Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. A theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the Deformatio...

The Teukolsky Master Equation describes the dynamics of massless fields with spin on a Kerr black hole. Under separation variables, spin-reversal for this equation is accomplished through so-called Teukolsky--Starobinsky identities. These identities are associated to constants, which spin-dependent. We collect some properties constants and dispel myths present in literature. show that, contrary...

We show that the difference equation xn = f3(xn−1) f2(xn−2) f1(xn−3), n ∈ N0, where fi ∈ C[(0,∞),(0,∞)], i ∈ {1,2,3}, is periodic with period 4 if and only if fi(x) = ci/x for some positive constants ci, i ∈ {1,2,3} or if fi(x) = ci/x when i = 2 and fi(x) = cix if i ∈ {1,3}, with c1c2c3 = 1. Also, we prove that the difference equation xn = f4(xn−1) f3(xn−2) f2(xn−3) f1(xn−4), n ∈ N0, where fi ∈...

In this work we study spacelike and timelike surfaces of revolution in Minkowski space E1 that satisfy the linear Weingarten relation aH+bK = c, where H and K denote the mean curvature and the Gauss curvature of the surface and a, b and c are constants. The classification depends on the causal character of the axis of revolution. We will give a first integral of the equation of the generating c...

The decidability of algebraic higher-order matching is proved. Algebraic higher-order matching is a matching where the constant term in equation is built of first-order constants and constants of a base type. This result is particularly appealing in the light of the last result of Loader.

Binding energy of the 1 − state (ortho-positronium) in QED is calculated using the one-photon exchange Bethe-Salpeter equation in the Feynman and Coulomb gauges for different coupling constants α. Calculations show there is a remarkable difference in values of the binding energy for different coupling constants in these two gauges.

The formation constants of the species formed in the systems H+ + cytidine 5-monophosphate (CMP)and H+ + cytidine 5-monophosphate + Tl (I) ion have been determined in aqueous solution in a widepH range of 1.5 to 10.5 at 25 °C and different ionic strengths ranging from 0.1 to 1.5 moldm-3NaClO4, NaNO3, and NaCl using potentiometric-spectrophotometric technique. The composition ofthe complexes was...

In this research, the protonation constant value of tannic acid was determined at 25 °C and different ionic strengths (0.1 to 0.7 mol/dm3 NaCl) using potentiometric titration technique. The dependence of protonation constant on ionic strength was modeled and discussed by a Debye-Hückel type equation. Then, based on the obtained data from experiments, the minimizing Sum o...

A method for predicting liquid densities of binary mixtures from heat of vaporization and liquid densityat boiling point temperature (ΔHvap and n b ρ ) as scaling constants, is presented. B2(T) follows a promisingcorresponding-states principle. Calculation of α(T) and b(T), the two other temperature-dependentconstants of the equation of state, are made possible by scaling. As a result ΔHvap and...