The Logical Properties of Filters of Lattice Implication Algebra

In this paper, we discuss some propertie s of lattice implication algebra and difine the transitivity of implication in a set, we show the transitivity of implication and the substitution Theorem hold i n filters. So every filter of lattice implication algebra satisfies the Syllogis m and substitution Theorem of propositional logic.

N维等价向量组中的向量替换

本文证明了两个n维等价线性无关的向量组A(α1,α2,…αm)和β(β1,β2,…,βm)的性质,对A组中的任一向量αj,在β组中至少可以找到一个向量βi替换αj,使α1,…,α-1,β1,αj+1,…,αm与向量组B等价。同时指出了这种替换的条件。

A Resistant Quantum Key Exchange Protocol and Its Corresponding Encryption Scheme

The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant quantum cryptography very urgent. This motivate us to design a new key exchange protocol and eneryption scheme in this paper. Firstly, some acknowledged mathematical problems was introduced, such as ergodic matrix problem and tensor decomposition problem, the two problems have been proved to NPC hard. From the computational complexity prospective, NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them. From the algebraic structures prospective, non-commutative cryptography has been considered to resist quantum. The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures, so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures. Secondly, a new problem was constructed based on the introduced problems in this paper, then a key exchange protocol and a public key encryption scheme were proposed based on it. Finally the security analysis, efficiency, recommended parameters, performance evaluation and etc. were also been given. The two schemes has the following characteristics, provable security,security bits can be scalable, to achieve high efficiency, quantum resistance, and etc.

The Nilpotency of Lie Triple Algebras

In this paper, we mainly concerned about the nilpotence of Lie triple algebras.We give the definition of nilpotence of the Lie triple algebra and obtained that if Lie triplealgebra is nilpotent, then its standard enveloping Lie algebra is nilpotent.

Algebraic algorithm for reliability index weighted capacity of communication network

Communication network has communication capacity and connection reliability of the links. They canbe independently defined and can be used separately, and when the reliability of a communication network isanalyzed from a macroscopical angle of view, it is more objective to express the performance index of a commu-nication network as a whole. The reliability index weighted capacity is just obtained by integrating these two pa-rameters. It is necessary to further study the algorithm to calculate the reliability index of the communicationnetwork with a complicated topologic structure and a whole algebraic algorithm is therefore proposed for calcula-tion of the reliability index weighted capacity of a communication network with a topologic structure. The wholecomputational procedure of the algorithm is illustrated with a typical example.

Inverse problem in linear algebra

With the increasingly widespread application of linear algebra theory, and in its opposite direction is not enough emphasis, linear algebra, several important points： matrix, determinant, linear equations, linear transformations, matrix keratosis and other anti-deepening understanding of the basics and improve the comprehensive ability to solve problems.

Iterative Methods for Parametric Linear Systems with Linear Functions

This paper mainly proposes a new C-XSC （C- for eXtended Scientific Computing） software for the symmetric single step method and relaxation method for computing an enclosure for the solution set and compares the methods with others＇ and then makes some modifications and finally, examples illustrating the applicability of the proposed methods are given.

su(1,2) Algebraic Structure of XYZ Antiferromagnetic Model in Linear Spin-Wave Frame

The XYZ antiferromagnetic model in linear spin-wave frame is shown explicitly to have an su（1,2） algebraic structure： the Hamiltonian can be written as a linear function of the su（1,2） algebra generators. Based on it, the energy eigenvalues are obta/ned by making use of the similar transformations, and the algebraic diagonalization method is investigated. Some numerical solutions are given, and the results indicate that only one group solution could be accepted in physics.

Analytical Results of Eigenstates and Eigenenergies for Three Kinds of Models Describing N-mode Multiphoton Process

We obtain. the exact analytical results of all the eigenvalues and eigenstates for three kinds of models describing N-mode multiphoton process without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter lambda for three kinds of models describing N-mode multiphoton process. The parameter is shown to be determined by the roots of a polynomial and is solvable analytically or numerically. Moreover, these three kinds of models can be processed with the same procedure.

Aerodynamic Performances of Wind Turbine Airfoils Using a Panel Method

One of the key features of Laplace＇s Equation is the property that allows the equation governing the flow field to be converted from a 3D problem throughout the field to a 2D problem for finding the potential on the surface. The solution is then found using this property by distributing ＂singularities＂ of unknown strength over discretized portions of the surface： panels. Hence the flow field solution is found by representing the surface by a number of panels, and solving a linear set of algebraic equations to determine the unknown strengths of the singularities. In this paper a Hess-Smith Panel Method is then used to examine the aerodynamics of NACA 4412 and NACA 23015 wind turbine airfoils. The lift coefficient and the pressure distribution are predicted and compared with experimental result for low Reynolds number. Results show a good agreement with experimental data.

ADJACENCY PRESERVING MAPS ON THE SPACE OF SELF-ADJOINT OPERATORS

The authors extend Hua’s fundamental theorem of the geometry of Hermitian matri- ces to the in?nite-dimensional case. An application to characterizing the corresponding Jordan ring automorphism is also presented.

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.

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).

Localized Excitations of a Generalised Jimbo-Miwa Equation

Jimbo-Miwa(JM) equation is one of the famous(3+1)-dimensional conditionally integrable nonlinear dynamical systems. It is pointed out that JM equation and its generalized form possess some types of interesting nonlinear excitations such as the algebraic lump-type line solitons, the lumpoff-type half line solitons, and segment solitons.

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.

Variational algorithms for linear algebra

Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices.We show that the solutions of linear systems of equations and matrix–vector multiplications can be translated as the ground states of the constructed Hamiltonians.Based on the variational quantum algorithms,we introduce Hamiltonian morphing together with an adaptive ans?tz for efficiently finding the ground state,and show the solution verification.Our algorithms are especially suitable for linear algebra problems with sparse matrices,and have wide applications in machine learning and optimisation problems.The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation.We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations.We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.

Tightness of certain monomials

For a quantized enveloping algebra of finite type, one can associate a natural monomial to a dominant weight. We show that these monomials for types A5 and D4 are semitight(i.e., a Z-linear combination of elements in the canonical basis) by a direct calculation.

MINIMAL INVERSION AND ITS ALGORITHMS OF DISCRETE-TIME NONLINEAR SYSTEMS

The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.

ON CONTROLLABILITY FOR STOCHASTIC CONTROL SYSTEMS WHEN THE COEFFICIENT IS TIME-VARIANT

This paper investigates the controllability problem of time-variant linear stochastic controlsystems.A sufficient and necessary condition is established for stochastic exact controllability,whichprovides a useful algebraic criterion for stochastic control systems.Furthermore,when the stochasticsystems degenerate to deterministic systems,the algebraic criterion becomes the counterpart for thecomplete controllability of deterministic control systems.