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Renormalization Group Flow of Hexatic MembranesApr 17 2013We investigate hexatic membranes embedded in Euclidean D-dimensional space using a reparametrization invariant formulation combined with exact renormalization group (RG) equations. An XY-model coupled to a fluid membrane, when integrated out, induces ... More

Lee-Yang model from the functional renormalization groupDec 27 2016Jun 13 2017We investigate the critical properties of the Lee-Yang model in less than six spacetime dimensions using truncations of the functional renormalization group flow. We give estimates for the critical exponents, study the dependence on the regularization ... More

Renormalization of multicritical scalar models in curved spaceOct 15 2018Mar 14 2019We consider the leading order perturbative renormalization of the multicritical $\phi^{2n}$ models and some generalizations in curved space. We pay particular attention to the nonminimal interaction with the scalar curvature $\frac{1}{2}\xi \phi^2 R$ ... More

RG flows of Quantum Einstein Gravity on maximally symmetric spacesJan 21 2014We use the Wetterich-equation to study the renormalization group flow of $f(R)$-gravity in a three-dimensional, conformally reduced setting. Building on the exact heat kernel for maximally symmetric spaces, we obtain a partial differential equation which ... More

Functional renormalization group of the non-linear sigma model and the O(N) universality classJul 18 2012Mar 18 2013We study the renormalization group flow of the O(N) non-linear sigma model in arbitrary dimensions. The effective action of the model is truncated to fourth order in the derivative expansion and the flow is obtained by combining the non-perturbative renormalization ... More

Fixed-Functionals of three-dimensional Quantum Einstein GravityAug 09 2012We study the non-perturbative renormalization group flow of f(R)-gravity in three-dimensional Asymptotically Safe Quantum Einstein Gravity. Within the conformally reduced approximation, we derive an exact partial differential equation governing the RG-scale ... More

Off-diagonal heat-kernel expansion and its application to fields with differential constraintsDec 20 2011The off-diagonal heat-kernel expansion of a Laplace operator including a general gauge-connection is computed on a compact manifold without boundary up to third order in the curvatures. These results are used to study the early-time expansion of the traced ... More

RG flows of Quantum Einstein Gravity in the linear-geometric approximationDec 22 2014Apr 28 2015We construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields. Applying a linear-geometric approximation the structure of the ... More

Fixed Functionals in Asymptotically Safe GravityFeb 06 2013We summarize the status of constructing fixed functionals within the f(R)-truncation of Quantum Einstein Gravity in three spacetime dimensions. Focusing on curvatures much larger than the IR-cutoff scale, it is shown that the fixed point equation admits ... More

Scaling and superscaling solutions from the functional renormalization groupAug 11 2015Oct 14 2015We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed points of ... More

Spectral dimensions from the spectral actionOct 29 2014Jan 11 2015The generalised spectral dimension $D_{ S}(T)$ provides a powerful tool for comparing different approaches to quantum gravity. In this work, we apply this formalism to the classical spectral actions obtained within the framework of almost-commutative ... More

A proper fixed functional for four-dimensional Quantum Einstein GravityApr 28 2015Realizing a quantum theory for gravity based on Asymptotic Safety hinges on the existence of a non-Gaussian fixed point of the theory's renormalization group flow. In this work, we use the functional renormalization group equation for the effective average ... More

Scheme dependence and universality in the functional renormalization groupOct 28 2013Apr 27 2015We prove that the functional renormalization group flow equation admits a perturbative solution and show explicitly the scheme transformation that relates it to the standard schemes of perturbation theory. We then define a universal scheme within the ... More

Functional perturbative RG and CFT data in the $ε$-expansionMay 16 2017Jan 17 2018We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. ... More

New universality class in three dimensions: The critical Blume-Capel modelJun 21 2017Sep 25 2017We study the Blume-Capel universality class in $d=\frac{10}{3}-\epsilon$ dimensions. The RG flow is extracted by looking at poles in fractional dimension of three loop diagrams using $\overline{\rm MS}$. The theory is the only nontrivial universality ... More

Gravitational form factors and decoupling in 2DMar 19 2018Mar 26 2018We calculate and analyse non-local gravitational form factors induced by quantum matter fields in curved two-dimensional space. The calculations are performed for scalars, spinors and massive vectors by means of the covariant heat kernel method up to ... More

