Searching Arxiv, refresh for possibly better results.

total 3493took 0.10s

New Examples on Lavrentiev Gap Using FractalsJun 11 2019Jun 13 2019Zhikov showed 1986 with his famous checkerboard example that functionals with variable exponents can have a Lavrentiev gap. For this example it was crucial that the exponent had a saddle point whose value was exactly the dimension. In 1997 he extended ... More

On the uniqueness of a solution to a stationary convection-diffusion equation with a generalized divergence-free driftJun 01 2017In this paper we establish the uniqueness of a solution to a stationary convection-diffusion equation in divergence form with an exponentially summable generalized divergence-free drift.

New Examples on Lavrentiev Gap Using FractalsJun 11 2019Zhikov showed 1986 with his famous checkerboard example that functionals with variable exponents can have a Lavrentiev gap. For this example it was crucial that the exponent had a saddle point whose value was exactly the dimension. In 1997 he extended ... More

Schmidt decomposition for non-collinear biphoton angular wave functionsNov 08 2014Schmidt modes of non-collinear biphoton angular wave functions are found analytically. The experimentally realizable procedure is described for their separation. Parameters of the Schmidt decomposition are used for evaluation of the degree of biphoton's ... More

Data-driven goodness-of-fit testsAug 01 2007Dec 18 2007We introduce a new general class of statistical tests. The class contains Neyman's smooth tests and data-driven efficient score tests as special examples. We prove general consistency theorems for the tests from the class. The paper shows that the tests ... More

Phenomenological implications of an alternative Hamiltonian constraint for quantum cosmologyNov 02 2005In this paper we review a model based on loop quantum cosmology that arises from a symmetry reduction of the self dual Plebanski action. In this formulation the symmetry reduction leads to a very simple Hamiltonian constraint that can be quantized explicitly ... More

A question by Alexei Aleksandrov and logarithmic determinantsAug 28 2001We answer negatively to the question posed by Aleksandrov concerning analytic functions of Smirnov's class in the unit disk with pure imaginary boundary values. We also find new sufficient conditions for representations of functions of Smirnov's class ... More

Zeros of Gaussian Analytic FunctionsJul 06 2000We prove and discuss three results on zero distribution of gaussian analytic functions: (i) the Edeleman-Kostlan formula for the expectation of the counting measure; (ii) a variation on the theme of Calabi's rigidity theorem; (iii) Offord's estimate of ... More

Extending the exact sequence of nonabelian $H^1$, using nonabelian $H^2$ with coefficients in crossed modulesAug 26 2016In this note, following Dedecker and Debremaeker, we extend the cohomology exact sequence for nonabelian $H^1$, using nonabelian $H^2$ with coefficients in crossed modules.

Existence of perfect Morse functions on spaces with semi-free circle actionFeb 15 2002Apr 01 2003Let $M$ be a compact oriented simply-connected manifold of dimension at least 8. Assume $M$ is equipped with a torsion-free semi-free circle action with isolated fixed points. We prove $M$ has a perfect invariant Morse-Smale function. The major ingredient ... More

Marketing features of dropshipping in system of e-commerceMay 10 2015Today dropshipping wins the Internet promptly and transformed to one of the basic tools of marketing in e-commerce. Marketing features, mechanisms and value dropshipping in the conditions of network economy of the XXI century reveal in article. The author ... More

Mathematics of Knowledge Refinement: Probabilistic Arithmetic, with no unknowns and no infinity. Part I. Generalized Probabilistic Arithmetic. Basic definitions and propertiesNov 01 2011May 22 2012An approach to build Probabilistic Arithmetic in which initial values of all correlated random variables are known, but with varying degrees of accuracy. As a result of the proposed Probabilistic Arithmetic operations, variable values, degrees of their ... More

QUBIC ExperimentMay 16 2016QUBIC is a ground-based experiment, currently under construction, that uses the novel bolometric interferometry technology. It is dedicated to measure the primordial B-modes of CMB. As a bolometric interferometer, QUBIC has high sensitivity and good systematics ... More

Surfaces containing two circles through each pointDec 30 2015We find all analytic surfaces in space $\mathbb{R}^3$ such that through each point of the surface one can draw two transversal circular arcs fully contained in the surface. The problem of finding such surfaces traces back to the works of Darboux from ... More

