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Gravitational-wave parameter estimation with gaps in LISA: a Bayesian data augmentation methodJul 10 2019By listening to gravity in the low frequency band, between 0.1 mHz and 1 Hz, the future space-based gravitational-wave observatory LISA will be able to detect tens of thousands of astrophysical sources from cosmic dawn to the present. The detection and ... More

Existence and Uniqueness of Global Solutions to Fully Nonlinear First Order Elliptic SystemsAug 02 2014Dec 08 2014Let $F : \mathbb{R}^n \times \mathbb{R}^{N\times n} \rightarrow \mathbb{R}^N$ be a Caratheodory map. In this paper we consider the problem of existence and uniqueness of weakly differentiable global strong a.e. solutions $u: \mathbb{R}^n \longrightarrow ... More

Tutorial for Bayesian forensic likelihood ratioApr 12 2013In the Bayesian paradigm for presenting forensic evidence to court, it is recommended that the weight of the evidence be summarized as a likelihood ratio (LR) between two opposing hypotheses of how the evidence could have been produced. Such LRs are necessarily ... More

Generative, Fully Bayesian, Gaussian, Openset Pattern ClassifierJul 23 2013Jul 24 2013This report works out the details of a closed-form, fully Bayesian, multiclass, openset, generative pattern classifier using multivariate Gaussian likelihoods, with conjugate priors. The generative model has a common within-class covariance, which is ... More

Groups, non-additive entropy and phase transitionsApr 01 2014We investigate the possibility of discrete groups furnishing a kinematic framework for systems whose thermodynamic behaviour may be given by non-additive entropies. Relying on the well-known result of the growth rate of balls of nilpotent groups, we see ... More

Generalised Solutions for Fully Nonlinear PDE Systems and Existence-Uniqueness TheoremsJan 25 2015Nov 07 2016We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of Distributions to ... More

Note on a Nonlinear Differential EquationMar 26 2014We give evaluations in closed form of certain non linear differential equations

Diophantine equations coming from binomial near-collisionsJan 12 2019Feb 25 2019In this paper we solve the Diophantine equation $\binom{m}{l}-\binom{n}{k}=d$ (where m,n are positive integers unknowns) when (k,l)=(3,6) for various values of d and when (k,l)=(8,2) and d=1. As a byproduct of our results we will obtain that (k,l)-near ... More

Computing weighted Szeged and PI indices from quotient graphsApr 22 2019The weighted Szeged index and the weighted vertex-PI index of a connected graph $G$ are defined as $wSz(G) = \sum_{e=uv \in E(G)} (deg (u) + deg (v))n_u(e)n_v(e)$ and $wPI_v(G) = \sum_{e=uv \in E(G)} (deg(u) + deg(v))( n_u(e) + n_v(e))$, respectively, ... More

Group classification of charged particle motion in stationary electromagnetic fieldsJul 18 2017In this paper we classify in terms of Lie point symmetries the three-dimensional nonrelativistic motion of charged particles in arbitrary time-independent electromagnetic fields. The classification is made on the ground of equivalence transformations, ... More

On the Representation of Involutive Jamesian FunctionsJun 20 2017Sep 09 2017Involutive Jamesian Functions are functions aimed to predict the outcome of an athletic competition. They were introduced in 1981 by Bill James, but until recently little was known regarding their form. Using methods from quasigroup theory we are able ... More

Weak versus $\mathcal{D}$-solutions to linear hyperbolic first order systems with constant coefficientsJul 10 2015Jan 24 2018We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is the usual notion ... More

Generalised Solutions for Fully Nonlinear PDE Systems and Existence-Uniqueness TheoremsJan 25 2015Feb 20 2017We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of Distributions to ... More

Solution of Polynomial Equations with Nested RadicalsJun 08 2014Mar 16 2017In this note we present solutions of arbitrary polynomial equations in nested periodic radicals.

