The full automorphism group of T‾

Let $\stackrel{￣}{G}$ be the wonderful compactification of a simple affine algebraic group G of adjoint type defined over $\mathbb{C}$. Let $\stackrel{￣}{T}?\stackrel{￣}{G}$ be the closure of a maximal torus $T?G$. We prove that the group of all automorphisms of the variety $\stackrel{￣}{T}$ is the semi-direct product $N_G(T)?D$, where $N_G(T)$ is the normalizer of T in G and D is the group of all automorphisms of the Dynkin diagram, if $G\ne \mathrm{PSL}(2,\mathbb{C})$. Note that if $G=\mathrm{PSL}(2,\mathbb{C})$, then $\stackrel{￣}{T}=\mathbb{C}{\mathbb{P}}^1$ and so in this case $\text{Aut}(\stackrel{￣}{T})=\mathrm{PSL}(2,\mathbb{C})$.     

Brauer–Clifford equivalence of full matrix algebras

The Brauer–Clifford group was introduced to describe the Clifford theory for finite groups. It was proved that it has a natural homomorphism into a Brauer group, and the kernel of this homomorphism is the set of all equivalence classes of G-algebras which are full matrix algebras. In this paper, we prove that this kernel is isomorphic to a second cohomology group. In the Clifford theory for finite groups situation, we characterize families of characters which yield elements in the full matrix subgroup of the Brauer–Clifford group as those where an appropriate character has Schur index one. We also show, in this case, how to compute the element of the second cohomology group associated with this family of characters.     

Geodesic flow, connecting orbits and almost full foliation

We study in this article a special dynamical behavior of geodesic flow on T2. Our example shows that there is an area-preserving monotone twist map for which all minimal periodic orbits can be connected, and at the same time for a certain rational rotation number the minimal set is almost an invariant curve.     

The ring of Colombeau’s full generalized quaternions

In this paper, we introduce the ring of Colombeau full generalized quaternion, and we study its algebraic and topological properties. We prove that the ring of Colombeau full generalized quaternion is Gelfand, normal, duo and some related properties. Moreover, we study the essential ideals of this ring.     

k—full整数的分布（Ⅱ）

设k≥2是固定整数。自然数n称为k-full,如果对n的任一素因子p,均有p~k|n。以A_k(x)表示不超过x的k-full整数的个数,则可将A_k(x)写成如下形式: 这里γ_(i,k)(0≤i≤k-1)是非零常数,△_k(x)A_k(x)之误差项,本文在Riemann猜想成立的假设下证明了下结面论: 定理设。若Riemann猜想成立,则有:对k≥10成立。对2≤k≤9则得到了关于△_k(t)dt之渐近估计,其误差项为O(x_k~(a′+2))(ε>0)。     

Distributional chaos for operators with full scrambled sets

In this article we answer in the negative the question of whether hypercyclicity is sufficient for distributional chaos for a continuous linear operator (we even prove that the mixing property does not suffice). Moreover, we show that an extremal situation is possible: There are (hypercyclic and non-hypercyclic) operators such that the whole space consists, except zero, of distributionally irregular vectors.     

Gagliardo–Nirenberg inequalities and non-inequalities: The full story

We investigate the validity of the Gagliardo–Nirenberg type inequality

(1)${6f6}_{W^{s,p}(\mathrm{\Omega })}?{6f6}_{W^{s_1,p_1}(\mathrm{\Omega })}^{\theta }{6f6}_{W^{s_2,p_2}(\mathrm{\Omega })}^{1?\theta },$

with $\mathrm{\Omega }?{\mathbb{R}}^N$. Here, $0\le s_1\le s\le s_2$ are non negative numbers (not necessarily integers), $1\le p_1,p,p_2\le \infty$, and we assume the standard relations

$s=\theta s_1+(1?\theta )s_2,1/p=\theta /p_1+(1?\theta )/p_2\text{ for some }\theta \in (0,1).$

By the seminal contributions of E. Gagliardo and L. Nirenberg, (1) holds when $s_1,s_2,s$ are integers. It turns out that (1) holds for “most” of values of $s_1,\dots ,p_2$, but not for all of them. We present an explicit condition on $s_1,s_2,p_1,p_2$ which allows to decide whether (1) holds or fails.     

