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A Totient Function InequalityFeb 09 2010Feb 06 2012A new unconditional inequality of the totient function is contributed to the literature. This result is associated with various unsolved problems about the distribution of prime numbers.

Note on Integer Factoring Methods IVFeb 28 2008Sep 25 2008This note continues the theoretical development of deterministic integer factorization algorithms based on systems of polynomials equations. The main result establishes a new deterministic time complexity bench mark in integer factorization.

Note on the Merit Factors of SequencesJun 02 2005Jul 10 2013A method for estimating the merit factors of sequences will be provided. The result is also effective in determining the nonexistence of certain infinite collections of cyclic difference sets and cyclic matrices and associated binary sequences.

A Note on the Zero-Free Regions of the Zeta FunctionAug 28 2009Oct 12 2012This short note contributes a new zero-free region of the zeta function. This zero-free region has the form {s : Re(s) > a}, where a = 21/40.

The Error Term In The Primes Counting FunctionAug 11 2009This article considers the error term of the primes counting function. It applies some recent results on the densities of prime numbers in short intervals to derive an improvement of the error term from subexponential size to fractional exponential size. ... More

Counting Primes Rationally And IrrationallyJul 29 2019The recent technique for estimating lower bounds of the prime counting function $\pi(x)=\#\{p \leq x: p\text{ prime}\}$ by means of the irrationality measures $\mu(\zeta(s)) \geq 2$ of special values of the zeta function claims that $\pi(x) \gg \log \log ... More

Note on the Theory of Correlation FunctionsMar 18 2016Sep 02 2016The purpose of this note is to improve the current theoretical results for the correlation functions of the Mobius sequence $\{\mu(n): n\geq 1 \}$ and the Liouville sequence $\{\lambda(n): n\geq 1 \}$.

Irrationality Measure of PiFeb 23 2019May 18 2019The first estimate of the upper bound $\mu(\pi)\leq42$ of the irrationality measure of the number $\pi$ was computed by Mahler in 1953, and more recently it was reduced to $\mu(\pi)\leq7.6063$ by Salikhov in 2008. Here, it is shown that $\pi$ has the ... More

Densities Of Primes And Primitive RootsJul 14 2017Nov 17 2018Let $u\neq \pm 1,v^2$ be a fixed integer, let $p\geq 2$ be a prime, and let $\text{ord}_p(u)=d \:|\: p-1$ be the order of $u \text{ mod } p$. This note provides an effective lower bound $\pi_u(x)=\# \{ p\leq x:\text{ord}_p(u)=p-1 \}\gg x (\log x)^{-1}$ ... More

Topics In Primitive RootsMay 01 2014Mar 12 2015This monograph considers a few topics in the theory of primitive roots g(p) modulo a prime p>=2. A few estimates of the least primitive roots g(p) and the least prime primitive roots g^*(p) modulo p, a large prime, are determined. One of the estimate ... More

Generalized Artin Primitive Root ConjectureApr 02 2015Sep 19 2018An asymptotic formula for the number of integers with the primitive root 2, and a generalized Artin primitive root conjecture for composite integers is presented here.

Irrationality of the Zeta ConstantsDec 13 2012Sep 16 2016A general technique for proving the irrationality of the zeta constants $\zeta(s)$ for odd $s = 2n + 1 \geq 3$ from the known irrationality of the beta constants $L(2n+1)$ is developed in this note. The results on the irrationality of the zeta constants ... More

A Divisor Function InequalityDec 09 2009Feb 09 2010This short note provides an unconditional proof of a well known inequality of the divisor function. This is an unsolved problem in pure mathematics and the distribution of prime numbers. Furthermore, the technique is completely elementary.

Simple Zeros Of The Zeta FunctionJun 03 2013Jul 15 2016This note studies the Laurent series of the inverse zeta function $1/\zeta(s)$ at any fixed nontrivial zero $\rho$ of the zeta function $\zeta(s)$, and its connection to the simplicity of the nontrivial zeros.

