Archimedean ordered semigroups as ideal extensions

The main result of the paper is a structure theorem concerning the ideal extensions of archimedean ordered semigroups. We prove that an archimedean ordered semigroup which contains an idempotent is an ideal extension of a simple ordered semigroup containing an idempotent by a nil ordered semigroup. Conversely, if an ordered semigroup S is an ideal extension of a simple ordered semigroup by a nil ordered semigroup, then S is archimedean. As a consequence, an ordered semigroup is archimedean and contains an idempotent if and only if it is an ideal extension of a simple ordered semigroup containing an idempotent by a nil ordered semigroup.     

Algebraic geometry over algebraic structures. IV. Equational domains and codomains

We introduce and study equational domains and equational codomains. Informally, an equational domain is an algebra every finite union of algebraic sets over which is an algebraic set; an equational codomain is an algebra every proper finite union of algebraic sets over which is not an algebraic set.     

Self Extending Rings

A ring R is an IPQ (isomorphic proper quotient)-ring if R ? R/A for every proper ideal A ? R. If every ideal A ? R satisfies: either R ? A or R ? R/A, then R is called an SE (self extending)-ring. It is shown that with one exception, an abelian group G is the additive group of an IPQ-ring if and only if G is the additive group of an SE-ring. The one exception is the infinite cyclic group Z. The zeroring with additive group Z is an SE-ring, but a ring with infinite cyclic additive group is not an IPQ-ring. Since the structure of the additive groups of IPQ-rings is known, the structure of the additive groups of SE-rings is completely determined.     

關於Borsuk的絕對同倫擴充性質的討論

<正> 序言.在同倫論中,常常需要考慮滿足這種性質的拓撲空間X設Y為任意的一個正規空間,B為Y的任何一個非空閉集,任何一個由B×(0,1)+Y×(0)到X的映像都可以扩充為一個由Y×(0,1)到X的映像,我們稱這種性質為絕對同倫扩充性質,具有這種性質的空間以及用AHE表示.Borsuk曾經介紹這樣一個重要的定理:     

Electromagnetic and thermal modelling of axisymmetric induction furnaces

A numerical method to describe the thermo-electric behavior of an induction heating furnace is introduced. It is obtained by using an enthalpy formulation concerning the thermal model and an integral representation of the electromagnetic potential in an unbounded domain. A BEM-FEM method is used and an iterative algorithm together with numerical results for an industrial heating system are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Restricted left principal ideal rings

A ring is an LD-ring ifR is left bounded, ifR/J is a left Artinian left principal ideal ring for every proper idealJ inR, and ifR has finite left Goldie dimension. IfR is non-Artinian thenR is an order in a simple Artinian ringS. The ideal theory of LD-rings is investigated, and we discuss some conditions under which an LD-ring is an hereditary ring, and some under which an LD-ring is a Noetherian, bounded, maximal Asano order. A central localization of an LD-ring is an LD-ring, and the center of some LD-rings is a Krull-domain. This research was supported in part by the National Science Foundation Grant GP 23861.     

Excellent扩张和弱维数

在这篇文章里，我们证明了，当环Ｓ是Ｒ的ｅｘｃｅｌｌｅｎｔ扩张，Ｍ是Ｓ－模时，Ｍ做为Ｓ－模的弱维数与Ｍ做为Ｒ－模的弱维数相等。     

The Turaev genus of an adequate knot

The Turaev genus of a knot is an obstruction to the knot being alternating. An adequate knot is a generalization of an alternating knot. A natural problem is a characterization of the Turaev genus of an adequate knot. In this paper, we show that the Turaev genus of an adequate knot is realized by the genus of the Turaev surface associated to an adequate diagram of the knot using the Khovanov homology. As a result, we obtain the additivity of the Turaev genus of adequate knots, and show that the Turaev genus of an adequate knot is “often” preserved under mutation. We also show that an n-semi-alternating knot is of Turaev genus n. This is the first examples of adequate knots of Turaev genus two or more.     

