publicationDate
stringlengths
1
2.79k
title
stringlengths
1
36.5k
abstract
stringlengths
1
37.3k
id
stringlengths
9
47
1996-09-26
Gravitional coupling constant in higher dimensions
Assuming the equivalence of FRW-cosmological models and their Newtonian counterparts, we propose using the Gauss law in arbitrary dimension a general relation between the Newtonian gravitational constant G and the gravitational coupling constant \kappa.
9609061v1
2003-10-22
Unimodular relativity and cosmological constant : Comments
We show that the conclusion that matter stress-energy tensor satisfies the usual covariant continuity law, and the cosmological constant is still a constant of integration arrived at by Finkelstein et al (42, 340, 2001) is not valid.
0310102v1
2005-04-07
An Issue to the Cosmological Constant Problem
According to general relativity, the present analysis shows on geometrical grounds that the cosmological constant problem is an artifact due to the unfounded link of this fundamental constant to vacuum energy density of quantum fluctuations.
0504031v1
2002-03-27
The Cosmological Constant
Various contributions to the cosmological constant are discussed and confronted with its recent measurement. We briefly review different scenarious -- and their difficulties -- for a solution of the cosmological constant problem.
0203252v1
2000-11-13
Background Independent Open String Field Theory and Constant B-Field
We calculate the background independent action for bosonic and supersymmetric open string field theory in a constant B-field. We also determine the tachyon effective action in the presence of constant B-field.
0011108v1
2000-12-08
Newton's Constant isn't constant
This article contains a brief pedagogical introduction to various renormalization group related aspects of quantum gravity with an emphasis on the scale dependence of Newton's constant and on black hole physics.
0012069v1
2003-12-26
Adelic Universe and Cosmological Constant
In the quantum adelic field (string) theory models, vacuum energy -- cosmological constant vanish. The other (alternative ?) mechanism is given by supersymmetric theories. Some observations on prime numbers, zeta -- function and fine structure constant are also considered.
0312291v1
2003-11-25
An end-to-end construction for compact constant mean curvature surfaces
We explain how the current knowledge on the set of complete noncompact constant mean curvature surfaces can be exploited to produce new examples of compact constant mean curvature surfaces of genus greater than or equal to 3.
0311457v1
2006-06-29
Constant and Equivariant Cyclic Cohomology
In this note we prove that the constant and equivariant cyclic cohomology of algebras coincide. This shows that constant cyclic cohomology is rich and computable.
0606741v1
2001-08-15
The Origin of the Planck's Constant
In this paper, we discuss an equation which does not contain the Planck's constant, but it will turn out the Planck's constant when we apply the equation to the problems of particle diffraction.
0108072v1
2007-05-02
Hermitian manifolds of pointwise constant antiholomorphic sectional curvatures
In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.
0705.0236v1
2007-06-01
On cosmological constant in Causal Set theory
Resolution of the cosmological constant problem based on Causal Set theory is discussed. It is argued that one should not observe any spacetime variations in cosmological constant if Causal Set approach is correct.
0706.0041v1
2007-08-23
Coxeter multiarrangements with quasi-constant multiplicities
We study structures of derivation modules of Coxeter multiarrangements with quasi-constant multiplicities by using the primitive derivation. As an application, we show that the characteristic polynomial of a Coxeter multiarrangement with quasi-constant multiplicity is combinatorially computable.
0708.3228v1
2008-03-17
Perturbative solutions to the extended constant scalar curvature equations on asymptotically hyperbolic manifolds
We prove local existence of solutions to the extended constant scalar curvature equations introduced by A. Butscher, in the asymptotically hyperbolic setting. This gives a new local construction of asymptotically hyperbolic metrics with constant scalar curvature.
0803.2437v1
2009-03-25
The Blaschke-Lebesgue problem for constant width bodies of revolution
We prove that among all constant width bodies of revolution, the minimum of the ratio of the volume to the cubed width is attained by the constant width body obtained by rotation of the Reuleaux triangle about an axis of symmetry.