Arithmetically defined dense subgroups of Morava stabilizer groupsJul 26 2006May 23 2007For every prime $p$ and integer $n\ge 3$ we explicitly construct an abelian variety $A/\F_{p^n}$ of dimension $n$ such that for a suitable prime $l$ the group of quasi-isogenies of $A/\F_{p^n}$ of $l$-power degree is canonically a dense subgroup of the ... More

Formulas for the approximation of the complete Elliptic IntegralsApr 25 2011In this article we give evaluations of the two complete elliptic integrals $K$ and $E$ in the form of Ramanujans type-$\pi$ formulas. The result is a formula for $\Gamma(1/4)^2\pi^{-3/2}$ with accuracy about 120 digits per term.

Eisenstein Series, Alternative Modular Bases and Approximations of $1/π$Nov 15 2010In this article using the theory of Eisenstein series, we give rise to the complete evaluation of two Gauss hypergeometric functions. Moreover we evaluate the modulus of each of these functions and the values of the functions in terms of the complete ... More

The complete evaluation of Rogers Ramanujan and other continued fractions with elliptic functionsAug 07 2010Jun 24 2014In this article we present evaluations of continued fractions studied by Ramanujan. More precisely we give the complete polynomial equations of Rogers-Ramanujan and other continued fractions, using tools from the elementary theory of the Elliptic functions. ... More

On partial evaluation of a continued fraction of Ramanujan and evaluations of hyperbolic seriesMar 26 2018In this article we give partial evaluation of a continued fraction of Ramanujan. We mostly make of use Jacobi elliptic functions.E

On the complete solution of the general quintic using Rogers-Ramanujan continued fractionSep 30 2015In this article we give solution of the general quintic equation by means of the Rogers-Ramanujan continued fraction. More precisely we express a root of the quintic as a known algebraic function of the Rogers-Ramanujan continued fraction.

On Generalized Integrals and Ramanujan-Jacobi Special FunctionsSep 25 2013Nov 15 2015In this article we consider new generalized functions for evaluating integrals and roots of functions. The construction of these generalized functions is based on Rogers-Ramanujan continued fraction, the Ramanujan-Dedekind eta, the elliptic singular modulus ... More

Generalized Elliptic Integrals and ApplicationsApr 04 2013Jun 22 2013We use some general properties, presented in previous work, to evaluate special cases of integrals relating Rogers-Ramanujan continued fraction, eta function and elliptic integrals.

The Graovac-Pisanski Index of Zig-Zag Tubulenes and the Generalized Cut MethodFeb 14 2017Apr 10 2017The Graovac-Pisanski index, which is also called the modified Wiener index, was introduced in 1991 by A. Graovac and T. Pisanski. This variation of the classical Wiener index takes into account the symmetries of a graph. In 2016 M. Ghorbani and S. Klav\v{z}ar ... More

Formula for calculating the Wiener polarity index with applications to benzenoid graphs and phenylenesJan 18 2018Aug 09 2018The Wiener polarity index of a graph is defined as the number of unordered pairs of vertices at distance three. In recent years, this topological index was extensively studied since it has many known applications in chemistry and also in network theory. ... More

On the Dirichlet Problem for Fully Nonlinear Elliptic Hessian SystemsNov 18 2014Apr 27 2015We consider the problem of existence and uniqueness of strong solutions $u: \Omega \subset \mathbb{R}^n \longrightarrow \mathbb{R}^N$ in $(H^{2}\cap H^{1}_0)(\Omega)^N$ to the problem \[\label{1} \tag{1} \left\{ \begin{array}{l} F(\cdot,D^2u ) \,=\, f, ... More

Nucleosynthesis and gamma-ray linesJan 11 2011Astrophysical gamma-ray spectroscopy is an invaluable tool for studying nuclear astrophysics, supernova structure, recent star formation in the Milky Way and mixing of nucleosynthesis products in the interstellar medium. After a short, historical, introduction ... More

Ramanujan type $1/π$ Approximation FormulasNov 14 2011In this article we use theoretical and numerical methods to evaluate in a closed-exact form the parameters of Ramanujan type $1/\pi$ formulas.

