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2012-02-13 | Steiner symmetrization and the initial coefficients of univalent functions | We study the behavior of the initial coefficients of univalent functions
under the Steiner symmetrization, and give some applications to functions of
class \Sigma. | 1202.2633v1 |
2012-03-26 | On the Boundedness of Solutions of a Rational System with a Variable Coefficient | We establish the boundedness character of solutions of a system of rational
difference equations with a variable coefficient | 1203.5770v1 |
2012-06-22 | Smoothing estimates for variable coefficients Schroedinger equation with electromagnetic potentials | In this paper we develop the classical multiplier technique to prove a virial
identity and smoothing estimates (in a perturbative setting) for the
electromagnetic variable coefficients Schroedinger equation. | 1206.5177v1 |
2013-06-02 | Derivation of the coefficient squared probability law in quantum mechanics | If one assumes there is probability of perception in quantum mechanics, then
unitarity dictates that it must have the coefficient squared form, in agreement
with experiment. | 1306.0213v1 |
2014-03-26 | Extraction of the symmetry energy coefficients from the masses differences of isobaric nuclei | The nuclear symmetry energy coefficients of finite nuclei are extracted by
using the differences between the masses of isobaric nuclei. Based on the
masses of more than 2400 nuclei with $A=9-270$, we investigate the model
dependence in the extraction of symmetry energy coefficient. We find that the
extraction of the symmetry energy coefficients is strongly correlated with the
forms of the Coulomb energy and the mass dependence of the symmetry energy
coefficient adopted. The values of the extracted symmetry energy coefficients
increase by about 2 MeV for heavy nuclei when the Coulomb correction term is
involved. We obtain the bulk symmetry energy coefficient $S_0=28.26\pm1.3$ MeV
and the surface-to-volume ratio $\kappa=1.26\pm 0.25 $ MeV if assuming the mass
dependence of symmetry energy coefficient $a_{\rm
sym}(A)=S_0(1-\kappa/A^{1/3})$, and $S_0=32.80\pm1.7$ MeV, $\kappa=2.82\pm0.57$
MeV when $a_{\rm sym}(A)=S_0 (1+\kappa/A^{1/3})^{-1}$ is adopted. | 1403.6560v2 |
2014-09-16 | Distribution of zeros of polynomials with positive coefficients | We describe the limit zero distributions of sequences of polynomials with
positive coefficients. | 1409.4640v1 |
2014-11-29 | Continuous and robust clustering coefficients for weighted and directed networks | We introduce new clustering coefficients for weighted networks. They are
continuous and robust against edge weight changes. Recently, generalized
clustering coefficients for weighted and directed networks have been proposed.
These generalizations have a common property, that their values are not
continuous. They are sensitive with edge weight changes, especially at zero
weight. With these generalizations, if vanishingly low weights of edges are
truncated to weight zero for some reason, the coefficient value may change
significantly from the original value. It is preferable that small changes of
edge weights cause small changes of coefficient value. We call this property
the continuity of generalized clustering coefficients. Our new coefficients
admit this property. In the past, few studies have focused on the continuity of
generalized clustering coefficients. In experiments, we performed comparative
assessments of existing and our generalizations. In the case of a real world
network dataset (C. Elegans Neural network), after adding random edge weight
errors, though the value of one discontinuous generalization was changed about
436%, the value of proposed one was only changed 0.2%. | 1412.0059v1 |
2016-02-13 | Fast Computation of the Kinship Coefficients | For families, kinship coefficients are quantifications of the amount of
genetic sharing between a pair of individuals. These coefficients are critical
for understanding the breeding habits and genetic diversity of diploid
populations. Historically, computations of the inbreeding coefficient were used
to prohibit inbred marriages and prohibit breeding of some pairs of pedigree
animals. Such prohibitions foster genetic diversity and help prevent recessive
Mendelian disease at a population level.
This paper gives the fastest known algorithms for computing the kinship
coefficient of a set of individuals with a known pedigree. The algorithms given
here consider the possibility that the founders of the known pedigree may
themselves be inbred, and they compute the appropriate inbreeding-adjusted
kinship coefficients. The exact kinship algorithm has running-time $O(n^2)$ for
an $n$-individual pedigree. The recursive-cut exact kinship algorithm has
running time $O(s^2m)$ where $s$ is the number of individuals in the largest
segment of the pedigree and $m$ is the number of cuts. The approximate
algorithm has running-time $O(n)$ for an $n$-individual pedigree on which to
estimate the kinship coefficients of $\sqrt{n}$ individuals from $\sqrt{n}$
founder kinship coefficients. | 1602.04368v1 |
2016-03-31 | Improved bounds for Fourier coefficients of Siegel modular forms | The goal of this paper is to improve existing bounds for Fourier coefficients
of higher genus Siegel modular forms of small weight. | 1603.09556v1 |
2016-05-02 | On the $C^1$ regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients | We prove $C^1$ regularity of solutions to divergence form elliptic systems
with Dini-continuous coefficients | 1605.00535v1 |
2016-06-15 | Modal analysis of the scattering coefficients of an open cavity in a waveguide | The characteristics of an acoustic scatterer are often described by
scattering coefficients. The understanding of the mechanisms involved in the
frequency dependent features of the coefficients has been a challenge task,
owing to the complicated coupling between the waves in open space and the modes
inside the finite scatterer. In this paper, a frequency-dependent modal
description of the scattering coefficient is utilized to study the modal
properties of the scatterer. The important role that eigenmodes play in
defining the features of the scattering coefficients is revealed via an
expansion of the coefficients by the eigenmodes. The results show the local
extrema of the scattering coefficients can be attributed to the
constructive/destructive interference of resonant and non-resonant modes. In
particular, an approximated equation, which is equivalent to the standard Fano
formula, is obtained to describe the sharp anti-symmetric Fano characteristics
of the scattering coefficients. The special cases where scattering is dominated
by a single resonance eigenmode, corresponding to the "resonance transmission",
are also illustrated. | 1606.05676v1 |
2016-09-17 | Convolution identities for Tetranacci numbers | We give convolution identities without binomial coefficients for Tetranacci
numbers and convolution identities with binomial coefficients for Tetranacci
and Tetranacci-type numbers. | 1609.05272v1 |
2016-11-29 | Strictly Hyperbolic Equations with Coefficients Low-Regular in Time and Smooth in Space | We consider the Cauchy problem for strictly hyperbolic $m$-th order partial
differential equations with coefficients low-regular in time and smooth in
space. It is well-known that the problem is $L^2$ well-posed in the case of
Lipschitz continuous coefficients in time, $H^s$ well-posed in the case of
Log-Lipschitz continuous coefficients in time (with an, in general, finite loss
of derivatives) and Gevrey well-posed in the case of H\"older continuous
coefficients in time (with an, in general, infinite loss of derivatives). Here,
we use moduli of continuity to describe the regularity of the coefficients with
respect to time, weight sequences for the characterization of their regularity
with respect to space and weight functions to define the solution spaces. We
establish sufficient conditions for the well-posedness of the Cauchy problem,
that link the modulus of continuity and the weight sequence of the coefficients
to the weight function of the solution space. The well-known results for
Lipschitz, Log-Lipschitz and H\"older coefficients are recovered. | 1611.09548v2 |
2017-01-22 | Some divisibility properties of binomial coefficients | In this paper, we gave some properties of binomial coefficient. | 1701.06217v1 |
2017-01-30 | Bounds on Distance to Variety in Terms of Coefficients of Bivariate Polynomials | A short note on bounds on distance to variety of a point in terms of the
Taylor coefficients at the point. | 1701.08613v1 |