0903.4284v1
2009-04-17
On the isotropy constant of projections of polytopes
The isotropy constant of any $d$-dimensional polytope with $n$ vertices is bounded by $C \sqrt{n/d}$ where $C>0$ is a numerical constant.
0904.2632v1
2009-06-01
The difference between two Stieltjes constants
The Stieltjes constants are the coefficients of the Laurent expansion of the Hurwitz zeta function and surprisingly little is known about them. In this paper we derive some relations for the difference between two Stieltjes constants together with various other relationships.
0906.0277v1
2010-02-02
Embedded minimal and constant mean curvature annulus touching spheres
We show that a compact embedded minimal or constant mean curvature annulus with non-vanishing Gaussian curvature which is tangent to two spheres of same radius or tangent to a sphere and meeting a plane in constant contact angle is rotational.
1002.0438v1
2010-06-19
Projective spherically symmetric Finsler metrics with constant flag curvature in R^n
We investigate projective spherically symmetric Finsler metrics with constant flag curvature in $R^n$ and give the complete classification theorems. Furthermore, a new class of Finsler metrics with two parameters on n-dimensional disk are found to have constant negative flag curvature.
1006.3890v1
2011-08-11
Polygonal homographic orbits in spaces of constant curvature
We prove that the geometry of the 2-dimensional $n$-body problem for spaces of constant curvature $\kappa\neq 0$, $n\geq 3$, does not allow for polygonal homographic solutions, provided that the corresponding orbits are irregular polygons of non-constant size.
1108.2478v2
2012-06-29
On curves of constant torsion I
We give an explicit construction of a closed curve with constant torsion and everywhere positive curvature. We also discuss the restrictions on closed curves of constant torsion when they are constrained to lie on convex surfaces.
1206.7086v1
2012-12-28
New Inequalities for q-ary Constant-Weight Codes
Using double counting, we prove Delsarte inequalities for $q$-ary codes and their improvements. Applying the same technique to $q$-ary constant-weight codes, we obtain new inequalities for $q$-ary constant-weight codes.
1212.6453v1
2013-01-10
Double logarithmic inequality with a sharp constant in four space dimensions
We prove a Log Log inequality with a sharp constant in four dimensions for radially symmetric functions. We also show that the constant in the Log estimate is almost sharp.
1301.2353v1
2013-01-31
Seshadri constants and degrees of defining polynomials
In this paper, we study a relation between Seshadri constants and degrees of defining polynomials. In particular, we compute the Seshadri constants on Fano varieties obtained as complete intersections in rational homogeneous spaces of Picard number one.
1301.7633v1
2015-07-05
Dynamics of the cosmological and Newton's constant
A modification of general relativity is presented in which Newton's constant and the cosmological constant become a conjugate pair of dynamical variables.
1507.01229v1
2016-04-18
Ptolemy constant and uniformity
We study Ptolemy constant and uniformity constant in various plane domains including triangles, quadrilaterals and ellipses.
1604.05367v2
2018-04-02
On generalized constant ratio surfaces with higher codimension
In this paper, we study generalized constant ratio surfaces in the Euclidean 4-space. We also obtain a classifications of constant slope surfaces.
1804.00721v1
2020-06-03
Semilattice ordered algebras with constants
We continue our studies on semilattice ordered algebras. This time we accept constants in the type of algebras. We investigate identities satisfied by such algebras and describe the free objects in varieties of semilattice ordered algebras with constants.
2006.02372v1
2021-11-04
Lebesgue Constants For Cantor Sets
We evaluate the values of the Lebesgue constants in polynomial interpolation for three types of Cantor sets. In all cases, the sequences of Lebesgue constants are not bounded. This disproves the statement by Mergelyan.
