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Nonparametric estimation of the fragmentation kernel based on a PDE stationary distribution approximationOct 25 2017Apr 11 2019We consider a stochastic individual-based model in continuous time to describe a size-structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We address here the problem of nonparametric estimation ... More

A note on independence number, connectivity and $k$-ended treeOct 26 2018A $k$-ended tree is a tree with at most $k$ leaves. In this note, we give a simple proof for the following theorem. Let $G$ be a connected graph and $k$ be an integer ($k\geq 2$). Let $S$ be a vertex subset of $G$ such that $\alpha_{G}(S) \leq k + \kappa_{G}(S)- ... More

Local property of maximal plurifinely plurisubharmonic functionsApr 05 2016In this paper, we prove that a continuous $\mathcal F$-plurisubharmonic functions defined in an $\mathcal F$-open set in $\mathbb C^n$ is $\mathcal F$-maximal if and only if it is $\mathcal F$-locally $\mathcal F$-maximal.

"Cultural additivity" and how the values and norms of Confucianism, Buddhism, and Taoism co-exist, interact, and influence Vietnamese society: A Bayesian analysis of long-standing folktales, using R and StanMar 05 2018Every year, the Vietnamese people reportedly burned about 50,000 tons of joss papers, which took the form of not only bank notes, but iPhones, cars, clothes, even housekeepers, in hope of pleasing the dead. The practice was mistakenly attributed to traditional ... More

Membership criteria and containments of powers of monomial idealsAug 17 2018Jan 18 2019We present a close relationship between matching number, covering numbers and their fractional versions in combinatorial optimization and ordinary powers, integral closures of powers, and symbolic powers of monomial ideals. This relationship leads to ... More

Associated primes of powers of edge ideals and ear decompositions of graphsJun 04 2015Jul 17 2018In this paper, we give a complete description of the associated primes of every power of the edge ideal in terms of generalized ear decompositions of the graph. This result establishes a surprising relationship between two seemingly unrelated notions ... More

Saturation and associated primes of powers of edge idealsNov 28 2014For the edge ideal I of an arbitrary simple graph G we describe the monomials of the saturation of a power of I in terms of (vertex) weighted graphs associated with the monomials. This description allows us to characterize the embedded associated primes ... More

Hilbert polynomials of non-standard bigraded algebrasNov 11 2002This paper is a systematic study of the Hilbert polynomial of a bigraded algebra R which are generated by elements of bidegrees (1,0), (d_1,1),...,(d_r,1), where d_1,...,d_r are non-negative integers. The obtained results can be applied to study Rees ... More

Bayesian inverse problems for Burgers and Hamilton-Jacobi equations with white-noise forcingApr 14 2011May 10 2011The paper formulates Bayesian inverse problems for inference in a topological measure space given noisy observations. Conditions for the validity of the Bayes formula and the well-posedness of the posterior measure are studied. The abstract theory is ... More

A note on spanning trees of connected $K_{1,t}$-free graphs whose stems have a few leavesOct 19 2018Let $T$ be a tree, a vertex of degree one is called a leaf. The set of leaves of $T$ is denoted by $Leaf(T)$. The subtree $T-Leaf(T)$ of $T$ is called the stem of $T$ and denoted by $Stem(T).$ In this note, we give a sharp sufficient condition to show ... More

Generalized power central group identities in almost subnormal subgroups of $\GL_n(D)$Jan 18 2018Mar 19 2019In this paper, we study almost subnormal subgroups of the general linear group $\GL_n(D)$ of degree $n\ge 1$ over a division ring $D$ that satisfy a generalized power central group identity.

