Additive Maps Preserving the Star Partial Order on B(H)

Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only if one of the following assertions holds. （1） There exist a nonzero complex number a and two unitary operators U and V on H such that φ（X） = a UXV or φ（X） = α UX^＊ V for all X ∈B（H）. （2） There exist a nonzero a and two anti-unitary operators U and V on H such that φ（X） = αUXV or φ（X） = aUX^＊ Vfor all X∈ B（H）.

The Lawson Partial Order on Wrpp Semigroups

In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups,of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.

The Existence of Coupled Solutions for a Kind of Nonlinear Operator Equations in Partial Ordered Linear Topology Space

The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method. Some new existence results are obtained.

Partial Orders on Right Inverse Semigroups

It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigroup. We construct partial orders on S by some kind of its subsemigroups and uncover that partial orders on S have close contact with partial orders on S/Y.

Results of Associated Implication Algebra on a Partial Ordered Set

Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implication algebra is discussed. Also, the concept of filter is proposed with some basic properties being studied.

Continuity of Solution Mappings for Parametric Set Optimization Problems under Partial Order Relations

This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.

Partial Ordering of Range Symmetric Matrices and M-Projectors with Respect to Minkowski Adjoint in Minkowski Space

In this paper, we obtain some new characterizations of the range symmetric matrices in the Minkowski Space M by using the Block representation of the matrices. These characterizations are used to establish some results on the partial ordering of the range symmetric matrices with respect to the Minkowski adjoint. Further, we establish some results regarding the partial ordering of m-projectors with respect to the Minkowski adjoint and manipulate them to characterize some sets of range symmetric elements in the Minkowski Space M. All the results obtained in this paper are an extension to the Minkowski space of those given by A. Hernandez, et al. in [The star partial order and the eigenprojection at 0 on EP matrices, Applied Mathematics and Computation, 218: 10669-10678, 2012].

A New Relationship Between Partial Orders of Normal Matrices and Their Squares

A new relationship between partial orders of normal matrices and their squares is established.

A New Class of Partial Orders

Let R be a unital*-ring.For any a,w,b∈R,we apply the w-core inverse to define a new class of partial orders in R,called the w-core partial order.Suppose that a,b∈R are w-core invertible.We say that a is below b under the w-core partial order if a_(w)^(#)a=a_(w)^(#)b and a_(w)a_(w)^(#)=bwa_(w)^(#),where a_(w)^(#)denotes the w-core inverse of a.Characterizations of the w-core partial order are given,and its relationships with several types of partial orders are also considered.In particular,we show that the core partial order coincides with the a-core partial order,and the star partial order coincides with the a*-core partial order.

The L^(*) Partial Order on the Set of Group Matrices

In this paper,we use the Lowner partial order and the star partial order to introduce a new partial order(denoted by"L^(*)")on the set of group matrices,and get some characteristics and properties of the new partial order.In particular,we prove that the L*partial order is a special kind of the core partial order and it is equivalent to the star partial order under some conditions.We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.

A Partial Order in the Knot Table Ⅱ

A partial order on the set of the prime knots can be defined by the existence of a surjective homomorphism between knot groups. In the previous paper, we determined the partial order in the knot table. In this paper, we prove that 31 and 41 are minimal elements. Further, we study which surjection a pair of a periodic knot and its quotient knot induces, and which surjection a degree one map can induce.

Quasiresiduals in Semigroups with Natural Partial Order

A semigroup （S, .） is called right （left） quasiresiduated if for any a, b in S there exists x in S such that ax≤s b （xa≤s b） with respect to the natural partial order ≤s of S. This concept has its origin in the theory of residuated semigroups, but can also be seen as a generalization of the right （left） simplicity of semigroups. It is first studied for totally-, resp., trivially-ordered semigroups, and then for semigroups with idempotents. In particular, the cases when （S≤s） is directed downwards and when S contains a zero （with respect to a more restrictive definition） are dealt with. Throughout, examples are given; in total, 30 classes of （often well-known） semigroups of this kind are specified.

Some new fixed point results under constraint inequalities in comparable complete partially ordered Menger PM-spaces

In this paper,we introduce the concept of comparable T-completeness of a partially ordered Menger PM-space and discuss the existence of fixed points for mappings satisfying certain conditions in the framework of a comparable T-complete partially ordered Menger PM-space.We obtain some new results which generalize many known ones in the literature.Moreover,we derive some consequent results and give an example to illustrate our main result.

Common Fixed Point Result of Multivalued and Singlevalued Mappings in Partially Ordered Metric Space

In recent times the fixed point results in partially ordered metric spaces has greatly developed. In this paper we prove common fixed point results for multivalued and singlevalued mappings in partially ordered metric space. Our theorems generalized the theorem in [1] and extends the many more recent results in such spaces.

Application of the Adomian Decomposition Method (ADM) for Solving the Singular Fourth-Order Parabolic Partial Differential Equation

In this paper, the ADM method is used to construct the solution of the singular fourth-order partial differential equation.

PARTIAL ORDERING AND PERCEPTION OF MOLECULAR STRUCTURES

Ⅰ. INTRODUCTION Computer-assisted molecular design and synthetic planning is an important aspect in modern chemical research. To give assistance to chemical design, a computer should acquire the ability to recognize chemical structures, namely, the internal representation (adjacent matrix) and external representation (linear notation, 2-D or 3-D molecular graphics and struc-

NEWTON-LIK E METNODS IN PARTIALLY ORDERED BANACH SPACES

We provide convergence results and error estimates for Newton-like methods in generalized Banach spaces.The idea of a generalized norm is used whichis defined to be a map from a linear space into a partially ordered Banach space.Convergence results and error estimates are improved compared with the real norm theory.

Equivalence relation and partial ordering of parallel mechanisms with applications to mechanism synthesis and mobility analysis

Motion type (or motion pattern) of a mechanism is defined as the set of all rigid motions achievable by the mechanism’s end-effector;the motion type of a parallel mechanism equals the intersection set of all subchain motion types.The motion type of a non-instantaneous parallel mechanism locally agrees with a regular submanifold (or a Lie subgroup in particular) of the special Euclidean group SE(3).Based on submanifold germs of SE(3), we can define an equivalence relation and a partial order relation for both motion types and parallel mechanisms: two motion types are equivalent if and only if they agree on an open neighbor-hood around the identity element of SE(3);two motion types are comparable if and only if one is a submanifold of the other on an open neighborhood around the identity of SE(3).It is also possible to define equivalence relation and partial ordering on the col-lection of parallel mechanisms.In this paper, we first study properties of the equivalence and partial order relation of both motion types and parallel mechanisms, then we discuss their application in type synthesis, mobility analysis and non-overconstrained ness realization of parallel mechanisms.

FORCED OSCILLATIONS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FUNCTIONAL PARTIAL DIFFERENTIAL EQUATIONS

In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities.

Study of Fixed Point Theorems for Higher Dimension in Partially Ordered Metric Spaces

In this paper, we establish the existence and uniqueness of fixed points of operator , when n is an arbitrary positive integer and X is a partially ordered complete metric space. We have shown examples to verify our work. Our results generalize the recent fixed point theorems cited in [1]-[4] etc. and include several recent developments.