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Note that the family of closed curves C_N={(x,y)in R^2;x^(2N)+y^(2N)=1} for N=1,2,3,... approaches the boundary of [-1,1]^2 as N to infty. In this paper we exhibit a natural parameterization of these curves and generalize to a larger class of equations.
The polynomial $f_{2n}(x)=1+x+cdots+x^{2n}$ and its minimizer on the real line $x_{2n}=operatorname{arg,inf} f_{2n}(x)$ for $ninBbb N$ are studied. Results show that $x_{2n}$ exists, is unique, corresponds to $partial_x f_{2n}(x)=0$, and resides on t
The treated matrix equation $(1+ae^{-frac{|X|}{b}})X=Y$ in this short note has its origin in a modelling approach to describe the nonlinear time-dependent mechanical behaviour of rubber. We classify the solvability of $(1+ae^{-frac{|X|}{b}})X=Y$ in g
We study ternary sequences associated with a multidimensional continued fraction algorithm introduced by the first author. The algorithm is defined by two matrices and we show that it is measurably isomorphic to the shift on the set ${1,2}^mathbb{N}$
A ${00,01,10,11}$-valued function on the vertices of the $n$-cube is called a $t$-resilient $(n,2)$-function if it has the same number of $00$s, $01$s, $10$s and $11$s among the vertices of every subcube of dimension $t$. The Friedman and Fon-Der-Fla
We show that Bose-Einstein correlations of identical particles in hadron and nucleus high energy collisions, lead to long range rapidity correlations in the azimuthal angle. These correlations are inherent features of the CGC/saturation approach, how