Depth and regularity of powers of sums of idealsJan 24 2015Jan 01 2016Given arbitrary homogeneous ideals $I$ and $J$ in polynomial rings $A$ and $B$ over a field $k$, we investigate the depth and the Castelnuovo-Mumford regularity of powers of the sum $I+J$ in $A \otimes_k B$ in terms of those of $I$ and $J$. Our results ... More

Spanning trees with at most 4 leaves in $K_{1,5}-$free graphsApr 25 2018Oct 19 2018In 2009, Kyaw proved that every $n$-vertex connected $K_{1,4}$-free graph $G$ with $\sigma_4(G)\geq n-1$ contains a spanning tree with at most $3$ leaves. In this paper, we prove an analogue of Kyaw's result for connected $K_{1,5}$-free graphs. We show ... More

Homogenization error for two scale Maxwell equationsDec 09 2015For two scale elliptic equations in a domain $D$, standard homogenization errors are deduced with the assumption that the solution $u_0$ of the homogenized equation belongs to $H^2(D)$. For two scale Maxwell equations, the corresponding required regularity ... More

Homogenization of multiscale Maxwell wave equationsMay 21 2017We study homogenization of multiscale Maxwell wave equation that depends on $n$ separable microscopic scales in a domain $D\subset{\mathbb R}^d$ on a finite time interval $(0,T)$. Due to the non-compactness of the embedding of $H_0(\curl,D)$ in $L^2(D)^d$, ... More

Bayesian inverse problems for recovering coefficients of two scale elliptic equationsJul 17 2018Aug 03 2018We consider the Bayesian inverse homogenization problem of recovering the locally periodic two scale coefficient of a two scale elliptic equation, given limited noisy information on the solution. We consider both the uniform and the Gaussian prior probability ... More

High dimensional finite elements for multiscale Maxwell wave equationsAug 07 2017We develop an essentially optimal numerical method for solving multiscale Maxwell wave equations in a domain $D\subset{\mathbb R}^d$. The problems depend on $n+1$ scales: one macroscopic scale and $n$ microscopic scales. Solving the macroscopic multiscale ... More

Hierarchical multiscale finite element method for multi-continuum mediaJun 11 2019Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of model reduction. One of the approaches is multi-continuum technique, where ... More

Order-Reduction Abstractions for Safety Verification of High-Dimensional Linear SystemsFeb 20 2016Order-reduction is a standard automated approximation technique for computer-aided design, analysis, and simulation of many classes of systems, from circuits to buildings. For a given system, these methods produce a reduced-order system where the dimension ... More

Depth and regularity modulo a principal idealJun 29 2017Jan 29 2018We study the relationship between depth and regularity of a homogeneous ideal I and those of (I,f) and I:f, where f is a linear form or a monomial. Our results has several interesting consequences on depth and regularity of edge ideals of hypegraphs and ... More

Symbolic powers of sums of idealsFeb 06 2017Apr 16 2019Let $I$ and $J$ be nonzero ideals in two Noetherian algebras $A$ and $B$ over a field $k$. Let $I+J$ denote the ideal generated by $I$ and $J$ in $A\otimes_k B$. We prove the following expansion for the symbolic powers: $$(I+J)^{(n)} = \sum_{i+j = n} ... More

Depth functions of powers of homogeneous idealsApr 16 2019We settle a conjecture of Herzog and Hibi, which states that the function depth $S/Q^n$, $n \ge 1$, where $Q$ is a homogeneous ideal in a polynomial ring $S$, can be any convergent numerical function. We also give a positive answer to a long-standing ... More

Angle-Encoded Swarm Optimization for UAV Formation Path PlanningDec 19 2018This paper presents a novel and feasible path planning technique for a group of unmanned aerial vehicles (UAVs) conducting surface inspection of infrastructure. The ultimate goal is to minimise the travel distance of UAVs while simultaneously avoid obstacles, ... More

Enhanced discrete particle swarm optimization path planning for UAV vision-based surface inspectionJun 14 2017In built infrastructure monitoring, an efficient path planning algorithm is essential for robotic inspection of large surfaces using computer vision. In this work, we first formulate the inspection path planning problem as an extended travelling salesman ... More

Determining White Noise Forcing From Eulerian Observations in the Navier Stokes EquationMar 19 2013Apr 18 2014The Bayesian approach to inverse problems is of paramount importance in quantifying uncertainty about the input to and the state of a system of interest given noisy observations. Herein we consider the forward problem of the forced 2D Navier Stokes equation. ... More

