A metric of non-negative sectional curvature on the direct product S2 × S2 of two two-spheres may be introduced as follows: take spheres (S2 i , gi), i = 1, 2 with rotationally symmetric metrics of non-negative curvature and consider the factor space of (S2, g1) × (S2, g2) × S1 by the action of the family of isometries Ĩτ (φ1, φ2) acting as the composition of a rotation of the first factor by a...

In experiments similar to that of Fig. 1, linear plots of 1/K+ influx against the reciprocal of the external K+ concentration were fitted to the data by the method of least squares. Values of K, and VmaX. were calculated from these plots according to the usual relationships: 1/Vmax. equals 1/K+ influx when l/[K+] equals zero, and -1/K, equals l/[K+] when 1/K+ influx equals zero. The values of K...

We show that if H is a group of polynomial growth whose growth rate is at least quadratic then the Lp compression of the wreath product Z oH equals max { 1 p , 1 2 } . We also show that the Lp compression of Z oZ equals max { p 2p−1 , 2 3 } and the Lp compression of (Z oZ)0 (the zero section of Z oZ, equipped with the metric induced from Z o Z) equals max { p+1 2p , 3 4 } . The fact that the Hi...

the natural gas consumption in iran has been continuously increasing due to several reasons including low prices of natural gas, development of gas supply networks, people’s salary increase, incorrect consumption culture and the increase of national economy growth.  although, the global natural gas consumption has increased by 38% since 2001, the national consumption in iran has increased by 11...

Physics as a discipline embeds conceptual meaning about the physical world in mathematical formalism. The associated with symbols depends on context, and physicists can shift by manipulating those symbols. We present an analysis of different meanings equals sign “=” that be inferred from introductory upper-level physics textbooks. Five distinct meanings/categories are identified: causality, bal...

The Pseudo-Smarandache Function is part of number theory. The function comes from the Smarandache Function. The Pseudo-Smarandache Function is represented by Z(n) where n represents any natural number. The value for a given Z(n) is the smallest integer such that 1+2+3+ . . . + Z(n) is divisible by n. Within the Pseudo-Smarandache Function, there are several formulas which make it easier to find...

We revisit the Lee-Friedrichs model as a of atomic resonances in hydrogen atom, using dipole-moment matrix-element functions which have been exactly computed by Nussenzveig. The Hamiltonian H is positive and has absolutely continuous spectrum. Although return probability amplitude $$R_{\Psi }(t) = (\Psi , \exp (-iHt) \Psi )$$ initial state $$\Psi $$ taken so-called Weisskopf–Wigner (W.W.) state...