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Hilbert series of nearly holomorphic sections on generalized flag manifoldsMar 12 2014Apr 09 2014Let X=G/P be a complex flag manifold and E->X be a G-homogeneous holomorphic vector bundle. Fix a U-invariant Kaehler metric on X with U in G maximal compact. We study the sheaf of nearly holomorphic sections and show that the space of global nearly holomorphic ... More

Nearly holomorphic sections on compact Hermitian symmetric spacesSep 11 2012Let X be a K\"ahler manifold, and E be a Hermitian vector bundle on X. We investigate the space N(X,E) of nearly holomorphic sections in E, which generalizes the notion of nearly holomorphic functions introduced by Shimura. If X=U/K is a compact Hermitian ... More

Higher Laplacians on pseudo-Hermitian symmetric spacesOct 14 2014Let $X=G/H$ be a symmetric space for a real simple Lie group $G$, equipped with a $G$-invariant complex structure. Then, $X$ is a pseudo-Hermitian manifold, and in this geometric setting, higher Laplacians $L_m$ are defined for each positive integer $m$, ... More

An exponential time upper bound for Quantum Merlin-Arthur games with unentangled proversOct 28 2015We prove a deterministic exponential time upper bound for Quantum Merlin-Arthur games with k unentangled provers. This is the first non-trivial upper bound of QMA(k) better than NEXP and can be considered an exponential improvement, unless EXP=NEXP. The ... More

An exponential time upper bound for Quantum Merlin-Arthur games with unentangled proversOct 28 2015Nov 28 2016We prove a deterministic exponential time upper bound for Quantum Merlin-Arthur games with k unentangled provers. This is the first non-trivial upper bound of QMA(k) better than NEXP and can be considered an exponential improvement, unless EXP=NEXP. The ... More

Equivalences for Morse homologyMay 25 1999An explicit isomorphism between Morse homology and singular homology is constructed via the technique of pseudo-cycles. Given a Morse cycle as a formal sum of critical points of a Morse function, the unstable manifolds for the negative gradient flow are ... More

Existence of nearly holomorphic sections on compact Hermitian symmetric spacesMar 11 2013Let $X=U/K$ be a compact Hermitian symmetric space, and let $\sE$ be a $U$-homogeneous Hermitian vector bundle on $X$. In a previous paper, we showed that the space of nearly holomorphic sections is well-adapted for harmonic analysis in $L^2(X,\sE)$ provided ... More

Cellular Network Architectures for the Society in MotionAug 30 2017Due to rising mobility worldwide, a growing number of people utilizes cellular network services while on the move. Persistent urbanization trends raise the number of daily commuters, leading to a situation where telecommunication requirements are mainly ... More

Quotients, automorphisms and differential operatorsJan 30 2012Jun 29 2013Let $V$ be a $G$-module where $G$ is a complex reductive group. Let $Z:=\quot VG$ denote the categorical quotient and let $\pi\colon V\to Z$ be the morphism dual to the inclusion $\O(V)^G\subset\O(V)$. Let $\phi\colon Z\to Z$ be an algebraic automorphism. ... More

Structure of the degenerate principal series on symmetric R-spaces and small representationsDec 14 2012Jan 06 2014Let $G$ be a simple real Lie group with maximal parabolic subgroup $P$ whose nilradical is abelian. Then $X=G/P$ is called a symmetric $R$-space. We study the degenerate principal series representations of $G$ on $C^\infty(X)$ in the case where $P$ is ... More

From Superstrings to M TheoryDec 08 1998In this talk I will survey some of the basic facts about superstring theories in 10 dimensions and the dualities that relate them to M theory in 11 dimensions. Then I will mention some important unresolved issues.

