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A new characterization of partial metric completenessFeb 08 2019In this article, we present a new characterization of the completeness of a partial metric space--which we call \textit{orbital characterization}-- using fixed point results.

Partial quasi-metric completeness via Kannan-type fixed pointsFeb 08 2019In this short note, we obtain partial quasi-metric versions of Kannan's fixed point theorem for self-mappings. Moreover, we use these fixed points results to characterize a certain type of completeness in partial quasi-metric spaces. We have reported ... More

Chatterjea type fixed point in Partial $b$-metric spacesFeb 08 2019In this paper, we give and prove two Chatterjea type fixed point theorems on partial $b$-metric space. We propose an extension to the Banach contraction principle on partial $b$-metric space which was already presented by Shukla and also study some related ... More

Advances in Startpoint Theory for quasi-pseudometric spacesDec 05 2014This paper presents some startpoint (endpoint, fixed point) theorems for mutli-valued maps that generalize recent results proved by Y. U. Gaba \cite{rico, ricoo}.

Startpoints and $(α,γ)$-Contractions in Quasi-Pseudometric SpacesAug 22 2014We introduce the concept of $\it{ startpoint}$ and $\it{endpoint}$ for multivalued maps defined on a quasi-pseudometric space. We investigate the relation between these new concepts and the existence of fixed points for these set valued maps.

Fixed points for weak contractions in metric type spacesDec 01 2014May 10 2015In this article, we prove some fixed point theorems in metric type spaces. This article is just a generalization some results previously proved in \cite{niyi-gaba}. In particular, we give some coupled common fixed points theorems under weak contractions. ... More

$(C_α,C_β)$-admissible functions in quasi-pseudometric type spacesMay 15 2015In this article, we give some fixed point results in left $K$-complete quasi-pseudometric type spaces for self-mappings that are $(C_\alpha,C_\beta)$-admissible.

An order theoretic approach in fixed point theoryNov 07 2014In the present article, we show the existence of a coupled fixed point for an order preserving mapping in a preordered left K-complete quasi-pseudometric space using a preorder induced by an appropriate function. We also define the concept of left-weakly ... More

$η$-metric structuresSep 22 2017In this paper, we discuss recent results about generalized metric spaces and fixed point theory. We introduce the notion of $\eta$-cone metric spaces, give some topological properties and prove some fixed point theorems for contractive type maps on these ... More

Fixed point on partial metric type spacesSep 07 2018In this paper, we study some new fixed point results for self maps defined on partial metric type spaces. In particular, we give common fixed point theorems in the same setting. Some examples are given which illustrate the results.

Quasi-uniform type spacesMar 15 2019In this article, we introduce and investigate the concept of partial quasi-metric type space as a generalization of both partial quasi-metric and quasi-metric type spaces. We show that many important constructions studied in K\"unzi's theory of partial ... More

($2k+1)^{th}$-order Fixed points in $G$-metric spacesSep 22 2017We establish three major fixed-point theorems for functions satisfying an odd power type contractive condition in G-metric spaces. We first consider the case of a single mapping, followed by that of a triplet of mappings and we conclude by the case of ... More

Common Coupled Fixed Point Theorems for Maps in a $T_0$-ultra-quasi-metric SpaceDec 03 2014In this article, we prove the existence of common fixed points for a pair of maps on a $q$-spherically complete $T_0$-ultra-quasi-metric space. The present article is a generalization, in the assymmetric setting of the paper of Rao et al.\cite{Rao}. The ... More

$n$-tuple fixed point in $φ$-ordered $G$-metric spacesSep 22 2017We use three seminal approaches in the study of fixed point theory, the so called $G$-metrics, multidimensional fixed points and partially ordered spaces. More precisely, we extend known results from the theory of quasi-pseudometric spaces to the $G$-metric ... More

Some extensions of Banach'\ CP in $G$-metric spacesMar 24 2017We present different extensions of the Banach contraction principle in the $G$-metric space setting. More precisely, we consider mappings for which the contractive condition is satisfied by a power of the mapping and for which the power depends on the ... More

Fixed point theorems for $(\varepsilon,λ)$-uniformly locally contractive mapping defined on $\varepsilon$-chainable $G$-metric type spacesFeb 23 2017In this article, we discuss fixed point results for $(\varepsilon,\lambda)$-uniformly locally contractive self mapping defined on $\varepsilon$-chainable $G$-metric type spaces. In particular, we show that under some more general conditions, certain fixed ... More

