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2011-07-19 | Removal of UV cutoff for the Nelson model with variable coefficients | We consider the Nelson model with variable coefficients. Nelson models with
variable coefficients arise when one replaces in the usual Nelson model the
flat Minkowski metric by a static metric, allowing also the boson mass to
depend on position. We study the removal of the ultraviolet cutoff. | 1107.3815v1 |
2011-12-14 | Mixed Boundary Value Problems of Semilinear Elliptic PDEs and BSDEs with Singular Coefficients | In this paper, we prove that there exists a unique weak solution to the mixed
boundary value problem for a general class of semilinear second order elliptic
partial differential equations with singular coefficients. Our approach is
probabilistic. The theory of Dirichlet forms and backward stochastic
differential equations with singular coefficients and infinite horizon plays a
crucial role. | 1112.3148v1 |
2011-12-21 | A Loewner variational method in the theory of schlicht functions | A Loewner variational method is developed that allows to calculate arbitrary
continuous coefficient functionals of the second, third and fourth coefficients
of schlicht functions. Based on this method an improved lower bound for the
Milin-constant(0.034856..) is given, as well as an improved lower bound for the
maximal modulus of the seventh coefficient of odd schlicht
functions(1.006763..). | 1112.5187v2 |
2012-02-06 | A probabilistic interpretation of a sequence related to Narayana polynomials | A sequence of coefficients appearing in a recurrence for the Narayana
polynomials is generalized. The coefficients are given a probabilistic
interpretation in terms of beta distributed random variables. The recurrence
established by M. Lasalle is then obtained from a classical convolution
identity. Some arithmetical properties of the generalized coefficients are also
established. | 1202.1203v3 |
2012-03-08 | Generating multivariate extreme value distributions | We define in a probabilistic way a parametric family of multivariate extreme
value distributions. We derive its copula, which is a mixture of several
complete dependent copulas and total independent copulas, and the bivariate
tail dependence and extremal coefficients. Based on the obtained results for
these coefficients, we propose a method to built multivariate extreme value
distributions with prescribed tail/extremal coefficients. We illustrate the
results with examples of simulation of these distributions. | 1203.1875v1 |
2012-03-18 | A Remark on Coefficients of Jacobi Matrices Arising from a Schrodinger Operator | A discrete analogue of a Schrodinger type operator proposed by J. Bellissard
has a singular continuous spectrum. In this remark we answer the conjecture
formulated by D. Bessis, M. Mehta and P. Moussa on the coefficients of that
operator. It turns out that the coefficients have a more complicated behavior
than it was conjectured. | 1203.4005v1 |
2012-03-26 | Variation of Hilbert Coefficients | For a Noetherian local ring $(\RR, \m)$, the first two Hilbert coefficients,
$e_0$ and $e_1$, of the $I$-adic filtration of an $\m$-primary ideal $I$ are
known to code for properties of $\RR$, of the blowup of $\spec(\RR)$ along
$V(I)$, and even of their normalizations. We give estimations for these
coefficients when $I$ is enlarged (in the case of $e_1$ in the same integral
closure class) for general Noetherian local rings. | 1203.5578v1 |
2012-05-20 | On reconstruction of Lamé coefficients from partial Cauchy data in three dimensions | For the isotropic Lam\'e system, we prove in dimensions three or larger that
both Lam\'e coefficients are uniquely recovered from partial Cauchy data on an
arbitrary open subset of the boundary provided that the coefficient $\mu$ is a
priori close to a constant. | 1205.4436v1 |
2012-06-19 | A real analytic family of fundamental solutions of elliptic partial differential operators with real constant coefficients | We construct of a family of fundamental solutions for elliptic partial
differential operators with real constant coefficients. The elements of such a
family are expressed by means of jointly real analytic functions of the
coefficients of the operators and of the spatial variable. We show regularity
properties in the frame of Schauder spaces for the corresponding single layer
potentials. | 1206.4211v1 |
2012-09-03 | Absence of Renormalization of the Specific Heat Coefficient of the Interacting Fermion Systems | Contrary to the longtime and widely conceived belief, we proved that the
specific heat coefficient $\gamma$ --also called Sommerfeld coefficient -- of
the interacting Fermion system is not renormalized by the wave-function
renormalization factor $Z$ as far as the system remains a Fermi liquid state. | 1209.0328v2 |
2012-11-30 | On the Coefficients of a Hyperbolic Hydrodynamic Model | Based on the Nakajima-Zubarev type nonequilibrium density operator, we derive
a hyperbolic hydrodynamical equation. Microscopic Kubo-formulas for all
coefficients in the hyperbolic hydrodynamics are obtained. Coefficients
$\alpha_{i}$'s and $\beta_{i}$'s in the Israel-Stewart equation are given as
current-weighted correlation lengths which are to be calculated in statistical
