The primary purpose of this paper is to introduce the, 2- coprobabilistic normed space, coprobabilistic dual space of 2- coprobabilistic normed space and give some facts that are related of them

In the present work, a Z-scan technique was used to study the nonlinear optical properties, represented by the nonlinear refractive index and nonlinear absorption coefficients of the Ag nanoparticles. In this technique, a pulsed second harmonic Nd :YAG laser at wavelength 532 nm was used. The results show that the nonlinear refractive index and nonlinear absorption coefficients of the Ag nanoparticles are found to be dependent on the size these nanoparticles.

The optical transmission and absorption spectra in UV-VIS were recorded in the wavelength range 350-800 nm for different glass compositions in the system: (CuO)x (PbO)50-x (Bi2O3)50 (x=2.5, 5.0, 7.5, 10.0, 12.5, 15.0, 20.0). Absorption coefficient {α (λ)}, optical energy gap (Eopt), refractive index (n), optical dielectric constant (ε`), Urbach energy (Ee), constant B and ratio of carrier concentration to the effective mass (N/m) have been reported. The effects of compositions of glasses on these parameters have been discussed. It has been indicated that a small compositional modification of the glasses lead to an important change in all the optical properties including non-linear behavior. The optical parameters were found to b

The aim of this paper is to introduce the definition of a general fuzzy norned space as a generalization of the notion fuzzy normed space after that some illustrative examples are given then basic properties of this space are investigated and proved.

For example when V and U are two general fuzzy normed spaces then the operator  is a general fuzzy continuous at u  V if and only if u in V implies S(u) in U.

    In this paper , we study some approximation  properties of the strong difference and study the relation between the strong difference and the weighted modulus of continuity

     Our goal in the present paper is to introduce a new type of fuzzy inner product space. After that, to illustrate this notion, some examples are introduced. Then we prove that that every fuzzy inner product space is a fuzzy normed space. We also prove that the cross product of two fuzzy inner spaces is again a fuzzy inner product space. Next, we prove that the fuzzy inner product is a non decreasing function. Finally, if U is a fuzzy complete fuzzy inner product space and D is a fuzzy closed subspace of U, then we prove that U can be written as a direct sum of D and the fuzzy orthogonal complement    of D.

The conventional solid-state reaction method was utilized to prepare a series of superconducting samples of the nominal composition Bi_2-xPb_0.3W_xSr₂Ca₂Cu₃O_10+d with 0≤x≤0.5 of 50 nm particle size of tungsten sintered at 850⁰C for 140h in air . The influence of substitution with W NPs at bismuth (Bi) sites was characterized by the X-ray diffraction (XRD), scanning electron microscopy (SEM) and dc electrical resistivity. Room temperature X-ray diffraction analysis revealed that there exists two phases, i.e. Bi-(2223) and Bi-(2212), in addition to the impurity phases of (SrCa) _2Cu2O3, Sr₂Ca₂Cu_7<