Subjects: Mathematics >> Applied Mathematics submitted time 2024-02-22
Abstract： In this paper, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderon-Zygmund type estimate in Besov spaces with more general assumptions on coefficients for both homogeneous equations and non-homogeneous equations. This study of regularity estimates expands the Calderon-Zygmund theory in the Heisenberg group.
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Subjects: Mathematics >> Applied Mathematics Subjects: Physics >> Interdisciplinary Physics and Related Areas of Science and Technology submitted time 2023-07-04
Abstract：
Based on the Golomb's pseudorandomness assumptions on idea pseudorandom sequences and FIPS 140-2 pseudorandomness test, this paper first presents a new approach for improving the pseudorandomness of pseudorandom sequences. Second, using a generalized synchronization theorem, and three chaotic maps constructs one 8-dimensional chaotic generalized synchronization system (8DCGSS). Then using the 8DCGSS designs a chaotic
pseudorandom number generator (CPRNG). The keyspace of the CPRNG is larger than 2^{1117}. Third, using FIPS 140-2 pseudorandomness test criterions and generalized FIPS 140-2 pseudorandomness test criterions measures, respectively, the pseudorandomness of the keystreams with length 20 000, 100 000 and 1 000 000 generated via the CPRNG, an Matlab PRNG, an RC4 algorithm, and an m-sequence with period 2^{20} - 1, and the corresponding improved keystreams by our approach. The results show that the presented approach can increase significantly the pseudorandomness of the keystreams generated by the four PRNGs. The key streams generated by the m-sequence do not have sound pseudorandomness when the lengths of the key streams are less than 100 000.
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Subjects: Mathematics >> Applied Mathematics submitted time 2023-02-15
Abstract： In recent years, mixed integer linear programming (MILP, in short) gradually becomes a popular tool of automated cryptanalyses in symmetric ciphers, which can be used to search differential characteristics and linear approximations with high probability/correlation. A key problem in the MILP method is how to build a proper model that can be solved efficiently in the MILP solvers like Gurobi or Cplex. It is known that a MILP problem is NP-hard, and the numbers of variables and inequalities are two important measures of its scale and time complexity. Whilst the solution space and the variables in many MILP models built for symmetric cryptanalyses are fixed without introducing dummy variables, the cardinality, i.e., the number of inequalities, is a main factor that might affect the runtime of MILP models. We notice that the norm of a MILP model, i.e., the maximal absolute value of all coefficients in its inequalities, is also an important factor affecting its runtime. In this work we will illustrate the effects of two parameters cardinality and norm of inequalities on the runtime of Gurobi by a large number of cryptanalysis experiments. Here we choose the popular MILP solver Gurobi and view it a black box, construct a large number of MILP models with different cardinalities or norms by means of differential analyses and impossible differential analyses for some classic block ciphers with SPN structure, and observe their runtimes in Gurobi. As a result, our experiments show that although minimizing the number of inequalities and the norm of coefficients might not always minimize the runtime, it is still a better choice in most situations.
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.
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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 >> 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 >> 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 >> Statistics and Probability Subjects: Mathematics >> Applied Mathematics submitted time 2022-03-30
Abstract：
In this paper, we propose and study a novel continuous-time model, based on the well-known constant elasticity of variance (CEV) model, to describe the asset price process. The basic idea is that the volatility elasticity of the CEV model can not be treated as a constant from the perspective of stochastic analysis. To address this issue, we deduce the price process of assets from the perspective of volatility elasticity, propose the constant volatility elasticity (CVE) model, and further derive a more general variable volatility elasticity (VVE) model. Moreover, our model can describe the positive correlation between volatility and asset prices existing in the commodity markets, while CEV model can only describe the negative correlation. Through the empirical research on the financial market, many assets, especially commodities, often show this positive correlation phenomenon in some time periods, which shows that our model has strong practical application value. Finally, we provide the explicit pricing formula of European options based on our model. This formula has an elegant form convenient to calculate, which is similarly to the renowned Black-Scholes formula and of great significance to the research of derivatives market.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics submitted time 2021-12-15
Abstract： We analyze properties of degree and clustering of a hyperbolic geometric model of complex networks in small parameter case $\tau<1, 2\sigma<1$. We find that the probability of k-degree goes to 0 and the global clustering coefficient goes to 0 in probability too as the number of nodes $N\to\infty$ for some specific growth $R(N)$ of the region radius. Here the scale-free degree is failed and the connection between neighbors are very weak. The transition of properties of the model with the parameter $\sigma$ changes seems to show that the mobility is important to keep society full and stable communication, otherwise a silence society. Some analysis technique and method are first applied for such model.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics Subjects: Computer Science >> Computer Software Subjects: Information Science and Systems Science >> Other Disciplines of Information Science and Systems Science submitted time 2021-10-11
Abstract： "
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics submitted time 2021-09-22