2111.02631v1
2022-07-10
A note on starshaped hypersurfaces with almost constant mean curvature in space forms
We show that closed starshaped hypersurfaces of space forms with almost constant mean curvature or almost constant higher order mean curvature are closed to geodesic spheres.
2207.04509v1
2018-09-30
Constant Curvature Conditions For Generalized Kropina Spaces
The classification of Finsler spaces of constant curvature is an interesting and important topic of research in differential geometry. In this paper we obtain necessary and sufficient conditions for generalized Kropina space to be of constant flag curvature.
1810.00429v1
2020-03-24
Complete self-shrinkers with constant norm of the second fundamental form
In this paper, we classify $3$-dimensional complete self-shrinkers in Euclidean space $\mathbb R^{4}$ with constant squared norm of the second fundamental form $S$ and constant $f_{4}$.
2003.11464v1
2021-05-06
Minimizing costs of communication with random constant weight codes
We present a framework for minimizing costs in constant weight codes while maintaining a certain amount of differentiable codewords. Our calculations are based on a combinatorial view of constant weight codes and relay on simple approximations.
2105.02504v1
2022-01-25
Varying Coupling Constants and Their Interdependence
Since Dirac predicted in 1937 possible variation of gravitational constant and other coupling constants from his large number hypothesis, efforts continue to determine such variation without success. Such efforts focus on the variation of one constant while assuming all others pegged to their currently measured values....
2201.11667v4
2022-04-26
Lattices Without a Big Constant and With Noise
We show how Frieze's analysis of subset sum solving using lattices can be done with out any large constants and without flipping. We apply the variant without the large constant to inputs with noise.
2204.12340v1
2022-11-04
Umbilicity of constant mean curvature hypersurfaces into space forms
In this paper we establish conditions on the length of the traceless part of the second fundamental form of a complete constant mean curvature hypersurface immersed in a space of constant sectional curvature in order to show that it is totally umbilical.
2211.02238v1
2023-02-23
On a conjectural series of Sun for the mathematical constant $β(4)$
Series expansions for the mathematical constant $\beta(4)$ are rare in the history. With the help of the operator method and a hypergeometric transformation, we prove a surprising conjectural series of Sun for $\beta(4)$. Furthermore, we find five new series for the same constant in this paper.
2303.05402v1
1999-08-31
Time-Varying Fine-Structure Constant Requires Cosmological Constant
Webb et al. presented preliminary evidence for a time-varying fine-structure constant. We show Teller's formula for this variation to be ruled out within the Einstein-de Sitter universe, however, it is compatible with cosmologies which require a large cosmological constant.
9908356v1
2002-05-16
Quintessence and the cosmological constant
Quintessence -- the energy density of a slowly evolving scalar field -- may constitute a dynamical form of the homogeneous dark energy in the universe. We review the basic idea in the light of the cosmological constant problem. Cosmological observations or a time variation of fundamental `constants' can distinguish qui...
0205267v1
2003-07-09
Aging of the Universe and the fine structure constant
In this paper the aging of the Universe is investigated in the frame of quantum hyperbolic heat transport equation. For the open universe, when t to \infty, hbar to \infty, c to 0 and fine structure constant alpha is constant. Key words: Quantum heat transport; Open universe; Fine structure constant.
0307168v1
2002-10-19
The speed of light need not be constant
Recent observations of the fine structure of spectral lines in the early universe have been interpreted as a variation of the fine structure constant. From the assumed validity of Maxwell equations in general relativity and well known experimental facts, it is proved that $e$ and $\hbar$ are absolute constants. On th...
0210066v1
1999-12-09
Decay Constant of Pseudoscalar Meson in the Heavy Mass Limit
The leptonic decay constant of the pseudoscalar mesons a calculated by use of the relativistic constituent quark model constructed on the point form of Poincare-covariant quantum mechanics. We discuss the role relativistic corrections for decay constants of pseudoscalar mesons with heavy quarks. We consider the heavy m...
