14,046 research outputs found
Less redundant codes for variable size dictionaries
We report on a family of variable-length codes with less redundancy than the flat code used in most of the variable size dictionary-based compression methods. The length of codes belonging to this family is still bounded above by [log_2/ |D|] where |D| denotes the dictionary size. We describe three of these codes, namely, the balanced code, the phase-in-binary code (PB), and the depth-span code (DS). As the name implies, the balanced code is constructed by a height balanced tree, so it has the shortest average codeword length. The corresponding coding tree for the PB code has an interesting property that it is made of full binary phases, and thus the code can be computed efficiently using simple binary shifting operations. The DS coding tree is maintained in such a way that the coder always finds the longest extendable codeword and extends it until it reaches the maximum length. It is optimal with respect to the code-length contrast. The PB and balanced codes have almost similar improvements, around 3% to 7% which is very close to the relative redundancy in flat code. The DS code is particularly good in dealing with files with a large amount of redundancy, such as a running sequence of one symbol. We also did some empirical study on the codeword distribution in the LZW dictionary and proposed a scheme called dynamic block shifting (DBS) to further improve the codes' performance. Experiments suggest that the DBS is helpful in compressing random sequences. From an application point of view, PB code with DBS is recommended for general practical usage
The monotonicity results and sharp inequalities for some power-type means of two arguments
For with , we define
M_{p}=M^{1/p}(a^{p},b^{p})\text{if}p\neq 0 \text{and} M_{0}=\sqrt{ab}, where
and stand for the arithmetic mean, Heronian mean,
logarithmic mean, identric (exponential) mean, the first Seiffert mean, the
second Seiffert mean, Neuman-S\'{a}ndor mean, power-exponential mean and
exponential-geometric mean, respectively. Generally, if is a mean of
and , then is also, and call "power-type mean". We prove the
power-type means , , , are increasing in on
and establish sharp inequalities among power-type means ,
, , , , , , % . From this a
very nice chain of inequalities for these means
L_{2}<P<N_{1/2}<He<A_{2/3}<I<Z_{1/3}<Y_{1/2} follows. Lastly, a conjecture is
proposed.Comment: 11 page
Nucleation in binary polymer blends: A self-consistent field study
We study the structure and thermodynamics of the critical nuclei in metastable binary polymer blends using the self-consistent field method. At the mean-field level, our results are valid throughout the entire metastable region and provide a smooth crossover from the classical capillary-theory predictions near the coexistence curve to the density functional predictions of Cahn and Hilliard (properly transcribed into expressions involving the parameters of the binary polymer blends) near the spinodal. An estimate of the free energy barrier provides a quantitative criterion (the Ginzburg criterion) for the validity of the (mean-field) self-consistent approach. The region where mean-field theory is valid and where there can be a measurable nucleation rate is shown to be poorly described by the existing limiting theories; our predictions are therefore most relevant in this region. We discuss our results in connection with recent experimental observations by Balsara and co-workers
Neutrino and anti-neutrino transport in accretion disks
We numerically solve the one dimensional Boltzmann equation of the neutrino
and anti-neutrino transport in accretion disks and obtain the fully energy
dependent and direction dependent neutrino and anti-neutrino emitting spectra,
under condition that the distribution of the mass density,temperature and
chemical components are given. Then, we apply the resulting neutrino and
anti-neutrino emitting spectra to calculate the corresponding annihilation rate
of neutrino pairs above the neutrino dominated accretion disk and find that the
released energy resulting from the annihilation of neutrino pairs can not
provide sufficient energy for the most energetic short gamma ray bursts whose
isotropic luminosity can be as high as ergs/s unless the high
temperature zone where the temperature is beyond 10 MeV can stretch over 200 km
in the disk. We also compare the resulting luminosity of neutrinos and
anti-neutrinos with the results from the two commonly used approximate
treatment of the neutrino and anti-neutrino luminosity: the Fermi-Dirac black
body limit and a simplified model of neutrino transport, i.e., the gray body
model, and find that both of them overestimate the neutrino/anti-neutrino
luminosity and their annihilation rate greatly. Additionally, as did in Sawyer
(2003), we also check the validity of the two stream approximation, and find
that it is a good approximation to high accuracy.Comment: Phys. Rev. D in press, 15 preprint papers, 5 figure
Some new applications for heat and fluid flows via fractional derivatives without singular kernel
This paper addresses the mathematical models for the heat-conduction
equations and the Navier-Stokes equations via fractional derivatives without
singular kernel.Comment: This is a preprint of a paper whose final and definite form will be
published in Thermal Science. Paper Submitted 28/ Dec /2016; Revised
20/Jan/2016; Accepted for publication 21/Jan/201
Laboratory photo-chemistry of pyrene clusters: an efficient way to form large PAHs
In this work, we study the photodissociation processes of small PAH clusters
(e.g., pyrene clusters). The experiments are carried out using a quadrupole ion
trap in combination with time-of-flight (QIT-TOF) mass spectrometry. The
results show that pyrene clusters are converted into larger PAHs under the
influence of a strong radiation field. Specifically, pyrene dimer cations
(e.g., [CHCH] or CH), will
photo-dehydrogenate and photo-isomerize to fully aromatic cations (PAHs) (e.g.,
CH) with laser irradiation. The structure of new formed PAHs
and the dissociation energy for these reaction pathways are investigated with
quantum chemical calculations. These studies provide a novel efficient
evolution routes for the formation of large PAHs in the interstellar medium
(ISM) in a bottom-up process that will counteract the top-down conversion of
large PAHs into rings and chains, and provide a reservoir of large PAHs that
can be converted into C and other fullerenes and large carbon cages
Periodicities in the occurrence of aurora as indicators of solar variability
A compilation of records of the aurora observed in China from the Time of the Legends (2000 - 3000 B.C.) to the mid-18th century has been used to infer the frequencies and strengths of solar activity prior to modern times. A merging of this analysis with auroral and solar activity patterns during the last 200 years provides basically continuous information about solar activity during the last 2000 years. The results show periodicities in solar activity that contain average components with a long period (approx. 412 years), three middle periods (approx. 38 years, approx. 77 years, and approx. 130 years), and the well known short period (approx. 11 years)
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