Note on the Theory of Correlation FunctionsMar 18 2016Jan 14 2019The purpose of this note is to improve the current theoretical results for the correlation functions of the Mobius sequence $\{\mu(n): n\geq 1 \}$ and the Liouville sequence $\{\lambda(n): n\geq 1 \}$.

Primes In Fractional SequencesSep 08 2018Some results for fractional sequences of integers such as the sequence $\left \{[x/n]^2+1:n \leq x\right \}$ generated by the quadratic polynomial $n^2+1$, and the sequence $\left \{[x/n]^3+2:n \leq x\right \}$ generated by the cubic polynomial $n^3+2$, ... More

Irrationality Measure of PiFeb 23 2019The first estimate of the upper bound $\mu(\pi)\leq42$ of the irrationality measure of the number $\pi$ was computed by Mahler in 1953, and more recently it was reduced to $\mu(\pi)\leq7.6063$ by Salikhov in 2008. Here, it is shown that $\pi$ has the ... More

Note on Integer Factoring Methods INov 07 2006This note presents the basic mathematical structure of a new integer factorization method based on systems of linear Diophantine equations.

Deterministic Integer Factorization AlgorithmsAug 05 2013Aug 28 2013This note presents a deterministic integer factorization algorithm of running time complexity O(N^(1/6+e)), e > 0. This improves the current performances of deterministic integer factorization algorithms rated at O(N^(1/4+e)) arithmetic operations. Equivalently, ... More

Character Sums Over The Prime NumbersMay 22 2012A few elementary estimates of a basic character sum over the prime numbers are derived here. These estimates are nontrivial for character sums modulo large q. In addition, an omega result for character sums over the primes is also included.

On Evaluation of Nonlinear Exponential SumsMar 05 2005This paper provides a technique for evaluating some nonlinear Gaussian sums in closed forms. The evaluation is obtained from the known values of simpler exponential sums.

Primes In Arithmetic Progressions And Primitive RootsJan 11 2017Oct 06 2018Let $x\geq 1$ be a large number, and let $1 \leq a <q $ be integers such that $\gcd(a,q)=1$ and $q=O(\log^c)$ with $c>0$ constant. This note proves that the counting function for the number of primes $p \in \{p=qn+a: n \geq1 \}$ with a fixed primitive ... More

Irrationality of the Zeta ConstantsDec 13 2012Jun 22 2018A general technique for proving the irrationality of the zeta constants $\zeta(s)$ for odd $s = 2n + 1 \geq 3$ from the known irrationality of the beta constants $L(2n+1)$ is developed in this note. The results on the irrationality of the zeta constants ... More

The Error Term of the Summatory Euler Phi FunctionJun 12 2012Dec 30 2015A sharper estimate of the summatory Euler phi function is presented in this work. It improves the established estimate in the current mathematical literature. The corresponding estimate for the normalized summatory Euler phi function, an omega result, ... More

Asymptotic For Primitive Roots Producing PolynomialsSep 02 2016Oct 21 2016Let $x \geq 1$ be a large number, let $f(x) \in \mathbb{Z}[x]$ be a prime polynomial of degree $\text{deg}(f)=m$, and let $u\ne \pm 1, v^2$ be a fixed integer. Assuming the Bateman-Horn conjecture, an asymptotic counting function for the number of primes ... More

Note on the ABC ConjectureJun 09 2006This note imparts heuristic arguments and theorectical evidences that contradict the abc conjecture over the rational numbers. In addition, the rudimentary datails for transforming this problem into the doimain of equidistribution theory are provided. ... More

Note on the Theory of Perfect NumbersFeb 08 2011Mar 03 2011A perfect number is a number whose divisors add up to twice the number itself. The existence of odd perfect numbers is a millennia-old unsolved problem. This note proposes a proof of the nonexistence of odd perfect numbers. More generally, the same analysis ... More

Oscillations in Mertens Theorems and Other Finite Sums and ProductsMay 25 2010Jul 10 2013This note simplifies the proof of a recent result on the oscillation of the prime product in Martens Theorem, and provides a quantitative expression for the error term. In addition, the corresponding oscillation results for the finite sums of the reciprocal ... More