9912285v1
1994-06-22
Super W-Symmetries, Covariantly Constant Forms And Duality Transformations
On a supersymmetric sigma model the covariantly constant forms are related to the conserved currents that are generators of a super W-algebra extending the superconformal algebra. The existence of covariantly constant forms restricts the holonomy group of the manifold. Via duality transformation we get new covariantly ...
9406150v1
2005-09-09
Brane Universes and the Cosmological Constant
The cosmological constant problem and brane universes are reviewed briefly. We discuss how the cosmological constant problem manifests itself in various scenarios for brane universes. We review attempts - and their difficulties - that aim at a solution of the cosmological constant problem.
0509062v2
1999-03-12
Seshadri constants on algebraic surfaces
Seshadri constants are local invariants, introduced by Demailly, which measure the local positivity of ample line bundles. Recent interest in Seshadri constants stems on the one hand from the fact that bounds on Seshadri constants yield, via vanishing theorems, bounds on the number of points and jets that adjoint linea...
9903072v1
2003-10-25
A Proof that Euler's Constant Gamma is an Irrational Number
The attributes of Euler's constant Gamma have been a baffling problem to the world's mathematicians in the number theory field. In 1900, when German mathematician D. Hilbert addressed the 2nd International Congress of Mathematicians, he suggested twenty-three previously unsolved problems to the international mathematic...
0310404v1
2005-02-16
Extremal cases of exactness constant and completely bounded projection constant
We investigate some extremal cases of exactness constant and completely bounded projection constant. More precisely, for an $n$-dimensional operator space $E$ we prove that $\lambda_{cb}(E) = \sqrt{n}$ if and only if $ex(E) = \sqrt{n}$, which is equivalent to $\lambda_{cb}(E) < \sqrt{n}$ if and only if $ex(E) < \sqrt{n...
0502335v3
2005-03-14
Seshadri constants on ruled surfaces: the rational and the elliptic cases
We study the Seshadri constants on geometrically ruled surfaces. The unstable case is completely solved. Moreover, we give some bounds for the stable case. We apply these results to compute the Seshadri constant of the rational and elliptic ruled surfaces. Both cases are completely determined. The elliptic case provide...
0503253v1
2005-12-07
A note on multiple Seshadri constants on surfaces
We give a bound for the multiple Seshadri constants on surfaces with Picard number 1. The result is a natural extension of the bound of A. Steffens for simple Seshadri constants. In particular, we prove that the Seshadri constant $\epsilon(L; r)$ is maximal when $rL^2$ is a square.
0512147v1
2006-04-17
Seshadri constants in finite subgroups of abelian surfaces
Given an etale quotient q:X->Y of smooth projective varieties we relate the simple Seshadri constant of a line bundle M on Y with the multiple Seshadri constant of q*M in the points of the fiber. We apply this method to compute the Seshadri constant of polarized abelian surfaces in the points of a finite subgroup.
0604363v1
2003-11-17
Search for Possible Variation of the Fine Structure Constant
Determination of the fine structure constant alpha and search for its possible variation are considered. We focus on a role of the fine structure constant in modern physics and discuss precision tests of quantum electrodynamics. Different methods of a search for possible variations of fundamental constants are compared...
0311080v1
2007-04-08
Theta constants identities for Jacobians of cyclic 3-sheeted covers of the sphere and representations of the symmetric group
We find identities between theta constants with rational characteristics evaluated at period matrix of $R,$ a cyclic 3 sheeted cover of the sphere with $3k$ branch points $\lambda_1...\lambda_{3k}.$ These identities follow from Thomae formula \cite{BR}. This formula expresses powers of theta constants as polynomials in...
0704.1032v1
2007-05-25
The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space
It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the three dimensional upper half space is given by the Sobolev constant. This is achieved by a duality argument relating the problem to a Hardy-Littlewood-Sobolev type inequality whose sharp constant is determined as well.
