Five New MVL Current Mode Differential Absolute Value Circuits Based on Carbon Nano-tube Field Effect Transistors(CNTFETs)

Carbon Nano-Tube Field Effect Transistors(CNTFETs) are being widely studied as possible successors to silicon MOSFETs.Using current mode has many advantages such as performing sum operation by means of a simple wired connection.Also,direction of the current can be used to exhibit the sign of digits.It is expected that the advantages of current mode approaches will become even more important with increased speed requirements and decreased supply voltage.In this paper,we present five new circuit designs for differential absolute value in current mode logic which have been simulated by CNTFET model.The considered base current for this model is 2 μA and supply voltage is 0.9 V.In all of our designs we used N-type CNTFET current mirrors which operate as truncated difference circuits.The operation of Differential Absolute Value circuit calculates the difference between two input currents and our circuit designs are operate in 8 logic levels.

STUDYING THE FOCAL VALUE OF ORDINARY DIFFERENTIAL EQUATIONS BY NORMAL FORM THEORY

We present a new method to calculate the focal value of ordinary differential equation by applying the theorem defined the relationship between the normal form and focal value,with the help of a symbolic computation language M ATHEMATICA,and extending the matrix representation method.This method can be used to calculate the focal value of any high order terms.This method has been verified by an example.The advantage of this method is simple and more readily applicable.the result is directly obtained by substitution.

DIFFERENTIAL POLYNOMIALS SHARING ONE VALUE

In this paper, we investigate uniqueness problems of differential polynomials of meromorphic functions. Let a, b be non-zero constants and let n, k be positive integers satisfying n ≥ 3k ＋ 12. If f^n＋ af^（k）and g^n＋ ag^（k）share b CM and the b-points of f^n＋ af^（k）are not the zeros of f and g, then f and g are either equal or closely related.

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM OF SYSTEMS FOR QUASILINEAR ORDINARY DIFFERENTIAL EQUAT1ONS

In this paper, we study the singular perturbation of boundary value problem of systemsfor quasilinear ordinary differential equations:where xf. y ,h,A,B and C belong to Rn and a is a diagonal matrix. Under the appropriate assumptions, using the technique of diagonalization and the theory of differential inequalities we obtain the existence of solution and its componentwise uniformly valid asymptotic estimation.

MIXED BOUNDARY VALUE PROBLEM FOR SECOND－ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE

In this paper.the following ined boundary value problem for second-order system of differential equations of the elliptic type will be discussed to find the function u and v such that they satisfy:The solution of this problem is found by means of the theory of generalized analutic function and the integral equation method for solving boundary value problems.

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR HIGHER ORDINARY DIFFERENTIAL EQUATION

In this paper we study the singular perturbation of boundary value problems with perturbations both in the operator and in the interval ends. So as to prove the existence and uniqueness of solution of perturbed problem, to establish the asymptotic expression involving three parameters. Thus, the iterative equation of finding the asymptotic solution is derived and the estimation of the remainder term is given out. We extend results of [l]-[5].

UNIQUENESS OF SOLUTIONS OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR THIRD QRDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

By making use of the differential inequalities, in this paper we study the uniqueness of solutions of the two kinds of the singularly perturbed boundary value problems for the nonlinear third order ordinary differential equation with a small parameter ε>0: where i=1, 2; a(?)(ε), β(ε) and γ(ε) are functions defined on (0, ε_o], while ε_o>0 is a constant.This paper is the continuation of our works [4, 6].

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEMS FOR SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS ON INFINITE INTERVAL(Ⅰ)

In this paper existence, uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameterare examined, where are constants, and i=0,1.

A KIND OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM FOR NONLINEAR VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper,a kind of boundary value problems for Volterra functional differential equation is studied.\$\$εx″(t)=f(t,x(t),\(t),x(t-τ),x′(t),ε),t∈(0,1), x(t)=φ(t,ε),t∈[-τ,0], ax(1)+bx′(1)=A(ε).\$\$\ \ By using the theory of differential inequality,the author proves the existence of the solutions and a uniformly valid asymptotic expansion of the solution is given as well.

