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It is shown that every outer *-automorphism of a real C*-algebra can be uniquely extended to an injective envelope of real C*-algebra. It is proven that if a real C*-algebra is a simple, then its injective envelope is also simple, and it is a real AW*-factor. The example of a real C*-algebra that is not real AW*-algebra and the injective envelope is a real AW*-factor of type III, which is not a real W*-algebra is constructed. This leads to the interesting result that up to isomorphism, the class of injective real (resp. complex) AW*-factors of type III is at least one larger than the class injective real (resp. complex) W*-factors of type III.

We propose a novel framework to remove transient objects from input videos for 3D scene reconstruction using Gaussian Splatting. Our framework consists of the following steps. In the first step, we propose an unsupervised training strategy for a classification network to distinguish between transient objects and static scene parts based on their different training behavior inside the 3D Gaussian Splatting reconstruction. In the second step, we improve the boundary quality and stability of the detected transients by combining our results from the first step with an off-the-shelf segmentation method. We also propose a simple and effective strategy to track objects in the input video forward and backward in time. Our results show an improvement over the current state of the art in existing sparsely captured datasets and significant improvements in a newly proposed densely captured (video) dataset. More results and code are available at https://transient-3dgs.github.io.

Measurement of numerical values of the anomalous density, $\sigma$, which plays important role in Bose -- Einstein condensation, and, especially, determination of its sign, has been a long standing problem. We develop Hartree -- Fock -- Bogoliubov theory taking account arbitrary phase of the condensate wave function. We show that, the sign of $\sigma$ directly related to the phase, and, hence is not observable. Despite this, its absolute value can be extracted from measurements of the sound velocity and condensed fraction. We present theoretical prediction for $\vert \sigma \vert$ for a BEC in a uniform box., Comment: 24 pages, 7 figures

The Harary reconstruction conjecture states that any graph with more than four edges can be uniquely reconstructed from its set of maximal edge-deleted subgraphs. In 1977, M\"uller verified the conjecture for graphs with $n$ vertices and $n \log_2(n)$ edges, improving on Lov\'as's bound of $\log(n^2-n)/4$. Here, we show that the reconstruction conjecture holds for graphs which have exactly one cycle and and three non-isomorphic subtrees.

We use the Dirac continuum model to study the propagation of electronic wave packets in graphene with periodically arranged circular potential steps. The time propagation of the wave packets are calculated using the split-operator method for different size, height and separation of the barriers. The time propagation of the wave packets is calculated using the split-operator method for various barrier sizes, heights, and separations. We found that, despite the pronounced Klein tunneling effect in graphene, the presence of a lattice of defects significantly impacts the propagation properties of the wave packets. For example, depending on the height and size of the incident wave packet, the transmission probability can decrease by more than 20\%. The alteration of the polarity of the potential barriers also contributes to the transmission probabilities of the wave packet in graphene. The obtained results could provide valuable insights into the fundamental understanding of charge carrier dynamics in graphene-based nanodevices.

We present a study of the multiwavelength (MW) variability of the blazar AO 0235+164 based on the radio-to-$\gamma$-ray data covering a long time period from 1997 to 2023. The radio data are represented by the 1-22 GHz measurements from the RATAN-600 radio telescope, the 5 and 8 GHz data from the RT-32 telescopes, and the 37 GHz data from the RT-22 telescope. The optical measurements in the $R$-band were collected with the 1-m Zeiss-1000 and 0.5-m AS-500/2 telescopes. Additionally we used the archive data at 230~GHz from the SMA and the $\gamma$-ray data in the 0.1-100 GeV band from the Fermi-LAT point source 4FGL-DR2 catalogue. The variability properties during four epochs containing major flares and one epoch of relatively low activity were analysed. A significant correlation ($\geq\!2\sigma$) between the radio, optical, and $\gamma$-ray bands is found for all these periods with time delays from 0 to 1.7 yrs. The relation between time delay and frequency is described by a linear law with a negative slope of -10 day/GHz. The discovered properties of MW variability for the low activity period and for flaring states suggest that the mechanisms dominating the radio-$\gamma$-ray variations are not substantially different. The detected quasi-periodic oscillations of about 6 and 2 years are tentative, as the time span of the observations includes fewer than 4 full cycles for the radio and optical data and only about 3 cycles for the Fermi-LAT data. The physical parameters of the radio jet were obtained using the Hedgehog model applied to the average radio spectrum of AO 0235+164 in the range 0.1-300 GHz. The effectiveness of replacing electrons with protons in the synchrotron radio emission of relativistic jets is shown for describing the nature of blazars and the generation of high energy neutrinos., Comment: Accepted 2024 October 30 for publication in MNRAS

