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The Auslander-Reiten Translation in Submodule CategoriesApr 14 2005Sep 30 2005Let $\Lambda$ be an artin algebra and $S(\Lambda)$ the category of all embeddings $(A\subseteq B)$ where $B$ is a finitely generated $\Lambda$-module and $A$ is a submodule of $B$. Then $S(\Lambda)$ is an exact Krull-Schmidt category which has Auslander-Reiten ... More

Operations on Arc Diagrams and Degenerations for Invariant Subspaces of Linear Operators. Part IISep 28 2016For a partition $\beta$, denote by $N_\beta$ the nilpotent linear operator of Jordan type $\beta$. Given partitions $\beta$, $\gamma$, we investigate the representation space ${}_2{\mathbb V}_{\gamma}^\beta$ of all short exact sequences $$ \mathcal E: ... More

From Schritte and Wechsel to Coxeter GroupsJan 16 2019The PLR-moves of neo-Riemannian theory, when considered as reflections on the edges of an equilateral triangle, define the Coxeter group~$\widetilde S_3$. The elements are in a natural one-to-one correspondence with the triangles in the infinite Tonnetz. ... More

Hall polynomials via automorphisms of short exact sequencesOct 11 2009We present a sum-product formula for the classical Hall polynomial which is based on tableaux that have been introduced by T. Klein in 1969. In the formula, each summand corresponds to a Klein tableau, while the product is taken over the cardinalities ... More

The entries in the LR-tableauMar 23 2009Oct 27 2009Let $\Gamma$ be the Littlewood-Richardson tableau corresponding to an embedding $M$ of a subgroup in a finite abelian $p$-group. Each individual entry in $\Gamma$ yields information about the homomorphisms from $M$ into a particular subgroup embedding, ... More

Bounded Submodules of ModulesAug 13 2004Let $m$, $n$ be positive integers such that $m\leq n$. We consider all pairs $(B,A)$ where $B$ is a finite dimensional $T^n$-bounded $k[T]$-module and $A$ is a submodule of $B$ which is $T^m$-bounded. They form the objects of the submodule category $S_m(k[T]/T^n)$ ... More

2:3:4-Harmony within the TritaveSep 01 2017Aug 01 2018In the Pythagorean tuning system, the fifth is used to generate a scale of 12 notes per octave. In this paper, we use the octave to generate a scale of 19 notes per tritave; one can play this scale on a traditional piano. In this system, the octave becomes ... More

From Littlewood-Richardson sequences to subgroup embeddings and backSep 18 2007Let $\alpha$, $\beta$, and $\gamma$ be partitions describing the isomorphism types of the finite abelian $p$-groups $A$, $B$, and $C$. From theorems by Green and Klein it is well-known that there is a short exact sequence $0\to A\to B\to C\to 0$ of abelian ... More

2:3:4-Harmony within the TritaveSep 01 2017Apr 07 2019In the Pythagorean tuning system, the fifth is used to generate a scale of 12 notes per octave. In this paper, we use the octave to generate a scale of 19 notes per tritave; one can play this scale on a traditional piano. In this system, the octave becomes ... More

Systems of submodules and a remark by M.C.R. ButlerJul 27 2005Sep 13 2006Fix a poset $P$ and a natural number $n$. For various commutative local rings $\Lambda$, each of Loewy length $n$, consider the category $\textrm{sub}_\Lambda P$ of $\Lambda$-linear submodule representations of $P$. We give a criterion for when the underlying ... More

From Schritte and Wechsel to Coxeter GroupsJan 16 2019Mar 25 2019The PLR-moves of neo-Riemannian theory, when considered as reflections on the edges of an equilateral triangle, define the Coxeter group $\widetilde S_3$. The elements are in a natural one-to-one correspondence with the triangles in the infinite Tonnetz. ... More

A Construction of Metabelian GroupsJul 29 2004Oct 25 2004In 1934, Garrett Birkhoff has shown that the number of isomorphism classes of finite metabelian groups of order $p^{22}$ tends to infinity with $p$. More precisely, for each prime number $p$ there is a family $(M_\lambda)_{\lambda=0,...,p-1}$ of indecomposable ... More

