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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. We show that the variations of the speed of light $c$, the
gravitational constant $G$, the Planck constant $h$, and the Boltzmann constant
$k$ are interrelated: $G\thicksim c^{3}\thicksim h^{3/2}\thicksim k^{3/2}$.
Thus, constraining any one of the constants leads to inadvertently constraining
all the others. It may not be possible to determine the variation of a constant
without concurrently considering the variation of others. We discuss several
astrophysical observations that have been explained recently with the
concomitant variation of two or more constants. We also analyze the reported
and unexplained 35 micro-gram decrease of 1 Kg Pt-Ir working standards over 22
years of measurements and show that the Kibble balance, that measures mass in
units of Planck constant, cannot determine the variation of h when h and c
variations are interrelated as determined in here.
|
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 quintessence from a cosmological constant.
|
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 the other hand, the speed of light need not be constant.
|
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 mass limit of decay constant for two-particle system with
equal masses.
|
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 constant forms, thus restricting the holonomy group of the new
manifold.
|
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 linear series separate. On the other hand it has become increasingly
clear by now that Seshadri constants are highly interesting invariants quite in
their own right. Except in the simplest cases, however, they are already in the
case of surfaces very hard to control or to compute explicitly---hardly any
explicit values of Seshadri constants are known so far. The purpose of the
present paper is to study these invariants on algebraic surfaces. On the one
hand, we prove a number of explicit bounds for Seshadri constants and Seshadri
submaximal curves, and on the other hand, we give complete results for abelian
surfaces of Picard number one. A nice feature of this result is that it allows
to explicitly compute the Seshadri constants---as well as the unique
irreducible curve that accounts for it---for a whole class of surfaces. It also
shows that Seshadri constants have an intriguing number-theoretic flavor in
this case.
|
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 mathematical field. The 7th of these problems pertained to
Euler's constant Gamma. After investigating this problem for many years, the
author has proved that Euler's constant Gamma is an irrational number.
|
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 provides an interesting picture of how particular is the behavior of the
Seshadri constants.
|
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 and those related to optical measurements
are considered in detail.
|
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 $\lambda_1...\lambda_{3k}.$ We apply the representation of the
symmetric group to find relations between the polynomials and hence between the
associated theta constants.
|
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 values of the Seshadri constant are accounted for by the
geometry of $X$.
|
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 between vectors in $\mathrm{GF}(q^m)^n$ and
subspaces of $\mathrm{GF}(q)^m$ or $\mathrm{GF}(q)^n$, and use it to establish
a relation between constant-rank codes and constant-dimension codes. We then
derive bounds on the maximum cardinality of constant-rank codes with given rank
weight and minimum rank distance. Finally, we investigate the asymptotic
behavior of the maximal cardinality of constant-rank codes with given rank
weight and minimum rank distance.
|
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 surfaces is given.
|
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 Kerr-Newman spacetime must vanish.
|
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 for these constants. Other generalizations of representations
of $\gamma$ are given.
|
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 the Khinchin-Levy constant. These two results suggests that B2
is irrational, supporting the common believe that there is an infinity of
twins.
|
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 of the smooth surfaces using conserved quantities, which
can be converted into a discrete theory in a natural way.
|
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 Fano 3-folds with Picard number one in detail.
|
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 the data of Ryberg, Davisson and Germer, Compton, or that used by
Planck himself. In the new approach Planck's constant is tied to macroscopic
conventions of Newtonian origin, which are dispensable. The precision of other
fundamental constants is substantially improved by eliminating Planck's
constant. The electron mass is determined about 67 times more precisely, and
the unit of electric charge determined 139 times more precisely. Improvement in
the experimental value of the fine structure constant allows new types of
experiment to be compared towards finding "new physics." The long-standing goal
of eliminating reliance on the artifact known as the International Prototype
Kilogram can be accomplished to assist progress in fundamental physics.
|
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. Conjectures on the non-sharp constants are given.
|
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 recently obtained for classical billiards on constant
curvature surfaces.
|
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 largest known constant dimension codes for the given
parameters.
|
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
transformation) is finitely generated. Similarly one may consider the algebra
of constants of a locally nilpotent linear derivation of a finitely generated
(not necessarily commutative or associative) algebra which is relatively free
in a variety of algebras over K. Now the algebra of constants is usually not
finitely generated. Except for some trivial cases this holds for the algebra of
constants of the free metabelian Lie algebra L/L" with d generators. We show
that the vector space of the constants in the commutator ideal L'/L" is a
finitely generated module over the algebra of constants in K[X]. For small d,
we calculate the Hilbert series of the algebra of constants in L/L" and find
the generators of the module of the constants in L'/L". This gives also an
(infinite) set of generators of the Lie algebra of constants in L/L".
|
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 prescription to obtain cosmological constant from the phase transitions of
the early universe when topological defects, namely monopole might have
existed.
|
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 case. The main step here is the analysis of finite groups.
|
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 manifold $(N, g_1)$ satisfying a geometric assumption. In
particular, we can prove that there exists a metric with constant $Q$-curvature
on the connected sum $N #M$.
|
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 complete description of four- and six-dimensional Kaehler gradient
Ricci solitons with constant scalar curvature.
|
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 constant is studied.
|
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 $\mathbb
H^5$, which give affirmative partial answers to Chen's conjecture and
Generalized Chen's conjecture.
|
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(z) acting on classical points in the projective line,
relative to the spherical metric.
|
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 properties of the band structure in mixed phase
space. We compute the exchange constants for free electrons and show that the
geometrical contribution is generally important. Our formalism allows us to
study the exchange constants in the presence of spin-orbit interaction (SOI).
