STABILIZATION OF VIBRATING BEAM BY VELOCITY FEEDBACK CONTROL

A flexible structure consisting of a Euler-Bernoulli beam with co-located sensors and actuators is considered. The control is a shear force in proportion to velocity. It is known that uniform exponential stability can be achieved with velocity feedback. A sensitivity asymptotic analysis of the system's eigenvalues and eigenfunctions is set up. The authors prove that, for K-1 epsilon (0, + infinity), all of the generalized eigenvectors of A form a Riesz basis of H. It is also proved that the optimal exponential decay rate can be obtained from the spectrum of the system for 0 < K-1 < + infinity.

Applicability of standard forward column/row recurrence equations for ALFs

Fully normalized associated Legendre functions(fnALFs)are a set of orthogonal basis functions that are usually calculated by using the recurrence equation.This paper presented the applicability and universality of the standard forward column/row recurrence equation based on the isolated singular factor method and extended-range arithmetic.Isolating a singular factor is a special normalization method that can improve the universality of the standard forward row recurrence equation to a certain extent,its universality can up to degree hundreds.However,it is invalid for standard forward column recurrence equation.The extended-range arithmetic expands the double-precision number field to the quad-precision numberfield.The quad-precision numberfield can retain more significant digits in the operation process and express larger and smaller numbers.The extended-range arithmetic can significantly improve the applicability and universality of the standard forward column/row recurrence equations,its universality can up to degree several thousand.However,the quad-precision numberfield operation needs to occupy more storage space,which is why its operation speed is slow and undesirable in practical applications.In this paper,the X-number method is introduced in the standard forward row recurrence equation for thefirst time.With the use of the X-number method,fnALFs can be recursed to 4.2 billion degree by using standard forward column/row recurrence equations.

The Existence and Uniqueness of a New Boundary Value Problem(Type of Problem“E”)for a Class of Semi Linear(Power Type Nonlinearities)Mixed Hyperbolic-Elliptic System Equations of Keldysh Type with Changing Time Direction

In present work studied the new boundary value problem for semi linear(Power-type nonlinearities)system equations of mixed hyperbolic-elliptic Keldysh type in the multivariate dimension with the changing time direction.Considered problem and equation belongs to the modern level partial differential equations.Applying methods of functional analysis,topological methods,“ε”-regularizing.and continuation by the parameter at the same time with aid of a prior estimates,under assumptions conditions on coefficients of equations of system,the existence and uniqueness of generalized and regular solutions of a boundary problem are established in a weighted Sobolev's space.In this work one of main idea consists of show that the new boundary value problem which investigated in case of linear system equations can be well-posed when added nonlinear terms to this linear system equations,moreover in this case constructed new weithged spaces,the identity between of strong and weak solutions is established.

Influence of Extraction Barrier on the Loss Process of Photogenerated Charge Carrier in Polymer Bulk Heterojunction Solar Cells

Based on a full device model adopting three-dimensional Pauli master equation approach, the charge carrier loss process due to poor extraction channels between electrode and active layer in polymer bulk heterojunction（BHJ） solar cells was studied. The influence of barrier height on device performance was simulated to reveal the importance of electrode improvement. It was found that relatively large extraction barrier height（over 0.40 eV） can lead to the significant diminishing of the overall charge collection efficiency, since bimolecular recombination rate would increase to a high level due to enhanced space charge accumulation effect near electrodes. In contrast, the percentage of charge carrier annihilated due to geminate recombination did not change significantly with barrier height variation. Our simulation results may provide the basis for a more accurate model and potential direction of polymer BHJ solar cells improvement.