The qq-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 qq-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

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

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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

The value of repeated lumbar puncture to test for xanthochromia, in patients with clinical suspicion of subarachnoid haemorrhage, with CT-negative and initial traumatic tap.

OBJECTIVES: For the diagnosis of subarachnoid haemorrhage (SAH), the presence of cerebrospinal fluid (CSF) xanthochromia is still considered the gold standard for patients with a thunderclap headache, in the absence of blood on brain CT scan. However, a traumatic lumbar puncture (LP) typically results in high concentrations of oxyhaemoglobin in CSF, impairing the detection of xanthochromia and preventing the reliable exclusion of SAH. In this context, the value of a repeat lumbar puncture has not yet been described. MATERIALS AND METHODS: A retrospective case series of suspected SAH patients, with a negative CT scan and initial traumatic LP, managed with a repeat LP to assess for CSF xanthochromia. Clinical notes, laboratory and imaging results were reviewed. RESULTS: Between August 2011 and January 2020, 31 patients with suspected SAH were referred to our neurosurgical unit following negative CT and traumatic LP. A repeat LP was performed in 7 of the 31 patients, 2.4 days (±0.79 SD) after the first traumatic LP. CSF spectrophotometry analysis from repeated LP in all 7 patients was negative for xanthochromia. No adverse clinical events were recorded on average 18 months following discharge. CONCLUSION: A repeat LP performed following a traumatic tap can still yield xanthochromia-negative CSF, thereby, excluding SAH, avoiding unnecessary invasive angiography and overall promoting the safer management of these patients