mechanics. | 1211.7173v1 |
2013-01-30 | Jumps of ternary cyclotomic coefficients | It is known that two consecutive coefficients of a ternary cyclotomic
polynomial $\Phi_{pqr}(x)=\sum_k a_{pqr}(k)x^k$ differ by at most one. In this
paper we give a criterion on $k$ to satisfy $|a_{pqr}(k)-a_{pqr}(k-1)|=1$. We
use this to prove that the number of nonzero coefficients of the $n$th ternary
cyclotomic polynomial is greater than $n^{1/3}$. | 1301.7174v1 |
2013-03-27 | From Fourier to Gegenbauer: Dimension walks on spheres | We show that the even- resp. odd-dimensional Schoenberg coefficients in
Gegenbauer expansions of isotropic positive definite functions on the d-sphere
can be expressed as linear combinations of Fourier resp. Legendre coefficients,
and we give closed form expressions for the coefficients involved in these
expansions. | 1303.6856v2 |
2013-04-18 | Unimodality via Kronecker products | We present new proofs and generalizations of unimodality of the q-binomial
coefficients \binom{n}{k}_q as polynomials in q. We use an algebraic approach
by interpreting the differences between numbers of certain partitions as
Kronecker coefficients of representations of S_n. Other applications of this
approach include strict unimodality of the diagonal q-binomial coefficients and
unimodality of certain partition statistics. | 1304.5044v2 |
2013-05-14 | On the relationships between Fourier - Stieltjes coefficients and spectra of measures | We construct examples of uncountable compact subsets of complex numbers with
the property that any Borel measure on the circle group taking values of its
Fourier coefficients from this set has natural spectrum. For measures with
Fourier coefficients tending to 0 we construct tho open set with this property. | 1305.3324v2 |
2013-06-21 | Strict unimodality of q-binomial coefficients | We prove strict unimodality of the q-binomial coefficients \binom{n}{k}_q as
polynomials in q. The proof is based on the combinatorics of certain Young
tableaux and the semigroup property of Kronecker coefficients of S_n
representations. | 1306.5085v2 |
2013-07-30 | On Poisson operators and Dirichlet-Neumann maps in H^s for divergence form elliptic operators with Lipschitz coefficients | We consider second order uniformly elliptic operators of divergence form in
$\R^{d+1}$ whose coefficients are independent of one variable. Under the
Lipschitz condition on the coefficients we characterize the domain of the
Poisson operators and the Dirichlet-Neumann maps in the Sobolev space
$H^s(\R^d)$ for each $s\in [0,1]$. Moreover, we also show a factorization
formula for the elliptic operator in terms of the Poisson operator. | 1307.8151v1 |
2013-08-13 | Multivalued backward doubly stochastic differential equations with time delayed coefficients | In this paper, we deal with a class of multivalued backward doubly stochastic
differential equations with time delayed coefficients. Based on a slight
extension of the existence and uniqueness of solutions for backward doubly
stochastic differential equations with time delayed coefficients, we establish
the existence and uniqueness of solutions for these equations by means of
Yosida approximation. | 1308.2748v2 |
2013-09-26 | Fourier Coefficients Of Some Cusp Forms | The possible values of the nth Fourier coefficients a(n) of some cusp forms
f(z) of weight k => 12 are studied in this article. In particular, the values
of the tau function are investigated in some details, and proved that tau(p) =!
0 for all primes p => p_0. | 1309.6965v2 |
2013-11-10 | Constant Coefficients in the Radial Komatu-Loewner Equation for Multiple Slits | The radial Komatu-Loewner equation is a differential equation for certain
normalized conformal mappings that can be used to describe the growth of slits
within multiply connected domains. We show that it is possible to choose
constant coefficients in this equation in order to generate given disjoint
slits and that those coefficients are uniquely determined under a suitable
normalization of the differential equation. | 1311.2279v1 |
2013-12-11 | On correct solvability of a Dirichlet problem for generalized Manjeron equation with non-smooth coefficients | In the paper obtained equivalent system of Fredholm integral equations in the
study of the Dirichlet problem for the generalized Manjeron equation with
non-smooth coefficients in non-classical treatment (1), (4). When non-smooth
conditions on the coefficients of the equation in a rectangular region for this
problem posed are found correct solvability conditions in integral form based
on the method of integral representations. | 1312.3318v1 |
2014-02-16 | The coefficients of the period polynomials | A general description of the Vi\`ete coefficients of the gaussian period
polynomials is given, in terms of certain symmetric representations of the
subgroups and the corresponding quotient groups of the multiplicative group
\mathbf{F}_{p}^{*} of a finite prime field of characteristics p, an odd prime
number. The known values of these coefficients are recovered by this technique
and further results of general nature are presented. | 1402.3833v1 |
2014-03-19 | Divisors of Fourier coefficients of modular forms | Let $d(n)$ denote the number of divisors of $n$. In this paper, we study the
