Subjects: Physics >> Physics of Gases, Plasmas, and Electric Discharges Subjects: Mathematics >> Mathematics (General) submitted time 2022-12-27
Abstract: For 3D vector fields, the governing formula of invariant manifolds grown from a hyperbolic cycle is given in cylindrical coordinates. The initial growth directions depend on the Jacobian matrices of Poincaré map on that cycle, for which an evolution formula is deduced to reveal the relationship among Jacobians of different Poincaré sections. The evolution formula also applies to cycles in arbitrary finite $n$-dim autonomous continuous-time dynamical systems. Non-Möbiusian/Möbiusian saddle cycles and a dummy X-cycle are constructed analytically as demonstration. A real-world numeric example of analyzing a magnetic field timeslice on EAST is presented.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Control and Optimization. submitted time 2022-12-12
Abstract:
In this paper, we study the problem of integral input-to-state stabilization in different norms for parabolic PDEs with integrable inputs. More precisely, we apply the method of backstepping to design a boundary control law for certain linear parabolic PDEs with destabilizing terms and $L^r$-inputs, and establish the integral input-to-state stability in the spatial $L^p$-norm and $W^{1,p}$-norm, respectively, for the closed-loop system, whenever $p in 1,+ infty $ and $r in p,+ infty $. In order to deal with singularities in the case of $p in 1,2)$, we employ the approximative Lyapunov method to analyze the stability in different norms. Concerning with the appearance of external inputs, we apply the method of functional analysis and the theory of series to prove the unique existence and regularity of solution to the closed-loop system.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Algebra and Number Theory submitted time 2022-12-07
Abstract:
In this paper, we briefly review the characteristics of the fifth-generated method and the research results of the tone calculation, derive and prove the fractional formula of the ascending fifth’s tone series and the descending fifth’s tone series using fifth-generated method, and prove the simple formula of the fifth-generated method by combining two fractional formula of the ascending fifth’s tone series and the descending fifth’s tone series. These formulas can be used to directly calculate the pitch at any position in these series, without chain computing the middle pitch from the initial pitch. According to the simple calculation formula, the ascending and descending fifth’s tone series can be combined into a fifth’s tone series whose independent variable is an integer number. In this paper, a simple formula is used to calculate the interval between each tone and the initial tone in the fifth’s series. Based on the theory of uniform distribution, it is concluded that the infinite tone the series are Uniform Distribution within the octave. According to the three-gap theory, the number of intervals and the number of their occurrences in the pentatonic scale, the heptonic scale, the twelve-tone scale, the 60-tone of King Fang and the 360-tone of Qian Lezhi are analyzed and illustrated.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematical Physics submitted time 2022-12-07
Abstract: In this article we employ classical tricks to give local and global well-posedness to MagnetoElasticity System. Different from many cases, we consider the equation which the magnetic field satisfies is Landau-Lifshitz system without viscidity, i.e. the Schrodinger flow. As is well known, people can not obtain ¨ global existence of Schrodinger flow at general cases. However, the reason why we do what others can not ¨ do is the Schrodinger flow with non-zero convection term.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics (General) submitted time 2022-12-04
Abstract: In this paper, I found the two reasons of overfitting of cross entropy: boundary samples occupy a larger
and larger share as the length of normal vector becomes longer and longer, boundary samples do not
fit their probability density function well.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics submitted time 2022-11-09
Abstract: In recent years, mixed integer linear programming (MILP, in short) is widely used to search differential characteristics and linear approximations with high probability and gradually becomes a powerful tool of automated cryptanalysis in symmetric ciphers. A key problem in the MILP method is how to fully characterize a set $S subseteq {0,1 }^n$ with as few linear integer inequalities $L$ as possible, which is called a full linear integer inequality characterization (FLIIC, in short) problem. In this work we establish a complete theory to solve the best solution of a FLIIC problem. We start from plain sets which can be characterized by exactly one linear integer inequality, and give their essential properties, including type, sparsity, degeneration, order, minimal and maximal element, norm and its bound, etc. Based on these essential properties, we further provide an efficient algorithm of solving a FLIIC problem with $S$, which can produce all minimal plain closures of $S$ and output a best FLIIC theoretically. As examples, we give their best solutions for differential properties of some common S-boxes used in block ciphers.
