arXiv subjects

Alexander Pavlov

Publications and source records attributed to Alexander Pavlov.

At least 19 recordsLinked to original sources

arXiv2026

Capture-Quiet Decomposition: A Verification Theorem for Chess Endgame Tablebases

We present the Capture-Quiet Decomposition (CQD), a structural theorem for verifying Win-Draw-Loss (WDL) labelings of chess endgame tablebases. The theorem decomposes every legal position into exactly one of three categories -- terminal, capture, or quiet -- and shows that a WDL labeling is correct if and only if: (1) terminal positions are labeled correctly, (2) capture positions are consistent with verified sub-models of smaller piece count, and (3) quiet positions satisfy retrograde consistency within the same endgame. The key insight is that capture positions anchor the labeling to externally verified sub-models, breaking the circularity that allows trivial fixpoints (such as the all-draw labeling) to satisfy self-consistency alone. We validate CQD exhaustively on all 35 three- and four-piece endgames (42 million positions), all 110 five-piece endgames, and all 372 six-piece endgames -- 517 endgames in total -- with the decomposed verifier producing identical violation counts to a full retrograde baseline in every case.

cs.AI↗

arXiv2022

Revealing the Mysteries of Venus: The DAVINCI Mission

The Deep Atmosphere Venus Investigation of Noble gases, Chemistry, and Imaging (DAVINCI) mission described herein has been selected for flight to Venus as part of the NASA Discovery Program. DAVINCI will be the first mission to Venus to incorporate science-driven flybys and an instrumented descent sphere into a unified architecture. The anticipated scientific outcome will be a new understanding of the atmosphere, surface, and evolutionary path of Venus as a possibly once-habitable planet and analog to hot terrestrial exoplanets. The primary mission design for DAVINCI as selected features a preferred launch in summer/fall 2029, two flybys in 2030, and descent sphere atmospheric entry by the end of 2031. The in situ atmospheric descent phase subsequently delivers definitive chemical and isotopic composition of the Venus atmosphere during a cloud-top to surface transect above Alpha Regio. These in situ investigations of the atmosphere and near infrared descent imaging of the surface will complement remote flyby observations of the dynamic atmosphere, cloud deck, and surface near infrared emissivity. The overall mission yield will be at least 60 Gbits (compressed) new data about the atmosphere and near surface, as well as first unique characterization of the deep atmosphere environment and chemistry, including trace gases, key stable isotopes, oxygen fugacity, constraints on local rock compositions, and topography of a tessera.

astro-ph.EP↗

arXiv2021

Crystal polarity discrimination for GaN nanowires on graphene

We present experimental data and computational analysis of the formation of GaN nanowires on graphene virtual substrates. We show that GaN nanowires on graphene exhibit nitrogen polarity. We employ the DFT-based computational analysis to demonstrate that among different possible configurations of Ga and N atoms only the N-polar one is stable. We suggest that polarity discrimination occurs due to the dipole interaction between the GaN nanocrystal and $\pi$-orbitals of the graphene sheet.

cond-mat.mes-hall↗

arXiv2020

Controlling wave-front shape and propagation time with tunable disordered non-Hermitian multilayers

Unique and flexible properties of non-Hermitian photonic systems attract ever-increasing attention via delivering a whole bunch of novel optical effects and allowing for efficient tuning light-matter interactions on nano- and microscales. Together with an increasing demand for the fast and spatially compact methods of light governing, this peculiar approach paves a broad avenue to novel optical applications. Here, unifying the approaches of disordered metamaterials and non-Hermitian photonics, we propose a conceptually new and simple architecture driven by disordered loss-gain multilayers and, therefore, providing a powerful tool to control both the passage time and the wave-front shape of incident light with different switching times. For the first time we show the possibility to switch on and off kink formation by changing the level of disorder in the case of adiabatically raising wave fronts. At the same time, we deliver flexible tuning of the output intensity by using the nonlinear effect of loss and gain saturation. Since the disorder strength in our system can be conveniently controlled with the power of the external pump, our approach can be considered as a basis for different active photonic devices.

physics.optics↗

arXiv2020

Channeling and radiation of electrons and positrons in diamond hetero-crystals

We analyze numerically the radiation and channeling properties of ultrarelativistic electrons and positrons propagating through a periodically bent diamond crystal grown on a straight single-crystal diamond substrate. Such systems can be called hetero-crystals and they are one of the experimentally realized samples for the implementation of crystalline undulators. We state that in such systems the channeling and radiation properties of projectiles are sensitive to the projectile particles energy as well as on the beam propagation direction, i.e. on whether the beam of particles enters the crystal from the side of substrate or from the side of periodically bent crystal. The predictions made are important for design and practical realization of new crystalline undulators.