Quasiparticle approach to molecules interacting with quantum solventsOct 05 2016Understanding the behavior of molecules interacting with superfluid helium represents a formidable challenge and, in general, requires approaches relying on large-scale numerical simulations. Here we demonstrate that experimental data collected over the ... More

Dynamics of quadratic polynomials, I: Combinatorics and geometry of the Yoccoz puzzleMar 01 1995This work studies combinatorics and geometry of the Yoccoz puzzle for quadratic polynomials. It is proven that the moduli of the ``principal nest'' of annuli grow at linear rate. As a corollary we obtain complex a priori bounds and local connectivity ... More

On exotic algebraic structures on affine spacesJun 02 1995By an exotic algebraic structure on the affine space ${\bf C}^n$ we mean a smooth affine algebraic variety which is diffeomorphic to ${\bf R}^{2n}$ but not isomorphic to ${\bf C}^n$. This is a survey of the recent developement on the subject, which emphasizes ... More

KISS approach to credit portfolio modelingJul 11 2011A simple, yet reasonably accurate, analytical technique is proposed for multi-factor structural credit portfolio models. The accuracy of the technique is demonstrated by benchmarking against Monte Carlo simulations. The approach presented here may be ... More

On 2-systoles of hyperbolic 3-manifoldsMay 23 2012Jul 08 2012We investigate the geometry of $\pi_1$-injective surfaces in closed hyperbolic 3-manifolds. First we prove that for any $e>0$, if the manifold $M$ has sufficiently large systole $\sys_1(M)$, the genus of any such surface in $M$ is bounded below by $\exp((1/2-e)\sys_1(M))$. ... More

Geodesics, volumes and Lehmer's conjectureJun 09 2011In this report I discuss the relations between systoles and volumes of hyperbolic manifolds and a conjecture of Lehmer about the Mahler measure of non-cyclotomic polynomials.

Enhancement of the electric dipole moment of the electron in the YbF moleculeMay 27 1997We calculate an effective electric field on the unpaired electron in the YbF molecule. This field determines sensitivity of the molecular experiment to the electric dipole moment of the electron. We use experimental value of the spin-doubling constant ... More

On the class of caustic on the moduli space of odd spin curvesSep 08 2015Jan 20 2019Let $C$ be a smooth projective curve of genus $g\geq 3$ and let $\eta$ be an odd theta characteristic on it such that $h^0(C,\eta) = 1$. Pick a point $p$ from the support of $\eta$ and consider the one-dimensional linear system $|\eta + p|$. In general ... More

Polarization spin-tensors in two-spinor formalism and Behrends-Fronsdal spin projection operator for $D$-dimensional caseFeb 07 2019In the work, the recurrent differential relations that connecting the polarization spin-tensor of the wave function of a free massive particle of an arbitrary spin for $D=4$ and new formula of the $D$-dimensional Behrends-Fronsdal spin projection operator ... More

Nonlinear electromagnetic response and Higgs mode excitation in BCS superconductors with impuritiesFeb 05 2019Feb 12 2019We reveal that due to the presence of disorder oscillations of the order parameter amplitude called the Higgs mode can be effectively excited by the external electromagnetic radiation in usual BCS superconductors. This mechanism works for superconductors ... More

Parallel Algorithm for Frequent Itemset Mining on Intel Many-core SystemsDec 28 2018Frequent itemset mining leads to the discovery of associations and correlations among items in large transactional databases. Apriori is a classical frequent itemset mining algorithm, which employs iterative passes over database combining with generation ... More

$γW$-box Inside-Out: Nuclear Polarizabilities Distort the Beta Decay SpectrumDec 11 2018Mar 06 2019I consider the $\gamma W$-box correction to superallowed nuclear $\beta$-decays in the framework of dispersion relations. I address a novel effect of a distortion of the emitted electron energy spectrum by nuclear polarizabilities and show that this effect, ... More

Steklov problem on differential formsMay 24 2017In this paper we study spectral properties of Dirichlet-to-Neumann map on differential forms obtained by a slight modification of the definition due to Belishev and Sharafutdinov. The resulting operator $\Lambda$ is shown to be self-adjoint on the subspace ... More

