A family of WZ pairs and q-identities

The Ramanujan Journal - We observe that $$(F(n+k+1,k)+G(n+k,k), G(n+k,k))$$ is a WZ pair provided that (F(n, k), G(n, k)) is a WZ pair. This observation enables us to...     

A reduction formula for Waring numbers through generalized Paley graphs

Journal of Algebraic Combinatorics - We give a reduction formula for the Waring number g(k, q) over a finite field $$\mathbb {F}_q$$ . By exploiting the relation between g(k, q)...     

Automorphism subgroups for designs with $$\lambda =1$$ λ = 1

Designs, Codes and Cryptography - Given an integer $$k\ge 3$$ and a group G of odd order,  if there exists a 2-(v, k, 1)-design and if v is sufficiently large then there...     

Representations of finite number of quadratic forms with same rank

The Ramanujan Journal - Let m, n be positive integers with $$m\le n$$ . Let $$\kappa (m,n)$$ be the largest integer k such that for any (positive definite and integral) quadratic forms...     

On the arithmetic mean of the size of cross-union families

Acta Mathematica Hungarica - Let $$n > k > 1$$ be integers, $$[n] = \{1, \ldots, n\}$$ the standard $$n$$ -element set and $${[n]\choose k}$$ the collection of all its $$k$$ -subsets....     

Isomorphism of maximum length circuit codes

Designs, Codes and Cryptography - Douglas (J Comb Theory 6(4):323–339, 1969) proved that for odd spread k and dimension $$d={\frac{1}{2}(3k+3)}$$ all maximum length (d, k) circuit...     

Sparse graphs and an augmentation problem

Mathematical Programming - For two integers $$k>0$$ and $$\ell $$ , a graph $$G=(V,E)$$ is called $$(k,\ell )$$ -tight if $$|E|=k|V|-\ell $$ and $$i_G(X)\le k|X|-\ell $$ for each...     

Solutions to nonlinear Neumann problems with an inverse square potential

Let Ω be an open bounded domain in with smooth boundary . We are concerned with the critical Neumann problem

Antipodal Krein Graphs and Distance-Regular Graphs Close to Them

Doklady Mathematics - An antipodal nonbipartite distance-regular graph Γ of diameter 3 has an intersection array $$\{ k,(r - 1){{c}_{2}},\;1;\;1,\;{{c}_{2}},\;k\} $$ ( $${{c}_{2}} < k -...     

A nondegeneracy result for a nonlinear elliptic equation

Let Ω be a smooth bounded domain of with N ≥ 5. In this paper we prove, for ɛ > 0 small, the nondegeneracy of the solution of the problem

Formule de torsion pour le facteur epsilon d’un caractère sur une surface

Let be a smooth proper surface over a finite field of characteristic p > 2, and let be a rank one smooth l-adic sheaf (l ≠ p) on a dense open subset . In this paper, under some assumptions on the wild ramification of , we prove a torsion formula for the epsilon factor (that is the global constant) of the functional equation of the L-function . Our torsion formula is a generalization to higher dimension of the classical torsion formula for the local constants.

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Résumé  Soit une surface propre et lisse sur un corps fini de caractéristique p > 2, et un caractère l-adique (avec l ≠ p) lisse sur un ouvert dense . Sous certaines hypothèses sur la ramification sauvage de , on prouve une formule de torsion pour le facteur epsilon (i.e. la constante globale) de l’équation fonctionnelle de la fonction . Notre formule de torsion est une généralisation en dimension supérieure de la formule de torsion pour les constantes locales, qui est à la base de la théorie des constantes locales.

     

Approximation by the Complex form of a Link Operator Between the Phillips and the Szász–Mirakjan Operators

Results in Mathematics - The link operator $${P_{\alpha}^\rho(f,x)=\sum_{k=1}^\infty s_{\alpha,k}(x)\int_0^\infty \theta_{\alpha,k}^\rho(t)f(t)dt+e^{-\alpha x}f(0)}$$ , $${\alpha, \rho >...     

Bifurcations of Positive and Negative Continua in Quasilinear Elliptic Eigenvalue Problems

The main result of this work is a Dancer-type bifurcation result for the quasilinear elliptic problem

Mori dreamness of blowups of weighted projective planes

Archiv der Mathematik - We consider the blowup X(a, b, c) of a weighted projective space $${\mathbb {P}}(a,b,c)$$ at a general nonsingular point. We give a sufficient condition...     

Density of Derivatives of Simple Partial Fractions in Hardy Spaces in the Half-Plane

Mathematical Notes - It is proved that the sums $$ \sum_{k=1}^{n} \frac{1}{(z-a_{k})^{2}}\mspace{2mu}, \qquad \operatorname{Im}a_{k} < 0, \quad n \in \mathbb{N}, $$ are dense in all Hardy...     

A $$\mathrm {GL}_3$$ GL 3 analog of Selberg’s result on S(t)

The Ramanujan Journal - We are concerned with counting self-conjugate $$(s,s+1,s+2)$$ -core partitions. A Motzkin path of length n is a path from (0, 0) to (n, 0) which stays...     

Tauberian theorems for iterations of weighted mean summable integrals

Positivity - Let p be a positive weight function on $$A:=[1, \infty )$$ which is integrable in Lebesgue’s sense over every finite interval (1, x) for $$1<\infty $$ , in...     

Inequalities for Taylor series involving the divisor function

Czechoslovak Mathematical Journal - Let $$T(q) = \sum\limits_{k = 1}^\infty {d(k){q^k},\,\,\,\,\left| q \right| < 1,} $$ where d(k) denotes the number of positive divisors of the natural...     

Surfaces with many solitary points

It is classically known that a real cubic surface in cannot have more than one solitary point (or -singularity, locally given by x ² + y ² + z ² = 0) whereas it can have up to four nodes (or -singularity, locally given by x ² + y ² − z ² = 0). We show that on any surface of degree d ≥ 3 in the maximum possible number of solitary points is strictly smaller than the maximum possible number of nodes. Conversely, we adapt a construction of Chmutov to obtain surfaces with many solitary points by using a refined version of Brusotti’s Theorem. Combining lower and upper bounds, we deduce: , where denotes the maximum possible number of solitary points on a real surface of degree d in . Finally, we adapt this construction to get real algebraic surfaces in with many singular points of type for all k ≥ 1.      

On Finsler manifolds with hyperbolic geodesic flows

Archiv der Mathematik - Let (M, F) be a closed $$C^\infty $$ Finsler manifold and $$\varphi $$ its geodesic flow. In the case that $$\varphi $$ is Anosov, we extend to the Finsler setting...