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A useful underestimate for the convergence of integral functionalsJun 19 2015This article deals with the lower compactness property of a sequence of integrands and the use of this key notion in various domains: convergence theory, optimal control, non-smooth analysis. First about the interchange of the weak epi-limit and the symbol ... More

An efficient implementation of Slater-Condon rulesNov 25 2013Slater-Condon rules are at the heart of any quantum chemistry method as they allow to simplify $3N$-dimensional integrals as sums of 3- or 6-dimensional integrals. In this paper, we propose an efficient implementation of those rules in order to identify ... More

Store-to-Leak Forwarding: Leaking Data on Meltdown-resistant CPUsMay 14 2019Meltdown and Spectre exploit microarchitectural changes the CPU makes during transient out-of-order execution. Using side-channel techniques, these attacks enable leaking arbitrary data from memory. As state-of-the-art software mitigations for Meltdown ... More

One-dimension cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates in a trap potentialAug 11 2012By means of new general variational method we report a direct solution for the quintic self-focusing nonlinearity and cubic-quintic 1D Gross Pitaeskii equation (GPE) in a harmonic confined potential. We explore the influence of the 3D transversal motion ... More

statmod: Probability Calculations for the Inverse Gaussian DistributionMar 22 2016Jul 28 2016The inverse Gaussian distribution (IGD) is a well known and often used probability distribution for which fully reliable numerical algorithms have not been available. Our aim in this article is to develop software for this distribution for the R programming ... More

Fixed-Node Diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctionsAug 15 2014The potential energy curve of the F$_2$ molecule is calculated with Fixed-Node Diffusion Monte Carlo (FN-DMC) using Configuration Interaction (CI)-type trial wavefunctions. To keep the number of determinants reasonable (the first and second derivatives ... More

Parallel Transport of Higher Flat Gerbes as an Extended Homotopy Quantum Field TheoryFeb 28 2018We prove that the parallel transport of a flat (higher) gerbe on any given target space gives rise to an extended homotopy quantum field theory. In case the target space is the classifying space of a finite group, we provide explicit formulae for this ... More

The Little Bundles OperadJan 15 2019Feb 10 2019Hurwitz spaces are homotopy quotients of the braid group action on the moduli space of principal bundles over a punctured plane. By considering a certain model for this homotopy quotient we build an aspherical topological operad that we call the little ... More

The Little Bundles OperadJan 15 2019Aug 05 2019Hurwitz spaces are homotopy quotients of the braid group action on the moduli space of principal bundles over a punctured plane. By considering a certain model for this homotopy quotient we build an aspherical topological operad that we call the little ... More

Equivariant Higher Hochschild Homology and Topological Field TheoriesSep 18 2018We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group $G$. As coefficients, we allow $E_\infty$-algebras with $G$-action. For this homology theory, we establish an equivariant version of excision ... More

Equivariant Higher Hochschild Homology and Topological Field TheoriesSep 18 2018May 10 2019We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group $G$. As coefficients, we allow $E_\infty$-algebras with $G$-action. For this homology theory, we establish an equivariant version of excision ... More

Parallel Transport of Higher Flat Gerbes as an Extended Homotopy Quantum Field TheoryFeb 28 2018Jul 18 2019We prove that the parallel transport of a flat $n-1$-gerbe on any given target space gives rise to an $n$-dimensional extended homotopy quantum field theory. In case the target space is the classifying space of a finite group, we provide explicit formulae ... More

Bose-Einstein condensates in optical lattices: mathematical analysis and analytical approximate formulaeJul 14 2011We show that the Gross-Pitaevskii equation with cubic nonlinearity, as a model to describe the one dimensional Bose-Einstein condensates loaded into a harmonically confined optical lattice, presents a set of ground states which is orbitally stable for ... More