The Power of M TheoryOct 12 1995A proposed duality between type IIB superstring theory on R^9 X S^1 and a conjectured 11D fundamental theory (``M theory'') on R^9 X T^2 is investigated. Simple heuristic reasoning leads to a consistent picture relating the various p-branes and their ... More

Superstring DualitiesSep 26 1995Oct 09 1995This talk is divided into two parts. The first part reviews some of the duality relationships between superstring theories. These relationships are interpreted as providing evidence for the existence of a unique underlying fundamental theory. The second ... More

Update on String TheoryApr 28 2003The first part of this report gives a very quick sketch of how string theory concepts originated and evolved during its first 25 years (1968-93). The second part presents a somewhat more detailed discussion of the highlights of the past decade. The final ... More

Comments on Born-Infeld TheoryMar 20 2001The low-energy effective action of supersymmetric D-brane systems consists of two terms, one of which is of the Born-Infeld type and one of which is of the Chern-Simons type. I briefly review the status of our understanding of these terms for both the ... More

Remarks on Non-BPS D-BranesAug 12 1999Following Sen's discovery of various stable non-BPS D-branes, K-theory has been shown to be the appropriate mathematical framework for classifying conserved D-brane charges. The classification accounts for known D-branes and predicts some new ones including ... More

Beyond Gauge TheoriesJul 27 1998Sep 01 1998Superstring theory, and a recent extension called M theory, are leading candidates for a quantum theory that unifies gravity with the other forces. As such, they are certainly not ordinary quantum field theories. However, recent duality conjectures suggest ... More

Symplectic branching laws and Hermitian symmetric spacesOct 28 2011Let $G$ be a complex simple Lie group, and let $U \subseteq G$ be a maximal compact subgroup. Assume that $G$ admits a homogenous space $X=G/Q=U/K$ which is a compact Hermitian symmetric space. Let $\mathscr{L} \rightarrow X$ be the ample line bundle ... More

Linear maps preserving fibersSep 14 2007Jan 18 2008Let $G\subset\GL(V)$ be a complex reductive group where $\dim V<\infty$, and let $\pi\colon V\to\quot VG$ be the categorical quotient. Let $\NN:=\pi\inv\pi(0)$ be the null cone of $V$, let $H_0$ be the subgroup of $\GL(V)$ which preserves the ideal $\I$ ... More

Linear maps preserving invariantsAug 21 2007Nov 13 2007Let $G\subset\GL(V)$ be a complex reductive group. Let $G'$ denote $\{\phi\in\GL(V)\mid p\circ\phi=p\text{for all} p\in\C[V]^G\}$. We show that, in general, $G'=G$. In case $G$ is the adjoint group of a simple Lie algebra $\lieg$, we show that $G'$ is ... More

Lifting automorphisms of quotients of adjoint representationsJan 26 2013Nov 24 2013Let $\mathfrak g_i$ be a simple complex Lie algebra, $1\leq i \leq d$, and let $G=G_1\times...\times G_d$ be the corresponding adjoint group. Consider the $G$-module $V=\oplus r_i\mathfrak g_i$ where $r_i\geq 1$ for all $i$. We say that $V$ is \emph{large} ... More

Algebras of invariant differential operatorsApr 13 2018Apr 17 2018We prove that an invariant subalgebra A_n^W of the Weyl algebra A_n is a Galois order over an adequate commutative subalgebra \Gamma when W is a two-parameters irreducible unitary reflection group G(m,1,n), m\geq 1, n\geq 1, including the Weyl group of ... More

The Kazdan-Warner equation on canonically compactifiable graphsJul 26 2017We study the Kazdan-Warner equation on canonically compactifiable graphs. These graphs are distinguished as analytic properties of Laplacians on these graphs carry a strong resemblance to Laplacians on open pre-compact manifolds.

Adaptive circular deconvolution by model selection under unknown error distributionDec 07 2009Dec 10 2013We consider a circular deconvolution problem, in which the density $f$ of a circular random variable $X$ must be estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y$ of $X$. The additive measurement error is supposed to be ... More

On the Floer homology of cotangent bundlesAug 20 2004Feb 24 2005This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle of a compact orientable manifold M. The first result is a new uniform estimate for the solutions of the Floer equation, which allows ... More

Courant's Nodal Domain Theorem for Positivity Preserving FormsDec 20 2017We introduce a notion of nodal domains for positivity preserving forms. This notion generalizes the classical ones for Laplacians on domains and on graphs. We prove the Courant nodal domain theorem in this generalized setting using purely analytical methods. ... More

