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It is proved that: each collectively order continuous set of operators from an Archimedean ordered vector space to an ordered vector space is collectively order bounded; each collectively order to norm bounded set of operators from an ordered Banach space with a closed generating cone to a normed space is norm bounded; collectively r-continuous sets agree with collectively order bounded ones when the space in the range has a generating cone. Several applications to operator semigroups are given.

A collectively $\sigma$-Levi set of operators is a generalization of the $\sigma$-Levi operator. By use of collective order convergence, we investigate relations between collectively $\sigma$-Levi and collectively compact sets of operators.

Collective versions of order convergences and corresponding types of collectively qualified sets of operators in vector lattices are investigated. It is proved that every collectively order continuous set of operators between Archimedean vector lattices is collectively order bounded.

We prove collective versions of semi-duality theorems for sets of almost (limitedly, order) L-weakly compact operators.

A set of bounded linear operators from a Banach space to a Banach lattice is collectively L-weakly compact whenever union of images of the unit ball is L-weakly compact. We extend the Meyer-Nieberg duality theorem to collectively L-weakly compact sets of operators, study relations between these sets and collectively almost limited sets, and discuss the domination problem for collectively compact sets and collectively L-weakly compact sets.

Variational inequalities offer a versatile and straightforward approach to analyzing a broad range of equilibrium problems in both theoretical and practical fields. In this paper, we consider a composite generally non-monotone variational inequality represented as a sum of $L_q$-Lipschitz monotone and $L_p$-Lipschitz generally non-monotone operators. We applied a special sliding version of the classical Extragradient method to this problem and obtain better convergence results. In particular, to achieve $\varepsilon$-accuracy of the solution, the oracle complexity of the non-monotone operator $Q$ for our algorithm is $O\left(L_p^2/\varepsilon^2\right)$ in contrast to the basic Extragradient algorithm with $O\left((L_p+L_q)^2/\varepsilon^2\right)$. The results of numerical experiments confirm the theoretical findings and show the superiority of the proposed method., Comment: 12 pages, 1 algorithm, 3 figures

We study operators carrying disjoint bounded subsets of a Banach lattice into compact, weakly compact, and limited subsets of a Banach space. Surprisingly, these operators behave differently with classical compact, weakly compact, and limited operators. We introduce and investigate d-Andrews operators which carry disjoint bounded sets onto Dunford--Pettis sets., Comment: 14 pages

Over the past few years, one of the most notable advancements in AI research has been in foundation models (FMs), headlined by the rise of language models (LMs). As the models' size increases, LMs demonstrate enhancements in measurable aspects and the development of new qualitative features. However, despite researchers' attention and the rapid growth in LM application, the capabilities, limitations, and associated risks still need to be better understood. To address these issues, we introduce an open Multimodal Evaluation of Russian-language Architectures (MERA), a new instruction benchmark for evaluating foundation models oriented towards the Russian language. The benchmark encompasses 21 evaluation tasks for generative models in 11 skill domains and is designed as a black-box test to ensure the exclusion of data leakage. The paper introduces a methodology to evaluate FMs and LMs in zero- and few-shot fixed instruction settings that can be extended to other modalities. We propose an evaluation methodology, an open-source code base for the MERA assessment, and a leaderboard with a submission system. We evaluate open LMs as baselines and find that they are still far behind the human level. We publicly release MERA to guide forthcoming research, anticipate groundbreaking model features, standardize the evaluation procedure, and address potential societal drawbacks., Comment: The paper version comparable with the release code v.1.1.0 of the benchmark MERA. ACL-2024 main track camera ready version

We prove that an order continuous Banach lattice E is a KB-space if and only if each positive compact operator on E is a KB operator. We give conditions on quasi-KB (resp., quasi-Levi) operators to be KB (resp., Levi), study norm completeness and domination for these operators, and show that neither KB nor Levi operators are stable under rank one perturbations.

We investigate the duality and norm completeness in the classes of limitedly--L-weakly compact and Dunford--Pettis--L-weakly compact and operators from Banach spaces to Banach lattices.

We introduce new class of limitedly L-weakly compact operators from a Banach space to a Banach lattice. This class is a proper subclass of the Bourgain-Diestel operators and it contains properly the class of L-weakly compact operators. We give its efficient characterization in term of sequences, investigate the domination problem, and study the completeness of this class of operators.