Electron-acoustic-phonon interaction in core/shell Ge/Si and Si/Ge nanowiresJul 05 2016Jul 07 2016General expressions for the electron- and hole-acoustical-phonon deformation potential Hamiltonian (H_{E-DP}) are derived for the case of Ge/Si and Si/Ge core/shell nanowire structures (NWs) with circular cross section. Based on the short-range elastic ... More

Spin density distribution in open-shell transition metal systems: A comparative post-Hartree-Fock, Density Functional Theory and quantum Monte Carlo study of the CuCl2 moleculeMay 16 2014We present a comparative study of the spatial distribution of the spin density (SD) of the ground state of CuCl2 using Density Functional Theory (DFT), quantum Monte Carlo (QMC), and post-Hartree-Fock wavefunction theory (WFT). A number of studies have ... More

Spectral inequalities for Jacobi operators and related sharp Lieb-Thirring inequalities on the continuumOct 14 2013In this paper we approximate a Schr\"odinger operator on $L^2(\R)$ by Jacobi operators on $\ell^2(\Z)$ to provide new proofs of sharp Lieb-Thirring inequalities for the powers $\gamma=1/2$ and $\gamma=3/2$. To this end we first investigate spectral inequalities ... More

Gorensteinness and iteration of Cox rings for Fano type varietiesMar 19 2019We show that finitely generated Cox rings are Gorenstein. This leads to a refined characterization of varieties of Fano type: they are exactly those projective varieties with Gorenstein canonical quasicone Cox ring. We then show that for varieties of ... More

Long-Range Superharmonic Josephson CurrentJan 27 2011Jul 23 2011We consider a long superconductor-ferromagnet-superconductor junction with one spin-active region. It is shown that an \textit{odd} number of Cooper pairs cannot have a long-range propagation when there is \textit{only one} spin-active region. When temperature ... More

Polynomial bound for partition rank in terms of analytic rankFeb 26 2019Let $G_1, \dots, G_k$ be vector spaces over a finite field $\mathbb{F} = \mathbb{F}_q$ with a non-trivial additive character $\chi$. The analytic rank of a multilinear form $\alpha \colon G_1 \times \dots \times G_k \to \mathbb{F}$ is defined as $\operatorname{arank}(\alpha) ... More

On the Complexity of SailsFeb 07 2011Dec 15 2011This paper analyses stable commutator length in groups Z^r * Z^s. We bound scl from above in terms of the reduced wordlength (sharply in the limit) and from below in terms of the answer to an associated subset-sum type problem. Combining both estimates, ... More

SL(n)-Contravariant $L_p$-Minkowski ValuationsOct 26 2014All SL(n)-contravariant $L_p$-Minkowski valuations on polytopes are completely classified. The prototypes of such valuations turn out to be the asymmetric $L_p$-projection body operators.

On eigenvalue and eigenvector estimates for nonnegative definite operatorsMar 16 2005In this article we further develop a perturbation approach to the Rayleigh--Ritz approximations from our earlier work. We both sharpen the estimates and extend the applicability of the theory to nonnegative definite operators . The perturbation argument ... More

An exponential estimate for Hilbert space-valued Ornstein--Uhlenbeck processesDec 22 2016Let $Z$ be a $H$-valued Ornstein--Uhlenbeck process, $b\colon[0,1]\times H \rightarrow H$ and $h\colon[0,1] \rightarrow H$ be a bounded, Borel measurable functions with $\|b\|_\infty \leq 1$ then $\mathbb E \exp \alpha \left| \int\limits_0^1 b(t, Z_t ... More

A topological classification of molecules and chemical reactions with a perplectic structureDec 20 2018Mar 01 2019In this paper, a topological classification of molecules and their chemical reactions is proposed on a single particle level . We consider zero-dimensional electronic Hamiltonians in a real-space tight-binding basis with spinless time-reversal symmetry ... More

