Approximate Controllability Of Semilinear Systems Using Integral Contractors

In this article, a non-autonomous (time-varying) semilinear system is considered and its approximate controllability is investigated. The notion of 'bounded integral contractor', introduced by Altman, has been exploited to obtain sufficient conditions for approximate controllability. This condition is weaker than Lipschitz condition. The main theorems of Naito [11, 12] are obtained as corollaries of our main results. An example is also given to show how our results weaken the conditions assumed by Sukavanam[17].

Forms of relativistic dynamics with World Line Condition and separability

he Dirac generator formalism for relativistic Hamiltonian dynamics is reviewed along with its extension to constraint formalism. In these theories evolution is with respect to a dynamically defined parameter, and thus time evolution involves an eleventh generator. These formulations evade the No-Interaction Theorem. But the incorporation of separability reopens the question, and together with the World Line Condition leads to a second no-interaction theorem for systems of three or more particles. Proofs are omitted, but the results of recent research in this area is highlighted.

Bearing capacity factor N-c under phi=0 condition for piles in clays

Bearing capacity factor N-c for axially loaded piles in clays whose cohesion increases linearly with depth has been estimated numerically under undrained (phi=0) condition. The Study follows the lower bound limit analysis in conjunction With finite elements and linear programming. A new formulation is proposed for solving an axisymmetric geotechnical stability problem. The variation of N-c with embedment ratio is obtained for several rates of the increase of soil cohesion with depth; a special case is also examined when the pile base was placed on the stiff clay stratum overlaid by a soft clay layer. It was noticed that the magnitude of N-c reaches almost a constant value for embedment ratio greater than unity. The roughness of the pile base and shaft affects marginally the magnitudes of N-c. The results obtained from the present study are found to compare quite well with the different numerical solutions reported in the literature.

Culture Condition Dependent Changes Of 4-Thiouridine In The Transfer-Rna Of Azotobacter-Vinelandii

4..T~iouridine, a thionucleoside present in the transfer RNA of the free living, nitrogen-fixing ?actenu~ Azotobacter »inelandii shows a culture condition dependent change. When thebacterium IS grown Intheabsen~e ofanyfixed nit~ogen thetRNA contains 4-thiouridine to theextent of 45% of the total sulphur Incorporated. This gets reduced to 5%when the bacterium is grown in the presen~e of.e~ces~ ofamm~nium salt.Instead, a new thionucleoside which appears to be a derivative of 4-thloundlne IS found In the tRNA to the extent of 28%of the total sulphur incorporated.

A necessary and sufficient condition for acyclic graphs

This letter gives a new necessary and sufficient condition to determine whether a directed graph is acyclic.

A note on the application of a radiation condition for a source in a rotating stratified fluid

The motion due to an oscillatory point source in a rotating stratified fluid has been studied by Sarma & Naidu (1972) by using threefold Fourier transforms. The solution obtained by them in the hyperbolic case is wrong since they did not make use of any radiation condition, which is always necessary to get the correct solution. Whenever the motion is created by a source, the condition of radiation is that the sources must remain sources, not sinks of energy and no energy may be radiated from infinity into the prescribed singularities of the field. The purpose of the present note is to explain how Lighthill's (1960) radiation condition can be applied in the hyperbolic case to pick the correct solution. Further, the solution thus obtained is reiterated by an alternative procedure using Sommerfeld's (1964) radiation condition.

Vertical uplift resistance of circular plate anchors in clays under undrained condition

The vertical uplift resistance of circular plate anchors, embedded horizontally in a clayey stratum whose cohesion increases linearly with depth, has been obtained under undrained (phi = 0) condition. The axi-symmetric static limit analysis formulation in combination with finite elements proposed recently by the authors has been employed. The variation of the uplift factor (F,) with changes in the embedment ratio (H/B) has been computed for several rates of increases of soil cohesion with depth. It is noted that in all the cases, the magnitude of F-c increases continuously with depth up to a certain value of H-cr/B beyond which the uplift factor becomes essentially constant. The proposed static limit analysis formulation is seen to provide acceptable results even for the two other simple chosen axi-symmetric problems.

Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.

