in this paper. (1) we determine the complex-valued solutions of the following variant of van vleck's functional equation $$int_{s}f(sigma(y)xt)dmu(t)-int_{s}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin s,$$ where $s$ is a semigroup, $sigma$ is an involutive morphism of $s$, and $mu$ is a complex measure that is linear combinations of dirac measures $(delta_{z_{i}})_{iin i}$, such that for all $iin i$,...

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...

The sine-Gordon equation has hyperelliptic al function solutions over a hyperelliptic Jacobian for y = f(x) of arbitrary genus g. This article gives an extension of the sine-Gordon equation to that over subvarieties of the hyperelliptic Jacobian. We also obtain the condition that the sine-Gordon equation in a proper subvariety of the Jacobian is defined.

We will investigate the superstability of the hyperbolic trigonometric functional equation from the following functional equations: fx y ± gx − y λfxgy andfx y ± gx − y λgxfy, which can be considered the mixed functional equations of the sine function and cosine function, the hyperbolic sine function and hyperbolic cosine function, and the exponential functions, respectively.

description of lactation curve were investigated using sine function, compare it with two functions (dijekstra and wood). the data contained 32233 dairy milk yield records from 93 first parity iranian holstein cows that had calving between aug. 2008 and jul. 2009. actual milk production per day and subsequently the actual production of each animal were available in the first lactation. lactatio...

in this paper, we are interested to study the sine-gordon equation in generalized functions theory introduced by colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the colombeau algebra). then we study the association concept with the classical solution.

We show that high-dimensional analogues of the sine function (more precisely, the d-dimensional polar sine and the d-th root of the d-dimensional hypersine) satisfy a simplex-type inequality in a real preHilbert space H. Adopting the language of Deza and Rosenberg, we say that these d-dimensional sine functions are d-semimetrics. We also establish geometric identities for both the d-dimensional...

We prove that the τ-function of the integrable discrete sine-Gordon model apart from the " standard " bilinar identities obeys a number of " non-standard " ones. They can be combined into a bivector 3-dimensional difference equation which is shown to contain Hirota's difference analogue of the sine-Gordon equation and both auxiliary linear problems for it. We observe that this equation is most ...

Dit proefscrift werd mede mogelijk gemaakt met financï ele steun van de Koninklijke Nederlandse Akademie van Wetenschappen (KNAW). " Allah will exalt those who believe among you and those who have knowledge to high ranks. " (QS Al-Mujaadalah 58:11) for: my beloved ones Contents 1 Josephson junctions and sine-Gordon equations: an Introduction 3 1.1 Josephson junctions with phase shift 5 1.2 Sine...