Abstract： In the early days of the epidemic of coronavirus disease 2019 (COVID-19), due to insufficient knowledge of the pandemic, inadequate nucleic acid tests, lack of timely data reporting, etc., the origin time of the onset of COVID-19 is difficult to determine. Therefore, source tracing is crucial for infectious disease prevention and control. The purpose of this paper is to infer the origin time of pandemic of COVID-19 based on a data and model hybrid driven method. We model the testing positive rate to fit its actual trend, and use the least squares estimation to obtain the optimal model parameters. Further, the kernel density estimation is applied to infer the origin time of pandemic given the specific confidence probability. By selecting 12 representative regions in the United States for analysis, the dates of the first infected case with 50% confidence probability are mostly between August and October 2019, which are earlier than the officially announced date of the first confirmed case in the United States on January 20, 2020. The experimental results indicate that the COVID-19 pandemic in the United States starts to spread around September 2019 with a high confidence probability. In addition, the existing confirmed cases are also used in Wuhan City and Zhejiang Province in China to infer the origin time of COVID-19 and provide the confidence probability. The results show that the spread of COVID-19 pandemic in China is likely to begin in late December 2019. " " "
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics Subjects: Management Science >> Management Engineering Subjects: Information Science and Systems Science >> Other Disciplines of Information Science and Systems Science submitted time 2020-03-31
Abstract： The goal of this paper is to establish the general framework of consensus equilibria for Mining-Pool Games in Blockchain Ecosystems, and in particular to explain the stable in the sense for the existence of consensus equilibria related to mining gap game’s behaviors by using one new concept called “consensus games (CG)” in Blockchain Ecosystems, here, the Blockchain ecosystem mainly means the economic activities by taking into the account of three types of different factors which are expenses, reward mechanism and mining power for the work on blockschain by applying the key consensus called “Proof of Work” due to Nakamoto in 2008. In order to do so, we first give an outline how the general existence of consensus equilibria for Mining-Pool Games is formulated, and then used to explain the stable for Gap Games for Bitcoin in the sense by the existence of consensus equilibria under the framework of Blockchain consensus, we then establish a general existence result for consensus equilibria of general mining gap games by using the profit functions for miners as the payoffs in game theory.As applications, the general existence results for consensus equilibria of Gap games are established, which not only help us to claim the existence for the general stability for Gap games under the general framework of Blockchain ecosystems, but also allow us to illustrate a number of different phenomenons on the study of mining-pool games with possible impacts due to miners’ gap behaviors with scenarios embedded in Bitcoin economics. Our study on the explanation for the stability of mining gap game for Blockchain ecosystems shows that the concept of consensus equilibria may play a important role for the development of fundamental theory for consensus economics.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics submitted time 2019-07-16
Abstract： Scheduling problem of intelligent processing system is studied. This problem is a part of Problem B of 2018 China Undergraduate Mathematical Contest in Modeling. The system consists of a Rail Guide Vehicle (RGV), several Computer Number Controllers (CNC) and other components. RGV manages multiple CNCs to finish multiple units of material. RGV scheduling scheme determines the efficiency of the system. Taking RGV's moving path as decision variable, RGV's operation ending time on CNCs as time nodes, and material processing remaining time as state variables, the mathematical model of the problem is developed. However, the subscripts of some parameters are decision variables in this model. By defining new variables and constraints, the model is modified to exclude the decision-variable subscripts and piecewise functions, and the model is transformed into a nonlinear mixed integer programming model. Finally, a numerical example is given, which illustrates the correctness and operability of the model.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Computational Mathematics. Subjects: Mathematics >> Applied Mathematics submitted time 2017-08-22
Abstract：Many numerical methods have been proposed in the last 30 years for inverse problems. While very successful in many cases, progress has lagged in other areas of applications which are forced to rely on {\em limited-aperture} measurements. In this paper, we introduce some techniques to retrieve the other data that can not be measured directly. We consider the inverse acoustic scattering of time harmonic plane waves and take the scattering amplitude to be the measurements. Assume that the scattering amplitude can only be measured with observation directions restricted in $S^{n-1}_0$, which is compactly supported in the unit sphere. Based on the reciprocity relation of the scattering amplitude, we prove a special symmetric structure of the corresponding multi-static response matrix. This will also be verified by numerical examples. Combining this, with the help of the Green's formula for the scattered field, we introduce an iterative scheme to retrieve approximate {\em full-aperture} scattering amplitude. As an application, using a recently proposed direct sampling method [28], we consider the fast and robust sampling methods with {\em limited-aperture} measurements. Some numerical simulations are conducted with noisy data, and the results will further verify the effectiveness and robustness of the proposed data retrieval method and of the sampling method for inverse acoustic scattering problems.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics submitted time 2017-04-07
Abstract：研究了动态围堵嫌犯问题, 假设网络边长相等, 交巡警与嫌犯的速度相等. 建立了嫌犯移动信息更新下的交巡警调度问题的0-1线性整数规划模型, 模型利用点截集条件使调度后的警力形成围堵圈, 并对嫌犯的逃跑行为建模, 由此得到了动态围堵嫌犯问题的动态模拟模型. 算例考虑分割非等边长网络的边, 然后将分割后的网络视为等边长网络.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Applied Mathematics submitted time 2016-07-07
Abstract：自博弈论中有趣的海盗分金问题（Pirate Game(PG)）提出以来，其在理论分析上，仅摘要：自博弈论中有趣的海盗分金问题（Pirate Game(PG)）提出以来，其在理论分析上，仅限于逆向递推法和数列递推法。本文首先借鉴这两种方法建立一阶差分模型；而后，考虑到每个海盗不是绝对理性的，等级高的海盗需要依赖等级低一级的海盗的决策而做出最优决策，建立二阶时滞差分模型，在数学原理上对 PG 做深入分析：当τ= 0 时，与实际情况偏差较大；当时滞量 τ=1 时，模型的解和一阶差分模型的解一致，即在现实生活中也存在着做决策时直接咨询自己的第一副手的社会群体。从而，在现代分析方法的层次上，本文给出一个 PG 的新的合理的数学解释。
Peer Review Status:Awaiting Review
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