From Schritte and Wechsel to Coxeter GroupsJan 16 2019Apr 04 2019The PLR-moves of neo-Riemannian theory, when considered as reflections on the edges of an equilateral triangle, define the Coxeter group $\widetilde S_3$. The elements are in a natural one-to-one correspondence with the triangles in the infinite Tonnetz. ... More

Finite direct sums of cyclic embeddings and an application to invariant subspace varietiesJul 19 2016In his 1951 book "Infinite Abelian Groups", Kaplansky gives a combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group. In this paper we use partial maps on Littlewood-Richardson tableaux to ... More

The boundary of the irreducible components for invariant subspace varietiesAug 31 2014Oct 03 2016Given partitions $\alpha$, $\beta$, $\gamma$, the short exact sequences $0\to N_\alpha \to N_\beta \to N_\gamma \to 0$ of nilpotent linear operators of Jordan types $\alpha$, $\beta$, $\gamma$, respectively, define a constructible subset $\mathbb V_{\alpha,\gamma}^\beta$ ... More

The Swiss Cheese Theorem for Linear Operators with Two Invariant SubspacesSep 19 2014We study systems $(V,T,U_1,U_2)$ consisting of a finite dimensional vector space $V$, a nilpotent $k$-linear operator $T:V\to V$ and two $T$-invariant subspaces $U_1\subset U_2\subset V$. Let $\mathcal S(n)$ be the category of such systems where the operator ... More

Operations on Arc Diagrams and Degenerations for Invariant Subspaces of Linear OperatorsFeb 13 2012Jun 26 2013We study geometric properties of varieties associated with invariant subspaces of nilpotent operators. There are reductive algebraic groups acting on these varieties. We give dimensions of orbits of these actions. Moreover, a combinatorial characterization ... More

Arc diagram varietiesNov 25 2012Jun 26 2013Let $k$ be an algebraically closed field and $\alpha$, $\beta$, $\gamma$ be partitions. An algebraic group acts on the constructible set of short exact sequences of nilpotent $k$-linear operators of Jordan types $\alpha$, $\beta$, and $\gamma$, respectively; ... More

Extensions of Simple Modules and the Converse of Schur's LemmaMar 13 2009May 13 2009The converse of Schur's lemma (or CSL) condition on a module category has been the subject of considerable study in recent years. In this note we extend that work by developing basic properties of module categories in which the CSL condition governs modules ... More

Abelian groups with a $p^2$-bounded subgroup, revisitedMay 25 2006Apr 10 2007Let $R$ be a commutative local uniserial ring of length $n$, $p$ a generator of the maximal ideal, and $k$ the radical factor field. The pairs $(B,A)$ where $B$ is a finitely generated $R$-module and $A\subset B$ a submodule of $B$ such that $p^mA=0$ ... More

Box moves on Littlewood-Richardson tableaux and an application to invariant subspace varietiesJul 19 2016May 14 2019In his 1951 book "Infinite Abelian Groups", Kaplansky gives a combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group. In this paper we first use partial maps on Littlewood-Richardson tableaux ... More

Finite direct sums of cyclic embeddingsMay 14 2019In this paper we generalize Kaplansky's combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group given in his 1951 book ``Infinite Abelian Groups''. For this we introduce partial maps on Littlewood-Richardson ... More

The Auslander-Reiten Components in the Rhombic PictureApr 07 2012Oct 10 2012For an indecomposable module $M$ over a path algebra of a quiver of type $\widetilde{\mathbb A}_n$, the Gabriel-Roiter measure gives rise to four new numerical invariants; we call them the multiplicity, and the initial, periodic and final parts. We describe ... More

Invariant Subspaces of Nilpotent Linear Operators. IAug 28 2006Dec 05 2006Let $k$ be a field. We consider triples $(V,U,T)$, where $V$ is a finite dimensional $k$-space, $U$ a subspace of $V$ and $T \:V \to V$ a linear operator with $T^n = 0$ for some $n$, and such that $T(U) \subseteq U$. Thus, $T$ is a nilpotent operator ... More