2017-02-22 | Simultaneous determination of the drift and diffusion coefficients in stochastic differential equations | In this work, we consider a one-dimensional It{\^o} diffusion process X t
with possibly nonlinear drift and diffusion coefficients. We show that, when
the diffusion coefficient is known, the drift coefficient is uniquely
determined by an observation of the expectation of the process during a small
time interval, and starting from values X 0 in a given subset of R. With the
same type of observation, and given the drift coefficient, we also show that
the diffusion coefficient is uniquely determined. When both coefficients are
unknown, we show that they are simultaneously uniquely determined by the
observation of the expectation and variance of the process, during a small time
interval, and starting again from values X 0 in a given subset of R. To derive
these results, we apply the Feynman-Kac theorem which leads to a linear
parabolic equation with unknown coefficients in front of the first and second
order terms. We then solve the corresponding inverse problem with PDE technics
which are mainly based on the strong parabolic maximum principle. | 1702.06859v1 |
2017-08-05 | Optimization of Non Binary Parity Check Coefficients | This paper generalizes the method proposed by Poulliat et al. for the
determination of the optimal Galois Field coefficients of a Non-Binary LDPC
parity check constraint based on the binary image of the code. Optimal, or
almost-optimal, parity check coefficients are given for check degree varying
from 4 to 20 and Galois Field varying from GF(64) up to GF(1024). For all given
sets of coefficients, no codeword of Hamming weight two exists. A reduced
complexity algorithm to compute the binary Hamming weight 3 of a parity check
is proposed. When the number of sets of coefficients is too high for an
exhaustive search and evaluation, a local greedy search is performed. Explicit
tables of coefficients are given. The proposed sets of coefficients can
effectively replace the random selection of coefficients often used in NB-LDPC
construction. | 1708.01761v2 |
2017-09-12 | Elementary proof of congruences involving sum of binomial coefficients | We provide elementary proof of several congruences involving single sum and
multisums of binomial coefficients. | 1709.04039v2 |
2018-01-03 | Local Coefficients Revisited | Two simple "simplicial approximation" tricks are invoked to prove basic
results involving (co)-homology with local coefficients. | 1801.01148v1 |
2018-05-29 | Properties of interaction networks, structure coefficients, and benefit-to-cost ratios | In structured populations the spatial arrangement of cooperators and
defectors on the interaction graph together with the structure of the graph
itself determines the game dynamics and particularly whether or not fixation of
cooperation (or defection) is favored. For a single cooperator (and a single
defector) and a network described by a regular graph the question of fixation
can be addressed by a single parameter, the structure coefficient. As this
quantity is generic for any regular graph, we may call it the generic structure
coefficient. For two and more cooperators (or several defectors) fixation
properties can also be assigned by structure coefficients. These structure
coefficients, however, depend on the arrangement of cooperators and defectors
which we may interpret as a configuration of the game. Moreover, the
coefficients are specific for a given interaction network modeled as regular
graph, which is why we may call them specific structure coefficients. In this
paper, we study how specific structure coefficients vary over interaction
graphs and link the distributions obtained over different graphs to spectral
properties of interaction networks. We also discuss implications for the
benefit-to-cost ratios of donation games. | 1805.11359v2 |
2018-10-06 | Large Eddy Simulation of a NACA0015 Circulation Control Airfoil Using Synthetic Jets | Large eddy simulation of a NACA0015 circulation control airfoil using
synthetic jets is conducted. A chord Reynolds number of 110000, the excitation
frequency of 175 Hz, the momentum coefficients of 0.0044 to 0.0688, and the
angles of attack of 0{\deg}, 6{\deg}, and 12{\deg} are employed in this study.
The numerical results presented in this paper show good agreement with the
experimental results. Fluctuations in the lift and drag coefficients on the
non-actuated airfoil are found to be governed by the vortex shedding frequency.
Provided that the momentum coefficient is sufficiently high, the lift and drag
coefficients tend to fluctuate at the synthetic jet frequency. The mean lift
coefficient linearly increases with the momentum coefficient at a low momentum
coefficient range and its incremental rate begins to decline at a high momentum
coefficient range. Increasing the angle of attack of the airfoil is observed to
slightly reduce the slope of the lift increment. | 1810.02914v1 |
2018-12-03 | Recursion Relations in Witten Diagrams and Conformal Partial Waves | We revisit the problem of performing conformal block decomposition of
exchange Witten diagrams in the crossed channel. Using properties of conformal
blocks and Witten diagrams, we discover infinitely many linear relations among
the crossed channel decomposition coefficients. These relations allow us to
formulate a recursive algorithm that solves the decomposition coefficients in
terms of certain seed coefficients. In one dimensional CFTs, the seed
coefficient is the decomposition coefficient of the double-trace operator with
the lowest conformal dimension. In higher dimensions, the seed coefficients are
the coefficients of the double-trace operators with the minimal conformal
twist. We also discuss the conformal block decomposition of a generic contact
Witten diagram with any number of derivatives. As a byproduct of our analysis,
we obtain a similar recursive algorithm for decomposing conformal partial waves
in the crossed channel. | 1812.01006v3 |
2019-02-07 | Recovering time-dependent singular coefficients of the wave-equation-One Dimensional Case | We give a way to recover time-dependent singular coefficients of the
wave-equation in the one-dimensional case. | 1902.02619v1 |
2019-04-15 | Fast Inference in Capsule Networks Using Accumulated Routing Coefficients | We present a method for fast inference in Capsule Networks (CapsNets) by
taking advantage of a key insight regarding the routing coefficients that link
capsules between adjacent network layers. Since the routing coefficients are
responsible for assigning object parts to wholes, and an object whole generally
contains similar intra-class and dissimilar inter-class parts, the routing
coefficients tend to form a unique signature for each object class. For fast
inference, a network is first trained in the usual manner using examples from
the training dataset. Afterward, the routing coefficients associated with the
training examples are accumulated offline and used to create a set of "master"
routing coefficients. During inference, these master routing coefficients are
used in place of the dynamically calculated routing coefficients. Our method
effectively replaces the for-loop iterations in the dynamic routing procedure
with a single matrix multiply operation, providing a significant boost in
inference speed. Compared with the dynamic routing procedure, fast inference
decreases the test accuracy for the MNIST, Background MNIST, Fashion MNIST, and
Rotated MNIST datasets by less than 0.5% and by approximately 5% for CIFAR10. | 1904.07304v1 |
2019-06-08 | Frequency-Dependent Perceptual Quantisation for Visually Lossless Compression Applications | The default quantisation algorithms in the state-of-the-art High Efficiency
Video Coding (HEVC) standard, namely Uniform Reconstruction Quantisation (URQ)
and Rate-Distortion Optimised Quantisation (RDOQ), do not take into account the
perceptual relevance of individual transform coefficients. In this paper, a
Frequency-Dependent Perceptual Quantisation (FDPQ) technique for HEVC is
proposed. FDPQ exploits the well-established Modulation Transfer Function (MTF)
characteristics of the linear transformation basis functions by taking into
account the Euclidean distance of an AC transform coefficient from the DC
coefficient. As such, in luma and chroma Cb and Cr Transform Blocks (TBs), FDPQ
quantises more coarsely the least perceptually relevant transform coefficients
(i.e., the high frequency AC coefficients). Conversely, FDPQ preserves the
integrity of the DC coefficient and the very low frequency AC coefficients.