Leading order CFT analysis of multi-scalar theories in d>2Sep 13 2018Apr 08 2019We investigate multi-field multicritical scalar theories using CFT constraints on two- and three-point functions combined with the Schwinger-Dyson equation. This is done in general and without assuming any symmetry for the models, which we just define ... More

Vacuum effective actions and mass-dependent renormalization in curved spaceFeb 08 2019We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss ... More

Renormalization group flows and fixed points for a scalar field in curved space with nonminimal $F(φ)R$ couplingNov 06 2017Using covariant methods, we construct and explore the Wetterich equation for a non-minimal coupling $F(\phi)R$ of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered non-minimal coupling $\xi \phi^2 ... More

Vacuum effective actions and mass-dependent renormalization in curved spaceFeb 08 2019Mar 02 2019We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss ... More

A functional perspective on emergent supersymmetryMay 23 2017Jan 09 2018We investigate the emergence of ${\cal N}=1$ supersymmetry in the long-range behavior of three-dimensional parity-symmetric Yukawa systems. We discuss a renormalization approach that manifestly preserves supersymmetry whenever such symmetry is realized, ... More

Leading order CFT analysis of multi-scalar theories in d>2Sep 13 2018We investigate multi-field multicritical scalar theories using CFT constraints on two- and three-point functions combined with the Schwinger-Dyson equation. This is done in general and without assuming any symmetry for the models, which we just define ... More

Leading CFT constraints on multi-critical models in d>2Mar 14 2017Apr 20 2017We consider the family of renormalizable scalar QFTs with self-interacting potentials of highest monomial $\phi^{m}$ below their upper critical dimensions $d_c=\frac{2m}{m-2}$, and study them using a combination of CFT constraints, Schwinger-Dyson equation ... More

Form factors and decoupling of matter fields in four-dimensional gravityDec 02 2018Jan 31 2019We extend previous calculations of the non-local form factors of semiclassical gravity in $4D$ to include the Einstein-Hilbert term. The quantized fields are massive scalar, fermion and vector fields. The non-local form factor in this case can be seen ... More

Gravitational corrections to Yukawa systemsApr 06 2009Apr 26 2010We compute the gravitational corrections to the running of couplings in a scalar-fermion system, using the Wilsonian approach. Our discussion is relevant for symmetric as well as for broken scalar phases. We find that the Yukawa and quartic scalar couplings ... More

Higher Derivative Gravity from the Universal Renormalization Group MachineNov 07 2011Feb 28 2012We study the renormalization group flow of higher derivative gravity, utilizing the functional renormalization group equation for the average action. Employing a recently proposed algorithm, termed the universal renormalization group machine, for solving ... More

Asymptotic safety and the gauged SU(N) nonlinear sigma-modelOct 05 2010May 18 2011We study the beta functions of the leading, two-derivative terms of the left-gauged SU(N) nonlinear sigma-model in d dimensions. In d>2, we find the usual Gaussian ultraviolet fixed point for the gauge coupling and an attractive non-Gaussian fixed point ... More

Quantum corrections in Galileon theoriesOct 01 2013Nov 24 2014We calculate the one-loop quantum corrections in the cubic Galileon theory, using cutoff regularization. We confirm the expected form of the one-loop effective action and that the couplings of the Galileon theory do not get renormalized. However, new ... More

On spectroscopic structure of two interacting electrons in a quantum dotFeb 07 2001Mar 12 2003The shifted 1/N expansion technique, used by El-Said (Phys. Rev. B 61, 13026 (2000)), to study the relative Hamiltonian of two interacting electrons confined in a quantum dot, is investigated. El-Said's results from SLNT are revised and results from an ... More

Spherical-separablility of non-Hermitian Dirac Hamiltonians and pseudo-PT-symmetryNov 25 2007Jan 24 2008A non-Hermitian P$_{\phi}$T$_{\phi}$-symmetrized spherically-separable Dirac Hamiltonian is considered. It is observed that the descendant Hamiltonians H$_{r}$, H$_{\theta}$, and H$_{\phi}$ play essential roles and offer some user-feriendly options as ... More

