In this article we investigate filters of cozero sets for real-valued continuous functions, calledcoz-filters. Much is known for z-ultrafilters and their correspondence with maximal ideals of C (X). Similarly, a correspondence will be established betweencoz-ultrafilters and minimal prime ideals of C (X). We will further notice various properties of coz-ultrafilters in relation toP-spaces and F-spaces. In the last two sections, the collection of cozultrafilters will be topologized, and then compared to the hull-kernel and the inverse topologies placed on the collection of minimal prime ideals of C (X) and general lattice-ordered groups.

In this experimental work, the polycrystalline samples of ternary compound InGaTe2 and binary compound PbT2 were initially synthesized and then by grinding and mixing given amounts of PbTe and InGaTe2 (as impurity), two types of compounds given by the formula (PbTe)1-x (InGaTe2)x having two different mole percentages of x=0.5 and x=1 were synthesized, respectively. By studying the variations of thermoelectric power (a) and electrical conductivity (er) of samples versus the temperature, the values of energy gap for the above two compounds were evaluated. Experimental results show that, the pure PbTe is a typical p type semiconductor, but introducing the ternary compound InGaTe2 into the crystal, its conductivity changes from p to n. The energy gap of PbTe is increased by increasing the mole percentage of the InGaTe2 impurity. Increasing the impurity content, up to x=0.5 mole percent causes the conductivity to increase, but further increase of the impurity content, causes the conductivity to decrease. Thermoelectric power increases with the temperature and its maximum value is larger for the compound with lesser impurity content.

In this paper we study some sufficient conditions for commutativity of a ring according to Jacobsons'idea. Jacobson proved that if R is a ring satisfying xn= x (n>1) for each x Î R, then R is commutative. In this paper, we show that R is commutative if for every x, y 2 R there exists a positive integer n= n (x, y) such that (x [x, y])n = x [x, y].

Let CF (X) be the socle of C (X) and LCF (X)={FÎC (X):`SF=X}, where SF is the union of all open subsets U in X such that | U\ Z (f) |< ¥, LCF (X) is called the locally socle of C (X) and it is a z-ideal of C (X) containing CF (X)…

A theoretical search is conducted to determine the mass spectra and wave functions of the higher di-molecular type of meson states X(3872)"," Y(4140),Z(4430),X(5568) in the Hellmann potential, with relativistic effects and corrections. Femtoscopic J/ψ bound states have essential concepts in high-energy physics, especially in creating two-point correlation functions for the hadronic molecule channels that build the T_cc state. We analytically calculated the radial part of the Schrödinger equation using the transformation to relativistic space using the normal ordering operators. The excited states of eigenenergy are obtained. The constituent mass of the di-molecular type of mesons was determined, which appears due to relativistic effects. It is informative to describe strong interactions and bound states mechanisms using quantum field theory ideas and quantum mechanics. At the conclusion of this research, we will provide advancements in the higher meson states mass spectra in the relativistic limit. The results provide satisfaction in comparison with experimental data and the work of other researchers.

To investigate the electromagnetic interaction of molecules inside the nanotubes, first, the structure of nanotubes B16N16 was optimized with hybrid density functional theory (B3LYP) using the EPR-II basis set, then Cu, Cu+, Cu++were located in nanotube and we studied the total energy, band gap energy, electrical potential, changes of band gap energy in terms of total energy and dipole moment in the B16N16-X (X=Cu, Cu+, Cu++) systems. Also, to investigate the electromagnetic interaction of molecules inside the nanotubes, we studied the nuclear magnetic resonance properties (NMR) and shielding parameters between nanotubes.