We investigate heavy-light quark systems within the framework of the QCD instanton vacuum, focusing on the $N_f = 1$ light flavor case. We derive an effective heavy-light quark interaction from the low-energy QCD partition function and construct a heavy-meson effective Lagrangian. The physical residual mass of heavy mesons, $\Lambda$, is determined by employing compositeness and normalization conditions. We calculate the masses of $D$ and $B$ mesons and their weak decay constants to the leading order and next-to-leading order in the $1/m_Q$ expansion. The current results for $f_D$ and $f_B$ are in good agreement with recent lattice QCD data and PDG average values., Comment: 13 pages, 4 figures. Discussion part was improved, and additional references were added

Although various visual localization approaches exist, such as scene coordinate and pose regression, these methods often struggle with high memory consumption or extensive optimization requirements. To address these challenges, we utilize recent advancements in novel view synthesis, particularly 3D Gaussian Splatting (3DGS), to enhance localization. 3DGS allows for the compact encoding of both 3D geometry and scene appearance with its spatial features. Our method leverages the dense description maps produced by XFeat's lightweight keypoint detection and description model. We propose distilling these dense keypoint descriptors into 3DGS to improve the model's spatial understanding, leading to more accurate camera pose predictions through 2D-3D correspondences. After estimating an initial pose, we refine it using a photometric warping loss. Benchmarking on popular indoor and outdoor datasets shows that our approach surpasses state-of-the-art Neural Render Pose (NRP) methods, including NeRFMatch and PNeRFLoc., Comment: Project website at https://gsplatloc.github.io/

Let $f$ be a polynomial-like map with dominant topological degree $d_t\geq 2$ and let $d_{k-1}

Under a natural assumption on the dynamical degrees, we prove that the Green currents associated to any H\'enon-like map in any dimension have H\"older continuous super-potentials, i.e., give H\"older continuous linear functionals on suitable spaces of forms and currents. As a consequence, the unique measure of maximal entropy is the Monge-Amp\`ere of a H\"older continuous plurisubharmonic function and has strictly positive Hausdorff dimension. Under the same assumptions, we also prove that the Green currents are woven. When they are of bidegree $(1,1)$, they are laminar. In particular, our results generalize results known until now only in algebraic settings, or in dimension 2.

In this paper, we study the dynamics of geodesics of Fuchsian meromorphic connections with real periods, giving a precise characterization of the possible $\omega$-limit sets of simple geodesics in this case. The main tools are the study of the singular flat metric associated to the meromorphic connection, an explicit description of the geodesics nearby a Fuchsian pole with real residue larger than $-1$ and a far-reaching generalization to our case of the classical Teichm\"uller lemma for quadratic differentials.

We prove that, within any holomorphic family of endomorphisms of $\mathbb P^k(\mathbb C)$ in any dimension $k \geq 1$ and algebraic degree $d \geq 2$, the measurable holomorphic motion associated to dynamical stability in the sense of Berteloot-Bianchi-Dupont preserves the class of equilibrium states associated with weight functions $\psi$ satisfying $\sup\psi - \inf \psi < \log d$.

In this paper we establish some basic properties of superderivations of Lie superalgebras. Under certain conditions, for solvable Lie superalgebras with given nilradicals, we give estimates for upper bounds to dimensions of complementary subspaces to the nilradicals. Moreover, under these conditions we describe the solvable Lie superalgebras of maximal rank. Namely, we prove that an arbitrary solvable Lie superalgebra of maximal rank is isomorphic to the maximal solvable extension of nilradical of maximal rank.

This article provides quasi-optimal a priori error estimates for an optimal control problem constrained by an elliptic obstacle problem where the finite element discretization is carried out using the symmetric interior penalty discontinuous Galerkin method. The main proofs are based on the improved $L^2$-error estimates for the obstacle problem, the discrete maximum principle, and a well-known quadratic growth property. The standard (restrictive) assumptions on mesh are not assumed here.

Given measurements from sensors and a set of standard forces, an optimization based approach to identify weakness in structures is introduced. The key novelty lies in letting the load and measurements to be random variables. Subsequently the conditional-value-at-risk (CVaR) is minimized subject to the elasticity equations as constraints. CVaR is a risk measure that leads to minimization of rare and low probability events which the standard expectation cannot. The optimization variable is the (deterministic) strength factor which appears as a coefficient in the elasticity equation, thus making the problem nonconvex. Due to uncertainty, the problem is high dimensional and, due to CVaR, the problem is nonsmooth. An adjoint based approach is developed with quadrature in the random variables. Numerical results are presented in the context of a plate, a large structure with trusses similar to those used in solar arrays or cranes, and a footbridge.

Classifying Frobenius algebras is a key question that has been addressed in various contexts. The structure of finite-dimensional Frobenius algebras depends on the base field and the dimension of the algebra, leading to different classification results depending on whether the base field has characteristic zero, characteristic $p$, or other properties. Frobenius algebras over fields of characteristic zero have been well-studied, often related to semisimple algebra theory. The behavior of Frobenius algebras over fields of positive characteristic presents new challenges, with connections to modular representation theory. In the paper, we first classify all associative algebra structures on a two-dimensional vector space over any base field equipped with a non-degenerate bilinear form. We then identify which of these are Frobenius algebras. Lists of canonical representatives of the isomorphism classes of these algebras are provided for a base field with characteristics not equal to two or three, as well as for characteristics two and three.