On the quasi - exact solvability of a singular potential in D - dimensions; confined and unconfinedJan 27 2001Oct 10 2001The D -dimensional quasi - exact solutions for the singular even - power anharmonic potential $V(q)=aq^2+bq^{-4}+cq^{-6}$ are reported. We show that whilst Dong and Ma's [5] quasi - exact ground - state solution (in D=2) is beyond doubt, their solution ... More

Label Visualization and Exploration in IRDec 10 2016There is a renaissance in visual analytics systems for data analysis and sharing, in particular, in the current wave of big data applications. We introduce RAVE, a prototype that automates the generation of an interface that uses facets and visualization ... More

New variant of ElGamal signature schemeJan 15 2013In this paper, a new variant of ElGamal signature scheme is presented and its security analyzed. We also give, for its theoretical interest, a general form of the signature equation.

The Perron-Frobenius Theorem for Markov SemigroupsJan 23 2014Let $P^V_t$, $t\ge0$, be the Schrodinger semigroup associated to a potential $V$ and Markov semigroup $P_t$, $t\ge0$, on $C(X)$. Existence is established of a left eigenvector and right eigenvector corresponding to the spectral radius $e^{\lambda_0t}$ ... More

On the discretization of backward doubly stochastic differential equationsJul 09 2009In this paper, we are dealing with the approximation of the process (Y,Z) solution to the backward doubly stochastic differential equation with the forward process X . After proving the L2-regularity of Z, we use the Euler scheme to discretize X and the ... More

On the n-dimensional extension of Position-dependent mass Lagrangians: nonlocal transformations, Euler--Lagrange invariance and exact solvabilityApr 06 2019The n-dimensional extension of the one dimensional Position-dependent mass (PDM) Lagrangians under the nonlocal point transformations by Mustafa <cite>38</cite> is introduced. The invariance of the n-dimensional PDM Euler-Lagrange equations is examined ... More

Matter and Light in FlatlandJan 28 2004Using a non-material current through three new dimensions. It was possible to build a particle-space model (a higher dimensional object intersecting a lower dimensional world). The new dimensions solve the old problem of equal sign walls huge electric ... More

Scaling in many-body systems and proton structure functionOct 17 2001The observation of scaling in processes in which a weakly interacting probe delivers large momentum ${\bf q}$ to a many-body system simply reflects the dominance of incoherent scattering off target constituents. While a suitably defined scaling function ... More

On a 1D nonlocal transport equation with nonlocal velocity and subcritical or supercritical diffusionMar 16 2016Apr 11 2016We study a 1D transport equation with nonlocal velocity with subcritical or supercritical dissipation. For all data in the weighted Sobolev space $H^{k}(w_{\lambda,\kappa}) \cap L^{\infty},$ with $k=\max(0,3/2-\alpha)$ and $w_{\lambda, \kappa}$ is a given ... More

On the correlation energies for two interacting electrons in a parabolic quantum dotJul 09 2001Jul 10 2001The correlation energies for two interacting electrons in a parabolic quantum dot are studied via a pseudo-perturbation recipe. It is shown that the central spike term, ($m^2-1/4)/r^2$, plays a distinctive role in determining the spectral properties of ... More

The Hohenberg-Kohn Theorem for Schrodinger SemigroupsNov 26 2017At the basis of much of computational chemistry is density functional theory, as initiated by the Hohenberg-Kohn theorem. The theorem states that, when nuclei are fixed, nuclear potentials are determined by $1$-electron densities. We recast and derive ... More

Heat-kernel estimates for random walk among random conductances with heavy tailDec 14 2008Dec 30 2009We study models of discrete-time, symmetric, $\Z^{d}$-valued random walks in random environments, driven by a field of i.i.d. random nearest-neighbor conductances $\omega_{xy}\in[0,1]$, with polynomial tail near 0 with exponent $\gamma>0$. We first prove ... More

On the Differentiability of Quaternion FunctionsMar 26 2012Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show that the elementary ... More

A Frobenius formula for the structure coefficients of double-class algebras of Gelfand pairsFeb 06 2015We generalise some well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs. This leads to a Frobenius formula for Gelfand pairs. For a given Gelfand pair, the structure coefficients of its associated ... More

The Adaptive LQ RegulatorJan 14 2019Mar 14 2019The optimal adaptive control of a linear system in a signal-plus-noise setting with infinite horizon LQ regulator cost is studied. The class of partially observed linear systems for which the certainty equivalence property holds is identified. It is also ... More

Reply to the Comment 'On large-N expansion'Dec 13 2002Fernandez Comment [1] on our pseudo-perturbative shifted-l expansion technique [2,3] is either unfounded or ambiguous.

