10,023 research outputs found
q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers
Get PDFWe 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
"Closing the R&D Gap, Evaluating the Sources of R&D Spending"
Get PDFBoth spending and tax policies have been implemented in the United States with the goal of stimulating private sector research and development (R&D). Karier questions whether current R&D policy, especially the research and experimentation tax credit, can contribute to closing the gap between nondefense expenditures on R&D in the United States and such expenditures in other countries, such as Japan and Germany. He also explores possible changes to our current R&D policy to make it more effective.
Optimal solution of the nearest correlation matrix problem by minimization of the maximum norm
Get PDFThe nearest correlation matrix problem is to find a valid (positive semidefinite) correlation matrix, R(m,m), that is nearest to a given invalid (negative semidefinite) or pseudo-correlation matrix, Q(m,m); m larger than 2. In the literature on this problem, 'nearest' is invariably defined in the sense of the least Frobenius norm. Research works of Rebonato and Jaeckel (1999), Higham (2002), Anjos et al. (2003), Grubisic and Pietersz (2004), Pietersz, and Groenen (2004), etc. use Frobenius norm explicitly or implicitly. However, it is not necessary to define 'nearest' in this conventional sense. The thrust of this paper is to define 'nearest' in the sense of the least maximum norm (LMN) of the deviation matrix (R-Q), and to obtain R nearest to Q. The LMN provides the overall minimum range of deviation of the elements of R from those of Q. We also append a computer program (source codes in FORTRAN) to find the LMN R from a given Q. Presently we use the random walk search method for optimization. However, we suggest that more efficient methods based on the Genetic algorithms may replace the random walk algorithm of optimization.Nearest correlation matrix problem; Frobenius norm; maximum norm; LMN correlation matrix; positive semidefinite; negative semidefinite; positive definite; random walk algorithm; Genetic algorithm; computer program; source codes; FORTRAN; simulation
De Maiestate / Praeside M. Jacobo Thomasio, Moralis Philosoph. P. P., publice disputabit Johannes Dunte, R. L. Author & Respon: ad diem 9. Septembr. H L. Q. C.
No full textDE MAIESTATE / PRAESIDE M. JACOBO THOMASIO, MORALIS PHILOSOPH. P. P., PUBLICE DISPUTABIT JOHANNES DUNTE, R. L. AUTHOR & RESPON: AD DIEM 9. SEPTEMBR. H L. Q. C.
De Maiestate / Praeside M. Jacobo Thomasio, Moralis Philosoph. P. P., publice disputabit Johannes Dunte, R. L. Author & Respon: ad diem 9. Septembr. H L. Q. C. (1)
Titelblatt (1)
Widmung (2)
Text (3)
Beiträge (21
Integrable boundaries for the q-Hahn process
Get PDFTaking inspiration from the harmonic process with reservoirs introduced by
Giardin\`a, Kurchan and the author in arXiv:1904.01048, we propose integrable
boundary conditions for its trigonometric deformation which is known as the
q-Hahn process. Following the formalism established by Mangazeev and Lu in
arXiv:1903.00274 using the stochastic R-matrix, we argue that the proposed
boundary conditions can be derived from a transfer matrix constructed in the
framework of Sklyanin's extension of the quantum inverse scattering method and
consequently preserve the integrable structure of the model. The approach
avoids the explicit construction of the K-matrix.Comment: v1: One figure and 16 pages v2: added symmetric limit and improved
conclusio
Asymmetric Total Syntheses of Ansamacrolactams (+)-Q-1047H-A-A and (+)-Q-1047H-R-A
No full textThe total syntheses of ansamacrolactams (+)-Q-1047H-A-A (16) and (+)-Q-1047H-R-A (17) have been achieved for the first time In 17 steps, leading to the reassignment of the relative stereochemistries and absolute configurations of their natural counterparts. The key steps In the synthetic work included an asymmetric chelation-controlled vinylogous Mukaiyama aldol reaction for the stereoselective synthesis of the syn-aldol adduct 7b and an intramolecular SmI2-mediated Reformatsky reaction for the formation of the macrocyclic lactam 14.Chemistry, OrganicSCI(E)PubMed4ARTICLE4812-8151
Undecidability of Q(2)
Get PDFIt is shown that the compositum Q(2) of all degree 2 extensions of Q has undecidable theory.articl
CANONICAL-TRANSFORMATIONS OF Q-BOSONIC OSCILLATORS
No full textWithin the framework of R matrix of quantum group, canonical q-transformations for bosonic q-oscillators are presented. The commutation relations are covariant under quantum group Sp(q)(2n).Physics, MultidisciplinarySCI(E)中国科学引文数据库(CSCD)0ARTICLE1121-1242
Finite linear spaces admitting a projective group PSU(3,q) with q even
No full textAbstractThis article is a contribution to the study of the automorphism groups of finite linear spaces. In particular we look at simple groups and prove the following theorem:Let G=PSU(3,q) with q even and G acts line-transitively on a finite linear space S. Then S is one of the following cases:(i)A projective plane;(ii)A regular linear space with parameters (b,v,r,k)=(q2(q2−q+1),q3+1,q2−q+1,q+1). This is called the Hermitian unitary design
- …
