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Multiple Lattice Rules for Multivariate $L_\infty$ Approximation in the Worst-Case SettingSep 05 2019We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are trigonometric polynomials ... More

Spectral properties of graphs associated to the Basilica groupAug 28 2019We provide the foundation of the spectral analysis of the Laplacian on the orbital Schreier graphs of the basilica group, the iterated monodromy group of the quadratic polynomial $z^2-1$. This group is an important example in the class of self-similar ... More

On the trend to global equilibrium for Kuramoto OscillatorsAug 21 2019In this paper, we study the convergence to the stable equilibrium for Kuramoto oscillators. Specifically, we derive estimates on the rate of convergence to the global equilibrium for solutions of the Kuramoto-Sakaguchi equation in a large coupling strength ... More

Curvature properties of Melvin magnetic metricAug 20 2019This paper aims to investigate the curvature restricted geometric properties admitted by Melvin magnetic spacetime metric, a warped product metric with $1$-dimensional fibre. For this, we have considered a Melvin type static, cylindrically symmetric spacetime ... More

Optimal Control for Chemotaxis Systems and Adjoint-Based Optimization with Multiple-Relaxation-Time Lattice Boltzmann ModelsAug 11 2019This paper is devoted to continuous and discrete adjoint-based optimization approaches for optimal control problems governed by an important class of Nonlinear Coupled Anisotropic Convection-Diffusion Chemotaxis-type System (NCACDCS). This study is motivated ... More

Structure of Finite-Dimensional ProtoriAug 08 2019A Structure Theorem for Protori is derived for the category of finite-dimensional protori(compact connected abelian groups), which details the interplay between the properties of density, discreteness, torsion, and divisibility within a finite-dimensional ... More

Modeling random traffic accidents by conservation lawsJul 31 2019We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents and is based on a scalar conservation law with space-dependent flux function. ... More

Multiple asymptotics of Kinetic Equations with Internal StatesJul 25 2019The run and tumble process is well established in order to describe the movement of bacteria in response to a chemical stimulus. However the relation between the tumbling rate and the internal state of bacteria is poorly understood. The present study ... More

Tracking Holistic Object RepresentationsJul 21 2019Recent advances in visual tracking are based on siamese feature extractors and template matching. For this category of trackers, latest research focuses on better feature embeddings and similarity measures. In this work, we focus on building holistic ... More

Tracking Holistic Object RepresentationsJul 21 2019Aug 06 2019Recent advances in visual tracking are based on siamese feature extractors and template matching. For this category of trackers, latest research focuses on better feature embeddings and similarity measures. In this work, we focus on building holistic ... More

Asymptotic analysis of exit time for dynamical systems with a single well potentialJun 11 2019We study the exit time from a bounded multi-dimensional domain $\Omega$ of the stochastic process $\mathbf{Y}_\varepsilon=\mathbf{Y}_\varepsilon(t,a)$, $t\geqslant 0$, $a\in \mathcal{A}$, governed by the overdamped Langevin dynamics \begin{equation*} ... More

Study of semi-linear $σ$-evolution equations with frictional and visco-elastic dampingJun 11 2019In this article, we study semi-linear $\sigma$-evolution equations with double damping including frictional and visco-elastic damping for any $\sigma\ge 1$. We are interested in investigating not only higher order asymptotic expansions of solutions but ... More

Generalizations of the Drift Laplace Equation in the Heisenberg Group and a Class of Grushin-Type SpacesJun 03 2019We find fundamental solutions to p-Laplace equations with drift terms in the Heisenberg group and Grushin-type planes. These solutions are natural generalizations to the fundamental solutions discovered by Beals, Gaveau, and Greiner for the Laplace equation ... More

On $L_2$-approximation in Hilbert spaces using function valuesMay 07 2019Jun 28 2019We study $L_2$-approximation of functions from Hilbert spaces $H$ in which function evaluation is a continuous linear functional, using function values as information. Under certain assumptions on $H$, we prove that the $n$-th minimal worst-case error ... More

Elliptic problems and holomorphic functions in Banach spacesApr 05 2019In the first part we show that a vector-valued almost separably valued function $f$ is holomorphic (harmonic) if and only if it is dominated by an $L^1_\mathrm{loc}$ function and there exists a separating set $W\subset X'$ such that $\langle f,x'\rangle$ ... More

