Controlling Chaotic Vibrations of a Quarter-Car Model Excited by Road Surface Profile using Parametric Excitation.

Chaotic Vibrations are considered for a quarter-car model excited by the road surface profile. The equation of motion is obtained in the form of a classical Duffing equation and it is modeled with deliberate introduction of parametric excitation force term to enable us manipulate the behavior of the system. The equation of motion is solved using the Method of Multiple Scales. The steady-state solutions with and without the parametric excitation force term is investigated using NDSolve MathematicaTM Code and the nonlinear dynamical system’s analysis is by a study of the Bifurcations that are observed from the analysis of the trajectories, and the calculation of the Lyapunov. In making the system more strongly nonlinear the excitation amplitude value is artificially increased to various multiples of the actual value. Results show that the system’s response can be extremely sensitive to changes in the amplitude and the that chaos is evident as the system is made more nonlinear and that with the introduction of parametric excitation force term the system’s motion becomes periodic resulting in the elimination of chaos and the reduction in amplitude of vibration.

Discriminant Analysis and Logistic Regression Applying To Credit Risk Management

The financial crisis that is currently shaking the world, particularly the successive failures of the major banks have brought the issue of banking risks, including credit risk, back to the forefront. This risk must now be managed by more sophisticated methods. In this paper we present two methods that allow us to establish two functions, namely Fisher discriminant analysis and logistic regression; these two functions allow us to evaluate the risk of non-repayment incurred by a bank in the light of our data. It emerges that Fisher discriminant analysis is more effective or efficient than logistic regression for the evaluation of the risk of non-repayment of credit. Discriminant analysis and logistic regression are two methods of credit risk management here the problem we are trying to solve is how to help banks choose the most efficient method between the latter two.

Predictive Continuum Constitutive Modeling of Unfilled and Filled Rubbers

The general CSE model fits Treloar’s uniaxial extension test and predicts unfitted uniaxial compression, equibiaxial extension, biaxial extension, pure shear, and simple shear tests. As a newly proposed method, the general CSE model, along with the stress-softening ratio, the residualstretch ratio, and the weighted piecewise two-point interpolation function, fits the Cheng–Chen’s test and the Diani–Fayolle–Gilormini’s test in cyclic uniaxial extension at different pre-stretches and predicts corresponding responses at untested pre-stretches. Physical mechanisms of the Mullins effect have also been predicted based on the evolution of constitutive parameters.

Memory Event-triggered Output Feedback Synchronization Control for Complex Dynamic Network with Bounded Distributed Delays

In this paper, the method of memory event triggering output feedback is used to study the synchronization of complex dynamic network with bounded distributed delays when the target node is known or unknown. A memory event triggering scheme is proposed to reduce the transmission of data packets and shorten the transient process, and the network transmission delay is considered. The data packet signals released in recent times are stored at the sensor side and the controller side, which are used to generate event trigger function and design memory output feedback controller. By using Lyapunov stability theory, a sufficient condition for exponentially ultimately bounded of error dynamic system is given in the form of linear matrix inequalities (LMIs). Finally, an example proves the validity and feasibility of the theoretical results.

Stability of Contact Discontinuity with General Perturbation for the Compressible Navier-Stokes Equations with Reaction Diffusion

In this article,for the compressible Navier-Stokes equations which have reaction diffusion, the stability of contact discontinuities is considered. The new characteristic for the flow is appearance of the divergence between energy gained and lost because of the reaction . In the energy equations,the term related to the mass fraction of the reactant leads to new technical problem. To solve this problem, in terms of the solutions,a new system should be set up. Using the anti-derivative method and the elaborated energy method, we obtain that as long as the general perturbation of the initial datum plane and the strength of the contact wave are properly small, the contact wave is nonlinear and stable. As a byproduct, we can establish the convergence velocity of contact wave.

Asymptotical Synchronization of Drive-Response Networks by Sample-Data-Based Event-Triggered Control with Quantization and Cyber-Attacks

This paper addresses the asymptotic synchronization problem for a kind of drive-response complex networks (DRCNs) under cyber-attacks by using network control systems (NCSs). In order to reduce the pressure of communication and save the communication bandwidth on NCSs, some sampled-data-based event-triggered synchronization feedback controllers and logarithmic quantizers are designed by taking into account the effect of the NCSs’ transmission delays. Using Lyapunov stability theories, several sufficient conditions are obtained to guarantee the existence of sampleddata- based event-triggered synchronization controllers for the DRCNs with distributed-delay. Then, the state feedback gains are obtained by solving certain linear matrix inequalities (LMIs). Finally, a numerical example is provided to illustrate the effectiveness of the sampled-data-based eventtriggered control scheme.

Application of the Oscillation Symmetry to the Electromagnetic Interactions of Some Particles, Nuclei, and Atoms

The oscillation symmetry is first applied to electromagnetic interactions of particles and nuclei. It is shown that the differences between successive masses plotted versus their mean values and the electromagnetic decay widths Γee of 0^−(1^−−) b¯b and c¯c mesons, plotted versus their masses, agree with such symmetry. Then it is shown that the variation of the energy differences between different levels of several nuclei from 8Be to 20Ne, corresponding to given electric or magnetic transitions, display also oscillating behaviours. The electromagnetic widths of the electric and magnetic transitions between excited levels of these nuclei, plotted versus the corresponding differences between energies agree also with this property. The oscillating periods describe also an oscillation, the same for E1, M1, and E2 transitions. It is also the case for the multiplicative factor used β, and for ratios between these parameters. The oscillation symmetry is then applied to atomic energy levels of several neutral atoms from hydrogen to phosphorus. The data exhibit nice oscillations when plotted in the same way as before. The oscillations in various nuclear and atomic periods of different elements (A) exhibit the same shape and can be fitted by the same distribution.

Some Approaches for Fuzzy Multiobjective Programming Problems

In this paper we discuss two approaches to bring a balance between effectiveness and efficiency while solving a multiobjective programming problem with fuzzy objective functions. To convert the original fuzzy optimization problem into deterministic terms, the first approach makes use of the Nearest Interval Approximation Operator (Approximation approach) for fuzzy numbers and the second one takes advantage of an Embedding Theorem for fuzzy numbers (Equivalence approach). The resulting optimization problem related to the first approach is handled via Karush- Kuhn-Tucker like conditions for Pareto Optimality obtained for the resulting interval optimization problem. A Galerkin like scheme is used to tackle the deterministic counterpart associated to the second approach. Our approaches enable both faithful representation of reality and computational tractability. They are thus in sharp contrast with many existing methods that are either effective or efficient but not both. Numerical examples are also supplemented for the sake of illustration.

Weak Nontrivial Solutions to Discrete Nonlinear Two-Point Boundary-Value Problems of Kirchhoff Type

"We prove the existence of at least one weak nontrivial solutions for a discrete nonlinear two-point boundary-value problems of Kirchhoff type. The main existence results are obtained by using the technique of geometric mountain pass and the Ekelands variational principle."