First, the quadratic functional equation of Pexider type will be solved. By applying this result, we will also solve some functional equations of Pexider type which are closely associated with the quadratic equation.

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

aSchool of Science, Beijing University of Posts and Telecommunications, Beijing 100876, People’s Republic of China; bCollege of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, People’s Republic of China; cKey Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, People’s Republic...

In the present paper we outline the stochastic limit approach to superfluidity. The Hamiltonian describing the interaction between the Bose condensate and the normal phase is introduced. Sufficient in the stochastic limit condition of superfluidity is proposed. Existence of superfluidity in the stochastic limit of this system is proved and the non– linear (quadratic) equation of motion describi...

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

It is known that the satisfiability problem for equations over free partially commutative monoids is decidable but computationally hard. In this paper we consider the satisfiability problem for equations over free partially commutative monoids under the constraint that the solution is a subset of the alphabet. We prove that this problem is NP-complete for quadratic equations and that its unifor...

A construction is given for a planar rational Pythagorean hodograph spiral which interpolates any two-point G Hermite data that a spiral can match. When the curvature at one of the points is zero, the construction gives the unique interpolant that is the involute of a rational Pythagorean hodograph curve of the form cubic over linear. Otherwise, the spiral comprises an involute of a Tschirnhaus...

We prove that in a free group the length of the value of each variable in a minimal solution of a standard quadratic equation is bounded by 2s for orientable equation and by 12s for non-orientable equation, where s is the sum of the lengths of the coefficients.

We reformulate the dual gauge model of the long-distance Yang-Mills theory in terms of the two-point Wightman functions formalism. In the flux-tube scheme of Abelian dominance and monopole condensation, the analytic expressions of both monopole-and dual gauge boson-fields propagators are obtained. Formally, new features of higher order quadratic equations for a monopole field are given. Finally...

Small codimensional embedded manifolds defined by equations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension. This allows us to prove the Hartshorne Conjecture for manifolds defined by quadratic equations and to obtain the list of such Hartshorne manifolds.