Mix-point property in quasi-pseudometric spacesMar 01 2017In this article, we give new results in the startpoint theory for quasi-pseudometric spaces. The results we present provide us with the existence of startpoint (endpoint, fixed point) for multi-valued maps defined on a bicomplete quasi-pseudometric space. ... More

Common fixed points via $λ$-sequences in $G$-metric spacesMar 24 2017In this article, we use $\lambda$-sequences to derive common fixed points for a family of self-mappings defined on a complete $G$-metric space. We imitate some existing techniques in our proofs and show that the tools emlyed can be used at a larger scale. ... More

Fixed point theorems in $G$-metric spaceFeb 27 2017In this article, we present a new type of fixed point for single valed mapping in a $G$-complete $G$-metric space.

New fixed point results on $G$-metric spacesFeb 23 2017In this note, we discuss some fixed point theorems for contractive self mappings defined on a $G$-metric spaces. More precisely, we give fised point theorems for mappings with a contractive iterate at a point.

Stochastic Memristive Devices for Computing and Neuromorphic ApplicationsApr 22 2013Nanoscale resistive switching devices (memristive devices or memristors) have been studied for a number of applications ranging from non-volatile memory, logic to neuromorphic systems. However a major challenge is to address the potentially large variations ... More

Neutrino Interactions with Nucleons and Nuclei: Importance for Long-Baseline ExperimentsFeb 01 2016Mar 19 2016This article reviews our present knowledge of neutrino interactions with nucleons. It then discusses the interactions with nuclei, the target material of all presently running and planned long-baseline experiments. Particular emphasis is placed on descriptions ... More

The universal eta-invariant for manifolds with boundaryMar 09 2014Oct 23 2014We extend the theory of the universal eta-invariant to the case of relative bordism groups of manifolds with boundaries. This allows the construction of secondary descendants of the universal eta-invariant. We obtain an interpretation of Laures' f-invariant ... More

Quantum corrected model for plasmonic nanoparticles: A boundary element method implementationMay 13 2015We present a variant of the recently developed quantum corrected model (QCM) for plasmonic nanoparticles [Nature Commun. 3, 825 (2012)] using non-local boundary conditions. The QCM accounts for electron tunneling in narrow gap regions of coupled metallic ... More

Neutrino Interactions and Long Baseline PhysicsApr 30 2015This is a very short review of neutrino-nucleus interactions and their influence on the analysis of long-baseline experiments.

Membrane Instantons from Toda Field TheoryAug 20 2014Sep 01 2014Four-dimensional quaternion-Kaehler metrics with an isometry are determined by solutions to the SU($\infty$) Toda equation. We set up a perturbation theory to construct approximate solutions to the latter which can be interpreted as membrane instanton ... More

Flavour and CP ViolationApr 13 2013In this talk I review the status of B mixing in the Standard Model and the room for new physics in B_s and B_d mixing in the light of recent LHCb data.

Spectral Statistics and Dynamical Localization: sharp transition in a generalized Sinai billiardJul 12 1999We consider a Sinai billiard where the usual hard disk scatterer is replaced by a repulsive potential with $V(r)\sim\lambda r^{-\alpha}$ close to the origin. Using periodic orbit theory and numerical evidence we show that its spectral statistics tends ... More

Ab-initio calculation of optical absorption in semiconductors: A density-matrix descriptionAug 21 2001We show how to describe Coulomb renormalization effects and dielectric screening in semiconductors and semiconductor nanostructures within a first-principles density-matrix description. Those dynamic variables and approximation schemes which are required ... More

Anti-B --> X(s) gamma: Standard Model and BeyondMay 14 2008Jul 13 2008We present a concise review of the recent theoretical progress concerning the standard model calculation of the inclusive radiative anti-B --> X(s) gamma decay. Particular attention is thereby devoted to the calculations of the next-to-next-to-leading ... More

How To Kill a PenguinJun 23 2007Within constrained minimal-flavor-violation the large destructive flavor-changing Z-penguin managed to survive eradication so far. We give a incisive description of how to kill it using the precision measurements of the Z -> b anti-b pseudo observables. ... More

Review on new physics in heavy flavors: B-meson sectorMar 24 2013Nov 26 2013A brief review of theoretical aspects of new-physics searches in flavor physics is given. Special attention is thereby devoted to B_s mixing and the interplay of high- and low-p_T observations.

