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The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as SAT problems and therefore SAT is important both practically and theoretically. From both of these perspectives, better understanding the patterns and structure implicit in SAT data is of significant value. In this paper, we describe several advances that we believe will help open the door to such understanding: we introduce hardware accelerated algorithms for fast SAT problem generation, a geometric SAT encoding that enables the use of transformer architectures typically applied to vision tasks, and a simple yet effective technique we term head slicing for reducing sequence length representation inside transformer architectures. These advances allow us to scale our approach to SAT problems with thousands of variables and tens of thousands of clauses. We validate our architecture, termed Satisfiability Transformer (SaT), on the SAT prediction task with data from the SAT Competition (SATComp) 2022 problem sets. Prior related work either leveraged a pure machine learning approach, but could not handle SATComp-sized problems, or was hybrid in the sense of integrating a machine learning component in a standard SAT solving tool. Our pure machine learning approach achieves prediction accuracies comparable to recent work, but on problems that are an order of magnitude larger than previously demonstrated. A fundamental aspect of our work concerns the very nature of SAT data and its suitability for training machine learning models. We both describe experimental results that probe the landscape of where SAT data can be successfully used for learning and position these results within the broader context of complexity and learning., Comment: 22 pages

To determine the relative distances and peculiar velocities of 140 groups and clusters of galaxies at low redshifts ($z$ < 0.12), we used the fundamental plane (FP) of early-type galaxies (from the Sloan Digital Sky Survey (SDSS) data). We constructed the Hubble diagram for the relative distances of galaxy groups/clusters versus their radial velocities in the cosmic microwave background (CMB) reference frame in the flat $\Lambda$ cold dark matter ($\Lambda$CDM) model ($\Omega_m=0.3$, $H_0=70$~km~s$^{-1}$ Mpc$^{-1}$). We have found that the standard logarithmic deviation for groups and clusters of galaxies on the Hubble diagram (minus peculiar velocities) is $\pm0.0173$ ($N$ = 140), which corresponds to a deviation of $70\pm2.8$~km~s$^{-1}$ Mpc$^{-1}$ in the Hubble constant. For a sample of galaxy systems ($N$ = 63), the X-ray luminosity of which is in an interval of (0.151--4)~$\times 10^{44}$~erg/s, this quantity turned out to be $70\pm2.1$~km~s$^{-1}$ Mpc$^{-1}$. The root-mean-square deviations of peculiar velocities with quadratic accounting for errors are $^{1/2}$ = $714\pm7$~km/s and $600\pm7$~km/s, respectively. For five large superclusters of galaxies from the SDSS region, the average peculiar velocity relaive to the CMB reference frame is $+240\pm250$~km/s. We detected no outflow of galaxy systems from the void (Giant Void, $\alpha \approx 13^h, \delta \approx 40^\circ, z \approx 0.107$) formed by groups and clusters of galaxies., Comment: 10 pages, 5 figures. Accepted for publication in Astronomy Reports

This work is a continuation of the work of Kopylova and Kopylov (2016) to build a fundamental plane (FP) of groups and clusters of galaxies -- here a sample of galaxies systems is increased from 94 to 172 objects. We have studied the ratios between the basic characteristics of groups and clusters of galaxies according to the archival data of SDSS, 2MASX and NED catalogs. Measured parameters ($\log L_K$, $\log R_e$ and $\log \sigma$) of clusters of galaxies determine the fundamental plane in the near infrared region: $L_K \propto R_e^{0.77\pm0.09} \sigma^{1.44\pm0.12}$. The form of the FP of groups/clusters is consistent with the FP of the early -- types of galaxies (SDSS, $r$-band) determined in the same way. Direct regression relative to the padius $\log r_e$ in the kpc gives a projection of the FP -- $\log R_e=0.98(\pm0.06)\,\log \sigma-0.56(\pm0.04)<\log \langle I_e \rangle+3.57(\pm0.07)$, that can be used to determine the distances of the systems of galaxies. The root-mean-square deviation of the FP zero-point is 0.07 which is equal to the 16\% error in determining the distance of the group or cluster of galaxies. For the first time, we measured the peculiar velocities of the superclusters of galaxies. The mean peculiar velocity of the 5 superclusters of galaxies relative to the CMB is $+75\pm360$~km~s$^{-1}$., Comment: 14 pages, 7 figures, 1 table. Astrophysical Bulletin, 2024, 79, 1. Key results in Figures 6 and 7