Submodule Categories of Wild Representation TypeSep 21 2004Let $\Lambda$ be a commutative local uniserial ring of length at least seven with radical factor ring $k$. We consider the category $S(\Lambda)$ of all possible embeddings of submodules of finitely generated $\Lambda$-modules and show that $S(\Lambda)$ ... More

Two Partial Orders for Littlewood-Richardson TableauxMar 31 2015Feb 24 2016In this manuscript we show that two partial orders defined on the set of Littlewood-Richardson fillings of a~given shape $(\alpha,\beta,\gamma)$ are equivalent if $\beta\setminus\gamma$ is a horizontal and vertical strip. In fact, we give two proofs for ... More

Spectral covolatility estimation from noisy observations using local weightsDec 05 2011May 23 2013We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an appropriate estimation ... More

Discretisation of stochastic control problems for continuous time dynamics with delayFeb 17 2006As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow for delay in ... More

Quantum dynamics in transverse-field Ising models from classical networksJul 20 2017Jan 23 2018The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field ... More

An upper limit to photons from first data taken by the Pierre Auger ObservatoryJan 03 2007Many models for ultra-high energy cosmic rays postulate exotic scenarios to explain the sources or the nature of these particles. A characteristic feature of these models is the prediction of a significant flux of photons at ultra-high energy. The Pierre ... More

Yet another criterion for global existence in the 3D relativistic Vlasov-Maxwell systemJun 05 2014We prove that solutions of the 3D relativistic Vlasov-Maxwell system can be extended, as long as the quantity $\sigma_{-1}(t, x) = \max_{|\omega|=1} \,\int_{R^3} \frac{dp}{\sqrt{1+p^2}}\, \frac{1}{(1+v\cdot\omega)}\, f(t, x, p)$ is bounded in $L^2_x$. ... More

The fundamentals of non-singular dislocations in the theory of gradient elasticity: dislocation loops and straight dislocationsSep 10 2012The fundamental problem of non-singular dislocations in the framework of the theory of gradient elasticity is presented in this work. Gradient elasticity of Helmholtz type and bi-Helmholtz type are used. A general theory of non-singular dislocations is ... More

Peach-Koehler forces within the theory of nonlocal elasticityJan 29 2005We consider dislocations in the framework of Eringen's nonlocal elasticity. The fundamental field equations of nonlocal elasticity are presented. Using these equations, the nonlocal force stresses of a straight screw and a straight edge dislocation are ... More

Twist disclination in the field theory of elastoplasticityApr 23 2003Sep 30 2003In this paper we study the twist disclination within the elastoplastic defect theory. Using the stress function method, we found exact analytical solutions for all characteristic fields of a straight twist disclination in an infinitely extended linear ... More

On gradient field theories: gradient magnetostatics and gradient elasticityJun 30 2014In this work the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For gradient magnetostatics, non-singular expressions for ... More

Screw dislocations in the field theory of elastoplasticityMar 04 2002Sep 30 2002A (microscopic) static elastoplastic field theory of dislocations with moment and force stresses is considered. The relationship between the moment stress and the Nye tensor is used for the dislocation Lagrangian. We discuss the stress field of an infinitely ... More

A simple bijection between permutation matrices and descending plane partitions without special partsMay 04 2016Sep 19 2016We present a simple bijection between permutation matrices and descending plane partitions without special parts. This bijection involves the inversion words of permutations and the (well-known) representation of descending plane partitions as families ... More

Multiple hard scattering and parton correlations in the protonNov 04 2014This proceedings contribution gives a brief introduction to the theoretical description of double parton scattering and discusses several open problems.

Nonvanishing and Central Critical Values of Twisted $L$-functions of Cusp Forms on AverageFeb 09 2015Let $f$ be a holomorphic cusp form of integral weight $k \geq 3$ for $\Gamma_{0}(N)$ with nebentypus character $\psi$. Generalising work of Kohnen and Raghuram we construct a kernel function for the $L$-function $L(f,\chi,s)$ of $f$ twisted by a primitive ... More

Alexander-Beck modules detect the unknotOct 26 2016We introduce the Alexander-Beck module of a knot as a canonical refinement of the classical Alexander module, and we prove that this new invariant is an unknot-detector.

