25,114 research outputs found
q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers
No full textWe introduce, characterise and provide a combinatorial interpretation for the so-called q-Jacobi–Stirling numbers.
This study is motivated by their key role in the (reciprocal) expansion of any power of a second order
q-differential operator having the q-classical polynomials as eigenfunctions in terms of other even order operators,
which we explicitly construct in this work. The results here obtained can be viewed as the q-version of
those given by Everitt et al. and by the first author, whilst the combinatorics of this new set of numbers is a
q-version of the Jacobi–Stirling numbers given by Gelineau and the second author
Burst pressure of steel reinforced flexible pipe
No full textThe burst pressure of steel reinforced flexible pipe (SRFP) considering plasticity is investigated through experimental, theoretical and numerical methods. The results obtained from the aforementioned methods are in good agreement with each other, which illustrates the accuracy and reliability of the proposed theoretical and numerical models. The mechanical responses of PE layers and the steel strips are studied in detail, and the rationality of the strain uniformity assumption for the steel strip's cross section in the theoretical model is confirmed from its von Mises stress variation along the width at different points in FEM. Some influential parameters of SRFP on the burst pressure are also investigated in order to guide its cross-section design. The theoretical model and the FEM proposed in this paper can not only give an estimation to the safety and reliability of the pipe when it is subjected to internal pressure, but can also provide some reference for improving and optimizing its cross-section design
BIHYBRIDIZATION MODEL OF Y1-XPRXBA2CU3O7-Y
No full textWe have used the bihybridization model to study the superconducting characteristics of Y1-xPrxBa2Cu3O7-y, including the energy gap, effective interaction, and the critical temperature T(c) and given a formula for T(c) at low impurity concentrations. The results show that the hybridization of Pr 4f states with CuO2 valence-band states may be the reason for the abnormal characteristics of Y1-xPrxBa2Cu3O7-y. The Coulomb repulsion + U(f) between the Pr 4f states can destroy the superconductivity by hybridization of the f electrons with the conduction electrons and hence reduce T(c) significantly. Also, the localized character of the Pr 4f states can localize the carriers of the CuO2 band states and suppress the effect of - U centers.Physics, Condensed MatterSCI(E)6ARTICLE1410230-102375
Some Monotonicity Properties of the q-Gamma Function
No full textWe prove some properties of completely monotonic functions and apply them to obtain
new results on gamma and q-gamma functions
Fishbone instability driven by trapped fast ions in a toroidal plasma with reversed magnetic shear
No full textBased on the non-perturbative approach, the hybrid code MARS-K is applied to study fishbone (FB) instabilities driven by trapped fast ions in a toroidal plasma with q profile nearly being flat or non-monotonic. We explore the dependency of the FB with variation in the fast ion distribution, thermal particle kinetic effects, safety factor (q) profile and plasma resistivity. When the safety factor minimum value is larger than unity (i.e.), the mode can be excited by isotropic or anisotropic fast ions, with the latter strongly enhancing the mode growth rate. The mode frequency increases with increasing, and is more easily triggered in a equilibrium with two q = 1 surfaces, compared with the case with one or no q = 1 surface. Kinetic contributions from transit resonance of passing fast ions and from bounce resonance of trapped fast ions strongly enhance mode instability. The passing thermal ions induced Landau damping has a strong stabilization effect. Furthermore, in such a weak, even reversed magnetic shear plasma, the radial mode structure of FB mode monotonically decreases to zero at q = 1 flux surface instead of a step-like function, and it depends on the kinetic contributions from particles. In addition, the plasma resistivity significantly stabilizes the mode near the marginally unstable point
Generalized -Catalan numbers
No full textRecent work of the first author, Negut and Rasmussen, and of Oblomkov and Rozansky in the context of Khovanov–Rozansky knot homology produces a family of polynomials in q and t labeled by integer sequences. These polynomials can be expressed as equivariant Euler characteristics of certain line bundles on flag Hilbert schemes. The q, t-Catalan numbers and their rational analogues are special cases of this construction. In this paper, we give a purely combinatorial treatment of these polynomials and show that in many cases they have nonnegative integer coefficients. For sequences of length at most 4, we prove that these coefficients enumerate subdiagrams in a certain fixed Young diagram and give an explicit symmetric chain decomposition of the set of such diagrams. This strengthens results of Lee, Li and Loehr for (4, n) rational q, t-Catalan numbers
Tobin's Q and Financial Policy
No full textRecent research in macroeconomics has emphasized the importance of linking the financial and real sectors and the need for working with optimizing models. Tobin’s Q model of investment would appear to provide a framework that can satisfy these two criteria. In contrast to the original presentation of the Q model, the formal development has not recognized that the firm actively participates in a number of financial markets; in this broader context, we show that Q is likely to be an uninformative and possibly misleading signal for investment expenditures . We then endeavor to turn this negative theoretical result to positive advantage in resolving a number of empirical problems with Q models, but the modifications dictated by the theory receive little support from the data.
Combinatorics of q,t-parking functions
No full textAbstractIn [A conjectured combinatorial formula for the Hilbert series for diagonal harmonics, in: Proceedings of FPSAC 2002 Conference, Melbourne, Australia, Discrete Math., in press] Haglund, Haiman, and the present author conjectured a combinatorial formula CHn(q,t) for the Hilbert series of diagonal harmonics as a weighted sum of parking functions. Another equivalent combinatorial formula was proposed by the present author in [Multivariate analogues of Catalan numbers, parking functions, and their extensions, UCSD doctoral thesis, June 2003]. These formulas involve three statistics on parking functions called area, dinv, and pmaj. In this article, we use the pmaj statistic to solve several combinatorial problems posed in [A conjectured combinatorial formula for the Hilbert series for diagonal harmonics, in: Proceedings of FPSAC 2002 Conference, Melbourne, Australia, Discrete Math., in press]. In particular, we derive a recursion satisfied by the combinatorial Hilbert series and show that qn(n−1)/2CHn(1/q,q)=[n+1]qn−1
Influence of Nanofillers on Electrical Characteristics of Epoxy Resins Insulation
No full textEpoxy resin is widely used in high voltage apparatus as insulation. Fillers are often added to epoxy resin to enhance its mechanical, thermal and chemical properties. The addition of fillers can deteriorate electrical performance. With the new development in nanotechnology, it has been widely anticipated that the combination of nanoparticles with traditional resin systems may create nanocomposite materials with enhanced electrical, thermal and mechanical properties. In the present paper we have carried out a comparative study on dielectric properties and space charge behaviour of epoxy resin/nanocomposites with nano-fillers of SiO2 and Al2O3. The epoxy resin (LY556), commonly used in power apparatus, was used to investigate the dielectric behaviour of epoxy resin/nanocomposites with different filler concentrations. The epoxy resin/nanocomposite thin film samples were prepared and tests were carried out to measure their dielectric permittivity and tan delta value in frequency range of 1Hz- 1MHz. The space charge behaviours were also observed by using the pulse electroacoustic (PEA) technique. In addition, traditional epoxy resin/microcomposites were also prepared and tested and the test results were compared with those obtained from epoxy resin/nanocomposites
The effectiveness of eHealth interventions on moderate-to-vigorous intensity physical activity among cardiac rehabilitation participants: a systematic review and meta-analysis
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