Partially adaptive nonparametric instrumental regressionMar 16 2010Apr 10 2012We consider the problem of estimating the structural function in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The proposed estimator is based ... More

Estimates and computations in Rabinowitz-Floer homologyJul 11 2009Dec 06 2009The Rabinowitz-Floer homology of a Liouville domain W is the Floer homology of the free period Hamiltonian action functional associated to a Hamiltonian whose zero energy level is the boundary of W. It has been introduced by K. Cieliebak and U. Frauenfelder. ... More

A smooth pseudo-gradient for the Lagrangian action functionalDec 23 2008Nov 04 2009We study the action functional associated to a smooth Lagrangian function on the cotangent bundle of a manifold, having quadratic growth in the velocities. We show that, although the action functional is in general not twice differentiable on the Hilbert ... More

On the Measurability of Stochastic Fourier Integral OperatorsMar 15 2019This work deals with the measurability of Fourier integral operators (FIOs) with random phase and amplitude functions. The key ingredient is the proof that FIOs depend continuously on their phase and amplitude functions, taken from suitable classes. The ... More

Deterministic and stochastic damage detection via dynamic response analysisMay 31 2019The paper proposes a method of damage detection in elastic materials, which is based on analyzing the time-dependent (dynamic) response of the material excited by an acoustic signal. Starting from a mathematical model of the acoustic wave, we calibrate ... More

Vector Fields and Luna StrataOct 16 2011May 23 2012Let V be a G-module where G is a complex reductive group. Let Z:=V//G denote the categorical quotient. One can ask if the Luna stratification of Z is intrinsic. That is, if phi : Z\to Z is any automorphism, does phi send strata to strata? In a paper of ... More

Linear maps preserving orbitsOct 07 2009Nov 03 2010Let H\subset\GL(V) be a connected complex reductive group where V is a finite-dimensional complex vector space. Let v\in V and let G=\{g\in\GL(V)\mid gHv = Hv\}. Following Ra\"is we say that the orbit Hv is \emph{characteristic for H} if the identity ... More

On non-overdetermined inverse scattering at zero energy in three dimensionsMay 31 2006We develop the d-bar -approach to inverse scattering at zero energy in dimensions d>=3 of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability ... More

Absence of exponentially localized solitons for the Novikov-Veselov equation at positive energyOct 05 2010Jan 24 2011In this note we show that the Novikov-Veselov equation at positive energy (an analog of KdV in 2+1 dimensions) has no exponentially localized solitons ( in the two-dimensional sense).

Understanding Gravitational Clustering with Non-Linear Perturbation TheoryFeb 21 1997I discuss new results concerning the evolution of the bispectrum due to gravitational instability from gaussian initial conditions using one-loop perturbation theory (PT). Particular attention is paid to the transition from weakly non-linear scales to ... More

Large-Scale Structure in Brane-Induced Gravity I. Perturbation TheoryJun 24 2009Jul 19 2009We study the growth of subhorizon perturbations in brane-induced gravity using perturbation theory. We solve for the linear evolution of perturbations taking advantage of the symmetry under gauge transformations along the extra-dimension to decouple the ... More

Cosmological Perturbations: Entering the Non-Linear RegimeDec 21 1996We consider one-loop corrections to the bispectrum and skewness of cosmological density fluctuations induced by gravitational evolution. As has been established by comparison with numerical simulations, tree-level perturbation theory (PT) describes these ... More

Noncommutative Counterparts of the Springer ResolutionApr 20 2006Springer resolution of the set of nilpotent elements in a semisimple Lie algebra plays a central role in geometric representation theory. A new structure on this variety has arisen in several representation theoretic constructions, such as the (local) ... More

Cohomology of tilting modules over quantum groups and $t$-structures on derived categories of coherent sheavesFeb 28 2004Feb 21 2006The paper is concerned with cohomology of the small quantum group at a root of unity, and of its upper triangular subalgebra, with coefficients in a tilting module. We relate it to a certain t-structure on the derived category of equivariant coherent ... More