Complexity Analysis of Accelerated MCMC Methods for Bayesian InversionJul 10 2012Apr 30 2013We study Bayesian inversion for a model elliptic PDE with unknown diffusion coefficient. We provide complexity analyses of several Markov Chain-Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior ... More

Polynomial approximations of a class of stochastic multiscale elasticity problemsNov 28 2015We consider a class of elasticity equations in ${\mathbb R}^d$ whose elastic moduli depend on $n$ separated microscopic scales, are random and expressed as a linear expansion of a countable sequence of random variables which are independently and identically ... More

Kleene stars of the plane, polylogarithms and symmetriesNov 22 2018We extend the definition and construct several bases for polylogarithms Li T , where T are some series, recognizable by a finite state (multiplicity) automaton of alphabet 4 X = {x 0 , x 1 }. The kernel of this new "polylogarithmic map" Li $\bullet$ is ... More

Computationally-driven, high throughput identification of CaTe and Li$_\textrm{3}$Sb as promising candidates for high mobility $p$-type transparent conducting materialsNov 13 2018High-performance $p$-type transparent conducting materials (TCMs) must exhibit a rare combination of properties including high mobility, transparency and $p$-type dopability. The development of high-mobility/conductivity $p$-type TCMs is necessary for ... More

Ultra-high strain in epitaxial silicon carbide nanostructures utilizing residual stress amplificationJan 05 2017Strain engineering has attracted great attention, particularly for epitaxial films grown on a different substrate. Residual strains of SiC have been widely employed to form ultra-high frequency and high Q factor resonators. However, to date the highest ... More

Nonparametric estimation of the fragmentation kernel based on a PDE stationary distribution approximationOct 25 2017We consider a stochastic individual-based model in continuous time to describe a size-structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We address here the problem of nonparametric estimation ... More

Branching of Hydraulic Cracks in Gas or Oil Shale with Closed Natural Fractures: How to Master PermeabilityDec 06 2018While the hydraulic fracturing technology, aka fracking (or fraccing, frac), has become highly developed and astonishingly successful, a consistent formulation of the associated fracture mechanics that would not conflict with some observations is still ... More

Reconciling Bayesian and Total Variation Methods for Binary InversionJun 06 2017Apr 09 2018A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization. On the other hand, sparse or noisy data often demands a probabilistic approach to the reconstruction of images, ... More

Cultural evolution in Vietnam's early 20th century: a Bayesian networks analysis of Franco-Chinese house designsMar 03 2019The study of cultural evolution has taken on an increasingly interdisciplinary and diverse approach in explicating phenomena of cultural transmission and adoptions. Inspired by this computational movement, this study uses Bayesian networks analysis, combining ... More

Estimating the Division Kernel of a Size-Structured PopulationSep 09 2015May 19 2016We consider a size-structured population describing the cell divisions. The cell population is described by an empirical measure and we observe the divisions in the continuous time interval [0, T ]. We address here the problem of estimating the division ... More

Non-integrated defect relations for the Gauss map of a complete minimal surface with finite total curvature in $\mathbb R^m$Oct 04 2017In this article, we give the non-integrated defect relations for the Gauss map of a complete minimal surface with finite total curvature in $\mathbb R^m.$ This is a continuation of previous work of Ha-Trao [J. Math. Anal. Appl., \textbf{430} (2015), 76-84.], ... More

Spanning trees in a Claw-free graph whose stems have at most $k$ branch verticesFeb 27 2018Let $T$ be a tree, a vertex of degree one and a vertex of degree at least three is called a leaf and a branch vertex, respectively. The set of leaves of $T$ is denoted by $Leaf(T)$. The subtree $T-Leaf(T)$ of $T$ is called the stem of $T$ and denoted ... More

Modified defect relations of the Gauss map and the total curvature of a complete minimal surfaceOct 09 2017Oct 12 2017In this article, we propose some conditions on the modified defect relations of the Gauss map of a complete minimal surface $M$ to show that $M$ has finite total curvature.