Persistent Contextual Values as Inter-Process LayersOct 14 2016Mobile applications today often fail to be context aware when they also need to be customizable and efficient at run-time. Context-oriented programming allows programmers to develop applications that are more context aware. Its central construct, the ... More

Multiphonon emission model of spin-dependent exciton formation in organic semiconductorsOct 18 2004The maximum efficiency in organic light-emitting diodes (OLEDs) depends on the ratio, $r=k_S/k_T$, where $k_S$ ($k_T$) is the singlet (triplet) exciton formation rate. Several recent experiments found that r increases with increasing oligomer length from ... More

Charge fluctuations and dephasing in coulomb coupled conductorsNov 12 1999It is shown that the dephasing rate in Coulomb coupled mesoscopic structures is determined by charge relaxation resistances. The charge relaxation resistance together with the capacitance determines the RC-time of the mesoscopic structure and at small ... More

Decoherence from Vacuum FluctuationsMay 28 2001Vacuum fluctuations are a source of irreversibility and decoherence. We investigate the persistent current and its fluctuations in a ring with an in-line quantum dot with an Aharonov-Bohm flux through the hole of the ring. The Coulomb blockade leads to ... More

Variational Inequalities and Improved Convergence Rates for Tikhonov Regularisation on Banach SpacesJul 13 2011In this paper we derive higher order convergence rates in terms of the Bregman distance for Tikhonov like convex regularisation for linear operator equations on Banach spaces. The approach is based on the idea of variational inequalities, which are, however, ... More

Orthogonal projectors onto spaces of periodic splinesAug 24 2016The main result of this paper is a proof that for any integrable function $f$ on the torus, any sequence of its orthogonal projections $(\widetilde{P}_n f)$ onto periodic spline spaces with arbitrary knots $\widetilde{\Delta}_n$ and arbitrary polynomial ... More

The Complexity of Linear Tensor Product Problems in (Anti-) Symmetric Hilbert SpacesOct 31 2011Aug 14 2012We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its worst case error ... More

Constraints on the Geometry of the VHE Emission in LS 5039 from Photon-Photon DeabsorptionSep 05 2006Nov 20 2006A detailed parameter study of the gamma-gamma absorption effects in LS 5039 is presented. For a range of plausible locations of the VHE gamma-ray emission region and the allowable range of viewing angles, the de-absorbed, intrinsic VHE gamma-ray spectra ... More

Charmless 2- and 3-body B decays and the angle alpha (phi2)Oct 20 2004We present preliminary measurements of branching fractions and CP-asymmetry parameters in two- and three-body charmless hadronic B decays. The available data sample consists of 227 million Upsilon(4S) B decays collected with the BABAR detector at the ... More

On the existence of (H,A)-stable sheaves on K3 or abelian surfacesFeb 20 2013We give an existence result on (H,A)-stable sheaves on a K3 or abelian surface X with primitive triple of invariants (rank,first Chern class,Euler characteristics) in the integral cohomology lattice. Such a result yields the existence of singular projective ... More

Round Table Summary: Stellar interferometry as a tool to investigate atmospheres and to compare observations with modelsApr 02 2003Long-baseline interferometry at optical and near-infrared wavelengths is an emerging technology which is quickly becoming a useful tool to investigate stellar atmospheres and to compare observations with models. Stellar atmosphere models have so far mainly ... More

Tate duality and transfer in Hochschild cohomologyNov 26 2012We show that dualising transfer maps in Hochschild cohomology of symmetric algebras commutes with Tate duality. This extends a well-known result in group cohomology.

Cohomology of quiver moduli, functional equations, and integrality of Donaldson-Thomas type invariantsMar 02 2009A system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert scheme-type) framed versions of quiver moduli is derived. This is applied to wall-crossing ... More

Counting rational points of quiver moduliMay 18 2005It is shown that rational points over finite fields of moduli spaces of stable quiver representations are counted by polynomials with integer coefficients. These polynomials are constructed recursively using an identity in the Hall algebra of a quiver. ... More

Cohomology of non-commutative Hilbert schemesJun 11 2003Sep 04 2003Non-commutative Hilbert schemes, introduced by M. V. Nori, parametrize left ideals of finite codimension in free algebras. More generally, parameter spaces of finite codimensional submodules of free modules over free algebras are considered. Cell decompositions ... More

