Geometry Theorem Proving by Decomposing Polynomial System into Strong Regular Sets

This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is true and exclude other components for which the geometry theorem is false. Two examples are given to show that the geometry theorems are conditionally true for some components which are excluded by other methods.

Characteristic Decomposition: From Regular Sets to Normal Sets

In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomial set into ?nitely many strong characteristic pairs, each of which is formed with the reduced lexicographic Gr?bner basis and the normal W-characteristic set of a characterizable ideal.

A POLYNOMIAL ALGORITHM FOR FINDING THEMINIMUM FEEDBACK VERTEX SET OF A3-REGULAR SIMPLE GRAPH

A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.

THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS

A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..

基于Lie群表示的保体积2D-3D点集配准算法

2D-3D点集配准的目标是寻找三维原始点集与二维目标投影点集之间的对应关系和最优变换.为了给出配准问题的解析解,避免投影引起的体积退化,提出基于Lie群表示的保体积2D-3D点集配准算法.首先,考虑投影矩阵和旋转矩阵的非交换性,引入Lie群表示,将配准问题形式化为一个Lie群优化问题.利用局部线性化方法,将Lie群优化问题转化为一个可计算的二次规划问题.其次,为了避免体积退化,考虑约束变换后的三维点集的投影与二维目标点集的投影具有相同的体积.为便于计算,引入Jensen-Bregman LogDet散度作为保体积正则项,将计算点集的体积差异转化为计算协方差矩阵之间的差异.然后,通过交替求解对应关系和最优变换,形成完整且可解的迭代策略.最后,在两个经典数据集上进行对比实验和消融实验,验证了该算法的精确性和有效性.

基于隐结构模型与频繁项集探讨特发性肺纤维化的辨证用药规律

目的:探讨中医治疗特发性肺纤维化(IPF)的辨证用药规律,为临床治疗IPF提供参考。方法:在中国知网、万方数据知识服务平台、PubMed、Embase等数据库中,检索建库至2021年8月8日辨证应用中药汤剂治疗IPF的相关文献,提取证型、症状及中药处方信息,构建IPF医案数据库,采用隐结构模型、频繁项集等数据挖掘方法分析中药汤剂内服治疗IPF的辨证用药规律。结果:共纳入文献39篇,包含病例1497例。纳入文献共包含症状163个,如咳嗽、乏力、气短等,将频次3的53个症状作为显变量构建IPF的隐结构模型,该模型提示气虚血瘀是IPF的常见证型。纳入文献包含的处方中共涉及中药163味,其中高频药物包括黄芪、甘草、丹参、当归、党参等;挖掘出“症状-中药”频繁项集5项,如“胸痛乏力+舌有瘀斑+脉沉细+丹参+桃仁+党参”;“证型-症状-中药”频繁项集4项,如“气虚血瘀+胸闷乏力+舌有瘀斑+黄芪+丹参+当归”。结论:气虚血瘀是IPF的临床常见证型,中药汤剂治疗IPF多以黄芪、甘草、丹参为主要药物,药物配伍根据临床辨证选择。

REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW

In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing solutions for the following elliptic equations{-△u=λ∑1Bδ（x0,j）（u-kj）p＋,in Ω,u=0,onΩ is a bounded simply-connected smooth domain, ki （i = 1,… , k） is prescribed positive constant. The result we prove is that for any given non-degenerate critical pointX0=（x0,1,…,x0,k of the Kirchhoff-Routh function defined on Ωk corresponding to （ k1,……kk ）there exists a stationary classical solution approximating stationary k points vortex solution. Moreover, as λ→＋∞ shrinks to {x05}, and the local vorticity strength near each x0,j approaches kj, j = 1,… , k. This result makes the study of the above problem with p _〉 0 complete since the cases p 〉 1, p = 1, p = 0 have already been studied in [11, 12] and [13] respectively.

Assessment of Contingent Liabilities for Risk Assets Evolutions Built on Brownian Motion

This paper is a generalization of the results of the previous papers. Using these results a class of evolutions of risk assets based on the geometric Brownian motion is constructed. Among these evolutions of risk assets, the important class of the random processes is the random processes with parameters built on the basis of the discrete geometric Brownian motion. For this class of random processes the interval of non-arbitrage prices are found for the wide class of contingent liabilities. In particular, for the payoff functions of standard options call and put of the European type the fair prices of super-hedge are obtained. Analogous results are obtained for the put and call of arithmetical options of Asian type. For the parameters entering in the definition of random process the description of all statistical estimates is presented. Statistical estimate for which the fair price of super-hedge for the payoff functions of standard call and put options of European type is minimal is indicated. From the formulas found it follows that the fair price of super-hedge can be less than the price of the underlying asset. In terms of estimates the simple formula for the fair price of super-hedge is found. Every estimates can be realized in the reality. This depends on the distribution function of the observed dates in the financial market.

