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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.... | 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 |
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