质代数的有限条件

设Ａ为有零因子的质代数。若Ａ为有限维代数，则它的所有幂零元张成的向量空间亦为有限维。本文证明其逆，即：若Ａ的所有幂零元张成的向量空间有限维，则Ａ为有限维单代数。

高斯整环R(m^(1/2))及其商环

推广了文[1]、[2]的结论。当m≡1(mod4)时,证明了高斯整环R(m^(1/2))=Z[ω]的一些性质:R(m^(1/2))的商环的结构和R(m^(1/2))中质代数整数的判别条件。

Research on Thermodynamic Properties of Polybrominated Diphenylamine by Neural Network

Based on the location of bromine substituents and conjugation matrix, a new substituent po- sition index ~X not only was defined, but also molecular shape indexes Km and electronega- tivity distance vectors Mm of diphenylamine and 209 kinds of polybrominated diphenylamine （PBDPA） molecules were calculated. Then the quantitative structure-property relationships （QSPR） among the thermodynamic properties of 210 organic pollutants and 0X, K3, M29, M36 were founded by Leaps-and-Bounds regression. Using the four structural parameters as input neurons of the artificial neural network, three satisfactory QSPR models with network structures of 4：21：1, 4：24：1, and 4：24：1 respectively, were achieved by the back-propagation algorithm. The total correlation coefficients R were 0.9999, 0.9997, and 0.9995 respectively and the standard errors S were 1.036, 1.469, and 1.510 respectively. The relative mean deviation between the predicted value and the experimental value of Sθ, AfHe and △fGθ- were 0.11%, 0.34% and 0.24% respectively, which indicated that the QSPR models had good stability and superior predictive ability. The results showed that there were good nonlinear correlations between the thermodynamic properties of PBDPAs and the four structural pa- rameters. Thus, it was concluded that the ANN models established by the new substituent position index were fully applicable to predict properties of PBDPAs.

Model for Software Behaviour Detection Based on Process Algebra and System Call

Behaviour detection models based on automata have been studied widely. By add- ing edge ε, the local automata are combined into global automata to describe and detect soft- ware behaviour. However, these methods in- troduce nondeterminacy, leading to models that are imprecise or inefficient. We present a model of software Behaviour Detection based on Process Algebra and system call （BDPA）. In this model, a system call is mapped into an action, and a function is mapped into a process We construct a process expression for each function to describe its behaviour. Without con- strutting automata or introducing nondeter- minacy, we use algebraic properties and algo- rithms to obtain a global process expression by combining the process expressions derived from each function. Behaviour detection rules and methods based on BDPA are determined by equivalence theory. Experiments demon- strate that the BDPA model has better preci- sion and efficiency than traditional methods.

New Matrix Loop Algebra and Its Application

A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly,as its application,the multi-component TC equation hierarchy is obtained,then by use of trace identity the Hamiltonian structure of the above system is presented.Finally,the integrable couplings of the obtained system is worked out by the expanding matrix Loop algebra.

Amplitude-Nth-power squeezing of PB phase coherent states

PB Phase Coherent States are very important quantum states in quantum optics. In order to investigate the amplitude-Nth-power squeezing of PB Phase Coherent States, we introduce the algebraic properties of the PB phase operator and the PB Phase Coherent States which are constructed by PB phase theory. We applied amplitude-Nth-power squeezing theory to define the Amplitude-Nth-Power Squeezing of PB Phase Coherent States and investigate the characteristic of the amplitude-Nth-power squeezing of PB Phase Coherent States. We obtained surprising results, in that the results were different from the other quantum states. As for |Z〉(PB Phase Coherent State), the results show that when Z is a real number there only exists amplitude-Nth-power squeezing of component; when Z is a complex number, there exists amplitude-Nth-power squeezing of component and component; when Z is a pure imaginary number, if N is odd, then there does not exist amplitude-Nth-power squeezing of component, but there exists amplitude-Nth-power squeezing of component and if N is even, then there exists amplitude-Nth-power squeezing of component, but there does not exist amplitude-Nth-power squeezing of component.