The monoid of families of quiver representationsMay 15 2001A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, i.e. subvarieties of the varieties of representations. The study of this monoid leads to interesting interactions between ... More

A Systematic Search for Trojan Planets in the Kepler dataJul 26 2013Trojans are circumstellar bodies that reside in characteristic 1:1 orbital resonances with planets. While all the trojans in our Solar System are small (< ~100 km), stable planet-size trojans may exist in extrasolar planetary systems, and the Kepler telescope ... More

From form factors to generalized parton distributionsJun 25 2013I present an extraction of generalized parton distributions from selected data on the electromagnetic nucleon form factors. The extracted distributions can in particular be used to quantify the contribution to the proton spin from the total angular momentum ... More

A note on hook length formulas for treesApr 12 2010In this short note we discuss recent results on hook length formulas of trees unifying some earlier results, and explain hook length formulas naturally associated to families of increasingly labelled trees.

A note on naturally embedded ternary treesFeb 16 2009Mar 09 2009In this note we consider ternary trees naturally embedded in the plane in a deterministic way such that the root has position zero, or in other words label zero, and the children of a node with position $j$ have positions $j-1$, $j$, and $j+1$, for all ... More

Gas in Shearing Density WavesDec 04 1997We examine the development of a transient spiral arm in a disk galaxy made up of both gas and stars. To this end we have performed numerical simulations in a shearing sheet (basically a rectangular patch of a disc) that contains gas in the form of clouds ... More

Optimal synchronization on strongly connected directed networksNov 10 2009In this paper we construct and analyse strongly connected sparse directed networks with an enhanced propensity for synchronization (PFS). Two types of PFS-enhanced networks are considered: (i) an eigenratio minimizing ensemble with non-vanishing complex ... More

The synchronization transition in correlated oscillator populationsOct 07 2008Jun 15 2010The synchronization transition of correlated ensembles of coupled Kuramoto oscillators on sparse random networks is investigated. Extensive numerical simulations show that correlations between the native frequencies of adjacent oscillators on the network ... More

Homology and the stability problem in the Thompson group familyNov 18 2014Mar 24 2015We prove that Thompson's group V is acyclic. The strategy of our proof stems from the context of homological stability and stable homology. We first use algebraic K-theory methods to compute the stable homology for automorphism groups of algebraic theories ... More

Dynamical quantum phase transitions: scaling and universalityMay 10 2015Oct 05 2015Dynamical quantum phase transitions (DQPTs) at critical times appear as non-analyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge ... More

Knapsack in hyperbolic groupsJul 18 2018Recently knapsack problems have been generalized from the integers to arbitrary finitely generated groups. The knapsack problem for a finitely generated group $G$ is the following decision problem: given a tuple $(g, g_1, \ldots, g_k)$ of elements of ... More

A View From AboveSep 04 2017This activity has been developed as a resource for the "EU Space Awareness" educational programme. As part of the suite "Our Fragile Planet" together with the "Climate Box" it addresses aspects of weather phenomena, the Earth's climate and climate change ... More

A quantified Tauberian theorem for Laplace-Stieltjes transformNov 21 2017We prove a quantified Tauberian theorem involving Laplace-Stieltjes transform which is motivated by the work of Ingham and Karamata. For this, we consider functions which are locally of bounded variation and, therefore, get a generalisation of some results ... More

A babystep-giantstep method for faster deterministic integer factorizationAug 31 2016Jul 06 2017In 1977, Strassen presented a deterministic and rigorous algorithm for solving the problem of computing the prime factorization of natural numbers $N$. His method is based on fast polynomial arithmetic techniques and runs in time $\widetilde{O}(N^{1/4})$, ... More

An End-to-End Probabilistic Network Calculus with Moment Generating FunctionsJul 03 2005May 01 2006Network calculus is a min-plus system theory for performance evaluation of queuing networks. Its elegance stems from intuitive convolution formulas for concatenation of deterministic servers. Recent research dispenses with the worst-case assumptions of ... More