Uniqueness and Stability for the Shock Reflection-Diffraction Problem for Potential FlowMar 29 2019Jul 21 2019When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational, and asymptotic ... More

Uniqueness and Stability for the Shock Reflection-Diffraction Problem for Potential FlowMar 29 2019Apr 30 2019When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational, and asymptotic ... More

Uniqueness and Stability for the Shock Reflection-Diffraction Problem for Potential FlowMar 29 2019When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational, and asymptotic ... More

Protori and Torsion-Free Abelian GroupsMar 19 2019The Resolution Theorem for Compact Abelian Groups is applied to show that the profinite subgroups of a finite-dimensional compact connected abelian group (protorus) which induce tori quotients comprise a lattice under intersection (meet) and $+$ (join), ... More

Transfer operators, atomic decomposition and the BestiaryMar 16 2019Arbieto and S. recently used atomic decomposition to study transfer operators. We give a long list of old and new expanding dynamical systems for which those results can be applied, obtaining the quasi-compactness of transfer operator acting on Besov ... More

Transfer operators and atomic decompositionMar 16 2019Apr 16 2019We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the associated potential, ... More

Transfer operators and atomic decompositionMar 16 2019We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the associated potential, ... More

A mixed problem for the Laplace operator in a domain with moderately close holesMar 14 2019We investigate the behavior of the solution of a mixed problem in a domain with two moderately close holes. We introduce a positive parameter $\epsilon$ and we define a perforated domain $\Omega_{\epsilon}$ obtained by making two small perforations in ... More

Anisotropy-based robust performance criteria for statistically uncertain linear continuous time invariant stochastic systemsMar 05 2019This paper is concerned with robust performance criteria for linear continuous time invariant stochastic systems driven by statistically uncertain random processes. The uncertainty is understood as the deviation of imprecisely known probability distributions ... More

Filippov flows and mean-field limits in the kinetic singular Kuramoto modelMar 04 2019The agent-based singular Kuramoto model was proposed in [60] as a singular version of the Kuramoto model of coupled oscillators that is consistent with Hebb's rule of neuroscience. In such paper, the authors studied its well-posedness via the concept ... More

Fatou-Type Theorems and Boundary Value Problems for Elliptic Systems in the Upper Half-SpaceFeb 21 2019We survey recent progress in a program aimed at proving general Fatou-type results and establishing the well-posedness of a variety of boundary value problems in the upper half-space ${\mathbb{R}}^n_{+}$ for second-order, homogeneous, constant complex ... More

On Curvature properties of Nariai SpacetimesFeb 08 2019The charged Nariai spacetimes are the exact solutions of Einstein-Maxwell field equations with positive cosmological constant and such a spacetime is the direct topological product of a $2$-dimentional de-Sitter spacetime with a round $2$-sphere of constant ... More

On Curvature properties of Nariai SpacetimesFeb 08 2019Aug 20 2019The charged Nariai spacetimes are the exact solutions of Einstein-Maxwell field equations with positive cosmological constant and such a spacetime is the direct topological product of a $2$-dimentional de-Sitter spacetime with a round $2$-sphere of constant ... More

Mixing via controllability for randomly forced nonlinear dissipative PDEsFeb 01 2019We continue our study of the problem of mixing for a class of PDEs with very degenerate noise. As we established earlier, the uniqueness of stationary measure and its exponential stability in the dual-Lipschitz metric holds under the hypothesis that the ... More

Submanifold geometry in symmetric spaces of noncompact typeJan 14 2019In this survey article we provide an introduction to submanifold geometry in symmetric spaces of noncompact type. We focus on the construction of examples and the classification problems of homogeneous and isoparametric hypersurfaces, polar and hyperpolar ... More

Extending partial isometries of antipodal graphsJan 14 2019Aug 10 2019We prove EPPA (extension property for partial automorphisms) for all antipodal classes from Cherlin's list of metrically homogeneous graphs, thereby answering a question of Aranda et al. This paper should be seen as the first application of a new general ... More

Extending partial isometries of antipodal graphsJan 14 2019We prove EPPA (extension property for partial automorphisms) for all antipodal classes from Cherlin's list of metrically homogeneous graphs, thereby answering a question of Aranda et al. This paper should be seen as the first application of a new general ... More