The results of measurements in two series, each series of 4 Runs and about 50 days each Run, are presented. A multi-cathode counter with an iron cathode is used in these measurements. In both series we have observed some excess in count rates in sidereal time while no excess has been observed in terrestrial time. In the first series from 27.12.22 to 24.07.23 we have observed the excess in the period between 8 a.m. and 12 a.m. of sidereal time with a confidence level more than 6 \sigma, in the second series from 21.09.23 to 03.04.24 in the period between 6 p.m. and 10 p.m. of sidereal time with a confidence level more than 4 \sigma. The fact that in terrestrial time we do not observe a similar effect as in sidereal time suggests that probably this effect is of galactic origin and that this may be caused by dark photons. Future steps are suggested to validate these results., Comment: 8 pages, 6 figures, minor changes to the text to improve readability

Characterization of atmospheric turbulence is essential to understanding image quality of astronomical telescopes and applying adaptive optics systems. In this study, the vertical distributions of optical turbulence at the Peak Terskol Observatory (43.27472N 42.50083E, 3127 m a.s.l.) using the Era-5 re-analysis, scintillation measurements and sonic anemometer data are investigated. For the reanalysis grid node closest to the observatory, vertical profiles of the structural constant of the air refractive index turbulent fluctuations $C^2_n$ were obtained. The calculated $C^2_n(z)$ vertical profiles are compared with the vertical distribution of turbulence intensity obtained from tomographic measurements with Shack-Hartmann sensor. The Fried parameter r0 at the location of Terskol Peak Observatory was estimated. Using combination of atmospheric models and scheme paramaterization of turbulence, $C^2_n(z)$ profiles at Mt. Kurapdag were obtained. The r0 values at the Peak Terskol Observatory are compared with estimated values of this length at the ten astronomical sites including Ali, Lenghu and Daocheng., Comment: 27 pages, 13 figures

We report the results of a study of the distribution of galaxies in the projection along the radius ($R \leq 3R_{200c}$) for 157~groups and clusters of galaxies in the local Universe (0.01 < $z$ < 0.10) with line-of-sight velocity dispersions~200~km~s$^{-1}$ < $ \sigma$ < 1100~km~s$^{-1}$. We introduce a new observed boundary for the halos of clusters of galaxies, which we identify with the splashback radius $R_{\rm{sp}}$. We also identified the core of groups/clusters of galaxies with the radius$R_c$. These radii are determined by the observed integrated distribution of the number of galaxies as a function of squared angular radius from the center of the group/cluster, which (usually) coincides with the brightest galaxy. We found for the entire sample that the boundary of dark matter $R_{\rm{sp}}$ for groups/clusters of galaxies is proportional to the radius $R_{\rm{200c}}$ of the virialized region. We measured the mean radius $\langle R_{\rm{sp}} \rangle = 1.14\pm0.02$~Mpc for groups of galaxies ($\sigma \leq 400$~km~s$^{-1}$) and $\langle R_{\rm{sp}} \rangle = 2.00\pm0.07$~Mpc for clusters of galaxies ($\sigma > 400$~km~s$^{-1}$). The mean ratio of radii is $\langle R_{\rm{sp}}/R_{\rm{200c}} \rangle = 1.40\pm0.02$}, or $\langle R_{\rm{sp}}/R_{\rm{200m}} \rangle = 0.88\pm0.02$., Comment: 15 pages, 7 figures, 2 tables. The article provides references to the X-ray luminosity of galaxy clusters and clarifies the descriptions of the columns

