Nash Equilibrium Seeking in Quadratic Noncooperative Games Under Two Delayed Information-Sharing Schemes

In this paper, we propose non-model-based strategies for locally stable convergence to Nash equilibrium in quadratic noncooperative games where acquisition of information (of two different types) incurs delays. Two sets of results are introduced: (a) one, which we call cooperative scenario, where each player employs the knowledge of the functional form of his payoff and knowledge of other players’ actions, but with delays; and (b) the second one, which we term the noncooperative scenario, where the players have access only to their own payoff values, again with delay. Both approaches are based on the extremum seeking perspective, which has previously been reported for real-time optimization problems by exploring sinusoidal excitation signals to estimate the Gradient (first derivative) and Hessian (second derivative) of unknown quadratic functions. In order to compensate distinct delays in the inputs of the players, we have employed predictor feedback. We apply a small-gain analysis as well as averaging theory in infinite dimensions, due to the infinite-dimensional state of the time delays, in order to obtain local convergence results for the unknown quadratic payoffs to a small neighborhood of the Nash equilibrium. We quantify the size of these residual sets and corroborate the theoretical results numerically on an example of a two-player game with delays.

     

On Mixed Pressure-Velocity Regularity Criteria in Lorentz Spaces

In this paper the authors derive regular criteria in Lorentz spaces for LerayHopf weak solutions v of the three-dimensional Navier-Stokes equations based on the formal equivalence relationπ≌|v|²,whereπdenotes the fluid pressure and v denotes the fluid velocity.It is called the mixed pressure-velocity problem(the P-V problem for short).It is shown that if(π/(e-^|(x)|²+|v|^θ∈L^p(0,T;L^q,∞),where 0≤θ≤1 and 2/p+3/q=2-θ,then v is regular on(0,T].Note that,ifΩ,is periodic,e^-|x|2 may be replaced by a positive constant.This result improves a 2018 statement obtained by one of the authors.Furthermore,as an integral part of the contribution,the authors give an overview on the known results on the P-V problem,and also on two main techniques used by many authors to establish sufficient conditions for regularity of the so-called Ladyzhenskaya-Prodi-Serrin(L-P-S for short)type.     

Spectral density functions of bivariable stable polynomials

The Ramanujan Journal - The relationship between a stable multivariable polynomial p(z) and the Fourier coefficients of its spectral density function $$1/|p(z)|^2$$ , is further investigated. In...     

A Series of Analogues to the AT2R Prototype Antagonist C38 Allow Fine Tuning of the Previously Reported Antagonist Binding Mode

We here report on our continued studies of ligands binding to the promising drug target angiotensin II type 2 receptor (AT₂R). Two series of compounds were synthesized and investigated. The first series explored the effects of adding small substituents to the phenyl ring of the known selective nonpeptide AT₂R antagonist C38 , generating small but significant shifts in AT₂R affinity. One compound in the first series was equipotent to C38 and showed similar kinetic solubility, and stability in both human and mouse liver microsomes. The second series was comprised of new bicyclic derivatives, amongst which one ligand exhibited a five-fold improved affinity to AT₂R as compared to C38 . The majority of the compounds in the second series, including the most potent ligand, were inferior to C38 with regard to stability in both human and mouse microsomes. In contrast to our previously reported findings, ligands with shorter carbamate alkyl chains only demonstrated slightly improved stability in microsomes. Based on data presented herein, a more adequate, tentative model of the binding modes of ligand analogues to the prototype AT₂R antagonist C38 is proposed, as deduced from docking redefined by molecular dynamic simulations.     

Bimodal Therapeutic Agents Against Glioblastoma,One of the Most Lethal Forms of Cancer

About 95 % of people diagnosed with glioblastoma die within five years. Glioblastoma is the most aggressive central nervous system tumour. It is necessary to make progress in the glioblastoma treatment so that advanced chemotherapy drugs or radiation therapy or, ideally, two-in-one hybrid systems should be implemented. Tyrosine kinase receptors–inhibitors and boron neutron capture therapy (BNCT), together, could provide a therapeutic strategy. In this work, sunitinib decorated-carborane hybrids were prepared and biologically evaluated identifying excellent antitumoral- and BNCT-agents. One of the selected hybrids was studied against glioma-cells and found to be 4 times more cytotoxic than sunitinib and 1.7 times more effective than ¹⁰B-boronophenylalanine fructose complex when the cells were irradiated with neutrons.     

Singular Integrals with Variable Kernels in Dyadic Settings

Acta Mathematica Sinica, English Series - In this paper we explore conditions on variable symbols with respect to Haar systems, defining Calderón–Zygmund type operators with respect to...     

High‐temperature kinetics of the reaction between CN and hydrocarbons using a novel high‐enthalpy flow tube

More than 70 molecules of varied nature have been identified in the envelopes of carbon‐rich stars through their spectral fingerprints in the microwave or far infrared regions. Many of them are carbon chain molecules and radicals, and a significant number are unique to the circumstellar medium. The determination of relevant laboratory kinetics data is critical to keep up with the development of the high spectral and spatial resolution observations and of the refinement of chemical models. Neutral–neutral reactions of the CN radical with unsaturated hydrocarbons could be a dominant route in the formation of cyanopolyynes, even at low temperatures and deserve a detailed laboratory investigation. The approach we have developed aims to bridge the temperature gap between resistively heated flow tubes and shock tubes. The present kinetic measurements are obtained using a new reactor combining a high‐enthalpy source with a flow tube and a pulsed laser photolysis–laser‐induced fluorescence system to probe the undergoing chemical reactions. The high‐enthalpy flow tube has been used to measure the rate constant of the reaction of the CN radical with propane (C₃H₈), propene (C₃H₆), allene (C₃H₄), 1,3‐butadiene (1,3‐C₄H₆), and 1‐butyne (C₄H₆) over a temperature range extending from 300 to 1200 K. All studied reactions of CN with unsaturated hydrocarbons are rapid, with rate coefficients greater than 10^?10 cm³ · molecule^?1 · s^?1 and exhibit slight negative temperature dependence above room temperature. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 44: 753–766, 2012     

Process interpretation of current entropic bounds

We show for Markov diffusion processes that the quadratic entropic bound, recently derived for the rate functions of nonequilibrium currents, can be seen as being produced by an effective process that creates current fluctuations in a sub-optimal way by modifying only the non-reversible part of the drift or force of the process considered while keeping its reversible part constant. This provides a clear interpretation of the bound in terms of a physical process, which explains, among other things, its relation to the fluctuation relation, linear response, and reversible limits. The existence of more general quadratic bounds, and related uncertainty relations, for physical quantities other than currents is also discussed.     

The construction of numerically Calabi–Yau orders on projective surfaces

In this paper, we construct a vast collection of maximal numerically Calabi–Yau orders utilising a noncommutative analogue of the well-known commutative cyclic covering trick. Such orders play an integral role in the Mori program for orders on projective surfaces and although we know a substantial amount about them, there are relatively few known examples.     

Jacquet modules of ladder representations

We compute the Jacquet modules for a certain class of irreducible representations of the general linear group over a non-Archimedean local field. This class contains the Speh representations.