Efficient Membership Testing for Pseudovarieties of Finite SemigroupsMay 02 2018Jun 15 2018We consider the complexity of deciding membership of a given finite semigroup to a fixed pseudovariety. While it is known that there exist pseudovarieties with NP-complete or even undecidable membership problems, for many well-known pseudovarieties the ... More

A novel water-Cherenkov detector design with retro-reflectors to produce antipodal ringsAug 29 2018Since Kamiokande, the basic design of water-Cherenkov detectors has not changed: the walls of a water tank are lined with photodetectors that capture Cherenkov photons produced by relativistic particles. However, with this design the majority of photons ... More

A mixed precision semi-Lagrangian algorithm and its performance on acceleratorsMar 22 2016In this paper we propose a mixed precision algorithm in the context of the semi-Lagrangian discontinuous Galerkin method. The performance of this approach is evaluated on a traditional dual socket workstation as well as on a Xeon Phi and an NVIDIA K80. ... More

The potential of the HAWC Observatory to observe violations of Lorentz InvarianceAug 17 2015The framework of relativistic quantum-field theories requires Lorentz Invariance. Many theories of quantum gravity, on the other hand, include violations of Lorentz Invariance at small scales and high energies. This generates a lot of interest in establishing ... More

Contractive Families on Compact SpacesDec 02 2013A family f_1,...,f_n of operators on a complete metric space X is called contractive if there exists lambda < 1 such that for any x,y in X we have d(f_i(x),f_i(y)) leq lambda d(x,y) for some i. Stein conjectured that for any contractive family there is ... More

Classification theorem for strong triangle blocking arrangementsSep 23 2018A strong triangle blocking arrangement is a geometric arrangement of some line segments in a triangle with certain intersection properties. It turns out that they are closely related to blocking sets. Our aim in this paper is to prove a classification ... More

Non-normal affine monoidsSep 27 2012Jun 07 2015We give a geometric description of the set of holes in a non-normal affine monoid $Q$. The set of holes turns out to be related to the non-trivial graded components of the local cohomology of $k[Q]$. From this, we see how various properties of $k[Q]$ ... More

Heights and totally real numbersJun 12 2012Nov 18 20131973 Schinzel proved that the standard logarithmic height h on the maximal totally real field extension of the rationals is either zero or bounded from below by a positive constant. In this paper we study this property for canonical heights associated ... More

On a construction of the basic spin representations of symmetric groupsNov 19 2009We present an inductive method for constructing the basic spin representations of the double covers of the symmetric groups over fields of any characteristic.

Gorensteinness and iteration of Cox rings for Fano type varietiesMar 19 2019Apr 08 2019We show that finitely generated Cox rings are Gorenstein. This leads to a refined characterization of varieties of Fano type: they are exactly those projective varieties with Gorenstein canonical quasicone Cox ring. We then show that for varieties of ... More

Decomposing Sets of InversionsNov 15 2011Aug 06 2012In this note we consider the question how the set of inversions of a permutation $\pi \in S_n$ can be partitioned into two subset, such that those are itself inversion sets of permutations. This is archived by exploiting a connection to a graph theoretical ... More

Invariant rings of sums of fundamental representations of ${\rm SL}_n$ and colored hypergraphsJul 25 2018The fundamental representations of the special linear group ${\rm SL}_n$ over the complex numbers are the exterior powers of $\mathbb{C}^n$. We consider the invariant rings of sums of arbitrary many copies of these ${\rm SL}_n$-modules. The symbolic method ... More

Spin Waves as Metric in a Kinetic Space-TimeApr 17 2003Nov 29 20041) A wave equation is derived from the kinetic equations governing media with rotational as well as translational degrees of freedom. In this wave the fluctuating quantity is a vector, the bulk spin. The transmission is similar to compressive waves but ... More

On the geometric properties of the semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equationJan 10 2016The semi-Lagrangian discontinuous Galerkin method, coupled with a splitting approach in time, has recently been introduced for the Vlasov--Poisson equation. Since these methods are conservative, local in space, and able to limit numerical diffusion, they ... More

