20,821 research outputs found
Interlacing Log-concavity of the Boros-Moll Polynomials
We introduce the notion of interlacing log-concavity of a polynomial sequence
, where is a polynomial of degree m with
positive coefficients . This sequence of polynomials is said to be
interlacing log-concave if the ratios of consecutive coefficients of
interlace the ratios of consecutive coefficients of for any . Interlacing log-concavity is stronger than the log-concavity. We show that
the Boros-Moll polynomials are interlacing log-concave. Furthermore we give a
sufficient condition for interlacing log-concavity which implies that some
classical combinatorial polynomials are interlacing log-concave.Comment: 10 page
Proof of a Conjecture of Hirschhorn and Sellers on Overpartitions
Let denote the number of overpartitions of . It was
conjectured by Hirschhorn and Sellers that \bar{p}(40n+35)\equiv 0\ ({\rm
mod\} 40) for . Employing 2-dissection formulas of quotients of theta
functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating
function for modulo 5. Using the -parametrization of
theta functions given by Alaca, Alaca and Williams, we give a proof of the
congruence \bar{p}(40n+35)\equiv 0\ ({\rm mod\} 5). Combining this congruence
and the congruence \bar{p}(4n+3)\equiv 0\ ({\rm mod\} 8) obtained by
Hirschhorn and Sellers, and Fortin, Jacob and Mathieu, we give a proof of the
conjecture of Hirschhorn and Sellers.Comment: 11 page
The q-WZ Method for Infinite Series
Motivated by the telescoping proofs of two identities of Andrews and Warnaar,
we find that infinite q-shifted factorials can be incorporated into the
implementation of the q-Zeilberger algorithm in the approach of Chen, Hou and
Mu to prove nonterminating basic hypergeometric series identities. This
observation enables us to extend the q-WZ method to identities on infinite
series. As examples, we will give the q-WZ pairs for some classical identities
such as the q-Gauss sum, the sum, Ramanujan's sum and
Bailey's sum.Comment: 17 page
Isolation, Kinetics, and Performance of a Novel Phenol Degrading Strain
Efficient phenol-degrading bacteria is still the key to the biological treatment of phenol-containing wastewater. In this research, a novel phenol-degrading strain N8 was isolated. According to the 16S rDNA identification, it was concluded that the N8 strain was Bacillus sp. IARI-J-20. The wastewater treatment experiments showed that the phenol
degrading rate of N8 reached 92.8 % at 24 h with the inoculation amount of 15 %, temperature of 30 °C, pH of 7.2, yeast extract addition of 0.08 %, and initial phenol concentration of 225 mg L–1. Haldane’s model was fit for the growth kinetics of the phenol-degrading strain N8 over a wide range of initial phenol concentrations (50–1200 mg L–1),
with kinetic values μmax = 0.33 h−1, Ks = 79.16 mg L–1, and Ki = 122 mg L–1. The yield coefficient reached maximal value when the phenol concentration was 400 mg L–1. When the initial phenol concentration was more than 400 mg L–1, the inhibition effect of phenol became predominant.
This work is licensed under a Creative Commons Attribution 4.0 International License
Skyrmion-skyrmion and skyrmion-edge repulsions in skyrmion-based racetrack memory
Magnetic skyrmions are promising for building next-generation magnetic
memories and spintronic devices due to their stability, small size and the
extremely low currents needed to move them. In particular, skyrmion-based
racetrack memory is attractive for information technology, where skyrmions are
used to store information as data bits instead of traditional domain walls.
Here we numerically demonstrate the impacts of skyrmion-skyrmion and
skyrmion-edge repulsions on the feasibility of skyrmion-based racetrack memory.
The reliable and practicable spacing between consecutive skyrmionic bits on the
racetrack as well as the ability to adjust it are investigated. Clogging of
skyrmionic bits is found at the end of the racetrack, leading to the reduction
of skyrmion size. Further, we demonstrate an effective and simple method to
avoid the clogging of skyrmionic bits, which ensures the elimination of
skyrmionic bits beyond the reading element. Our results give guidance for the
design and development of future skyrmion-based racetrack memory.Comment: 15 pages, 6 figure
On Solving a Generalized Chinese Remainder Theorem in the Presence of Remainder Errors
In estimating frequencies given that the signal waveforms are undersampled
multiple times, Xia et. al. proposed to use a generalized version of Chinese
remainder Theorem (CRT), where the moduli are which are
not necessarily pairwise coprime. If the errors of the corrupted remainders are
within \tau=\sds \max_{1\le i\le k} \min_{\stackrel{1\le j\le k}{j\neq i}}
\frac{\gcd(M_i,M_j)}4, their schemes can be used to construct an approximation
of the solution to the generalized CRT with an error smaller than .
Accurately finding the quotients is a critical ingredient in their approach. In
this paper, we shall start with a faithful historical account of the
generalized CRT. We then present two treatments of the problem of solving
generalized CRT with erroneous remainders. The first treatment follows the
route of Wang and Xia to find the quotients, but with a simplified process. The
second treatment considers a simplified model of generalized CRT and takes a
different approach by working on the corrupted remainders directly. This
approach also reveals some useful information about the remainders by
inspecting extreme values of the erroneous remainders modulo . Both of
our treatments produce efficient algorithms with essentially optimal
performance. Finally, this paper constructs a counterexample to prove the
sharpness of the error bound
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