Thereby, we find sizable differences between the exchange constants of helical
and cycloidal spin spirals. Furthermore, we discuss how to calculate the
exchange constants based on a gauge-field approach in the case of the Rashba
model with an additional exchange splitting and show that the exchange
constants obtained from this gauge-field approach are in perfect agreement with
those obtained from the quantum field theoretical method.
|
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 numbers, Cauchy numbers of the first kind and Bernoulli numbers of
the second kind. In addition, two interesting series with rational terms are
given for Euler's constant and the constant ln(2*pi), and yet another
generalization of Euler's constant is proposed and various formulas for the
calculation of these constants are obtained. Finally, in the paper, we mention
that almost all the constants considered in this work admit simple
representations via the Ramanujan summation.
|
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 function on the boundary, we say that $\Omega$ has the {\it constant
flow property}. This gives rise to an overdetermined parabolic problem, and our
aim is to classify the manifolds having this property. In fact, if the metric
is analytic, we prove that $\Omega$ has the constant flow property if and only
if it is an {\it isoparametric tube}, that is, it is a solid tube of constant
radius around a closed, smooth, minimal submanifold, with the additional
property that all equidistants to the boundary (parallel hypersurfaces) are
smooth and have constant mean curvature. Hence, the constant flow property can
be viewed as an analytic counterpart to the isoparametric property. Finally, we
relate the constant flow property with other overdetermined problems, in
particular, the well-known Serrin problem on the mean-exit time function, and
discuss a counterexample involving minimal free boundary immersions into
Euclidean balls.
|
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. However, the roles played in the foundations of the theories
are sharply different. In quantum theory, Planck's constant is crucial to the
structure of the theory. On the other hand, in classical electrodynamics,
Planck's constant is optional, since it appears only as the scale factor for
the (homogeneous) source-free contribution to the general solution of Maxwell's
equations. Since classical electrodynamics can be solved while taking the
homogenous source-free contribution in the solution as zero or non-zero, there
are naturally two different theories of classical electrodynamics, one in which
Planck's constant is taken as zero and one where it is taken as non-zero. The
textbooks of classical electromagnetism present only the version in which
Planck's constant is taken to vanish.
|
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 for their evaluation.
|
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 $d=2$.
|
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 when the dimension of the manifold is not less than $62$.
|
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 propagation which enables us to view constant propagation as a
particular case of copy propagation and formulate a novel data flow analysis
that unifies these two transformations.
|
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 from known linear codes.
|
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 $\epsilon_1$. The model with constant $\epsilon_2$ is ruled out
by the observations at the $3\sigma$ confidence level, and the model with
constant $\bar\eta$ is consistent with the observations at the $1\sigma$
confidence level. The potential for the model with constant $\bar\eta$ is also
obtained from the Hamilton-Jacobi equation. Although the observations constrain
the constant-roll inflation to be slow-roll inflation, the $n_s-r$ results from
the constant-roll inflation are not the same as those from the slow-roll
inflation even when $\bar\eta\sim 0.01$.
|
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 asymptotic behavior of zeros of certain cross-products of Bessel functions.
|
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 verification. Yet, the advent of micro-architectural
attacks makes constant-time as it exists today far less useful.
This paper lays foundations for constant-time programming in the presence of
speculative and out-of-order execution. We present an operational semantics and
a formal definition of constant-time programs in this extended setting. Our
semantics eschews formalization of microarchitectural features (that are
instead assumed under adversary control), and yields a notion of constant-time
that retains the elegance and tractability of the usual notion. We demonstrate
the relevance of our semantics in two ways: First, by contrasting existing
Spectre-like attacks with our definition of constant-time. Second, by
implementing a static analysis tool, Pitchfork, which detects violations of our
extended constant-time property in real world cryptographic libraries.
|
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 significantly smaller. This is expected to reduce
transients in the closed loop trajectories. The proposed approached is compared
to potential competing techniques.
|
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 can be expressed as the values of integrals. Examples
include the Euler-Mascheroni constant $\gamma$, the Euler-Gompertz constant
$\delta$, and the Riemann-zeta constants $\zeta(k)$ for $k \ge 2$. In many
cases we can use the integral representation for the constant to construct a
linear functional for which $L(e_0)$ equals the given constant and $L(e_1)$,
$L(e_2)$, . . . are rational numbers. In this case, under the specified
conditions, we obtain rational approximations for our constant. In particular,
we execute this procedure for the previously mentioned constants $\gamma$,
$\delta$, and $\zeta(k)$. We note that our approximations are not strong enough
to study the arithmetic properties of these constants.
|
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 non-zero Lie algebra we construct a l.c.K Lie algebra.
|
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 will prove a criterion for Macaulay constants
to be equal. In this case, as the example (2) shows, there are no bounds from
above to the Macaulay constants of the dimension polynomial for starting
generator.
|
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 case of non-constant electric potentials.
|
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 root trading function. We derive the value function for
liquidity providers, marginal price function, price impact function,
impermanent loss function, and greeks for constant power root market markers.
In particular, we find that as the power q varies from the range of -infinity
to 1, the power root function interpolates between the harmonic (q=-1),
geometric (q=0), and arithmetic (q=1) means. This provides a toggle that trades
off between price slippage for traders and impermanent loss for liquidity
providers. As the power q approaches 1, slippage is low and impermanent loss is
high. As q approaches to -1, price slippage increases and impermanent loss
decreases.
|
2205.07452v1
|
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