Arithmetic Kleinian groups generated by elements of finite orderOct 19 2016Jul 07 2017We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. This implies, in particular, that there exist only finitely many conjugacy classes of cocompact two generated arithmetic Kleinian ... More

On evolutionary selection of blackjack strategiesNov 16 2017We apply the approach of evolutionary programming to the problem of optimization of the blackjack basic strategy. We demonstrate that the population of initially random blackjack strategies evolves and saturates to a profitable performance in about one ... More

Dimension Theory Approach to the Complexity of Almost Periodic TrajectoriesOct 09 2017We introduce and study a dimensional-like characteristic of an uniformly almost periodic function, which we call the Diophantine dimension. By definition, it is the exponent in the asymptotic behavior of the inclusio length. Diophantine dimension is connected ... More

Fluctuations of the aperture-averaged orbital angular momentum after propagation through turbulenceJan 05 2018Jan 09 2018In the recent paper [1] it was shown that for paraxial propagation of scalar waves, the transverse linear momentum and orbital angular momentum (OAM) are related to the wave coherence function. Although both of these quantities are conserved during free-space ... More

Busy beavers and Kolmogorov complexityMar 15 2017The idea to find the "maximal number that can be named" can be traced back to Archimedes (see his Psammit). From the viewpoint of computation theory the natural question is "which number can be described by at most n bits"? This question led to the definition ... More

Derivation of Schrodinger's equationFeb 07 2017In this article, a model of a material particle in chaotic motion (while maintaining a definite size and trajectory) is presented. On the basis of this model, the following is achieved: --to express Planck's constant through the main features of a stationary ... More

Discriminant and Hodge classes on the space of Hitchin's coversMar 31 2019We continue the study of the rational Picard group of the moduli space of Hitchin's spectral covers started in P. Zograf's and D. Korotkin's work [11]. In the first part of the paper we expand the ``boundary'', ``Maxwell stratum'' and ``caustic'' divisors ... More

Population protocols with unreliable communicationFeb 26 2019Mar 06 2019Population protocols are a model of distributed computation intended for the study of networks of independent computing agents with dynamic communication structure. Each agent has a finite number of states, and communication opportunities occur nondeterministically, ... More

Hopfological algebra and categorification at a root of unity: the first stepsSep 04 2005Mar 25 2006Any finite-dimensional Hopf algebra H is Frobenius and the stable category of H-modules is triangulated monoidal. To H-comodule algebras we assign triangulated module-categories over the stable category of H-modules. These module-categories are generalizations ... More

Heisenberg algebra and a graphical calculusSep 16 2010A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of the Heisenberg ... More

A functor-valued invariant of tanglesMar 27 2001Sep 21 2002We construct a family of rings. To a plane diagram of a tangle we associate a complex of bimodules over these rings. Chain homotopy equivalence class of this complex is an invariant of the tangle. On the level of Grothendieck groups this invariant descends ... More

Continuity of the Mixing OperatorAug 16 2005Oct 03 2005Mixed distributions are considered as a results of application of a linear operator, which maps mixing measures to mixed measures. The main result is a proof of continuity of this mixing operator. Corollaries for parametric families of distributions (usually ... More

Proof of Gal's conjecture for the D series of generalized associahedraJun 09 2011In this short note we consider generalized associahedra of type D_n. We prove that these simple flag polytopes are not nestohedra for n > 3, but the statement of Gal's conjecture holds for them.

Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesicsDec 19 2013Apr 04 2014We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon-Nikod\'ym property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that any thick ... More

Surfaces containing two circles through each pointDec 30 2015Nov 04 2016We find all analytic surfaces in space $\mathbb{R}^3$ such that through each point of the surface one can draw two transversal circular arcs fully contained in the surface. The problem of finding such surfaces traces back to the works of Darboux from ... More

On fields of definition of arithmetic Kleinian reflection groupsOct 26 2007Apr 01 2008We show that degrees of the real fields of definition of arithmetic Kleinian reflection groups are bounded by 35.