0705.3833v1
2008-01-21
Seshadri constants on surfaces of general type
We study Seshadri constants of the canonical bundle on minimal surfaces of general type. First, we prove that if the Seshadri constant $\eps(K_X,x)$ is between 0 and 1, then it is of the form $(m-1)/m$ for some integer $m\ge 2$. Secondly, we study values of $\eps(K_X,x)$ for a very general point $x$ and show that small...
0801.3245v1
2008-03-06
Constant-Rank Codes
Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random network coding. In this paper, we show that constant-rank codes are closely related to constant-dimension codes and we study the properties of constant-rank codes. We first introduce a relation bet...
0803.0778v2
2009-04-09
Certain Constant Angle Surfaces Constructed on Curves
In this paper we classify certain special ruled surfaces in $\R^3$ under the general theorem of characterization of constant angle surfaces. We study the tangent developable and conical surfaces from the point of view the constant angle property. Moreover, the natural extension to normal and binormal constant angle sur...
0904.1475v1
2009-04-15
On Newman-Penrose constants of stationary electrovacuum spacetimes
A theorem related to the Newman-Penrose constants is proven. The theorem states that all the Newman-Penrose constants of asymptotically flat, stationary, asymptotically algebraically special electrovacuum spacetimes are zero. Straightforward application of this theorem shows that all the Newman-Penrose constants of the...
0904.2240v1
2009-12-12
Addison-type series representation for the Stieltjes constants
The Stieltjes constants $\gamma_k(a)$ appear in the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function $\zeta(s,a)$ about its only pole at $s=1$. We generalize a technique of Addison for the Euler constant $\gamma=\gamma_0(1)$ to show its application to finding series representations...
0912.2391v1
2010-02-22
Remark on the irrationality of the Brun's constant
We have calculated numerically geometrical means of the denominators of the continued fraction approximations to the Brun constant B2. We get values close to the Khinchin constant. Next we calculated the n-th square roots of the denominators of the n-th convergents of these continued fractions obtaining values close to...
1002.4174v1
2010-09-14
Almost Kähler manifolds of constant antiholomorphic sectional curvature
It is proved that if an AK2-manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional curvature, then it is a 6-dimensional manifold of constant negative sectional curvature or a K\"ahler manifold of constant holomorphic sectional curvature.
1009.2712v1
2010-10-11
Discrete constant mean curvature surfaces via conserved quantities
This survey article is about discrete constant mean curvature surfaces defined by an approach related to integrable systems techniques. We introduce the notion of discrete constant mean curvature surfaces by first introducing properties of smooth constant mean curvature surfaces. We describe the mathematical structure ...
1010.1978v1
2012-02-29
Seshadri constants via toric degenerations
We give a method to estimate Seshadri constants on toric varieties at any point. By using the estimations and toric degenerations, we can obtain some new computations or estimations of Seshadri constants on non-toric varieties. In particular, we investigate Seshadri constants on hypersurfaces in projective spaces and F...
1202.6664v2
2012-03-25
Quantum Theory without Planck's Constant
Planck's constant was introduced as a fundamental scale in the early history of quantum mechanics. We find a modern approach where Planck's constant is absent: it is unobservable except as a constant of human convention. Despite long reference to experiment, review shows that Planck's constant cannot be obtained from t...
1203.5557v1
2012-07-19
On the radius constants for classes of analytic functions
Radius constants for several classes of analytic functions on the unit disk are obtained. These include the radius of starlikeness of a positive order, radius of parabolic starlikeness, radius of Bernoulli lemniscate starlikeness, and radius of uniform convexity. In the main, the radius constants obtained are sharp. Co...
1207.4529v1
2012-08-12
On Totally integrable magnetic billiards on constant curvature surface
We consider billiard ball motion in a convex domain of a constant curvature surface influenced by the constant magnetic field. We prove that if the billiard map is totally integrable then the boundary curve is necessarily a circle. This result is a manifestation of the so-called Hopf rigidity phenomenon which was recen...