Hilbert subspaces of the spaces ℓp having full measure

In the spacel _p, 1 p 2, every probability measure is supported on some Hubert subspace. For p>2 there exist measures, in particular, Gaussian measures in the spacel _p, for which each Hilbert subspace has measure zero.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad Nauk SSSR, Vol. 55, pp. 3–14, 1976.     

On slow flows of the full nonlinear Doi–Edwards polymer model

The full Doi–Edwards model constitutive equation derived by Palierne (Phys Rev Lett 93:136001-1–136001-4, (2004) is discussed in detail. The corresponding configurational probability equation is next solved for slow flows, and the solution is used to calculate the material constants: zero-shear viscosity and the normal stress differences.     

Church–Rosser property of a simple reduction for full first-order classical natural deduction

A system of typed terms which corresponds with the classical natural deduction with one conclusion and full logical symbols is defined. Church–Rosser property of the system is proved using an extended method of parallel reduction.     

A presentation for the singular part of the full transformation semigroup

The (full) transformation semigroup T_n\mathcal{T}_{n} is the semigroup of all functions from the finite set {1,…,n} to itself, under the operation of composition. The symmetric group S_n í T_n{\mathcal{S}_{n}\subseteq \mathcal{T}_{n}} is the group of all permutations on {1,…,n} and is the group of units of T_n\mathcal{T}_{n}. The complement T_n\S_n\mathcal{T}_{n}\setminus \mathcal{S}_{n} is a subsemigroup (indeed an ideal) of T_n\mathcal{T}_{n}. In this article we give a presentation, in terms of generators and relations, for T_n\S_n\mathcal{T}_{n}\setminus \mathcal{S}_{n}, the so-called singular part of T_n\mathcal{T}_{n}.     

Low Mach number limit of the full compressible Navier–Stokes–Maxwell system

This paper deals with the low Mach number limit of the full compressible Navier–Stokes–Maxwell system. It is justified rigorously that, for the well-prepared initial data, the solutions of the full compressible Navier–Stokes–Maxwell system converge to that of the incompressible Navier–Stokes–Maxwell system as the Mach number tends to zero.     

Asymptotic stability for a non-autonomous full von Kármán beam with thermo-viscoelastic damping

In this paper, we study the asymptotic behavior for a one-dimensional non-autonomous full von Kármán beam with a thermo-viscoelastic damping in the internal feedback. By introducing a suitable energy and some Lyapunov functionals, under some restrictions on the non-autonomous functions and the relaxation function, we show the asymptotic behavior of the solution and establish a general decay result for the energy.     

A second order accuracy for a full discretized time-dependent Navier–Stokes equations by a two-grid scheme

We study a second-order two-grid scheme fully discrete in time and space for solving the Navier–Stokes equations. The two-grid strategy consists in discretizing, in the first step, the fully non-linear problem, in space on a coarse grid with mesh-size H and time step Δt and, in the second step, in discretizing the linearized problem around the velocity u _H computed in the first step, in space on a fine grid with mesh-size h and the same time step. The two-grid method has been applied for an analysis of a first order fully-discrete in time and space algorithm and we extend the method to the second order algorithm. This strategy is motivated by the fact that under suitable assumptions, the contribution of u _H to the error in the non-linear term, is measured in the L ² norm in space and time, and thus has a higher-order than if it were measured in the H ¹ norm in space. We present the following results: if h ² = H ³ = (Δt)², then the global error of the two-grid algorithm is of the order of h ², the same as would have been obtained if the non-linear problem had been solved directly on the fine grid.     

The incompressible limit of the full Navier–Stokes–Fourier system on domains with rough boundaries

We study the incompressible limit of the full Navier–Stokes–Fourier system on condition that the boundary of the spatial domain oscillates with the amplitude and wave length proportional to the Mach number. Assuming the fluid satisfies the complete slip boundary conditions on the oscillating boundary, we identify the asymptotic limit, and, in particular, establish strong (pointwise) convergence of the velocities towards a solenoidal vector field.