Lepton flavor violation in supersymmetric low-scale seesaw modelsDec 04 2013The minimal supersymmetric standard model with a low scale see-saw mechanism is presented. Within this framework, the lepton flavour violation in the charged lepton sector is thoroughly studied. Special attention is paid to the individual loop contributions ... More

Dynamical description of Tychonian UniverseApr 26 2013Mar 16 2015Using Mach's principle, we will show that the observed diurnal and annual motion of the Earth can just as well be accounted as the diurnal rotation and annual revolution of the Universe around the fixed and centered Earth. This can be performed by postulating ... More

Linearity in minimal resolutions of monomial idealsFeb 24 2017Mar 24 2017Let $S = k[x_1, \dotsc, x_n]$ be a polynomial ring over a field $k$ and let $M$ be a graded $S$-module with minimal free resolution $\mathbb{F}_\bullet$. Its linear part $lin(\mathbb{F}_\bullet)$ is obtained by deleting all non-linear entries from the ... More

The Linear Ordering Polytope via RepresentationsSep 23 2011Oct 25 2011Let $P_n$ denote the $n$-th linear ordering polytope. We define projections from $P_n$ to the $n$-th permutahedron and to the $(n-1)$-st linear ordering polytope. Both projections are equivariant with respect to the natural $\Sn$-action and they project ... More

SL(n)-Covariant $L_p$-Minkowski ValuationsSep 18 2012Jul 01 2015All continuous SL(n)-covariant $L_p$-Minkowski valuations defined on convex bodies are completely classified. The $L_p$-moment body operators turn out to be the nontrivial prototypes of such maps.

A comparison of semi-Lagrangian discontinuous Galerkin and spline based Vlasov solvers in four dimensionsMar 06 2018The purpose of the present paper is to compare two semi-Lagrangian methods in the context of the four-dimensional Vlasov--Poisson equation. More specifically, our goal is to compare the performance of the more recently developed semi-Lagrangian discontinuous ... More

Small totally $p$-adic algebraic numbersFeb 16 2018Jan 10 2019The purpose of this note is to give a short and elementary proof of the fact, that the absolute logarithmic Weil-height is bounded from below by a positive constant for all totally p-adic numbers which are neither zero nor a root of unity. The proof is ... More

An adaptive step size controller for iterative implicit methodsSep 29 2017Jun 09 2018The automatic selection of an appropriate time step size has been considered extensively in the literature. However, most of the strategies developed operate under the assumption that the computational cost (per time step) is independent of the step size. ... More

Frequency Based Index Estimating the Subclusters' Connection StrengthOct 19 2017Oct 25 2017In this paper, a frequency coefficient based on the Sen-Shorrocks-Thon (SST) poverty index notion is proposed. The clustering SST index can be used as the method for determination of the connection between similar neighbor sub-clusters. Consequently, ... More

Radiation Damping of a Polarizable ParticleAug 20 2017A polarizable body moving in an external electromagnetic field will slow down. This effect is referred to as radiation damping and is analogous to Doppler cooling in atomic physics. Using the principles of special relativity we derive an expression for ... More

A GPU accelerated and error-controlled solver for the unbounded Poisson equation in three dimensionsDec 06 2016An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. While the error of all involved approximations can be fully controlled, the overall ... More

A response-matrix-centred approach to presenting cross-section measurementsMar 15 2019Mar 21 2019The current canonical approach to publishing cross-section data is to unfold the reconstructed distributions. Detector effects like efficiency and smearing are undone mathematically, yielding distributions in true event properties. This is an ill-posed ... More

The Intersection Problem for Finite SemigroupsJun 13 2018We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We introduce compressibility ... More

An improved upper bound for the grid Ramsey problemSep 25 2018For a positive integer $r$, let $G(r)$ be the smallest $N$ such that, whenever the edges of the Cartesian product $K_N \times K_N$ are $r$-coloured, then there is a rectangle in which both pairs of opposite edges receive the same colour. In this paper, ... More

