<p style='text-indent:20px;'>The global asymptotic stability of the unique positive equilibrium point and rate convergence solutions system two recursive sequences has been studied recently. Here we generalize this study to <inline-formula><tex-math id="M1">$ p $</tex-math></inline-formula> id="M2">$x_{n+1}^{(j)}=A+\left(x_{n-m}^{(j+1) mod (p)} \;\;/ x_{n}^{(j+1...

Given any diagonal cyclic subgroup $\Lambda \subset GL(n+1,k)$ of order $d$, let $I_d\subset k[x_0,\ldots, x_n]$ be the ideal generated by all monomials $\{m_{1},\ldots, m_{r}\}$ degree $d$ which are invariants $\Lambda$. $I_d$ is a monomial Togliatti system, provided $r \leq \binom{d+n-1}{n-1}$, and in this case projective toric variety $X_d$ parameterized $(m_{1},\ldots, m_{r})$ called $GT$-v...

We investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

Abstract We study the number of ordered k -partitions a multiset with equal sums, having elements $$\alpha _1,\ldots ,\alpha _n$$ α 1 , … n and multiplicities $$m_1,\ldots ,m_n$$ m</mml:mi...

The main goal of this paper is to study the bifurcation a second order rational difference equation $$x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+Cx_{n-1}}, ~~n=0, 1, 2, \ldots$$ with positive parameters $\alpha, \beta, A, B, C$ and non-negative initial conditions $\{x_{-k}, x_{-k+1}, \ldots, x_{0}\}$. We dynamic behavior direction period-two cycle. Numerical discussion figures are given suppo...

Abstract When $k\geqslant 4$ and $0\leqslant d\leqslant (k-2)/4$ , we consider the system of Diophantine equations \begin{align*}x_1^j+\ldots +x_k^j=y_1^j+\ldots +y_k^j\quad (1\leqslant j\leqslant k,\, j\ne k-d).\end{align*} We show that in this cousin a Vinogradov system, there is paucity non-diagonal positive integral solutions. Our quantitative estimates are particularly sharp when $d=o\!\le...

Let G be an additive finite abelian group and $$\Gamma \subset {\rm End} (G)$$ a subset of the endomorphism G. A sequence $$S = g_1 \cdot \ldots g_{\ell}$$ over is ( $$\Gamma$$ -)weighted zero-sum if there are $$\gamma_1, \ldots, \gamma_{\ell} \in \Gamma$$ such that $$\gamma_1 (g_1) + (g_{\ell})=0$$ . We construct transfer homomorphisms from norm monoids (of Galois algebraic number fields with ...

Let E be a vector lattice, $$\lambda _1,\lambda _2,\ldots ,\lambda _k$$ scalars and $$\varphi _1,\ldots ,\varphi pairwise independent regular linear functionals on E. We show that if $$k<m$$ then $$\sum _{j=1}^k\lambda _j\varphi _j^m$$ is orthogonally additive only _j$$ or $$-\varphi lattice homomorphism for each j, $$1\le j\le k$$ . Moreover, $$m\ge 2$$ , we provide an example to this result d...

A hyperbolic polynomial (HP) is a real univariate with all roots real. By Descartes' rule of signs HP coefficients nonvanishing has exactly $c$ positive and $p$ negative counted multiplicity, where are the numbers sign changes preservations in sequence its coefficients. We consider HPs distinct moduli roots. ask question when order w.r.t. on half-line completely determines polynomial. When ther...

We obtain the criterion of best approximant for multivariable functions in $L_{p_1,\ldots p_n}$ space.