Algorithm for factoring some RSA and Rabin moduliMar 21 2013In this paper we present a new efficient algorithm for factoring the RSA and the Rabin moduli in the particular case when the difference between their two prime factors is bounded. As an extension, we also give some theoretical results on factoring integers. ... More

Structure coefficients of the Hecke algebra of $(S_{2n},B_n)$Dec 21 2012Mar 03 2014The Hecke algebra of the pair $(S_{2n},B_n)$, where $B_n$ is the hyperoctahedral subgroup of $S_{2n}$, was introduced by James in 1961. It is a natural analogue of the center of the symmetric group algebra. In this paper, we give a polynomiality property ... More

Standard Spectral Dimension for the Polynomial Lower Tail Random Conductances modelJul 26 2009Oct 27 2010We study models of continuous-time, symmetric, $\Z^{d}$-valued random walks in random environments, driven by a field of i.i.d. random nearest-neighbor conductances $\omega_{xy}\in[0,1]$ with a power law with an exponent $\gamma$ near 0. We are interested ... More

Note on the Heat-Kernel Decay for Random Walk among Random Conductances with Heavy TailMar 18 2009Dec 31 2009Results have been moved to a published article, see arXiv:0812.2669v4[math.PR]

$k$-partial permutations and the center of the wreath product $\mathcal{S}_k\wr \mathcal{S}_n$ algebraFeb 06 2019We generalize the concept of partial permutations of Ivanov and Kerov and introduce $k$-partial permutations. This allows us to show that the structure coefficients of the center of the wreath product $\mathcal{S}_k\wr \mathcal{S}_n$ algebra are polynomials ... More

Witten deformation using Lie groupoidsMar 27 2019We express Witten's deformation of Morse functions using deformation to the normal cone and $C^*$-modules. This allows us to obtain asympotitcs of the `large eigenvalues'. Our methods extend to Morse functions along a foliation. We construct the Witten ... More

Comment on 'Two-dimensional position-dependent massive particles in the presence of magnetic fields"Mar 27 2019Using the well known position-dependent mass (PDM) von Roos Hamiltonian, Dutra and Oliveira (2009 J. Phys. A: Math. Theor. 42 025304) have studied the problem of two-dimensional PDM particles in the presence of magnetic fields. They have reported exact ... More

Perturbed Coulombic potentials in Dirac and Klein-Gordon equationsJul 10 2003Feb 17 2004A relativistic extension of our pseudo-shifted $\ell$-expansion technique is presented to solve for the eigenvalues of Dirac and Klein-Gordon equations. Once more we show the numerical usefulness of its results via comparison with available numerical ... More

The Adaptive LQ RegulatorJan 14 2019The optimal adaptive control of a linear system in a signal-plus-noise setting with infinite horizon LQ regulator cost is studied. The class of partially observed linear systems for which the certainty equivalence property holds is identified. It is also ... More

On the deformation groupoid of the inhomogeneous pseudo-differential CalculusJun 22 2018Jul 20 2018In 1974, Folland and Stein constructed an inhomogeneous pseudo-differential calculus based on analysis on the Heisenberg group. This Heisenberg calculus was generalized by several authors, to any subbundle of the tangent bundle. van Erp and Yuncken, following ... More

Conditions on the generator for forging ElGamal signatureJan 14 2013This paper describes new conditions on parameters selection that lead to an efficient algorithm for forging ElGamal digital signature. Our work is inspired by Bleichenbacher's ideas.