Covering complete graphs by monochromatically bounded setsMay 25 2017Given a $k$-colouring of the edges of the complete graph $K_n$, are there $k-1$ monochromatic components that cover its vertices? This important special case of the well-known Lov\'asz-Ryser conjecture is still open. In this paper we consider a strengthening ... More

Sets in Almost General PositionJan 26 2016Erd\H{o}s asked the following question: given $n$ points in the plane in almost general position (no 4 collinear), how large a set can we guarantee to find that is in general position (no 3 collinear)? F\"uredi constructed a set of $n$ points in almost ... More

A Dynamical Bogomolov PropertyMar 07 2011A field F is said to have the Bogomolov Property related to a height function h, if h(a) is either zero or bounded from below by a positive constant for all a in F. In this paper we prove that the maximal algebraic extension of a number field K, which ... More

Generalized Monotone Triangles: an extended Combinatorial Reciprocity TheoremJul 18 2012In a recent work, the combinatorial interpretation of the polynomial alpha(n;k1,k2,...,kn) counting the number of Monotone Triangles with bottom row k1 < k2 < ... < kn was extended to weakly decreasing sequences k1 >= k2 >= ... >= kn. In this case the ... More

Semi-Lagrangian Vlasov simulation on GPUsJul 18 2019In this paper, our goal is to efficiently solve the Vlasov equation on GPUs. A semi-Lagrangian discontinuous Galerkin scheme is used for the discretization. Such kinetic computations are extremely expensive due to the high-dimensional phase space. The ... More

Pseudorandomness of the Ostrowski sum-of-digits functionNov 09 2016For an irrational $\alpha\in(0,1)$, we investigate the Ostrowski sum-of-digits function $\sigma_\alpha$. For $\alpha$ having bounded partial quotients and $\vartheta\in\mathbb R\setminus\mathbb Z$, we prove that the function $g:n\mapsto \mathrm e(\vartheta ... More

A non-Golod ring with a trivial product on its Koszul homologyNov 16 2015Jan 30 2017We present a monomial ideal $\mathfrak{a} \subset S$ such that $S/\mathfrak{a}$ is not Golod, even though the product on its Koszul homology is trivial. This constitutes a counterexample to a well-known result by Berglund and J\"ollenbeck (the error can ... More

Stanley depth and simplicial spanning treesOct 14 2014Mar 09 2015We show that for proving the Stanley conjecture, it is sufficient to consider a very special class of monomial ideals. These ideals (or rather their lcm lattices) are in bijection with the simplicial spanning trees of skeletons of a simplex. We apply ... More

Completing the classification of representations of $\mathrm{SL}_n$ with complete intersection invariant ringDec 05 2018We present a full list of all representations of the special linear group $\mathrm{SL}_n$ over the complex numbers with complete intersection invariant ring, completing the classification of Shmelkin. For this task, we combine three techniques. Firstly, ... More

A non-Golod ring with a trivial product on its Koszul homologyNov 16 2015We present a monomial ideal $\mathfrak{a} \subset S$ such that $S/\mathfrak{a}$ is not Golod, even though the product on its Koszul homology is trivial. This constitutes a counterexample to a well-known theorem by Berglund and J\"ollenbeck (the error ... More

Wormhole Effects on Yang-Mills TheoryJul 25 1994In this paper wormhole effects on $SO(3)$ YM theory are examined. The wormhole wave functions for the scalar, the vector and the tensor expansion modes are computed assuming a small gauge coupling which leads to an effective decoupling of gravity and ... More

sl3-foam homology calculationsDec 11 2012Feb 20 2013We exhibit a certain infinite family of three-stranded quasi-alternating pretzel knots which are counterexamples to Lobb's conjecture that the sl_3-knot concordance invariant s_3 (suitably normalised) should be equal to the Rasmussen invariant s_2. For ... More