Quasi-exceptional sets and equivariant coherent sheaves on the nilpotent coneFeb 06 2001In math.AG/0005152 a certain $t$-structure on the derived category of equivariant coherent sheaves on the nil-cone of a simple complex algebraic group was introduced (the so-called perverse $t$-structure corresponding to the middle perversity). In the ... More

Pilot Wave model that includes creation and annihilation of particlesNov 12 2010Nov 16 2010The purpose of this paper is to come up with a Pilot Wave model of quantum field theory that incorporates particle creation and annihilation without sacrificing determinism. This has been previously attempted in an article by the same author titled "Incorporating ... More

Spinor fields in Causal Set TheoryAug 21 2008The goal of this paper is to define fermionic fields on causal set. This is done by the use of holonomies to define vierbines, and then defining spinor fields by taking advantage of the leftover degrees of freedom of holonomies plus additional scalar ... More

Universal geometric entanglement close to quantum phase transitionsNov 16 2007Mar 24 2008Under successive Renormalization Group transformations applied to a quantum state $\ket{\Psi}$ of finite correlation length $\xi$, there is typically a loss of entanglement after each iteration. How good it is then to replace $\ket{\Psi}$ by a product ... More

Proving Craig and Lyndon Interpolation Using Labelled Sequent CalculiJan 21 2016We have recently presented a general method of proving the fundamental logical properties of Craig and Lyndon Interpolation (IPs) by induction on derivations in a wide class of internal sequent calculi, including sequents, hypersequents, and nested sequents. ... More

Falsification or Confirmation: From Logic to PsychologyOct 30 2015Corroboration or confirmation is a prominent philosophical debate of the 20th century. Many philosophers have been involved in this debate most notably the proponents of confirmation led by Hempel and its most powerful criticism by the falsificationists ... More

Formulas for phase recovering from phaseless scattering data at fixed frequencyFeb 08 2015Feb 14 2015We consider quantum and acoustic wave propagation at fixed frequency for compactly supported scatterers in dimension $d\ge 2$. In these framework we give explicit formulas for phase recovering from appropriate phaseless scattering data. As a corollary, ... More

Explicit formulas and global uniqueness for phaseless inverse scattering in multidimensionsDec 16 2014We consider phaseless inverse scattering for the Schr\"odinger equation with compactly supported potential in dimension $d\ge 2$. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we give also a ... More

Expressing QFT in terms of QM with single extra dimension and classical hidden variable fieldSep 12 2013Oct 30 2015The goal of this paper is to re-express QFT in terms of two "classical" fields living in ordinary space with single extra dimension. The role of the first classical field is to set up an injection from the set of values of extra dimension into the set ... More

Approximating the moments of marginals of high-dimensional distributionsNov 02 2009Nov 16 2012For probability distributions on $\mathbb{R}^n$, we study the optimal sample size N = N(n,p) that suffices to uniformly approximate the pth moments of all one-dimensional marginals. Under the assumption that the marginals have bounded 4p moments, we obtain ... More

Some problems in asymptotic convex geometry and random matrices motivated by numerical algorithmsMar 19 2007The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions -- computing the size of projections of high dimensional polytopes and estimating ... More

Upper bounds on the rate of quantum ergodicityMar 17 2005We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation of an upper ... More

Conservation laws of semidiscrete canonical Hamiltonian equationsFeb 25 2004There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs. The same result holds for semidiscrete Hamiltonian ... More

Universality in Gaussian Random Normal MatricesNov 30 2013We prove that for Gaussian random normal matrices the correlation function has universal behavior. Using the technique of orthogonal polynomials and identities similar to the Christoffel-Darboux formula, we find that in the limit, as the dimension of ... More

Invertibility of symmetric random matricesFeb 01 2011Mar 16 2012We study n by n symmetric random matrices H, possibly discrete, with iid above-diagonal entries. We show that H is singular with probability at most exp(-n^c), and the spectral norm of the inverse of H is O(sqrt{n}). Furthermore, the spectrum of H is ... More

The use of test functions to help define quadratic Lagrangian on a causal setJul 12 2018In some other papers, the Lagrangians in the causal sets included coefficients that were to be computed by integrating over Alexandrov set. In those other papers, this integral was explicitly evaluated, which resulted in rather sophisticated expressions. ... More

