A set of fixed points of the Hopfield type neural network is under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter the analytic description of the fixed points set has been obtained. A set of fixed points of the Hopfield type neural network is under investigation. Its conn...

In this paper, we discuss a class of integrodifferential equations with nonlocal conditions via a fractional derivative of the type: D t x(t) = Ax(t) + t Z 0 B(t − s)x(s)ds + tf (t, x(t)) , t ∈ [0, T ], n ∈ Z, q ∈ (0, 1], x(0) = g(x) + x0. Some sufficient conditions for the existence of mild solutions for the above system are given. The main tools are the resolvent operators and fixed point the...

We show that the lattice of all ideals of a ring $R$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. For this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (A)$ of a subset $A$ of a ring $R$ forfixed $r , sin [0,1] $ and show that $A$ is an ideal of $R$ if, and only if, its generalizedcharacteristic function $chi _{s}^{...

It is shown that any desired radiation pattern f (β) ∈ L 2 (S 2), where S 2 is the unit sphere in R 3 , can be generated by a suitable distribution of small, acoustically soft particles D m ⊂ D, 1 ≤ m ≤ M , in an a priori given bounded domain D ⊂ R 3. In this theory the geometrical shape of a small particle D m is arbitrary, the boundary S m of D m is Lipschitz uniformly with respect to m. The ...

High quality key-dependent S-boxes can break the preconditions of many cryptanalysis technologies, but it is difficult to construct them efficiently. Here, we proposed a method for fast constructing good key-dependent S-boxes, which are generated by means of a key-dependent affine transformation on a good base S-box. We proved their security by classifying the evaluative criteria of S-boxes int...

In this paper, we introduce four new types of contractions called in order Kanan-S-type tricyclic contraction, Chattergea-S-type Riech-S-type Cirić-S-type and prove the existence uniqueness for a fixed point each situation.

Let S(r) denote the w-sphere with a linear involution having a fixed point set of codimension r, where O ^ r ^ w . We pick some fixed point as a base point and consider the set [S(r); S(t)] of base point preserving equivariant homotopy classes of maps from S(r) to S(t). This has a natural group structure for n—r^l and is abelian if n—r^2. There is a suspension functor S without action and one 2...

we show that the lattice of all ideals of a ring $r$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. for this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (a)$ of a subset $a$ of a ring $r$ forfixed $r , sin [0,1] $ and show that $a$ is an ideal of $r$ if, and only if, its generalizedcharacteristic function $chi _{s}^{...

let $r$ be a commutative noetherian ring with non-zero identity, $fa$ an ideal of $r$, and $x$ an $r$--module. here, for fixed integers $s, t$ and a finite $fa$--torsion $r$--module $n$, we first study the membership of $ext^{s+t}_{r}(n, x)$ and $ext^{s}_{r}(n, h^{t}_{fa}(x))$ in the serre subcategories of the category of $r$--modules. then, we present some conditions which ensure the exi...

Let A q (α ′ , α, k) be the scattering amplitude, corresponding to a local potential q(x), x ∈ R 3 , q(x) = 0 for |x| > a, where a > 0 is a fixed number, α ′ , α ∈ S 2 are unit vectors, S 2 is the unit sphere in R 3 , α is the direction of the incident wave, k 2 > 0 is the energy. We prove that given an arbitrary function f (α ′) ∈ L 2 (S 2), an arbitrary fixed α 0 ∈ S 2 , an arbitrary fixed k ...