4,867 research outputs found

### Nonnegative and strictly positive linearization of Jacobi and generalized Chebyshev polynomials

In the theory of orthogonal polynomials, as well as in its intersection with
harmonic analysis, it is an important problem to decide whether a given
orthogonal polynomial sequence $(P_n(x))_{n\in\mathbb{N}_0}$ satisfies
nonnegative linearization of products, i.e., the product of any two
$P_m(x),P_n(x)$ is a conical combination of the polynomials
$P_{|m-n|}(x),\ldots,P_{m+n}(x)$. Since the coefficients in the arising
expansions are often of cumbersome structure or not explicitly available, such
considerations are generally very nontrivial. In 1970, G. Gasper was able to
determine the set $V$ of all pairs $(\alpha,\beta)\in(-1,\infty)^2$ for which
the corresponding Jacobi polynomials
$(R_n^{(\alpha,\beta)}(x))_{n\in\mathbb{N}_0}$, normalized by
$R_n^{(\alpha,\beta)}(1)\equiv1$, satisfy nonnegative linearization of
products. In 2005, R. Szwarc asked to solve the analogous problem for the
generalized Chebyshev polynomials
$(T_n^{(\alpha,\beta)}(x))_{n\in\mathbb{N}_0}$, which are the quadratic
transformations of the Jacobi polynomials and orthogonal w.r.t. the measure
$(1-x^2)^{\alpha}|x|^{2\beta+1}\chi_{(-1,1)}(x)\,\mathrm{d}x$. In this paper,
we give the solution and show that
$(T_n^{(\alpha,\beta)}(x))_{n\in\mathbb{N}_0}$ satisfies nonnegative
linearization of products if and only if $(\alpha,\beta)\in V$, so the
generalized Chebyshev polynomials share this property with the Jacobi
polynomials. Moreover, we reconsider the Jacobi polynomials themselves,
simplify Gasper's original proof and characterize strict positivity of the
linearization coefficients. Our results can also be regarded as sharpenings of
Gasper's one.Comment: The second version puts more emphasis on strictly positive
linearization of Jacobi polynomials. We reorganized the structure, added
several references and corrected a few typos. We added a geometric
interpretation of the set $V^{\prime}$ and some comments on its interior. We
added a detailed comparison to Gasper's classical result. Title and abstract
were changed. These are the main change

### Tur\'{a}n's inequality, nonnegative linearization and amenability properties for associated symmetric Pollaczek polynomials

An elegant and fruitful way to bring harmonic analysis into the theory of
orthogonal polynomials and special functions, or to associate certain Banach
algebras with orthogonal polynomials satisfying a specific but frequently
satisfied nonnegative linearization property, is the concept of a polynomial
hypergroup. Polynomial hypergroups (or the underlying polynomials,
respectively) are accompanied by $L^1$-algebras and a rich, well-developed and
unified harmonic analysis. However, the individual behavior strongly depends on
the underlying polynomials. We study the associated symmetric Pollaczek
polynomials, which are a two-parameter generalization of the ultraspherical
polynomials. Considering the associated $L^1$-algebras, we will provide
complete characterizations of weak amenability and point amenability by
specifying the corresponding parameter regions. In particular, we shall see
that there is a large parameter region for which none of these amenability
properties holds (which is very different to $L^1$-algebras of locally compact
groups). Moreover, we will rule out right character amenability. The crucial
underlying nonnegative linearization property will be established, too, which
particularly establishes a conjecture of R. Lasser (1994). Furthermore, we
shall prove Tur\'{a}n's inequality for associated symmetric Pollaczek
polynomials. Our strategy relies on chain sequences, asymptotic behavior,
further Tur\'{a}n type inequalities and transformations into more convenient
orthogonal polynomial systems.Comment: Main changes towards first version: The part on associated symmetric
Pollaczek polynomials was extended (with more emphasis on Tur\'{a}n's
inequality and including a larger parameter region), and the part on little
$q$-Legendre polynomials became a separate paper. We added several references
and corrected a few typos. Title, abstract and MSC class were change

