We establish an asymptotic formula for the number of lattice points in sets $$\begin{aligned} {\textbf{S}}_{h_1, h_2, h_3}(\lambda ): =\left\{ x\in {\mathbb {Z}}_+^3:\lfloor h_1(x_1)\rfloor +\lfloor h_2(x_2)\rfloor h_3(x_3)\rfloor =\lambda \right\} \quad \text {with}\quad \lambda \in {Z}}_+; \end{aligned}$$ where functions $$h_1, h_3$$ are constant multiples regularly varying form $$h(x):=x^c\e...

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...

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 ...

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...

There has been considerable recent progress in identifying candidate materials for the transverse-field Ising chain (TFIC), a paradigmatic model quantum criticality. Here, we study local spin dynamical structure factor of different components disordered region TFIC. We show that low-frequency dynamics spins Ising- and directions have strikingly distinctive temperature dependencies. This leads t...

We prove that given a measure preserving system \begin{document}$ (X,\mathcal{B},\mu,T_1,\dots, T_d) $\end{document} with commuting, ergodic transformations id="M2">\begin{document}$ T_i such id="M3">\begin{document}$ T_iT_j^{-1} are for all id="M4">\begin{document}$ i \neq j $\end{document}</i...

The $k$-token graph $T_k(G)$ is the whose vertices are $k$-subsets of a $G$, with two adjacent if their symmetric difference an edge $G$. We explore when well-covered graph, that is, all its maximal independent sets have same cardinality. For bipartite graphs we classify well-covered. arbitrary show $T_2(G)$ well-covered, then girth $G$ at most four. include upper and lower bounds on independen...

We introduce a two-temperature Ising model as prototype of superstatistic critical phenomena. The is described by two temperatures ($T_1,T_2$) in zero magnetic field. To predict the phase diagram and numerically estimate exponents, we develop Metropolis Swendsen-Wang Monte Carlo method. observe that there non-trivial line, separating ordered disordered phases. propose an analytic equation for l...

We present a gate-voltage tunable transmon qubit (gatemon) based on planar InAs nanowires that are selectively grown high resistivity silicon substrate using III-V buffer layers. show low loss superconducting resonators with an internal quality of $2\times 10^5$ can readily be realized these substrates after the removal demonstrate coherent control and readout gatemon device relaxation time, $T...