average value of $d(a(p))$, where $p$ is a prime and $a(p)$ is the $p$-th
Fourier coefficient of a normalized Hecke eigenform of weight $k \ge 2$ for
$\Gamma_0(N)$ having rational integer Fourier coefficients. | 1403.4709v1 |
2014-03-24 | On an explicit representation of central $(2k+1)$-nomial coefficients | We propose an explicit representation of central $(2k+1)$-nomial coefficients
in terms of finite sums over trigonometric constructs. The approach utilizes
the diagonalization of circulant boolean matrices and is generalizable to all
$(2k+1)$-nomial coefficients, thus yielding a new family of combinatorical
identities. | 1403.5942v1 |
2014-08-04 | Approximation of elliptic equations with BMO coefficients | We study solution techniques for elliptic equations in divergence form, where
the coefficients are only of bounded mean oscillation (BMO). For
$|p-2|<\varepsilon$ and a right hand side in $W^{-1}_p$ we show convergence of
a finite element scheme, where $\varepsilon$ depends on the oscillation of the
coefficients. | 1408.0724v1 |
2014-08-22 | Measures for orthogonal polynomials with unbounded recurrence coefficients | Systems of orthogonal polynomials whose recurrence coefficients tend to
infinity are considered. A summability condition is imposed on the coefficients
and the consequences for the measure of orthogonality are discussed. Also
discussed are asymptotics for the polynomials. | 1408.5349v3 |
2014-10-14 | Low-rank approximation of elliptic boundary value problems with high-contrast coefficients | We analyze the convergence of degenerate approximations to Green's function
of elliptic boundary value problems with high-contrast coefficients. It is
shown that the convergence is independent of the contrast if the error is
measured with respect to suitable norms. This lays ground to fast methods
(so-called hierarchical matrix approximations) which do not have to be adapted
to the coefficients. | 1410.3717v1 |
2014-11-03 | On the coefficients of TYZ expansion of locally Hermitian symmetric spaces | In this paper we address the problem of studying those K\"ahler manifolds
whose first two coefficients of the associated TYZ expansion vanish and we
prove that for a locally Hermitian symmetric space this happens only in the
flat case. We also prove that there exist nonflat locally Hermitian symmetric
spaces where all the odd coefficients vanish. | 1411.0455v1 |
2014-11-19 | Dissipative Heat Decomposition in Stochastic Energetics: Implication of the Instantaneous Diffusion Coefficient in Nonequilibrium Steady States | We give a decomposition expression for dissipative heat using the
instantaneous diffusion coefficient in a nonequilibrium steady state. The
dissipative heat can be expressed using three diffusion coefficients:
instantaneous, equilibrium, and drift. An experimental application of the
decomposition expression permits us to evaluate the heat dissipation rate from
single-trajectory data only. We also numerically demonstrate this method. | 1411.5155v1 |
2014-12-18 | Iterated bar complexes and E_n-homology with coefficients | The first author proved in a previous paper that the n-fold bar construction
for commutative algebras can be generalized to E_n-algebras, and that one can
calculate E_n-homology with trivial coefficients via this iterated bar
construction. We extend this result to E_n-homology and E_n-cohomology of a
commutative algebra A with coefficients in a symmetric A-bimodule. | 1412.6032v2 |
2014-12-22 | Sign changes of coefficients of certain Dirichlet series | In this paper, we give criteria for infinitely many sign changes of the
coefficients of any Dirichlet series if the coefficients are real numbers. We
also provide examples where our criteria are applicable. | 1412.7044v1 |
2015-01-08 | On the coefficients of power sums of arithmetic progressions | We investigate the coefficients of the polynomial \[
S_{m,r}^n(\ell)=r^n+(m+r)^n+(2m+r)^n+\cdots+((\ell-1)m+r)^n. \] We prove that
these can be given in terms of Stirling numbers of the first kind and
$r$-Whitney numbers of the second kind. Moreover, we prove a necessary and
sufficient condition for the integrity of these coefficients. | 1501.01843v1 |
2015-05-05 | Coefficient Extraction Formula and Furstenberg's Theorems | In this article, using a Proposition of Furstenberg, we give a coefficient
extraction formula for algebraic series that is valid for all fields, of which
the Flajolet-Soria coefficient extraction formula for the complex field is a
special case. | 1505.01379v3 |
2015-06-30 | Generating functions for the osp(1|2) Clebsch-Gordan coefficients | Generating functions for Clebsch-Gordan coefficients of osp(1|2) are derived.
These coefficients are expressed as q goes to - 1 limits of the dual q-Hahn
polynomials. The generating functions are obtained using two different
approaches respectively based on the coherent-state representation and the
position representation of osp(1j2). | 1507.00018v1 |
2015-08-20 | Square function estimates on layer potentials for higher-order elliptic equations | In this paper we establish square-function estimates on the double and single
layer potentials for divergence-form elliptic operators, of arbitrary even
order 2m, with variable t-independent coefficients in the upper half-space.