Peer Review Status:Awaiting Review
Subjects: Information Science and Systems Science >> Methodology of System Engineering Subjects: Mathematics >> Applied Mathematics submitted time 2022-10-30
Abstract: Multifactor impact analysis is an important part of economic quantitative analysis, and there are many methods. Among them, structural decomposition analysis (SDA) is widely used in the application of input-output techniques. In this paper, the defects of SDA are explained in depth, and the new multifactor and multi-order impact analysis (MMIA) technique is fully described. Firstly, the basic concepts of multifactor impact analysis and multifactor-multi-order impact analysis are defined. Secondly, the relationship between multifactor- multi-order impact analysis and Taylor series is clarified. Thirdly, the concepts and techniques of forward analysis and reverse analysis are proposed. Finally, several applications of MMIA under the input-output techniques framework are briefly described.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics submitted time 2022-10-19 Cooperative journals: 《桂林电子科技大学学报》
Abstract: As the extension of a complementarity problem, the weighted complementarity problem is an important kind of equilibrium problem, which could be used to model a larger class of practical equilibrium problems in economy and finance.Because of the nonzero weight vector, the weighted complementarity problem is usually more complicated than the complementarity problem. There is little available work about the algorithms for the weighted complementarity problem. In this paper, an interior-point algorithm is extended from linear optimization to weighted complementarity problems. Based on an equivalent reformulation of central path, a full-modified-Newton step feasible interior-point algorithm is proposed for solving a class of linear weighted complementarity problems over the nonnegative orthant. There is no linear search at each iteration.Under appropriate assumptions, we prove the feasibility of the algorithm, and obtain the iteration complexity. The numerical results illustrate that the algorithm is effective.
Subjects: Mathematics >> Geometry and Topology submitted time 2022-10-12
Abstract:本文给出了若干四元数体射影平面的多重双角锥的非稳定同伦群。
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics submitted time 2022-10-12
Abstract:随机函数可逆性问题是密码学中一类重要的问题,例如Hash函数原像恢复,分组密码密钥恢复,离散对称问题求解等等。在这个工作中,我们将随机函数可逆性问题从一维推广到高维,并提出了一个新的广义生日碰撞原理。基于该原理,我们给出了多随机函数可逆性问题的一个求解算法。该算法可以解决1980年Hellman在分组密码TMTO攻击中只能使用一对明密文数据而不能使用多个数据的公开问题,以及Biryukov和Shamir在2000年提出的带BSW采样的TMDTO攻击中只能使用极其少量的明密文数据而不是全部数据的公开问题。
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics (General) submitted time 2022-10-10
Abstract: In weibo APP, there are many almost same images whose only difference are watermark and resolution. In order to find out the most similar image efficiently, this paper proposes a algorithm named multi-level fingerprint, which contains 5 character strings and 3 vectors. On a dataset of 1 million images from WEIBO APP, multi-level fingerprint achieves a precision 97.69% and QPS 345.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics submitted time 2022-09-27 Cooperative journals: 《桂林电子科技大学学报》
Abstract: In this paper, the asymptotic stability of a second order differential integral equation is studied without using lyapunov direct method. When differential integral equations have infinite terms or time delay is unbounded, it is difficult to use Lyapunov direct method to solve the asymptotic stability of zero solution of differential integral equations. In this paper, by using the fixed point theorem, we obtain the necessary and sufficient conditions for the asymptotic stability of the zero solution of a class of neutral second order differential integral equations with infinite delay. Then the fixed point theorem not only solves the asymptotic stability problem of the zero solution of the second order differential integral equation, but also relieves the previous strict restriction on infinite delay, and significantly reduces the restriction on function g .
Subjects: Mathematics >> Applied Mathematics submitted time 2022-09-27 Cooperative journals: 《桂林电子科技大学学报》
Abstract: Two parameters for Brownian motion and the increment of the law of the iterated logarithm problem, using two parameter Brownian motion and increment as a tool, the law of the iterated logarithm for large deviation of Brownian motion and its incremental results about violations of the law of the iterated logarithm for the appropriate improvement, and promote the Brownian motion of two parameters, finally got two parameters Brownian motion increment of triple logarithmic law. Two parameters of Brownian motion is made up of Brownian motion is derived, with a series of and the probability of Brownian motion corresponding to the nature and the characteristics of the analysis, so with the help of predecessors, Brownian motion and Brownian motion increment of the law of the iterated logarithm for research, the two parameters of Brownian motion law of the iterated logarithm for qualification, reinforced conditions after the two parameters of the Brownian motion of a functional limit as a result, the two parameters of the Brownian motion of incremental triple logarithmic law. The theory verifies the correctness of the results.