NuSTAR observation of the Arches cluster: X-ray spectrum extraction from a 2D imageAug 31 2017The NuSTAR mission performed a long (200 ks) observation of the Arches stellar cluster in 2015. The emission from the cluster represents a mixture of bright thermal (kT~2 keV) X-rays and the extended non-thermal radiation of the molecular cloud around ... More

Canonical bases for sl(2,C)-modules of spherical monogenics in dimension 3Mar 29 2010Jun 17 2010Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as sl(2,C)-modules. As finite-dimensional irreducible sl(2,C)-modules, they have canonical bases which are, by construction, orthogonal. In this note, we show that these ... More

The Fischer Decomposition for the H-action and Its ApplicationsFeb 02 2010Recently the Fischer decomposition for the H-action of the Pin group on Clifford algebra valued polynomials has been obtained. We apply this tool to get various decompositions of special monogenic and inframonogenic polynomials in terms of two sided monogenic ... More

Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spacesNov 03 2011Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly described for the spaces of k-homogeneous polynomial solutions of the Hodge-de Rham system in the Euclidean space R^m which take values in the space of s-vectors. In this ... More

Strongly solvable spherical subgroups and their combinatorial invariantsDec 13 2012Mar 26 2015A subgroup H of an algebraic group G is said to be strongly solvable if H is contained in a Borel subgroup of G. This paper is devoted to establishing relationships between the following three combinatorial classifications of strongly solvable spherical ... More

On the solutions of generalized discrete Poisson equationJun 19 2007The set of common numerical and analytical problems is introduced in the form of the generalized multidimensional discrete Poisson equation. It is shown that its solutions with square-summable discrete derivatives are unique up to a constant. The proof ... More

A Model Structure On The Category Of Small Acyclic CategoriesAug 05 2015In this paper, we show that the Thomason model structure restricts to a Quillen equivalent cofibrantly generated model structure on the category of acyclic categories, whose generating cofibrations are the same as those generating the Thomason model structure. ... More

Finite speed of propagation for the thin film equation in spherical geometryFeb 06 2018We show that a double degenerate thin film equation, which originated from modeling of viscous coating flow on a spherical surface, has finite speed of propagation for nonnegative strong solutions and hence there exists an interface or free boundary separating ... More

On the Role of Sparsity in Compressed Sensing and Random Matrix TheoryAug 03 2009We discuss applications of some concepts of Compressed Sensing in the recent work on invertibility of random matrices due to Rudelson and the author. We sketch an argument leading to the optimal bound N^{-1/2} on the median of the smallest singular value ... More

Jet Production at Low and High $Q^2$ and Determination of the Strong Coupling $α_s$ at H1Jun 21 2010Two recent measurements of inclusive jet, 2-jet and 3-jet cross sections in deep-inelastic $ep$ scattering from the H1 collaboration are presented. The measurements are performed at low $5<Q^2<100$ GeV$^2$ and high $150<Q^2<15000$ GeV$^2$ virtualities ... More

Gauge Theories for Gravity on a LineJun 24 1992Professor M. C. Polivanov and I met only a few times, during my infrequent visits to the-then Soviet Union in the 1970's and 1980's. His hospitality at the Moscow Steclov Institute made the trips a pleasure, while the scientific environment that he provided ... More

On the splitting of polynomial functorsFeb 03 2012Oct 04 2012We develop methods for proving that certain extensions of polynomial functors do not split naturally. As an application we give a functorial description of the third and the fourth stable homotopy groups of the classifying spaces of free abelian groups. ... More

On the homology of the dual de Rham complexJan 18 2010We study the homology of the dual de Rham complex as functors on the category of abelian groups. We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a corrected version of the proof of Jean's ... More

Conditional symmetries for systems of PDEs: new definitions and their application for reaction-diffusion systemsMay 20 2010Sep 20 2010New definitions of $Q$-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that different types of $Q$-conditional symmetry of a system generate a hierarchy ... More

Affine Grassmannians of group schemes and exotic principal bundles over A^1Aug 14 2013Jan 16 2014Let G be a simple simply-connected group scheme over a regular local scheme U. Let E be a principal G-bundle over A^1_U trivial away from a subscheme finite over U. We show that E is not necessarily trivial and give some criteria of triviality. To this ... More