A general framework for the polynomiality property of the structure coefficients of double-class algebrasApr 07 2015Take a sequence of couples $(G_n,K_n)_n$, where $G_n$ is a group and $K_n$ is a sub-group of $G_n.$ Under some conditions, we are able to give a formula that shows the form of the structure coefficients that appear in the product of double-classes of ... More

Spectral Functions and Nuclear ResponseSep 17 2007I discuss the relation between the nuclear response and the Green function describing the propagation of a nucleon in the nuclear medium. Within this formalism, the widely used expressions in terms of spectral functions can be derived in a consistent ... More

Final state interactions in the electroweak nuclear responseFeb 13 2006I review the description of the electroweak nuclear response at large momentum transfer within nonrelativistic many-body theory. Special consideration is given to the effects of final state interactions, which are known to be large in both inclusive and ... More

Neutron star matter equation of state and gravitational wave emissionJul 21 2005The EOS of strongly interacting matter at densities ten to fifteen orders of magnitude larger than the typical density of terrestrial macroscopic objects determines a number of neutron star properties, including the pattern of gravitational waves emitted ... More

Electron- and neutrino-nucleus scatteringAug 19 2004I review the main features of the nuclear response extracted from electron scattering data. The emerging picture clearly shows that the shell model does not provide a fully quantitative description of nuclear dynamics. On the other hand, many body approaches ... More

HI deficiency in groups : what can we learn from EridanusSep 14 2004The HI content of the Eridanus group of galaxies is studied using the GMRT observations and the HIPASS data. A significant HI deficiency up to a factor of 2-3 is observed in galaxies in the Eridanus group. The deficiency is found to be directly correlated ... More

Scaling in many-body systems and proton responseApr 15 2002The observation of scaling in processes in which a weakly interacting probe delivers large momentum ${\bf q}$ to a many-body system reflects the dominance of incoherent scattering off target constituents. While a suitably defined scaling function can ... More

Energy-levels crossing and radial Dirac equation: Supersymmetry and quasi-parity spectral signaturesMar 09 2007Aug 20 2007The (3+1)-dimensional Dirac equation with position dependent mass in 4-vector electromagnetic fields is considered. Using two over-simplified examples (the Dirac-Coulomb and Dirac-oscillator fields), we report energy-levels crossing as a spectral property ... More

Dirac and Klein-Gordon particles in complex Coulombic fields; a similarity transformationJan 14 2003Mar 06 2003The observation that the existance of the amazing reality and discreteness of the spectrum need not be attributed to the Hermiticity of the Hamiltonian is reemphasized in the context of the non-Hermitian Dirac and Klein-Gordon Hamiltonians. Complex Coulombic ... More

On a 1D nonlocal transport equation with nonlocal velocity and subcritical or supercritical diffusionMar 16 2016Oct 01 2017We study a 1D transport equation with nonlocal velocity with subcritical or supercritical dissipation. For all data in the weighted Sobolev space $H^{k}(w_{\lambda,\kappa}) \cap L^{\infty},$ with $k=\max(0,3/2-\alpha)$ and $w_{\lambda, \kappa}$ is a given ... More

Polynomialité des coefficients de structure des algèbres de doubles-classesDec 05 2014In this thesis we studied the structure coefficients and especially their dependence on $n$ in the case of a sequence of double-class algebras. The first chapter is dedicated to the study of the structure coefficients in the general cases of centers of ... More

A new deformed Schioberg-type potential and ro-vibrational energies for some diatomic moleculesSep 24 2014Apr 24 2015We suggest a new deformed Schioberg-type potential for diatomic molecules. We show that it is equivalent to Tietz-Hua oscillator potential. We discuss how to relate our deformed Schi\"oberg potential to Morse, to Deng-Fan , to the improved Manning-Rosen, ... More

Weak error in negative Sobolev spaces for the stochastic heat equationApr 25 2013In this paper, we make another step in the study of weak error of the stochastic heat equation by considering norms as functional.

Global existence for the critical dissipative surface quasi-geostrophic equationSep 30 2012Apr 23 2014In this article, we study the critical dissipative surface quasi-geostrophic equation (SQG) in $ \mathbb{R}^2$. Motivated by the study of the homogeneous statistical solutions of this equation, we show that for any large initial data $\theta_{0}$ liying ... More

Uncertainty relations for multiple measurements with applicationsAug 29 2012Uncertainty relations express the fundamental incompatibility of certain observables in quantum mechanics. Far from just being puzzling constraints on our ability to know the state of a quantum system, uncertainty relations are at the heart of why some ... More

The Heavy Photon Search Experiment at Jefferson LabOct 08 2013Oct 25 2013The Heavy Photon Search (HPS) is a new experiment at Jefferson Lab that will search for heavy U(1) vector bosons (heavy photons or dark photons) in the mass range of 20 MeV/c$^2$ to 1 GeV/c$^2$. Dark photons in this mass range are theoretically favorable ... More

