On compactness and cocompactness conditions for R-tors,R-pr and (big) lattices of classes of modules

We study conditions related to compactness and cocompactness for some (big) lattices of classes of modules and preradicals. Also, we give some characterizations in terms of rings and modules.     

Rings of Constants of the Form k[f]

Let k[X] be the algebra of polynomials in n variables over a field k of characteristic zero, and let f ? k[X]? k. We present a construction of a derivation d of k[X] whose ring of constants is equal to the integral closure of k[f] in k[X]. A similar construction for fields of rational functions is also given.     

An effective heuristic for the two-dimensional irregular bin packing problem

This paper proposes an adaptation, to the two-dimensional irregular bin packing problem of the Djang and Finch heuristic (DJD), originally designed for the one-dimensional bin packing problem. In the two-dimensional case, not only is it the case that the piece’s size is important but its shape also has a significant influence. Therefore, DJD as a selection heuristic has to be paired with a placement heuristic to completely construct a solution to the underlying packing problem. A successful adaptation of the DJD requires a routine to reduce computational costs, which is also proposed and successfully tested in this paper. Results, on a wide variety of instance types with convex polygons, are found to be significantly better than those produced by more conventional selection heuristics.     

A nanofiber-based optical conveyor belt for cold atoms

We demonstrate optical transport of cold cesium atoms over millimeter-scale distances along an optical nanofiber. The atoms are trapped in a one-dimensional optical lattice formed by a two-color evanescent field surrounding the nanofiber, far red- and blue-detuned with respect to the atomic transition. The blue-detuned field is a propagating nanofiber-guided mode while the red-detuned field is a standing-wave mode which leads to the periodic axial confinement of the atoms. Here, this standing wave is used for transporting the atoms along the nanofiber by mutually detuning the two counter-propagating fields which form the standing wave. The performance and limitations of the nanofiber-based transport are evaluated and possible applications are discussed.     

Convergence of Ising interfaces to Schrammʼs SLE curves

We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schramm?s SLE curves with parameters κ=3$\kappa =3$ and κ=16/3$\kappa =16/3$, respectively.     

Denseness results in the theory of algebraic fields

We study when the property that a field is dense in its real and p-adic closures is elementary in the language of rings and deduce that all models of the theory of algebraic fields have this property.     

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.