Cauchy problem for the Zakharov System Arising from Ion-Acoustic Modes with low regularity data

We prove local well-posedness results for the Zakharov System Arising from Ion-Acoustic Modes in two spacial dimension with large initial data in low regularity Sobolev space \(   (\dot{H}^1 \bigcup H^{\frac{1}{2}})\times L^2 \times H^{-1}  \).  Using ”derivative sharing”, the local well-posedness results in \( (\dot{H}^1 \bigcup H^{\frac{1}{2}-\delta})\times H^{\delta} \times H^{-1+\delta}\)  are also obtained, for any  0 \(\leq \delta \leq 1/2 \).     

Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times

Queueing Systems - We study the occurrence of large queue lengths in the GI / GI / d queue with heavy-tailed Weibull-type service times. Our analysis hinges on a...     

Lazy groupoids

Semigroup Forum - A binary operation f(x, y) is said to be lazy if every operation that can be obtained from f by composition is equivalent to f(x, y), f(x, x) or x. We...     

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)...     

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...     

On the Lang–Trotter conjecture for two elliptic curves

The Ramanujan Journal - We extend the author’s earlier computation and give coefficient formulas for the (quasimodular) Poincaré square series of weight 3 / 2 and...     

On the integrability of the differential systems in dimension two and of the polynomial differential systems in arbitrary dimension

This is a survey on recent results providing sufficient conditions for the existence of a first integral, first for vector fields defined on real surfaces, and second for polynomial vector fields in \(R^n\) or \(C^n\) with \(n\geq 2\). We also provide an open question and some applications based on the existence of such first integrals.               

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...     

On the Diophantine equation $$x^2+3^a41^b=y^n $$ x 2 + 3 a 41 b = y n

Periodica Mathematica Hungarica - In this paper we find all positive integer solutions (x, y, n, a, b) of the equation in the title for non negative integers a...     

An extension of the Kakutani–Bohnenblust characterization of $$L^p$$ L p -spaces to $$p\in (0,\infty )$$ p ∈ ( 0 , ∞ )

Positivity - For $$p\in [1,\infty )$$ , S. Kakutani and H.F. Bohnenblust have given characterizations of $$L^p$$ as a Banach lattice. We generalize that result to $$p\in (0,\infty...     

Holzer’s theorem in k[t]

The Ramanujan Journal - Let a, b, c be nonzero polynomials in k[t] where k[t] is the ring of polynomials with coefficients in k. We prove that if $$ax^2 \,{+}\, by^2 \,{+}\, cz^2...     

Exact tail asymptotics for fluid models driven by an M/M/c queue

Queueing Systems - In this paper, we investigate exact tail asymptotics for the stationary distribution of a fluid model driven by the M / M / c queue, which is...     

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...     

Multiple solutions with sign information for superlinear (p, q)-equations

Positivity - We consider a nonlinear Dirichlet problem driven by the (p, q)-Laplacian and with a Carathéodory reaction f(z, x) which is ( $$p-1$$ )-superlinear in $$x\in...     

Stars at infinity in Teichmüller space

Geometriae Dedicata - We investigate a metric structure on the Thurston boundary of  Teichmüller space. To do this, we develop tools in sup metrics and apply Minsky’s...     

Cesàro matrix and (1, 1; r)-convex sequences

Positivity - This paper deals with (1, 1; r)-convexity of sequences. First, we prove several results on the sets of (1, 1; r)-convex sequences for various values...     

A Class of Invertible Subelliptic Operators in S(m,g)-Classes

Results in Mathematics - Given a self-adjoint second order differential operator L with positive characteristic and subellipticity of order 1 ≤ τ < 2....     

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...     

Color Representations of Ising Models

Journal of Theoretical Probability - In Steif and Tykesson (J Prob 16:899–955, 2019), the authors introduced the so-called general divide and color models. One of the best-known...     

Random attractor of stochastic Zakharov lattice system

In this paper, we consider a lattice system of stochastic Zakharov equation with white noise. We first show that the solutions of the system determine a continuous random dynamical system with random absorbing set. And then we prove the random  asymptotic compact on the random absorbing set. Finally, we obtain the existence of a random attractor for the system.