Convexity and the "Pythagorean" metric of space(-time)Jun 06 2016We address the question about the reasons why the "Wick-rotated", positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces providing the kinematic ... More

Entropies from coarse-graining: convex polytopes vs. ellipsoidsJul 16 2015We examine the Boltzmann/Gibbs/Shannon $\mathcal{S}_{BGS}$ and the non-additive Havrda-Charv\'{a}t / Dar\'{o}czy/Cressie-Read/Tsallis \ $\mathcal{S}_q$ \ and the Kaniadakis $\kappa$-entropy \ $\mathcal{S}_\kappa$ \ from the viewpoint of coarse-graining, ... More

Extensive limit of a non-extensive entanglement entropyMar 21 2014An important calculation has been that of the (von Neumann) entanglement entropy of the ground state of 1-dimensional lattice models at criticality and of their massive perturbations. This entropy turned out to be, generally, non-extensive. It was noticed, ... More

Asymptotic cones and quantum gravitySep 23 2013Asymptotic cones are structures that encode how a metric space appears when seen from far away. We discuss their meaning and potential significance for quantum gravity.

The geodesic rule and the spectrum of the vacuumJun 30 2006We analyze the consequences of a recent argument justifying the validity of the "geodesic rule" which can be used to determine the density of global topological defects. We derive a formula that provides a rough estimate of the number of string-like defects ... More

Entropy and curvature variations from effective potentialsApr 22 2005By using the Jacobi metric of the configuration space, and assuming ergodicity, we calculate the Boltzmann entropy $S$ of a finite-dimensional system around a non-degenerate critical point of its potential energy $V$. We compare $S$ with the entropy of ... More

Tsallis entropy composition and the Heisenberg groupJan 01 2013We present an embedding of the Tsallis entropy into the 3-dimensional Heisenberg group, in order to understand the meaning of generalized independence as encoded in the Tsallis entropy composition property. We infer that the Tsallis entropy composition ... More

A stochastic derivation of the geodesic ruleFeb 09 2006We argue that the geodesic rule, for global defects, is a consequence of the randomness of the values of the Goldstone field $\phi$ in each causally connected volume. As these volumes collide and coalescence, $\phi$ evolves by performing a random walk ... More

Algebra and calculus for Tsallis thermostatisticsJul 03 2005We construct generalized additions and multiplications, forming fields, and division algebras inspired by the Tsallis thermo-statistics. We also construct derivations and integrations in this spirit. These operations do not reduce to the naively expected ... More

On the Loss of Compactness in the Vectorial Heteroclinic Connection ProblemApr 17 2008Apr 14 2015We give an alternative proof of the theorem of Alikakos-Fusco [AF] concerning existence of heteroclinic solutions to a Hamiltonian ODE system on the whole real line which arises in the theory of phase transitions. Our method is variational but differs ... More

Lagrangian immersions in the product of Lorentzian two manifoldMar 03 2014Mar 26 2014For Lorentzian 2-manifolds $(\Sigma_1,g_1)$ and $(\Sigma_2,g_2)$ we consider the two product para-K\"ahler structures $(G^{\epsilon},J,\Omega^{\epsilon})$ defined on the product four manifold $\Sigma_1\times\Sigma_2$, with $\epsilon=\pm 1$. We show that ... More

On minimal Lagrangian surfaces in the product of Riemannian two manifoldsMay 07 2013May 27 2013Let $(\Sigma_1,g_1)$ and $(\Sigma_2,g_2)$ be connected, complete and orientable Riemannian two manifolds. Consider the two canonical K\"ahler structures $(G^{\epsilon},J,\Omega^{\epsilon})$ on the product 4-manifold $\Sigma_1\times\Sigma_2$ given by $ ... More

A Remark on Global $W^{1,p}$ Bounds for Harmonic Functions with Lipschitz Boundary ValuesJan 02 2016Jul 01 2016In this note we show that gradient of Harmonic functions on a smooth domain with Lipschitz boundary values is pointwise bounded by a universal function which is in $L^p$ for all finite $p\geq 1$.