Real-coded genetic algorithm for machining condition optimization

In this paper, we consider the machining condition optimization models presented in earlier studies. Finding the optimal combination of machining conditions within the constraints is a difficult task. Hence, in earlier studies standard optimization methods are used. The non-linear nature of the objective function, and the constraints that need to be satisfied makes it difficult to use the standard optimization methods for the solution. In this paper, we present a real coded genetic algorithm (RCGA), to find the optimal combination of machining conditions. We present various issues related to real coded genetic algorithm such as solution representation, crossover operators, and repair algorithm in detail. We also present the results obtained for these models using real coded genetic algorithm and discuss the advantages of using real coded genetic algorithm for these problems. From the results obtained, we conclude that real coded genetic algorithm is reliable and accurate for solving the machining condition optimization models.

Stability of an unsupported vertical circular excavation in clays under undrained condition

By using the axisymmetric finite elements static limit analysis formulation, proposed recently by the authors, the stability numbers (gamma H/c(o)) for an unsupported vertical circular excavation in clays, whose cohesion increases with depth, have been determined under undrained condition; gamma = unit weight, H., height of the excavation and c(o) = cohesion along ground surface. The results are obtained for various values of H/b and m; where b = the radius of the excavation and m = a non-dimensional parameter which accounts for the rate of the increase of cohesion with depth. The values of the stability numbers increase continuously both with increases in H/b and m. The results obtained in this study compare well with those available in literature.(C) 2009 Elsevier Ltd. All rights reserved.

A voltage-sensorless control method to balance the input currents of a three-wire boost rectifier under unbalanced input voltages condition

This paper proposes a control method that can balance the input currents of the three-phase three-wire boost rectifier under unbalanced input voltage condition. The control objective is to operate the rectifier in the high-power-factor mode under balanced input voltage condition but to give overriding priority to the current balance function in case of unbalance in the input voltage. The control structure has been divided into two major functional blocks. The inner loop current-mode controller implements resistor emulation to achieve high-power-factor operation on each of the two orthogonal axes of the stationary reference frame. The outer control loop performs magnitude scaling and phase-shifting operations on current of one of the axes to make it balanced with the current on the other axis. The coefficients of scaling and shifting functions are determined by two closed-loop prportional-integral (PI) controllers that impose the conditions of input current balance as PI references. The control algorithm is simple and high performing. It does not require input voltage sensing and transformation of the control variables into a rotating reference frame. The simulation results on a MATLAB-SIMULINK platform validate the proposed control strategy. In implementation Texas Instrument's digital signal processor TMS320F24OF is used as the digital controller. The control algorithm for high-power-factor operation is tested on a prototype boost rectifier under nominal and unbalanced input voltage conditions.

Effect of boundary condition description on convergence of solution in a boundary-value problem

It is well known that the numerical accuracy of a series solution to a boundary-value problem by the direct method depends on the technique of approximate satisfaction of the boundary conditions and on the stage of truncation of the series. On the other hand, it does not appear to be generally recognized that, when the boundary conditions can be described in alternative equivalent forms, the convergence of the solution is significantly affected by the actual form in which they are stated. The importance of the last aspect is studied for three different techniques of computing the deflections of simply supported regular polygonal plates under uniform pressure. It is also shown that it is sometimes possible to modify the technique of analysis to make the accuracy independent of the description of the boundary conditions.

Exact analysis of Burgers equation on semiline with flux condition at the origin

The initial boundary value problem for the Burgers equation in the domain x greater-or-equal, slanted 0, t > 0 with flux boundary condition at x = 0 has been solved exactly. The behaviour of the solution as t tends to infinity is studied and the “asymptotic profile at infinity” is obtained. In addition, the uniqueness of the solution of the initial boundary value problem is proved and its inviscid limit as var epsilon → 0 is obtained.

Cross-polarization from the dipolar reservoir under the mismatched Hartmann-Hahn condition

Cross-polarization from the dipolar reservoir for a range of mismatched Hartmann-Hahn conditions has been considered. Experiment, in general, agrees with the dispersive Lorentzian behavior expected on the basis of quasi-equilibrium theory. It is observed that inclusion of additional mechanisms of polarization transfer lead to an improvment of the fit of the experimental results. The utility of extending the technique to the case of ordered long chain molecules, such as liquid crystals, for the measurement of the local dipolar field is also presented. (C) 2002 Elsevier Science (USA).