1208.2455v1
2013-01-25
New Lower Bounds for Constant Dimension Codes
This paper provides new constructive lower bounds for constant dimension codes, using different techniques such as Ferrers diagram rank metric codes and pending blocks. Constructions for two families of parameters of constant dimension codes are presented. The examples of codes obtained by these constructions are the l...
1301.5961v1
2013-02-04
Weitzenboeck derivations of free metabelian Lie algebras
A nonzero locally nilpotent linear derivation of the polynomial algebra K[X] in d variables over a field K of characteristic 0 is called a Weitzenboeck derivation. The classical theorem of Weitzenboeck states that the algebra of constants (which coincides with the algebra of invariants of a single unipotent transformat...
1302.0825v1
2013-02-12
On Topological Defects and Cosmological Constant
Einstein introduced Cosmological Constant in his field equations in an ad hoc manner. Cosmological constant plays the role of vacuum energy of the universe which is responsible for the accelerating expansion of the universe. To give theoretical support it remains an elusive goal to modern physicists. We provide a presc...
1302.2716v1
2013-07-31
The optimal constants in Holder-Brascamp-Lieb inequalities for discrete Abelian groups
The optimal constants are found for Lebesgue norm multilinear inequalities of Holder-Brascamp-Lieb type for arbitrary discrete Abelian groups. Previously a criterion for finiteness of the constants had been established for finitely generated Abelian groups, and the optimal constant had been found in the torsion-free ca...
1307.8442v1
2013-10-02
Connected sum construction of constant Q-curvature manifolds in higher dimensions
For a compact Riemannian manifold $(M, g_2)$ with constant $Q$-curvature of dimension $n\geq 6$ satisfying nondegeneracy condition, we show that one can construct many examples of constant $Q$-curvature manifolds by gluing construction. We provide a general procedure of gluing together $(M,g_2)$ with any compact manifo...
1310.0860v1
2014-06-06
On the Maxwell Constants in 3D
Using tools from functional analysis we show that for bounded and convex domains in three dimensions, the Maxwell constants are bounded from below and above by Friedrichs' and Poincare's constants.
1406.1723v3
2014-09-11
On gradient Ricci solitons with constant scalar curvature
We use the theory of isoparametric functions to investigate gradient Ricci solitons with constant scalar curvature. We show rigidity of gradient Ricci solitons with constant scalar curvature under some conditions on the Ricci tensor, which are all satisfied if the manifold is curvature homogeneous. This leads to a comp...
1409.3359v1
2014-12-08
An inequality for a periodic uncertainty constant
An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A particular minimization problem for a non-periodic (Heisenberg) uncertainty const...
1412.2694v2
2014-12-23
On biharmonic hypersurfaces with constant scalar curvatures in $\mathbb E^5(c)$
We prove that proper biharmonic hypersurfaces with constant scalar curvature in Euclidean sphere $\mathbb S^5$ must have constant mean curvature. Moreover, we also show that there exist no proper biharmonic hypersurfaces with constant scalar curvature in Euclidean space $\mathbb E^5$ or hyperbolic space $\mathbb H^5$, ...
1412.7394v1
2015-03-18
Vacuum energy and the cosmological constant
The accelerating expansion of the Universe points to a small positive value for the cosmological constant or vacuum energy density. We discuss recent ideas that the cosmological constant plus LHC results might hint at critical phenomena near the Planck scale.
1503.05483v1
2015-04-13
Spherically Symmetric Finsler Metrics With Constant Ricci And Flag Curvature
Spherically symmetric metrics form a rich and important class of metrics. Many well-known Finsler metrics of constant flag curvature can be locally expressed as a spherically symmetric metric on R^n. In this paper, we study spherically symmetric metrics with constant Ricci curvature and constant flag curvature.