Integrated photonic platform for quantum information with continuous variablesApr 20 2018Integrated quantum photonics provides a scalable platform for the generation, manipulation, and detection of optical quantum states by confining light inside miniaturized waveguide circuits. Here we show the generation, manipulation, and interferometric ... More

Estimates of isospin breaking contributions to baryon massesSep 20 2006Jun 30 2007We estimate the isospin breaking contributions to the baryon masses which we analyzed recently using a loop expansion in the heavy baryon approximation to chiral effective field theory. To one loop, the isospin breaking corrections come from the effects ... More

Irreducible polynomials with several prescribed coefficientsJan 26 2016We study the number of irreducible polynomials over $\mathbf{F}_{q}$ with some coefficients prescribed. Using the technique developed by Bourgain, we show that there is an irreducible polynomial of degree $n$ with $r$ coefficients prescribed in any location ... More

Any shape can ultimately cross information on two-dimensional abelian sandpile modelsAug 04 2017In this paper we study the abelian sandpile model on the two-dimensional grid with uniform neighborhood, and prove that any family of neighborhoods defined as scalings of a continuous non-flat shape can ultimately perform crossing.

Predicting Movie Genres Based on Plot SummariesJan 15 2018This project explores several Machine Learning methods to predict movie genres based on plot summaries. Naive Bayes, Word2Vec+XGBoost and Recurrent Neural Networks are used for text classification, while K-binary transformation, rank method and probabilistic ... More

Learning to Rank Personalized Search Results in Professional NetworksMay 16 2016LinkedIn search is deeply personalized - for the same queries, different searchers expect completely different results. This paper presents our approach to achieving this by mining various data sources available in LinkedIn to infer searchers' intents ... More

A parametrization of the baryon octet and decuplet massesNov 27 2007May 05 2008We construct a general parametrization of the baryon octet and decuplet mass operators including the three-body terms using the unit operator and the symmetry-breaking factors $M^d=\textrm{diag} (0,1,0)$ and $M^s=\textrm{diag} (0,0,1)$ in conjunction ... More

Decuplet baryon magnetic moments in a QCD-based quark model beyond quenched approximationApr 23 1998We study the decuplet baryon magnetic moments in a QCD-based quark model beyond quenched approximation. Our approach for unquenching the theory is based on the heavy baryon perturbation theory in which the axial couplings for baryon - meson and the meson-meson-photon ... More

Beyond socket options: making the Linux TCP stack truly extensibleJan 07 2019The Transmission Control Protocol (TCP) is one of the most important protocols in today's Internet. Its specification and implementations have been refined for almost forty years. The Linux TCP stack is one of the most widely used TCP stacks given its ... More

Local property of maximal plurifinely plurisubharmonic functionsApr 05 2016Oct 12 2016In this paper, we prove that a continuous $\mathcal F$-plurisubharmonic functions defined in an $\mathcal F$-open set in $\mathbb C^n$ is $\mathcal F$-maximal if and only if it is $\mathcal F$-locally $\mathcal F$-maximal.

Beyond socket options: making the Linux TCP stack truly extensibleJan 07 2019May 22 2019The Transmission Control Protocol (TCP) is one of the most important protocols in today's Internet. Its specification and implementations have been refined for almost forty years. The Linux TCP stack is one of the most widely used TCP stacks given its ... More

A dynamical constraint on interstellar dust models from radiative torque disruptionDec 20 2018Mar 16 2019Interstellar dust is an essential component of the interstellar medium (ISM) and plays critical roles in astrophysics. Achieving an accurate model of interstellar dust is therefore of great importance. Interstellar dust models are usually built based ... More

Properties and alignment of interstellar dust grains toward Type Ia Supernovae with anomalous polarization curvesOct 07 2015Recent photometric and polarimetric observations of type Ia supernovae (SNe Ia) show unusually low total-to-selective extinction ratio ($R_{V}<2$) and wavelength of maximum polarization ($\lambda_{max}<0.4\mu m$) for several SNe Ia, which indicates peculiar ... More