A Dedekind Psi Function InequalityDec 01 2011Dec 22 2011This note shows that the Dedekind psi function achieves its extreme values on the subset of primorial integers N_k = 2*3*5*...*p_k, where p_k is the kth prime. In particular, the inequality psi(N_k) > cloglog N_k, where c = 1.08... is a universal constant, ... More

Topic In Elliptic Curves Over Finite Fields: The Groups of PointsMar 22 2011Apr 05 2011This article is a short introduction to the theory of the groups of points of elliptic curves over finite fields. It is concerned with the elementary theory and practice of elliptic curves cryptography, the new generation of public key systems. The material ... More

The Product $e π$ Is IrrationalJun 19 2017Jun 01 2018This note shows that the product $e \pi$ of the natural base $e$ and the circle number $\pi$ is an irrational number.

A Simple Proof Of The Prime Number TheoremOct 09 2015It is shown that the Mean Value Theorem for arithmetic functions, and simple properties of the zeta function are sufficient to assemble proofs of the Prime Number Theorem, and Dirichlet Theorem. These are among the simplest proofs of the asymptotic formulas ... More

Asymptotic For Primitive Roots Producing PolynomialsSep 02 2016Let $x \geq 1$ be a large number, let $f(x) \in \mathbb{Z}[x]$ be a prime polynomial of degree $\text{deg}(f)=m$, and let $u\ne \pm 1, v^2$ be a fixed integer. Assuming the Bateman-Horn conjecture, an asymptotic counting function for the number of primes ... More

The Zeta Quotient $ζ(3)/ π^3$ is IrrationalJun 18 2019This note proves that the first odd zeta value does not have a closed form formula $\zeta(3)\ne r \pi^3$ for any rational number $r \in \mathbb{Q}$. Furthermore, assuming the irrationality of the second odd zeta value $\zeta(5)$, it is shown that $\zeta(5)\ne ... More

Irrationality Measure of PiFeb 23 2019Jun 26 2019The first estimate of the upper bound $\mu(\pi)\leq42$ of the irrationality measure of the number $\pi$ was computed by Mahler in 1953, and more recently it was reduced to $\mu(\pi)\leq7.6063$ by Salikhov in 2008. Here, it is shown that $\pi$ has the ... More

Results for Wieferich PrimesDec 21 2017May 05 2018Let $v\geq 2$ be a fixed integer, and let $x \geq 1$ and $z \geq x$ be large numbers. The exact asymptotic formula for the number of Wieferich primes $p$ such that $ v^{p-1} \equiv 1 \bmod p^2$ in the short interval $[x,x+z]$ is proposed in this note. ... More

Rapidly Convergent Series of the Divisors FunctionsJul 28 2014This note gives a few rapidly convergent series representations of the sums of divisors functions. These series have various applications such as exact evaluations of some power series, computing estimates and proving the existence results of some special ... More

Least Prime Primitive RootsSep 01 2017This note presents an upper bound for the least prime primitive roots $g^*(p)$ modulo $p$, a large prime. The current literature has several estimates of the least prime primitive root $g^*(p)$ modulo a prime $p\geq 2$ such as $g^*(p)\ll p^c, c>2.8$. ... More

Complexity of Computing Quadratic NonresiduesFeb 10 2005Aug 25 2005This note provides new methods for constructing quadratic nonresidues in finite fields of characteristic p. It will be shown that there is an effective deterministic polynomial time algorithm for constructing quadratic nonresidues in finite fields.

Cyclic Difference Sets And Cyclic Hadamard MatricesSep 29 2011Dec 20 2011The collection of cyclic Hadamard matrices {H = (a_{i - j}) : 0 <= i, j < n, and a_i = -1, 1} of order n is characterized by the orthogonality relation HH^T = nI. Only two of such matrices are currently known. It will be shown that this collection consists ... More

The Zeta Quotient $ζ(3)/ π^3$ is IrrationalJun 18 2019Jul 29 2019This note proves that the first odd zeta value does not have a closed form formula $\zeta(3)\ne r \pi^3$ for any rational number $r \in \mathbb{Q}$. Furthermore, assuming the irrationality of the second odd zeta value $\zeta(5)$, it is shown that $\zeta(5)\ne ... More