Norm varieties and algebraic cobordismApr 15 2003We outline briefly results and examples related with the bijectivity of the norm residue homomorphism. We define norm varieties and describe some constructions. We discuss degree formulas which form a major tool to handle norm varieties. Finally we formulate ... More

Large Deviations and Phase Transition for Random Walks in Random Nonnegative PotentialsSep 27 2006We establish large deviation principles and phase transition results for both quenched and annealed settings of nearest-neighbor random walks with constant drift in random nonnegative potentials on $\mathbb Z^d$. We complement the analysis of \cite{Zer}, ... More

Magnetoresistance and localization in bosonic insulatorsSep 01 2011Jul 12 2013We study the strong localization of hard core bosons. Using a locator expansion we find that in the insulator, unlike for typical fermion problems, nearly all low-energy scattering paths come with positive amplitudes and hence interfere constructively. ... More

On the Quantum Kolmogorov Complexity of Classical StringsJul 19 2007Jun 09 2009We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant. Both complexities are defined as the minimal length of any (classical resp. quantum) computer program that outputs the corresponding string. It ... More

A Grothendieck-Witt space for stable infinity categories with dualityOct 31 2016We construct a Grothendieck-Witt space for any stable infinity category with duality. If we apply our construction to perfect complexes over a commutative ring in which 2 is invertible we recover the classical Grothendieck-Witt space. Our Grothendieck-Witt ... More

The Dipole Anisotropy of Galactic Cosmic RaysNov 20 2018The arrival directions of Galactic cosmic rays exhibit anisotropies up to the level of one per-mille over various angular scales. Recent observations of TeV-PeV cosmic rays show that the dipole anisotropy has a strong energy dependence with a phase-flip ... More

A Note on the generating function of p-Bernoulli numbersJul 02 2018Jul 04 2018We use analytic combinatorics to give a direct proof of the closed formula for the generating function of $p$-Bernoulli numbers.

Deep Generative Networks For Sequence PredictionApr 18 2018This thesis investigates unsupervised time series representation learning for sequence prediction problems, i.e. generating nice-looking input samples given a previous history, for high dimensional input sequences by decoupling the static input representation ... More

Gasper's determinant theorem, revisitedApr 09 2018Let $n \ge 2$ be a natural number, $M$ a real $n \times n$ matrix, $s$ the sum of the entries of $M$ and $q$ the sum of their squares. With $\alpha := s/n$ and $\beta := q/n$, Gasper's determinant bound says that $ |\det M| \le \beta^{n/2}$, and in case ... More

First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effectAug 11 2017Mar 25 2018A fluctuating interfacial profile in one dimension is studied via Langevin simulations of the Edwards-Wilkinson equation with non-conserved noise and the Mullins-Herring equation with conserved noise. The profile is subject to either periodic or Dirichlet ... More

Analysis of mesoscale forecasts using ensemble methodsOct 24 2016Mesoscale forecasts are now routinely performed as elements of operational forecasts and their outputs do appear convincing. However, despite their realistic appearance at times the comparison to observations is less favorable. At the grid scale these ... More

Asymptotic equivalence and sufficiency for volatility estimation under microstructure noiseJan 18 2010The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment ... More

Asymptotics of the average height of 2--watermelons with a wallJul 06 2006Sep 04 2006We generalize the classical work of de Bruijn, Knuth and Rice (giving the asymptotics of the average height of Dyck paths of length $n$) to the case of $p$--watermelons with a wall (i.e., to a certain family of $p$ nonintersecting Dyck paths; simple Dyck ... More

Nonintersecting lattice paths on the cylinderNov 19 2003Feb 18 2004We show how a formula concerning ``vicious walkers'' (which basically are nonintersecting lattice paths) on the cylinder given by P.J. Forrester can be proved and generalized by using the Lindstr\"om--Gessel--Viennot method, after having things set up ... More

Ornstein-Uhlenbeck processes driven by cylindrical Lévy processesDec 16 2012May 28 2014In this article we introduce a theory of integration for deterministic, operator-valued integrands with respect to cylindrical L\'evy processes in separable Banach spaces. Here, a cylindrical L\'evy process is understood in the classical framework of ... More