EPPA for two-graphs and antipodal metric spacesDec 28 2018We prove that the class of two-graphs has the extension property for partial automorphisms (EPPA, or Hrushovski property), thereby answering a question of Macpherson. In other words, we show that the class of graphs has the extension property for switching ... More

Hypercomplex Generalizations of Gaussian-type MeasuresDec 15 2018The article is devoted to a new type of measures which are hypercomplex generalizations of Gaussian-type measures. The considered such measures are related with solutions of high order hyperbolic PDEs and related Markov processes. Their characteristic ... More

Dynamic Ecological System AnalysisNov 29 2018Sep 11 2019This article develops a new mathematical method for holistic analysis of nonlinear dynamic compartmental systems in the context of ecology. The method is based on the novel dynamic system and subsystem partitioning methodologies through which compartmental ... More

Dynamic Ecological System AnalysisNov 29 2018Sep 07 2019This article develops a new mathematical method for holistic analysis of nonlinear dynamic compartmental systems in the context of ecology. The method is based on the novel dynamic system and subsystem partitioning methodologies through which compartmental ... More

Nonlinear Decomposition Principle and Fundamental Matrix Solutions for Dynamic Compartmental SystemsNov 29 2018Mar 13 2019A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the novel mutually exclusive and exhaustive system and subsystem decomposition methodologies. A deterministic mathematical ... More

Nonlinear Decomposition Principle and Fundamental Matrix Solutions for Dynamic Compartmental SystemsNov 29 2018Sep 07 2019A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning methodologies. A deterministic ... More

Nonlinear Decomposition Principle and Fundamental Matrix Solutions for Dynamic Compartmental SystemsNov 29 2018May 10 2019A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the novel mutually exclusive and exhaustive system and subsystem decomposition methodologies. A deterministic mathematical ... More

Nonlinear Decomposition Principle and Fundamental Matrix Solutions for Dynamic Compartmental SystemsNov 29 2018Jun 07 2019A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning methodologies. A deterministic ... More

Dynamic Ecological System MeasuresNov 22 2018Sep 07 2019A new mathematical method for the dynamic analysis of nonlinear compartmental systems in the context of ecology has recently been developed by the author and was presented in a separate article. Based on this methodology, multiple new dynamic ecological ... More

Periodicity induced by noise and interaction in the kinetic mean-field FitzHugh-Nagumo modelNov 01 2018Jun 21 2019We consider the long-time behavior of a population of mean-field oscillators modeling the activity of interacting excitable neurons in large population. Each neuron is represented by its voltage and recovery variables, which are solution to a FitzHugh-Nagumo ... More

Periodicity induced by noise and interaction in the kinetic mean-field FitzHugh-Nagumo modelNov 01 2018We consider the long-time behavior of a population of mean-field oscillators modeling the activity of interacting excitable neurons in large population. Each neuron is represented by its voltage and recovery variables, which are solution to a FitzHugh-Nagumo ... More

Traces and Extensions of Bounded Divergence-Measure Fields on Rough Open SetsOct 30 2018We prove that an open set $\Omega \subset \mathbb{R}^n$ can be approximated by smooth sets with uniformly bounded perimeters from the interior if and only if the open set $\Omega$ satisfies \begin{align*} &\qquad \qquad\qquad\qquad\qquad\qquad\qquad \mathscr{H}^{n-1}(\partial ... More

Existence of Traveling Fronts and Pulses in Lateral Inhibition Neuronal Networks with Sigmoidal Firing Rate FunctionsOct 11 2018The purpose of this work is to rigorously prove the existence of traveling waves in neural field models with lateral inhibition synaptic coupling types and sigmoidal firing rate functions. In the case of traveling fronts, we utilize theory of linear operators ... More

Hypersurfaces in space forms satisfying some generalized Einstein metric conditionOct 02 2018Mar 02 2019The difference tensor C.R - R.C of Einstein manifolds, some quasi-Einstein manifolds and Roter type manifolds, of dimension n > 3, satisfy the following curvature condition: (A) C.R - R.C = Q(S,C) - (k /(n-1)) Q(g,C). We investigate hypersurfaces M in ... More