A sequence of connections and a characterization of Kähler manifoldsSep 29 1998We study a sequence of connections which is associated with a Riemannian metric and an almost symplectic structure on a manifold. We prove that if this sequence is trivial (i.e. constant) or 2-periodic, then the manifold has a canonical K\"ahler structure. ... More

Parshin Residues via Coboundary OperatorsJul 25 2007Dec 05 2010The article consist of two main parts: an analog of the Leray Theory for Singular Varieties and its application to the Theory of Parshin's Residues. The first part is independent from the second. It uses the theory of Whitney stratifications. The second ... More

When is the set of embeddings finite up to isotopy?Jun 09 2011Dec 27 2015Given a manifold N and a number m, we study the following question: is the set of isotopy classes of embeddings N->S^m finite? In case when the manifold N is a sphere the answer was given by A. Haefliger in 1966. In case when the manifold N is a disjoint ... More

Link homology and categorificationMay 12 2006Sep 01 2006This is a short survey of algebro-combinatorial link homology theories which have the Jones polynomial and other link polynomials as their Euler characteristics.

The defect of weak approximation for homogeneous spaces. IIApr 30 2008May 10 2008Let X be a homogeneous space of a connected linear algebraic group G' over a number field k, containing a k-point x. Assume that the stabilizer of x in G' is connected. Using the notion of a quasi-trivial group, recently introduced by Colliot-Th\'el\`ene, ... More

On distinguishability of hypothesesAug 20 2013Oct 23 2013We consider the problems of hypothesis testing on a probability measure of independent sample, on solution of ill-posed problem, on deconvolution problem and on Poisson mean measure. For all these setups necessary conditions and sufficient conditions ... More

The Sharp Lower Bound of Asymptotic Efficiency of Estimators in the Zone of Moderate Deviation ProbabilitiesJun 07 2012For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the lower bound ... More

Convolution equations on lattices: periodic solutions with values in a prime characteristic fieldJun 29 2006Feb 13 2007These notes are inspired by the theory of cellular automata. A linear cellular automaton on a lattice of finite rank or on a toric grid is a discrete dinamical system generated by a convolution operator with kernel concentrated in the nearest neighborhood ... More

Constraints on SIDM with flavor mixingMay 09 2001The self-interacting dark matter (SIDM) model with flavor mixing (astro-ph/0010616) was proposed to resolve problems of the CDM model on small scales by keeping attractive features of both SIDM and annihilating dark matter, and simultaneously avoid their ... More

Surface morphology coarsening in a nonlocal systemFeb 22 2015Direct comparison is made of the steady-sates and coarsening dynamics in a local system and its nonlocal generalization. The example system is the surface of a solid film in a strong electric field; the morphological evolution of the surface is described, ... More

The giant frequency shift of intramolecular O-H vibration band in the raman spectra of water on the silver surfaceAug 19 2016The giant frequency shift was observed in Raman spectra for inramolecular O-H vibration band. The effect was observed in SERS-condition experiment, when exciting light was focused by short-focus objective on the Ag-surface, merged in water. The shift ... More

Patterns in knot cohomology IJan 30 2002Cohomology theory of links, introduced by the author, is combinatorial. Dror Bar-Natan recently wrote a program that found ranks of cohomology groups of all prime knots with up to 11 crossings. His surprising experimental data is discussed in this note. ... More

Adaptive two-dimensional wavelet transformation based on the Haar systemOct 03 2014The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar bases generated ... More

Dynamics of quadratic polynomials, III: Parapuzzle and SBR measuresJun 15 1996This is a continuation of notes on dynamics of quadratic polynomials. In this part we transfer the our prior geometric result to the parameter plane. To any parameter value c in the Mandelbrot set (which lies outside of the main cardioid and little Mandelbrot ... More

Supergeometry in mathematics and physicsDec 22 2015This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The second part discusses ... More

Lectures on Exotic Algebraic Structures on Affine SpacesJan 16 1998Jun 10 1998These notes are based on the lecture courses given at the Ruhr-Universit{\"a}t-Bochum (03--08.02.1997) and at the Universit{\'e} Paul Sabatier (Toulouse, 08-12.01.1996).

