单圈图的最大特征值的上界的改进

Let G（V, E） be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V（Cm）. The G - E（Cm） are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui ： i = 1, 2 , m}. Let κ = ec＋1. Forj = 1,2,...,k- 1, let δij = max{dv ： dist（v, ui） = j,v ∈ Ti}, δj = max{δij ： i = 1, 2,..., m}, δ0 = max{dui ： ui ∈ V（Cm）}. Then λ1（G）≤max{max 2≤j≤k-2 （√δj-1-1＋√δj-1）,2＋√δ0-2,√δ0-2＋√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 （G） is the largest eigenvalue of the adjacency matrix of G.     

Linear combination of composition operators on $$H^\infty $$ H ∞ and the Bloch space

Archiv der Mathematik - Let $$\lambda _i (i=1,\ldots ,k)$$ be nonzero complex scalars and $$\varphi _i (i=1,..,k)$$ be analytic self-maps of the unit disk $$\mathbb {D}$$ . We show that the...     

The extension of the $$D(-k)$$ D ( - k ) -pair $$\{k,k+1\}$$ { k,k + 1 } to a quadruple

Periodica Mathematica Hungarica - Let $$n\ne 0$$ be an integer. A set of m distinct positive integers $$\{a_1,a_2,\ldots ,a_m\}$$ is called a D(n)-m-tuple if $$a_ia_j + n$$ is a perfect square for...     

On the average sum of the kth divisor function over values of quadratic polynomials

The Ramanujan Journal - Let $$F(x) \in \mathbb {Z}[x_1 , x_2 ,\ldots , x_n ]$$ , $$n\ge 3$$ , be an n-variable quadratic polynomial with a nonsingular quadratic part. Using the circle method we...     

Hamming weight distributions of multi-twisted codes over finite fields

Designs, Codes and Cryptography - Let $${\mathbb {F}}_q$$ denote the finite field of order q,  and let $$n = m_1+m_2+\cdots +m_\ell ,$$ where $$m_1,m_2,\ldots ,m_\ell $$ are arbitrary...     

On the distribution of the sum of digits of sums $$a+b$$ a + b

The Ramanujan Journal - Let $${\mathcal {A}}$$ , $${\mathcal {B}}$$ be large subsets of $$\{1,\ldots ,N\}$$ . We study the distribution of the sum of binary digits of the sums $$a+b$$ with...     

A finite field approach to the Carlitz–Riordan q-Catalan numbers

Journal of Algebraic Combinatorics - Let q be a prime power and $${\mathbb {F}}_q$$ be the finite field with q elements. Suppose that $$n\ge 1$$ and $${{\mathscr {F}}}=\{E_1,\ldots ,E_{2n-1}\}$$ is...     

Menon-type identities with respect to sets of units

The Ramanujan Journal - Let $$n\ge 1$$ and let $$\mathbb {Z}_n^\star $$ be the group of units in the ring of residual classes modulo n, let $$m\ge 0$$ , $$k\ge 0$$ , $$m+k\ge 1$$ , $$u_1,\ldots...     

On the number of solutions of $$x_1\cdots x_{p^k}=g$$ x 1 ⋯ x p k = g in a finite p-group

Archiv der Mathematik - Let G be a finite p-group, $$g\in G$$ , $$A\subseteq G$$ , and $$q:=p^k\ge |G|$$ . We determine, modulo p, the number of solutions $$(x_1,\ldots ,x_q)\in A^q$$ of the...     

Unmixedness and arithmetic properties of matroidal ideals

Let $$R=k[x_1,\ldots ,x_n]$$ be the polynomial ring in n variables over a field k and let I be a matroidal ideal of degree d. In this paper, we study the unmixedness properties and the arithmetical rank of I. Moreover, we show that $$ara(I)=n-d+1$$. This answers the conjecture made by Chiang-Hsieh (Comm Algebra 38:944–952, 2010, Conjecture).     