Hypersurfaces in space forms satisfying some generalized Einstein metric conditionOct 02 2018The difference tensor C.R - R.C of Einstein manifolds, some quasi-Einstein manifolds and Roter type manifolds, of dimension n > 3, satisfy the following curvature condition: (A) C.R - R.C = Q(S,C) - (k /(n-1)) Q(g,C). We investigate hypersurfaces M in ... More

The Lattice of Profinite Subgroups of ProtoriSep 27 2018Compact connected abelian groups, or protori, have intrinsic structural characteristics that present for the entire category. In the case of finite-dimensional torus-free protori, The Resolution Theorem for Compact Abelian Groups sets the stage for demonstrating ... More

The Main Decomposition of Finite-Dimensional ProtoriSep 12 2018A protorus is a compact connected abelian group. We use a result on finite rank torsion-free abelian groups and Pontryagin Duality to considerably generalize a well-known factorization of a finite-dimensional protorus into a product of a torus and a torus-free ... More

Cauchy Fluxes and Gauss-Green Formulas for Divergence-Measure Fields over General Open SetsSep 04 2018Jan 18 2019We establish the interior and exterior Gauss-Green formulas for divergence-measure fields in $L^p$ over general open sets, motivated by the rigorous mathematical formulation of the physical principle of balance law via the Cauchy flux in the axiomatic ... More

The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in $\mathbb R^d$ does not always remain unaltered during the flexSep 02 2018Being motivated by the theory of flexible polyhedra, we study the Dirichlet and Neumann eigenvalues for the Laplace operator in special bounded domains of Euclidean $d$-space. The boundary of such a domain is an embedded simplicial complex which allows ... More

The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in $\mathbb R^d$ does not always remain unaltered during the flexSep 02 2018Mar 16 2019Being motivated by the theory of flexible polyhedra, we study the Dirichlet and Neumann eigenvalues for the Laplace operator in special bounded domains of Euclidean $d$-space. The boundary of such a domain is an embedded simplicial complex which allows ... More

On the Formalization of Higher Inductive Types and Synthetic Homotopy TheoryAug 31 2018The goal of this dissertation is to present synthetic homotopy theory in the setting of homotopy type theory. We will present various results in this framework, most notably the construction of the Atiyah-Hirzebruch and Serre spectral sequences for cohomology, ... More

On Hilbert problem for Beltrami equations in quasihyperbolic domainsJul 24 2018Jan 09 2019It is studied the Hilbert boundary value problem for the nondegenerate Beltrami equations in domains $D$ of the complex plane $\mathbb C$ with the so--called quasihyperbolic boundary condition. It is proved the existence of solutions of this problem with ... More

A simple device for microinjections, manipulations and measurements using an electromorphological chip under microinterferometric control of the interface and membrane processes at the thickness range of 5-1000 nm at different anglesJul 23 2018Micromanipulations, perfusions and measurements performed using glass microelectrodes filled with an electrolyte is a conventional technique for experimental morphological and membrane electrophysiological studies at a single cell and membrane surface ... More

Mertens Sums requiring Fewer Values of the Möbius functionJul 16 2018We discuss certain identities involving $\mu(n)$ and $M(x)=\sum_{n\leq x}\mu(n)$, the functions of M\"{o}bius and Mertens. These identities allow calculation of $M(N^d)$, for $d=2,3,4,\ldots\ $, as a sum of $O_d \left( N^d(\log N)^{2d - 2}\right)$ terms, ... More

On the multilevel internal structure of the asymptotic distribution of resonancesJul 08 2018Oct 26 2018We prove that the asymptotic distribution of resonances has a multilevel internal structure for the following classes of Hamiltonians H: Schr\"odinger operators with point interactions in $\mathbb{R}^3$, quantum graphs, and 1-D photonic crystals. In the ... More

Schrödinger operators with distributional potentials and boundary conditions dependent on the eigenvalue parameterJun 26 2018We study various direct and inverse spectral problems for the one-dimensional Schr\"{o}dinger equation with distributional potential and boundary conditions containing the eigenvalue parameter.