On a vector-valued generalisation of viscosity solutions for general PDE systemsDec 25 2018We propose a theory of non-differentiable solutions which applies to fully nonlinear PDE systems and extends the theory of viscosity solutions of Crandall-Ishii-Lions to the vectorial case. Our key ingredient is the discovery of a notion of extremum for ... More

Representability of Aut_F and End_FJan 05 2003Recently N. Nitsure showed that for a coherent sheaf F on a noetherian scheme the automorphism functor Aut_F is representable if and only if F is locally free. Here we remove the noetherian hypothesis and show that the same result holds for the endomorphism ... More

Approximation of Sums of PrimesMar 27 2009In this work we consider sums of primes that converging very slow. We set as a base, a reformulation of analytic prime number theorem and we use the values of Riemann Zeta function for the approximation. We also give the truncation error of these approximations ... More

Nonuniqueness in Vector-Valued Calculus of Variations in $L^\infty$ and some Linear Elliptic SystemsApr 18 2013Apr 15 2014For a Hamiltonian $H \in C^2(\mathbb{R}^{N \times n})$ and a map $u:\Omega \subseteq \mathbb{R}^n /!\longrightarrow \mathbb{R}^N$, we consider the supremal functional \[ \label{1} \tag{1} E_\infty (u,\Omega) \ :=\ \big\|H(Du)\big\|_{L^\infty(\Omega)} ... More

Optimal Infinity-Quasiconformal ImmersionsJun 26 2012Jul 18 2014For a Hamiltonian $K \in C^2(\mathbb{R}^{N \times n})$ and a map $u:\Omega \subseteq \mathbb{R}^n \longrightarrow \mathbb{R}^N$, we consider the supremal functional \[ \label{1} \tag{1} E_\infty (u,\Omega) \ :=\ \big\|K(Du)\big\|_{L^\infty(\Omega)} . ... More

On 4-fold covering movesFeb 19 2003Jan 22 2004We prove the existence of a finite set of moves sufficient to relate any two representations of the same 3-manifold as a 4-fold simple branched covering of S^3. We also prove a stabilization result: after adding a fifth trivial sheet two local moves suffice. ... More

Comodule categories and the geometry of the stack of formal groupsMar 15 2005Feb 14 2007We generalise recent results of M. Hovey and N. Strickland on comodule categories for Landweber exact algebras using the formalism of algebraic stacks.

The general solution of Schrodigers differential equationOct 31 2009In this note we solve theoretically the Schrodingers differential equation using results based on our previous work which concern semigroup operators. Our method does not use eigenvectors or eigenvalues and the solution depends only from the selected ... More

A General Method for Constructing Ramanujan Formulas for $1/π^ν$Jul 07 2012In this article we give the theoretical background for generating Ramanujan type $1/\pi^{2\nu}$ formulas. As applications of our method we give a general construction of $1/\pi^4$ series and examples of $1/\pi^6$ series. We also study the elliptic alpha ... More

On a General Sextic Equation Solved by the Rogers Ramanujan Continued FractionNov 22 2011Sep 16 2012In this article we solve a general class of sextic equations. The solution follows if we consider the $j$-invariant and relate it with the polynomial equation's coefficients. The form of the solution is a relation of Rogers-Ramanujan continued fraction. ... More

On Algebraic FunctionsMay 05 2013Mar 27 2014In this note we consider functions with Moebius-periodic rational coefficients. These functions under some conditions take algebraic values and can be recovered by theta functions and the Dedekind eta function. Special cases are the elliptic singular ... More