Recent Developments in Bbar -> X_s gammaJun 14 2007Jun 23 2007We present a concise review of the recent theoretical progress concerning the standard model calculation of the inclusive radiative Bbar -> X_s gamma decay. Particular attention is thereby devoted to the calculations of the next-to-next-to-leading order ... More

Theoretical Status of K->pinunubar DecaysMay 15 2006We present a concise review of the theoretical status of rare K->pinunubar decays in and beyond the standard model. Particular attention is thereby devoted to the recent calculation of the next-to-next-to-leading order corrections to the charm quark contribution ... More

The Quantum Mechanics of Being and Its ManifestationApr 04 2016How can quantum mechanics be (i) the fundamental theoretical framework of contemporary physics and (ii) a probability calculus that presupposes the events to which, and on the basis of which, it assigns probabilities? The question is answered without ... More

The Pondicherry interpretation of quantum mechanics: An overviewDec 23 2004Feb 24 2005An overview of the Pondicherry interpretation of quantum mechanics is presented. This interpretation proceeds from the recognition that the fundamental theoretical framework of physics is a probability algorithm, which serves to describe an objective ... More

Why the laws of physics are just soFeb 26 2002Does a world that contains chemistry entail the validity of both the standard model of elementary particle physics and general relativity, at least as effective theories? This article shows that the answer may very well be affirmative. It further suggests ... More

Making sense of a world of clicksFeb 26 2002In a recent article O. Ulfbeck and A. Bohr (Foundations of Physics 31, 757, 2001) have stressed the genuine fortuitousness of detector clicks, which has also been pointed out, in different terms, by the present author (American Journal of Physics 68, ... More

Two theories of decoherenceAug 01 2001Theories of decoherence come in two flavors---Platonic and Aristotelian. Platonists grant ontological primacy to the concepts and mathematical symbols by which we describe or comprehend the physical world. Aristotelians grant it to the physical world. ... More

Quantum Nonlocality ExplainedNov 05 2014Feb 11 2015Quantum theory's violation of remote outcome independence is assessed in the context of a novel interpretation of the theory, in which the unavoidable distinction between the classical and quantum domains is understood as a distinction between the manifested ... More

Quantum mechanics explainedJul 02 2006Jul 14 2006The physical motivation for the mathematical formalism of quantum mechanics is made clear and compelling by starting from an obvious fact - essentially, the stability of matter - and inquiring into its preconditions: what does it take to make this fact ... More

A space for the quantum worldJul 02 2001Epistemic interpretations of quantum mechanics fail to address the puzzle posed by the occurrence of probabilities in a fundamental physical theory. This is a puzzle about the physical world, not a puzzle about our relation to the physical world. Its ... More

The world according to quantum mechanics (or, the 18 errors of Henry P. Stapp)May 21 2001Several errors in Stapp's interpretation of quantum mechanics and its application to mental causation (Henry P. Stapp, "Quantum theory and the role of mind in nature," e-Print quant-ph/0103043) are pointed out. An interpretation of (standard) QM that ... More

Electromagnetic Waves in Variable MediaApr 09 2011Jul 16 2012Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one coordinate, general ... More

Diffraction of Electromagnetic WavesNov 18 2009Feb 02 2010The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these representatives. ... More

On Dynamic Breadth-First Search in External-MemoryFeb 20 2008We provide the first non-trivial result on dynamic breadth-first search (BFS) in external-memory: For general sparse undirected graphs of initially $n$ nodes and O(n) edges and monotone update sequences of either $\Theta(n)$ edge insertions or $\Theta(n)$ ... More

Projective quantum spacesOct 06 1994Associated to the standard $SU_{q}(n)$ R-matrices, we introduce quantum spheres $S_{q}^{2n-1}$, projective quantum spaces $CP_{q}^{n-1}$, and quantum Grassmann manifolds $G_{k}(C_{q}^{n})$. These algebras are shown to be homogeneous quantum spaces of ... More

Constraints on Neutralino masses and mixings from Cosmology and Collider PhysicsJul 11 2007Aug 09 2007Bounds on cross section measurements of chargino pair production at LEP yield a bound on the chargino mass. If the GUT relation is assumed, the lightest neutralino must be heavier than $\approx 45 -50\GeV$. If no GUT relation is assumed, no lower bound ... More

Eine untere Massenschranke fuer Neutralinos aus Supernova-KuehlungJul 29 2004In my diploma thesis I calculate a lower mass bound of the lightest nutralino assuming an additional supernova cooling mechanism. I consider elektron-positron annihilation and nucleon-nucleon bremsstrahlung as cooling processes. These cooling processes ... More