physics.acc-ph↗

arXiv2020

Unambiguous scattering matrix for non-Hermitian systems

$\mathcal{PT}$ symmetry is a unique platform for light manipulation and versatile use in unidirectional invisibility, lasing, sensing, etc. Broken and unbroken $\mathcal{PT}$-symmetric states in non-Hermitian open systems are described by scattering matrices. A multilayer structure, as a simplest example of the open system, has no certain definition of the scattering matrix, since the output ports can be permuted. The uncertainty in definition of the exceptional points bordering $\mathcal{PT}$-symmetric and $\mathcal{PT}$-symmetry-broken states poses an important problem, because the exceptional points are indispensable in applications as sensing and mode discrimination. Here we derive the proper scattering matrix from the unambiguous relation between the $\mathcal{PT}$-symmetric Hamiltonian and scattering matrix. We reveal that the exceptional points of the scattering matrix with permuted output ports are not related to the $\mathcal{PT}$ symmetry breaking. Nevertheless, they can be employed for finding a lasing onset as demonstrated in our time-domain calculations and scattering-matrix pole analysis. Our results are important for various applications of the non-Hermitian systems including encircling exceptional points, coherent perfect absorption, $\mathcal{PT}$-symmetric plasmonics, etc.

physics.optics↗

arXiv2018

Hidden symmetries in mixmaster-type universe

A model of multidimensional mixmaster-type vacuum universe is considered. It belongs to a class of pseudo-Euclidean chains characterized by root vectors. An algebraic approach of our investigation is founded on construction of Cartan matrix of the spacelike root vectors in Wheeler -- DeWitt space. Kac -- Moody algebras can be classified according to their Cartan matrix. By this way a hidden symmetry of the model considered is revealed. It is known, that gravitational models which demonstrate chaotic behavior are associated with hyperbolic Kac -- Moody algebras. The algebra considered in our paper is not hyperbolic. The square of Weyl vector is negative. The mixmaster-type universe is associated with a simply-laced Lorentzian Kac -- Moody algebra. Since the volume of the configuration space is infinite, the model is not chaotic.

gr-qc↗

arXiv2017

Ulrich Bundles on Elliptic Curves and Theta Functions

Let $E$ be a smooth elliptic curve over $\mathbb{C}$. For $E$ embedded into $\mathbb{P}^2$ as Hesse cubic and $V$ an Ulrich bundle on $E$ we derive a explicit presentation of $V$ using Moore matrices and theta functions.

math.AG↗

arXiv2017

Koszul duality between Betti and Cohomology numbers in Calabi-Yau case

Let $X$ be a smooth projective Calabi-Yau variety and $L$ a Koszul line bundle on $X$. We show that for Betti numbers of a maximal Cohen-Macaulay module over the homogeneous coordinate ring $A$ of $X$ there are formulas similar to the formulas for cohomology number. This similarity is realized via the box-product resolution of the diagonal $Δ_X \subset X \times X$.

math.AG↗

arXiv2016

Intrinsic time in Geometrodynamics: introduction and application to Friedmann cosmology

An intrinsic local time in Geometrodynamics is obtained with using a scaled Dirac's mapping. By addition of a background metric, one can construct a scalar field. It is suitable to play a role of intrinsic time. Cauchy problem was successfully solved in conformal variables because they are physical ones. First, the intrinsic time as a logarithm of determinant of spatial metric, was applied to a cosmological problem by Misner. A global time is exist under condition of constant mean curvature slicing of spacetime. A volume of hypersurface and the so-called mean York's time are canonical conjugated pair. So, the volume is the intrinsic global time by its sense. The experimentally observed redshift in cosmology is the evidence of its existence. An intrinsic time of homogeneous models is global. The Friedmann equation by its sense ties time intervals. Exact solutions of the Friedmann equation in Standard cosmology with standard and conformal units are presented. Theoretical curves interpolated the Hubble diagram on latest supernovae are expressed in analytical form. The class of functions in which the concordance model is described is Weierstrass meromorphic functions. The Standard cosmological model is used for fitting the modern Hubble diagram. The physical interpretation of the modern data from concept of conformal magnitudes is simpler, so is preferable.

gr-qc↗

arXiv2016

Betti numbers of MCM modules over the cone of an elliptic normal curve

We apply Orlov's equivalence to derive formulas for the Betti numbers of maximal Cohen-Macaulay modules over the cone an elliptic curve $(E,x)$ embedded into $\mathbb{P}^{n-1}$, by the full linear system $|\mathcal{O}(nx)|$, for $n>3$. The answers are given in terms of recursive sequences. These results are applied to give a criterion of (Co-)Koszulity. In the last two sections of the paper we apply our methods to study the cases $n=1,2$. Geometrically these cases correspond to the embedding of an elliptic curve into a weighted projective space. The singularities of the corresponding cones are called minimal elliptic. They were studied by K.Saito, where he introduced the notation $\widetilde{E_8}$ for $n=1$, $\widetilde{E_7}$ for $n=2$ and $\widetilde{E_6}$ for the cone over a smooth cubic, that is, for the case $n=3$. For the singularities $\widetilde{E_7}$ and $\widetilde{E_8}$ we obtain formulas for the Betti numbers and the numerical invariants of MCM modules analogous to the case of a plane cubic.

