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.

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.

begin{abstract} the relations between the spectrum of the matrix $q+r$ and the spectra of the matrices $(gamma + delta)q+(alpha + beta)r-qr-rq$, $qr-rq$, $alpha beta r-qrq$, $alpha rqr-(qr)^{2}$, and $beta r-qr$ have been given on condition that the matrix $q+r$ is diagonalizable, where $q$, $r$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of order $...

begin{abstract} The relations between the spectrum of the matrix $Q+R$ and the spectra of the matrices $(gamma + delta)Q+(alpha + beta)R-QR-RQ$, $QR-RQ$, $alpha beta R-QRQ$, $alpha RQR-(QR)^{2}$, and $beta R-QR$ have been given on condition that the matrix $Q+R$ is diagonalizable, where $Q$, $R$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of ord...

First, an integer programming model is proposed to find an α-labeling for quadratic graphs. Then, a Tabu search algorithm is developed to solve large scale problems. The proposed approach can generate α-labeling for special classes of quadratic graphs, not previously reported in the literature. Then, the main theorem of the paper is presented. We show how a problem in graph theory c...

We consider Presburger arithmetic (PA) extended by scalar multiplication an algebraic irrational number $\alpha$, and call this extension $\alpha$-Presburger ($\alpha$-PA). show that the complexity of deciding sentences in $\alpha$-PA is substantially harder than PA. Indeed, when $\alpha$ quadratic $r\geq 4$, with $r$ alternating quantifier blocks at most $c\ r$ variables inequalities requires ...

We show that Whitham type equations u_t + u u_x -L = 0, where L is a general Fourier multiplier operator of order \alpha \in [-1,1], \alpha\neq allow for small solutions to be extended beyond their expected existence time. The result valid range quadratic dispersive with inhomogeneous symbols in the given by \alpha, and should extendable other same relative strength.

The Sch\"{o}nberg-Chandrasekhar limit in post main sequence evolution for stars of masses the range $1.4\lesssim M/M_{\odot}\lesssim 6$ gives maximum pressure that stellar core can withstand, once central hydrogen is exhausted. It usually expressed as a quadratic function $1/\alpha$, with $\alpha$ being ratio mean molecular weight to envelope. Here, we revisit this scenarios where balance equat...

We revise a previous result about the Fr\"ohlich dynamics in strong coupling limit obtained [Gri17]. In latter it was shown that time evolution applied to initial state $\varphi_0 \otimes \xi_\alpha$, where $\varphi_0$ is electron ground of Pekar energy functional and $\xi_\alpha$ associated coherent phonons, can be approximated by global phase for times small compared $\alpha^2$. present note ...

We analyze the thermodynamic Casimir effect occurring in a gas of non-interacting bosons confined by two parallel walls with strongly anisotropic dispersion inherited from an underlying lattice. In direction perpendicular to confining standard quadratic is replaced term $|{\bf p}|^{\alpha}$ $\alpha \geq 2$ treated as parameter. derive closed, analytical expression for force depending on dimensi...