Low-temperature conductance and DC current noise in a quantum wire with impurityApr 04 1996Apr 12 1996The nonlinear conductance for tunneling through an impurity in a Luttinger liquid and the nonequilibrium DC current noise are calculated exactly for low temperatures. We present a pedestrian pathway towards the exact solution which is based on analytic ... More

Non-linear numerical Schemes in General RelativityJan 25 2002This thesis describes the application of numerical techniques to solve Einstein's field equations in three distinct cases. First we present the first long-term stable second order convergent Cauchy characteristic matching code in cylindrical symmetry ... More

The density-matrix renormalization group in the age of matrix product statesAug 20 2010Jan 03 2011The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the further development ... More

Derivations with Quantum Group ActionMay 11 2000The derivations of a left coideal subalgebra B of a Hopf algebra A which are compatible with the comultiplication of A (that is, the covariant first order differential calculi, as defined by Woronowicz, on a quantum homogeneous space) are related to certain ... More

The Little Bang: Searching for quark-gluon matter in relativistic heavy-ion collisionsSep 14 2000Sep 19 2000I review the status of the search for quark-gluon plasma in relativistic heavy-ion collisions. The available data provide strong evidence for the "three pillars of the Little Bang model": strong radial expansion of the collision fireball with Hubble-like ... More

An identity for derivativesJun 24 2016We present a generalization of a formula of higher order derivatives and give a short proof.

Pointwise differentiability of higher order for distributionsMar 28 2018For distributions, we build a theory of higher order pointwise differentiability comprising, for order zero, \L ojasiewicz's notion of point value. Results include Borel regularity of differentials, higher order rectifiability of the associated jets, ... More

A Sobolev Poincaré type inequality for integral varifoldsAug 27 2008May 25 2009In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown to be sharp. ... More

Twisted K-theory and obstructions against positive scalar curvature metricsAug 18 2011Jun 17 2013We decompose the twisted index obstruction $\theta(M)$ against positive scalar curvature metrics for oriented manifolds with spin universal cover into a pairing of a twisted $K$-homology with a twisted $K$-theory class and prove that $\theta(M)$ does ... More

A problem of I. Raşa on Bernstein polynomials and convex functionsAug 27 2016We present an elementary proof of a conjecture by I. Ra\c{s}a which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive very recently by the use of stochastic convex orderings. Moreover, we derive the ... More

Mapping class groups of compression bodies and 3-manifoldsJul 18 2006Jul 16 2007We analyze the mapping class group of extendible automorphisms of the exterior boundary W of a compression body of dimension 3 or 4, which extend over the compression body (Q,V), where V is the interior boundary. Those that extend as automorphisms of ... More

Coincidence free pairs of mapsJun 01 2006This paper centers around two basic problems of topological coincidence theory. First, try to measure (with help of Nielsen and minimum numbers) how far a given pair of maps is from being loose, i.e. from being homotopic to a pair of coincidence free ... More

Manin's conjecture for a certain singular cubic surfaceApr 01 2005We prove Manin's conjecture for a singular cubic surface S with a singularity of type E6. If U is the open subset of S obtained by deleting the unique line from S, then the number of rational points in U with anticanonical height bounded by B behaves ... More

Some Applications of the Isoperimetric Inequality for Integral VarifoldsAug 27 2008In this work the Isoperimetric Inequality for integral varifolds is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calder\'on's and Zygmund's theory of first order differentiability for functions ... More

Manin's conjecture for a quintic del Pezzo surface with A_2 singularityOct 08 2007Manin's conjecture is proved for a split del Pezzo surface of degree 5 with a singularity of type A_2.

Counting integral points on universal torsorsOct 22 2008Feb 13 2009Manin's conjecture for the asymptotic behavior of the number of rational points of bounded height on del Pezzo surfaces can be approached through universal torsors. We prove several auxiliary results for the estimation of the number of integral points ... More

On the regularity of special difference divisorsSep 06 2012In this note we prove that the difference divisors associated with special cycles on unitary Rapoport-Zink spaces of signature (1,n-1) in the unramified case are always regular.