The Girth of Cayley graphs of Sylow 2-subgroups of symmetric groups $S_{2^n}$ on diagonal basesJun 22 2018A diagonal base of a Sylow 2-subgroup $P_n(2)$ of symmetric group $S_{2^n}$ is a minimal generating set of this subgroup consisting of elements with only one non-zero coordinate in the polynomial representation. For different diagonal bases Cayley graphs ... More

Shift operators, residue families and degenerate LaplaciansJun 07 2018We introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry breaking differential ... More

On short expressions for cosets of permutation subgroupsMay 30 2018Oct 22 2018Following Babai's algorithm for the string isomorphism problem, we determine that it is possible to write expressions of short length describing certain permutation cosets, including all permutation subgroups; this is feasible both in the original version ... More

Selections and Higher Separation AxiomsMay 19 2018Oct 15 2018This survey presents some historical background and recent developments in the area of selections for set-valued mappings along with several open questions. It was written with the hope that the presented material may pique an interest in the selection ... More

The Dirichlet problem for semi-linear equationsApr 16 2018Mar 11 2019We study the Dirichlet problem for the semi--linear partial differential equations ${\rm div}\,(A\nabla u)=f(u)$ in simply connected domains $D$ of the complex plane $\mathbb C$ with continuous boundary data. We prove the existence of the weak solutions ... More

The Dirichlet problem for semi-linear equationsApr 16 2018Jan 03 2019We study the Dirichlet problem for the semi--linear partial differential equations in the simple connected domains $D$ in $\mathbb C$, the linear part of which is written in a divergence (anisotropic !) form. Thanking to a factorization theorem established ... More

The Dirichlet problem for semi-linear equationsApr 16 2018Apr 08 2019We study the Dirichlet problem for the semi--linear partial differential equations ${\rm div}\,(A\nabla u)=f(u)$ in simply connected domains $D$ of the complex plane $\mathbb C$ with continuous boundary data. We prove the existence of the weak solutions ... More

Abelian networks IV. Dynamics of nonhalting networksApr 10 2018An abelian network is a collection of communicating automata whose state transitions and message passing each satisfy a local commutativity condition. This paper is a continuation of the abelian networks series of Bond and Levine (2016), for which we ... More

Distributed Online Optimization for Multi-Agent Optimal TransportApr 04 2018Aug 09 2019In this work, we propose and investigate a scalable, distributed iterative algorithm for large-scale optimal transport of collectives of autonomous agents. We formulate the problem as one of steering the collective towards a target probability measure ... More

Distributed Online Optimization for Multi-Agent Optimal TransportApr 04 2018Jun 05 2019In this work, we propose and investigate a scalable, distributed iterative algorithm for large-scale optimal transport of collectives of autonomous agents. We formulate the problem as one of steering the collective towards a target probability measure ... More

On the Morse-Bott property of analytic functions on Banach spaces with Lojasiewicz exponent one halfMar 30 2018Apr 04 2018It is a consequence of the Morse-Bott Lemma on Banach spaces that a smooth Morse-Bott function on an open neighborhood of a critical point in a Banach space obeys a Lojasiewicz gradient inequality with the optimal exponent one half. In this article we ... More

Projective geometry of Sasaki-Einstein structures and their compactificationMar 26 2018Aug 10 2019We show that the standard definitions of Sasaki structures have elegant and simplifying interpretations in terms of projective differential geometry. For Sasaki-Einstein structures we use projective geometry to provide a resolution of such structures ... More

Synchronization of stochastic mean field networks of Hodgkin-Huxley neurons with noisy channelsMar 12 2018Dec 28 2018In this work we are interested in a mathematical model of the collective behavior of a fully connected network of finitely many neurons, when their number and when time go to infinity. We assume that every neuron follows a stochastic version of the Hodgkin-Huxley ... More

Traveling Wave Solutions to a Neural Field Model With Oscillatory Synaptic Coupling TypesMar 04 2018Jun 26 2018In this paper, we investigate the existence, uniqueness, and spectral stability of traveling waves arising from a single threshold neural field model with one spatial dimension, a Heaviside firing rate function, axonal propagation delay, and biologically ... More

Emergence of oscillatory behaviors for excitable systems with noise and mean-field interaction, a slow-fast dynamics approachFeb 18 2018Jul 05 2018We consider the long-time dynamics of a general class of nonlinear Fokker-Planck equations, describing the large population behavior of mean-field interacting units. The main motivation of this work concerns the case where the individual dynamics is excitable, ... More