1505.04182v1
2015-12-03
The Lipschitz Constant of a Nonarchimedean Rational Function
Let K be a complete, algebraically closed nonarchimedean valued field, and let f(z) be a non-constant rational function in K(z). We provide explicit bounds for the Lipschitz constant of f(z) acting on the Berkovich projective line, relative to the Favre/Rivera-Letelier d(x,y)-metric, and for the Lipschitz constant of f...
1512.01136v1
2017-01-30
Geometrical contributions to the exchange constants: Free electrons with spin-orbit interaction
Using thermal quantum field theory we derive an expression for the exchange constant that resembles Fukuyama's formula for the orbital magnetic susceptibility (OMS). Guided by this formal analogy between the exchange constant and OMS we identify a contribution to the exchange constant that arises from the geometrical p...
1701.08872v2
2017-03-24
A note on some constants related to the zeta-function and their relationship with the Gregory coefficients
In this paper new series for the first and second Stieltjes constants (also known as generalized Euler's constant), as well as for some closely related constants are obtained. These series contain rational terms only and involve the so-called Gregory coefficients, which are also known as (reciprocal) logarithmic number...
1703.08601v2
2017-09-11
Geometric rigidity of constant heat flow
Let $\Omega$ be a compact Riemannian manifold with smooth boundary and let $u_t$ be the solution of the heat equation on $\Omega$, having constant unit initial data $u_0=1$ and Dirichlet boundary conditions ($u_t=0$ on the boundary, at all times). If at every time $t$ the normal derivative of $u_t$ is a constant functi...
1709.03447v2
2017-10-01
The Contrasting Roles of Planck's Constant in Classical and Quantum Theories
We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum theories. In both theories, Planck's constant sets the scale of atomic phenomena...
1710.01616v1
2018-05-05
On a method of evaluation of zeta-constants based on one number theoretic approach
New formulas for approximation of zeta-constants were derived on the basis of a number-theoretic approach constructed for the irrationality proof of certain classical constants. Using these formulas it's possible to approximate certain zeta-constants and their combinations by rational fractions and construct a method f...
1805.02076v1
2019-05-15
When a spherical body of constant diameter is of constant width?
{\bf Abstract.} Let $D$ be a convex body of diameter $\delta$, where $0 < \delta < \frac{\pi}{2}$, on the $d$-dimensional sphere. We prove that $D$ is of constant diameter $\delta$ if and only if it is of constant width $\delta$ in the following two cases. The first case is when $D$ is smooth. The second case is when $...
1905.06369v1
2019-05-22
Constant diameter and constant width of spherical convex bodies
In this paper we show that a spherical convex body $C$ is of constant diameter $\tau$ if and only if $C$ is of constant width $\tau$, for $0<\tau<\pi$. Moreover, some applications to Wulff shapes are given.
1905.09098v2
2019-08-13
Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation
We first present a warped product manifold with boundary to show the non-uniqueness of the positive constant scalar curvature and positive constant boundary mean curvature equation. Next, we construct a smooth counterexample to show that the compactness of the set of "lower energy" solutions to the above equation fails...
1908.04815v1
2020-06-04
On the universality of Somos' constant
We show that Somos' constant is universal in sense that is similar to the universality of the Khinchin constant. In addition we introduce generalized Somos' constants, which are universal in a similar sense.
2006.02882v3
2022-07-08
Copy Propagation subsumes Constant Propagation
Constant propagation and copy propagation are code transformations that may avoid some load operations and can enable other optimizations. In literature, constant and copy propagations are considered two independent transformations requiring two different data flow analyses. Here we give a generic definition for copy p...
2207.03894v1
2017-06-21
Constant Composition Codes as Subcodes of Linear Codes
In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on LVFC bound. On the other hand, a class of constant composition codes is derived fro...
1706.06997v2
2018-02-05
The observational constraint on constant-roll inflation
We discuss the constant-roll inflation with constant $\epsilon_2$ and constant $\bar\eta$. By using the method of Bessel function approximation, the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor to scalar ratio are derived up to the first order of $...