This generalizes known results for variable-coefficient second-order operators,
and also for constant-coefficient higher-order operators. | 1508.04988v1 |
2015-08-26 | Multidimensional BSDEs with uniformly continuous coefficients: the general result | In this paper, by introducing a new notion of envelope of the stochastic
process, we construct a family of random differential equations whose solutions
can be viewed as solutions of a family of ordinary differential equations and
prove that the multidimensional backward stochastic differential equations
(BSDEs for short) with the general uniformly continuous coefficients are
uniquely solvable. As a result, we solve the open problem of multidimensional
BSDEs with uniformly continuous coefficients. | 1508.06671v1 |
2015-11-23 | Exponential decay rate of partial autocorrelation coefficients of ARMA and short-memory processes | We present a short proof of the fact that the exponential decay rate of
partial autocorrelation coefficients of a short-memory process, in particular
an ARMA process, is equal to the exponential decay rate of the coefficients of
its infinite autoregressive representation. | 1511.07091v2 |
2015-11-30 | Convoluted Fourier Coefficients of GL(n)-Automorphic Functions. Part 1 | We study certain cases of convoluted Fourier coefficients of
$GL_n$-automorphic functions. We establish identities that express them in
terms of Fourier coefficients related to unipotent orbits. The most general
case that is studied is $(n)\circ(k,2^{n-1})$. The conclusions for this case is
only up to a conjecture that I state. However there are certain special cases
and other examples that are not based on any conjecture. | 1511.09374v1 |
2016-01-11 | On Milstein approximations with varying coefficients: the case of super-linear diffusion coefficients | A new class of explicit Milstein schemes, which approximate stochastic
differential equations (SDEs) with superlinearly growing drift and diffusion
coefficients, is proposed in this article. It is shown, under very mild
conditions, that these explicit schemes converge in $\mathcal L^p$ to the
solution of the corresponding SDEs with optimal rate. | 1601.02695v1 |
2016-01-28 | Gradient estimates for solutions of the Lamé system with partially infinite coefficients in dimensions greater than two | We establish upper bounds on the blow-up rate of the gradients of solutions
of the Lam\'{e} system with partially infinite coefficients in dimensions
greater than two as the distance between the surfaces of discontinuity of the
coefficients of the system tends to zero. | 1601.07879v1 |
2016-02-08 | On p-adic approximation of sums of binomial coefficients | We propose higher-order generalizations of Jacobsthal's $p$-adic
approximation for binomial coefficients. Our results imply explicit formulae
for linear combinations of binomial coefficients $\binom{ip}{p}$
($i=1,2,\dots$) that are divisible by arbitrarily large powers of prime $p$. | 1602.02632v2 |
2016-02-29 | On Fourier coefficients of modular forms of half integral weight at squarefree integers | We show that the Dirichlet series associated to the Fourier coefficients of a
half-integral weight Hecke eigenform at squarefree integers extends
analytically to a holomorphic function in the half-plane $\re
s\textgreater{}\tfrac{1}{2}$. This exhibits a high fluctuation of the
coefficients at squarefree integers. | 1602.08924v2 |
2016-04-04 | Weak Error for the Euler Scheme Approximation of Diffusions with Non-Smooth Coefficients * | We study the weak error associated with the Euler scheme of non degenerate
diffusion processes with non smooth bounded coefficients. Namely, we consider
the cases of H{\"o}lder continuous coefficients as well as piecewise smooth
drifts with smooth diffusion matrices. | 1604.00771v3 |
2016-04-13 | Hölder regularity for Maxwell's equations under minimal assumptions on the coefficients | We prove global H\"older regularity for the solutions to the time-harmonic
anisotropic Maxwell's equations, under the assumptions of H\"older continuous
coefficients. The regularity hypotheses on the coefficients are minimal. The
same estimates hold also in the case of bianisotropic material parameters. | 1604.03741v2 |
2016-05-24 | Exponential decay of scattering coefficients | We study an aspect of the following general question: which properties of a
signal can be characterized by its scattering transform? We show that the
energy contained in high order scattering coefficients is upper bounded by the
energy contained in the high frequencies of the signal. This result links the
decay of the scattering coefficients of a signal with the decay of its Fourier
transform. Additionally, it allows to generalize some results of Mallat (2012),
by relaxing the admissibility condition on the wavelet family. | 1605.07464v1 |
2016-06-20 | Infinite Product Exponents for Modular Forms | Recently, D. Choi obtained a description of the coefficients of the infinite
product expansions of meromorphic modular forms over $\Gamma_0(N)$. Using this
result, we provide some bounds on these infinite product coefficients for
holomorphic modular forms. We give an exponential upper bound for the growth of
these coefficients. We show that this bound is also a lower bound in the case
that the genus of the associated modular curve $X_0(N)$ is $0$ or $1$. | 1606.06122v1 |
2016-07-02 | Convergence rates of finite difference schemes for the linear advection and wave equation with rough coefficient | We prove convergence rates of explicit finite difference schemes for the
linear advection and wave equation in one space dimension with H\"older
continuous coefficient. The obtained convergence rates explicitly depend on the
H\"older regularity of the coefficient and the modulus of continuity of the
initial data. We compare the theoretically established rates with the
experimental rates of a couple of numerical examples. | 1607.00525v1 |
2016-07-18 | Spacetime Variation of Lorentz-Violation Coefficients at Nonrelativistic Scale | When the Standard-Model Extension (SME) is applied in curved spacetime, the
Lorentz-violation coefficients must depend on spacetime position. This work
describes some of the consequences of this spacetime variation. We focus on
effects that appear at a nonrelativistic scale and extract sensitivity of