Coexistence of critical orbit types in sub-hyperbolic polynomial mapsJun 17 1994We establish necessary and sufficient conditions for the realization of mapping schemata as post-critically finite polynomials, or more generally, as post-critically finite polynomial maps from a finite union of copies of the complex numbers {\bf C} to ... More

Hubbard forestsAug 13 1992The theory of Hubbard trees provides an effective classification of non-linear post-critically finite polynomial maps from \C to itself. This note will extend this classification to the case of maps from a finite union of copies of \C to itself. Maps ... More

The Origin of MassFeb 11 2009Dynamical chiral symmetry breaking and confinement are two crucial features of Quantum Chromodynamics responsible for the nature of the hadron spectrum. These phenomena, presumably coincidental, can account for 98% of the mass of our visible universe. ... More

Symbolic dynamics and semigroup theoryNov 09 2018A major motivation for the development of semigroup theory was, and still is, its applications to the study of formal languages. Therefore, it is not surprising that the correspondence $\mathcal X\mapsto B(\mathcal X)$, associating to each symbolic dynamical ... More

L'utilità di una teoria inutile-Crittografia, firma digitale e teoria dei numeriFeb 14 2011The theory of numbers was supposed to be the less useful branch of mathematics. At the same time, cryptography was thought to be a military or a diplomatic issue. In this note we show how the two concepts are today strictly related and how this link affects ... More

Higgs decay into photons through a spin-2 loopAug 28 2012Sep 04 2012A new particle with proprieties similar to those of the Higgs boson in the Standard Model (SM) has been recently discovered. The biggest discrepancy is related to its diphoton decay, whose branching ratio seems to be around two times larger with respect ... More

Debunking some myths about biometric authenticationMar 01 2012Biometric authentication systems are presented as the best way to reach high security levels in controlling access to IT systems or sensitive infrastructures. But several issues are often not taken properly into account. In order for the implementation ... More

Alternative Symmetries in Quantum Field Theory and GravityFeb 25 2011A general, incomplete and partisan overview of various areas of the theoretical investigation is presented. Most of this activity stems from the search for physics beyond quantum field theory and general relativity, a titanic struggle that, in my opinion, ... More

Ansatz for baryonic wave function obtained from a mesonic oneNov 28 2018Dec 10 2018Based on ideas that relate meson and baryon spectrum considering SUSY QM and light front holography, we propose a procedure to obtain LFWF for baryons starting from mesonic ones. We apply a procedure suggested for Gaussian ansatz used to study mesons. ... More

Large $z$ Asymptotics for Special Function Solutions of Painlevé II in the Complex PlaneApr 02 2018Oct 03 2018In this paper we obtain large $z$ asymptotic expansions in the complex plane for the tau function corresponding to special function solutions of the Painlev\'e II differential equation. Using the fact that these tau functions can be written as $n\times ... More

All states, except the identity, are nonclassical: entanglement of joint statisticsJun 05 2016Simple measurement protocols reveal that every states is nonclassical excluding just the identity state. We show that this is a consequence of the fact that we can always find a joint measurement whose statistics is not separable.

A note on Seiberg-Witten central chargeMay 11 1999Oct 19 1999The central charge for the Seiberg-Witten low-energy effective Action is computed using Noether supercharges. A reliable method to construct supersymmetric Noether currents is presented.

Three Questions on Lorentz ViolationDec 18 2006We review the basics of the two most widely used approaches to Lorentz violation - the Stardard Model Extension and Noncommutative Field Theory - and discuss in some detail the example of the modified spectrum of the synchrotron radiation. Motivated by ... More

Graphene and Black Holes: novel materials to reach the unreachableDec 15 2014The case for a dedicated laboratory, to test hep-th models on analogue systems, is briefly made. The focus is on graphene.