math.AC↗

arXiv2016

Intrinsic time in Friedmann-Robertson-Walker universe

A global intrinsic time in Friedmann - Robertson - Walker models is proportional to a scaling factor of the spatial metric. The aim of the paper is to study an applicability of the intrinsic global time chosen to nearest non-symmetric cases by taking into account linear metric perturbations. Scalar linear perturbations add some corrections to the effective energy density in the Hubble law. The metric vector and tensor perturbations in linear approximation do not influence the intrinsic time.

gr-qc↗

arXiv2015

Moore Matrices and Ulrich Bundles on an Elliptic Curve

We give normal forms of determinantal representations of a smooth projective plane cubic in terms of Moore matrices. Building on this, we exhibit matrix factorizations for all indecomposable vector bundles of rank 2 and degree 0 without nonzero sections, also called Ulrich bundles, on such curves.

math.AG↗

arXiv2015

Betti Tables of MCM Modules Over the Cone of a Plane Cubic

We show that for maximal Cohen-Macaulay modules over a homogeneous coordinate rings of smooth Calabi-Yau varieties $X$ computation of Betti numbers can be reduced to computations of dimensions of certain $\operatorname{Hom}$ groups in the bounded derived category $D^b(X)$. In the simplest case of a smooth elliptic curve $E$ imbedded into $\mathbb{P}^2$ as a smooth cubic we use our formula to get explicit answers for Betti numbers. Description of the automorphism group of the derived category $D^b(E)$ in terms of the spherical twist functors of Seidel and Thomas plays a major role in our approach. We show that there are only four possible shapes of the Betti tables up to a shifts in internal degree, and two possible shapes up to a shift in internal degree and taking syzygies.

math.AC↗

arXiv2014

Realization of white light cavity for ulra-short optical signal storage and Processing

We have demonstrated that chirped Bragg gratings can compensate for a chromatic dispersion by reflecting different wavelengths at different location along the axis of the gratings. In this paper, we make use of such a dispersion-compensating property to create a white light cavity (WLC) effect that cancels the round trip phase shift due to propagation as the optical frequency is tuned. A pair of LCBGs is used to make the cavity. To fulfill WLC condition, the dispersion profile of the LCBGs is tailored by adjusting parameters such as chirping rate, modulation depth and the length of the grating region. Numerical simulation shows WLC bandwidth is ~10GHz.

physics.optics↗

arXiv2013

Ultra-short pulse transmission in a passive white light cavity based on chirped Bragg gratings

It is widely accepted that Bragg reflection from linearly chirped Bragg gratings (LCBGs) can compensate for a chromatic dispersion by reflecting different wavelengths at different location along the axis of the gratings for ultra-short pulses. In this paper, we studied the possibility of making use of such a dispersion-compensating property to construct a white light cavity (WLC). A pair of LCBGs is suggested as the reflectors of the cavity. The analytical and numerical analysis shows that the reflection by a LCBG does not solely occur at the position where Bragg condition is reached. The accumulated effect of multiple scatterings at different locations inside the LCBG produces a positive group delay, preventing the WLC to be realized with simple LCBG.

physics.optics↗

arXiv2010

Quasi-multipliers of Hilbert and Banach C*-bimodules

Quasi-multipliers for a Hilbert C*-bimodule V were introduced by Brown, Mingo and Shen 1994 as a certain subset of the Banach bidual module V**. We give another (equivalent) definition of quasi-multipliers for Hilbert C*-bimodules using the centralizer approach and then show that quasi-multipliers are, in fact, universal (maximal) objects of a certain category. We also introduce quasi-multipliers for bimodules in Kasparov's sense and even for Banach bimodules over C*-algebras, provided these C*-algebras act non-degenerately. A topological picture of quasi-multipliers via the quasi-strict topology is given. Finally, we describe quasi-multipliers in two main situations: for the standard Hilbert bimodule l_2(A) and for bimodules of sections of Hilbert C*-bimodule bundles over locally compact spaces.

math.OA↗

arXiv2010

Quantization of branched coverings

We identify branched coverings (continuous open surjections p:Y->X of Hausdorff spaces with uniformly bounded number of pre-images) with Hilbert C*-modules C(Y) over C(X) and with faithful unital positive conditional expectations E:C(Y)->C(X) topologically of index-finite type. The case of non-branched coverings corresponds to projective finitely generated modules and expectations (algebraically) of index-finite type. This allows to define non-commutative analogues of (branched) coverings.

math.OA↗