completed experiments to derivatives of SME coefficient fields. | 1607.05211v1 |
2016-08-05 | Exact Russell-Type Modular Equations | This paper provides some statistics for the coefficients of Russell- Type
modular equations for the modular function, {\lambda}({\tau}). The results hold
uniformly for all odd primes. They do not rely on any numerical evaluations of
coefficients of q expansions of {\lambda}. The method relies on an internal
structure of the coefficients of {\lambda} expressed in terms of multiplicative
functions defined on integer partitions. The method may be extended to other
types of modular equations. | 1608.01765v1 |
2017-02-15 | On homology with coefficients and generalized inductions | In group representations several inductions given by tensoring with
appropriate bimodules may be reconstructed via homology of $G$-posets with
$G$-equivariant coefficients. For this purpose, we need various local
categories of a finite group $G$, which afford the coefficients. Consequently,
the functors among local categories give rise to the homology constructions
naturally, and may be used to reformulate some existing results, as well as to
deduce new statements. | 1702.04496v2 |
2017-03-24 | Additive bases with coefficients of newforms | Let $f(z)=\sum_{n=1}^{\infty}a(n) e^{2\pi i nz}$ be a normalized Hecke
eigenform in $S_{2k}^{\text{new}}(\Gamma_0(N))$ with integer Fourier
coefficients. We prove that there exists a constant $C(f)>0$ such that any
integer is a sum of at most $C(f)$ coefficients $a(n) $. It holds
$C(f)\ll_{\varepsilon,k}N^{\frac{6k-3}{16}+\varepsilon}$. | 1703.08473v1 |
2017-04-01 | Symmetry and Piezoelectricity: Evaluation of $α$-Quartz coefficients | Piezoelectric coefficients of $\alpha$-Quartz are derived from symmetry
arguments based on Neumann's Principle with three different methods: Fumi,
Landau-Lifshitz and Royer-Dieulesaint. While Fumi method is tedious and
Landau-Lifshitz requires additional physical principles to evaluate the
piezoelectric coefficients, Royer-Dieulesaint is the most elegant and most
efficient of the three techniques. | 1704.01012v1 |
2017-04-05 | Quantitative unique continuation of solutions to higher order elliptic equations with singular coefficients | We investigate the quantitative unique continuation of solutions to higher
order elliptic equations with singular coefficients. Quantitative unique
continuation described by the vanishing order is a quantitative form of strong
unique continuation property. We characterize the vanishing order of solutions
for higher order elliptic equations in terms of the norms of coefficient
functions in their respective Lebesgue spaces. New versions of quantitative
Carleman estimates are established. | 1704.01446v2 |
2017-05-27 | Explicit formulas and vanishing conditions for certain coefficients of Drinfeld-Goss Hecke eigenforms | We obtain a closed form polynomial expression for certain coefficients of
Drinfeld-Goss double-cuspidal modular forms which are eigenforms for the degree
one Hecke operators with power eigenvalues, and we use those formulas to prove
vanishing results for an infinite family of those coefficients. | 1705.09795v1 |
2017-06-08 | Consistency Results for Stationary Autoregressive Processes with Constrained Coefficients | We consider stationary autoregressive processes with coefficients restricted
to an ellipsoid, which includes autoregressive processes with absolutely
summable coefficients. We provide consistency results under different norms for
the estimation of such processes using constrained and penalized estimators. As
an application we show some weak form of universal consistency. Simulations
show that directly including the constraint in the estimation can lead to more
robust results. | 1706.02492v1 |
2017-07-21 | Binomial collisions and near collisions | We describe efficient algorithms to search for cases in which binomial
coefficients are equal or almost equal, give a conjecturally complete list of
all cases where two binomial coefficients differ by 1, and give some identities
for binomial coefficients that seem to be new. | 1707.06893v2 |
2017-10-12 | Kinetic theory for strong uniform shear flow of granular media at high density | We discuss the uniform shear flow of a fluidized granular bed composed of
monodisperse Hertzian spheres. Considering high densities around the glass
transition density of inelastic Hertzian spheres, we report kinetic theory
expressions for the Newtonian viscosity as well as the Bagnold coefficient. We
discuss the dependence of the transport coefficients on density and coefficient
of restitution. | 1710.04480v1 |
2017-10-17 | Oscillatory behavior and equidistribution of signs of Fourier coefficients of cusp forms | In this paper, we discuss questions related to the oscillatory behavior and
the equidistribution of signs for certain subfamilies of Fourier coefficients
of integral weight newforms with a non-trivial nebentypus as well as Fourier
coefficients of eigenforms of half-integral weight reachable by the Shimura
correspondence. | 1710.06211v3 |
2017-12-26 | Weak hamiltonian Wilson Coefficients from Lattice QCD | In this work we present a calculation of the Wilson Coefficients $C_1$ and
$C_2$ of the Effective Weak Hamiltonian to all-orders in $\alpha_s$, using
lattice simulations. Given the current availability of lattice spacings we
restrict our calculation to unphysically light $W$ bosons around 2 GeV and we
study the systematic uncertainties of the two Wilson Coefficients. | 1712.09241v1 |
2018-04-09 | Definite Sums as Solutions of Linear Recurrences With Polynomial Coefficients | We present an algorithm which, given a linear recurrence operator $L$ with
polynomial coefficients, $m \in \mathbb{N}\setminus\{0\}$, $a_1,a_2,\ldots,a_m
\in \mathbb{N}\setminus\{0\}$ and $b_1,b_2,\ldots,b_m \in \mathbb{K}$, returns
a linear recurrence operator $L'$ with rational coefficients such that for
every sequence $h$, \[ L\left(\sum_{k=0}^\infty \prod_{i=1}^m \binom{a_i n +
b_i}{k} h_k\right) = 0 \] if and only if $L' h = 0$. | 1804.02964v1 |
2018-04-12 | On the largest Kronecker and Littlewood--Richardson coefficients | We give new bounds and asymptotic estimates for Kronecker and
Littlewood--Richardson coefficients. Notably, we resolve Stanley's questions on
the shape of partitions attaining the largest Kronecker and
