A tri-Hamiltonian formulation of a new soliton hierarchy associated with so(3,R)

A third Hamiltonian operator is presented for a new hierarchy of bi-Hamiltonian soliton equations, thereby showing that this hierarchy is tri-Hamiltonian. Additionally, an inverse hierarchy of common commuting symmetries is also presented.     

一类Hamilton算子,遗传对称及可积系

本文构造了一类矩阵微分Hamilton算子并且生成了新的遗传对称和相应的可积系,进一步提出了一个新可积族的双Hamilton结构和公共遗传强对称算子。     

Operator algebras with contractive approximate identities

We give several applications of a recent theorem of the second author, which solved a conjecture of the first author with Hay and Neal, concerning contractive approximate identities; and another of Hay from the theory of noncommutative peak sets, thereby putting the latter theory on a much firmer foundation. From this theorem it emerges there is a surprising amount of positivity present in any operator algebras with contractive approximate identity. We exploit this to generalize several results previously available only for C^?-algebras, and we give many other applications.     

Exceptional Pairs in Hereditary Categories

We study the category 𝒞(X, Y) generated by an exceptional pair (X, Y) in a hereditary category ?. If r = dim _k Hom(X, Y) ≥ 1 we show that there are exactly 3 possible types for 𝒞(X, Y), all derived equivalent to the category of finite dimensional modules mod(H _r ) over the r-Kronecker algebra H _r . In general 𝒞(X, Y) will not be equivalent to a module category. More specifically, if ? is the category of coherent sheaves over a weighted projective line 𝕏, then 𝒞(X, Y) is equivalent to the category of coherent sheaves on the projective line ?¹ or to mod(H _r ) and, if 𝕏 is wild, then every r ≥ 1 can occur in this way.     

Spin labeling artery method perfusion MRI study of SPG4 and SCA3/MJD

Background

Spinocerebellar ataxia type 3 (SCA3) and Machado–Joseph disease (MJD) are similar diseases that are often referred to jointly as SCA3/MJD. As the most common autosomal-dominantly inherited subtype of hereditary spastic paraplegia (HSP), HSP4 (or SPG4) has overlapping symptoms with SCA3/MJD, which hinders their diagnoses. Arterial spin labeling (ASL) is a noninvasive, contrast-agent free, magnetic resonance perfusion imaging method used to obtain maps of the cerebral blood flow (CBF). Here, we investigated the diagnostic value of ASL in SCA3/MJD and SPG4 patients.

Methods

A total of 13 SPG4 cases, 38 SCA3/MJD cases (22 onset patients and 16 genetic abnormality-only patients), and 27 healthy volunteers were examined by ASL. Data were processed to obtain the regional CBF (rCBF) and comparatively studied.

Results

In the pons, cerebellar dentate nucleus, and cerebellar cortex, rCBF of the onset SCA3/MJD group was significantly lower than that of the normal control group. In the cerebellar dentate nucleus and cerebellar cortex, the rCBF of the non-onset SCA3/MJD group was significantly lower than that of the control group. In the pons and cerebellar cortex, the rCBF of the onset SCA3/MJD group was significantly lower than that of the SPG4 group.

Conclusions

SCA3/MJD lesions are mainly located in the cerebellum and brainstem. Gray matter and white matter were both involved, although the deep cerebellar nuclei may be the earliest involved region. Cerebellar and brainstem lesions of SCA3/MJD were more severe than those of SPG4. ASL can aid the diagnosis of SCA3/MJD and SPG4.     

A Characterization of Group Rings

In this paper we prove that every coseparable involutory Hopf algebra over the ring of integers Z which is a free Z-module is the group ring of some group. This result was proved independently for Hopf algebras which are finitely generated Z-modules by H.-J. Schneider [6], using similar techniques. We then give some examples of coseparable Hopf algebras over number rings which are not group algebras, and give an example of a cocommutative coseparable coalgebra over a number ring which cannot be given a multiplicative structure making it into a Hopf algebra. The Hopf algebra structure theory required for this paper is found in [1], [4], and [5]. For completeness we give proofs here of the coalgebra analogues to some “well-known” facts about separable algebras.     

Local bijective gabriel correspondence and relative fully boundedness in τ-noetherian rings

Let Rbe a right τ-noetherian ring, where τ denotes a hereditary torsion theory on the category of right R-modules. It is shown that every essential τ-closed right ideal of every prime homomorphic image of Rcontains a nonzero two-sided ideal if and only if any two τ-torsionfree injective indecomposable right R-modules with identical associated prime ideals are isomorphic, and for any τ-closed prime ideal Pthe annhilator of a finitely generated P-tame right R-module cannot be a prime ideal properly contained in P. Furthermore, if in the last condition finitely generated is replaced by r-noetherian, then all τ-noetherian τ-torsionfree modules turn out to be finitely annihilated.     

Lattice Properties of Torsion Theories

The main purpose of this brief note is to show that the sets of all hereditary torsion theories which are noetherian, strongly noetherian, or of finite type, respectively, form a sublattice of the lattice of all hereditary torsion theories for the category R-mod.