A modern resistive magnetohydrodynamics solver using C++ and the Boost libraryJul 11 2014In this paper we describe the implementation of our C++ resistive magnetohydrodynamics solver. The framework developed facilitates the separation of the code implementing the specific numerical method and the physical model, on the one hand, from the ... More

A multifractal boundary spectrum for SLE$_κ(ρ)$May 27 2019We study SLE$_\kappa(\rho)$ curves, with $\kappa$ and $\rho$ chosen so that the curves hit the boundary. More precisely, we study the sets on which the curves collide with the boundary at a prescribed "angle" and determine the almost sure Hausdorff dimension ... More

Piatetski-Shapiro sequences via Beatty sequencesJul 17 2017Integer sequences of the form $\lfloor n^c\rfloor$, where $1<c<2$, can be locally approximated by sequences of the form $\lfloor n\alpha+\beta\rfloor$ in a very good way. Following this approach, we are led to an estimate of the difference \[\sum_{n\leq ... More

A digit reversal property for Stern polynomialsOct 01 2016Nov 15 2017We consider the following polynomial generalization of Stern's diatomic series: let $s_1(x,y)=1$, and for $n\geq 1$ set $s_{2n}(x,y)=s_n(x,y)$ and $s_{2n+1}(x,y)=x\,s_n(x,y)+y\,s_{n+1}(x,y)$. The coefficient $[x^iy^j]s_n(x,y)$ is the number of hyperbinary ... More

Structure preserving numerical methods for the Vlasov equationApr 09 2016To preserve a number of physically relevant invariants is a major concern when considering long time integration of the Vlasov equation. In the present work we consider the semi-Lagrangian discontinuous Galerkin method for the Vlasov-Poisson system. We ... More

A study on conserving invariants of the Vlasov equation in semi-Lagrangian computer simulationsJan 10 2016Mar 07 2017The semi-Lagrangian discontinuous Galerkin method, coupled with a splitting approach in time, has recently been introduced for the Vlasov--Poisson equation. Since these methods are conservative, local in space, and able to limit numerical diffusion, they ... More

The relative effects of dimensionality and multiplicity of hypotheses on the F-test in linear regressionNov 19 2015Nov 07 2016Recently, several authors have re-examined the power of the classical F-test in linear regression in a `large-p, large-n' framework (cf. Zhong and Chen (2011), Wang and Cui (2013)). They highlight the loss of power as the number of regressors p increases ... More

A low-rank algorithm for weakly compressible flowApr 12 2018In this paper, we propose a numerical method for solving weakly compressible fluid flow based on a dynamical low-rank projector splitting. The low-rank splitting scheme is applied to the Boltzmann equation with BGK collision term, which results in a set ... More

A note on friezes of type $Λ_4$ and $Λ_6$Feb 22 2018We point out a certain connection between Conway-Coxeter friezes of triangulations and $p$-angulated generalisation of frieze patterns recently introduced by Holm and J{\o}rgensen: the friezes of type $\Lambda_p$ coincide with Conway-Coxeter friezes of ... More

A note on extensions of $\mathbb{Q}^{tr}$Aug 27 2014In this note we investigate the behaviour of the absolute logarithmic Weil-height h on extensions of the field $\mathbb{Q}^{tr}$ of totally real numbers. It is known that there is a gap between zero and the next smallest value of h on $\mathbb{Q}^{tr}$, ... More

A digit reversal property for an analogue of Stern's sequenceSep 17 2017We consider a variant of Stern's diatomic sequence, studied recently by Northshield. We prove that this sequence $b$ is invariant under \emph{digit reversal} in base $3$, that is, $b_n=b_{n^R}$, where $n^R$ is obtained by reversing the base-$3$ expansion ... More