Littlewood--Richardson coefficients. We apply the results to asymptotics of the
number of standard Young tableaux of skew shapes. | 1804.04693v2 |
2018-05-01 | Simultaneous behaviour of the Fourier coefficients of two Hilbert modular cusp forms | In this article, we study the simultaneous sign changes of the Fourier
coefficients of two Hilbert cusp forms of different integral weights. We also
study the simultaneous non-vanishing of Fourier coefficients, of two distinct
non-zero primitive Hilbert cuspidal non-CM eigenforms of integral weights, at
powers of a fixed prime ideal. | 1805.00230v1 |
2018-05-04 | Distribution Dependent SDEs with Singular Coefficients | Under integrability conditions on distribution dependent coefficients,
existence and uniqueness are proved for McKean-Vlasov type SDEs with
non-degenerate noise. When the coefficients are Dini continuous in the space
variable, gradient estimates and Harnack type inequalities are derived. These
generalize the corresponding results derived for classical SDEs, and are new in
the distribution dependent setting. | 1805.01682v1 |
2018-05-08 | Integrability of the Basener-Ross model with time-dependent coefficients | The Basener-Ross system is a known model in Population Dynamics for the
interaction of consumers and resources in an isolated habitat. For an extended
version with time-dependent coefficients as a model of possible variations of
the environtmental conditions, some relations among the coefficients are
provided leading to the integrability of the system. | 1805.02910v1 |
2018-05-10 | On logarithmic coefficients of certain starlike functions related to the vertical strip | In the present paper two certain subclasses of the starlike functions
associated with the vertical strip are considered. The main aim of this paper
is to investigate some basic properties of these classes such as, subordination
relations, sharp inequalities for sums involving logarithmic coefficients and
estimate of logarithmic coefficients. | 1805.03997v3 |
2018-05-21 | Strichartz estimates for Schrödinger operators with square potential with time-dependent coefficients | Strichartz estimates for a time-decaying harmonic oscillator were proven with
some assumptions of coefficients for the time-decaying harmonic potentials. The
main results of this paper are to remove these assumptions and to enable us to
deal with the more general coefficient functions. Moreover, we also prove
similar estimates for time-decaying homogeneous magnetic fields. | 1805.07991v3 |
2018-06-07 | $L_p$-estimates for time fractional parabolic equations with coefficients measurable in time | We establish the $L_p$-solvability for time fractional parabolic equations
when coefficients are merely measurable in the time variable. In the spatial
variables, the leading coefficients locally have small mean oscillations. Our
results extend a recent result in [6] to a large extent. | 1806.02635v2 |
2018-06-11 | Big polynomial rings with imperfect coefficient fields | We previously showed that the inverse limit of standard-graded polynomial
rings with perfect coefficient field is a polynomial ring, in an uncountable
number of variables. In this paper, we show that the same result holds with
arbitrary coefficient field. We also prove an analogous result for
ultraproducts of polynomial rings. | 1806.04208v2 |
2018-06-15 | A bound of the $β$-mixing coefficient for point processes in terms of their intensity functions | We prove a general inequality on $\beta$-mixing coefficients of point
processes depending uniquely on their $n$-th order intensity functions. We
apply this inequality in the case of determinantal point processes and show
that the rate of decay of the $\beta$-mixing coefficients of a wide class of
DPPs is optimal. | 1806.05910v2 |
2018-08-21 | Functional convergence for moving averages with heavy tails and random coefficients | We study functional convergence of sums of moving averages with random
coefficients and heavy-tailed innovations. Under some standard moment
conditions and the assumption that all partial sums of the series of
coefficients are a.s. bounded between zero and the sum of the series we obtain
functional convergence of the corresponding partial sum stochastic process in
the space $D[0,1]$ of c\`{a}dl\`{a}g functions with the Skorohod $M_{2}$
topology. | 1808.07023v1 |
2018-09-05 | Parabolic Systems with measurable coefficients in weighted Sobolev spaces | In this paper we present a weighted $L_p$-theory of parabolic systems on a
half space. The leading coefficients are assumed to be only measurable in $t$
and have small bounded mean oscillations (BMO) with respect to $x$, and the
lower order coefficients are allowed to blow up near the boundary. | 1809.01325v2 |
2018-12-10 | On the Interrelation between Dependence Coefficients of Extreme Value Copulas | For extreme value copulas with a known upper tail dependence coefficient we
find pointwise upper and lower bounds, which are used to establish upper and
lower bounds of the Spearman and Kendall correlation coefficients. We shown
that in all cases the lower bounds are attained on Marshall--Olkin copulas, and
the upper ones, on copulas with piecewise linear dependence functions. | 1812.03766v1 |
2019-01-22 | Moser's estimates for degenerate Kolmogorov equations with non-negative divergence lower order coefficients | We prove the local boundedness of the solutions to degenerate second order
partial differential equations of Kolmogorov type with measurable coefficients
in divergence form, under minimal integrability assumption on the lower order
coefficients. | 1901.07345v2 |
2019-02-24 | Path-Distribution Dependent SDEs with Singular Coefficients | In this paper, existence and uniqueness are proved for path-dependent
McKean-Vlasov type SDEs with integrability conditions. Gradient estimates and
Harnack type inequalities are derived in the case that the coefficients are
Dini continuous in the space variable. These generalize the corresponding
results derived for classical functional SDEs with singular coefficients. | 1902.08953v1 |
2019-03-19 | An asymptotic Formula for the iterated exponential Bell Numbers | In 1938 E. T. Bell introduced "The Iterated Exponential Integers". He proved
that these numbers may be expressed by polynomials with rational coefficients.