Truck routing and scheduling

The problem is part of a complex software solution for truck itinerary construction for one of the largest public road transportation companies in the EU. In practice a minor improvement on the operational cost per tour can decide whether a freight services company is profitable or not. Thus the optimization of routes has key importance in the operation of such companies. Given an initial location and an asset state one must be able to calculate a cost optimal itinerary containing all Point of Interests. Such an itinerary is an executable plan which exactly specifies the location and activity of an asset during the whole timespan of the itinerary. If parking places and gas stations are included in the planning then it is NP hard to find an optimal solution. This means that for long range tours an approximately optimal solution for refueling has to be given within an acceptable running time. Also the corridoring of the trucks is an important problem so that we try to optimize the performance, hence tours cannot be recalculated at each data arrival. The vehicle assignment part of this work is already finished and applied with very good results. The remaining part is subject of an ongoing research which started at January 2014. The company started to apply and test our product in the beginning of 2015 under increased human supervision. As a consequence of the project a large cost saving is anticipated by the company.     

An Alternative Approach to Elliptical Motion

Elliptical rotation is the motion of a point on an ellipse through some angle about a vector. The purpose of this paper is to examine the generation of elliptical rotations and to interpret the motion of a point on an ellipsoid using elliptic inner product and elliptic vector product. To generate an elliptical rotation matrix, first we define an elliptical ortogonal matrix and an elliptical skew symmetric matrix using the associated inner product. Then we use elliptic versions of the famous Rodrigues, Cayley, and Householder methods to construct an elliptical rotation matrix. Finally, we define elliptic quaternions and generate an elliptical rotation matrix using those quaternions. Each method is proven and is provided with several numerical examples.     

Effective bounds for very ample line bundles

Let be an ample line bundle on a non singular projective -fold . It is first shown that is very ample for . The proof develops an original idea of Y.T. Siu and is based on a combination of the Riemann-Roch theorem together with an improved Noetherian induction technique for the Nadel multiplier ideal sheaves. In the second part, an effective version of the big Matsusaka theorem is obtained, refining an earlier version of Y.T. Siu: there is an explicit polynomial bound of degree in the arguments, such that is very ample for . The refinement is obtained through a new sharp upper bound for the dualizing sheaves of algebraic varieties embedded in projective space. Oblatum 30-I-1995 & 18-V-1995     

Determination of the insulated inclusion in conductivity problem and related Eshelby conjecture

In the study of composites, it is important to determine the shape of inclusions. There is an interesting case in conductivity problem that the inclusion is insulated. In present paper, we first obtain the representation formula of the solution to an exterior problem, and then prove that for any uniform loading such solution can be extended into the inclusion as an affine function if and only if the insulated inclusion is an ellipse or an ellipsoid. We also show that an analogous result holds for the elasticity problem, which is related to Eshelby conjecture. The main results in this paper are motivated by Ammari, Kang, Kim and Lee (2013), Ammari, Kang and Lim (2005), Kang and Milton (2008), and Liu (2008).     

Invariant properties of representations under cleft extensions

The main aim of this paper is to give the invariant properties of representations of algebras under cleft extensions over a semisimple Hopf algebra. Firstly, we explain the concept of the cleft extension and give a relation between the cleft extension and the crossed product which is the approach we depend upon. Then, by making use of them, we prove that over an algebraically closed field k, for a finite dimensional Hopf algebra H which is semisimple as well as its dual H*, the representation type of an algebra is an invariant property under a finite dimensional H-cleft extension . In the other part, we still show that over an arbitrary field k, the Nakayama property of a k-algebra is also an invariant property under an H -cleft extension when the radical of the algebra is H-stable.     

Relations Between Algebras and Their Subalgebras of Invariants

We prove that, if H is a finite-dimensional semisimple Hopf algebra, and A is an FCR H-module algebra over an algebraically closed field, then A is a PI-algebra, provided the subalgebra of invariants is a PI-algebra. We also show that if A is an affine algebra with an action of a finite group G by automorphisms, the subalgebra of the fixed points A^G is in the center of A, and the characteristic of the ground field is either zero or relatively prime to the order of G, then A^G is affine. Analogous results are proved for graded algebras and H-module algebras over a semisimple triangular Hopf algebra over a field of characteristic zero. We prove also that, if A is an H-module algebra with an identity element, and H is either a semisimple group algebra or its dual, then, if A is semiprimitive (semiprime), then so is A^H.     