Compared with RDOQ, which is the most widely used transform coefficient-level
quantisation technique in video coding, FDPQ successfully achieves bitrate
reductions of up to 41%. Furthermore, the subjective evaluations confirm that
the FDPQ-coded video data is perceptually indistinguishable (i.e., visually
lossless) from the raw video data for a given Quantisation Parameter (QP). | 1906.03395v1 |
2019-09-05 | Frieze patterns with coefficients | Frieze patterns, as introduced by Coxeter in the 1970's, are closely related
to cluster algebras without coefficients. A suitable generalization of frieze
patterns, linked to cluster algebras with coefficients, has only briefly
appeared in an unpublished manuscript by Propp. In this paper we study these
frieze patterns with coefficients systematically and prove various fundamental
results, generalizing classic results for frieze patterns. As a consequence we
see how frieze patterns with coefficients can be obtained from classic frieze
patterns by cutting out subpolygons from the triangulated polygons associated
to classic Conway-Coxeter frieze patterns. We address the question of which
frieze patterns with coefficients can be obtained in this way and solve this
problem completely for triangles. Finally, we prove a finiteness result for
frieze patterns with coefficients by showing that for a given boundary sequence
there are only finitely many (non-zero) frieze patterns with coefficients with
entries in a discrete subset of the complex numbers. | 1909.02332v1 |
2019-09-12 | Sharp Large Deviations for empirical correlation coefficients | We study Sharp Large Deviations for Pearson's empirical correlation
coefficients in the Spherical and Gaussian cases | 1909.05570v1 |
2019-10-28 | Accurate calculation of field expansion coefficients in FEM magnetostatic simulations | FEM simulations are a standard step in the design of accelerator magnets. It
is custom for accelerator applications to characterize the field quality in
terms of field expansion coefficients. With a commonly accepted approach,
expansion coefficients are calculated by means of a Fourier transform of the
local FEM solution at points on an arc. The accuracy of the coefficients
calculated this way depends strongly on the FEM mesh configuration and simple
refinement of the mesh does not always improve accuracy. The accuracy of the
expansion coefficients calculation can be improved by using the data on the
magnetization of elements in the magnet yoke, obtained in the solution, instead
of using directly the local solution. Since currents and the yoke magnetization
are the only sources of the field, with these data the field expansion
coefficients can be calculated at any remote point. We derive closed forms for
calculating expansion coefficients and implemented these results in the ANSYS
add-on. Results for a case study are presented, which demonstrate that
expansion coefficients can be calculated with good accuracy even for a rather
coarse mesh. | 1910.12696v1 |
2019-11-26 | Closure coefficients in scale-free complex networks | The formation of triangles in complex networks is an important network
property that has received tremendous attention. The formation of triangles is
often studied through the clustering coefficient. The closure coefficient or
transitivity is another method to measure triadic closure. This statistic
measures clustering from the head node of a triangle (instead of from the
center node, as in the often studied clustering coefficient). We perform a
first exploratory analysis of the behavior of the local closure coefficient in
two random graph models that create simple networks with power-law degrees: the
hidden-variable model and the hyperbolic random graph. We show that the closure
coefficient behaves significantly different in these simple random graph models
than in the previously studied multigraph models. We also relate the closure
coefficient of high-degree vertices to the clustering coefficient and the
average nearest neighbor degree. | 1911.11410v2 |
2020-02-28 | The third logarithmic coefficient for the class S | In this paper we give an upper bound of the third logarithmic coefficient for
the class $\mathcal{S}$ of univalent functions in the unit disc. | 2002.12865v1 |
2020-04-29 | Eulerianity of Fourier coefficients of automorphic forms | We study the question of Eulerianity (factorizability) for Fourier
coefficients of automorphic forms, and we prove a general transfer theorem that
allows one to deduce the Eulerianity of certain coefficients from that of
another coefficient. We also establish a `hidden' invariance property of
Fourier coefficients. We apply these results to minimal and next-to-minimal
automorphic representations, and deduce Eulerianity for a large class of
Fourier and Fourier-Jacobi coefficients. In particular, we prove Eulerianity
for parabolic Fourier coefficients with characters of maximal rank for a class
of Eisenstein series in minimal and next-to-minimal representations of groups
of ADE-type that are of interest in string theory. | 2004.14244v3 |
2021-01-19 | A survey on the theory of multiple Dirichlet series with arithmetical coefficients on the numerators | We survey some recent developments in the analytic theory of multiple
Dirichlet series with arithmetical coefficients on the numerators. | 2101.07449v1 |
2021-03-02 | Power series with inverse binomial coefficients and harmonic numbers | We construct the generating function for products of inverse central binomial
coefficients with harmonic numbers. | 2103.01879v1 |
2021-07-16 | Geometric Value Iteration: Dynamic Error-Aware KL Regularization for Reinforcement Learning | The recent boom in the literature on entropy-regularized reinforcement
learning (RL) approaches reveals that Kullback-Leibler (KL) regularization
brings advantages to RL algorithms by canceling out errors under mild
assumptions. However, existing analyses focus on fixed regularization with a
constant weighting coefficient and do not consider cases where the coefficient
is allowed to change dynamically. In this paper, we study the dynamic
coefficient scheme and present the first asymptotic error bound. Based on the
dynamic coefficient error bound, we propose an effective scheme to tune the
coefficient according to the magnitude of error in favor of more robust
learning. Complementing this development, we propose a novel algorithm,
Geometric Value Iteration (GVI), that features a dynamic error-aware KL
coefficient design with the aim of mitigating the impact of errors on
performance. Our experiments demonstrate that GVI can effectively exploit the
trade-off between learning speed and robustness over uniform averaging of a
constant KL coefficient. The combination of GVI and deep networks shows stable
learning behavior even in the absence of a target network, where algorithms
with a constant KL coefficient would greatly oscillate or even fail to
converge. | 2107.07659v2 |
2021-07-21 | A closed formula of Littlewood-Richardson coefficients | We give a closed formula of the Littlewood-Richardson coefficients. | 2107.09907v2 |
2021-11-02 | On the $RO(G)$-graded coefficients of $Q_8$ equivariant cohomology | In this paper, we calculate the $RO(G)$-graded coefficients of
$H\underline{\mathbb{Z}}$, the Eilenberg-MacLane spectrum of constant Mackey
functor for quaternion group $Q_8$. | 2111.01926v1 |
2021-11-19 | Fibonacci Identities Involving Reciprocals of Binomial Coefficients | We derive some Fibonacci and Lucas identities which contain inverse binomial
coefficients. Extension of the results to the general Horadam sequence is
possible, in some cases. | 2112.00622v1 |
2022-04-05 | Existence, uniqueness and approximation of solutions of SDEs with superlinear coefficients in the presence of discontinuities of the drift coefficient | Existence, uniqueness, and $L_p$-approximation results are presented for
scalar stochastic differential equations (SDEs) by considering the case where,
the drift coefficient has finitely many spatial discontinuities while both
coefficients can grow superlinearly (in the space variable). These
discontinuities are described by a piecewise local Lipschitz continuity and a
piecewise monotone-type condition while the diffusion coefficient is assumed to
be locally Lipschitz continuous and non-degenerate at the discontinuity points
of the drift coefficient. Moreover, the superlinear nature of the coefficients
is dictated by a suitable coercivity condition and a polynomial growth of the
(local) Lipschitz constants of the coefficients. Existence and uniqueness of
strong solutions of such SDEs are obtained. Furthermore, the classical
$L_p$-error rate $1/2$, for a suitable range of values of $p$, is recovered for
a tamed Euler scheme which is used for approximating these solutions. To the
best of the authors' knowledge, these are the first existence, uniqueness and
approximation results for this class of SDEs. | 2204.02343v1 |
2022-04-12 | Lattice paths and negatively indexed weight-dependent binomial coefficients | In 1992, Loeb considered a natural extension of the binomial coefficients to
negative entries and gave a combinatorial interpretation in terms of hybrid
sets. He showed that many of the fundamental properties of binomial
coefficients continue to hold in this extended setting. Recently, Formichella
and Straub showed that these results can be extended to the $q$-binomial