Discrepancy results for the Van der Corput sequenceOct 04 2017Let $d_N=ND_N(\omega)$ be the discrepancy of the Van der Corput sequence in base $2$. We improve on the known bounds for the number of indices $N$ such that $d_N\leq \log N/100$. Moreover, we show that the summatory function of $d_N$ satisfies an exact ... More

The Lecture Hall Cone as a toric deformationSep 05 2018The Lecture Hall cone is a simplicial cone whose lattice points naturally correspond to Lecture Hall partitions. The celebrated Lecture Hall Theorem of Bousquet-M\'elou and Eriksson states that a particular specialization of its multivariate Ehrhart series ... More

Evaluation of the Intel Xeon Phi and NVIDIA K80 as accelerators for two-dimensional panel codesNov 06 2015To predict the properties of fluid flow over a solid geometry is an important engineering problem. In many applications so-called panel methods (or boundary element methods) have become the standard approach to solve the corresponding partial differential ... More

Moving Five-Branes and CosmologyOct 03 2002We discuss low-energy heterotic M-theory with five-branes in four and five dimensions and its application to moving brane cosmology.

The No-Boundary Wave Function and the Duration of the Inflationary PeriodSep 07 1994For the simplest minisuperspace model based on a homogeneous, isotropic metric and a minimally coupled scalar field we derive analytic expressions for the caustic which separates Euklidean and Minkowskian region and its breakdown value $\p_*$. This value ... More

Spontaneous breaking of Lorentz symmetry in (2+1)-dimensional QEDApr 21 2016Jul 21 2016The phase diagram of massless quantum electrodynamics in three space-time dimensions as a function of fermion flavor number $N$ exhibits two well-known phases: at large $N > N_c^{conf}$ the system is in a conformal gapless state, while for small $N < ... More

The structure of DGA resolutions of monomial idealsOct 20 2016Let $I \subset k[x_1, \dotsc, x_n]$ be a squarefree monomial ideal a polynomial ring. In this paper we study multiplications on the minimal free resolution $\mathbb{F}$ of $S/I$. In particular, we characterize the possible vectors of total Betti numbers ... More

Motion planning in high-dimensional spacesJun 19 2018Jul 19 2018Motion planning is a key tool that allows robots to navigate through an environment without collisions. The problem of robot motion planning has been studied in great detail over the last several decades, with researchers initially focusing on systems ... More

Newton-Machian analysis of Neo-tychonian model of planetary motionsJan 25 2013Feb 06 2013The calculation of the trajectories in the Sun-Earth-Mars system will be performed in two different models, both in the framework of Newtonian mechanics. First model is well-known Copernican system, which assumes the Sun is at rest and all the planets ... More

Relative convergence estimates for the spectral asymptotic in the Large Coupling LimitFeb 13 2009We prove optimal convergence estimates for eigenvalues and eigenvectors of a class of singular/stiff perturbed problems. Our profs are constructive in nature and use (elementary) techniques which are of current interest in computational Linear Algebra ... More

Linearizability of Saturated PolynomialsJul 09 2015Jul 14 2015Brjuno and R\"ussmann proved that every irrationally indifferent fixed point of an analytic function with a Brjuno rotation number is linearizable, and Yoccoz proved that this is sharp for quadratic polynomials. Douady conjectured that this is sharp for ... More

Invariant Hochschild cohomology of smooth functionsAug 24 2018Sep 26 2018Given an action of a Lie group on a smooth manifold, we discuss the induced action on the Hochschild cohomology of smooth functions, and notions of invariance on this space. Depending on whether one considers invariance of cochains or invariance of cohomology ... More

Rasmussen's spectral sequences and the sl(N)-concordance invariantsOct 11 2013Jul 18 2014Combining known spectral sequences with a new spectral sequence relating reduced and unreduced sl(N)-homology yields a relationship between the Homflypt-homology of a knot and its sl(N)-concordance invariants. As an application, some of the sl(N)-concordance ... More