Modified defect relations of the Gauss map of complete minimal surfaces on annular endsAug 13 2014In this article, we study the modified defect relations of the Gauss map of complete minimal surfaces in $\mathbb R^3$ and $ \mathbb R^4$ on annular ends. We obtain results which are similar to the ones obtained by Fujimoto~[J. Differential Geometry \textbf{29} ... More

Comment on arXiv:0709.3700 "Orientation dependence of the optical spectra in graphene at high frequencies"Jun 08 2016Zhang et al. reported in [Phys. Rev. B 77, 241402(R) (2008)] a theoretical study of the optical spectra of monolayer graphene employing the Kubo formula within a tight-binding model. Their calculations predicted that at high frequencies the optical conductivity ... More

Ramification of the Gauss Map of Complete Minimal Surfaces in R^3 and R^4 on Annular EndsApr 26 2013Nov 30 2014In this article, we study the ramification of the Gauss map of complete minimal surfaces in R^3 and R^4 on annular ends. We obtain results which are similar to the ones obtained by Fujimoto and Ru for (the whole) complete minimal surfaces, thus we show ... More

A note on a unicity theorem for the Gauss maps of complete minimal surfaces in Euclidean four-spaceDec 14 2016The classical result of Nevanlinna states that two nonconstant meromorphic functions on the complex plane having the same images for five distinct values must be identically equal to each other. In this paper, we give a similar uniqueness theorem for ... More

Singular holomorphic foliations by curves I: Integrability of holonomy cocycle in dimension 2Mar 30 2014Jul 29 2016We study the holonomy cocycle H of a holomorphic foliation \Fc by Riemann surfaces defined on a compact complex projective surface X satisfying the following two conditions: 1) its singularities E are all hyperbolic; 2) there is no holomorphic non-constant ... More

Recent developments in the theory of separately holomorphic mappingsJan 14 2009We describe a part of the recent developments in the theory of separately holomorphic mappings between complex analytic spaces. Our description focuses on works using the technique of holomorphic discs.

Green currents for quasi-algebraically stable meromorphic self-maps of CP^kFeb 09 2009Dec 30 2011We construct a canonical Green current T_f for every quasi-algebraically stable meromorphic self-map f of CP^k such that its first dynamical degree \lambda_1(f) is a simple root of its characteristic polynomial and that \lambda_1(f) > 1. We establish ... More

Algebraic degrees for iterates of meromorphic self-maps of $¶^k$Mar 22 2006We first introduce the class of quasi-algebraically stable meromorphic maps of $\P^k.$ This class is strictly larger than that of algebraically stable meromorphic self-maps of $\P^k.$ Then we prove that all maps in the new class enjoy a recurrent property. ... More

Note on abstract stochastic semilinear evolution equationsAug 28 2015Nov 14 2016This paper is devoted to studying abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces. First, we prove the existence of unique local mild solutions and show their regularity. Second, we show the regular dependence ... More

An Elementary Approach to a Curious Identity from RamanujanApr 19 2019In his notebooks, Ramanujan wrote the following identity: \begin{equation} \sqrt{2 \left(1 - \frac{1}{3^2}\right) \left(1 - \frac{1}{7^2}\right) \left(1 - \frac{1}{11^2}\right) \left(1 - \frac{1}{19^2}\right)} \ = \ \left(1 + \frac{1}{7}\right) \left(1 ... More

General Relativity in noncommutative spacetime as a unified framework for all interactions and the Higgs fieldDec 05 2015Dec 11 2015General Relativity in the noncommutative spacetime of ${\cal M}^4 \times Z_2 \times Z_2$ is constructed based on a new type of fermions in addition to the known chiral quark-leptons. While this theory has a finite physical spectrum, all the known interactions ... More

Ground state of the mass-critical inhomogeneous nonlinear Schrodinger functionalMay 01 2019We study the ground state problem of the nonlinear Schrodinger functional with a mass-critical inhomogeneous nonlinear term. We provide the optimal condition for the existence of ground states and show that in the critical focusing regime there is a universal ... More