Comment on "Noncommutative gauge theories and Lorentz symmetry, Phys. Rev. D {\bf 70}, 125004 (2004) by R.Banerjee, B.Chakraborty and K.Kumar"Feb 15 2011We show that Lorentz symmetry is generally absent for noncommutative (abelian) gauge theories and obtain a compact formula for the divergence of the Noether currents that allows a throughout study of this instance of symmetry violation. We use that formula ... More

Remarks on analyticity and unitarity in the presence of a Strongly Interacting Light HiggsOct 21 2013Apr 25 2014Applying the three axiomatic criteria of Lorentz invariance, analyticity and unitarity to scattering amplitudes involving the Goldstone bosons and the Higgs boson, we derive a general sum rule for the Strongly Interacting Light Higgs Lagrangian. This ... More

Towards autonomous ocean observing systems using Miniature Underwater Gliders with UAV deployment and recovery capabilitiesFeb 08 2019This paper presents preliminary results towards the development of an autonomous ocean observing system using Miniature Underwater Gliders (MUGs) that can operate with the support of Unmanned Aerial Vehicles (UAVs) and Unmanned Surface Vessels (USVs) ... More

Breaking the weak Heisenberg limitJul 26 2016We provide a very simple analytical and numerical case showing that the weak form of the Heisenberg limit can be beaten while the prior information is improved without bias problems.

Modelling and simulation of multifractal star-shaped particlesJan 22 2019The problem of constructing flexible stochastic models to describe the variability in shape of solid particles is challenging. Natural objects often exhibit mono- or multi-fractal features, i.e. irregular shapes and self-similar patterns. This paper presents ... More

Supersymmetric 4d gauge theories and IntegrabilityJul 25 2018This thesis is devoted to some particular aspects of integrability in $4d$ SUSY gauge theories. Taking advantage of the integrable structures emergent in the theory, non-local observables such as null polygonal Wilson loops are studied in $4d$ planar ... More

Curved Spacetimes and Curved Graphene: a status report of the Weyl-symmetry approachDec 15 2014This is a status report about the ongoing work on the realization of quantum field theory on curved graphene spacetimes that uses Weyl symmetry. The programme is actively pursued from many different perspectives. Here we point to what has been done, and ... More

Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic ScatteringJun 07 2017We provide universal expressions for the classical piece of the amplitude given by the graviton/photon exchange between massive particles of arbitrary spin, at both tree and one loop level. In the gravitational case this leads to higher order terms in ... More

Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded intervalFeb 10 2014Jul 08 2014We consider polynomials $p_n^{\omega}(x)$ that are orthogonal with respect to the oscillatory weight $w(x)=e^{i\omega x}$ on $[-1,1]$, where $\omega>0$ is a real parameter. A first analysis of $p_n^{\omega}(x)$ for large values of $\omega$ was carried ... More

Coherence for vectorial waves and majorizationMar 04 2016We show that majorization provides a powerful approach to the coherence conveyed by partially polarized transversal electromagnetic waves. Here we present the formalism, provide some examples and compare with standard measures of polarization and coherence ... More

Towards a proof of the Weak Gravity ConjectureOct 12 2018Oct 30 2018The Weak Gravity Conjecture (WGC) asserts a powerful consistency condition on gauge theories coupled to gravity, and it is widely believed that its proof will shed light on the quantum origin of gravitational interactions. Holography, and in particular ... More

SU(5) & A4May 06 2009The introduction of a Flavour Symmetry can represent an interesting way in which one can try to find an answer to some intriguing problems in Flavour Physics, like the hierarchy between the fermion masses or the particular values of mixing angles. In ... More

Asymptotic analysis of the Friedkin-Johnsen model when the matrix of the susceptibility weights approaches the identity matrixAug 30 2018Sep 19 2018In this paper we analyze the Friedkin-Johnsen model of opinions when the coefficients weighting the agent susceptibilities to interpersonal influence approach 1. We will show that in this case, under suitable assumptions, the model converges to a quasi-consensus ... More

Nonclassical states from the joint statistics of simultaneous measurementsJun 25 2015Nonclassicality cannot be a single-observable property since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior from the joint measurement of multiple observables. ... More

Notes on Conformal Soft Theorems and Recursion Relations in GravityJun 18 2019Celestial amplitudes are flat-space amplitudes which are Mellin-transformed to correlators living on the celestial sphere. In this note we present a recursion relation, based on a tree-level BCFW recursion, for gravitational celestial amplitudes and use ... More