Hypersingular nonlinear boundary-value problems with a small parameterFeb 11 2018For the first time, some hypersingular nonlinear boundary-value problems with a small parameter~$\varepsilon$ at the highest derivative are described. These problems essentially (qualitatively and quantitatively) differ from the usual linear and quasilinear ... More

Conformal Parametrisation of Loxodromes by Triples of CirclesFeb 06 2018We provide a parametrisation of a loxodrome by three specially arranged cycles. The parametrisation is covariant under fractional linear transformations of the complex plane and naturally encodes conformal properties of loxodromes. Selected geometrical ... More

Affine Connections on 3-Sasakian Homogeneous ManifoldsJan 31 2018Jan 28 2019The space of invariant affine connections on every $3$-Sasakian homogeneous manifold of dimension at least $7$ is described. In particular, the remarkable subspaces of invariant affine metric connections, and the subclass with skew-torsion, are also determined. ... More

Algorithmic Linearly Constrained Gaussian ProcessesJan 28 2018Jan 04 2019We algorithmically construct multi-output Gaussian process priors which satisfy linear differential equations. Our approach attempts to parametrize all solutions of the equations using Gr\"obner bases. If successful, a push forward Gaussian process along ... More

Steady-State Behavior of Some Load Balancing Mechanisms in Cloud Storage SystemsJan 06 2018In large storage systems, files are often coded across several servers to improve reliability and retrieval speed. We consider a system of $n$ servers storing files using a Maximum Distance Separable code (cf. \cite{li2016mean}). Specifically, each file ... More

Pricing double barrier options on homogeneous diffusions: a Neumann series of Bessel functions representationDec 21 2017This paper develops a novel analytically tractable Neumann series of Bessel functions representation for pricing (and hedging) European-style double barrier knock-out options, which can be applied to the whole class of one-dimensional time-homogeneous ... More

The Stieltjes integrals in the theory of harmonic and analytic functionsNov 07 2017Feb 17 2018We study various Stieltjes integrals as Poisson-Stieltjes, conjugate Poisson-Stieltjes, Schwartz-Stieltjes and Cauchy-Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the singular Hilbert-Stieltjes integral ... More

Toward the theory of semi-linear equationsOct 31 2017In this paper we study the semilinear partial differential equations in the plane the linear part of which is written in a divergence form. The main result is given as a factorization theorem. This theorem states that every weak solution of such an equation ... More

Spin Structures on Affine Kac-Moody Symmetric SpacesOct 30 2017Aug 27 2018We construct certain Fr\'echet principal $K$-bundles over affine Kac-Moody symmetric spaces by means of the natural projection $G\rightarrow G/K$ where $G$ is a (possibly twisted) geometric affine Kac-Moody group and $K$ is a real form when $G$ is complex ... More

Spin Structures on Affine Kac-Moody Symmetric SpacesOct 30 2017May 11 2019We construct certain Fr\'echet principal $K$-bundles over affine Kac-Moody symmetric spaces by means of the natural projection $G\rightarrow G/K$ where $G$ is a (possibly twisted) geometric affine Kac-Moody group and $K$ is a real form when $G$ is complex ... More

Curvature properties of Vaidya metricOct 17 2017As a generalization of the Schwarzschild solution, Vaidya presented a radiating metric to develop a model of the exterior of a star including its radiation field, called Vaidya metric. The present paper deals with the investigation on the curvature properties ... More

Curvature properties of Vaidya metricOct 17 2017May 07 2019As a generalization of the Schwarzschild solution, Vaidya presented a radiating metric to develop a model of the exterior of a star including its radiation field, called Vaidya metric. The present paper deals with the investigation on the curvature properties ... More

Correlation of boundary behavior of conjugate harmonic functionsOct 01 2017Mar 03 2018It is established that if a harmonic function $u$ on the unit disk $\mathbb D$ in $\mathbb C$ has angular limits on a measurable set $E$ of the unit circle $\partial\mathbb D$, then its conjugate harmonic function $v$ in $\mathbb D$ also has angular limits ... More

