A measure of mutual complete dependence in discrete variables through subcopula

Siburg and Stoimenov [12] gave a measure of mutual complete dependence of continuous variables which is different from Spearman's ρ and Kendall's τ. In this paper, a similar measure of mutual complete dependence is applied to discrete variables. Also two measures for functional relationships, which are not bijection, are investigated. For illustration of our main results, several examples are given.     

Synthesis and Characterization of Biodegradable Alternating Polyesteramides from Mixed Diamidediols and Sebacic Acid

A series of polyesteramide prepolymers[PrePEA（0/4,8）s] having mixed alternating bisesterdiamide units was synthesized via melt polycondensation from N,N＇-bis（2-hydroxyethyl）oxamide（0） and N,N＇-bis（2-hydroxyethyl）-adipamide（4） with sebacic acid（8） at different molar ratios.Chain extension of them was conducted with 2,2＇-（1,4-phenylene）-bis（2-oxazoline） and adipoyl biscaprolactamate as combined chain extenders.The chain extended polyesteramides[ExtPEA（0/4,8）s] were characterized by proton nuclear magnetic resonance（1H NMR）,gel permeation chromatography（GPC）,differential scanning calorimetry（DSC）,thermogravimetry analysis（TGA）,wide angle X-ray scattering,tensile test and enzymatic degradation.The results show that ExtPEA（0/4,8）s were crystalline polyesteramides.They had Tm up to 136.5 ℃ and initial decomposition temperature above 297.5 ℃.They crystallized in similar crystallites into Nylon-66 and degraded under the catalysis of protease or lipase.They are thermoplastic materials with tensile strength up to 21.5 MPa and elongation at break above 64.0％.     

Multipliers,covers, and stem extensions for Lie superalgebras

Suppose that the underlying field is of characteristic different from 2 and 3. We first prove that the so-called stem deformations of a free presentation of a finite-dimensional Lie superalgebra L exhaust all the maximal stem extensions of L; up to equivalence of extensions. Then we prove that multipliers and covers always exist for a Lie superalgebra and they are unique up to superalgebra isomorphisms. Finally, we describe the multipliers, covers, and maximal stem extensions of Heisenberg superalgebras and model filiform Lie superalgebras.     

半格分次弱Hopf代数的$G$-Cleft扩张

本文首先将Clifford幺半群代数分解为交叉积的半格直和,然后将这个结果通过$H$-$G$-cleft扩张推广到所谓的$G$-交叉积上.     

ALGEBRAIC EXTENSION OF ＊-A OPERATOR

In this paper, we study various properties of algebraic extension of *-A operator.Specifically, we show that every algebraic extension of *-A operator has SVEP and is isoloid.And if T is an algebraic extension of *-A operator, then Weyl's theorem holds for f(T), where f is an analytic functions on some neighborhood of σ(T) and not constant on each of the components of its domain.     

具有卷积的中心自反环

本文研究了具有卷积的中心自反环的性质,定义并引入了中心-自反环,显然,中心-自反环是自反环、中心自反环和-自反环的推广.给出了这类环的一些特征,研究了相关的环扩张,包括平凡扩张,Dorroh扩张和多项式扩张.     

Actions of Ore extensions and growth of polynomial H-identities

We show that if A is a finite-dimensional associative H-module algebra for an arbitrary Hopf algebra H, then the proof of the analog of Amitsur’s conjecture for H-codimensions of A can be reduced to the case when A is H-simple. (Here we do not require that the Jacobson radical of A is an H-submodule.) As an application, we prove that if A is a finite-dimensional associative H-module algebra where H is a Hopf algebra H over a field of characteristic 0 such that H is constructed by an iterated Ore extension of a finite-dimensional semisimple Hopf algebra by skew-primitive elements (e.g., H is a Taft algebra), then there exists integer PIexp^H(A). In order to prove this, we study the structure of algebras simple with respect to an action of an Ore extension.     

Beurling-Ahlfors扩张的伸张函数与ID-同胚

本文研究实轴上同胚在上半平面的扩张.利用拟对称函数ρ对伸张函数D作了较精细的估计.同时借助于诱导的边界函数对D、ρ在边界附近的性质作了进一步刻划.作为应用,我们分别给出上半平面存在ID-同胚扩张和IID-同胚扩张的充分条件.     

Edge proximity and matching extension in projective planar graphs

A graph $G$ with at least $2m+2$ vertices is said to be distance $d$ $m$-extendable if, for any matching $M$ of $G$ with $m$ edges in which the edges lie at distance at least $d$ pairwise, there exists a perfect matching of $G$ containing $M$. In this paper we prove that every 5-connected triangulation on the projective plane of even order is distance 3 7-extendable and distance 4 $m$-extendable for any $m$.     

Relativistic field formulation of simultaneous quantum measurement

The simultaneous measurement of Dirac field operators is formulated in analogy to the work of von Neumann and Arthurs-Kelly. Meter fields are coupled to the system field with a relativistically invariant bilinear interaction. Measurement of vacuum meter field expectation values provides for the simultaneous measurement of noncommuting system components. It is shown that two meter coupling allows for a simultaneous minimum in the variance of the subsequent meter measurements. A pseudoscalar self-interaction of the Dirac field is shown to allow simultaneous measurement of positive energy field operators with negative energy meters. The simultaneous measurement ofn noncommuting field operators is obtained by coupling the system ton fermionic fields. Also, in this paper the related concept of mutual simultaneous measurement is developed. This requires that any operators in the enlarged Hilbert space are measurable by the remaining fields as meters. System embedding into a larger Hilbert space results in added noise due to the zero point motion of the meter fields. By the negentropy principle of Brillouin, the added noise is equivalent to entropy. A criterion determining the interaction among fields is that the averaged added noise in the components of each quantum field is minimized. This criterion defines an optimum fermionic mass matrix through the determination of the entangling interaction.1. This work was sponsored by the Department of the Air Force under contract F19628-90-C-0002.