This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned and classical Pad\'e methods shown to be superior in performance to the approximants used in state-of-the-art software. The algorithm computes matrix--matrix products and also matrix inverses, but it can be implemented to avoid the computation of inverses, making it convenient for some problems. If the matrix A belongs to a Lie algebra, then exp(A) belongs to its associated Lie group, being a property which is preserved by diagonal Pad\'e approximants, and the algorithm has another option to use only these. Numerical experiments show the superior performance with respect to state-of-the-art implementations., Comment: 26 pages, 4 figures, 3 tables

The Spin Physics Detector collaboration proposes to install a universal detector in the second interaction point of the NICA collider under construction (JINR, Dubna) to study the spin structure of the proton and deuteron and other spin-related phenomena using a unique possibility to operate with polarized proton and deuteron beams at a collision energy up to 27 GeV and a luminosity up to $10^{32}$ cm$^{-2}$ s$^{-1}$. As the main goal, the experiment aims to provide access to the gluon TMD PDFs in the proton and deuteron, as well as the gluon transversity distribution and tensor PDFs in the deuteron, via the measurement of specific single and double spin asymmetries using different complementary probes such as charmonia, open charm, and prompt photon production processes. Other polarized and unpolarized physics is possible, especially at the first stage of NICA operation with reduced luminosity and collision energy of the proton and ion beams. This document is dedicated exclusively to technical issues of the SPD setup construction.

A unified theoretical approach to describe the properties of multimode squeezed light generated in a lossy medium is presented. This approach is valid for Markovian environments and includes both a model of discrete losses based on the beamsplitter approach and a generalized continuous loss model based on the spatial Langevin equation. For an important class of Gaussian states, we derive master equations for the second-order correlation functions and illustrate their solution for both frequency-independent and frequency-dependent losses. Studying the mode structure, we demonstrate that in a lossy environment no broadband basis without quadrature correlations between the different broadband modes exists. Therefore, various techniques and strategies to introduce broadband modes can be considered. We show that the Mercer expansion and the Williamson decomposition do not provide modes in which the maximal squeezing contained in the system can be measured. In turn, we find a new broadband basis that maximizes squeezing in the lossy system and present an algorithm to construct it., Comment: 23 pages, 7 figures

The paper demonstrates the prospects of Spark Plasma Sintering (SPS) for the high-speed diffusion welding of the high-strength ultrafine-grained (UFG) near-a Ti-5Al-2V alloy. The effect of increased diffusion welding intensity in the UFG Ti alloys is discussed also. The welds of the UFG near-a-Ti-5Al-2V alloy obtained by SPS are featured by high density, strength, and corrosion resistance. The rate of weld sealing in the UFG alloys has been shown to depend on the heating rate non-monotonously (with a pronounced maximum). At the stage of continuous heating and isothermic holding, the kinetics of the weld sealing was found to be determined by the exponential creep rate, the intensity of which in the coarse-grained (CG) alloys is limited by the diffusion rate in the crystal lattice whereas in the UFG alloys it is limited by the grain boundary diffusion rate., Comment: 62 pages, 3 tables, 24 figures, 61 references

The study focuses on corrosion fatigue processes taking place in an ultrafine-grained (UFG) near-a-titanium alloy Ti-2.5Al-2.6Zr (Russian industrial name PT7M) used in nuclear engineering. UFG structure formed with Rotary Swaging is found to increase resistance to corrosion fatigue. Parameters of the Basquin's equation are defined and the slope of the fatigue curve Sa-lg(N) is shown to depend (nonmonotonic dependence) on the UFG alloy annealing temperature. This effect can be explained with the patterns of microstructural evolution in a UFG alloy PT7M during annealing: (1) reduced density of lattice dislocations, (2) precipitation and dissolution of zirconium nanoparticles, (3) release of a''-phase particles causing internal stress fields along interphase (a-a'')-boundaries, and (4) intensive grain growth at elevated annealing temperatures. It is shown that the fatigue crack closure effect manifested as changing internal stress fields determined using XRD method may be observed in UFG titanium alloys., Comment: 54 pages, 2 tables, 19 figures, 64 referances