We prove that, for every invertible horizontal-like map (i.e., H{\'e}non-like map) in any dimension, the sequence of the dynamical degrees is increasing until that of maximal value, which is the main dynamical degree, and decreasing after that. Similarly, for polynomial-like maps in any dimension, the sequence of dynamical degrees is increasing until the last one, which is the topological degree. This is the first time that such a property is proved outside of the algebraic setting. Our proof is based on the construction of a suitable deformation for positive closed currents, which relies on tools from pluripotential theory and the solution of the $d$, $\bar \partial$, and $dd^c$ equations on convex domains.

A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.

In the paper, we consider the class of so-called endo-commutative algebras. From the identity imposed to specify this class, one can easily see that the product in this class preserves the square of elements. We give a complete classification of this class, up to isomorphism, over any basic field in dimension two. This elementary and self-contained exposition uses the recent result of one of the authors on description of the category of all $2$-dimensional algebras over any basic field.

Using a theoretical field Gaussian approximation we have studied Rabi coupled binary Bose system at low temperatures. We have derived extended Hugenholtz - Pines relations taking into account one body interaction (e.g. Rabi coupling) and studied the critical temperature $T_c$ of Bose-Einstein condensate transition. We have shown that, the shift of $T_c$ due to this interaction can not exceed $\sim 60 \%$ and goes to a plateau with increasing the parameter $\Omega_R/T_{c}^{0}$, where $\Omega_R$ is the intensity of the coupling and $T_{c}^{0}$ is the critical temperature of the system with $\Omega_R=0$. Moreover, the shift is always positive and does not depend on the sign of the one body interaction., Comment: 22 pages and 2 figures

We present an approach for the reconstruction of textured 3D meshes of human heads from one or few views. Since such few-shot reconstruction is underconstrained, it requires prior knowledge which is hard to impose on traditional 3D reconstruction algorithms. In this work, we rely on the recently introduced 3D representation $\unicode{x2013}$ neural implicit functions $\unicode{x2013}$ which, being based on neural networks, allows to naturally learn priors about human heads from data, and is directly convertible to textured mesh. Namely, we extend NeuS, a state-of-the-art neural implicit function formulation, to represent multiple objects of a class (human heads in our case) simultaneously. The underlying neural net architecture is designed to learn the commonalities among these objects and to generalize to unseen ones. Our model is trained on just a hundred smartphone videos and does not require any scanned 3D data. Afterwards, the model can fit novel heads in the few-shot or one-shot modes with good results.

Multicomponent quantum gases are ideal platforms to study fundamental phenomena arising from the mutual interaction between different constituents. Particularly, due to the repulsive interactions between two species, the system may exhibit a phase separation. We develop a mean-field-based theory for a two-component Bose mixture, which is equivalent to the Hartree-Fock-Bogoliubov approximation, and derive analytical expressions for the phase boundary and miscibility. The majority of existing theories, which are valid only for weakly interacting Bose gases, predict that the phase boundary is determined by the criterion $g_{ab}\leqslant\sqrt{g_{aa} g_{bb}}$ (where $g_{ab}$ is a coupling constant between the components $a$ and $b$). We show that in the Bose-Einstein-condensation phase ($T\leqslant T_c$) the system may remain in a stable and miscible phase also for larger values of $g_{ab}$, depending on the gas parameter $\gamma$ and temperature., Comment: Revised version. 34 pages, 14 figures

We prove that, in stable families of endomorphisms of $\mathbb{P}^k(\mathbb{C})$, all invariant measures whose measure-theoretic entropy is strictly larger than $(k-1)\log d$ at a given parameter can be followed holomorphically with the parameter in all the parameter space. As a consequence, almost all points (with respect to any such measure at any parameter) in the Julia set can be followed holomorphically without intersections. This generalizes previous results by Berteloot, Dupont, and the first author for the measure of maximal entropy, and provides a parallel in this setting to the probabilistic stability of H\'enon maps by Berger-Dujardin-Lyubich. Our proof relies both on techniques from the theory of stability/bifurcation in any dimension and on an explicit lower bound for the Lyapunov exponents for an ergodic measure in terms of its measure-theoretic entropy, due to de Th\'elin and Dupont. A local version of our result holds also for all measures supported on the Julia set with just strictly positive Lyapunov exponents and not charging the post-critical set. Analogous results hold in families of polynomial-like maps of large topological degree. In this case, as part of our proof, we also give a sufficient condition for the positivity of the Lyapunov exponents of an ergodic measure for a polynomial-like map in any dimension in term of its measure-theoretic entropy, generalizing to this setting the analogous result by de Th\'elin and Dupont valid on $\mathbb{P}^k(\mathbb{C})$.