Reversible Image Merging for Low-level Machine VisionApr 13 2016In this paper a hierarchical model for pixel clustering and image segmentation is developed. In the model an image is hierarchically structured. The original image is treated as a set of nested images, which are capable to reversibly merge with each other. ... More

Assertion checker for the C programming language based on computations over event tracesJan 12 2001This paper suggests an approach to the development of software testing and debugging automation tools based on precise program behavior models. The program behavior model is defined as a set of events (event trace) with two basic binary relations over ... More

Asymmetry of modal profiles of dipole-exchange spin waves in thin high-magnetic moment metallic ferromagnetic filmsSep 19 2012The asymmetry of the modal profiles for dipole-exchange spin waves propagating in in-plane magnetized ferromagnetic films at a right angle to the applied magnetic field has been investigated theoretically. It was found that in the large-magnetic moment ... More

Cardinal p and a theorem of PelczynskiJun 26 2000We show that it is consistent that for some uncountable cardinal k, all compactifications of the countable discrete space with remainders homeomorphic to $D^k$ are homeomorphic to each other. On the other hand, there are $2^c$ pairwise non-homeomorphic ... More

How weak is weak extent?Jun 26 2000A space X is star-Lindelof provided for every open cover U there is a finite subset A of X such that St(A,U)=X. We show that a Tychonoff star-Lindelof space can have arbitraryly big extent while the extent of a normal star-Lindelof space can not be greater ... More

Suspension theorems for links and link mapsOct 10 2006Sep 18 2008We present a new short proof of the explicit formula for the group of links (and also link maps) in the 'quadruple point free' dimension. Denote by L(m,p,q) (respectively, C(m-p,p)) the group of smooth embeddings S^p |_| S^q -> S^m (respectively, S^p ... More

Estimates in Shirshov height theoremNov 27 2014In 1993 E. I. Zelmanov asked the following question in Dniester Notebook: "Suppose that $F_{2, m}$ is a 2-generated associative ring with the identity $x^m=0$. Is it true, that the nilpotency degree of $F_{2, m}$ has exponential growth?" We show that ... More

Estimations of the particular periodicity in case of the extremal periods in Shirshov's Height theoremAug 31 2011Oct 12 2011Let us recall the well-known Shirshov's Height Theorem. "Let A be a finitely generated algebra of degree d. Then there exists a finite set Y which is the subset of A that A has and an integer h' = h(A) such that A has Shirshov's height h' over set Y. ... More

On equivalent resistance of electrical circuitsJun 26 2015While the standard (introductory physics) way of computing the equvalent resistance of non-trivial electrical ciruits is based on Kirchhoff's rules, there is a mathematically and conceptually simpler approach, called the method of nodal potentials, whose ... More

On consistency and inconsistency of nonparametric testsJul 24 2018Nov 12 2018For $\chi^2-$tests with increasing number of cells, Cramer-von Mises tests, tests generated $\mathbb{L}_2$- norms of kernel estimators and tests generated quadratic forms of estimators of Fourier coefficients we find necessary and sufficient conditions ... More

Eight models for coherence of radiation from incoherent sources and coherence of sunlightApr 11 2019Eight models for the coherence of the quasi-monochromatic light from spherical incoherent sources are constructed by placing incoherent monopole and dipole sources on the surface of a sphere, inside a ball and on a plane circular disk. All models allow ... More

Lefschetz exceptional collections in $S_k$-equivariant categories of $(\mathbb{P}^n)^k$Jul 04 2018We consider the bounded derived category of $S_k$-equivariant coherent sheaves on $(\mathbb{P}^n)^k$. The goal of this paper is to construct in this category a rectangular Lefschetz exceptional collection when this is possible, or a minimal Lefschetz ... More

Incompressible Modes Excited by Supersonic Shear in Boundary Layers: Acoustic CFS InstabilityOct 13 2016We present an instability for exciting incompressible modes (e.g. gravity or Rossby modes) at the surface of a star accreting through a boundary layer. The instability excites a stellar mode by sourcing an acoustic wave in the disk at the boundary layer, ... More

Maximal metrics for the first Steklov eigenvalue on surfacesJan 22 2018In recent years, eigenvalue optimization problems have received a lot of attention, in particular, due to their connection with the theory of minimal surfaces. In the present paper we prove that on any orientable surface there exists a smooth metric maximizing ... More

