HAJOS‘ CONJECTURE AND CONNECTIVITY OF EULERIAN GRAPHS

Hajos‘ conjecture asserts that a simple eulerian graph on n vertices can be decomposed into at most n-1/2 circuits,In this paper,we propose a new conjecture which is equivalent to Hajos‘ conjecture.and show that to prove Hajos‘ conjecture,it is sufficent to prove this new conjecture for 3-connected graphs.Furthermore,a special 3-cut is considered also.     

On the nonexistence of nontrivial small cycles of the µ function in 3x+1 conjecture

This paper studies the property of the recursive sequences in the 3x+ 1 conjecture.The authors introduce the concept ofμfunction,with which the 3x + 1 conjecture can be transformed into two other conjectures:one is eventually periodic conjecture of theμfunction and the other is periodic point conjecture.The authors prove that the 3x + 1 conjecture is equivalent to the two conjectures above.In 2007,J.L.Simons proved the non-existence of nontrivial 2-cycle for the T function.In this paper,the authors prove that theμfunction has no l-periodic points for 2≤l≤12.In 2005, J.L.Simons and B.M.M de Weger proved that there is no nontrivial 2-cycle for the T function for l≤68,and in this paper,the authors prove that there is no nontrivial l-cycle for theμfunction for 2≤l≤102.     

The Log-Concavity of Kazhdan-Lusztig Polynomials of Uniform Matroids

Elias, et al.(2016) conjectured that the Kazhdan-Lusztig polynomial of any matroid is logconcave. Inspired by a computer proof of Moll’s log-concavity conjecture given by Kauers and Paule,the authors use a computer algebra system to prove the conjecture for arbitrary uniform matroids.     

EDGE RECONSTRUCTION OF PLANAR GRAPHS WITH MINIMUM DEGREE AT LEAST THREE-(Ⅰ)

The object of this series of papers is to show that every planar graph ofminimum degree at least 3 is edge reconstructible. In this paper, we prove that such agraph with connectivity 2 is edge reconstructible.     

On functional decomposition of multivariate polynomials with differentiation and homogenization

This paper gives a theoretical analysis for the algorithms to compute functional decomposition for multivariate polynomials based on differentiation and homogenization which were proposed by Ye,Dai,and Lam(1999) and were developed by Faugere,Perret(2006,2008,2009).The authors show that a degree proper functional decomposition for a set of randomly decomposable quartic homogenous polynomials can be computed using the algorithm with high probability.This solves a conjecture proposed by Ye,Dai,and Lam(1999).The authors also propose a conjecture which asserts that the decomposition for a set of polynomials can be computed from that of its homogenization and show that the conjecture is valid with high probability for quartic polynomials.Finally,the authors prove that the right decomposition factors for a set of polynomials can be computed from its right decomposition factor space.     

A novel mixed integer programming formulation and progressively stochastic search for capacitated lot sizing

The capacitated multi-level lot sizing problem is to schedule a number of different items with a bill-of-materials structure over a horizon of finite periods.To advance techniques of solving this class of problems,this paper proposes a new mixed integer programming formulation.Theoretical proofs and computational tests are provided to show that this formulation is able to provide better linear programming relaxation lower bounds than a previously-proposed strong mixed integer programming formulation.Based on the new strong formulation,a progressively stochastic search approach is proposed for solving the problem.Computational results showed that the approach generates high quality solutions,especially for problems of large sizes.     

ON LOCAL STABILIZATION OF NONLINEAR CONTROL SYSTEMS

Based on the notion of maximal absolute observability and its normalforms,a new method for studying the local stabilization for a kind of nonlinearcontrol systems is established.Different from the previous results given by Byrnes-Isitori and others,this new method can deal with more general systems,and hasmuch simpler way to prove the stabilization conditions and to design the feedbacklaws.     

CONVOLUTION THEOREM AND ASYMPTOTIC EFFICIENCY IN TWO SIDE TRUNCATED DISTRIBUTION FAMILY—THE NORMAL CASE

In the distribution family with common support and the one side truncated distribution family, Bickle, I. A. Ibragimov and R. Z. Hasminskii proved two important convolution theorems. As to the two-side truncated case, we also proved a convolution theorem, which plays an extraordinary role in the efficiency theory. In this paper, we will study another kind of two-side truncated distribution family, and prove a convolution result with normal form. On the basis of this convolution result, a new kind of efficiency concept is given; meanwhile, we will show that MLE is an efficient estimate in this distribution family.     

THE LINEAR ARBORICITY 0F COMPOSITl0N GRAPHS

The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G.Akiyama,Exoo and Harary conjectured that la(G)=[Δ（G） 1/2] for any regular graph G.In this papedr,we prove the conjecture for some composition graphs,in particular,forcomplets multipartite graphs.     