Generalized wreath products of graphs and groupsOct 26 2013Inspired by the definition of generalized wreath product of permutation groups, we define the generalized wreath product of graphs, containing the classical Cartesian and wreath product of graphs as particular cases. We prove that the generalized wreath ... More

Graphene: QFT in curved spacetimes close to experimentsApr 09 2013A recently proposed step-by-step procedure, to merge the low-energy physics of the $\pi$-bonds electrons of graphene, and quantum field theory on curved spacetimes, is recalled. The last step there is the proposal of an experiment to test a Hawking-Unruh ... More

Autenticazione biometrica: Realtà e fantasiaJan 04 2012Feb 04 2012Biometrical authentication systems are often presented as the best and simplest way to reach higher security levels. But a deeper analysis shows that several risks are hidden and the service provider adopting those system has to carefully check its liabilities ... More

On the realization of fixed point portraits (an addendum to Goldberg, Milnor: Fixed point portraits)Oct 27 1991We establish that every formal critical portrait (as defined by Goldberg and Milnor), can be realized by a postcritically finite polynomial.

On postcritically finite polynomials, part 1: critical portraitsMay 15 1993We extend the work of Bielefeld, Fisher and Hubbard on Critical Portraits to the case of arbitrary postcritically finite polynomials. This determines an effective classification of postcritically finite polynomials as dynamical systems. This paper is ... More

Electroweak scale neutrinos and HiggsesDec 16 2008We present two different models with electroweak scale right-handed neutrinos. One of the models is created under the constraint that any addition to the Standard Model must not introduce new higher scales. The model contains right-handed neutrinos with ... More

Neutrino mixing from the double tetrahedral group T^{\prime}Jul 25 2007Nov 09 2007It is shown that it is possible to create successful models of flavor for both quarks and leptons using the discrete non-abelian group $T^{\prime}$ by itself. Two simple realizations are presented that can be used as the starting point for more general ... More

Topological Gravity, Kaluza-Klein Reduction, and the KinkJan 19 2004Mar 02 2004Kaluza-Klein reduction of the 3-dimensional gravitational Chern-Simons term leads to a 2-dimensional theory that supports a symmetry breaking solution and an associated kink interpolating between AdS and dS geometries.

Models of Flavor with Discrete SymmetriesNov 20 2002In an attempt to understand the observed patterns of lepton and quark masses, models invoking a flavor symmetry $G_f$, under which the Standard Model generations are charged, have been proposed. One particularly successful symmetry, U(2), has been extensively ... More

Using Weyl symmetry to make Graphene a real lab for fundamental physicsJul 30 2012In the first attempt to introduce gauge theories in physics, Hermann Weyl, around the 1920s, proposed certain scale transformations to be a fundamental symmetry of nature. Despite the intense use of Weyl symmetry that has been made over the decades, in ... More

Weyl-Gauge Symmetry of GrapheneJul 28 2010Jan 19 2011The conformal invariance of the low energy limit theory governing the electronic properties of graphene is explored. In particular, it is noted that the massless Dirac theory in point enjoys local Weyl symmetry, a very large symmetry. Exploiting this ... More

On (Schröedinger's) quest for new physics for lifeOct 07 2009Two recent investigations are reviewed: quantum effects for DNA aggregates and scars formation on virus capsids. The possibility that scars could explain certain data recently obtained by Sundquist's group in electron cryotomography of immature HIV-1 ... More

Breaking the weak Heisenberg limitJul 26 2016Mar 15 2017We provide a very simple case showing that the weak form of the Heisenberg limit can be beaten while the prior information is improved without bias.