On Algebraic Limits and Topological Properties of Sets of Möbius groups in $ \bar {R}^n $

Let G be the algebraic limit of a sequence $ \{ G_m\} $ of r generator subgroups of $ M(\bar {R}^n) $ . We prove that (i) if $ G_m $ is elementary, then G is elementary; (ii) if $ G_m $ is not non-elementary and non-discrete and G satisfies the Condition A, then G is not non-elementary and non-discrete. Let $ E_l = \{ (f_1, f_2,\ldots ,f_l): f_1,f_2,\ldots ,f_l\in M(\bar {R}^2), \langle \,f_1,f_2,\ldots , \,f_l \rangle\ elementary\} $ and $ D_l = \{ (f_1,f_2,\ldots ,f_l): f_1,f_2,\ldots ,f_l\in M(\bar {R}^2), \langle \,f_1,f_2,\ldots ,f_l \rangle\ discrete\} $ . we obtain that the set $ E_l , D_l\cup E_l $ and $ D_l\cap E_l^c $ are closed in $ \underbrace {M(\bar {R}^2)\times \cdots \times M(\bar {R}^2)}\limits _{l} $ .     

Linear functional equations and their solutions in generalized Orlicz spaces

Aequationes mathematicae - Assume that $$\Omega \subset \mathbb {R}^k$$ is an open set, V is a real separable Banach space and $$f_1,\ldots ,f_N :\Omega \rightarrow \Omega $$ , $$g_1,\ldots ,...     

A Snevily-type inequality for multisets

Acta Mathematica Hungarica - Alon [1] proved that if $$p$$ is an odd prime, $$1\le n < p$$ and $$a_1,\ldots,a_n$$ are distinct elements in $$Z_p$$ and $$b_1,\ldots,b_n$$ are arbitrary...     

On k-partitions of multisets with equal sums

The Ramanujan Journal - We study the number of ordered k-partitions of a multiset with equal sums, having elements $$\alpha _1,\ldots ,\alpha _n$$ and multiplicities $$m_1,\ldots ,m_n$$ . Denoting...     

Nonlinear $$\ast$$-Lie-type derivations on von Neumann algebras

Let \({\mathcal{H}}\) be a complex Hilbert space, \({\mathcal{B(H)}}\) be the algebra of all bounded linear operators on \({\mathcal{H}}\) and \({\mathcal{A} \subseteq \mathcal{B(H)}}\) be a von Neumann algebra without nonzero central abelian projections. Let \({p_n(x_1,x_2 ,\ldots ,x_n)}\) be the commutator polynomial defined by n indeterminates \({x_1, \ldots , x_n}\) and their skew Lie products. It is shown that a mapping \({\delta \colon \mathcal{A} \longrightarrow \mathcal{B(H)}}\) satisfies

$$\delta(p_n(A_1, A_2 ,\ldots , A_n))=\sum_{k=1}^np_n(A_1 ,\ldots , A_{k-1}, \delta(A_k), A_{k+1} ,\ldots , A_n)$$

for all \({A_1, A_2 ,\ldots , A_n \in \mathcal{A}}\) if and only if \({\delta}\) is an additive *-derivation. This gives a positive answer to Conjecture 4.2 of [14].

     

A note on the exceptional solutions of Jeśmanowicz’ conjecture concerning primitive Pythagorean triples

Periodica Mathematica Hungarica - Let $$(m,\ n)$$ be fixed positive integers such that $$m>n,\ \gcd (m,\ n)=1$$ and $$ mn\equiv 0 \pmod 2$$ . Then the triple $$(m^2-n^2,\ 2mn,\ m^2+n^2)$$ is...     

Reverse Brascamp–Lieb inequality and the dual Bollobás–Thomason inequality

Archiv der Mathematik - We prove that if $$f:{\mathbb {R}}^n\rightarrow [0,\infty )$$ is an integrable log-concave function with $$f(0)=1$$ and $$F_1,\ldots ,F_r$$ are linear subspaces of...     

An Endpoint Weak-Type Estimate for Multilinear Calderón–Zygmund Operators

Journal of Fourier Analysis and Applications - The purpose of this article is to provide an alternative proof of the weak-type $$\left( 1,\ldots ,1;\frac{1}{m}\right) $$ estimate for m-multilinear...     

Diophantine inequality by unlike powers of primes

The Ramanujan Journal - Suppose that $$\lambda _1,\ldots ,\lambda _5$$ are nonzero real numbers, not all of the same sign, satisfying that $$\frac{\lambda _1}{\lambda _2}$$ is irrational. Then for...     

图的上可嵌入性与独立顶点的新度和

Let G be a k(k ≤3)-edge connected simple graph with minimal degree ≥ 3,girth g,r=g12.For any independent set {a1,a2 , . . . , a 6/(4 k)} of G,if,then G is up-embeddable.