Perverse sheaves on affine flags and nilpotent cone of the Langlands dual groupJan 27 2002Sep 04 2007In math.RT/0201073 we constructed an equivalence between the derived category of equivariant coherent sheaves on the cotangent bundle to the flag variety of a simple algebraic group and a (quotient of) the category of constructible sheaves on the affine ... More

Perverse coherent sheaves (after Deligne)May 16 2000Jun 23 2010This note is mostly an exposition of an unpublished result of Deligne, which introduces an analogue of perverse $t$-structure on the derived category of coherent sheaves on a Noetherian scheme with a dualizing complex. Construction extends to the category ... More

The Bispectrum: From Theory to ObservationsApr 06 2000Jul 05 2000The bispectrum is the lowest-order statistic sensitive to the shape of structures generated by gravitational instability and is a potentially powerful probe of galaxy biasing and the Gaussianity of primordial fluctuations. Although the evolution of the ... More

Gravitational Clustering from Chi^2 Initial ConditionsFeb 01 2000Jun 13 2001We consider gravitational clustering from primoridal non-Gaussian fluctuations provided by a $\chi^2$ model, as motivated by some models of inflation. The emphasis is in signatures that can be used to constrain this type of models from large-scale structure ... More

Redshift Distortions: Perturbative and N-body ResultsAug 10 1998I discuss the evolution of the redshift-space bispectrum via perturbation theory (PT) and large high-resolution numerical simulations. At large scales, we give the multipole expansion of the bispectrum in PT, which provides a natural way to break the ... More

Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systemsDec 18 2011May 03 2012In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite size. This ... More

Ph.D. Thesis: Quantum Field Theory and Gravity in Causal SetsMay 14 2009This is is a copy of dissertation that I have submitted in defense of my ph.d. thesis, with some minor changes that I have made since then. The goal of the project is to generalize matter fields and their Lagrangians from regular space time to causal ... More

Novel definition of Grassmann numbers and spinor fieldsAug 06 2008May 25 2009The goal of this paper is to define fermionic field in terms of non-orthonormal vierbeins, where fluctuations away from orthonormality are viewed as fermionic field. Furthermore, Grassmann numbers are defined in a way that makes literal sense.

Gauge Fields in Causal Set TheoryJul 13 2008This is the second paper in a series on the dynamics of matter fields in the causal set approach to quantum gravity. We start with the usual expression for the Lagrangian of a charged scalar field coupled to a SU(n) Yang-Mills field, in which the gauge ... More

Use of sphere and curves to define Berezin integralAug 18 2009Sep 09 2015In this paper we will describe various ways of describing Berezin integral as a literal limit of the sum taken either over a surface (in our case, a sphere) or a curve.

Mountain Peak Detection in Online Social MediaAug 12 2015We present a system for the classification of mountain panoramas from user-generated photographs followed by identification and extraction of mountain peaks from those panoramas. We have developed an automatic technique that, given as input a geo-tagged ... More

On the Grothendieck-Serre conjecture on principal bundles in mixed characteristicJan 17 2015Nov 13 2016Let R be a regular local ring. Let G be a reductive R-group scheme. A conjecture of Grothendieck and Serre predicts that a principal G-bundle over R is trivial if it is trivial over the quotient field of R. The conjecture is known when R contains a field. ... More

Market selection with learning and catching up with the JonesesJun 15 2011Jan 15 2012We study the market selection hypothesis in complete financial markets, populated by heterogeneous agents. We allow for a rich structure of heterogeneity: individuals may differ in their beliefs concerning the economy, information and learning mechanism, ... More

The tie theoremsNov 15 2014Nov 29 2014Theorem. There are general position points A, B, C, P on the projective plane. Let A_P be the intersection point of lines AP and BC. Analogously define B_P and C_P. Take any points A_1, B_1, C_1 on AP, BP, CP, respectively. Let W_C be the intersection ... More

