Abstract Given $$E_0, E_1, F_0, F_1, E$$ E 0 , 1 F rearrangement invariant function spaces, $$a_0$$ a , $$a_1$$ $$\mathrm {b}_0$$ b {b}_1$$ {b}$$ slowly varying f...

This paper deals with the existence and multiplicity of solutions for a class Kirchhoff type elliptic systems involving nonlinearities Trudinger-Moser exponential growth. We first study following system: $$\begin{aligned} \left\{ \begin{array}{ll} -\big (a_1+b_1\Vert u\Vert ^{2(\theta _1-1)}\big )\Delta u= \lambda H_u(x,u,v) &{} \quad \text{ in }\ \ \Omega ,\\ (a_2+b_2\Vert v\Vert _2-1)}\big v=...

There are many extensions and generalizations of Gamma Beta functions in the literature. However, a new extension extended function B_(ζ〖, α〗_1)^(α_2;〖 m〗_1,〖 m〗_2 ) (a_1,a_2 was introduced presented here because its important properties. The has symmetric property, integral representations, Mellin transform, inverse transform statistical properties like distribution, mean, variance, moment cum...

In this paper, we study certain determinants over finite fields. Let $\mathbb{F}_q$ be the field of $q$ elements and let $a_1,a_2,\cdots,a_{q-1}$ all nonzero $\mathbb{F}_q$. $T_q=\left[\frac{1}{a_i^2-a_ia_j+a_j^2}\right]_{1\le i,j\le q-1}$ a matrix We obtain explicit value $\det T_q$. Also, as consequence our result, confirm conjecture posed by Zhi-Wei Sun.

In this paper we investigate the quantity of diagonal quartic surfaces $a_0 X_0^4 + a_1 X_1^4 a_2 X_2^4 +a_3 X_3^4 = 0$ which have a Brauer–Manin obstruction to Hasse principle. We are able find an asymptotic formula for such ordered by height. The proof uses generalization method Heath-Brown on sums over linked variables. also show that there exists no uniform generic generator in family.

We investigate a method of generating graph $G=(V,E)$ out an ordered list $n$ distinct real numbers $a_1, \dots, a_n$. These graphs can be used to test for the presence interesting structure in sequence. describe sequences exhibiting intricate hidden that was discovered this way. Our includes Deutsch, Erd\H{o}s, Freud & Hegyvari, Recaman, Quet, Zabolotskiy and Zizka. Since our observations are ...

Two abelian varieties A 1 , 2 A_1, A_2 <...

For an integer n, a set of m distinct nonzero integers {a_1,a_2,...,a_m} such that a_i a_j+n is perfect square for all 0<i<j<m+1, called D(n)-m-tuple. In this paper, we show there are infinitely many essentially different D(n)-quintuples with elements. We obtained result by constructing genus one curves on certain double cover A^2 branched along four curves.