Results for "Niko Tratnik"

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Resonance graphs of catacondensed even ring systemsJun 05 2019A catacondensed even ring system (shortly CERS) is a simple bipartite 2-connected outerplanar graph with all vertices of degree 2 or 3. In this paper, we investigate the resonance graphs (also called $Z$-transformation graphs) of CERS and firstly show ... More
The Edge-Szeged Index and the PI Index of Benzenoid Systems in Linear TimeJun 23 2016Aug 02 2016The edge-Szeged index of a graph $G$ is defined as $Sz_e(G) = \sum_{e=uv \in E(G)}m_u(e)m_v(e)$, where $m_u(e)$ denotes the number of edges of $G$ whose distance to $u$ is smaller than the distance to $v$ and $m_v(e)$ denotes the number of edges of $G$ ... 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
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
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
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
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
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
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
New methods for calculating the degree distance and the Gutman indexSep 07 2018In the paper we develop new methods for calculating the two well-known topological indices, the degree-distance and the Gutman index. Firstly, we prove that the Wiener index of a double vertex-weighted graph can be computed from the Wiener indices of ... More
The Szeged Index and the Wiener Index of Partial Cubes with Applications to Chemical GraphsSep 13 2016In this paper we study the Szeged index of partial cubes and hence generalize the result proved by V. Chepoi and S. Klav\v{z}ar, who calculated this index for benzenoid systems. It is proved that the problem of calculating the Szeged index of a partial ... More
The Edge-Wiener Index, the Szeged Indices and the PI Index of Benzenoid Systems in Sub-Linear TimeMay 08 2017In this paper, we investigate the edge-Wiener index, the Szeged index, the edge-Szeged index, and the PI index, which are some of the most studied distance-based topological indices. As the main result we show that for benzenoid systems these indices ... More
The Szeged Index and the Wiener Index of Partial Cubes with Applications to Chemical GraphsSep 13 2016Apr 10 2017In this paper we study the Szeged index of partial cubes and hence generalize the result proved by V. Chepoi and S. Klav\v{z}ar, who calculated this index for benzenoid systems. It is proved that the problem of calculating the Szeged index of a partial ... More
Resonance Graphs and Perfect Matchings of Graphs on SurfacesOct 02 2017Let $G$ be a graph embedded in a surface and let $\mathcal F$ be a set of even faces of $G$ (faces bounded by a cycle of even length). The resonance graph of $G$ with respect to $\mathcal F$, denoted by $R(G;\mathcal F)$, is a graph such that its vertex ... More
The edge-Hosoya polynomial of benzenoid chainsDec 15 2017The Hosoya polynomial is a well known vertex-distance based polynomial, closely correlated to the Wiener index and the hyper-Wiener index, which are widely used molecular-structure descriptors. In the present paper we consider the edge version of the ... More
The Graovac-Pisanski Index of Armchair NanotubesApr 27 2017The Graovac-Pisanski index, which is also called the modified Wiener index, considers the symmetries and the distances in molecular graphs. Carbon nanotubes are molecules made of carbon with a cylindrical structure possessing unusual valuable properties. ... More
Relationship Between the Hosoya Polynomial and the Edge-Hosoya Polynomial of TreesSep 14 2016We prove the relationship between the Hosoya polynomial and the edge-Hosoya polynomial of trees. The connection between the edge-hyper-Wiener index and the edge-Hosoya polynomial is established. With these results we also prove formulas for the computation ... More
Uniquely identifying the edges of a graph: the edge metric dimensionJan 31 2016Let $G=(V,E)$ be a connected graph, let $v\in V$ be a vertex and let $e=uw\in E$ be an edge. The distance between the vertex $v$ and the edge $e$ is given by $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A vertex $w\in V$ distinguishes two edges $e_1,e_2\in E$ ... More
Resonantly Equivalent Catacondensed Even Ring SystemsJan 24 2019In this paper we generalize the binary coding procedure of perfect matchings from catacondensed benzenoid graphs to catacondensed even ring systems (also called cers). Next, we study cers with isomorphic resonance graphs. For this purpose, we define resonantly ... More
Predicting Melting Points by the Graovac-Pisanski IndexSep 05 2017Theoretical molecular descriptors alias topological indices are a convenient means for expressing in a numerical form the chemical structure encoded in a molecular graph. The structure descriptors derived from molecular graphs are widely used in Quantitative ... More
The Graovac-Pisanski index of a connected bipartite graph is an integer numberSep 13 2017The Graovac-Pisanski index, also called the modified Wiener index, was introduced in 1991 and represents an extension of the original Wiener index, because it considers beside the distances in a graph also its symmetries. Similarly as Wiener in 1947 showed ... More
On the Clar Number of Benzenoid GraphsSep 13 2017A Clar set of a benzenoid graph $B$ is a maximum set of independent alternating hexagons over all perfect matchings of $B$. The Clar number of $B$, denoted by ${\rm Cl}(B)$, is the number of hexagons in a Clar set for $B$. In this paper, we first prove ... More
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
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.
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
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
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
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
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
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
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
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
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
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
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
A Summary of Recent Color Coherence ResultsSep 17 1998Recent experimental results on color coherence phenomena from e+e-, ep, and ppbar collisions are presented. The data are compared to analytic perturbative QCD calculations based on the modified leading logarithm approximation and the local parton hadron ... More
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
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
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
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 .
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
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.
Nonsmooth Convex Functionals and Feeble Viscosity Solutions of singular Euler-Lagrange EquationsAug 27 2013Apr 03 2014Let F be nonnegative, convex and smooth off a compact set K. We prove that continuous local minimisers of convex functionals are "very weak" viscosity solutions in the sense of Juutinen-Lindqvist of the highly singular Euler-Lagrange PDE expanded. The ... More
Quantum Limits of Eisenstein Series in H^3Nov 23 2015We study the quantum limits of Eisenstein series off the critical line for $\mathrm{PSL}_{2}(\mathcal{O}_{K})\backslash\mathbb{H}^{3}$, where $K$ is an imaginary quadratic field of class number one. This generalises the results of Petridis, Raulf and ... 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
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
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
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
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
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 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
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
Note on a Nonlinear Differential EquationMar 26 2014We give evaluations in closed form of certain non linear differential equations
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
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.
Solution of Polynomial Equations with Nested RadicalsJun 08 2014Mar 16 2017In this note we present solutions of arbitrary polynomial equations in nested periodic radicals.
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.
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
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
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
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.
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