Subjects: Mathematics >> Theoretical Computer Science submitted time 2022-09-27 Cooperative journals: 《桂林电子科技大学学报》
Abstract: To solve the reasonable allocation of campus resources, optimize the operation mode of the campus public transportation system, and meet the daily convenient travel of teachers and students, an optimization scheme of campus bus system based on 0-1 integer programming model was proposed.The study took Guilin University of Electronic Technology as an example, firstly, the present situation of student travel was investigated, the result shows that most students are willing to use campus bus, which means campus bus has certain development prospects. Through field measurement and collection of relevant geographical data, 0-1 integer planning was used to select the location of bus stops and ant colony algorithm was applied to optimize bus routes, and made a series of simulation experiments to test the carrying capacity of the campus bus system. Finally, it was concluded that the distribution location of 19 bus stations and the loop length generated by the optimal bus route is 4 805 meters, and under the restriction of the vehicle driving speed within 20km/h, at least 15 buses should be arranged to meet the time needs of most students. The results show that the optimized campus bus system planning is more reasonable, which meets the ravel needs of most teachers and students and is suitable for small and medium-sized campus traffic route planning.
Subjects: Mathematics >> Computational Mathematics. submitted time 2022-08-25
Abstract: In this paper, we study the linear complementarity problems on the monotone ex#2;tended second order cones. We demonstrate that the linear complementarity problem on the monotone extended second order cone can be converted into a mixed comple#2;mentarity problem on the non-negative orthant. We prove that any point satisfying the FB equation is a solution of the converted problem. We also show that the semi#2;smooth Newton method could be used to solve the converted problem, and we also provide a numerical example. Finally, we derive the explicit solution of a portfolio optimisation problem based on the monotone extended second order cone.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics (General) submitted time 2022-08-13
Abstract:This paper shows thatthe endograph metric and the $\Gamma$-convergenceare compatible on a large classof fuzzy set in $\mathbb{R}^m$.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Algebra and Number Theory submitted time 2022-08-07
Abstract: Cellular algebra is an algebraic structure received considerable attention in recent years, and graded algebra plays an important role in the theory of representation. Based on Wang Tao's research on precellular algebra, the definition of graded precellular algebra is given, and the representation theory of graded precellular algebra is discussed. Finally, the graded pre-cellularity of the regular semigroup algebra is studied.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Algebra and Number Theory submitted time 2022-08-07
Abstract: Cellular algebra is an algebraic structure received considerable attention in recent years, and regular semigroup is an important semigroup, which is one of the main research fields of semigroup algebra theory. Based on the standardly based algebra proposed by Du and Rui, which is a kind of generalized cellular algebra, and the generalized cellularity of regular semigroup algebra is studied.
Peer Review Status:Awaiting Review
Subjects: Dynamic and Electric Engineering >> Electrical Engineering Subjects: Mathematics >> Control and Optimization. submitted time 2022-08-07
Abstract: Quick-start generation units are critical devices and flexible resources to ensure a high penetration level of renewable energy in power systems. By considering the wind uncertainty, and both binary and continuous decisions of quick-start units within the intraday dispatch, we develop a Wasserstein-metric-based distributionally robust optimization model for the day-ahead network-constrained unit commitment (NCUC) problem with mixed integer recourse. We propose two feasible frameworks for solving the optimization problem. One approximates the continuous support of random wind power with finitely many events, the other leverages the extremal distributions instead. Both solution frameworks rely on the classic nested column-and-constraint generation (C&CG) method. It is shown that due to the sparsity of L1-norm Wasserstein metric, the continuous support of wind power generation could be represented by a discrete one with a small number of events, and the extremal distributions rendered are sparse as well. With this reduction, the distributionally robust NCUC model with complicated mixed-integer recourse problems can be efficiently handled by both solution frameworks. Numerical studies are carried out, demonstrating that the model considering quick-start generation units ensures unit commitment (UC) schedules to be more robust and cost effective, and the distributionally robust optimization method captures the wind uncertainty well in terms of out-of-sample tests.
Subjects: Dynamic and Electric Engineering >> Electrical Engineering Subjects: Mathematics >> Control and Optimization. submitted time 2022-08-07
Abstract: In this paper, a study of the day-ahead unit commitment problem with stochastic wind power generation is presented, which considers conditional and correlated wind power forecast errors through a distributionally robust optimization approach. Firstly, to capture the characteristics of random wind power forecast errors, the least absolute shrinkage and selection operator (Lasso) is utilized to develop a robust conditional error estimator, while an unbiased estimator is used to obtain the covariance matrix. The conditional error and the covariance matrix are then used to construct an enhanced ambiguity set. Secondly, we develop an equivalent mixed integer semidefinite programming (MISDP) formulation of the two-stage distributionally robust unit commitment model with a polyhedral support of random variables. Further, to efficiently solve this problem, a novel cutting plane algorithm that makes use of the extremal distributions identified from the second-stage semidefinite programming (SDP) problems is introduced. Finally, numerical case studies show the advantage of the proposed model in capturing the spatiotemporal correlation in wind power generation, as well as the economic efficiency and robustness of dispatch decisions.