High performance computing aspects of a dimension independent semi-Lagrangian discontinuous Galerkin codeJan 22 2015The recently developed semi-Lagrangian discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit numerical diffusion, ... More

Heights of points with bounded ramificationJan 16 2012Nov 18 2013Let $E$ be an elliptic curve defined over a number field $K$ with fixed non-archimedean absolute value $v$ of split-multiplicative reduction, and let $f$ be an associated Latt\`es map. Baker proved in 2003 that the N\'eron-Tate height on $E$ is either ... More

Small Sets with Large Difference SetsMay 24 2017For every $\epsilon > 0$ and $k \in \mathbb{N}$, Haight constructed a set $A \subset \mathbb{Z}_N$ ($\mathbb{Z}_N$ stands for the integers modulo $N$) for a suitable $N$, such that $A-A = \mathbb{Z}_N$ and $|kA| < \epsilon N$. Recently, Nathanson posed ... More

A magnetostatic energy formula arising from the $L^2$-orthogonal decomposition of the stray fieldNov 07 2016Jul 23 2018A formula for the magnetostatic energy of a finite magnet is proven. In contrast to common approaches, the new energy identity does not rely on evaluation of a nonlocal boundary integral inside the magnet or the solution of an equivalent Dirichlet problem. ... More

Spontaneous breaking of Lorentz symmetry in $(2+ε)$-dimensional QEDApr 21 2016Nov 15 2016The phase diagram of massless quantum electrodynamics in three space-time dimensions as a function of fermion flavor number $N$ exhibits two well-known phases: at large $N > N_c^{conf}$ the system is in a conformal gapless state, while for small $N < ... More

Evaluation of the Intel Xeon Phi 7120 and NVIDIA K80 as accelerators for two-dimensional panel codesNov 06 2015Mar 28 2018To optimize the geometry of airfoils for a specific application is an important engineering problem. In this context genetic algorithms have enjoyed some success as they are able to explore the search space without getting stuck in local optima. However, ... More

Betti posets and the Stanley depthSep 28 2015Feb 05 2016Let $S$ be a polynomial ring and let $I \subseteq S$ be a monomial ideal. In this short note, we propose the conjecture that the Betti poset of $I$ determines the Stanley projective dimension of $S/I$ or $I$. Our main result is that this conjecture implies ... More

Sharp bounds for the valence of certain harmonic polynomialsOct 25 2005D. Khavinson and G. Swiatek proved that harmonic polynomials p(z)+q(z), where p is holomorphic, q is antiholomorphic, and deg p = n > 1 = deg q, can have at most 3n-2 complex zeros. We show that this bound is sharp for all n by proving a conjecture of ... More

Algebraic Multilevel Methods for Markov ChainsNov 12 2017Dec 30 2017A new algebraic multilevel algorithm for computing the second eigenvector of a column-stochastic matrix is presented. The method is based on a deflation approach in a multilevel aggregation framework. In particular a square and stretch approach, first ... More

Polytopal affine semigroups with holes deep insideOct 16 2012Mar 20 2013Given a non-negative integer k, we construct a lattice 3-simplex P with the following property: The affine semigroup Q_P associated to P is not normal, and every element $q \in \sat{Q}_P \setminus Q_P$ has lattice distance at least k above every facet ... More

The structure of DGA resolutions of monomial idealsOct 20 2016Jun 20 2018Let $I \subset k[x_1, \dotsc, x_n]$ be a squarefree monomial ideal a polynomial ring. In this paper we study multiplications on the minimal free resolution $\mathbb{F}$ of $k[x_1, \dotsc, x_n]/I$. In particular, we characterize the possible vectors of ... More

Linear maps in minimal free resolutions of Stanley-Reisner ringsFeb 24 2017Jul 08 2019In this short note we give an elementary description of the linear part of the minimal free resolution of a Stanley-Reisner ring of a simplicial complex $\Delta$. Indeed, the differentials in the linear part are simply a compilation of restriction maps ... More