A general approach to nonlinear multiple control problems with perturbation consideration

In this paper, we consider a general nonlinear optimal control problem involving multiple criteria. We show that the problem can be transformed into a standard optimal control problem, and hence, is solvable by conventional techniques. However, the optimal control so obtained is of open loop nature and is rather sensitive to perturbations. Based on the first-order approximation, neighboring extremal approach is used to obtain a local linear feedback correction control law, leading to a combined controller. Two numerical examples are solved using the proposed method to demonstrate the effectiveness of the combined control.     

Nonexistence of positive solutions for 2 order integro-differential inequalities

In this paper, we shall show that under suitable conditions on f and K, the inequalities

imply that the integro-differential inequalities

have no positive solutions, respectively.     

Computing the Writhing Number of a Polygonal Knot

The writhing number measures the global geometry of a closed space curve or knot. We show that this measure is related to the average winding number of its Gauss map. Using this relationship, we give an algorithm for computing the writhing number for a polygonal knot with n edges in time roughly proportional to n^1.6. We also implement a different, simple algorithm and provide experimental evidence for its practical efficiency.     

The Discrete 2-Center Problem

We present an algorithm for computing the discrete 2-center of a set P of n points in the plane; that is, computing two congruent disks of smallest possible radius, centered at two points of P , whose union covers P . Our algorithm runs in time O(n ^4/3 log ⁵ n) . Received July 18, 1997, and in revised form March 17, 1998.     

Oscillation of impulsive partial difference equations with continuous variables

This paper is devoted to a class of linear impulsive partial difference equations with continuous variables. We establish a difference inequality without impulses, and use it to obtain various sufficient conditions for the oscillation of solutions.     

Comparison theorems for the oscillation of higher order difference equations with deviating arguments

The difference equation Δy + δp(k)f (y (g (k))) = 0, where p(k) is positive, is classified into four cases according to is odd or even and δ is 1 or −1. In each case, we shall offer comparison theorems for the oscillation of the difference equation. Examples are also included to illustrate the importance of the results obtained.     

On the asymptotic integration of nonlinear differential equations

The aim of the present paper is twofold. Firstly, the paper surveys the literature concerning a specific topic in asymptotic integration theory of ordinary differential equations: the class of second order equations with Bihari-like nonlinearity. Secondly, some general existence results are established with regard to a condition that has been found recently to be of significant use in the theory of elliptic partial differential equations.     

Unusually low-amplitude anisotropic wave-train events of cosmic ray intensity during 1981–1994

Investigation has been made for unusually low-amplitude anisotropic wave train events (LAE) for cosmic ray intensity data of Deep River neutron monitoring station during the period 1981–94. It has been observed that the phase of diurnal anisotropy remains in the same co-rotational direction for most of the LAEs while the phase shifts to early hours for some of the LAEs in diurnal anisotropy. During minimum solar activity, LAEs have been observed to be dominant. Solar wind plasma (SWP) parameters, inter-planetary magnetic field and various features at solar disk have also been studied. The amplitude remains low continuously for most of the days while the phase shifts to earlier hours. Occurrence of LAE is independent of the nature of interplanetary magnetic field (IMF).     

Effect of suction and injection on flow along a vertical plane surface

This study centres round the problem of flow of a liquid past a vertical porous flat plate. Considering two cases, when the plate is stationary and when it is in motion, the effect of porosity on the flow has been determined. It is found that, when the plate is stationary, the velocity of the liquid increases with increase in the suction velocity and decreases with increase in the injection velocity, and for a given suction or injection velocity, the velocity of the liquid increases with increase in time and approaches to the steady state case. But, when the plate is in motion, the velocity of the liquid decreases with increase in the suction velocity and increases with increase in the injection velocity in the constant film thickness region and also in the dynamic meniscus region provided that the gravitational force is greater than the surface tension force. In this case, the stagnation point and the minimum pressure point on the free surface have also been determined. In the case of injection there always exists a unique stagnation point and also a minimum pressure point. But in the case of suction the stagnation point does not always exist and there is no minimum pressure point.Nomenclature A _n roots of equation (3.18) - C function defined by equation (4.20) - C _n coefficients defined by equation (4.15) - F function of R ₀ and T ₀ defined by equation (4.23) - g acceleration of gravity - h film thickness at any point - h ₀ film thickness in the constant thickness region - h _m film thickness at the minimum pressure point - h _st film thickness at the stagnation point - L _m location of the minimum pressure point=h _m /h ₀ - L _st location of the stagnation point=h _st/h ₀ - n summation index - N function defined by equation (4.11) - p pressure - q flow rate - q ₀ flow rate in the constant thickness region - Q non-dimensional flow rate - R suction or injection Reynolds number=v ₀ h ₀/v - R ₀ suction or injection Reynolds number corresponding to the constant thickness region=v ₀ h/ - t time - T non-dimensional time=t/h ² - T ₀ non-dimensional parallel flow film thickness=h ₀(g/u _w )^1/2 - u vertical velocity - u perturbation velocity for u - u _s surface velocity - u _W withdrawal velocity of the plate - U steady part of the velocity u for the stationary plate - non-dimensional velocity=u/gh ² - U* non-dimensional velocity=U/gh ² - v horizontal velocity - v perturbation velocity for V - v ₀ velocity of suction or injection - V transient part of the velocity u for stationary plate - x, y coordinates - X non-dimensional x-coordinate=x ²/gh ⁴ - Y non-dimensional y-coordinate=y/h Greek Symbols _n roots of equation (3.14) - _n eigenvalues defined by equation (4.13) - _n functions defined by equation (4.14) - _n eigenvalues defined by equation (3.15) - _n non-dimensional eigenvalues= _n h/ - kinematic viscosity - liquid density - surface tension of the liquid air interface - stream function - non-dimensional stream function=/gh ³