Multiplicative dynamical systems in terms of the induced dynamics

Theoretical and Mathematical Physics - We realize an example of induced dynamics using new multiplicative determinant relations whose roots give the particle positions. We present both a general...     

序列空间上的可乘等距与渐进可乘等距

本文证明了（l^βn）的单位球面间的非满等距在一定条件下可被线性等距延拓至全空间。并刻画了l^p（P〉0）上的非满渐进可乘等距算子．     

Interval orders based on weak orders

One definition of an interval order is as an order isomorphic to that of a family of nontrivial intervals of a linearly ordered set with [a,b] < [c,d] if b c. Fishburn's theorem states that an order is an interval order if and only if it has no four-element restriction isomorphic to the ordered set (shown in Fig. 1) “ ”. We show that an order is isomorphic to a family of nontrivial intervals of a weak order, ordered as above, if and only if it has no restriction to one of the four ordered sets (shown in Fig. 2) “ ”, a six-element crown or a six-element fence.     

可加乘积模型的研究

文章将乘积模型推广为可加乘积模型,延伸了正测量数据的适用范围.方法具有更强的灵活性,同时也可避免维数祸根问题.文中主要采用B样条逼近技术、最小乘积相对误差(LPRE)方法,研究非参数函数的估计问题.并在一些条件下,证明了非参数函数具有最优收敛速度.最后,通过数值模拟和实例分析,比较了提出的方法和其它几种方法的有限样本表现,验证了新方法的有效性.     

Multiplicative Correlations

A multivariate distribution is said to have multiplicative correlation if the correlation matrix R = (r _ij ) is written as r _ij = δ _i δ _j or r _ij = −δ _i δ _j (i ≠ j) for a parameter vector . We first determine feasible values for and show that variables with such a correlation matrix can always be decomposed into a common “signal” variable plus individual “noise” variables. It is also shown that a special case of this correlation matrix implies a sum constraint among variables and vice versa. Such properties illustrate why many multivariate distributions have such a correlation structure. Furthermore, several invariance properties lead to simple relations among several multivariate distributions.     

Interval orders and circle orders

A finite poset is an interval order if its point can be mapped into real intervals so that x in the poset precisely when x's interval lies wholly to the left of y's; the poset is a circle order if its points can be mapped into circular disks in the plane so that x precisely when x's circular disk is properly included in y's. This note proves that every finite interval order is a circle order.     

Multiplicative posets

A functionf from the posetP to the posetQ is a strict morphism if for allx, y P withx we havef(x). If there is such a strict morphism fromP toQ we writeP Q, otherwise we writeP Q. We say a posetM is multiplicative if for any posetsP, Q withP M andQ M we haveP ×Q M. (Here (p ₁,q ₁)<(p ₂,q ₂) if and only ifp ₁<p ₂ andq ₁<q ₂.) This paper proves that well-founded trees with height are multiplicative posets.This research was supported in part by NSERC Grant #69-1325.     

Circle orders and angle orders

A poset is a circle order if its points can be mapped into circular disks in the plane so that x in the poset precisely when x's circular disk is properly included in y's; the poset is an angle order if its points can be mapped into unbounded angular regions that preserve < by proper inclusion. It is well known that many finite angle orders are not circle orders, but has been open as to whether every finite circle order is an angle order. This paper proves that there are finite circle orders that are not angle orders.     

Multiplicative Dirac structures on Lie groups

We study multiplicative Dirac structures on Lie groups. We show that the characteristic foliation of a multiplicative Dirac structure is given by the cosets of a normal Lie subgroup and, whenever this subgroup is closed, the leaf space inherits the structure of a Poisson–Lie group. We also describe multiplicative Dirac structures on Lie groups infinitesimally. To cite this article: C. Ortiz, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Jordan代数上的可乘Jordan导子

设A是Jordan代数,如果映射d:A→A满足任给a,b∈A,都有d(aob)=d(a)o b+aod(b),则称d为可乘Jordan导子.如果A含有一个非平凡幂等p,且A对于p的Peirce分解A=A_1⊕A_(1/2)⊕A_0满足:(1)设ai∈Ai(i=1,0),如果任给t_(1/2)∈A_(1/2),都有a_i○t_(1/2)=0,则a_i=0,则A上的可乘Jordan导子d.如果满足d(p)=0,则d是可加的.由此得到结合代数和三角代数满足一定条件时,其上的任意可乘Jordan导子是可加的.     

Multiplicative maps on ℬ(X)

A structural feature of multiplicative maps on ℬ(X) which sends some rank-1 operator to an operator of rank not greater than 1 is given, and based on it, some characterizations of automorphism of ℬ(X) are obtained and some multiplicative preserver problems are answered. Project supported by the National Natural Science Foundation of China (Grant No.19671055) and Provincial Natural Science Foundation of Shanxi.     

Multiplicative isometries on the Smirnov class

We show that T is a surjective multiplicative (but not necessarily linear) isometry from the Smirnov class on the open unit disk, the ball, or the polydisk onto itself, if and only if there exists a holomorphic automorphism Φ such that T(f)=f ○ Φ for every class element f or T(f) = [`(f<sup>°</sup> [`(j)] )]\overline {f^\circ \bar \varphi } for every class element f, where the automorphism Φ is a unitary transformation in the case of the ball and Φ(z ₁, ..., z _n ) = (l₁ z_i1 ,...,l_n z_in )(\lambda _1 z_{i_1 } ,...,\lambda _n z_{i_n } ) for |λ _j | = 1, 1 ≤ j ≤ n, and (i ₁; ..., i _n )is some permutation of the integers from 1through n in the case of the n-dimensional polydisk.     

保谱乘法映射

设X,Y为Banach空间,证明了B（X）到B（Y）的保谱乘法满射φ具有形式φ（T）＝ATA-1,其中A为X到Y上的同构．     

A Note on Multiplicative Ideal Theory

We state a semigroup version of (19.15)THEOREM and (36.2)THEOREM, and disprove (30.9)THEOREM of Gilmers book [3] for commutative semigroups. We give a condition for the Kronecker function ring D* with respect to a star-operation * on an integral domain D to be well-defined.2000 Mathematics Subject Classification: Primary 13A15 Secondary 20M14.     

Tilted symmetric orders are symmetric orders

We prove in this note that a ring which is derived equivalent to a symmetric order is again a symmetric order. Group rings of finite groups over an integral domain of characteristic 0 are symmetric orders.