A criterion for membership in archimedean semiringsSep 23 2004We prove an extension of the classical Real Representation Theorem (going back to Krivine, Stone, Kadison, Dubois and Becker and often called Kadison-Dubois Theorem). It is a criterion for membership in subsemirings (sometimes called preprimes) of a commutative ... More

Resolutions and Cohomologies of Toric Sheaves. The affine caseJun 28 2011We study equivariant resolutions and local cohomologies of toric sheaves for affine toric varieties, where our focus is on the construction of new examples of decomposable maximal Cohen-Macaulay modules of higher rank. A result of Klyachko states that ... More

Isometric Group Actions and the Cohomology of Flat Fiber BundlesMay 04 2011Using methods originating in the theory of intersection spaces, specifically a de Rham type description of the real cohomology of these spaces by a complex of global differential forms, we show that the Leray-Serre spectral sequence with real coefficients ... More

Another viewpoint on J-spacesDec 06 2010Dec 10 2010We give an interpretation of J-spaces in terms of symmetric spectra in symmetric sequences. As application we show how one can define graded endomorphism objects in a general situation. As example we discuss the motivic bigraded endomorphisms of a motivic ... More

Commutative S-algebras of prime characteristics and applications to unoriented bordismNov 14 2012May 14 2014The notion of highly structured ring spectra of prime characteristic is made precise and is studied via the versal examples S//p for prime numbers p. These can be realized as Thom spectra, and therefore relate to other Thom spectra such as the unoriented ... More

Viewing determinants as nonintersecting lattice paths yields classical determinantal identities bijectivelyOct 19 2010In this paper, we show how general determinants may be viewed as generating functions of nonintersecting lattice paths, using the Lindstr\"om-Gessel-Viennot interpretation of semistandard Young tableaux and the Jacobi-Trudi identity together with elementary ... More

Bijective proofs for Schur function identitiesSep 29 2009Gurevich, Pyatov and Saponov recently stated an expansion for the product of two Schur functions and gave a proof based on the Pluecker relations. Here we show that this identity is in fact a special case of a quite general Schur function identity, which ... More

Moduli for Equivariant Vector Bundles of Rank Two on Smooth Toric SurfacesMay 30 2002We give a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles. This note is a direct continuation of an earlier note where we developed a general description ... More

Recent diboson and multiboson results in ATLASJun 21 2019Recent measurements of the associated production of two or three massive vector bosons in proton-proton collisions at the Large Hadron Collider, collected by the ATLAS detector at a centre-of-mass energy of $\sqrt{s} = 13$ TeV, are reported. The diboson ... More

Iterated rings of bounded elements: ErratumOct 31 2005We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and in the author's article "Iterated rings of bounded elements and generalizations of Schm\"udgen's ... More

The Analytical Assembly Map and Index TheoryJun 24 2013Mar 06 2014In this paper we study the index theoretic interpretation of the analytical assembly map that appears in the Baum-Connes conjecture. In its general form it may be constructed using Kasparov's equivariant KK-theory. In the special case of a torsionfree ... More

Operads, Algebras and Modules in General Model CategoriesJan 11 2001In this paper we develop the theory of operads, algebras and modules in cofibrantly generated symmetric monoidal model categories. We give J-semi model strucures, which are a slightly weaker version of model structures, for operads and algebras and model ... More

Properties of Extensive Air ShowersFeb 12 2004Some general properties of extensive air showers are discussed. The main focus is put on the longitudinal development, in particular the energy flow, and on the lateral distribution of different air shower components. The intention of the paper is to ... More

On the non-uniform motion of dislocations: The retarded elastic fields, the retarded dislocation tensor potentials and the Liénard-Wiechert tensor potentialsOct 11 2012The purpose of this paper is the fundamental theory of the non-uniform motion of dislocations in two and three space-dimensions. We investigate the non-uniform motion of an arbitrary distribution of dislocations, a dislocation loop and straight dislocations ... More

The elastodynamic Liénard-Wiechert potentials and elastic fields of non-uniformly moving point and line forcesMay 23 2012The purpose of this paper is to investigate the fundamental problem of the non-uniform subsonic motion of a point force and line forces in an unbounded, homogeneous, isotropic medium in analogy to the electromagnetic Li\'enard-Wiechert potentials. The ... More