Equilibrium measures of meromorphic self-maps on non-Kahler manifoldsJan 15 2019Apr 17 2019Let $X$ be a compact complex non-K\"ahler manifold and $f$ a dominant meromorphic self-map of $X$. Examples of such maps are self-maps of Hopf manifolds, Calabi-Eckmann manifolds, non-tori nilmanifolds and their blowups. We prove that if $f$ has a dominant ... More

Blow-up profile of the focusing Gross-Pitaevskii minimizer under self-gravitating effectAug 27 2018We consider a Bose-Einstein condensate in a 2D dilute Bose gas, with an external potential and an interaction potential containing both of the short-range attractive self-interaction and the long-range self-gravitating effect. We prove the existence of ... More

Direct Growth of Graphene on Flexible Substrates Towards Flexible Electronics: A Promising PerspectiveDec 27 2017Aug 03 2018Graphene has recently been attracting considerable interest because of its exceptional conductivity, mechanical strength, thermal stability, etc. Graphene-based devices exhibit high potential for applications in flexible electronics, optoelectronics, ... More

Singular holomorphic foliations by curves II: Negative Lyapunov exponentDec 25 2018Let $\Fc$ be a holomorphic foliation by Riemann surfaces defined on a compact complex projective surface $X$ satisfying the following two conditions: $\bullet$ the singular points of $\Fc$ are all hyperbolic; $\bullet$ $\Fc$ is Brody hyperbolic. Then ... More

Renormalization of determinant lines in Quantum Field TheoryJan 29 2019Mar 08 2019On a compact manifold $M$, we consider the affine space $A$ of non self-adjoint perturbations of some invertible elliptic operator acting on sections of some Hermitian bundle, by some differential operator of lower order. We construct and classify all ... More

Corrigendum: Conical plurisubharmonic measure and new cross theoremsJan 21 2009Nov 04 2011In the previous version of this paper we prove a theorem on the boundary behavior of the conical plurisubharmonic measure. However, the proof turns out to be incomplete. In the present version we give a corrected proof of this theorem. We next apply it ... More

When Sets Are Not Sum-dominantMar 08 2019Given a set $A$ of nonnegative integers, define the sum set $A+A = \{a_i+a_j|a_i,a_j\in A\}$ and the difference set $A-A = \{a_i-a_j|a_i,a_j\in A\}$. The set $A$ is said to be sum-dominant if $|A+A|>|A-A|$. In answering a question by Nathanson, Hegarty ... More

Renormalization of determinant lines in Quantum Field TheoryJan 29 2019On a compact manifold $M$, we consider the affine space $A$ of non self-adjoint perturbations of some invertible elliptic operator acting on sections of some Hermitian bundle, by some differential operator of lower order. We construct and classify all ... More

Directed harmonic currents near hyperbolic singularitiesNov 24 2014Let \Fc be a holomorphic foliation by curves defined in a neighborhood of 0 in \C^2 having 0 as a hyperbolic singularity. Let T be a harmonic current directed by \Fc which does not give mass to any of the two separatrices. Then we show that the Lelong ... More

Wick squares of the Gaussian Free Field and Riemannian rigidityFeb 19 2019Mar 03 2019In this short note, we show that on a compact Riemannian manifold $(M,g)$ of dimension $(d=2,3)$ whose metric has negative curvature, the partition function $Z_g(\lambda)$ of a massive Gaussian Free Field or the fluctuations of the integral of the Wick ... More

Quantum Co-Adjoint Orbits of the Real Diamond GroupJan 07 2000Jan 08 2000We present explicit formulas for deformation quantization on the co-adjoint orbits of the real diamond Lie group. From this we obtain quantum half-plans, quantum hyperbolic cylinders, quantum hyperbolic paraboloids via Fedosov deformation quantization ... More