Launch of the Gaia space observatory started a new era in astrometry when the accuracy of star coordinates increased by thousands of times. Significant improvement of accuracy was also expected for the coordinates of the Solar system bodies. Gaia DR3 provided us with the data which could be used to test our expectations. In this work, we refine the orbits of a number of outer planetary satellites using both ground-based and Gaia observations. From thirteen outer satellites observed by Gaia, we chose six to obtain their orbits. Some specific moments in using observations of outer satellites made by Gaia are demonstrated. These pecularities stem from scanning motion of Gaia, in particular from the fact that the accuracy of observations is significantly different along and across the scanning direction. As expected, Gaia observations proved to be more precise than those made from Earth, which results in more accurate satellite ephemerides. We estimate accuracy of the ephemerides of considered satellites for the interval between 1996 and 2030. As astrometric positions published in Gaia DR3 were not corrected for the relativistic light deflection by the Sun, we took into account this effect, which slightly diminished the rms residuals. In addition, relativistic light deflection by the giant planets was estimated, which, as it turned out, can be neglected with the given accuracy of Gaia observations., Comment: accepted in MNRAS 28.03.2023, 9 pages, 8 figures

Single electron may have wavefunction of a macroscopic lengthscale but cannot be detected in two places. At the Solvay Conference of 1927, Einstein argued that in a combination with Bohr's postulate about wavefunction as an exhaustive characteristics of electron, this fact implies nonlocality related to the collapse of a macroscopic wavefunction of single electron. This was his objection to Bohr's quantum mechanics (QM) in favor of de Broglie's quantum theory. We perform an experimental test in low-temperature state of matter where electrons have macroscopic orbit-like wavefunctions and surprisingly observe nonlocality of that type. This nonlocality differs in principle from the well-known Einstein-Podolsky-Rosen (EPR) nonlocality because the former does not imply quantum entanglement and hence is beyond the no-communication theorem. Our observation is the first empirical justification of the choice in favor of QM in compare with de Broglie's theory. Moreover, now we can expand the current concept of reality and thus open the door to a realistic interpretation of quantum formalism. Ultimately, we thus come to a quantum model of Universe based on the standard QM.

We introduce and study the enveloping norms of regularly P-operators between Banach lattices E and F, where P is a subspace of the space L(E,F) of continuous operators from E to F. We prove that if P is closed in L(E,F) in the operator norm then the regularly P-operators forms a Banach space under the enveloping norm. Conditions providing that regularly P-operators forms a Banach lattice under the enveloping norm are given., Comment: arXiv admin note: substantial text overlap with arXiv:2208.02303

We propose a model describing spin-half quantum particles in curved spacetime in the framework of quantum field theory. Our model is based on embodying Einstein's equivalence principle and general covariance in the definition of quantum-particle states. With this model at hand, we compute several observables which characterise spin-half quantum particles in a gravitational field. In particular, we find that spin precesses in a normal Fermi frame, even in the absence of torsion. The effect appears to be complementary to free-fall non-universality we have recently reported about for spinless quantum particles. Furthermore, we find that quantum-particle gravitational-potential energy is insensitive to wave-packet spreading in the Earth's gravitational field, that is responsible for the non-universality of free fall in quantum theory. This theoretical result provides another channel for the experimental study of our quantum-particle model by using gravitational spectrometers. Finally, we also find that (elementary) fermions and antifermions are indistinguishable in gravity., Comment: To be published in Eur. Phys. J. C

Several recent papers were devoted to various modifications of limited, Grothendieck, and Dunford--Pettis operators, etc., through involving the Banach lattice structure. In the present paper, it is shown that many of these operators appear as operators affiliated to well known properties of Banach lattices, like the disjoint (dual) Schur property, the disjoint Grothendieck property, the property (d), and the sequential w*-continuity of the lattice operations. It is proved that the spaces consisting of regularly versions of the above operators are all Banach spaces. The domination problem for such operators is investigated., Comment: arXiv admin note: text overlap with arXiv:2208.02303

The Nuclotron-base Ion Collider fAcility (NICA) is under construction at the Joint Institute for Nuclear Research (JINR), with commissioning of the facility expected in late 2022. The Multi-Purpose Detector (MPD) has been designed to operate at NICA and its components are currently in production. The detector is expected to be ready for data taking with the first beams from NICA. This document provides an overview of the landscape of the investigation of the QCD phase diagram in the region of maximum baryonic density, where NICA and MPD will be able to provide significant and unique input. It also provides a detailed description of the MPD set-up, including its various subsystems as well as its support and computing infrastructures. Selected performance studies for particular physics measurements at MPD are presented and discussed in the context of existing data and theoretical expectations., Comment: 53 pages, 68 figures, submitted as a Review article to EPJA