53,829 research outputs found
q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers
Full text linkWe 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
-analogues of two supercongruences of Z.-W. Sun
Full text linksummary:We give several different -analogues of the following two congruences of \hbox {Z.-W. Sun}: where is an odd prime, is a positive integer, and is the Jacobi symbol. The proofs of them require the use of some curious -series identities, two of which are related to Franklin's involution on partitions into distinct parts. We also confirm a conjecture of the latter author and Zeng in 2012
Editorial: The interplay between compression and security for image and video communication and adaptation over networks
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Network Q
No full textA press release from Network Q announcing that they will begin featuring Brian McNaught, a gay columnist and author, for a monthly segment
Network Q
No full textA press release from Network Q announcing that they will begin featuring Brian McNaught, a gay columnist and author, for a monthly segment
On a congruence involving -Catalan numbers
Full text linkBased on a -congruence of the author and Petrov, we set up a -analogue of Sun–Tauraso’s congruence for sums of Catalan numbers, which extends a -congruence due to Tauraso
Tobin's Q and Financial Policy
Full text linkRecent 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.
Elastic and Transport Properties of the Tailorable Multifunctional Hierarchical Honeycombs
Full text linkIn this paper, we analytically studied the in-plane elastic and transport properties of a peculiar hexagonal honeycomb, i.e., the multifunctional hierarchical honeycomb (MHH). The MHH structure was developed by replacing the solid cell walls of the original regular hexagonal honeycomb (ORHH) with three kinds of equal-mass isotropic honeycomb sub-structures possessing hexagonal, triangular and Kagome lattices. Formulas to calculate the effective in-plane elastic properties and conductivities of the MHH structure at all densities were developed. Results show that the elastic properties of the MHH structure with the hexagonal sub-structure were weakly improved in contrast to those of the ORHH. However, the triangular and Kagome sub-structures result in substantial improvements by one or even three orders of magnitude on Young’s and shear moduli of the MHH structure, depending on the cell-wall thickness-to-length ratio of the ORHH. The present theory could be used in designing new tailorable hierarchical honeycomb structures for multifunctional applications
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