Hybrid Strategy of Particle Swarm Optimization and Simulated Annealing for Optimizing Orthomorphisms

Orthomorphism on F2^n is a kind of elementary pemmtation with good cryptographic properties. This paper proposes a hybrid strategy of Particle Swarm Optimization （PSO） and Sirrmlated Annealing （SA） for finding orthomorphisrm with good cryptographic properties. By experiment based on this strategy, we get some orthorrorphisrm on F2^n = 5, 6, 7, 9, 10） with good cryptographic properties in the open document for the first time, and the optirml orthorrrphism on F found in this paper also does better than the one proposed by Feng Dengguo et al. in stream cipher Loiss in difference uniformity, algebraic degree, algebraic irrarnity and corresponding pernmtation polynomial degree. The PSOSA hybrid strategy for optimizing orthomerphism in this paper makes design of orthorrorphisrm with good cryptographic properties automated, efficient and convenient, which proposes a new approach to design orthornorphisrm.

Neutrino Mass Generation in SO(4) Model

Generation of neutrino mass in SO（4） model is proposed here. The algebraic structure of SO （4） is same as to that ofSU（2）L x SU（2）R. It is shown that the spontaneous symmetry breaking results three massive as well as three massless gauge bosons. The standard model theory according to which there exist three massive gauge bosons and a massless one is emerged from this model. In the framework ofSU（2）L x SU（2）R a small Dirac neutrino mass is derived. It is also shown that such mass term may vanish with a special choice. The Majorana mass term is not considered here and thus in this model the neutrino mass does not follow seesaw structure.

Free Transverse Vibration Analysis of an Underwater Launcher Based on Fluid-Structure Interaction

A pneumatic launcher is theoretically investigated to study its natural transverse vibration in water. Considering the mass effect of the sealing cover, the launcher is simplified as a uniform cantilever beam with a top point mass. By introducing the boundary and continuity conditions into the motion equation, the natural frequency equation and the mode shape function are derived. An iterative calculation method for added mass is also presented using the velocity potential function to account for the mass effect of the fluid on the launcher. The first 2 order natural frequencies and mode shapes are discussed in external flow fields and both external and internal flow fields. The results show good agreement with both natural frequencies and mode shapes between the theoretical analysis and the FEM studies. Also, the added mass is found to decrease with the increase of the mode shape orders of the launcher. And because of the larger added mass in both the external and internal flow fields than that in only the external flow field, the corresponding natural frequencies of the former are relatively smaller.

Computed Tomography Using Level Set Method and Algebraic Reconstruction Technique

In this paper, a novel reconstruction technique based on level set method and algebraic reconstruction technique is proposed for multiphase flow computed tomography (CT) system. The curvature-driven noise reduction method is inserted into the conventional iteration procedure of algebraic reconstruction technique to improve the image quality and convergence speed with limited projection data. By evolving the image as a set of iso-intensity contours after each updation, the sufficient number of iterations for acceptable results is reduced by 80%-90%, while the image quality is enhanced obviously. Quantitative evaluation of image quality is given by using both relative image error and correlation coefficient. The resultant images can be utilized to detect flow regimes for monitoring industrial multiphase flow. Laboratory results demonstrate the feasibility of the proposed method. Phantoms of four typical flow regimes can be reconstructed from few-view projection data efficiently, and the corresponding image errors and correlation coefficients are acceptable for the cases tested in this paper.

Frobenius Property of a Cosemisimple Hopf Algebra

Let H be a cosemisimple Hopf algebra over an algebraically closed field k of characteristic zero. We show that if H is of type l ： 1 ＋ m ： p ＋ 1 ： q with p2 〈 q, or of type 1 ： 1 ＋ 1 ： m ＋ 1 ： n in the sense of Larson and Radford, then H has the Frobenius property, that is, Kaplansky conjecture is true for these Hopf algebras.