coefficients with arbitrary integer values and extended the work of Loeb
further by examining arithmetic properties of the $q$-binomial coefficients. In
this paper, we give an alternative combinatorial interpretation in terms of
lattice paths and consider an extension of the more general weight-dependent
binomial coefficients, first defined by the second author, to arbitrary integer
values. Remarkably, many of the results of Loeb, Formichella and Straub
continue to hold in the general weighted setting. We also examine important
special cases of the weight-dependent binomial coefficients, including
ordinary, $q$- and elliptic binomial coefficients as well as elementary and
complete homogeneous symmetric functions. | 2204.05505v2 |
2022-05-13 | Body Diagonal Diffusion Couple Method for Estimation of Tracer Diffusion Coefficients in a Multi-Principal Element Alloy | The estimation of (n-1)2 interdiffusion coefficients in an n component system
requires (n-1) diffusion paths to intersect or pass closely in the (n-1)
dimensional space according to the body diagonal diffusion couple method. These
interdiffusion coefficients are related to n(n-1) intrinsic (or n tracer
diffusion coefficients), which cannot be estimated easily following the
Kirkendall marker experiment in a multicomponent system despite their
importance for understanding the atomic mechanism of diffusion and the
physico-mechanical properties of materials. In this study, the estimation of
tracer diffusion coefficients from only two diffusion profiles following the
concept of the body diagonal diffusion couple method in a multicomponent system
is demonstrated. Subsequently, one can estimate the intrinsic and
interdiffusion coefficients. This reduces the overall effort up to a great
extent since it needs only two instead of (n-1) diffusion profiles irrespective
of the number of components, with an additional benefit of enabling the
estimation of all types of diffusion coefficients. The available tracer
diffusion coefficients estimated following the radiotracer method are compared
to the data estimated in this study following this method. This method can also
be extended to the systems in which the radiotracer method is not feasible. | 2205.06550v1 |
2022-06-15 | A smile is all you need: Predicting limiting activity coefficients from SMILES with natural language processing | Knowledge of mixtures' phase equilibria is crucial in nature and technical
chemistry. Phase equilibria calculations of mixtures require activity
coefficients. However, experimental data on activity coefficients is often
limited due to high cost of experiments. For an accurate and efficient
prediction of activity coefficients, machine learning approaches have been
recently developed. However, current machine learning approaches still
extrapolate poorly for activity coefficients of unknown molecules. In this
work, we introduce the SMILES-to-Properties-Transformer (SPT), a natural
language processing network to predict binary limiting activity coefficients
from SMILES codes. To overcome the limitations of available experimental data,
we initially train our network on a large dataset of synthetic data sampled
from COSMO-RS (10 Million data points) and then fine-tune the model on
experimental data (20 870 data points). This training strategy enables SPT to
accurately predict limiting activity coefficients even for unknown molecules,
cutting the mean prediction error in half compared to state-of-the-art models
for activity coefficient predictions such as COSMO-RS, UNIFAC, and improving on
recent machine learning approaches. | 2206.07048v1 |
2022-08-13 | Coefficient problems for certain Close-to-Convex Functions | In this paper, sharp bounds are established for the second Hankel determinant
of logarithmic coefficients for normalised analytic functions satisfying
certain differential inequality. | 2208.06638v1 |
2022-09-07 | Social Media Engagement and Cryptocurrency Performance | We study the problem of predicting the future performance of cryptocurrencies
using social media data. We propose a new model to measure the engagement of
users with topics discussed on social media based on interactions with social
media posts. This model overcomes the limitations of previous volume and
sentiment based approaches. We use this model to estimate engagement
coefficients for 48 cryptocurrencies created between 2019 and 2021 using data
from Twitter from the first month of the cryptocurrencies' existence. We find
that the future returns of the cryptocurrencies are dependent on the engagement
coefficients. Cryptocurrencies whose engagement coefficients are too low or too
high have lower returns. Low engagement coefficients signal a lack of interest,
while high engagement coefficients signal artificial activity which is likely
from automated accounts known as bots. We measure the amount of bot posts for
the cryptocurrencies and find that generally, cryptocurrencies with more bot
posts have lower future returns. While future returns are dependent on both the
bot activity and engagement coefficient, the dependence is strongest for the
engagement coefficient, especially for short-term returns. We show that simple
investment strategies which select cryptocurrencies with engagement
coefficients exceeding a fixed threshold perform well for holding times of a
few months. | 2209.02911v1 |
2022-10-21 | Estimating and computing Kronecker Coefficients: a vector partition function approach | We study the Kronecker coefficients $g_{\lambda, \mu, \nu}$ via a formula
that was described by Mishna, Rosas, and Sundaram, in which the coefficients
are expressed as a signed sum of vector partition function evaluations. In
particular, we use this formula to determine formulas to evaluate, bound, and
estimate $g_{\lambda, \mu, \nu}$ in terms of the lengths of the partitions
$\lambda, \mu$, and $\nu$. We describe a computational tool to compute
Kronecker coefficients $g_{\lambda, \mu, \nu}$ with $\ell(\mu) \leq 2,\
\ell(\nu) \leq 4,\ \ell(\lambda) \leq 8$. We present a set of new vanishing
conditions for the Kronecker coefficients by relating to the vanishing of the
related atomic Kronecker coefficients, themselves given by a single vector
partition function evaluation. We give a stable face of the Kronecker
polyhedron for any positive integers $m,n$. Finally, we give upper bounds on
both the atomic Kronecker coefficients and Kronecker coefficients. | 2210.12128v1 |
2023-02-27 | Robust High-Dimensional Time-Varying Coefficient Estimation | In this paper, we develop a novel high-dimensional coefficient estimation
procedure based on high-frequency data. Unlike usual high-dimensional
regression procedure such as LASSO, we additionally handle the heavy-tailedness
of high-frequency observations as well as time variations of coefficient
processes. Specifically, we employ Huber loss and truncation scheme to handle
heavy-tailed observations, while $\ell_{1}$-regularization is adopted to
overcome the curse of dimensionality. To account for the time-varying
coefficient, we estimate local coefficients which are biased due to the
$\ell_{1}$-regularization. Thus, when estimating integrated coefficients, we
propose a debiasing scheme to enjoy the law of large number property and employ
a thresholding scheme to further accommodate the sparsity of the coefficients.
We call this Robust thrEsholding Debiased LASSO (RED-LASSO) estimator. We show
that the RED-LASSO estimator can achieve a near-optimal convergence rate. In
the empirical study, we apply the RED-LASSO procedure to the high-dimensional
integrated coefficient estimation using high-frequency trading data. | 2302.13658v2 |
2023-03-15 | On the differential operators of odd order with PT-symmetric periodic matrix coefficients | In this paper we investigate the spectrum of the differential operators
generated by the ordinary differential expression of odd order with
PT-symmertic periodic matrix coefficients | 2303.08703v1 |
2023-03-30 | Interior transmission problems with coefficients of low regularity | We obtain parabolic transmission eigenvalue-free regions for both isotropic
andanisotropic interior transmission problems with coefficients which are
Lipschitznear the boundary | 2303.17199v1 |
2023-12-02 | A Goldbach theorem for Laurent polynomials with positive integer coefficients | We establish an analogue of the Goldbach conjecture for Laurent polynomials
with positive integer coefficients. | 2312.01189v1 |
2024-02-08 | Introducing q-deformed binomial coefficients of words | Gaussian binomial coefficients are q-analogues of the binomial coefficients
of integers. On the other hand, binomial coefficients have been extended to
finite words, i.e., elements of the finitely generated free monoids. In this
paper we bring together these two notions by introducing q-analogues of
binomial coefficients of words. We study their basic properties, e.g., by
extending classical formulas such as the q-Vandermonde and Manvel's et al.
identities to our setting. As a consequence, we get information about the
structure of the considered words: these q-deformations of binomial
coefficients of words contain much richer information than the original
coefficients. From an algebraic perspective, we introduce a q-shuffle and a
family q-infiltration products for non-commutative formal power series.