The research aims to analyze the impact that severe plastic deformation arising during Rotary Swaging has on mechanical properties and corrosion resistance of a near-a-titanium alloy Ti-2.5Al-2.6Zr (Russian industrial name PT7M). The nature of corrosion decay in fine-grained alloys caused by hot salt corrosion is known to vary from pit corrosion to intercrystalline corrosion at the onset of recrystallization processes. Resistance to hot salt corrosion in a fine-grained titanium alloy Ti-2.5Al-2.6Zr is shown to depend on the structural-phase state of grain boundaries that varies during their migration as a result of covering corrosive doping elements (aluminum, zirconium) distributed in the crystal lattice of a titanium alloy., Comment: 37 pages, 15 figures, 39 references

BM@N (Baryonic Matter at Nuclotron) is the first experiment operating and taking data at the Nuclotron/NICA ion-accelerating complex.The aim of the BM@N experiment is to study interactions of relativistic heavy-ion beams with fixed targets. We present a technical description of the BM@N spectrometer including all its subsystems., Comment: 34 pages, 47 figures, 6 tables

Hot rolled commercial metastable austenitic steel 321 with strongly elongated thin delta-ferrite particles in its microstructure was the object of investigations. Ultrafine-grained (UFG) microstructure in steel 321 was formed by Equal Channel Angular Pressing (ECAP) at 150 oC and 450 oC. When heating the UFG steel specimens, the nucleation of sigma-phase particles blocking the grain boundary migration was observed. The maximum elongation to failure (~250%) was achieved at the deformation temperature 750 oC. The process of superplastic deformation of the UFG steel 321 is controlled by simultaneous grain boundary sliding and power-law creep. The contribution of each process depends on the grain growth rate in the superplasticity regime as well as on defect accumulation on the grain boundaries. The fracture of the UFG steel 321 specimens has a cavitational character - an intensive formation of large elongated pores at the non-metallic particles as well as of the submicron pores at the sigma-phase particles in the course of superplastic deformation were observed., Comment: 41 pages, 2 tables, 15 figures, 78 references. arXiv admin note: text overlap with arXiv:2203.12102

Superplastic behavior of ultrafine-grained (UFG) Al-6Mg-0.12Sc-0.10Zr-0.1X alloys, where X = Yb (Alloy #1-Yb), Er (Alloy #2-Er), and Hf (Alloy #3-Hf), has been studied. The total content of Sc, Zr, Yb, Er, Hf in the alloys was 0.32 wt.% (0.117-0.118 at.%). The alloys used for benchmarking were Al-6Mg-0.12Sc-0.20Zr (Alloy #4-Zr) and Al-6Mg-0.22Sc-0.10Zr (Alloy #5-Sc). Their UFG microstructure was formed with ECAP. Two different types of deformation behavior during superplasticity were demonstrated. A simultaneous increase in yield stress and elongation to failure during superplastic deformation was discovered. High deformation temperatures were shown to cause a competition between dynamic (strain-induced) grain growth and dynamic recrystallization, leading to a finer grain microstructure. The values of strain hardening factor (n), strain rate sensitivity factor (m), and superplastic deformation threshold stress (Sp) were determined. The impact of the type and concentration of alloying elements on the deformation behavior and dynamic grain growth of Al-6%Mg alloys was investigated. It was established that the maximum elongation to failure in Alloy #1-Yb and Alloy #2-Er is observed at lower deformation temperatures than in Alloy #4-Zr and Alloy #5-Sc. The superplastic properties of Alloy #3-Hf are superior to those of Alloy #4-Zr and Alloy #5-Sc with high content of alloying elements (in at.%). Alloy #1-Yb manifests good elongation to failure (910%) at low temperatures (400 oC). The satisfiability of Hart's criterion for calculating uniform deformation value under superplastic conditions was verified. It was demonstrated that cavitation when pores are formed in large Al3X particles at high temperatures causes early failure of aluminum alloys., Comment: 41 pages, 19 figures, 4 tables, 43 references

We consider the Lambek invariants (introduced by Joachim Lambek in 1964) in the context of semiexact and homological categories in the sense of Grandis. We generalize the Lambek isomorphism theorem to semiexact and homological categories. Throughout the text, for completeness we give proofs of some lemmas which are known in the additive case for the case of semiexact and homological categories.

