3,843 research outputs found

### The $q$-log-convexity of Domb's polynomials

In this paper, we prove the $q$-log-convexity of Domb's polynomials, which
was conjectured by Sun in the study of Ramanujan-Sato type series for powers of
$\pi$. As a result, we obtain the log-convexity of Domb's numbers. Our proof is
based on the $q$-log-convexity of Narayana polynomials of type $B$ and a
criterion for determining $q$-log-convexity of self-reciprocal polynomials.Comment: arXiv admin note: substantial text overlap with arXiv:1308.273

### On the $q$-log-convexity conjecture of Sun

In his study of Ramanujan-Sato type series for $1/\pi$, Sun introduced a
sequence of polynomials $S_n(q)$ as given by
$S_n(q)=\sum\limits_{k=0}^n{n\choose k}{2k\choose k}{2(n-k)\choose n-k}q^k,$
and he conjectured that the polynomials $S_n(q)$ are $q$-log-convex. By
imitating a result of Liu and Wang on generating new $q$-log-convex sequences
of polynomials from old ones, we obtain a sufficient condition for determining
the $q$-log-convexity of self-reciprocal polynomials. Based on this criterion,
we then give an affirmative answer to Sun's conjecture

### Riordan Paths and Derangements

Riordan paths are Motzkin paths without horizontal steps on the x-axis. We
establish a correspondence between Riordan paths and
$(321,3\bar{1}42)$-avoiding derangements. We also present a combinatorial proof
of a recurrence relation for the Riordan numbers in the spirit of the
Foata-Zeilberger proof of a recurrence relation on the Schr\"oder numbers.Comment: 9 pages, 2 figure

### Phonon-assisted tunneling in asymmetric resonant tunneling structures

Based on the dielectric continuum model, we calculated the phonon assisted
tunneling (PAT) current of general double barrier resonant tunneling structures
(DBRTSs) including both symmetric and antisymmetric ones. The results indicate
that the four higher frequency interface phonon modes (especially the one which
peaks at either interface of the emitter barrier) dominate the PAT processes,
which increase the valley current and decrease the PVR of the DBRTSs. We show
that an asymmetric structure can lead to improved performance.Comment: 1 paper and 5 figure

### Computing Loops With at Most One External Support Rule

If a loop has no external support rules, then its loop formula is equivalent to a set of unit clauses; and if it has exactly one external support rule, then its loop formula is equivalent to a set of binary clauses. In this paper, we consider how to compute these loops and their loop formulas in a normal logic program, and use them to derive consequences of a logic program. We show that an iterative procedure based on unit propagation, the program completion and the loop formulas of loops with no external support rules can compute the same consequences as the “Expand ” operator in smodels, which is known to compute the well-founded model when the given normal logic program has no constraints. We also show that using the loop formulas of loops with at most one external support rule, the same procedure can compute more consequences, and these extra consequences can help ASP solvers such as cmodels to find answer sets of certain logic programs

### http://zoobank.org/urn:lsid:zoobank.org:pub:6999F7D6-7644-46C7-B86D-8D68E4E19179

www.mapress.com/zootaxa

### Spin Hall effect in the kagome lattice with Rashba spin-orbit interaction

We study the spin Hall effect in the kagom\'{e} lattice with Rashba
spin-orbit coupling. The conserved spin Hall conductance $\sigma_{xy}^{s}$ (see
text) and its two components, i.e., the conventional term $\sigma_{xy}^{s0}$
and the spin-torque-dipole term $\sigma_{xy}^{s\tau}$, are numerically
calculated, which show a series of plateaus as a function of the electron Fermi
energy $\epsilon_{F}$. A consistent two-band analysis, as well as a Berry-phase
interpretation, is also given. We show that these plateaus are a consequence of
the various Fermi-surface topologies when tuning $\epsilon_{F}$. In particular,
we predict that compared to the case with the Fermi surface encircling the
$\mathbf{\Gamma}$ point in the Brillouin zone, the amplitude of the spin Hall
conductance with the Fermi surface encircling the $\mathbf{K}$ points is twice
enhanced, which makes it highly meaningful in the future to systematically
carry out studies of the $\mathbf{K}$-valley spintronics.Comment: 7 pages, 3 figures. Phys. Rev. B (in press

### On oriented graphs with minimal skew energy

Let $S(G^\sigma)$ be the skew-adjacency matrix of an oriented graph
$G^\sigma$. The skew energy of $G^\sigma$ is defined as the sum of all singular
values of its skew-adjacency matrix $S(G^\sigma)$. In this paper, we first
deduce an integral formula for the skew energy of an oriented graph. Then we
determine all oriented graphs with minimal skew energy among all connected
oriented graphs on $n$ vertices with $m \ (n\le m < 2(n-2))$ arcs, which is an
analogy to the conjecture for the energy of undirected graphs proposed by
Caporossi {\it et al.} [G. Caporossi, D. Cvetkovi$\acute{c}$, I. Gutman, P.
Hansen, Variable neighborhood search for extremal graphs. 2. Finding graphs
with external energy, J. Chem. Inf. Comput. Sci. 39 (1999) 984-996.]Comment: 15 pages. Actually, this paper was finished in June 2011. This is an
updated versio

### Why does the Engel method work? Food demand, economies of size and household survey methods

Estimates of household size economies are needed for the analysis of poverty and inequality. This paper shows that Engel estimates of size economies are large when household expenditures are obtained by respondent recall but small when expenditures are obtained by daily recording in diaries. Expenditure estimates from recall surveys appear to have measurement errors correlated with household size. As well as demonstrating the fragility of Engel estimates of size economies, these results help resolve a puzzle raised by Deaton and Paxson (1998) about differences between rich and poor countries in the effect of household size on food demand

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