Finally, we apply our results to generalize a theorem of Eilenberg
characterizing so-called p-group languages. We show that a language is of this
type if and only if it is a Boolean combination of specific languages defined
through q-binomial coefficients seen as polynomials over $\mathbb{F}_p$. | 2402.05838v1 |
2024-03-19 | Reproducing the Acoustic Velocity Vectors in a Circular Listening Area | Acoustic velocity vectors are important for human's localization of sound at
low frequencies. This paper proposes a sound field reproduction algorithm,
which matches the acoustic velocity vectors in a circular listening area. In
previous work, acoustic velocity vectors are matched either at sweet spots or
on the boundary of the listening area. Sweet spots restrict listener's
movement, whereas measuring the acoustic velocity vectors on the boundary
requires complicated measurement setup. This paper proposes the cylindrical
harmonic coefficients of the acoustic velocity vectors in a circular area (CHV
coefficients), which are calculated from the cylindrical harmonic coefficients
of the global pressure (global CHP coefficients) by using the sound field
translation formula. The global CHP coefficients can be measured by a circular
microphone array, which can be bought off-the-shelf. By matching the CHV
coefficients, the acoustic velocity vectors are reproduced throughout the
listening area. Hence, listener's movements are allowed. Simulations show that
at low frequency, where the acoustic velocity vectors are the dominant factor
for localization, the proposed reproduction method based on the CHV
coefficients results in higher accuracy in reproduced acoustic velocity vectors
when compared with traditional method based on the global CHP coefficients. | 2403.12630v1 |
1994-05-16 | Chaotic Scattering Theory of Transport and Reaction-Rate Coefficients | The chaotic scattering theory is here extended to obtain escape-rate
expressions for the transport coefficients appropriate for a simple classical
fluid, or for a chemically reacting system. This theory allows various
transport coefficients such as the coefficients of viscosity, thermal
conductivity, etc., to be expressed in terms of the positive Lyapunov exponents
and Kolmogorov-Sinai entropy of a set of phase space trajectories that take
place on an appropriate fractal repeller. This work generalizes the previous
results of Gaspard and Nicolis for the coefficient of diffusion of a particle
moving in a fixed array of scatterers. | 9405010v1 |
1997-09-17 | Transport Coefficients of InSb in a Strong Magnetic Field | Improvement of a superconducting magnet system makes induction of a strong
magnetic field easier. This fact gives us a possibility of energy conversion by
the Nernst effect. As the first step to study the Nernst element, we measured
the conductivity, the Hall coefficient, the thermoelectric power and the Nernst
coefficient of the InSb, which is one of candidates of the Nernst elements.
From this experiment, it is concluded that the Nernst coefficient is smaller
than the theoretical values. On the other hand, the conductivity, the Hall
coefficient ant the thermoelectric power has the values expected by the theory. | 9709188v1 |
2003-08-11 | Methods of calculation of a friction coefficient: Application to the nanotubes | In this work we develop theoretical and numerical methods of calculation of a
dynamic friction coefficient. The theoretical method is based on an adiabatic
approximation which allows us to express the dynamic friction coefficient in
terms of the time integral of the autocorrelation function of the force between
both sliding objects. The motion of the objects and the autocorrelation
function can be numerically calculated by molecular-dynamics simulations. We
have successfully applied these methods to the evaluation of the dynamic
friction coefficient of the relative motion of two concentric carbon nanotubes.
The dynamic friction coefficient is shown to increase with the temperature. | 0308206v2 |
2005-03-21 | Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions | We evaluate the virial coefficients B_k for k<=10 for hard spheres in
dimensions D=2,...,8. Virial coefficients with k even are found to be negative
when D>=5. This provides strong evidence that the leading singularity for the
virial series lies away from the positive real axis when D>=5. Further analysis
provides evidence that negative virial coefficients will be seen for some k>10
for D=4, and there is a distinct possibility that negative virial coefficients
will also eventually occur for D=3. | 0503525v1 |
2005-10-18 | Demonstration of electron filtering to increase the Seebeck coefficient in ErAs:InGaAs/InGaAlAs superlattices | In this letter, we explore electron filtering as a technique to increase
Seebeck coefficient and the thermoelectric power factor of heterostructured
materials over that of the bulk. We present a theoretical model in which
Seebeck coefficient and the power factor can be increased in an InGaAs based
composite material. Experimental measurements of the cross-plane Seebeck
coefficient are presented and confirm the importance of the electron filtering
technique to decouple the electrical conductivity and Seebeck coefficient to
increase the thermoelectric power factor. | 0510490v1 |
2003-10-01 | One-loop calculation of mass dependent ${\cal O}(a)$ improvement coefficients for the relativistic heavy quarks on the lattice | We carry out the one-loop calculation of mass dependent ${\cal O}(a)$
improvement coefficients in the relativistic heavy quark action recently
proposed, employing the ordinary perturbation theory with the fictitious gluon
mass as an infrared regulator. We also determine renormalization factors and
improvement coefficients for the axial-vector current at the one-loop level. It
is shown that the improvement coefficients are infrared finite at the one-loop
level if and only if the improvement coefficients in the action are properly
tuned at the tree level. | 0310001v2 |
2006-03-31 | Dissipation coefficients for supersymmetric inflatonary models | Dissipative effects can lead to a friction term in the equation of motion for
an inflaton field during the inflationary era. The friction term may be linear
and localised, in which case it is described by a dissipation coefficient. The
dissipation coefficient is calculated here in a supersymmetric model with a two
stage decay process in which the inflaton decays into a thermal gas of light
particles through a heavy intermediate. At low temperatures, the dissipation
coefficient $\propto T^3$ in a thermal approximation. Results are also given
for a non-equilibrium anzatz. The dissipation coefficient is consistent with a
warm inflationary regime for moderate ($\sim 0.1$) values of the coupling
constants. | 0603266v1 |
2001-03-06 | Multiple reflection expansion and heat kernel coefficients | We propose the multiple reflection expansion as a tool for the calculation of
heat kernel coefficients. As an example, we give the coefficients for a sphere
as a finite sum over reflections, obtaining as a byproduct a relation between
the coefficients for Dirichlet and Neumann boundary conditions. Further, we
calculate the heat kernel coefficients for the most general matching conditions
on the surface of a sphere, including those cases corresponding to the presence
of delta and delta prime background potentials. In the latter case, the
multiple reflection expansion is shown to be non-convergent. | 0103037v2 |
2004-12-02 | Twistor Space Structure of the Box Coefficients of N=1 One-loop Amplitudes | We examine the coefficients of the box functions in N=1 supersymmetric
one-loop amplitudes. We present the box coefficients for all six point N=1
amplitudes and certain all $n$ example coefficients. We find for ``next-to
MHV'' amplitudes that these box coefficients have coplanar support in twistor
space. | 0412023v2 |
2001-12-04 | Periodicity properties of coefficients of half integral weight modular forms | In this paper we prove a theorem about the coefficients in a block of a half
integral weight modular form. We show that the result of Serre and Stark for
weight 1/2 forms does not generalize to higher higher weights.
Let f be a half integral weight cusp form of weight at leat 3/2. We consider
blocks of coefficients of f and prove that, under some weak assumptions on f,
if such a coefficient block is periodic when considered as a function of in the
square root of its index, then it must vanish completely. The proof is analytic
in nature and uses Shimura's lifting theorem together with estimates on the
order of growth of Fourier coefficients of modular forms. | 0112320v1 |
2004-03-09 | An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials | In 1997 the author found a criterion for the Riemann hypothesis for the
Riemann zeta function, involving the nonnegativity of certain coefficients
associated with the Riemann zeta function. In 1999 Bombieri and Lagarias
obtained an arithmetic formula for these coefficients using the ``explicit
formula'' of prime number theory. In this paper, the author obtains an
arithmetic formula for corresponding coefficients associated with the Euler
product of Hecke polynomials, which is essentially a product of L-functions
attached to weight 2 cusp forms (both newforms and oldforms) over Hecke
congruence subgroups. The nonnegativity of these coefficients gives a criterion
for the Riemann hypothesis for all these L-functions at once. | 0403148v2 |
2004-07-02 | A probabilistic approach to $q$-polynomial coefficients, Euler and Stirling numbers | It is known that Bernoulli scheme of independent trials with two outcomes is
connected with the binomial coefficients. The aim of this paper is to indicate
stochastic processes which are connected with the $q$-polynomial coefficients
(in particular, with the $q$-binomial coefficients, or the Gaussian
polynomials), Stirling numbers of the first and the second kind, and Euler
numbers in a natural way. A probabilistic approach allows us to give very
simple proofs of some identities for these coefficients. | 0407029v1 |
2004-09-27 | Apparent Singularities of Linear Difference Equations with Polynomial Coefficients | Let L be a linear difference operator with polynomial coefficients. We
consider singularities of L that correspond to roots of the trailing (resp.
leading) coefficient of L. We prove that one can effectively construct a left
multiple with polynomial coefficients L' of L such that every singularity of L'
is a singularity of L that is not apparent. As a consequence, if all
singularities of L are apparent, then L has a left multiple whose trailing and
leading coefficients equal 1. | 0409508v1 |
2005-10-27 | Coefficients for the Farrell-Jones Conjecture | We introduce the Farrell-Jones Conjecture with coefficients in an additive
category with G-action. This is a variant of the Farrell-Jones Conjecture about
the algebraic K- or L-Theory of a group ring RG. It allows to treat twisted
group rings and crossed product rings. The conjecture with coefficients is
stronger than the original conjecture but it has better inheritance properties.
