A classical result of Sz.-Nagy asserts that a Hilbert space contraction operator T can be dilated to unitary $${{\mathcal {U}}}$$ , i.e., $$T^n = P_{{\mathcal {H}}}{{\mathcal {U}}}^n|{{\mathcal {H}}}$$ for all $$n =0,1,2,\ldots $$ . more general multivariable setting these ideas is the setup where (i) unit disk replaced by domain $$\Omega contained in $${{\mathbb {C}}}^d$$ (ii) an -contraction,...

We present synthesis and $^{75}$As-nuclear quadrupole resonance (NQR) measurements for the noncentrosymmetric superconductor CaPtAs with a superconducting transition temperature $T_c$ of $\sim 1.5$ K. discovered two different forms during synthesis; one is high-temperature tetragonal form that was previously reported, other low-temperature consistent orthorhombic structure CaPtP. According to $...

Using $^{31}$P nuclear magnetic resonance (NMR) we investigate the recently discovered presaturation phase in highly frustrated two-dimensional spin system SrZnVO(PO$_4$)$_2$ [F. Landolt et al., Phys. Rev. B 104, 224435 (2021)]. Our data provide two pieces of evidence against presumed spin-nematic character this phase: i) NMR spectra reveal that it hosts a dipolar order and ii) 1/$T_1$ relaxati...

We derive a general expression for electric and magnetic part of the near-field energy density $N$ dipoles temperatures $T_1, \ldots, T_N$ immersed in background field having different temperature $T_b$. In contrast to former expressions this inclusion allows determining heated or cooled isotropic dipolar objects within an arbitrary environment which is thermalized at temperature. Furthermore, ...

Consider a finite collection $\{T_1, \ldots, T_J\}$ of differential operators with constant coefficients on $\mathbb{T}^n$ ($n\geq 2$) and the space smooth functions generated by this collection, namely, $f$ such that $T_j f \in C(\mathbb{T}^n)$, $1\leq j\leq J$. We prove if there are at least two linearly independent among their senior parts (relative to some mixed pattern homogeneity), then d...

In this paper, we investigate the role of square functions defined for a d-tuple commuting Ritt operators $$(T_1,\ldots ,T_d)$$ acting on general Banach space X. Firstly, prove that if admits $$H^\infty $$ joint functional calculus, then it verifies various function estimates. Then study converse when every $$T_k$$ is R-Ritt operator. Under last hypothesis, and X K-convex space, show estimates ...

We consider solutions of the matrix KP hierarchy that are elliptic functions first hierarchical time $t_1=x$. It is known poles $x_i$ and residues at $\rho_i^{\alpha \beta}=a_i^{\alpha}b_i^{\beta}$ such as $t_2$ move particles spin generalization Calogero-Moser model (elliptic Gibbons-Hermsen model). In this paper we establish correspondence with for whole hierarchy. Namely, show dynamics respe...

Let $ G = (V, E) be a finite simple connected graph. We say graph realizes code of the type 0^{s_1}1^{t_1}0^{s_2}1^{t_2}\cdots0^{s_k}1^{t_k} if and only can obtained from by some rule. Some classes graphs such as threshold chain mentioned above. The main objective this research article is to develop computationally feasible methods determine interesting theoretical invariants. present an effici...

A molecular Mott insulator $\kappa$-(ET)$_2$B(CN)$_4$ [ET = bis(ethylenedithio)tetrathiafulvalene] with a distorted triangular lattice exhibits quantum disordered state gapped spin excitation in the ground state. $^{13}$C nuclear magnetic resonance, magnetization, and torque measurements reveal that field suppresses valence bond order induces long-range above critical $\sim 8$ T. The spin-latti...