We consider solutions of the KP hierarchy which are elliptic functions $x=t_1$. It is known that their poles as $t_2$ move particles Calogero-Moser model. extend this correspondence to level hierarchies and find Hamiltonian $H_k$ model governs dynamics with respect $k$-th hierarchical time. The Hamiltonians obtained coefficients expansion spectral curve near marked point in Baker-Akhiezer funct...

Abstract Starting from the 3-wave interaction equations in 2+1 dimensions (i.e., two space and one time dimension), we complexify independent variables, thus doubling number of real hence work 4+2 dimensions: $$x_1$$ x 1 , $$x_2$$ 2 $$y_1$$ y</m...

Abstract We study and classify smooth bounded domains in an analytic Riemannian manifold which are critical for the heat content at all times $$t&gt;0$$ t &gt; 0 . do that by first computing variation of content, then showing $$\Omega $$ Ω</mml:...

Temperature-dependent dynamical spin correlations, which can be readily accessed via a variety of experimental techniques, hold the potential offering unique fingerprint quantum liquids and other intriguing states. In this work we present an in-depth study temperature-dependent structure factor $S({\bf q}, \omega)$ antiferromagnetic (AFM) Heisenberg spin-1/2 model on kagome lattice with additio...

We use a large N-body simulation to study the characteristic scales in density gradient profiles and around halos with masses ranging from $10^{12}$ $10^{15} h^{-1}{\rm M_\odot}$. investigate separately along major (T_1) minor (T_3) axes of local tidal tensor how depend on halo mass, formation time, environment. find two kinds prominent features profiles, deep `valley' `peak'. Gaussian Process ...

Petroleum fluid has been extensively studied at low magnetic fields by Nuclear Magnetic Resonance (NMR) Spectroscopy, but high field NMR studies are rarely found in this area. The aim of study is to determine the proton spin-lattice relaxation rate (1/T1), T1 relaxivity (R1), spin-spin (1/T2) and T2 (R2) paraffinic CH2 gamma CH3 peaks. For purpose, crude oil samples were taken from 3 separate w...

In this paper, we study the separtion axioms $T_0,T_1,T_2$ and $T_{5/2}$ on topological and semitopological residuated lattices and we show that they are equivalent on topological residuated lattices. Then we prove that for every infinite cardinal number $alpha$, there exists at least one nontrivial Hausdorff topological residuated lattice of cardinality $alpha$. In the follows, we obtain some ...

We consider solutions of the 2D Toda lattice hierarchy which are elliptic functions zeroth time t_0=x. It is known that their poles as t_1 move particles Ruijsenaars-Schneider model. The goal this paper to extend correspondence level hierarchies. show Hamiltonians govern dynamics with respect m-th hierarchical times t_m and \bar obtained from expansion spectral curve for Lax matrix model at mar...

Recently Galashin, Grinberg, and Liu introduced the refined dual stable Grothendieck polynomials, which are symmetric functions in $x=(x_1,x_2,\dots)$ with additional parameters $t=(t_1,t_2,\dots)$. The polynomials defined as a generating function for reverse plane partitions of given shape. They interpolate between Schur by Lam Pylyavskyy 2007. Flagged more version where lower upper bounds ent...

The ADAM33 gene is associated with the pathophysiology of Chronic Obstructive Pulmonary Disease (COPD) and atherosclerosis. In this study we investigated all-cause, COPD and cardiovascular mortality, in relation to single nucleotide polymorphisms (SNPs) in ADAM33 (Q_1, S_1, S_2, T_1 and T_2) that were genotyped in 1,390 subjects from the Vlagtwedde/Vlaardingen cohort. Participants were examined...