A counter-example to Martino's conjecture about generic Calogero-Moser familiesJan 21 2013Sep 25 2013The Calogero-Moser families are partitions of the irreducible characters of a complex reflection group derived from the block structure of the corresponding restricted rational Cherednik algebra. It was conjectured by Martino in 2009 that the generic ... More

Keisler's Order and Full Boolean-Valued ModelsOct 12 2018We prove a compactness theorem for full Boolean-valued models. As an application, we show that if $T$ is a complete countable theory and $\mathcal{B}$ is a complete Boolean algebra, then $\lambda^+$-saturated $\mathcal{B}$-valued models of $T$ exist. ... More

Fixed Points and Coincidences in Torus BundlesFeb 09 2010Minimum numbers of fixed points or of coincidence components (realized by maps in given homotopy classes) are the principal objects of study in topological fixed point and coincidence theory. In this paper we investigate fiberwise analoga and represent ... More

Cavity quantum electrodynamics with semiconductor quantum dots: The role of phonon-assisted cavity feedingDec 28 2009For a semiconductor quantum dot strongly coupled to a microcavity, we theoretically investigate phonon-assisted transitions from the exciton to a cavity photon, where the energy mismatch is compensated by phonon emission or absorption. By means of a Schrieffer-Wolff ... More

A Subjective and Probabilistic Approach to DerivativesJan 11 2010We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied probability ... More

Something about Z-penguins I want to tellAug 18 2008Oct 19 2008We stress that in models with constrained minimal flavor violation large negative corrections to the flavor-changing Z-penguin amplitudes are excluded by the precision measurements of the Z -> b anti-b pseudo observables performed at LEP and SLC. The ... More

Quantum mechanics and the manifestation of the worldApr 29 2014Aug 23 2014Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be consistent with ... More

Manifesting the Quantum WorldApr 27 2014In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the process by which ... More

This elusive objective existenceJan 29 2004Zurek's existential interpretation of quantum mechanics suffers from three classical prejudices, including the belief that space and time are intrinsically and infinitely differentiated. They compel him to relativize the concept of objective existence ... More

Unveiled reality: comment on d'Espagnat's note on measurementFeb 21 2001According to d'Espagnat we must choose between nonlinear breaks in quantum state evolution and weak objectivity. In this comment it is shown that this choice is forced on us by an inconsistent pseudo-realistic interpretation of quantum states. A strongly ... More

Binary evolution with relativistic jetsOct 20 1998Relativistic jets can extract mass-energy from a black hole. In semi-detached black hole binaries the jet ejection process constitutes a `consequential angular momentum loss' (CAML) process. The effect of this jet-induced CAML is to lower the transfer ... More

QBism, Bohr, and the quantum omelette tossed by de RondeAug 20 2016In his recent paper "QBism, FAPP and the Quantum Omelette" [1608.00548v1] de Ronde makes a variety of questionable claims concerning QBism, Bohr, and the present author's critical appraisal of QBism [1409.3312v1]. These claims are examined. Subsequently ... More

Time-dependent Density-Matrix Renormalization-Group MethodsFeb 18 2005In this paper recent substantial progress in applying the density-matrix renormalization-group (DMRG) to the simulation of the time-evolution of strongly correlated quantum systems in one dimension is reviewed. Various approaches to generating a time-evolution ... More

Strong normalisation for applied lambda calculiJul 04 2005Sep 28 2005We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting bottom is strongly normalising provided all its `stratified approximations' are. From this ... More

Pointwise differentiability of higher order for setsMar 28 2016The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that differentials are Borel ... More

Stripped red giants - Helium core white dwarf progenitors and their sdB siblingsOct 24 2016Some gaps in the mosaic of binary star evolution have recently been filled by the discoveries of helium-core white dwarf progenitors (often called extremely low mass (ELM) white dwarfs) as stripped cores of first-giant branch objects. Two varieties can ... More

Top quark mass measurements at the TevatronJun 06 2008The mass of the top quark has been measured at Fermilab using the Tevatron ppbar collider to a precision of less than 1%. I discuss the individual measurements that go into this result and its impact on our understanding of the standard model of the electroweak ... More

Prospects for Improving Competition in Mobile RoamingSep 26 2001Oct 22 2001The ability to make international roaming calls is of increasing importance to customers in Europe. This contrasts with various complaints that retail prices of roaming calls are rigid and excessive. The focus if the paper is on wholesale roaming, which ... More

Hunting down the quark-gluon plasma in relativistic heavy-ion collisionsFeb 22 1999Mar 05 1999The present status of the heavy-ion program to search for quark-gluon plasma is reviewed. The goal of this program is to recreate the Big Bang in the laboratory, by generating small chunks of exploding quark-gluon plasma (``The Little Bang''). I argue ... More

