Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control

This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package.     

Boundary null-controllability of linear diffusion–reaction equations

This Note deals with the boundary null-controllability of linear diffusion–reaction equations in a 2D bounded domain. We transform the determination of the sought HUM boundary control into the minimization of a continuous and strictly convex functional. In the case of a rectangular domain where the diffusion tensor is represented by a diagonal matrix, we establish a procedure based on the inner product method that uses a complete orthonormal family of Sturm–Liouville's eigenfunctions to express explicitly the sought control.     

Rigid tetranitroresorcinarenes

[reaction: see text]. o-alkylation of C2V-symmetrical resorcinarene tetraesters 2 with 2 equiv of 1,3-difluoro-4,6-dinitrobenzene readily affords conformationally rigid octanitro resorcinarene 3, which is a potential scaffold for the design of supramolecular structures.     

Penalty functions,Newton's method,and quadratic programming

In this paper, the search directions computed by two versions of the sequential quadratic programming (SQP) algorithm are compared with that computed by attempting to minimize a quadratic penalty function by Newton's method, and it is shown that the differences are attributable to ignoring certain terms in the equation for the Newton correction. Since the effect of ignoring these terms may be to make the resultant direction a poor descent direction for the quadratic penalty function, it is argued that the latter is an inappropriate merit function for use with SQP. A method is then suggested by which these terms may be included without losing the benefits gained from the use of the orthogonal transformations derived from the constraints Jacobian.The authors wish to thank A. R. Conn and N. I. M. Gould for spirited discussions which took place when the second author spent some time at Waterloo, Ontario, Canada; they also thank L. C. W. Dixon for the clarifications that he suggested to the penultimate draft of this paper.     

Amino Acid Derivatives,VII [1]: Synthesis and Antiviral Evaluation of α-Amino Acid Esters Bearing an Indazole Side Chain

Summary. A series of peptide and dipeptide derivatives conjugated with an indazole residue were synthesized. The new compounds were evaluated in vitro for cytotoxicity against Hepatitis-A virus (HAV-27), Herpes Simplex virus-1 (HSV-1), and Hepatitis-B virus (HBV) and showed moderate to high activity.     

A matrix formulation for the dynamic analysis of planar mechanisms using point coordinates and velocity transformation

This paper presents a matrix formulation for the dynamic analysis of planar mechanisms consisting of interconnected rigid bodies. The formulation initially uses the rectangular Cartesian coordinates of an equivalent constrained system of particles to define the configuration of the mechanical system. This results in a simple and straightforward procedure for generating the equations of motion. The equations of motion are then derived in terms of relative joint coordinates through the use of a velocity transformation matrix. The velocity transformation matrix relates the relative joint velocities to the Cartesian velocities. For the open-loop case, this process automatically eliminates all of the non-working constraint forces and leads to an efficient integration of the equations of motion. For the closed-loop case, suitable joints should be cut and few cut-joints constraint equations should be included for each closed loop. Two examples are used to demonstrate the generality and efficiency of the proposed method.