Generalized cut method for computing the edge-Wiener indexFeb 08 2019The edge-Wiener index of a connected graph $G$ is defined as the Wiener index of the line graph of $G$. In this paper it is shown that the edge-Wiener index of an edge-weighted graph can be computed in terms of the Wiener index, the edge-Wiener index, ... More

Existence and Uniqueness of Global Strong Solutions to Fully Nonlinear Second Order Elliptic SystemsAug 22 2014Feb 29 2016We consider the problem of existence and uniqueness of strong a.e. solutions $u: \mathbb{R}^n \longrightarrow \mathbb{R}^N$ to the fully nonlinear PDE system \[\label{1} \tag{1} F(\cdot,D^2u ) \,=\, f, \ \ \text{ a.e. on }\mathbb{R}^n, \] when $ f\in ... More

A Method for Computing the Edge-Hyper-Wiener Index of Partial Cubes and an Algorithm for Benzenoid SystemsSep 15 2016The edge-hyper-Wiener index of a connected graph $G$ is defined as $WW_e(G) = \frac{1}{2}\sum_{\lbrace e,f\rbrace \subseteq E(G)}d(e,f) + \frac{1}{2}\sum_{\lbrace e,f\rbrace \subseteq E(G)}d(e,f)^2$. We develop a method for computing the edge-hyper-Wiener ... More

Computing the Mostar index in networks with applications to molecular graphsApr 08 2019Recently, a bond-additive topological descriptor, named as the Mostar index, has been introduced as a measure of peripherality in networks. For a connected graph $G$, the Mostar index is defined as $Mo(G) = \sum_{e=uv \in E(G)} |n_u(e) - n_v(e)|$, where ... More

Common hypercyclic functions for translation operators with large gaps IIDec 05 2014We prove the existence of common hypercyclic entire functions for uncountable families of translation type operators. Contrary to our previous work [34], here the parameter which reflects the uncountable family lies on the unit circle. On the other hand ... More

Remarks on cosmological issues in some string theoretic brane worldsFeb 12 2001Nov 14 2001We examine, in the context of certain string compactifications resulting in five dimensional brane worlds the mechanisms of (self) tuning of the cosmological constant and the recovery of standard cosmological evolution. We show that self tuning can occur ... More

Non-radial solutions of the problem $-Δu = |u|^{4/(n-2)}u$ in $R^n$, $n\geq3$Feb 05 2012May 20 2012We prove the existence of an infinite sequence of distinct non-radial nodal $G-$invariant solutions for the following critical nonlinear elliptic problem: $({\mathrm{P}})\quad {*{20}c} {-\Delta u = |u|^{4/(n-2)}u},\quad u\in C^2(\mathbb{R}^n), \quad n\geq3}$ ... More

Almost additive entropyJan 06 2014We explore consequences of a hyperbolic metric induced by the composition property of the Harvda-Charvat/Dar\'{o}czy/Cressie-Read/Tsallis entropy. We address the special case of systems described by small deviations of the non-extensive parameter \ $q\approx ... More

Tsallis entropy and hyperbolicityAug 28 2013Some preliminary evidence suggests the conjecture that the collective behaviour of systems having long-range interactions may be described more effectively by the Tsallis rather than by the Boltzmann/Gibbs/Shannon entropy. To this end, we examine consequences ... More

Escort distributions and Tsallis entropyJun 22 2012We present an argument justifying the origin of the escort distributions used in calculations involving the Tsallis entropy. We rely on an induced hyperbolic Riemannian metric reflecting the generalized composition property of the Tsallis entropy. The ... More

Weak Chaos from Tsallis EntropyApr 26 2011Nov 29 2012We present a geometric, model-independent, argument that aims to explain why the Tsallis entropy describes systems exhibiting "weak chaos", namely systems whose underlying dynamics has vanishing largest Lyapunov exponent. Our argument relies on properties ... More