Beam Dynamics Studies at DAFNE: from Ideas to Experimental ResultsMay 17 2017DAFNE is the electron-positron collider operating at the energy of Phi-resonance, 1 GeV in the center of mass. The presently achieved luminosity is by about two orders of magnitude higher than that obtained at other colliders ever operated at this energy. ... More

Teaching Physics at School and CollegesFeb 08 2019Invited contribution to the inaugural issue of {\em Physics Educator.}

Tau function and moduli of spin curvesMay 30 2014The goal of the paper is to give an analytic proof of the formula of G. Farkas for the divisor class of spinors with multiple zeros in the moduli space of odd spin curves. We make use of the technique developed by Korotkin and Zograf that is based on ... More

Geometric Estimates in Interpolation by Linear Functions on an Euclidean BallMay 09 2019Let $B_n$ be the Euclidean unit ball in ${\mathbb R}^n$ given by the inequality $\|x\|\leq 1$, $\|x\|:=\left(\sum\limits_{i=1}^n x_i^2\right)^{\frac{1}{2}}$. By $C(B_n)$ we mean the space of continuous functions $f:B_n\to{\mathbb R}$ with the norm $\|f\|_{C(B_n)} ... More

Birational rigidity of a three-dimensional double coneAug 31 1998It is proved that a three-dimensional double cone is a birationally rigid variety. We also compute the group of birational automorphisms of such a variety. This work is based on the method of "untwisting" maximal singularities of linear system.

Birational automorphisms of a three-dimensional double quadric with an elementary singularityAug 17 1998It is proved that the group of birational automorphisms of a three-dimensional double quadric with a singular point arising from a double point on the branch divisor is a semidirect product of the free group generated by birational involutions of a special ... More

Variational evolution problems and nonlocal geometric motionOct 05 1997We consider two variational evolution problems related to Monge-Kantorovich mass transfer. These problems provide models for collapsing sandpiles and for compression molding. We prove the following connection between these problems and nonlocal geometric ... More

An invariant of tangle cobordismsJul 28 2002We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.

Birational models of del Pezzo fibrationsSep 27 2002This is a preliminary version of the paper for the Lecture Notes Series.

The Riemann problem with additional singularitiesOct 22 2001The Riemann problem is studied in the case when the unknown function has nonisolated singularities, concentrated on the real axis. The problem is used for the factorization of functions, holomorphic outside of the unit circle and the real axis, in the ... More

The group SU_3 is CayleyNov 19 2012Dec 08 2012A linear algebraic group G is over a field K is called a Cayley group if it admits a Cayley map, i.e., a G-equivariant K-birational isomorphism between the group variety G and its Lie algebra. We prove that the special unitary group in 3 variables SU_3 ... More

Linearization and categorificationMar 27 2016We discuss the notion of linearization through examples, which include the Price map, PageRank, representation theory, the Euler characteristic and quantum invariants. We also review categorification, which adds an additional layer of structure, in the ... More

Categorifications of the colored Jones polynomialFeb 06 2003The colored Jones polynomial of links has two natural normalizations: one in which the n-colored unknot evaluates to [n+1], the quantum dimension of the (n+1)-dimensional irreducible representation of quantum sl(2), and the other in which it evaluates ... More

Index of minimal spheres and isoperimetric eigenvalue inequalitiesMay 08 2019In the present paper we use twistor theory in order to solve two problems related to harmonic maps from surfaces to Euclidean spheres $\mathbb{S}^n$. First, we propose a new approach to isoperimetric inequalities based on energy index. Using this approach ... More

Geometric Estimates in Interpolation by Linear Functions on a Euclidean BallMay 09 2019May 11 2019Let $B_n$ be the Euclidean unit ball in ${\mathbb R}^n$ given by the inequality $\|x\|\leq 1$, $\|x\|:=\left(\sum\limits_{i=1}^n x_i^2\right)^{\frac{1}{2}}$. By $C(B_n)$ we mean the space of continuous functions $f:B_n\to{\mathbb R}$ with the norm $\|f\|_{C(B_n)} ... More