In this paper, we report the results obtained in the PHoton ELectron EXperiment (PHELEX) during 208 days of measurements in the search for dark photons using a multi-cathode counter with an iron cathode. We observed a systematic excess of single-electron events in four runs, with a confidence level better than 5 sigma, in the time interval from 8-00 to 12-00 in sidereal time. The fact that we observe this effect in the stellar frame while detecting the excess of count rate in the solar frame in different time intervals is evidence that this effect is of galactic origin. This strengthens our argument that we are indeed observing the effect of dark photons, Comment: 7 pages, 5 figures

The technique is described of the search for dark photons with a multicathode counter. The aim of experiment is to search for diurnal variations of the effect from conversion of dark photons at the surface of the metallic cathode. The results obtained within 160 days of the measurements are presented, Comment: 7 pages, 6 figures, minor corrections

First physics results of the BM@N experiment at the Nuclotron/NICA complex are presented on {\pi}+ and K+ meson production in interactions of an argon beam with fixed targets of C, Al, Cu, Sn and Pb at 3.2 AGeV. Transverse momentum distributions, rapidity spectra and multiplicities of $\pi^+$ and $K^+$ mesons are measured. The results are compared with predictions of theoretical models and with other measurements at lower energies., Comment: 29 pages, 20 figures

We present a study of the distribution of galaxies along the radius of 157 groups and clusters of galaxies (200~km~s$^{-1}$ < $\sigma$ < 1100~km~s$^{-1}$) of the local Universe (0.01 < $z$ < 0.1). We introduced a new boundary of galaxy systems and identified it with the splashback radius $R_{sp}$. We also identified the central region of galaxy systems with a radius of $R_c$. These radii are defined by the observed integrated distribution of the total number of galaxies depending on the squared distance from the center of the groups/clusters coinciding, as a rule, with the brightest galaxy. We show that the radius $R_{sp}$ is proportional to the $R_{200c}$ (radius of the virialized region of a galaxy cluster) and to the radius of the central region $R_c$ with a slope close to 1. Among the obtained dependences of the radii on X-ray luminosity, the $\log R_{sp}$ - $\log L_X$ relation has the lowest scatter. We measured $$ = $1.67\pm0.05$~Mpc for the total sample, $$ = $1.14\pm0.14$~Mpc for galaxy groups with $\sigma \leq$ 400~km~s$^{-1}$, $$ = $2.00\pm0.20$~Mpc for galaxy clusters with $\sigma$ > 400~km~s$^{-1}$. We found the average ratio of the radii $R_{sp}/R_{200c} = 1.40\pm0.02$ or $R_{sp}/R_{200m} = 0.88\pm0.02$.}, Comment: 7 pages, 3 figures, 1 table

The main points of experiment on the search of dark photons using multy-cathode counter are outlined. The evidence base to prove that the observed effect is really from dark photons is formulated. First data on diurnal variations are presented. The possible interpretation of the data is given for the case if they are expanded in future measurements., Comment: 7 pages, 3 figures, proceeding for 6th International Conference on Particle Physics and Astrophysics

We generalize some results on asymptotic and continuous group $L^p$-cohomology to Orlicz cohomology. In particular, we show that asymptotic Orlicz cohomology is a quasi-isometry invariant and that both notions coincide in the case of a locally compact second countable group. The case of degree $1$ is studied in more detail., Comment: To appear at Annales de l'Institut Fourier