Quantum co-adjoint orbits of $\MD_4$-groupsMar 09 2000Using $\star$-product on Co-adjoint orbits (K-orbits) of the $\MD_4$- groups we obtain quantum half-planes, quantum hyperbolic cylinders, quantum hyperbolic paraboloids...via Fedosov deformation quantization. From this we have corresponding unitary representations ... More

Polynomial behavior in mean of stochastic skew-evolution semiflowsFeb 12 2019In this paper, we are interested in the more general concept of a polynomial (in)stability in mean in which the polynomial behaviour in the classical sense is replaced by a weaker requirement with respect to some probability measure. This concept includes ... More

Normal restriction in finite groupsDec 04 2009In this paper, we will prove some sufficient conditions for the solvability of groups.

Positivity of mixed multiplicitiesNov 11 2002This paper studies mixed multiplicities of an arbitrary standard bigraded algebra and mixed multiplicities of two ideals I, J in a local ring (A,m), where I is an m-primary ideal and J an arbitrary ideal. The main results are criteria for their positivity ... More

Regularity of solutions of abstract linear evolution equationsAug 28 2015Jul 14 2016In this paper, we study regularity of solutions to linear evolution equations of the form $dX+AXdt=F(t)dt$ in a Banach space $H$, where $A$ is a sectorial operator in $H$ and $A^{-\alpha} F \, (\alpha>0)$ belongs to a weighted H\"{o}lder continuous function ... More

Note on regularity of solutions of abstract linear evolution equationsMay 06 2015In this paper, temporal and spatial regularity of mild solutions to two linear evolution equations with coefficients belonging to weighted H\"{o}lder continuous spaces is studied. The first equation is a deterministic equation and is treated in Banach ... More

Symmetric groups are determined by their character degreesMar 21 2011Let $G$ be a finite group. Let $X_1(G)$ be the first column of the ordinary character table of $G.$ In this paper, we will show that if $X_1(G)=X_1(S_n),$ then $G\cong S_n.$ As a consequence, we show that $S_n$ is uniquely determined by the structure ... More

Blow-up for biharmonic Schrodinger equation with critical nonlinearityJul 24 2018We consider the minimizers for the biharmonic nonlinear Schr\"odinger functional $$ \mathcal{E}_a(u)=\int_{\mathbb{R}^d} |\Delta u(x)|^2 d x + \int_{\mathbb{R}^d} V(x) |u(x)|^2 d x - a \int_{\mathbb{R}^d} |u(x)|^{q} d x $$ with the mass constraint $\int ... More

Lévy-driven causal CARMA random fieldsMay 22 2018We introduce L\'evy-driven causal CARMA random fields on $\mathbb{R}^d$, extending the class of CARMA processes. The definition is based on a system of stochastic partial differential equations which generalize the classical state-space representation ... More

Complex symmetry of first-order differential operators on Hardy spaceJan 08 2019Given holomorphic functions $\psi_0$ and $\psi_1$, we consider first-order differential operators acting on Hardy space, generated by the formal differential expression $E(\psi_0,\psi_1)f(z)=\psi_0(z)f(z)+\psi_1(z)f'(z)$. We characterize these operators ... More

Groups with normal restriction propertyDec 04 2009Let G be a finite group. A subgroup M of G is said to be an NR-subgroup if, whenever K is normal in M, then K^G\cap M=K, where K^G is the normal closure of K in G. Using the Classification of Finite Simple Groups, we prove that if every maximal subgroup ... More

Ergodic theory for Riemann surface laminations: a surveyDec 28 2017We survey some recent developments in the ergodic theory for hyperbolic Riemann surface laminations. The emphasis is on singular holomorphic foliations. These results not only illustrate the strong similarity between the ergodic theory of maps and that ... More

Extension of distributions, scalings and renormalization of QFT on Riemannian manifoldsNov 13 2014Let $M$ be a smooth manifold and $X\subset M$ a closed subset of $M$. In this paper, we introduce a natural condition of \emph{moderate growth} along $X$ for a distribution $t$ in $\mathcal{D}^\prime(M\setminus X)$ and prove that this condition is equivalent ... More

