Solvability Results on a Set-valued Input-output Equation

A class of set-valued Leontief input-output equation is introduced and two solvability theorems are obtained, which provide some corresponding existence, surjection as well as continuity results.

Finitely Generated Torsion-free Nilpotent Groups Admitting an Automorphism of Prime Order

Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.

SOME RESULTS ON CONTINUOUS TYPE CONDITIONAL INPUT-OUTPUT EQUATION-FIXED POINT AND SURJECTIVITY METHODS

Based on the classical(matrix type)input-output analysis,a type of nonlinear (continuous type) conditional Leontief model,input-output equation were introduced,as well as three corresponding questions,namely,solvability,continuity and surjectivity,and some fixed point and surjectivity methods in nonlinear analysis were used to deal with these questions. As a result,the main theorems are obtained,which provide some sufficient criterions to solve above questions described by the boundary properties of the enterprises consuming operator.

ON NONLINEAR ELLIPTIC HEMIVARIATIONAL INEQUALITIES OF SECOND ORDER

In this paper, a nonlinear hemivariational inequality of second order with a forcing term of subcritical growth is studied. Using techniques from multivalued analysis and the theory of nonlinear operators of monotone type, an existence theorem for the Dirichlet boundary value problem is proved.

FREDHOLM AND COMPACT MAPPINGS SHARING A VALUE

Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.

THE ■■-LEMMA UNDER SURJECTIVE MAPS

We consider the ■■-lemma for complex manifolds under surjective holomorphic maps.Furthermore,using Deligne-Griffiths-Morgan-Sullivan’s theorem,we prove that a product compact complex manifold satisfies the ■■-lemma if and only if all of its components do as well.

Some Surjectivity Theorems for Maximal Monotone Operators and Its Application

The main purpose of this paper is to study the surjectivity theorems for maximal monotone mapping in reflexive Banach spaces by using fixed point theory. We prove some new surjectivity theorems under some conditions and give its application in differential equation.

A Characterization of Semilinear Surjective Operators and Applications to Control Problems

In this paper we characterize a broad class of semilinear surjective operators given by the following formula where Z are Hilbert spaces, and is a suitable nonlinear function. First, we give a necessary and sufficient condition for the linear operator to be surjective. Second, we prove the following statement: If and is a Lipschitz function with a Lipschitz constant small enough, then and for all the equation admits the following solution .We use these results to prove the exact controllability of the following semilinear evolution equation , , where , are Hilbert spaces, is the infinitesimal generator of strongly continuous semigroup in the control function belong to and is a suitable function. As a particular case we consider the semilinear damped wave equation, the model of vibrating plate equation, the integrodifferential wave equation with Delay, etc.

VAGUE MAPPINGS

In this paper, the concepts of （α,β） vague mappings, surjective （α,β） vague mappings, injective （α,β） vague mappings, bijective （α,β） vague mappings, （α,β） adjoin vague mappings, （α,β） vague monomorphism, （α,β） vague epimorphism, （α,β） vague isomorphism, （α,β） Vague par-tition are introduced through the so-called （α,β） hierarchical divide vague relations We extend the results on fuzzy mappings, and obtain some of their properties.

Gravitational Space-Time Curve Generation via Accelerated Charged Particles

A force with an acceleration that is equal to multiples greater than the speed of light per unit time is exerted on a cloud of charged particles. The particles are resultantly accelerated to within an infinitesimal fraction of the speed of light. As the force or acceleration increases, the particles’ velocity asymptotically approaches but never achieves the speed of light obeying relativity. The asymptotic increase in the particles’ velocity toward the speed of light as acceleration increasingly surpasses the speed of light per unit time does not compensate for the momentum value produced on the particles at sub-light velocities. Hence, the particles’ inertial mass value must increase as acceleration increases. This increase in the particles’ inertial mass as the particles are accelerated produce a gravitational field which is believed to occur in the oscillation of quarks achieving velocities close to the speed of light. The increased inertial mass of the density of accelerated charged particles becomes the source mass (or Big “M”) in Newton’s equation for gravitational force. This implies that a space-time curve is generated by the accelerated particles. Thus, it is shown that the acceleration number (or multiple of the speed of light greater than 1 per unit of time) and the number of charged particles in the cloud density are surjectively mapped to points on a differential manifold or space-time curved surface. Two aspects of Einstein’s field equations are used to describe the correspondence between the gravitational field produced by the accelerated particles and the resultant space-time curve. The two aspects are the Schwarzchild metric and the stress energy tensor. Lastly, the possibility of producing a sufficient acceleration or electromagnetic force on the charged particles to produce a gravitational field is shown through the Lorentz force equation. Moreover, it is shown that a sufficient voltage can be generated to produce an acceleration/force on the particles that is multiples greater than the speed of light per unit time thereby generating gravity.

Surjective Lp-isometries on Grassmann spaces

Letϕ:Pc(M1)→Pc(M2)be a surjective Lp-isometry between Grassmann spaces of projections with the trace value c in semifinite factors M1 and M2.Based on the characterization of surjective Lp-isometries of unitary groups in finite factors,we show thatϕor I−ϕcan be extended to a∗-isomorphism or a∗-antiisomorphism.In particular,ϕis given by a∗-(anti-)isomorphism unless M1 and M2 are finite and c=12.

Second Order Nonlinear Evolution Inclusions Existence and Relaxation Results

This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.

Isometries in hyperbolic spaces

Suppose that f:Hn → Hn (n≥2) maps any r-dimensional hyperplane (1≤r【n) into an r-dimensional hyperplane. In this paper, we prove that f is an isometry if and only if f is a surjective map. This result gives an affirmative answer to a recent conjecture due to Li and Yao.

ABOUT A PROBLEM RAISED BY GOLAN

In the 19th problem of [1], J. S. Golan put forward the following question: 'For what kind of ring R is it true that the map γ_#:R-tors→S-tors is surjective for every ring surjective homomorphism r: R→S?' where both R and S are associative rings with identity, R-tors stands for a lattice composed of all hereditary torsion theories in left R-module category R-Mod and for each τ ∈ R-tors, γ_#(τ)=σ=(f_σ,f_σ)∈S-tors, in

The Semigroup of Surjective Transformations on an Infinite Set

For an infinite set X, denote by Ω(X) the semigroup of all surjective mappings from X to X. We determine Green's relations in Ω(X), show that the kernel (unique minimum ideal) of Ω(X) exists and det ermine its elemen ts and cardinali ty. For a cou ntably infinite set X, we describe the elements of Ω(X) for which the D-class and J-class coincide. We compare the results for Ω(X) with the corresponding results for other transformation semigroups on X.

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.

The Extension of Isometry between Unit Spheres of Normed Space E and l^1

The main result of this paper is to prove Fang and Wang＇s result by another method： Let E be any normed linear space and Vo ： S（E）→ S（l^1） be a surjective isometry. Then V0 can be linearly isometrically extended to E.

LOCALLY EKELAND'S VARIATIONAL PRINCIPLE AND SOME SURJECTIVE MAPPING THEOREMS

This paper shows that if a Gateaux differentiable functional f has a finite lower bound(although it need not attain it),then,for everyε>0,there exists some point zεsuch that‖f′(zε)‖ε1+h(‖zε‖),where h:[0,∞)→[0,∞)is a continuous function such that∫∞011+h(r)dr=∞.Applications are given to extremum problem and some surjective mappings.