Contradictory entropic joint uncertainty relations for complementary observables in two-level systemsJun 21 2013We show that different entropic measures of fluctuations lead to contradictory uncertainty relations for two complementary observables. We apply Tsallis and R\'{e}nyi entropies to the joint distribution emerging from a noisy simultaneous measurement of ... More

Signal detection without finite-energy limits to quantum resolutionMar 20 2012Jan 16 2013We show that there are extremely simple signal detection schemes where the finiteness of energy resources places no limit to the resolution. On the contrary, larger resolution can be obtained with lower energy. To this end the generator of the signal-dependent ... More

Contradictory uncertainty relationsApr 12 2011We show within a very simple framework that different measures of fluctuations lead to uncertainty relations resulting in contradictory conclusions. More specifically we focus on Tsallis and Renyi entropic uncertainty relations and we get that the minimum ... More

All states are nonclassical: entanglement of joint statisticsJun 05 2016Nov 21 2016Joint measurements of two observables reveal that every state is nonclassical, with the only trivial exception of the state with density matrix proportional to the identity. This naturally includes states considered universally as classical-like, such ... More

Two arguments for more fundamental building blocksFeb 18 2019We present two lines of reasoning, leading to elementary constituents more fundamental than the ones we know. One such arguments is new, and based on the holographic maximal bound for the number of degrees of freedom of any system. In this case, both ... More

Majorization of quantum polarization distributionsOct 03 2016Majorization provides a rather powerful partial-order classification of probability distributions depending only on the spread of the statistics, and not on the actual numerical values of the variable being described. We propose to apply majorization ... More

Generalized Reissner-Nordström solution in Metric-Affine GravityJun 02 1999We present the generalized Reissner-Nordstr\"om solution of the field equations of metric-affine gravity (MAG), endowed with electric and magnetic charges, as well as with gravito-electric and gravito-magnetic charges and a cosmological constant term. ... More

Topological Constraints on the Charge Distributions for the Thomson ProblemMar 02 2006The method of Morse theory is used to analyze the distributions of unit charges interacting through a repulsive force and constrained to move on the surface of a sphere -- the Thomson problem. We find that, due to topological reasons, the system may organize ... More

Convergence to equilibrium for the discrete coagulation-fragmentation equations with detailed balanceFeb 27 2007Nov 19 2007Under the condition of detailed balance and some additional restrictions on the size of the coefficients, we identify the equilibrium distribution to which solutions of the discrete coagulation-fragmentation system of equations converge for large times, ... More

Considerations on P vs NPNov 07 2007In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set E(A) containing ... More

Improved Lindstedt-Poincare method for the solution of nonlinear problemsMar 23 2003We apply the Linear Delta Expansion (LDE) to the Lindstedt-Poincare (``distorted time'') method to find improved approximate solutions to nonlinear problems. We find that our method works very well for a wide range of parameters in the case of the anharmonic ... More

Charging Interacting Rotating Black Holes in Heterotic String TheoryJan 16 2002May 28 2004We present a formulation of the stationary bosonic string sector of the whole toroidally compactified effective field theory of the heterotic string as a double Ernst system which, in the framework of General Relativity describes, in particular, a pair ... More

Some identification problems for integro-differential operator equationsNov 17 2000We consider, in a Hilbert space $H$, the convolution integro-differential equation $u''(t)-h*Au(t)=f(t)$, $0\le t\le T$, $h*v(t)=\int_0^t h(t-s)v(s) ds$, where $A$ is a linear closed densely defined (possibly selfadjoint and/or positive definite) operator ... More

Principle of Conservation of Computational ComplexityDec 04 2017Jan 03 2018In this manuscript, we derive the principle of conservation of computational complexity. We measure computational complexity as the number of binary computations (decisions) required to solve a problem. Every problem then defines a unique solution space ... More

Nonlinear Michelson interferometer for improved quantum metrologyApr 21 2015Aug 11 2015We examine quantum detection via a Michelson interferometer embedded in a gas with Kerr nonlinearity. This nonlinear interferometer is illuminated by pulses of classical light. This strategy combines the robustness against practical imperfections of classical ... More

Dwarf spheroidal galaxies as degenerate gas of free fermionsSep 10 2014Dec 16 2014In this paper we analyze a simple scenario in which Dark Matter (DM) consists of free fermions with mass $m_f$. We assume that on galactic scales these fermions are capable of forming a degenerate Fermi gas, in which stability against gravitational collapse ... More

Flexible sampling of discrete data correlations without the marginal distributionsJun 12 2013Nov 14 2013Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has gained popularity ... More