Defect of an octahedron in a rational latticeApr 22 2018Consider an arbitrary $n$-dimensional lattice $\Lambda$ such that $\mathbb{Z}^n \subset \Lambda \subset \mathbb{Q}^n$. Such lattices are called {\it rational} and can always be obtained by adding $m \le n$ rational vectors to $\mathbb{Z}^n$. {\it Defect ... More

Packing a cake into a boxMar 10 2010Given a cake in form of a triangle and a box that fits the mirror image of the cake, how to cut the cake into a minimal number of pieces so that it can be put into the box? The cake has an icing, so that we are not allowed to put it into the box upside ... More

On the number of real critical points of logarithmic derivatives and the Hawaii conjectureFeb 03 2009Jan 23 2011For a given real entire function $\phi$ with finitely many nonreal zeros, we establish a connection between the number of real zeros of the functions $Q=(\phi'/\phi)'$ and $Q_1=(\phi''/\phi')'$. This connection leads to a proof of the Hawaii conjecture ... More

Recent results of the DANSS experimentNov 18 2018DANSS is a one cubic meter highly segmented plastic scintillator detector. Its 2500 one meter long scintillator strips have a Gd-loaded reflective cover. The DANSS detector is placed under an industrial 3.1GW reactor of the Kalinin Nuclear Power plant ... More

Noncommutative Algebras, Nano-Structures, and Quantum Dynamics Generated by ResonancesDec 30 2004May 27 2005We observe ``quantum'' properties of resonance equilibrium points and resonance univariant submanifolds in the phase space. Resonances between Birkhoff or Floquet--Lyapunov frequencies generate quantum algebras with polynomial commutation relations. Irreducible ... More

A simple closed curve in $\mathbb{R}^3$ whose convex hull equals the half-sum of the curve with itselfJul 22 2018If $\Gamma$ is the range of a Jordan curve that bounds a convex set in $\mathbb{R}^2,$ then $\frac{1}{2}(\Gamma+\Gamma)=\mathsf{co}(\Gamma),$ where $+$ is the Minkowski sum and $\mathsf{co}$ is the convex hull. Answering a question of V.N. Ushakov, we ... More

On the spectra of Schwarz matrices with certain sign patternsJan 03 2012The direct and inverse spectral problems are solved for a wide subclass of the class of Schwarz matrices. A connection between the Schwarz matrices and the so-called generalized Hurwitz polynomials is found. The known results due to H. Wall and O. Holtz ... More

Dimensions of the Ascending and Descending Sets in Complex Stratified Morse TheoryMay 25 2010We present a new construction of gradient-like vector fields in the setting of Morse theory on a complex analytic stratification. We prove that the ascending and descending sets for these vector fields possess cell decompositions satisfying the dimension ... More

Affine lines on {\bf Q}-homology planes and group actionsNov 11 2006This note is a supplement to the papers: R. V. Gurjar, K. Masuda, M. Miyanishi and P. Russell, Affine lines on affine surfaces and the Makar-Limanov invariant, preprint, 2005, 42p. and T. Kishimoto and H. Kojima, Affine lines on {\bf Q}-homology planes ... More

Extending the exact sequence of nonabelian $H^1$, using nonabelian $H^2$ with coefficients in crossed modulesAug 26 2016Dec 08 2017In this note, following Dedecker and Debremaeker, we extend the cohomology exact sequence for nonabelian $H^1$, using nonabelian $H^2$ with coefficients in crossed modules.

On One Property of Tikhonov Regularization AlgorithmApr 23 2017Jun 07 2017For linear inverse problem with Gaussian random noise we show that Tikhonov regularization algorithm is minimax in the class of linear estimators and is asymptotically minimax in the sense of sharp asymptotic in the class of all estimators. The results ... More

Existence of equivariant models of G-varietiesApr 23 2018May 12 2018Let k_0 be a field of characteristic 0, and let k be a fixed algebraic closure of k_0. Let G be an algebraic k-group, and let Y be a G-variety over k. Let G_0 be a k_0 -model (k_0 -form) of G. We ask whether Y admits a G_0 -equivariant k_0 -model Y_0 ... More