Numerical Computing for a Class of Free Multipoint Boundary Value Problem of O.D.E in the Intervention of Exchange Rate

In this paper by means of generalized shooting method and homotopy technique a numerical method was given for computing free multipoint boundary value problem proposed in the intervention of exchange rate by Cadenillas and Femaado Zapatero. A numerical example was given for illustrating the validity of this method.

THE SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS

The singularly perturbed nonlinear boundary value problems are considered.Using the stretched variable and the method of boundary layer correction,the formal asymptotic expansion of solution is obtained.And then the uniform validity of solution is proved by using the differential inequalities.

THE SINGULARLY PERTURBED NONLOCAL BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER NONLINEAR ELLIPTIC EQUATIONS

In this paper,a class of singular perturbation of nonlocal boundary value problems for elliptic partial differential equations of higher order is considered by using the differential inequalities.The uniformly valid asymptotic expansion of solution is obtained.

MULTIPLE POSITIVE SOLUTIONS OF A SINGULAR (n-1,1) CONJUGATE BOUNDARY VALUE PROBLEM WITH DELAY

This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t<0), u (j) (0)=u(1)=0,(1≤j≤n-2).Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.An example to illustrate the application of this theorem is given. [FQ(6*2。39,X-W]

A NECESSARY AND SUFFICIENT CONDITION FOR SINGULAR NONLINEAR SECOND-ORDER BOUNDARY VALUE PROBLEMS TO HAVE POSITIVE SOLUTIONS

In this paper the following result is obtained: Suppose f(x,u,v) is nonnegative, continuous in ( a, b)×R +×R +; f may be singular at x=a (and/or x=b ) and v=0; f is nondecreasing on u for each x,v, nonincreasing on v for each x,u; there exists a constant q∈(0,1) such that t qf(x,t -1 u,tu)f(x,u,u)λ qf(x,λ -1 u,λu),0<t<1<λ, u∈R +. Then a necessary and sufficient condition for the equation u″+f(x,u,u)=0 on the boundary condition αu(a)-βu′(a)=0, γ(b)+δu′(b)=0 to have C 1(I) nonzero solutions is that 0<∫ b af(x,e(x),e(x))dx<∞, where α,β,γ,δ are nonnegative real numbers, Δ=(b-a)αγ+αδ+βγ>0, e(x)=G(x,x), G(x,y) is Green's function of above mentioned boundary value problem (when f(x,u,v)≡0). Received September 9,1996. Revised March 31,1997. 1991 MR Subject Classification: 34B.

Correcting the initialization of models with fractional derivatives via history-dependent conditions

Fractional differential equations are more and more used in modeling memory（history-dependent,nonlocal,or hereditary） phenomena.Conventional initial values of fractional differential equations are define at a point,while recent works defin initial conditions over histories.We prove that the conventional initialization of fractional differential equations with a Riemann–Liouville derivative is wrong with a simple counter-example.The initial values were assumed to be arbitrarily given for a typical fractional differential equation,but we fin one of these values can only be zero.We show that fractional differential equations are of infinit dimensions,and the initial conditions,initial histories,are define as functions over intervals.We obtain the equivalent integral equation for Caputo case.With a simple fractional model of materials,we illustrate that the recovery behavior is correct with the initial creep history,but is wrong with initial values at the starting point of the recovery.We demonstrate the application of initial history by solving a forced fractional Lorenz system numerically.

STRICT STABILITY OF IMPULSIVE SET VALUED DIFFERENTIAL EQUATIONS

In this paper, we develop strict stability concepts of ODE to impulsive hybrid set valued differential equations. By Lyapunov’s original method, we get some basic strict stability criteria of impulsive hybrid set valued equations.

Global Optimization for Solving Linear Non-Quadratic Optimal Control Problems

This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example.

On Systems of Boundary Value Problems for Differential Inclusions

Herein we consider the existence of solutions to second-order, two-point boundary value problems （BVPs） for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions.

Limit Boundary Value Problem for Nonlinear Differential Equation of the Second Order

1 .Introduetion Considered in thio PaPer 15 the exi tenoe of the solution of the limit boundaryvalue problem■ which occurs in the study of Physios