1802.01986v2
2018-02-12
On exact Pleijel's constant for some domains
We provide an explicit expression for the Pleijel constant for the planar disk and some of its sectors, as well as for $N$-dimensional rectangles. In particular, the Pleijel constant for the disk is equal to 0.4613019... Also, we characterize the Pleijel constant for some rings and annular sectors in terms of asymptoti...
1802.04357v1
2019-04-16
6+infinity new expressions for the Euler-Mascheroni constant
In the first part we present results of four ``experimental'' determinations of the Euler-Mascheroni constant $\gamma$. Next we give new formulas expressing the $\gamma$ constant in terms of the Ramanujan-Soldner constant $\mu$. Employing the cosine integral we obtain the infinity of formulas for $\gamma$.
1904.09855v1
2019-10-03
Constant-Time Foundations for the New Spectre Era
The constant-time discipline is a software-based countermeasure used for protecting high assurance cryptographic implementations against timing side-channel attacks. Constant-time is effective (it protects against many known attacks), rigorous (it can be formalized using program semantics), and amenable to automated ve...
1910.01755v3
2019-10-22
Uniqueness Results for Bodies of Constant Width in the Hyperbolic Plane
Following Santal\'{o}'s approach, we prove several characterizations of a disc among bodies of constant width, constant projections lengths, or constant section lengths on given families of geodesics.
1910.10248v1
2019-10-28
Optimizing the Kreiss constant
The Kreiss constant $K(A)$ of a stable matrix $A$ conveys information about the transient behavior of system trajectories in response to initial conditions. We present an efficient way to compute the Kreiss constant $K(A)$, and we show how feedback can be employed to make the Kreiss constant $K(A_{cl})$ in closed loop ...
1910.12572v1
2020-03-24
Rational Approximations via Hankel Determinants
Define the monomials $e_n(x) := x^n$ and let $L$ be a linear functional. In this paper we describe a method which, under specified conditions, produces approximations for the value $L(e_0 )$ in terms of Hankel determinants constructed from the values $L(e_1 )$, $L(e_2 )$, . . . . Many constants of mathematical interest...
2003.10616v1
2020-10-29
A Prime-Representing Constant
We present a constant and a recursive relation to define a sequence $f_n$ such that the floor of $f_n$ is the $n$th prime. Therefore, this constant generates the complete sequence of primes. We also show this constant is irrational and consider other sequences that can be generated using the same method.
2010.15882v1
2021-12-13
Statistical Lie algebras of a constant curvature and locally conformally Kähler Lie algebras
We show that a statistical manifold manifold of a constant non-zero curvature can be realised as a level line of Hessian potential on a Hessian cone. We construct a Sasakian structure on $TM\times\R$ by a statistical manifold manifold of a constant non-zero curvature on $M$. By a statistical Lie algebra of a constant n...
2112.06686v2
2022-02-05
Some Properties of Coefficients Kolchin Dimension Polynomial
The article presents a formula expressing Macaulay constants of a numerical polynomial through its minimizing coefficients. From this, we have that Macaulay constants of Kolchin dimension polynomials do not decrease. For the minimal differential dimension polynomial (this concept was introduced by W.Sitt in [5]) we w...
2202.02542v1
2022-03-20
Concentrations for nonlinear Schrodinger equation with magnetic potentials and constant electric potentials
This paper studies the concentration phenomena to nonlinear Schrodinger equations with magnetic potentials and constant electric potentials. We find that the magnetic field plays an important role in the location of concentrations if the electric potential is constant. This is a completely new result compared with the ...
2203.10464v2
2022-05-16
Constant Power Root Market Makers
The paper introduces a new type of constant function market maker, the constant power root market marker. We show that the constant sum (used by mStable), constant product (used by Uniswap and Balancer), constant reserve (HOLD-ing), and constant harmonic mean trading functions are special cases of the constant power ro...
2205.07452v1