The Terwilliger algebra of the halved folded 2n-cube from the viewpoint of its automorphism group action

Journal of Algebraic Combinatorics - Let $$\frac{1}{2}{\overline{H}}(2n,2)$$ denote the halved folded 2n-cube with vertex set X and let $$T{:}{=}T(x)$$ denote the Terwilliger algebra of...     

On Minimal Asymptotic Bases

Mathematical Notes - Let $$\mathbb N$$ denote the set of all nonnegative integers, and let $$A\subseteq\mathbb N$$ . Let $$h,n\in\mathbb N$$ , $$h\ge 2$$ and $$r_h(A,n)=\#\{(a_1,\dots,a_h)\in...     

Quantum observable generalized orthoalgebras

Positivity - Let $${{{\mathcal {S}}}}({\mathcal {H}})$$ denote the set of all self-adjoint operators (not necessarily bounded) on a Hilbert space $${\mathcal {H}}$$, which is the set of all...     

A note on commutator subgroups in groups of large cardinality

Monatshefte für Mathematik - If G is an uncountable group of regular cardinality $$\aleph $$, we shall denote by $${\mathfrak {L}L}_\aleph (G)$$ the set of all subgroups of G of cardinality...     

On the max-domain of attractions of bivariate elliptical arrays

Let be a triangular array of independent bivariate elliptical random vectors with the same distribution function as where is a bivariate spherical random vector. Under assumptions on the speed of convergence of we show in this paper that the maxima of this triangular array is in the max-domain of attraction of a new max-id. distribution function , provided that has distribution function in the max-domain of attraction of the Weibull distribution function . AMS 2000 Subject Classification Primary—60G70, 60F05     

Isoperimetric estimates in low-dimensional Riemannian products

Annals of Global Analysis and Geometry - Let $$(T^k,h_k)=(S_{r_1}^1\times S_{r_2}^1 \times \cdots \times S_{r_k}^1, dt_1^2+dt_2^2+\cdots +dt_k^2)$$ be flat tori, $$r_k\ge \cdots \ge r_2\ge...     

ON THE TAYLOR'S JOINT SPECTRUM OF 2n-TUPLE (L_A, R_B)

Let A= (A_1, …, A_n) and B=(B_1, …, B_n) be double commuting n-tuples of operators on Hilbert space H and let L_(A_i), and R_(B_j), decode the left and right multiplications induced by A_i and B_j, respectively. The following results are proven: Sp (L_A, R_B)=Sp(A)×Sp(B), Sp_e(L_A, R_B)=Sp_e(A)×Sp(B) ∪ Sp(A)×Sp_e(B).     

A SORT OF POLYNOMIAL IDENTITIES OF $\[{M_n}(F)\]$ WITH CHAR $\[F \ne 0\]$

Let $F$ denote a field, finite or infinite, with characteristic $\[p \ne 0\]$. In this paper, the author obtains the following result: The symmetric polynomial on $t$ letters $$\[{S_{sym(t)}}({x_1},{x_2}, \cdots ,{x_t}) = \sum\limits_{x \in sym(t)} {{X_{\pi 1}}{X_{\pi 2}} \cdots {X_{\pi t}}} \]$$ is a polynomial identity of $\[{M_n}(F)\]$ when $\[t \ge pn\]$, and this is sharp in the sense that if $\[t \le pn - 1\]$,it is not a polynomial identity of $\[{M_n}(F)\]$.     

算子n次方根的惟一性

B(H)表示定义在希尔伯特空间H上的所有有界线性算子的全体。对于A∈B(H),其中σ(A)和W(A)分别表示算子A的谱和数值域,N表示自然数集。关于算子A的n(n∈N)次方根,本文的主要结果是:(1)若σ(A)∩(-∞,0]=φ,则A有惟一的n次方根B∈B(H)且σ(B)(?)~(2/n)~o;(2)若(?)∩(-∞,0]=φ,则A有惟一的n次方根B∈B(H)且(?)(2/n)~o这里,S_(1/n)={λ∈C‖argλ|≤(1/2n)π}且S_(1/n)~o表示集合S+(1/n)的内部。     

A generalized variety problem

Semigroup Forum - Let $${\mathscr {C}}\! om $$ denote the variety of all commutative semigroups. For $$n\ge 1$$ let $${{\mathscr {N}}\! il }_n$$ (respectively $${\mathscr {N}}_n$$ ) denote the...     

