μk x, t ⎧ ⎨ ⎩ t t...

in this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...

In this paper, a von Neumann-type inequality is studied on an Eaton triple $ (V,G,D) $, where V real inner product space, G compact subgroup of the orthogonal group O (V) and D \subset closed convex cone. By using structure triple, refinement shown. special case = ( ) Cauchy-Schwarz obtained.

We consider Cauchy problem for ordinary differential equation with solution possessing a sequence of multiple poles. propose the generalized reciprocal function method. It reduces calculation pole to retrieval simple zero accordingly chosen function. Advantages this approach are illustrated by numerical examples. two representative test problems which constitute interest verification other meth...

A quantum theoretic representation of real and complex numbers is described here as equivalence classes of Cauchy sequences of quantum states of finite strings of qubits. There are 4 types of qubits each with associated single qubit annihilation creation (a-c) operators that give the state and location of each qubit type on a 2 dimensional integer lattice. The string states, defined as finite p...

In this paper, we study the notion of \(\mathcal{I}\)-localized and \(\mathcal{I}^*\)-localized sequences in \(S\)-metric spaces. Also, investigate some properties related to \(\mathcal{I}\)-Cauchy give idea \(\mathcal{I}\)-barrier a sequence same space. Finally, use for an be when ideal \(\mathcal{I}\) satisfies condition (AP).

in this paper we study the duality of bessel and g-bessel sequences in hilbertspaces. we show that a bessel sequence is an inner summand of a frame and the sum of anybessel sequence with bessel bound less than one with a parseval frame is a frame. next wedevelop this results to the g-frame situation.

In the case of equation (1.2) condition (1.4) coincides with the known Kruzhkov entropy condition [9]. If the function g(u) strictly increases then any weak solution of (1.1) is an entropy solution of this equation as well (cf. [2]) but for degenerate equations this may be violated and, in particular, entropy condition (1.4) is necessary for the uniqueness of solution to the Cauchy problem for ...

The approximate controllability of Sobolev-type Hilfer fractional control differential systems is the main emphasis this paper. We use calculus, Gronwall's inequality, semigroup theory, and Cauchy sequence to examine results for proposed system. application well-known fixed point theorem methodologies avoided in Finally, a heat equation discussed as an example.