Rate of parity violation from measure concentrationDec 04 2007We present a geometric argument determining the kinematic (phase-space) factor contributing to the relative rate at which degrees of freedom of one chirality come to dominate over degrees of freedom of opposite chirality, in models with parity violation. ... More

The EM algorithm and the Laplace ApproximationJan 24 2014The Laplace approximation calls for the computation of second derivatives at the likelihood maximum. When the maximum is found by the EM-algorithm, there is a convenient way to compute these derivatives. The likelihood gradient can be obtained from the ... More

Some results on Theory of Infinite Series and Divisor SumsDec 24 2009May 28 2014In this work we present and prove formulas having infinite and finite parts. The finite parts are divisor sums. These sums lead us to very interesting formulas when attached to infinite expressions

Solution of Polynomial Equations with Nested RadicalsJun 08 2014Dec 18 2014In this note we present solutions of arbitrary polynomial equations in nested periodic radicals.

A New Characterisation of $\infty$-Harmonic and $p$-Harmonic Maps via Affine Variations in $L^\infty$Sep 06 2015Aug 08 2016Let $u: \Omega \subseteq \mathbb{R}^n \longrightarrow \mathbb{R}^N$ be a smooth map and $n,N \in \mathbb{N}$. The $\infty$-Laplacian is the PDE system \[ \tag{1} \label{1} \Delta_\infty u \, :=\, \Big(Du \otimes Du + |Du|^2[Du]^\bot\! \otimes I\Big) :D^2u\, ... More

Magnetoresistance through spin polarized p-statesOct 24 2002Jul 23 2003We present a theoretical study of the ballistic magnetoresistance in Ni contacts using first-principles, atomistic electronic-structure calculations. In particular we investigate the role of defects in the contact region in order to explain the recently ... More

On the irreducibility of the two variable zeta-function for curves over finite fieldsSep 09 2002In [P] R. Pellikaan introduced a two variable zeta-function for a curve over a finite field and proved that it is a rational function. Here we show that its denominator is absolutely irreducible. This is motivated by work of J. Lagarias and E. Rains on ... More

Multiple ergodic averages for three polynomials and applicationsJun 22 2006Aug 25 2007We find the smallest characteristic factor and a limit formula for the multiple ergodic averages associated to any family of three polynomials and polynomial families of the form $\{l_1p,l_2p,...,l_kp\}$. We then derive several multiple recurrence results ... More

Common hypercyclic vectors for certain families of differential operatorsJun 17 2015Let (k(n)) n=1,2,... be a strictly increasing sequence of positive integers . We consider a specific sequence of differential operators Tk(n),{\lambda} , n=1,2,... on the space of entire functions , that depend on the sequence (k(n)) n=1,2,... and the ... More

The Wiener polarity index of benzenoid systems and nanotubesNov 09 2017In this paper, we consider a molecular descriptor called the Wiener polarity index, which is defined as the number of unordered pairs of vertices at distance three in a graph. Molecular descriptors play a fundamental role in chemistry, materials engineering, ... More

Computing weighted Szeged and PI indices from quotient graphsApr 22 2019Jun 02 2019The weighted Szeged index and the weighted vertex-PI index of a connected graph $G$ are defined as $wSz(G) = \sum_{e=uv \in E(G)} (deg (u) + deg (v))n_u(e)n_v(e)$ and $wPI_v(G) = \sum_{e=uv \in E(G)} (deg(u) + deg(v))( n_u(e) + n_v(e))$, respectively, ... More

On the Steiner hyper-Wiener index of a graphOct 20 2017May 15 2018In this paper, we study the Steiner hyper-Wiener index of a graph, which is obtained from the standard hyper-Wiener index by replacing the classical graph distance with the Steiner distance. It is shown how this index is related to the Steiner Hosoya ... More

Astrophysical gamma-ray lines: a probe of stellar nucleosynthesis and star formationApr 26 2004Astrophysical gamma-ray spectroscopy is a most valuable tool for studying nuclear astrophysics, as well as recent star formation in the Milky Way. After a short, historical, introduction to the field, I present a brief review of the most important current ... More