Existence results for linear evolution equations of parabolic typeMay 06 2015Apr 13 2017We study both strict and mild solutions to parabolic evolution equations of the form $dX+AXdt=F(t)dt+G(t)dW(t)$ in Banach spaces. First, we explore the deterministic case. The maximal regularity of solutions has been shown. Second, we investigate the ... More

The degree sequence of ideals and multiplicitiesMar 10 2015May 05 2015This paper investigates the relationship between multiplicities and the degree sequence of ideals in graded algebras, gives multiplicity equations of graded rings via the degree sequence of ideals, and characterizes mixed multiplicities and multiplicities ... More

Simple classical groups of Lie type are determined by their character degreesMay 21 2011Feb 22 2012In this paper, we will show that nonabelian simple classical groups of Lie type are uniquely determined by the structure of their complex group algebras.

Wick squares of the Gaussian Free Field and Riemannian rigidityFeb 19 2019In this short note, we show that on a compact Riemannian manifold $(M,g)$ of dimension $(d=2,3)$ whose metric has negative curvature, the partition function $Z_g(\lambda)$ of a massive Gaussian Free Field or the fluctuations of the integral of the Wick ... More

Blow-up profile of Bose-Einstein condensate with singular potentialsJul 25 2017The paper is concerned with the Bose-Einstein condensate described by the attractive Gross-Pitaevskii equation in R 2 , where the external potential is unbounded from below. We show that when the interaction strength increases to a critical value, the ... More

Solvable-by-finite maximal subgroups of skew linear groupsMar 23 2019Let $D$ be a non-commutative division ring with center $F$, $G$ a subnormal subgroup of $GL_n(D)$. In this note we show that if $G$ contains a non-abelian solvable-by-finite maximal subgroup, then $[D:F]<\infty$, and there exists a maximal subfield $K$ ... More

Influence of strongly closed 2-subgroups on the structure of finite groupsMay 24 2010Feb 24 2011Let $H\leq K$ be subgroups of a group G. We say that H is strongly closed in K with respect to G if whenever $a^g \in K$ where $a \in H, g \in G,$ then $a^g \in H.$ In this paper, we investigate the structure of a group G under the assumption that every ... More

Unbounded Weighted Composition Operators on Fock spaceApr 02 2018Nov 26 2018In this paper, we consider \emph{unbounded} weighted composition operators acting on Fock space, and investigate some important properties of these operators, such as $\calC$-selfadjoint (with respect to weighted composition conjugations), Hermitian, ... More

Complex powers of analytic functions and meromorphic renormalization in QFTMar 03 2015In this article, we study functional analytic properties of the meromorphic families of distributions $(\prod_{i=1}^p (f_j+i0)^{\lambda_j})_{(\lambda_1,\dots,\lambda_p) \in \mathbb{C}^p}$ using Hironaka's resolution of singularities, then using recent ... More

Groups with some arithmetic conditions on real class sizesJun 26 2013Let G be a finite group. An element x in G is a real element if x is conjugate to its inverse in G. For x in G, the conjugacy class x^G is said to be a real conjugacy class if every element of x^G is real. We show that if 4 divides no real conjugacy class ... More

2-Parts of real class sizesApr 25 2018Aug 16 2018We investigate the structure of finite groups whose non-central real class sizes have the same $2$-part. In particular, we prove that such groups are solvable and have $2$-length one. As a consequence, we show that a finite group is solvable if it has ... More

Real class sizesMar 01 2018In this paper, we study the structures of finite groups using some arithmetic conditions on the sizes of real conjugacy classes. We prove that a finite group is solvable if the prime graph on the real class sizes of the group is disconnected. Moreover, ... More

Absolutely superficial sequencesFeb 23 2014Absolutely superficial sequences was introduced by P. Schenzel in order to study generalized Cohen-Macaulay (resp. Buchsbaum) modules. For an arbitrary local ring, they turned out to be d-sequences. This paper established properties of absolutely superficial ... More