Since known proofs using controlled algebra carry over to the set-up with
coefficients we obtain new results about the original Farrell-Jones Conjecture.
The conjecture with coefficients implies the fibered version of the
Farrell-Jones Conjecture. | 0510602v1 |
1993-09-22 | Symmetry properties of SU3 vector coupling coefficients | A presentation of the problem of calculating the vector coupling coefficients
for $SU3 \supset SU2 \otimes U1$ is made, in the spirit of traditional
treatments of SU2 coupling. The coefficients are defined as the overlap matrix
element between product states and a coupled state with good SU3 quantum
numbers. A technique for resolution of the outer degeneracy problem, based upon
actions of the infinitesimal generators of SU3 is developed, which
automatically produces vector coupling coefficients with symmetries under
exchange of state labels which parallel the familiar symmetries of the SU2
case. An algorithm for efficient computation of these coefficients is outlined,
for which an ANSI C code is available. | 9309023v1 |
2003-12-16 | Symmetry energy coefficients for asymmetric nuclear matter | Symmetry energy coefficients of asymmetric nuclear matter are investigated as
the inverse of nuclear matter polarizabilities with two different approaches.
Firstly a general calculation shows they may depend on the neutron-proton
asymmetry itself. The choice of particular prescriptions for the density
fluctuations lead to certain isospin (n-p asymmetry) dependences of the
polarizabilities. Secondly, with Skyrme type interactions, the static limit of
the dynamical polarizability is investigated corresponding to the inverse
symmetry energy coefficient which assumes different values at different
asymmetries (and densities and temperatures). The symmetry energy coefficient
(in the isovector channel) is found to increase as n-p asymmetries increase.
The spin symmetry energy coefficient is also briefly investigated. | 0312064v1 |
2003-03-12 | Accurate relativistic many-body calculations of van der Waals coefficients C_8 and C_10 for alkali-metal dimers | We consider long-range interactions between two alkali-metal atoms in their
respective ground states. We extend the previous relativistic many-body
calculations of C_6 dispersion coefficients [Phys.Rev. Lett. {\bf 82}, 3589
(1999)] to higher-multipole coefficients C_8 and C_10. A special attention is
paid to usually omitted contribution of core-excited states. We calculate this
contribution within relativistic random-phase approximation and demonstrate
that for heavy atoms core excitations contribute as much as 10% to the
dispersion coefficients. We tabulate results for both homonuclear and
heteronuclear dimers and estimate theoretical uncertainties. The estimated
uncertainties for C_8 coefficients range from 0.5% for Li_2 to 4% for Cs_2. | 0303048v1 |
2007-06-15 | Materials with a desired refraction coefficient can be made by embedding small particles | A method is proposed to create materials with a desired refraction
coefficient, possibly negative one. The method consists of embedding into a
given material small particles. Given $n_0(x)$, the refraction coefficient of
the original material in a bounded domain $D \subset \R^3$, and a desired
refraction coefficient $n(x)$, one calculates the number $N(x)$ of small
particles, to be embedded in $D$ around a point $x \in D$ per unit volume of
$D$, in order that the resulting new material has refraction coefficient
$n(x)$. | 0706.2322v1 |
2007-10-10 | On numerical averaging of the conductivity coefficient using two-scale extensions | In this article we compare solutions to elliptic problems having rapidly
oscillated conductivity (permeability, etc) coefficient with solutions to
corresponding homogenized problems obtained from two-scale extensions of the
initial coefficient. The comparison is done numerically on several one and two
dimensional test problems with randomly generated coefficients for different
intensities of oscillation. The dependency of the approximation error on the
size of averaging is investigated. | 0710.2072v1 |
2008-02-11 | Comments on combinatorial interpretation of fibonomial coefficients - an email style letter | Up to our knowledge -since about 126 years we were lacking of classical type
combinatorial interpretation of Fibonomial coefficients as it was Lukas
\cite{1} - to our knowledge -who was the first who had defined Finonomial
coefficients and derived a recurrence for them (see Historical Note in
\cite{2,3}). Here we inform that a join combinatorial interpretation was found
\cite{4} for all binomial-type coefficient - Fibonomial coefficients included. | 0802.1381v1 |
2008-06-18 | Elliptic and parabolic second-order PDEs with growing coefficients | We consider a second-order parabolic equation in $\bR^{d+1}$ with possibly
unbounded lower order coefficients. All coefficients are assumed to be only
measurable in the time variable and locally H\"older continuous in the space
variables. We show that global Schauder estimates hold even in this case. The
proof introduces a new localization procedure. Our results show that the
constant appearing in the classical Schauder estimates is in fact independent
of the $L_{\infty}$-norms of the lower order coefficients. We also give a proof
of uniqueness which is of independent interest even in the case of bounded
coefficients. | 0806.3100v1 |
2008-10-30 | Neighboring ternary cyclotomic coefficients differ by at most one | A cyclotomic polynomial Phi_n(x) is said to be ternary if n=pqr with p,q and
r distinct odd prime factors. Ternary cyclotomic polynomials are the simplest
ones for which the behaviour of the coefficients is not completely understood.
Eli Leher showed in 2007 that neighboring ternary cyclotomic coefficients
differ by at most four. We show that, in fact, they differ by at most one.
Consequently, the set of coefficients occurring in a ternary cyclotomic
polynomial consists of consecutive integers.
As an application we reprove in a simpler way a result of Bachman from 2004
on ternary cyclotomic polynomials with an optimally large set of coefficients. | 0810.5496v1 |
2009-09-02 | Creating materials with a desired refraction coefficient | A method is given for creating material with a desired refraction
coefficient. The method consists of embedding into a material with known
refraction coefficient many small particles of size $a$. The number of
particles per unit volume around any point is prescribed, the distance between
neighboring particles is $O(a^{\frac{2-\kappa}{3}})$ as $a\to 0$, $0<\kappa<1$
is a fixed parameter. The total number of the embedded particle is
$O(a^{\kappa-2})$. The physical properties of the particles are described by
the boundary impedance $\zeta_m$ of the $m-th$ particle,
$\zeta_m=O(a^{-\kappa})$ as $a\to 0$. The refraction coefficient is the
coefficient $n^2(x)$ in the wave equation $[\nabla^2+k^2n^2(x)]u=0$. | 0909.0521v1 |
2009-12-21 | The K-level crossings of a random algebraic polynomial with dependent coefficients | For a random polynomial with standard normal coefficients, two cases of the
K-level crossings have been considered by Farahmand. When the coefficients are
independent, Farahmand was able to derive an asymptotic value for the expected
number of level crossings, even if K is allowed to grow to infinity.