Analysis of Set-Valued Stochastic Approximations: Applications to Noisy Approximate Value and Fixed point IterationsSep 14 2017Sep 04 2018The main aim of this paper is the development of Lyapunov function based sufficient conditions for stability (almost sure boundedness) and convergence of stochastic approximation algorithms (SAAs) with set-valued mean-fields, a class of model-free algorithms ... More

Resolution of singularities and geometric proofs of the Lojasiewicz inequalitiesAug 31 2017Jul 01 2019The Lojasiewicz inequalities for real analytic functions on Euclidean space were first proved by Stanislaw Lojasiewicz (1965) using methods of semianalytic and subanalytic sets, arguments later simplified by Bierstone and Milman (1988). In this article, ... More

Resolution of singularities and geometric proofs of the Lojasiewicz inequalitiesAug 31 2017Dec 20 2018The Lojasiewicz inequalities for real analytic functions on Euclidean space were first proved by Stanislaw Lojasiewicz (1965) using methods of semianalytic and subanalytic sets, arguments later simplified by Bierstone and Milman (1988). In this article, ... More

Resolution of singularities and geometric proofs of the Lojasiewicz inequalitiesAug 31 2017May 02 2019The Lojasiewicz inequalities for real analytic functions on Euclidean space were first proved by Stanislaw Lojasiewicz (1965) using methods of semianalytic and subanalytic sets, arguments later simplified by Bierstone and Milman (1988). In this article, ... More

Essentially isospectral transformations and their applicationsAug 24 2017We define and study the properties of Darboux-type transformations between Sturm--Liouville problems with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary conditions). ... More

Formal theory of cornered asymptotically hyperbolic Einstein metricsAug 08 2017This paper makes a formal study of asymptotically hyperbolic Einstein metrics given, as conformal infinity, a conformal manifold with boundary. The space on which such an Einstein metric exists thus has a finite boundary in addition to the usual infinite ... More

Existence, uniqueness and ergodic properties for time-homogeneous Itô-SDEs with locally integrable drifts and Sobolev diffusion coefficientsAug 03 2017Sep 04 2018Using elliptic and parabolic regularity results for strongly continuous sub-Markovian contraction resolvents and semigroups in $L^p$-spaces, we construct for every starting point weak solutions to SDEs in $d$-dimensional Euclidean space up to their explosion ... More

Some anomalous examples of lifting spacesAug 02 2017An inverse limit of a sequence of covering spaces over a given space $X$ is not, in general, a covering space over $X$ but is still a lifting space, i.e. a Hurewicz fibration with unique path lifting property. Of particular interest are inverse limits ... More

Measurable process selection theorem and non-autonomous inclusionsJul 19 2017A semi-process is an analog of the semi-flow for non-autonomous differential equations or inclusions. We prove an abstract result on the existence of measurable semi-processes in the situations where there is no uniqueness. Also, we allow solutions to ... More

Semiflow selection and Markov selection theoremsJul 15 2017The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup property arises naturally when the solutions of a differential equation are ... More

Generalized boundary triples, Weyl functions and inverse problemsJun 24 2017With a closed symmetric operator $A$ in a Hilbert space ${\mathfrak H}$ a triple $\Pi=\{{\mathcal H},\Gamma_0,\Gamma_1\}$ of a Hilbert space ${\mathcal H}$ and two abstract trace operators $\Gamma_0$ and $\Gamma_1$ from $A^*$ to ${\mathcal H}$ is called ... More

The Vanishing viscosity limit for some symmetric flowsJun 19 2017The focus of this paper is on the analysis of the boundary layer and the associated vanishing viscosity limit for two classes of flows with symmetry, namely, Plane-Parallel Channel Flows and Parallel Pipe Flows. We construct explicit boundary layer correctors, ... More

Effects of parametric uncertainties in cascaded open quantum harmonic oscillators and robust generation of Gaussian invariant statesJun 14 2017This paper is concerned with the generation of Gaussian invariant states in cascades of open quantum harmonic oscillators governed by linear quantum stochastic differential equations. We carry out infinitesimal perturbation analysis of the covariance ... More

Sticky matroids and Kantor's ConjectureApr 27 2017Dec 11 2018We prove the equivalence of Kantor's Conjecture and the Sticky Matroid Conjecture due to Poljak und Turz\'ik.