in this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. we characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. we also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

We demonstrate how to efficiently implement extremely high-dimensional compressive imaging of a bi-photon probability distribution. Our method uses fast-Hadamard-transform Kronecker-based compressive sensing to acquire the joint space distribution. We list, in detail, the operations necessary to enable fast-transform-based matrix-vector operations in the joint space to reconstruct a 16.8 millio...

In this paper, we built bitopological space on the concept of neutrosophic soft set, defined basic topological concepts spaces which are N3-(bi)*-open N3-(bi)*-closed (bi)*-neutrosophic interior, (bi)* closure, boundary, exterior and introduced their properties. addition, investigated relations these with counterparts in many examples.

Iron was inserted into the known crystal structure of the bismuth phosphate oxide Bi(6.67)(PO(4))(4)O(4) to ascertain its location in the vacancies associated with the bismuth ion located at the origin of the unit cell. Single-crystal X-ray diffraction refinements converged to a model of composition Bi(6)(Bi(0.32)Fe(0.68))(PO(4))(4)O(4) (hexabismuth iron tetraphosphate tetraoxide), in which Bi ...

Neighbourhoods are one of the important topics in topology that relies on two types neighbours a point and has many applications graph theory sciences medical sciences. In this work, some bi-j-neighbourhoods generalized bicovering approximation space introduced. Moreover, kinds rough sets using relations presented. Some properties these new covering discussed. Pawlaks’ studied case space. More ...

The most common transfer functions in neural networks are of the sigmoidal type. In this article other transfer functions are considered. Advantages of simple gaussians, giving hyperelliptical densities, and gaussian bar functions (sums of one-dimensional gaussians) are discussed. Bi-radial functions are formed from products of two sigmoids. Product of M bi-radial functions in N -dimensional pa...

For a fusion Banach frame ({Gn, vn}, S) for a Banach space E, if ({v∗ n(E), v∗ n}, T ) is a fusion Banach frame for E∗, then ({Gn, vn}, S; {v∗ n(E), v∗ n}, T ) is called a fusion bi-Banach frame for E. It is proved that if E has an atomic decomposition, then E also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a chara...