However, Bell gave no formulas for any of the coefficients except the trivial
one, which is always 1. Our task has been to find the coefficient of the
leading term, giving asymptotic information about these numbers. | 1903.07979v1 |
2019-04-14 | Wolff Type Potential Estimates for Stationary Stokes Systems with Dini-BMO Coefficients | The pointwise gradient estimate for weak solution pairs to the stationary
Stokes system with Dini-BMO coefficients is established via the
Havin-Maz'ya-Wolff type nonlinear potential of the nonhomogeneous term. In
addition, we present a pointwise bound for the weak solutions under no extra
regularity assumption on the coefficients. | 1904.06684v1 |
2019-04-16 | On a Subclass of p-Valent Functions with Negative Coefficients Defined by Using Rafid Operator | By using Rafid operator we define the subclass $R_{\mu,p}^\delta(\alpha;A,B)$
and $P_{\mu,p}^\delta(\alpha; A,B)$ of analytic and p-valent functions with
negative coefficients we investigate some sharp results including coefficients
estimates, distortion theorem, radii of starlikeness, convexity,
close-to-convexity, and modified-Hadamard product. Finally, we give an
application of fractional calculus and Bernadi-Libora-Livingstion operator. | 1904.07913v1 |
2019-05-14 | Non-existence of generalized splitting methods with positive coefficients of order higher than four | We prove that generalized exponential splitting methods making explicit use
of commutators of the vector fields are limited to order four when only real
coefficients are admitted. This generalizes the restriction to order two for
classical splitting methods with only positive coefficients. | 1905.05492v1 |
2019-12-14 | Scattering for critical wave equations with variable coefficients | We prove that solutions to the quintic semilinear wave equation with variable
coefficients in $\mathbb R^{1+3}$ scatter to a solution to the corresponding
linear wave equation. The coefficients are small and decay as $|x|\to\infty$,
but are allowed to be time dependent. The proof uses local energy decay
estimates to establish the decay of the $L^6$ norm of the solution as
$t\to\infty$. | 1912.06795v1 |
2019-12-31 | Fractional Dehn twists and modular invariants | In this note, we establish a relationship between fractional Dehn twist
coefficients of Riemann surface automorphisms and modular invariants of
holomorphic families of algebraic curves. Specially, we give a characterization
of pseudo-periodic maps with nontrivial fractional Dehn twist coefficients. We
also obtain some uniform lower bounds of non-zero fractional Dehn twist
coefficients. | 1912.13236v2 |
2020-01-08 | Logarithmic Stability for Coefficients Inverse Problem of Coupled Wave Equations | This paper investigates the identification of two coefficients in a coupled
hyperbolic system with an observation on one component of the solution. Based
on the the Carleman estimate for coupled wave equations a logarithmic type
stability result is obtained by measurement data only in a suitably chosen
subdomain under the assumption that the coefficients are given in a
neighborhood of some subboundary. | 2001.02379v2 |
2020-01-13 | Carleman estimate for complex second order elliptic operators with discontinuous Lipschitz coefficients | In this paper, we derive a local Carleman estimate for the complex second
order elliptic operator with Lipschitz coefficients having jump
discontinuities. Combing the result in [BL] and the arguments in [DcFLVW], we
present an elementary method to derive the Carleman estimate under the optimal
regularity assumption on the coefficients. | 2001.04071v1 |
2020-02-29 | Identification of Random Coefficient Latent Utility Models | This paper provides nonparametric identification results for random
coefficient distributions in perturbed utility models. We cover discrete and
continuous choice models. We establish identification using variation in mean
quantities, and the results apply when an analyst observes aggregate demands
but not whether goods are chosen together. We require exclusion restrictions
and independence between random slope coefficients and random intercepts. We do
not require regressors to have large supports or parametric assumptions. | 2003.00276v1 |
2020-03-09 | SDEs with random and irregular coefficients | We consider It\^o uniformly nondegenerate equations with random coefficients.
When the coefficients satisfy some low regularity assumptions with respect to
the spatial variables and Malliavin differentiability assumptions on the sample
points, the unique solvability of singular SDEs is proved by solving backward
stochastic Kolmogorov equations and utilizing a modified Zvonkin type
transformation. | 2003.04436v2 |
2020-03-12 | Bohr phenomenon for operator valued functions with fixed initial coefficient | The purpose of this article is to study Bohr inequalities involving the
absolute values of the coefficients of an operator valued function. To be more
specific, we establish an operator valued analogue of a classical result
regarding the Bohr phenomenon for scalar valued functions with fixed initial
coefficient. Apart from that, operator valued versions of other related and
well known results are obtained. | 2003.05810v1 |
2020-03-15 | Symplectic Eisenstein Series | We compute explicit formulae for the constant terms and Fourier coefficients
for Eisenstein series on $\operatorname{Sp}(4,\mathbb{R})$, in terms of zeta
functions and Whittaker functions. We also develop a generalisation of
Ramanujan sums to $\operatorname{Sp}(4,\mathbb{Z})$, which appears as
coefficients in the Fourier coefficients for the minimal Eisenstein series. | 2003.06890v1 |
2020-05-04 | On the $RO(G)$-graded coefficients of dihedral equivariant cohomology | We completely calculate the $RO(G)$-graded coefficients of ordinary
equivariant cohomology where $G$ is the dihedral group of order $2p$ for a
prime $p>2$ both with constant and Burnside ring coefficients. The authors
first proved it for $p=3$ and then the second author generalized it to
arbitrary $p$. These are the first such calculations for a non-abelian group. | 2005.01225v1 |