A New Criterion for Environmental Risk Management of Multiplication Processes

This paper aims to propose ERT （Expected Reaching Time）, a new risk adverse evaluation criterion of finite multiplication processes, and to examine its properties in relation to the dominance criterion. The ERT means the expected time that takes for an objective valiable to reach a target value. To deal with the environmental risk involved in the process, the expectation maximizing strategy may be the most well known. However, for many cases the dominance strategy rather than the expectation maximizing strategy is adopted and works very well. In this paper we first prove rigorously that minimization of the ERT is equivalent to the dominance criterion in the infinite period. Then we demonstrate by simulation that the ERT gives almost equal evaluation as the dominance criterion even for the finite multiplications, after showing that it is approximately proportional to the logarithm of the target value.     

关于状态变权向量公理化定义的若干结果

逐条分析状态变权向量原始定义中各条件的作用及其内在联系,给出一种改进的状态变权向量定义并讨论与之相关的若干约束条件.研究并解决了刘文奇就状态变权向量公理化定义条件所提出的一个猜想.最后,分析文献中关于状态变权向量的两种改进定义之间的关系.在状态变权向量等效意义下,证明了其中一种改进定义蕴涵着另一种改进定义.     

STRONG EMBEDDING OF HP-GRAPHS ON SURFACE WITH HIGHER GENUS

In 1990, Bondy posed the small circuit double cover （SCDC） conjecture： Every 2-connected graph has a circuit double cover （CDC） with the number of circuits less than ｜v｜ （the order of the vertex set V）. The strong embedding conjecture states that every 2-connected graph has a strong embedding on some surface in which the boundary of each face is a circuit. In this paper, HP-graph is defined as the graph which has a strong embedding on the projective plane with one face of valence ｜V｜ and the other faces of valence 3. And it is proved that the HP-graph has a strong embedding with ｜V｜ - 1 or less faces on some surface, which confirms both the SCDC conjecture and the strong embedding conjecture.     

ENDOMORPHISMS OF LIE ALGEBRA F[t]d／dt

Let F be a field of characteristic zero. W_n =is the Witt algebra over F, W_n~ =is Lie subalgebra of W_n. It is well known both W_n and W_n~ are simple infinite dimensional Lie algebra. In Zhao's paper, it was conjectured thatEnd(W_n~ ) - {0} = Aut(W_n~ ) and it was proved that the validity of this conjecture im-plies the validity of the well-known Jacobian conjecture. In this short note, we check theconjecture above for n = 1. We show End(W_1~ ) - {0} = Aut(W_1~ ).     

A New Discriminating Experiment on the Invariance Hypothesis of Light Speed

IMRODUCTIONThoughthetheoryofspecialrelativityhasalreadybecomethebasisofmodernphysics,experimentstoprovethistheoryhaveneverceased.Menhavenevercarriedoutsomanyexperimentstoverifyanyothertheoryinthehistoryofphysics.Thisonlygoestoprovethatscientistsstillhavedoubtsconerningthebasisofthistheory,andsuchdoubtsarecentredaroundthehyPOthesisoftheinvarianceofspeedoflight.Especiallyaftermenhavediscoveredtheabsoluteframegdefinedby3KCosmicBackgroundRadiationthroughexperiments,itappearstobemorenecessar…     

"无分红美式看涨期权不宜提前执行"的新的证明

利用自由边界方法对美氏看涨期权进行分解，对无分红的美式看涨期权提前执行不是最优的策略这一结论给出另一种证明。     

Recent Results on Constructing Boolean Functions with (Potentially) Optimal Algebraic Immunity Based on Decompositions of Finite Fields

Boolean functions with optimal algebraic immunity (OAI functions) are important cryptographic primitives in the design of stream ciphers. During the past decade, a lot of work has been done on constructing such functions, among which mathematics, especially finite fields, play an important role. Notably, the approach based on decompositions of additive or multiplicative groups of finite fields turns out to be a very successful one in constructing OAI functions, where some original ideas are contributed by Tu and Deng (2012), Tang, et al. (2017), and Lou, et al. (2015). Motivated by their pioneering work, the authors and their collaborators have done a series of work, obtaining some more general constructions of OAI functions based on decompositions of finite fields. In this survey article, the authors review our work in this field in the past few years, illustrating the ideas for the step-by-step generalizations of previous constructions and recalling several new observations on a combinatorial conjecture on binary strings known as the Tu-Deng conjecture. In fact, the authors have obtained some variants or more general forms of Tu-Deng conjecture, and the optimal algebraic immunity of certain classes of functions we constructed is based on these conjectures.

     

THE ASCENDING SUBGRAPH DECOMPOSITION OF K_n-H_(2n-1)

1.IntroductiollAlavi,Y.etal.presentedaconceptofsubgraphdecompositionin[1],whichiscalledascendingsubgraphdecomposition(abbreviatedASD).GivenagraphGwithqedges,C: ,5q5C: ,GissaidtohaveanASD,ifthereisnsuchthatGcanbedecomposedintonsubgraphsGIjGi,''3G.withouti…