L^2-Betti Numbers of Discrete Measured GroupoidsDec 22 2003There are notions of L^2-Betti numbers for discrete groups (Cheeger-Gromov, Lueck), for type II_1-factors (recent work of Connes-Shlyakhtenko) and for countable standard equivalence relations (Gaboriau). Whereas the first two are algebraically defined ... More

Integer cells in convex setsMar 16 2004Nov 04 2004Every convex body K in R^n has a coordinate projection PK that contains at least vol(0.1 K) cells of the integer lattice PZ^n, provided this volume is at least one. Our proof of this counterpart of Minkowski's theorem is based on an extension of the combinatorial ... More

A geometric condition implying energy equality for solutions of 3D Navier-Stokes equationMar 13 2008We prove that every weak solution $u$ to the 3D Navier-Stokes equation that belongs to the class $L^3L^{9/2}$ and $\n u$ belongs to $L^3L^{9/5}$ localy away from a 1/2-H\"{o}lder continuous curve in time satisfies the generalized energy equality. In particular ... More

Additive habits with power utility: Estimates, asymptotics and equilibriumAug 14 2011We consider a power utility maximization problem with additive habits in a framework of discrete-time markets and random endowments. For certain classes of incomplete markets, we establish estimates for the optimal consumption stream in terms of the aggregate ... More

Quantum State Tomography of a Single Qubit: Comparison of MethodsJul 17 2014Feb 08 2016The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical density matrix ... More

Electrostatics of Gapped and Finite Surface ElectrodesOct 23 2009Jan 30 2010We present approximate methods for calculating the three-dimensional electric potentials of finite surface electrodes including gaps between electrodes, and estimate the effects of finite electrode thickness and an underlying dielectric substrate. As ... More

On the energy of inviscid singular flowsMar 13 2008It is known that the energy of a weak solution to the Euler equation is conserved if it is slightly more regular than the Besov space $B^{1/3}_{3,\infty}$. When the singular set of the solution is (or belongs to) a smooth manifold, we derive various $L^p$-space ... More

On the Grothendieck-Serre Conjecture about principal bundles and its generalizationsOct 28 2018Let $U$ be a regular connected semi-local scheme over a field $k$. Let $G$ be a reductive group scheme over $U$. Then a principal $G$-bundle over $U$ is trivial, if it is rationally trivial. We give a direct proof of this statement without reducing first ... More

An Efficient Algorithm for the Multicomponent Compressible Navier-Stokes Equations in Low- and High-Mach Number RegimesNov 16 2017Oct 02 2018The goal of this study is to develop an efficient numerical algorithm applicable to a wide range of compressible multicomponent flows. Although many highly efficient algorithms have been proposed for simulating each type of the flows, the construction ... More

On algebras generated by positive operatorsOct 24 2017We study algebras generated by positive matrices, i.e., matrices with nonnegative entries. Some of our results hold in more general setting of vector lattices. We reprove and extend some theorems that have been recently shown by Kandi\'{c} and \v{S}ivic. ... More

Center Vortices and Topological ChargeJun 16 2017Jul 24 2017I review important aspects of the relation between center vortices and topological charge, leading to chiral symmetry breaking.

\b{eta}-KMS Green functions generating functionals - the convexity based approachMar 26 2018The notion of the stochastically positive \b{eta}-KMS (Euclidean time ) Green functionals on ( the abelian sectors of ) the CCR-algebras in Weyl form has been introduced .The main observation is that the essential properties of such functionals are stable ... More

On order automorphisms of the effect algebraMar 02 2018We give short proofs of two \v{S}emrl's descriptions of order automorphisms of the effect algebra. This sheds new light on both formulas that look quite complicated. Our proofs rely on Moln\'{a}r's characterization of order automorphisms of the cone of ... More

A new algebraic approach to the graph isomorphism and clique problemsMay 14 2019As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually this fundamental principle can be efficiently applicable in Computational Mathematics ... More

Concentration inequalities for random tensorsMay 02 2019We show how to extend several basic concentration inequalities for simple random tensors $X = x_1 \otimes \cdots \otimes x_d$ where all $x_k$ are independent random vectors in $\mathbb{R}^n$ with independent coefficients. The new results have optimal ... More