Properties of the set of admissible “state control” pair for a class of fractional semilinear evolution control systems

In this paper, we discuss a class of Caputo fractional evolution equations on Banach space with feedback control constraint whose value is non-convex closed in the control space. First, we prove the existence of solutions for the system with feedback control whose values are the extreme points of the convexified constraint that belongs to the original one. Secondly, we study the topological properties of the sets of admissible “state-control” pair for the original system with various feedback control constraints and the relations between them. Moreover, we obtain necessary and sufficient conditions for the solution set of original systems to be closed. In the end, an example is given to illustrate the applications of our main results.

Making Rule 23 Ideal: Using a Multifactor Test to Evaluate the Admissibility of Evidence at Class Certification

Circuit courts are split on whether and to what extent the Daubert standard should apply at class certification. Potential plaintiffs believe that application of Daubert would make it nearly impossible to obtain class certification. For potential defendants, the application of the standard is an important way to ensure that the certification process is fair. This Note examines the incentives underlying the push to apply the Daubert standard at class certification and the benefits and drawbacks associated with that proposal. It proposes a solution that balances the concerns of both plaintiffs and defendants by focusing on three factors: the obstacles to admissibility, the centrality of the evidence to certification, and the likelihood that evidence could evolve to an admissible state after full discovery. This standard could also be applied when admissibility concerns grounded in other provisions of the Federal Rules of Evidence are raised.

The Result of Loads Superposition Upon the Matter and Particularly Upon the Environment

It is analyzed: � the actions whose effects are different stresses that can load a body or the environment; � the superposition problem of two or several loads. On the basis of critical energy principle, a relationship is established, consisting of dimensionless values, for the evaluation the stress state with respect to a value defined as admissible state. The result can be applied to loads superposition in some cases, such as: � solid bodies; � environmental pollution with a single sort of pollutant; � environmental multiple pollution: chemical, radiations and magnetic.