Alternatively, it was shown that when the coefficients have a constant
covariance, the expected number of level crossings is reduced by half. In this
paper we are interested in studying the behavior for dependent standard normal
coefficients where the covariance is decaying and no longer constant. Using
techniques similar to those of Farahmand, we will be able to show that for a
wide range of covariance functions behavior similar to the independent case can
be expected. | 0912.4065v1 |
2010-04-26 | Motivic decompositions of projective homogeneous varieties and change of coefficients | We prove that under some assumptions on an algebraic group $G$,
indecomposable direct summands of the motive of a projective $G$-homogeneous
variety with coefficients in $\mathbb{F}_p$ remain indecomposable if the ring
of coefficients is any field of characteristic $p$. In particular for any
projective $G$-homogeneous variety $X$, the decomposition of the motive of $X$
in a direct sum of indecomposable motives with coefficients in any finite field
of characteristic $p$ corresponds to the decomposition of the motive of $X$
with coefficients in $\mathbb{F}_p$. We also construct a counterexample to this
result in the case where $G$ is arbitrary. | 1004.4417v2 |
2010-08-30 | Non-vanishing of Taylor coefficients and Poincaré series | We prove recursive formulas for the Taylor coefficients of cusp forms, such
as Ramanujan's Delta function, at points in the upper half-plane. This allows
us to show the non-vanishing of all Taylor coefficients of Delta at CM points
of small discriminant as well as the non-vanishing of certain Poincar\'e
series. At a "generic" point all Taylor coefficients are shown to be non-zero.
Some conjectures on the Taylor coefficients of Delta at CM points are stated. | 1008.5092v3 |
2011-04-18 | Evidence of electron fractionalization in the Hall coefficient at Mott criticality | Hall coefficient implies the mechanism for reconstruction of a Fermi surface,
distinguishing competing scenarios for Mott criticality such as electron
fractionalization, dynamical mean-field theory, and metal-insulator transition
driven by symmetry breaking. We find that electron fractionalization leaves a
signature for the Hall coefficient at Mott criticality in two dimensions, a
unique feature differentiated from other theories. We evaluate the Hall
coefficient based on the quantum Boltzman equation approach, guaranteeing gauge
invariance in both longitudinal and transverse transport coefficients. | 1104.3368v2 |
2011-06-02 | A new and efficient method for the computation of Legendre coefficients | An efficient procedure for the computation of the coefficients of Legendre
expansions is here presented. We prove that the Legendre coefficients
associated with a function f(x) can be represented as the Fourier coefficients
of an Abel-type transform of f(x). The computation of N Legendre coefficients
can then be performed in O(N log N) operations with a single Fast Fourier
Transform of the Abel-type transform of f(x). | 1106.0463v1 |
2011-06-23 | The expansion in ultraspherical polynomials: a simple procedure for the fast computation of the ultraspherical coefficients | We present a simple and fast algorithm for the computation of the
coefficients of the expansion of a function f(cos u) in ultraspherical
(Gegenbauer) polynomials. We prove that these coefficients coincide with the
Fourier coefficients of an Abel-type transform of the function f(cos u). This
allows us to fully exploit the computational efficiency of the Fast Fourier
Transform, computing the first N ultraspherical coefficients in just O (N log_2
N) operations. | 1106.4718v2 |
2011-10-27 | OPE coefficient functions in terms of composite operators only. Singlet case | A method for calculating coefficient functions of the operator product
expansion, which was previously derived for the non-singlet case, is
generalized for the singlet coefficient functions. The resulting formula
defines coefficient functions entirely in terms of corresponding singlet
composite operators without applying to elementary (quark and gluon) fields.
Both "diagonal" and "non-diagonal" gluon coefficient functions in the product
expansion of two electromagnetic currents are calculated in QCD. Their
renormalization properties are studied. | 1110.6059v2 |
2012-01-17 | Self-diffusion in granular gases: An impact of particles' roughness | An impact of particles' roughness on the self-diffusion coefficient in
granular gases is investigated. For a simplified collision model where the
normal and tangential restitution coefficients are assumed to be constant we
develop an analytical theory for the diffusion coefficient, which takes into
account non-Maxwellain form of the velocity-angular velocity distribution
function. We perform molecular dynamics simulations for a gas in a homogeneous
cooling state and study the dependence of the self-diffusion coefficient on
restitution coefficients. Our theoretical results are in a good agreement with
the simulation data. | 1201.3524v2 |
2012-01-23 | Constraints on the second order transport coefficients of an uncharged fluid | In this note we have tried to determine how the existence of a local entropy
current with non-negative divergence constrains the second order transport
coefficients of an uncharged fluid, following the procedure described in
\cite{Romatschke:2009kr}. Just on symmetry ground the stress tensor of an
uncharged fluid can have 15 transport coefficients at second order in
derivative expansion. The condition of entropy-increase gives five relations
among these 15 coefficients. So finally the relativistic stress tensor of an
uncharged fluid can have 10 independent transport coefficients at second order. | 1201.4654v2 |
2012-01-25 | Fourier coefficients of three-dimensional vector-valued modular forms | A thorough analysis is made of the Fourier coefficients for vector-valued
modular forms associated to three-dimensional irreducible representations of
the modular group. In particular, the following statement is verified for all
but a finite number of equivalence classes: if a vector-valued modular form
associated to such a representation has rational Fourier coefficients, then
these coefficients have "unbounded denominators", i.e. there is a prime number
p, depending on the representation, which occurs to an arbitrarily high power
in the denominators of the coefficients. This provides a verification in the
three-dimensional setting of a generalization of a long-standing conjecture
about noncongruence modular forms. | 1201.5165v2 |
2012-06-26 | Exact Recovery of Sparsely-Used Dictionaries | We consider the problem of learning sparsely used dictionaries with an
arbitrary square dictionary and a random, sparse coefficient matrix. We prove
that $O (n \log n)$ samples are sufficient to uniquely determine the
coefficient matrix. Based on this proof, we design a polynomial-time algorithm,
called Exact Recovery of Sparsely-Used Dictionaries (ER-SpUD), and prove that
it probably recovers the dictionary and coefficient matrix when the coefficient
matrix is sufficiently sparse. Simulation results show that ER-SpUD reveals the
true dictionary as well as the coefficients with probability higher than many
state-of-the-art algorithms. | 1206.5882v1 |
2012-07-13 | On extrapolation of virial coefficients of hard spheres | Several methods of extrapolating the virial coefficients, including those
proposed in this work, are discussed. The methods are demonstrated on
predicting higher virial coefficients of one-component hard spheres. Estimated
values of the eleventh to fifteenth virial coefficients are suggested. It has
been speculated that the virial coefficients, B_n, beyond B_{14} may decrease
with increasing n, and may reach negative values at large n. The extrapolation
techniques may be utilized in other fields of science where the art of
extrapolation plays a role. | 1207.3259v1 |
2012-10-06 | Fermion observables for Lorentz violation | The relationship between experimental observables for Lorentz violation in
the fermion sector and the coefficients for Lorentz violation appearing in the
lagrangian density is investigated in the minimal Standard-Model Extension. The
definitions of the 44 fermion-sector observables, called the tilde
coefficients, are shown to have a block structure. The c coefficients decouple
from all the others, have six subspaces of dimension 1, and one of dimension 3.
The remaining tilde coefficients form eight blocks, one of dimension 6, one of
dimension 2, three of dimension 5, and three of dimension 4. By inverting these
definitions, thirteen limits on the electron-sector tilde coefficients are
deduced. | 1210.2003v1 |
2012-10-28 | Dispersion for 1-d Scrodinger and wave equation with BV coefficients | In this paper we analyze the dispersion for one dimensional wave and
Schrodinger equations with BV coefficients. In the case of the wave equation we
give a complete answer in terms of the variation of the logarithm of the
coefficient showing that dispersion occurs if this variation is small enough
but it may fail when the variation goes beyond a sharp threshold. For the
Schrodigner equation we prove that the dispersion holds under the same
smallness assumption on the variation of the coefficient. But, whether
dispersion may fail for larger coefficients is unknown for the Schrodinger
equation. | 1210.7415v2 |
2012-11-27 | q-Catalan bases and their dual coefficients | We define q-Catalan bases which are a generalization of the q-polynomials
z^n(z,q)_n. The determination of their dual bases involves some q-power series
termed dual coefficients. We show how these dual coefficients occur in the
solution of some equations with q-commuting coefficients and solve an abstract
q-Segner recursion. We study the connection between this theory and Garsia's
(1981). The overall flavor of this work is to show how some properties of
q-Catalan numbers are in fact instances of much more general results on dual
coefficients. | 1211.6206v1 |
2013-07-10 | Long range interaction coefficients for ytterbium dimers | We evaluate the electric-dipole and electric-quadrupole static and dynamic
polarizabilities for the 6s^2 ^1S_0, 6s6p ^3P_0, and 6s6p ^3P_1 states and
estimate their uncertainties. A methodology is developed for an accurate
evaluation of the van der Waals coefficients of dimers involving excited state
atoms with strong decay channel to the ground state. This method is used for
evaluation of the long range interaction coefficients of particular
experimental interest, including the C_6 coefficients for the Yb-Yb
^1S_0+^3P_{0,1} and ^3P_0+^3P_0 dimers and C_8 coefficients for the ^1S_0+^1S_0
and ^1S_0+^3P_1 dimers. | 1307.2656v1 |
2013-07-23 | Polynomials with integer coefficients and their zeros | We study several related problems on polynomials with integer coefficients.