Evaluations of Derivatives of Jacobi Theta Functions in the originMay 28 2011In this article using Ramanujan's theory of Eisenstein series we evaluate completely the derivatives of the theta functions $\vartheta_1^{(2\nu+1)}(z)$ and $\vartheta_4^{(2\nu)}(z)$ in the origin in closed polynomials forms using only the first three ... More

An averaged Chowla and Elliott conjecture along independent polynomialsJun 27 2016Jan 05 2017We generalize a result of Matom\"aki, Radziwi{\l}{\l}, and Tao, by proving an averaged version of a conjecture of Chowla and a conjecture of Elliott regarding correlations of the Liouville function, or more general bounded multiplicative functions, with ... More

On the Gauss Circle ProblemOct 21 2014Dec 18 2014We analyze the double series of Bessel functions given by Ramanujan. Using a very simple lemma we establish the uniform convergence of these series. By this we address to the Gauss circle problem.

Evaluations of Ramanujan Continued FractionsDec 24 2009In this paper we present experimental ways of evaluating Ramanujan`s quantities which as someone can see are related with algebraic numbers. The good thing with algebraic numbers is that can be found in a closed form, from there approximations, using ... More

A general lower bound for the asymptotic convergence factorJun 01 2015We provide a rather general and very simple to compute lower bound for the asymptotic convergence factor of compact subsets of the set of complex numbers with connected complement and finitely many connected components .

Algebraic Equations Solved with Jacobi Elliptic FunctionsJul 01 2013Mar 27 2014In this article we solve a class of two parameter polynomial-quintic equation. The solution follows if we consider the Jacobian elliptic function $sn$ and relate it with the coefficients of the equation. The solution is the elliptic singular modulus $k$. ... More

Parametric Evaluations of the Rogers Ramanujan Continued FractionNov 15 2010In this article with the help of the inverse function of the singular moduli we evaluate the Rogers Ranmanujan continued fraction and his first derivative.

A joint analysis of the Drake equation and the Fermi paradoxJan 27 2013Feb 26 2013I propose a unified framework for a joint analysis of the Drake equation and the Fermi paradox, which enables a simultaneous, quantitative study of both of them. The analysis is based on a simplified form of the Drake equation and on a fairly simple scheme ... More

Generalised Solutions for Fully Nonlinear PDE Systems and Existence-Uniqueness TheoremsJan 25 2015May 29 2016We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of Distributions to ... More

A multidimensional Szemeredi theorem for Hardy sequences of different growthFeb 21 2012We prove a variant of the multidimensional polynomial Szemer\'edi theorem of Bergelson and Leibman where one replaces polynomial sequences with other sparse sequences defined by functions that belong to some Hardy field and satisfy certain growth conditions. ... More

Lattice Gauge Theory - Gravity duality and Coulomb's constant in five dimensionsJan 25 2012Mar 05 2012The purpose of this paper is to perform a quantitative check of gauge theory - gravity duality in a nonconformal, nonsupersymmetric context. In order to do so we define k5, an object extracted from the Wilson Loop, that plays the role of Coulomb's constant ... More

Ricci curvature, isoperimetry and a non-additive entropyFeb 18 2015Mar 17 2015Searching for the dynamical foundations of the Havrda-Charv\'{a}t/Dar\'{o}czy/Cressie-Read/Tsallis non-additive entropy, we come across a covariant quantity called, alternatively, a generalized Ricci curvature, an $N$-Ricci curvature or a Bakry-\'{E}mery-Ricci ... More

Nilpotence and the generalized uncertainty principle(s)Mar 11 2013Oct 09 2013We point out that some of the proposed generalized/modified uncertainty principles originate from solvable, or nilpotent at appropriate limits, "deformations" of Lie algebras. We briefly comment on formal aspects related to the well-posedness of one of ... More