Description of Incomplete Financial Markets for Time Evolution of Risk Assets

In the paper, a class of discrete evolutions of risk assets having the memory is considered. For such evolutions the description of all martingale measures is presented. It is proved that every martingale measure is an integral on the set of extreme points relative to some measure on it. For such a set of evolutions of risk assets, the contraction of the set of martingale measures on the filtration is described and the representation for it is found. The inequality for the integrals from a nonnegative random value relative to the contraction of the set of martingale measure on the filtration which is dominated by one is obtained. Using these inequalities a new proof of the optional decomposition theorem for super-martingales is presented. The description of all local regular super-martingales relative to the regular set of measures is presented. The applications of the results obtained to mathematical finance are presented. In the case, as evolution of a risk asset is given by the discrete geometric Brownian motion, the financial market is incomplete and a new formula for the fair price of super-hedge is founded.

Convergence Analysis of General Version of Gauss-Type Proximal Point Method for Metrically Regular Mappings

We introduce and study in the present paper the general version of Gauss-type proximal point algorithm (in short GG-PPA) for solving the inclusion , where T is a set-valued mapping which is not necessarily monotone acting from a Banach space X to a subset of a Banach space Y with locally closed graph. The convergence of the GG-PPA is present here by choosing a sequence of functions with , which is Lipschitz continuous in a neighbourhood O of the origin and when T is metrically regular. More precisely, semi-local and local convergence of GG-PPA are analyzed. Moreover, we present a numerical example to validate the convergence result of GG-PPA.

Einstein’s Dark Energy via Similarity Equivalence, ‘tHooft Dimensional Regularization and Lie Symmetry Groups

Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv2 leads to Einstein’s celebrated maximal energy equation E = mc2 and how in turn this can be dissected into the ordinary energy density E(O) = mc2/22 and the dark energy density E(D) = mc2(21/22) of the cosmos where m is the mass;v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.

东天山钨矿床时空分布、矿床类型及构造背景

东天山是中亚增生造山带的重要组成部分,蕴含了重要的铁、铜、镍、铅锌、金、钼、铷等矿床。近年来,东天山地区陆续发现了十余个大中型钨矿床,有望成为重要的钨矿资源基地。本文介绍了东天山地区钨矿床的地质特征、时空分布与构造背景,总结了东天山钨矿成矿规律,开展了成矿预测。东天山地区钨矿类型主要包括矽卡岩型、石英脉型及云英岩型,钨矿床的空间分布明显受控于前寒武纪结晶基底,成矿时间主要聚焦于三叠纪和晚石炭世。其中,中天山地块的矽卡岩型钨矿和东南缘的石英脉型钨矿形成于三叠纪,而中天山西南缘的矽卡岩型钨矿形成于晚石炭世,均与洋盆闭合之后的碰撞造山作用有关。根据东天山地区钨矿成矿规律,本文认为东天山地区钨矿找矿潜力巨大,提出了“前寒武纪基底+花岗岩+化探异常”的钨矿找矿预测思路,针对不同尺度的钨矿找矿勘查提出了建议。

蒙古国铜矿床主要类型、典型矿床、时空分布与构造背景

铜是蒙古国最重要的工业资源之一,在2010年之前,一直是蒙古国最主要的经济收入来源,但之后被煤炭资源所取代。总体上,蒙古国地质矿产研究与开发程度相对较低。蒙古国铜矿床可分为斑岩型、火山成因块状硫化物(VMS)型、与花岗岩有关铜矿、矽卡岩型、玄武岩型及砂岩型等6种类型,但最重要的具工业意义的铜矿床是斑岩型及VMS型。蒙古国铜矿床主要形成于新元古代末期(埃迪卡拉纪)、晚泥盆世、晚石炭世和三叠纪-早侏罗世等4个时期。空间上,蒙古铜矿床可大体分为南、北2条成矿带,分别与古亚洲洋和蒙古-鄂霍茨克洋的演化有关。南Cu矿带自北而南可进一步划分为北、中、南3个成矿亚带,分别是泥盆纪VMS型Cu-Zn及多金属、晚石炭世斑岩型Cu-Au和晚泥盆世斑岩型Cu-Au-Mo等成矿亚带;而北Cu矿带则可分为南、北2个亚带,且其铜矿化时代具有“西早东晚”的特征。蒙古斑岩铜矿床均形成于大洋板块俯冲背景下,属“俯冲型”斑岩铜矿,其中与古亚洲洋有关的南Cu矿带主要形成于俯冲带上方的洋内弧及弧后盆地环境,而与蒙古-鄂霍茨克洋俯冲有关的北Cu矿带则形成于陆缘弧环境。蒙古北Cu矿带受蒙古山弯构造的影响,向西不能延出国境,而其北、南亚带向东则分别延入俄罗斯外贝加尔和我国大兴安岭北部地区。对南Cu矿带而言,除了其北亚带(VMS型铜矿带)向西-西北延入我国阿尔山泰南部是可以确定外,其他2个亚带向两侧的延伸情况均不明朗,因此要理清它们的延伸,尤其是产有欧玉陶勒盖晚泥盆世超大型Cu-Au-Mo矿床的南亚带的区域延伸情况,尚需要系统的区域构造-地层-岩浆岩-矿床等对比研究工作。蒙古其他类型的铜矿,如矽卡岩型、与侵入岩有关热液型、玄武岩型、砂岩型及镁铁质层状杂岩型等矿床(点),目前均仅发现小型矿床或矿(化)点,其成矿及找矿潜力均有待进一步研究揭示。

Uniformly Bounded Set-Valued Composition Operators in the Spaces of Functions of Bounded Variation in the Sense of Riesz

We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.