2020-06-08 | Weighted sums of generalized polygonal numbers with coefficients 1 or 2 | In this article, we consider weighted sums of generalized polygonal numbers
with coefficients $1$ or $2$. We show that for any $m\ge10$, those weighted
sums of generalized $m$-gonal numbers represent every non-negative integers if
they only represent $1$, $m-4$, and $m-2$. Furthermore, we study
representations of sums of four generalized polygonal numbers with coefficients
$1$ or $2$. | 2006.04490v2 |
2020-11-20 | Notes on equivariant homology with constant coefficients | In this paper, for a finite group, we discuss a method for calculating
equivariant homology with constant coefficients. We apply it to completely
calculate the geometric fixed points of the equivariant spectrum representing
equivariant (co)homology with constant coefficients. We also treat a more
complicated example of inverting the standard representation in the equivariant
homology of split extraspecial groups at the prime 2. | 2011.10622v1 |
2020-11-24 | A generalized Montel theorem for a class of first order elliptic equations with measurable coefficients | In this paper we prove a generalization of Montel's theorem for a class of
first order elliptic equations with measurable coefficients involving
Hodge-Dirac operators. We then apply this result to sequences of solutions of
second order uniformly elliptic equations with measurable coefficients on
divergence form and show that this results in a precompactness result for such
sequences. | 2011.12185v1 |
2020-11-24 | Homological Polynomial Coefficients and the Twist Number of Alternating Surface Links | For $D$ a reduced alternating surface link diagram, we bound the twist number
of $D$ in terms of the coefficients of a polynomial invariant. To this end, we
introduce a generalization of the homological Kauffman bracket defined by
Krushkal. Combined with work of Futer, Kalfagianni, and Purcell, this yields a
bound for the hyperbolic volume of a class of alternating surface links in
terms of these coefficients. | 2011.12274v1 |
2020-12-30 | Matrix products of binomial coefficients and unsigned Stirling numbers | We study sums of the form $\sum_{k=m}^n a_{nk} b_{km}$, where $a_{nk}$ and
$b_{km}$ are binomial coefficients or unsigned Stirling numbers. In a few cases
they can be written in closed form. Failing that, the sums still share many
common features: combinatorial interpretations, Pascal-like recurrences,
inverse relations with their signed versions, and interpretations as
coefficients of change between polynomial bases. | 2012.15307v1 |
2021-01-09 | Transience of symmetric non-local Dirichlet forms | We establish transience criteria for symmetric non-local Dirichlet forms on
$L^2({\mathbb R}^d)$ in terms of the coefficient growth rates at infinity.
Applying these criteria, we find a necessary and sufficient condition for
recurrence of Dirichlet forms of symmetric stable-like with
unbounded/degenerate coefficients. This condition indicates that both of the
coefficient growth rates of small and big jump parts affect the sample path
properties of the associated symmetric jump processes. | 2101.03442v2 |
2021-03-06 | Estimates for Green's functions of elliptic equations in non-divergence form with continuous coefficients | We present a new method for the existence and pointwise estimates of a
Green's function of non-divergence form elliptic operator with Dini mean
oscillation coefficients. We also present a sharp comparison with the
corresponding Green's function for constant coefficients equations. | 2103.04071v2 |
2021-04-14 | Inverse Boundary Problem for the Two Photon Absorption Transport Equation | This work studies the inverse boundary problem for the two photon absorption
radiative transport equation. We show that the absorption coefficients and
scattering coefficients can be uniquely determined from the \emph{albedo}
operator. If scattering is absent, we do not require smallness of the incoming
source and the reconstructions of the absorption coefficients are explicit. | 2104.06566v2 |
2021-04-23 | Stochastic differential equations with irregular coefficients:~mind the gap! | Numerical methods for stochastic differential equations with non-globally
Lipschitz coefficients are currently studied intensively. This article gives an
overview of our work for the case that the drift coefficient is potentially
discontinuous complemented by other important results in this area. To make the
topic accessible to a broad audience, we begin with a heuristic on SDEs and a
motivation. | 2104.11505v1 |
2021-06-04 | Rademacher-Gaussian tail comparison for complex coefficients and related problems | We provide a generalisation of Pinelis' Rademacher-Gaussian tail comparison
to complex coefficients. We also establish uniform bounds on the probability
that the magnitude of weighted sums of independent random vectors uniform on
Euclidean spheres with matrix coefficients exceeds its second moment. | 2106.02421v1 |
2021-08-25 | A note on Chern coefficients and Cohen-Macaulay rings | In this paper, we investigate the relationship between the index of
reducibility and Chern coefficients for primary ideals. As an application, we
give characterizations of a Cohen-Macaulay ring in terms of its type,
irreducible multiplicity, and Chern coefficients with respect to certain
parameter ideals in Noetherian local rings. | 2108.11079v1 |
2021-09-19 | Dirichlet series and series with Stirling numbers | This paper presents a number of identities for Dirichlet series and series
with Stirling numbers of the first kind. As coefficients for the Dirichlet
series we use Cauchy numbers of the first and second kinds, hyperharmonic
numbers, derangement numbers, binomial coefficients, central binomial
coefficients, and Catalan numbers. | 2109.09167v3 |
2021-11-14 | On the coefficients of the distinct monomials in the expansion of $x_1(x_1+x_2)\cdots(x_1+x_2+\cdots+x_n)$ | We initiate the study of the coefficients of the distinct monomials in the
expansion of the multivariate polynomials
$x_1(x_1+x_2)\cdots(x_1+x_2+\cdots+x_n), n\in\N$. In particular we obtain
several results regarding their maximal coefficients. | 2111.07331v3 |
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