Vanishing largest Lyapunov exponent and Tsallis entropyMar 13 2012Jul 11 2013We present a geometric argument that explains why some systems having vanishing largest Lyapunov exponent have underlying dynamics aspects of which can be effectively described by the Tsallis entropy. We rely on a comparison of the generalised additivity ... More

Moduli of curve families and (quasi-)conformality of power-law entropiesDec 13 2015Feb 16 2016We present aspects of the moduli of curve families on a metric measure space which may prove useful in calculating, or in providing bounds to, non-additive entropies having a power-law functional form. We use as paradigmatic cases the calculations of ... More

Tsallis entropy induced metrics and CAT(k) spacesNov 20 2011Feb 06 2012Generalizing the group structure of the Euclidean space, we construct a Riemannian metric on the deformed set \ $\mathbb{R}^n_q$ \ induced by the Tsallis entropy composition property. We show that the Tsallis entropy is a "hyperbolic analogue" of the ... More

Geometric variations of the Boltzmann entropyApr 22 2008We perform a calculation of the first and second order infinitesimal variations, with respect to energy, of the Boltzmann entropy of constant energy hypersurfaces of a system with a finite number of degrees of freedom. We comment on the stability interpretation ... More

The role of Star Formation in the evolution of spiral galaxiesJan 27 2000Spiral galaxies offer a unique opportunity to study the role of star formation in galaxy evolution and to test various theoretical star formation schemes. I review some recent relevant work on the evolution of spiral galaxies. Detailed models are used ... More

Solutions of Vectorial Hamilton-Jacobi Equations are Rank-One Absolute Minimisers in $L^\infty$Apr 04 2016Jul 21 2016Given the supremal functional $E_\infty(u,\Omega')=ess\,\sup_{\Omega'} H(\cdot,D u)$ defined on $W^{1,\infty}_{loc}(\Omega,\mathbb{R}^N)$, $\Omega' \Subset \Omega\subseteq \mathbb{R}^n$, we identify a class of vectorial rank-one Absolute Minimisers by ... More

Absolutely Minimising Generalised Solutions to the Equations of Vectorial Calculus of Variations in $L^\infty$Feb 04 2015Nov 03 2016Consider the supremal functional \[ \tag{1} \label{1} E_\infty(u,A) \,:=\, \|L(\cdot,u,D u)\|_{L^\infty(A)},\quad A\subseteq \Omega, \] applied to $W^{1,\infty}$ maps $u:\Omega\subseteq \mathbb{R}\longrightarrow \mathbb{R}^N$, $N\geq 1$. Under certain ... More

Good weights for the Erdös discrepancy problemMar 05 2019The Erd\"os discrepancy problem, now a theorem by T. Tao, asks whether every sequence with values plus or minus one has unbounded discrepancy along all homogeneous arithmetic progressions. We establish weighted variants of this problem, for weights given ... More

On maximal surfaces in the space of oriented geodesics of hyperbolic 3-spaceJan 13 2010Feb 10 2010We study area-stationary, or maximal, surfaces in the space ${\mathbb L}({\mathbb H}^3)$ of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral K\"ahler structure. We prove that every holomorphic curve in ${\mathbb L}({\mathbb ... More

Big Data Visualization ToolsJan 25 2018Feb 22 2018Data visualization is the presentation of data in a pictorial or graphical format, and a data visualization tool is the software that generates this presentation. Data visualization provides users with intuitive means to interactively explore and analyze ... More

On moves between branched coverings of S^3: The case of four sheetsSep 22 2001Sep 25 2001A combinatorial presentation of closed orientable 3-manifolds as bi-tricolored links is given together with two versions of a calculus via moves to manipulate bi-tricolored links without changing the represented manifold. That is, we provide a finite ... More

Brief Research Notes on Transformation of Series and Special FunctionsJul 06 2009In this work we derive results concerning Elliptic Functions using as tools general formulas from previus work.