Role of intracluster supernovae in radio mini-halos in galaxy clustersFeb 08 2019A possibility of generating a population of cosmic-ray particles accelerated in supernovae typeIa (SNIa) remnants in the intracluster medium (ICM) is discussed. The presently constrained host-less SNIa rates in the clusters are found to be sufficient ... More

Two-dimensional position-dependent mass Lagrangians; Superintegrability and exact solvabilityMay 09 2017Nov 22 2017The two-dimensional extension of the one-dimensional PDM-Lagrangians and their nonlocal point transformation mappings into constant unit-mass exactly solvable Lagrangians is introduced. The conditions on the related two-dimensional Euler-Lagrange equations' ... More

Attention acts to suppress goal-based conflict under high competitionOct 29 2016It is known that when multiple stimuli are present, top-down attention selectively enhances the neural signal in the visual cortex for task-relevant stimuli, but this has been tested only under conditions of minimal competition of visual attention. Here ... More

Position-dependent-mass; Cylindrical coordinates, separability, exact solvability, and PT-symmetryJul 13 2010Jul 20 2010The kinetic energy operator with position-dependent-mass in cylindrical coordinates is obtained. The separability of the corresponding Schr\"odinger equation is discussed within radial cylindrical mass settings. Azimuthal symmetry is assumed and spectral ... More

Fusion algebras, symmetric polynomials, orbits of N-groups, and rank-level dualityJun 15 2004A method of computing fusion coefficients for Lie algebras of type $A_{n-1}$ on level $k$ was recently developed by A. Feingold and M. Weiner \cite{FW} using orbits of $\mathbb{Z}_n^k$ under the permutation action of $S_k$ on $k$-tuples. They got the ... More

Indistinguishable Particles in Quantum Mechanics: An IntroductionNov 01 2005In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This is, for electrons, ... More

Particle Statistics in Quantum Information ProcessingDec 29 2004Particle statistics is a fundamental part of quantum physics, and yet its role and use in the context of quantum information have been poorly explored so far. After briefly introducing particle statistics and the Symmetrization Postulate, I will argue ... More

Relativistic shifted-l expansion technique for Dirac and Klein-Gordon equationsOct 25 1999The shifted-i expansion technique (SLET) is extended to solve for Dirac particle trapped in spherically symmetric scalar and/or 4-vector potentials. A parameter {\lambda}=0,1 is introduced in such a way that one can obtain the Klein-Gordon (KG) bound ... More

2D H-atom in an arbitrary magnetic field via pseudoperturbation expansions through the quantum number lNov 01 1999The pseudoperturbative shifted-l expansion technique (PSLET) is introduced to determine nodeless states of the 2D Schrodinger equation with an arbitrary cylindrically symmetric potentials. Exact energy eigenvalues and eigenfunctions for the 2D Coulomb ... More

On Distinct Distances Between a Variety and a Point SetDec 08 2018Dec 11 2018We consider the problem of Erd\"os on determining the minimum number of distinct distances $f(n)$ that any set of $n$ points in the plane must determine. In a seminal paper, Erd\"os showed that $f(n) = O(n/\sqrt{\log n})$, and conjectured $f(n)=\Omega(n^c)$ ... More

Global well-posedness for the 2D stable Muskat problem in $H^{3/2}$Mar 20 2018Apr 22 2018We prove a global existence result of a unique strong solution in $\dot H^{5/2} \cap \dot H^{3/2}$ with small $\dot H^{3/2}$ norm for the 2D stable Muskat problem, hence allowing the interface to have arbitrary large finite slopes and finite energy (thanks ... More

Sparse polynomial approximation for optimal control problems constrained by elliptic PDEs with lognormal random coefficientsMar 13 2019In this work, we consider optimal control problems constrained by elliptic partial differential equations (PDEs) with lognormal random coefficients, which are represented by a countably infinite-dimensional random parameter with i.i.d. normal distribution. ... More

On Maximal Displacement of Bridges in the Random Conductance modelMar 21 2016Dec 18 2016We study a discrete time random walk in an environment of i.i.d. non-negative conductances in $\mathbb{Z}^d$. We consider the maximum displacements for bridges, i.e. we condition the random walk on returning to the origin, and we prove first a normal ... More

Quantum Pattern MatchingAug 31 2005We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a significant practical ... More

Stability of the Cosine-Sine Functional Equation on amenable groupsSep 19 2018In this paper we establish the stability of the functional equation \begin{equation*}f(xy)=f(x)g(y)+g(x)f(y)+h(x)h(y),\;x,y\in G,\end{equation*} where $G$ is an amenable group.

Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission conditionFeb 19 2010We study a two-scale reaction-diffusion system with nonlinear reaction terms and a nonlinear transmission condition (remotely ressembling Henry's law) posed at air-liquid interfaces. We prove the rate of convergence of the two-scale Galerkin method proposed ... More

A Bell Inequality with Quantum to Classical Violation $\frac{3}{2}$Sep 28 2015May 23 2016We introduce a Bell inequality in a bipartite spin-$\frac{1}{2}$ system with a quantum to classical violation ratio of $\frac{3}{2}$, exceeding the $\sqrt{2}$ violation of the Clauser-Horne-Shimony-Holt inequality. The increase is allowed by the use of ... More

Total neutrino and antineutrino nuclear cross sections around 1 GeVOct 30 2006Mar 09 2007We investigate neutrino-nucleus interactions at energies around 1 GeV. In this regime, the main contributions to the cross sections come from quasi-elastic and $\Delta$ production processes. Our formalism, based on the Impulse Approximation is well suited ... More

Estimates of the uncertainties associated with models of the nucleon structure functions in the $Δ$ production regionApr 07 2006Oct 06 2006Theoretical studies of the inclusive electron-nucleus cross section at beam energies up to few GeV show that, while the region of the quasi-elastic peak is understood at quantitative level, the data in the $\Delta$ production region are sizably underestimated. ... More

Algebro-geometric axioms for DCF$_{0,m}$Jan 16 2016We give an algebro-geometric first-order axiomatization of DCF$_{0,m}$ (the theory of differentially closed fields of characteristic zero with m commuting derivations) in the spirit of the classical geometric axioms of DCF$_0$.

Exact energy eigenvalues of the generalized Dirac-Coulomb equation via a modified similarity transformationOct 19 1999With the aid of a modified similarity transformation we obtained exact energy eigenvalues of the generalized Dirac-Coulomb equation. This equation consists of the time component of the Lorentz 4-vector potential V_v(r)=-A_1/r, and a Lorentz scalar potential ... More

Smallest singular value of sparse random matricesJun 05 2011Dec 20 2012We extend probability estimates on the smallest singular value of random matrices with independent entries to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances from below. ... More

Magnetic fingerprints on the spectra of one-electron and two-electrons interacting in parabolic quantum dotsOct 22 2000Feb 22 2001Magnetic fingerprints on the spectra of an interacting electron with a negatively charged ion in a parabolic quantum dot (QD), and of two interacting electrons in such a dot, are investigated via a pseudoperturbative methodical proposal. The effect of ... More

Energy levels of neutral atoms via a new perturbation methodJul 14 2000The energy levels of neutral atoms supported by Yukawa potential, $V(r)=-Z exp(-\alpha r)/r$, are studied, using both dimensional and dimensionless quantities, via a new analytical methodical proposal (devised to solve for nonexactly solvable Schrodinger ... More

Anharmonic oscillators energies via artificial perturbation methodJan 12 2000Feb 25 2000A new pseudoperturbative (artificial in nature) methodical proposal [15] is used to solve for Schrodinger equation with a class of phenomenologically useful and methodically challenging anharmonice oscillator potentials V(q)=\alpha_o q^2 + \alpha q^4. ... More

Bound states for spiked harmonic oscillators and truncated Coulomb potentialsOct 19 1999We propose a new analytical method to solve for the nonexactly solvable Schrodinger equation. Successfully, it is applied to a class of spiked harmonic oscillators and truncated Coulomb potentials. The utility of this method could be extended to study ... More

A Study on Placement of Social Buttons in Web PagesOct 10 2014With the explosion of social media in the last few years, web pages nowadays include different social network buttons where users can express if they support or recommend content. Those social buttons are very visual and their presentations, along with ... More