Pole placement controllers for linear time-delay systems with commensurate point delays

This paper investigates the exact and approximate spectrum assignment properties associated with realizable output-feedback pole-placement type controllers for single-input single-output linear time-invariant time-delay systems with commensurate point delays. The controller synthesis problem is discussed through the solvability of a set of coupled diophantine equations of polynomials. An extra complexity is incorporated to the above design to cancel extra unsuitable dynamics being generated when solving the above diophantine equations. Thus, the complete controller tracks any arbitrary prefixed (either finite or delaydependent) closed-loop spectrum. However, if the controller is simplified by deleting the above mentioned extra complexity, then the robust stability and approximated spectrum assignment are still achievable for a certain sufficiently small amount of delayed dynamics. Finally, the approximate spectrum assignment and robust stability problems are revisited under plant disturbances if the nominal controller is maintained. In the current approach, the finite spectrum assignment is only considered as a particular case to the designer‘s choice of a (delay-dependent) arbitrary spectrum assignment objective.     

The duality between Morrey spaces and its pre-dual spaces characterized by heat kernel

Let L be an elliptic operator, we give arguments about the duality estimate between Morrey spaces and its pre-dual spaces characterized by the heat kernel associated to L that is given in [6],[8].     

The interior proximal extragradient method for solving equilibrium problems

In this article we present a new and efficient method for solving equilibrium problems on polyhedra. The method is based on an interior-quadratic proximal term which replaces the usual quadratic proximal term. This leads to an interior proximal type algorithm. Each iteration consists in a prediction step followed by a correction step as in the extragradient method. In a first algorithm each of these steps is obtained by solving an unconstrained minimization problem, while in a second algorithm the correction step is replaced by an Armijo-backtracking linesearch followed by an hyperplane projection step. We prove that our algorithms are convergent under mild assumptions: pseudomonotonicity for the two algorithms and a Lipschitz property for the first one. Finally we present some numerical experiments to illustrate the behavior of the proposed algorithms.     

Evolution of hypersurfaces by the mean curvature minus an external force field

In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force.     

Towards a unified recurrent neural network theory: The uniformly pseudo-projection-anti-monotone net

In the past decades, various neural network models have been developed for modeling the behavior of human brain or performing problem-solving through simulating the behavior of human brain. The recurrent neural networks are the type of neural networks to model or simulate associative memory behavior of human being. A recurrent neural network (RNN) can be generally formalized as a dynamic system associated with two fundamental operators: one is the nonlinear activation operator deduced from the input-output properties of the involved neurons, and the other is the synaptic connections (a matrix) among the neurons. Through carefully examining properties of various activation functions used, we introduce a novel type of monotone operators, the uniformly pseudo-projectionanti-monotone (UPPAM) operators, to unify the various RNN models appeared in the literature. We develop a unified encoding and stability theory for the UPPAM network model when the time is discrete. The established model and theory not only unify but also jointly generalize the most known results of RNNs. The approach has lunched a visible step towards establishment of a unified mathematical theory of recurrent neural networks.     

A new modified remote user authentication scheme using smart cards

In 2000, a remote user authentication scheme using smart cards was proposed and the masquerade attacks were proved successful on this scheme. Recently, Kumar has suggested the idea of check digits to overcome the above attacks with a new scheme that removes these threats well. In this paper it is pointed out that the weakness still exists in Kumar＇s scheme, and the intruder can login to the remote system through having some information. A new scheme which can overcome these attacks and appears more secure and efficient than Kumar＇s is presented.     

Stochastic flows of mappings

In this paper,the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied.This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.     

Recovery of Bioactive Ellagitannins by Ultrasound/Microwave-Assisted Extraction from Mexican Rambutan Peel (Nephelium lappaceum L.)

Rambutan (Nephelium lappaceum L.) is a tropical fruit from Asia which has become the main target of many studies involving polyphenolic analysis. Mexico produces over 8 million tons per year of rambutan, generating a huge amount of agro-industrial waste since only the pulp is used and the peel, which comprises around 45% of the fruit’s weight, is left behind. This waste can later be used in the recovery of polyphenolic fractions. In this work, emerging technologies such as microwave, ultrasound, and the hybridization of both were tested in the extraction of phenolic compounds from Mexican rambutan peel. The results show that the hybrid technology extraction yielded the highest polyphenolic content (176.38 mg GAE/g of dry rambutan peel). The HPLC/MS/ESI analysis revealed three majoritarian compounds: geraniin, corilagin, and ellagic acid. These compounds explain the excellent results for the biological assays, namely antioxidant activity evaluated by the DPPH, ABTS, and LOI (Lipid oxidation inhibition) assays that exhibited great antioxidant capacity with IC₅₀ values of 0.098, 0.335, and 0.034 mg/mL respectively, as well as prebiotic activity demonstrated by a µMax (maximum growth) of 0.203 for Lactobacillus paracasei. Lastly, these compounds have shown no hemolytic activity, opening the door for the elaboration of different products in the food, cosmetic, and pharmaceutical industries.     

Activation of the Nrf2 Pathway as a Therapeutic Strategy for ALS Treatment

Amyotrophic lateral sclerosis is a progressive and fatal disease that causes motoneurons degeneration and functional impairment of voluntary muscles, with limited and poorly efficient therapies. Alterations in the Nrf2-ARE pathway are associated with ALS pathology and result in aberrant oxidative stress, making the stimulation of the Nrf2-mediated antioxidant response a promising therapeutic strategy in ALS to reduce oxidative stress. In this review, we first introduce the involvement of the Nrf2 pathway in the pathogenesis of ALS and the role played by astrocytes in modulating such a protective pathway. We then describe the currently developed activators of Nrf2, used in both preclinical animal models and clinical studies, taking into consideration their potentialities as well as the possible limitations associated with their use.     

Syntheses of Macrocyclic Amides from L-Amino Acid Esters by RCM

IntroductionThe discovery of stable and defined carbenecomplexes of molybdenum and ruthenium as efficientprecatalysts for olefin metathesis has made this transfor-mation one of the most important C—C bond formingreactions[1—11]. Specifically, ring-closi…