Martingales and Super-Martingales Relative to a Convex Set of Equivalent Measures

In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are founded. The description of all local regular super-martingales relative to a convex set of equivalent measures is presented. The notion of the complete set of equivalent measures is introduced. We prove that every bounded in some sense super-martingale relative to the complete set of equivalent measures is local regular. A new definition of the fair price of contingent claim in an incomplete market is given and the formula for the fair price of Standard Option of European type is found. The proved Theorems are the generalization of the famous Doob decomposition for super-martingale onto the case of super-martingales relative to a convex set of equivalent measures.

东天山印支期矿床地质特征、成因类型及成矿规律

东天山成矿带是我国重要成矿带之一,以古生代大规模成矿为特色。近年来,东天山成矿带陆续报道了一批印支期的成矿年龄,吸引了越来越多的关注。基于此,初步总结了东天山印支期矿床的地质特征、成因类型及成矿规律。结果表明:东天山印支期矿床的成矿元素丰富,金、钼、钨、铼、铷等均达到大型—超大型规模,还蕴含了锂、铍、铌、钽、钒、钛、铁等金属矿床,显示出东天山印支期成矿的重要性。印支期矿床的成因类型多样,既发育了岩浆型钒钛磁铁矿床、花岗岩型铷矿床、伟晶岩型锂铍铌钽矿床等岩浆矿床,又发育斑岩型钼铼矿床、矽卡岩型钨钼铷矿床、石英脉型钨矿床、造山型和浅成低温热液型金矿床等热液矿床。在空间分布上,印支期矿床集中分布于康古尔韧性剪切带和中天山地块及其东南缘,而其他构造单元成矿信息较少。虽然印支期矿床的分布具有时空相似性,但关键控矿要素明显不同,矽卡岩型钨矿床明显受中天山前寒武纪基底控制,钒钛磁铁矿床、花岗岩型铷矿床、伟晶岩型锂铍铌钽矿床和斑岩型钼矿床受不同性质的侵入岩控制,而造山型金矿床明显受韧性剪切带和断裂构造控制。因此,东天山印支期造山作用的资源潜力已初步显现,未来应加强东天山甚至新疆地区的印支期成矿作用研究和找矿勘查工作。

基于疗效加权FP-Growth算法的干燥综合征组方用药挖掘分析

目的以数据挖掘方法探索干燥综合征组方用药规律,并探讨加权FP-Growth算法在中药方剂挖掘中的应用,为中医临床用药分析提供新思路。方法以中医临床疗效作为加权标准,以集对分析为基础计算疗效基数ρ,以w=(ρ_(对照组)-ρ_(实验组))/ρ_(对照组)+δ计算最终加权值,以加权FP-Growth算法为关联规则分析方法进行数据挖掘,分别计算支持度及提升度,对挖掘结果进行支持度和提升度的分析,综合得出分析结果。结果最常用中药前5位为:麦冬、生地黄、甘草、白芍、北沙参。综合支持度及提升度分析挖掘结果后提出以麦冬、生地黄、北沙参、甘草为基本底方,丹参、玄参、黄芪为祛瘀,解毒,补气加减方向的代表。并挖掘出了两个值得关注的高支持度药团:补脾肾的茯苓-山茱萸-山药-丹皮药团及补气血的白芍-太子参-五味子-当归药团。结论干燥综合征临床用药以养阴生津药为主,配伍具有经典方特色。加权FP-Growth算法用于组方用药分析可提炼核心组方思路及加减方向,有助于中医药经验的继承与发展。

Three-dimensional inversion of knot defects recognition in timber cutting

The comprehensive utilization of wood is the main goal of log cutting,but knot defects increase the diffi-culty of rationally optimizing cutting.Due to the lack of real shape data of knot defects in logs,it is diffi cult for detection methods to establish a correlation between signal and defect morphology.An image-processing method is proposed for knot inversion based on distance regularized level set segmentation(DRLSE)and spatial vertex clustering,and with the inversion of the defects existing relative board position in the log,an inversion model of the knot defect is established.First,the defect edges of the top and bottom images of the boards are extracted by DRLSE and ellipse fi tting,and the major axes of the ellipses made coplanar by angle correction;second,the coordinate points of the top and bottom ellipse edges are extracted to form a spatial straight line;third,to solve the intersection dispersion of spatial straight lines and the major axis plane,K-medoids clustering is used to locate the vertex.Finally,with the vertex and the large ellipse,a 3D cone model is constructed which can be used to invert the shape of knots in the board.The experiment was conducted on ten defective larch boards,and the experimental results showed that this method can accurately invert the shapes of defects in solid wood boards with the advantages of low cost and easy operation.

Gap Functions and Error Bounds for Set-Valued Vector Quasi Variational Inequality Problems

One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.