The Algebraic Properties of a Type of Infinite Lower Triangular Matrices Related to Derivatives

In this paper, Jabotinsky matrices in [4, 5] are modified and a type of infinite lower triangular matrices T(f) is discussed. Some algebraic properties of T(f) are obtained and proved. Additionally, some inverse pairs and combinatorial identities associated with derivatives are obtained.

On higher analogues of Courant algebroids

In this paper, we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle TM ⊕∧nT*M for an m-dimensional manifold. As an application, we revisit Nambu-Poisson structures and multisymplectic structures. We prove that the graph of an (n + 1)-vector field π is closed under the higher-order Dorfman bracket iff π is a Nambu-Poisson structure. Consequently, there is an induced Leibniz algebroid structure on ∧nT*M. The graph of an (n+1)-form ω is closed under the higher-order Dorfman bracket iff ω is a premultisymplectic structure of order n, i.e., dω = 0. Furthermore, there is a Lie algebroid structure on the admissible bundle A ∧nT*M. In particular, for a 2-plectic structure, it induces the Lie 2-algebra structure given in (Baez, Hoffnung and Rogers, 2010).

A Construction of 1-Resilient Boolean Functions with Good Cryptographic Properties

This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified func- tions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the ＂continuity＂ of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known l-resilient functions modified by Tu-Deng and Tang- Carlet-Tang functions.

On the properties of some sets of von Neumann algebras under perturbation

Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity property and the set of all McDuff sub/actors of t are open and closed in the Hausdorff metric d2 induced by the trace norm; then we show that the set of all hyperfinite von Neumann subalgebras of L is closed in d2. We also consider the connection of perturbation of operator algebras under d2 with the fundamental group and the generator problem of type II1 factors. When M is a finite yon Neumann algebra with a normal faithful trace, the set of all von Neumann subalgebras B of M such that B ∪→ M is rigid is closed in the Hausdorff metric d2.

Morphism Categories of Gorenstein-projective Modules

Let A be an algebra of finite Cohen-Macaulay type and F its Cohen-Macaulay Auslander algebra. We are going to characterize the morphism category Mor（∧-Gproj） of Gorenstein-projective ∧-modules in terms of the module category F-mod by a categorical equivalence. Based on this, we obtain that some factor category of the epimorphism category Epi（∧-Gproj） is a Frobenius category, and also, we clarify the relations among Mor（∧-Gproj）, Mor（T2（∧）-Gproj） and Mor（△-Gproj）, where T2（∧） and △ are respectively the lower triangular matrix algebra and the Morita ring closely related to ∧.

RESULTS ON PERMUTATION SYMMETRIC BOOLEAN FUNCTIONS

This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions. The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptographic properties. The proposed method is algebraic in nature. As a by-product, the authors correct and generalize the corresponding results of St^nic~ and Maitra （2008）. Further, the authors give a complete classification of block-symmetric bent functions based on the results of Zhao and Li （2006）, and the result is the only one classification of a certain class of permutation symmetric bent functions after the classification of symmetric bent functions proposed by Savicky （1994）.

Pointwise multipliers for Besov spaces of dominating mixed smoothness-Ⅱ

We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R^d) with respect to pointwise multiplication. In addition, if p≤q, we are able to describe the space of all pointwise multipliers for S_(p,q)~rB(R^d).

Toeplitz operators on H^2(iR)

In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is computed.In addition,the characteristic equation of Toeplitz operators is obtained and the algebraic properties of Toeplitz operators are discussed.

Algebraic Properties of Toeplitz Operators on Discrete Commutative Groups

In this paper,a generalized Toeplitz operator is defined and some of results about the classical Toeplitz operator are generalized.In particular,we obtain the necessary and sufficient condition for the product of two such Toeplitz operators to still be Toeplitz operator and the necessary and sufficient condition for such Toeplitz operator to be normal operator.Finally,a necessary condition for two such Toeplitz operators to be commutative is established.