Eigenvector method,consistency test and inconsistency repairing for an incomplete fuzzy preference relation

In this paper, we extend the eigenvector method (EM) to priority for an incomplete fuzzy preference relation. We give a reasonable definition of multiplicative consistency for an incomplete fuzzy preference relation. We also give an approach to judge whether an incomplete fuzzy relation is acceptable or not. We develop the acceptable consistency ratio for an incomplete multiplicative fuzzy preference relation, which is simple and similar to Saaty’s consistency ratio (CR) for the multiplicative preference relation. If the incomplete fuzzy preference relation is not of acceptable consistency, we define a criterion to find the unusual and false element (UFE) in the preference relation, and present an algorithm to repair an inconsistent fuzzy preference relation until its consistency is satisfied with the consistency ratio. As a result, our improvement method cannot only satisfy the consistency requirement, but also preserve the initial preference information as much as possible. Finally, an example is illustrated to show that our method is simple, efficiency, and can be performed on computer easily.     

Optimal boundedness criteria for extended-real-valued functions

The notion of genuinely bounded below function is introduced and characterized by means of the concept of co-equilibrated function. As an application, we state two boundedness criteria for extended-real-valued functions, both optimal in a clearly defined sense. The first one says that an extended-real-valued function minorized by an affine map and coinciding from some value up with a co-equilibrated function is bounded below. The second criterion states that an extended-real-valued function minorized by an affine map is bounded below provided that one of its sub-level sets is co-equilibrated.     

完全k叉树的粘连度

相对于其他网络抗毁性的描述指标来说,图的粘连度是比较理想,也是比较合理的刻画参数．而完全k叉树作为重要的网络结构被广泛地应用在通信网和嵌入式系统芯片的优化设计方面．本文通过优化组合方法界定了完全k叉树的粘连度和毁裂度．从某种程度刻画了网络的抗毁性,为网络设计提供了一种客观的理论依据．完全k叉树的粘连度为1k＋1（kh＋1-1）,如h是奇数;1k＋1（（kh＋1-1）,如h是偶数．完全k叉树的毁裂度为（2k-1）kh-12,如h是奇数;kh＋22-1k-1,如h是偶数．     

A Newton-type univariate optimization algorithm for locating the nearest extremum

This paper introduces an algorithm for univariate optimization using linear lower bounding functions (LLBF's). An LLBF over an interval is a linear function which lies below the given function over an interval and matches the given function at one end point of the interval. We first present an algorithm using LLBF's for finding the nearest root of a function in a search direction. When the root-finding method is applied to the derivative of an objective function, it is an optimization algorithm which guarantees to locate the nearest extremum along a search direction. For univariate optimization, we show that this approach is a Newton-type method, which is globally convergent with superlinear convergence rate. The applications of this algorithm to global optimization and other optimization problems are also discussed.     

Finite Element Simulations of Magnetic Liquids with Free Boundaries

The main objective of this paper is to present an algorithm for finite element simulations of the dynamic behaviour of magnetic liquids with free boundaries. Starting with the governing equations we describe the discretization and solution strategy. As an example the shape of an oscillating drop is investigated where for a simplified problem an analytical approximation is available.     

Semiring and Semimodule Issues in MV-Algebras

It is known that an atomic right LCM domain need not be a UFD but is a projectivity-UFD if it is also modular. This paper studies a slightly weaker and easier condition, the RAMP (acronym for the property in the title) , which also ensures that an atomic right LCM domain will be a projectivity-UFD. Among other things it is shown that in an atomic LCM domain, modularity is equivalent to the pair RAMP and LAMP (the left-right analog of RAMP). This result is then used to show that an atomic LCM domain with conjugation is modular. An example is given of an atomic LCM domain that has neither the RAMP nor the LAMP. All rings are not-necessarily commutative integral domains. Recall that an atomic ring is one in which every nonzero nonunit is a product of atoms (i.e. irreducibles) . A ring R is a right LCM domain if for any two elements a and b in R, aR ∩ bR is a principal right ideal. A right LCM domain need not be a left LCM domain [3] . If a ring has both properties it is called an LCM domain. It Is known (see Example 2 below) that, unlike the commutative case, an atomic right LCM domain need not be a UFD (unique factorization domain). In [1] it is shown that if the ring is also modular then it is a projectivity-UFD (definition of the latter recalled below)