The amalgamation of high distance Heegaard splittings is always efficient

Let M be a compact orientable manifold, and F be an essential closed surface which cuts M into two 3-manifolds M ₁ and M ₂. Let be a Heegaard splitting for i = 1, 2. We denote by d(S _i ) the distance of . If d(S ₁), d(S ₂) ≥ 2(g(M ₁) + g(M ₂) − g(F)), then M has a unique minimal Heegaard splitting up to isotopy, i.e. the amalgamation of and . Ruifeng Qiu is supported by NSFC(10625102).     

Generalized valences

We have established that V(S_p, q; G), namely, the collection of all those edges of an arbitrary n-vertex hypergraph G, whose intersections with set S_p, p vertices, has a cardinality q, satisfies certain identity relations; in particular, if v(S_p q; G) = ¦V(S_p, q; G)¦, then $$\upsilon (S_p ,q;G) = \sum\nolimits_{i \geqslant 0} {( - 1)^i } C_{q + i}^q \sum\nolimits_{S_{q + i} \subset S_p } {\upsilon (S_{q + i} ,q + i;} G).$$ As applications we derive two new combinatorial identities.     

Arithmetic properties of cubic and overcubic partition pairs

The Ramanujan Journal - Let b(n) denote the number of cubic partition pairs of n. We affirm a conjecture of Lin by proving that $$\begin{aligned} b(49n+37)\equiv 0 \pmod {49} \end{aligned}$$for all...     

Generalized Sidon sets of perfect powers

The Ramanujan Journal - For $$h \ge 2$$ and an infinite set of positive integers A, let $$R_{A,h}(n)$$ denote the number of representations of the positive integer n as the sum of h distinct terms...     

A note on the Lebesgue–Ljunggren–Nagell equation $$ax^2+b^{2m}=4y^n$$ a x 2 + b 2 m = 4 y n

Periodica Mathematica Hungarica - Let a, b be fixed positive integers such that $$2\not \mid {ab}$$ , $$\gcd (a,b)=1$$ and a is square-free, and let $$h(-a)$$ denote the class number of...     

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...     

Fractional Gaussian estimates and holomorphy of semigroups

Let $$\Omega \subset {\mathbb {R}}^N$$ be an arbitrary open set, $$0<s<1$$ and denote by $$(e^{-t(-\Delta )_{{{\mathbb {R}}}^N}^s})_{t\ge 0}$$ the semigroup on $$L^2({{\mathbb {R}}}^N)$$ generated by the fractional Laplace operator. In the first part of the paper, we show that if T is a self-adjoint semigroup on $$L^2(\Omega )$$ satisfying a fractional Gaussian estimate in the sense that $$|T(t)f|\le Me^{-bt(-\Delta )_{{{\mathbb {R}}}^N}^s}|f|$$, $$0\le t \le 1$$, $$f\in L^2(\Omega )$$, for some constants $$M\ge 1$$ and $$b\ge 0$$, then T defines a bounded holomorphic semigroup of angle $$\frac{\pi }{2}$$ that interpolates on $$L^p(\Omega )$$, $$1\le p<\infty $$. Using a duality argument, we prove that the same result also holds on the space of continuous functions. In the second part, we apply the above results to the realization of fractional order operators with the exterior Dirichlet conditions.     

关于三次样条函数导数的某些不等式

设△:。~x。相似文献   

On the Diophantine equation $$Cx^{2}+D=2y^{q}$$ C x 2 + D = 2 y q

The Ramanujan Journal - Let C and D denote positive integers such that $$CD&gt;1$$ . In this paper we investigate the solvability of the Diophantine equation $$Cx^{2}+D=2y^{q}$$ , in positive...     

Noether’s problem for GL(2, 3)

We prove that Noether’s problem has an affirmative answer for the group GL(2, 3), over every field K. In particular, the group admits a generic polynomial over . As a consequence, so does the group . Research was partially supported by MCYT grant BFM2003-01898.