In this paper we consider two recovery problems based on information given with an error. First is the problem of optimal class $W^T_q = \{(t_1h_1,t_2h_2,\ldots)\in \ell_q\,:\,\|h\|_q\leqslant 1\}$, where $1\le q < \infty$ and $t_1\geqslant t_2\geqslant \ldots \geqslant 0$, in space $\ell_q$ when capacity inexact know either first $n\in\mathbb{N}$ elements a sequence error measured finite seque...

In the self-similar scenario for galaxy cluster formation and evolution, thermodynamic properties of X-ray emitting plasma can be predicted in their dependencies on halo mass redshift only. However, several departures from this simple have been observed. We show how our semi-analytic model $i(cm)z$, which modifies predictions through two temperature-dependent quantities, gas fraction $f_g=f_0 T...

In the diagnosis of myocardial infarction, magnetic resonance imaging can provide information about myocardial contractility and tissue characterization, including viability. In current clinical practice, separate scans are required for each aspect. A recently proposed method showed how the same information can be extracted from a single, short scan of 4 s, but made strong assumptions about the...

We study the bi-commutators $[T_1, [b, T_2]]$ of pointwise multiplication and Calder\'on-Zygmund operators, characterize their $L^{p_1}L^{p_2} \to L^{q_1}L^{q_2}$ boundedness for several off-diagonal regimes mixed-norm integrability exponents $(p_1,p_2)\neq(q_1,q_2)$. The strategy is based on a bi-parameter version recent approximate weak factorization method.

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...

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...

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 ...