This includes the integer Chebyshev problem, and the Schur problems on means of
algebraic numbers. We also discuss interesting applications to approximation by
polynomials with integer coefficients, and to the growth of coefficients for
polynomials with roots located in prescribed sets. The distribution of zeros
for polynomials with integer coefficients plays an important role in all of
these problems. | 1307.6200v1 |
2013-08-13 | How to Extend Karolyi and Nagy's BRILLIANT Proof of the Zeilberger-Bressoud q-Dyson Theorem in order to Evaluate ANY Coefficient of the q-Dyson Product | We show how to extend the Karolyi-Nagy beautiful proof of the
Zeilberger-Bressoud q-Dyson theorem, (first proved by Zeilberger and Bressoud
in 1985, and originally conjectured by George Andrews in 1975), that states
that the constant term of a certain Laurent polynomial equals the q-multinomial
coefficient, how to evaluate any other specific coefficient. The algorithm
implies that any such coefficient is always a certain rational function (that
the algorithm finds) times the q-multinomial coefficient. | 1308.2983v1 |
2013-09-25 | Matrix Fourier transform with discontinuous coefficients | The explicit construction of direct and inverse Fourier's vector transform
with discontinuous coefficients is presented. The technique of applying
Fourier's vector transform with discontinuous coefficients for solving problems
of mathematical physics.Multidimensional integral transformations with
non-separated variables for problems with discontinuous coefficients are
constructed in this work. The coefficient discontinuities focused on the of
parallel hyperplanes. In this work explicit formulas for the kernels in the
case of ideal coupling conditions are obtained; the basic identity of the
integral transform is proved; technique of integral transforms is developed | 1309.6566v1 |
2013-11-25 | A model for generating tunable clustering coefficients independent of the number of nodes in scale free and random networks | Probabilistic networks display a wide range of high average clustering
coefficients independent of the number of nodes in the network. In particular,
the local clustering coefficient decreases with the degree of the subtending
node in a complicated manner not explained by any current models. While a
number of hypotheses have been proposed to explain some of these observed
properties, there are no solvable models that explain them all. We propose a
novel growth model for both random and scale free networks that is capable of
predicting both tunable clustering coefficients independent of the network
size, and the inverse relationship between the local clustering coefficient and
node degree observed in most networks. | 1311.6401v1 |
2014-03-11 | Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces | We consider both divergence and non-divergence parabolic equations on a half
space in weighted Sobolev spaces. All the leading coefficients are assumed to
be only measurable in the time and one spatial variable except one coefficient,
which is assumed to be only measurable either in the time or the spatial
variable. As functions of the other variables the coefficients have small
bounded mean oscillation (BMO) semi-norms. The lower-order coefficients are
allowed to blow up near the boundary with a certain optimal growth condition.
As a corollary, we also obtain the corresponding results for elliptic
equations. | 1403.2459v1 |
2014-06-11 | Bounds on the Kronecker coefficients | We present several upper and lower bounds on the Kronecker coefficients of
the symmetric group. We prove $k$-stability of the Kronecker coefficients
generalizing the (usual) stability, and giving a new upper bound. We prove a
lower bound via the characters of $S_n$. We apply these and other results to
generalize Sylvester's unimodality of the $q$-binomial coefficients
$\binom{n}{k}_q$ as polynomials in $q$: we derive explicit sharp bounds on the
differences of their consecutive coefficients. | 1406.2988v2 |
2014-06-13 | A product formula for certain Littlewood-Richardson coefficients for Jack and Macdonald polynomials | Jack polynomials generalize several classical families of symmetric
polynomials, including Schur polynomials, and are further generalized by
Macdonald polynomials. In 1989, Richard Stanley conjectured that if the
Littlewood-Richardson coefficient for a triple of Schur polynomials is 1, then
the corresponding coefficient for Jack polynomials can be expressed as a
product of weighted hooks of the Young diagrams associated to the partitions
indexing the coefficient. We prove a special case of this conjecture in which
the partitions indexing the Littlewood-Richardson coefficient have at most 3
parts. We also show that this result extends to Macdonald polynomials. | 1406.3391v1 |
2014-10-20 | An overpartition analogue of the $q$-binomial coefficients | We define an overpartition analogue of Gaussian polynomials (also known as
$q$-binomial coefficients) as a generating function for the number of
overpartitions fitting inside the $M \times N$ rectangle. We call these new
polynomials over Gaussian polynomials or over $q$-binomial coefficients. We
investigate basic properties and applications of over $q$-binomial
coefficients. In particular, via the recurrences and combinatorial
interpretations of over q-binomial coefficients, we prove a Rogers-Ramaujan
type partition theorem. | 1410.5301v2 |
2015-03-18 | Re-visiting the Distance Coefficient in Gravity Model | This paper revisits the classic gravity model in international trade and
reexamines the distance coefficient. As pointed out by Frankel (1997), this
coefficient measures the relative unit transportation cost between short
distance and long distance rather than the absolute level of average
transportation cost. Our results confirm this point in the sense that the
coefficient has been very stable between 1991-2006, despite the obvious
technological progress taken place during this period. Moreover, by comparing
the sensitivity of these coefficients to change in oil prices at short periods
of time, in which technology remained unchanged, we conclude that the average
technology has indeed reduced the average trading cost. The results are robust
when we divide the aggregate international trades into different industries. | 1503.05283v2 |
2015-06-09 | Combinatorics on a family of reduced Kronecker coefficients | The reduced Kronecker coefficients are particular instances of Kronecker
coefficients that contain enough information to recover them. In this notes we
compute the generating function of a family of reduced Kronecker coefficients.
We also gives its connection to the plane partitions, which allows us to check
that this family satisfies the saturation conjecture for reduced Kronecker
coefficients, and that they are weakly increasing. Thanks to its generating
function we can describe our family by a quasipolynomial, specifying its degree
and period. | 1506.02829v1 |
2015-12-28 | Non-vanishing and sign changes of Hecke eigenvalues for half-integral weight cusp forms | In this paper, we consider three problems about signs of the Fourier
coefficients of a cusp form $\mathfrak{f}$ with half-integral
weight:\begin{itemize}\item[--]The first negative coefficient of the sequence
$\{\mathfrak{a}\_{\mathfrak{f}}(tn^2)\}\_{n\in \N}$,\item[--]The number of
coefficients $\mathfrak{a}\_{\mathfrak{f}}(tn^2)$ of same
signs,\item[--]Non-vanishing of coefficients
$\mathfrak{a}\_{\mathfrak{f}}(tn^2)$ in short intervals and in arithmetic
progressions,\end{itemize}where $\mathfrak{a}\_{\mathfrak{f}}(n)$ is the $n$-th
Fourier coefficient of $\mathfrak{f}$ and $t$ is a square-free integersuch that
$\mathfrak{a}\_{\mathfrak{f}}(t)\not=0$. | 1512.08400v1 |
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