321-polygon-avoiding permutations and Chebyshev polynomials

A 321-k-gon-avoiding permutation pi avoids 321 and the following four patterns: k(k+2)(k+3)...(2k-1)1(2k)23...(k+1), k(k+2)(k+3)...(2k-1)(2k)123...(k+1), (k+1)(k+2)(k+3)...(2k-1)1(2k)23...k, (k+1)(k+2)(k+3)...(2k-1)(2k)123...k. The 321-4-gon-avoiding permutations were introduced and studied by Billey and Warrington [BW] as a class of elements of the symmetric group whose Kazhdan-Lusztig, Poincare polynomials, and the singular loci of whose Schubert varieties have fairly simple formulas and descriptions. Stankova and West [SW] gave an exact enumeration in terms of linear recurrences with constant coefficients for the cases k=2,3,4. In this paper, we extend these results by finding an explicit expression for the generating function for the number of 321-k-gon-avoiding permutations on n letters. The generating function is expressed via Chebyshev polynomials of the second kind.Comment: 11 pages, 1 figur

Certain triple q-integral equations involving third Jackson qq-Bessel functions as kernel

In this paper, we employ the fractional $q$-calculus in solving a triple system of $q$-Integral equations, where the kernel is the third Jackson $q$-Bessel functions. The solution is reduced to two simultaneous Fredholm $q$-integral equation of the second kind. Examples are included. We also apply a result in~[Pacific J. Math. \textbf{275}(1) (2015)63--102] for solutions of dual $q^2$-integral equations to solve certain triple integral equations

Diagnostic value of nuclear cardiology in coronary artery disease

This thesis investigates the diagnostic value of cardiac positron emission tomography when compared to single photon emission computed tomography for detection of coronary artery disease. This prospective study involves comparison of myocardial perfusion single photon emission computed tomography with coronary calcium scores; optimization of nuclear cardiac protocols in cardiac phantom experiments; and determination of diagnostic performance of cardiac positron emission tomography in the evaluation of myocardial viability in patients with significant coronary disease

A determinant approach for generalized qq-Bernoulli polynomials and asymptotic results

In earlier work, we introduced three families of polynomials where the generating function of each set includes one of the three Jackson $q$-analogs of the Bessel function. This paper gives determinant representation for each family, their large $n$ asymptotics, and two expansion theorems for specific classes of entire functions. We include two examples

Optimization of Conical Micro-Diffusers and Micro-Nozzles Considering Entropy Generation

Fluid flow characteristics and entropy generation in a circular diffuser/nozzle element are studied numerically. The flow is assumed to be isothermal, laminar and incompressible with constant thermo-physical properties. The velocity field, mass flow rate, and entropy generation are investigated for several half angles in combination with several values of pressure drops. The effect of diffuser half angle on the entropy generation is investigated and discussed. Furthermore, the effect of the half angle of diffuser on the diffuser efficiency and the effect on the rectification efficiency are explained. It is shown that there is an optimum operation half angle for which the diffuser efficiency has a maximum value. In the case of a micro-diffuser 1 mm long with an inlet diameter of 100 μm, the optimum half angle was found to be 2.5°. These results are based on several parametric simulations ranging from 0 to 7° half angles and covering pressure drops between 500 and 2000 Pa.King Fahd University of Petroleum and Minerals (Deanship of Scientific Research

Quantum Correlations Dynamics In Two Coupled Semiconductor InAs Quantum Dots

We investigate the dynamics of quantum discord and concurrence between two excitonic qubits placed inside two coupled semiconductor quantum dots independently interacting with dephasing reservoirs. We explore their behavior against the dimensionless time and the temperature in both Markovian and non-Markovian environments. Moreover, we analyze the external electric field effects and the F\"orster interaction effects on these correlations. We show that, although the quantum correlations amount is strongly influenced by the variation of the electric field and the F\"orster interaction, their non-Markovian behavior is still preserved under the variation of these two parameters. Furthermore, we show that for large values of temperature and dimensionless time, unlike concurrence which vanishes, nonzero discord can still be observed.Comment: 15 pages, 12 figure

Statistical Error in Particle Simulations of Hydrodynamic Phenomena

We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Specifically, we establish how these errors depend on Mach number, Knudsen number, number of particles, etc. Expressions for the common hydrodynamic variables of interest such as flow velocity, temperature, density, pressure, shear stress and heat flux are derived using equilibrium statistical mechanics. Both volume-averaged and surface-averaged quantities are considered. Comparisons between theory and computations using direct simulation Monte Carlo for dilute gases, and molecular dynamics for dense fluids, show that the use of equilibrium theory provides accurate results.Comment: 24 pages postscript (including 16 figures

Cell Competition Modifies Adult Stem Cell and Tissue Population Dynamics in a JAK-STAT-Dependent Manner.

Throughout their lifetime, cells may suffer insults that reduce their fitness and disrupt their function, and it is unclear how these potentially harmful cells are managed in adult tissues. We address this question using the adult Drosophila posterior midgut as a model of homeostatic tissue and ribosomal Minute mutations to reduce fitness in groups of cells. We take a quantitative approach combining lineage tracing and biophysical modeling and address how cell competition affects stem cell and tissue population dynamics. We show that healthy cells induce clonal extinction in weak tissues, targeting both stem and differentiated cells for elimination. We also find that competition induces stem cell proliferation and self-renewal in healthy tissue, promoting selective advantage and tissue colonization. Finally, we show that winner cell proliferation is fueled by the JAK-STAT ligand Unpaired-3, produced by Minute(-/+) cells in response to chronic JNK stress signaling.This work was supported by a Cancer Research UK Programme Grant (E.P. and G.K. A12460), a Royal Society University Research fellowship to E.P. (UF090580), an EMBO Long-Term Fellowship (ALTF 1476-2012), NWO Rubicon grant (825.12.027) and a Dutch Cancer Society Fellowship (BUIT-2013-5847) to S.J.E.S, a Wellcome Trust PhD studentships to IK and Core grant funding from the Wellcome Trust Core (092096) and CRUK (C6946/A14492).This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.devcel.2015.06.01

β\beta-NMR of Isolated 8^{8}Li+^{+} Implanted into a Thin Copper Film

Depth-controlled $\beta$-NMR was used to study highly spin-polarized $^8$Li in a Cu film of thickness 100 nm deposited onto a MgO substrate. The positive Knight Shifts and spin relaxation data show that $^8$Li occupies two sites at low temperatures, assigned to be the substitutional ($S$) and octahedral ($O$) interstitial sites. Between 50 to 100 K, there is a site change from $O$ to $S$. The temperature dependence of the Knight shifts and spin-lattice relaxation rates at high temperatures, i.e. when all the Li are in the $S$ site, is consistent with the Korringa Law for a simple metal.Comment: Accepted for publication in Phys. Rev.

Spurious diffusion in particle simulations of the Kolmogorov flow

Particle simulations of the Kolmogorov flow are analyzed by the Landau-Lifshitz fluctuating hydrodynamics. It is shown that a spurious diffusion of the center of mass corrupts the statistical properties of the flow. The analytical expression for the corresponding diffusion coefficient is derived.Comment: 10 pages, no figure