Finite height lamination spaces for surfacesApr 11 2014We describe spaces of essential finite height (measured) laminations in a surface $S$ using a parameter space we call $\mathbb S$, an ordered semi-ring. We show that for every finite height essential lamination $L$ in $S$, there is an action of $\pi_1(S)$ ... More

Laminations with transverse measures in ordered abelian semigroupsJul 25 2014Jul 27 2016We describe a construction of ordered algebraic structures (ordered abelian semigroups, ordered commutative semirings, etc.) and describe applications to codimension-1 laminations. For a suitable ordered semi- algebraic structure $\mathbb L$ and measurable ... More

Measured lamination spaces for surface pairsApr 11 2014We calculate a projective space of essential measured laminations in a surface pair, which will be used in another paper to help describe spaces of "finite height laminations."

Nielsen numbers in topological coincidence theoryMay 07 2013We discuss coincidences of pairs (f_1, f_2) of maps between manifolds. We recall briefly the definition of four types of Nielsen numbers which arise naturally from the geometry of generic coincidences. They are lower bounds for the minimum numbers MCC ... More

On the Cox ring of Del Pezzo surfacesMar 04 2006Let S_r be the blow-up of P^2 in r general points, i.e., a smooth Del Pezzo surface of degree 9-r. For r <= 7, we determine the quadratic equations defining its Cox ring explicitly. The ideal of the relations in Cox(S_8) is calculated up to radical. As ... More

A Streamlined Proof of $\mathfrak{p}=\mathfrak{t}$Oct 22 2018We streamline Malliaris and Shelah's proof that $\mathfrak{p} = \mathfrak{t}$. In particular, we replace cofinality spectrum problems with models of $ZFC^-$, and we eliminate the use of peculiar cuts.

Decay estimates for the quadratic tilt-excess of integral varifoldsSep 17 2009Jun 08 2011This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space with its first variation given by either a Radon measure or a function in some Lebesgue space. Pointwise decay results for the quadratic tilt-excess are ... More

Second order rectifiability of integral varifolds of locally bounded first variationAug 27 2008Nov 17 2010In this work it is shown that every integral varifold in an open subset of Euclidian space of locally bounded first variation can be covered by a countable collection of submanifolds of class C^2. Moreover, the mean curvature of each member of the collection ... More

Intersections of special cycles on the Shimura variety for GU(1,2)Jun 10 2010We establish a close connection between intersection multiplicities of special cycles on arithmetic models of the Shimura variety for GU(1,2) and Fourier coefficients of derivatives of certain incoherent Eisenstein series, confirming a conjecture of Kudla ... More

On the flatness of local models for the symplectic groupNov 23 2000We investigate the bad reduction of certain Shimura varieties (associated to the symplectic group). More precisely, we look at a model of the Shimura variety at a prime p, with parahoric level structure at p. We show that this model is flat, as conjectured ... More

Borel Complexity and the Schröder-Bernstein PropertyOct 01 2018Oct 02 2018We introduce a new invariant of Borel reducibility, namely the notion of thickness; this associates to every sentence $\Phi$ of $\mathcal{L}_{\omega_1 \omega}$ and to every cardinal $\lambda$, the thickness $\tau(\Phi, \lambda)$ of $\Phi$ at $\lambda$. ... More

Stratifications of affine Deligne-Lusztig varietiesFeb 06 2018Affine Deligne-Lusztig varieties are analogues of Deligne-Lusztig varieties in the context of affine flag varieties and affine Grassmannians. They are closely related to moduli spaces of $p$-divisible groups in positive characteristic, and thus to arithmetic ... More

Sobolev functions on varifoldsSep 03 2015May 27 2016This paper introduces first order Sobolev spaces on certain rectifiable varifolds. These complete locally convex spaces are contained in the generally nonlinear class of generalised weakly differentiable functions and share key functional analytic properties ... More

Massive creation of entangled exciton states in semiconductor quantum dotsNov 05 2002An intense laser pulse propagating in a medium of inhomogeneously broadened quantum dots massively creates entangled exciton states. After passage of the pulse all single-exciton states remain unpopulated (self-induced transparency) whereas biexciton ... More

Market Implied Probability Distributions and Bayesian Skew EstimationNov 04 2009We review and illustrate how the volatility smile translates into a probability distribution, the market-implied probability distribution representing believes priced in. The effects of changes in the smile are examined. Special attention is given to ... More