### Leadership Selection in the Major Multilaterals

Leadership selection in the major global economic organizations produced unprecedented levels of public conflict during the 1990s. The convention that awards the IMF managing directorship to a European and the World Bank presidency to an American sparked conflict between the United States and Europe as well as growing discontent on the part of Japan and the developing countries. At the WTO, successive conflicts demonstrate deeper shortcomings in governance as membership expands rapidly and consensus decision making fails. Protracted efforts to choose new heads of these increasingly important organizations have undermined their legitimacy and distracted members from their core agendas. This selection process and its flaws provide a central theme for the analysis and prescriptions presented in this study, which focuses on the major international financial institutions (IFIs) and other global and regional multilaterals. Author Miles Kahler looks at the sources of conflict and presents recommendations for reform: in the short run, changes in the process, such as the use of search committees; in the long run, the dismantling of the US-European convention at the IFIs and changes in representation at the WTO. The author's diagnosis and policy recommendations have important implications for leadership selection in other regional and global organizations.

### Solar origins of coronal mass ejections

The large scale properties of coronal mass ejections (CMEs), such as morphology, leading edge speed, and angular width and position, have been cataloged for many events observed with coronagraphs on the Skylab, P-78, and SMM spacecraft. While considerable study has been devoted to the characteristics of the SMEs, their solar origins are still only poorly understood. Recent observational work has involved statistical associations of CMEs with flares and filament eruptions, and some evidence exists that the flare and eruptive-filament associated CMEs define two classes of events, with the former being generally more energetic. Nevertheless, it is found that eruptive-filament CMEs can at times be very energetic, giving rise to interplanetary shocks and energetic particle events. The size of the impulsive phase in a flare-associated CME seems to play no significant role in the size or speed of the CME, but the angular sizes of CMEs may correlate with the scale sizes of the 1-8 angstrom x-ray flares. At the present time, He 10830 angstrom observations should be useful in studying the late development of double-ribbon flares and transient coronal holes to yield insights into the CME aftermath. The recently available white-light synoptic maps may also prove fruitful in defining the coronal conditions giving rise to CMEs

### Discrete hardy spaces

We study the boundary behavior of discrete monogenic functions, i.e. null-solutions of a discrete Dirac operator, in the upper and lower half space. Calculating the Fourier symbol of the boundary operator we construct the corresponding discrete Hilbert transforms, the projection operators arising from them, and discuss the notion of discrete Hardy spaces. Hereby, we focus on the 3D-case with the generalization to the n-dimensional case being straightforward

### Multi-core computation of transfer matrices for strip lattices in the Potts model

The transfer-matrix technique is a convenient way for studying strip lattices
in the Potts model since the compu- tational costs depend just on the periodic
part of the lattice and not on the whole. However, even when the cost is
reduced, the transfer-matrix technique is still an NP-hard problem since the
time T(|V|, |E|) needed to compute the matrix grows ex- ponentially as a
function of the graph width. In this work, we present a parallel
transfer-matrix implementation that scales performance under multi-core
architectures. The construction of the matrix is based on several repetitions
of the deletion- contraction technique, allowing parallelism suitable to
multi-core machines. Our experimental results show that the multi-core
implementation achieves speedups of 3.7X with p = 4 processors and 5.7X with p
= 8. The efficiency of the implementation lies between 60% and 95%, achieving
the best balance of speedup and efficiency at p = 4 processors for actual
multi-core architectures. The algorithm also takes advantage of the lattice
symmetry, making the transfer matrix computation to run up to 2X faster than
its non-symmetric counterpart and use up to a quarter of the original space

### Observational data formats and identification of supplementary documentation for the National Geodetic Satellite Program

Observational formats for geodetic tracking data and supporting documentation for data reductio

- â€¦