In the last years there has been increasing interest in discrete models in classical and quantum physics (for a recent review see ). Several of such models are solved using the theory of the classical discrete polynomials . Important instances of such systems are the discrete oscillators of Charlier , Kravchuk oscillators [6, 8, 10, 12, 14] and Meixner oscillators  that are related to the polynomials of Charlier, Kravchuk and Meixner, respectively, and the finite radial oscillator [9, 11] related with the Hahn polynomials. For applications it is important to have recurrencerelationsfor the discrete wave function of such systems. Methods for obtaining such recurrencerelations have attracted the interest of several authors (see e.g. [19, 20] and references therein).
 R. Koekoek and R. F. Swarttouw The Askey-scheme of hypergeometric orthog- onal polynomials and its q-analogue. Reports of the Faculty of Technical Math- ematics and Informatics No. 94-05. Delft University of Technology. Delft 1994.  T.H. Koornwinder: Compact quantum groups and q-special functions. In Rep-
In a series of papers - we obtained the representation as hypergeometricfunctionsfor generalized Meixner, Charlier, Kravchuk and Hahn polynomials as well as the corresponding second order dierence equation that such polynomials satisfy. Notice that the coecients of those dierence equations are polynomials of xed degree and they depend on n as a
The only prerequisite of our approach is the knowledge of the second order dierence equation satised by the involved hypergeometric polynomials. The resulting expansion coecients are given in a compact, analytic, closed and formally simple form in terms of the polynomial coecients of the corresponding second-order dierence equation(s). Then, contrary to Market's, Ronveaux et al's and Lewanowicz's methods we do not require infor- mation about any kind of recurrence relation about the involved discretehypergeometric polynomials nor we need to solve any partial dierence equation for the polynomial(s) to be expanded, or \high" order recurrence relation for the connection coecients them- selves. Let us also underline that, opposite to Koepf and Schmersau's method, we do not use any symbolic means, as well as we directly provide the expansion coecients in a single step.
in (2.14) we can proceed as in the previous section, i.e., use the Eqs. (A.1)–(A.5) to transform (2.14) into one of the formulas (A.1)–(A.5) or in a sum of linearly independent Laguerre polynomials and solve the resulting equations for the unknown coefficients. Let us consider some examples. The first two are taken from  and the other two are new.
The hypergeometric polynomials in a continous or a discrete variable, whose canonical forms are the so-called classical orthogonal polynomial systems, are objects which naturally appear in a broad range of physical and mathematical elds from quantum mechanics, the theory of vibrating strings and the theory of group representations to numerical analysis and the theory of Sturm-Liouville dierential and dierence equations. Often, they are encoun- tered in the form of a three term recurrence relation (TTRR) which connects a polynomial of a given order with the polynomial of the contiguous orders. This relation can be directly found, in particular, by use of Lanczos-type methods, tight-binding models or the appli- cation of the conventional discretisation procedures to a given dierential operator. Here the distribution of zeros and its asymptotic limit, characterized by means of its moments around the origin, are found for the continuous classical (Hermite, Laguerre, Jacobi, Bessel) polynomials and for the discrete classical (Charlier, Meixner, Kravchuk, Hahn) polynomials by means of a general procedure which (i) only requires the three-term recurrence relation and (ii) avoids the often high-brow subleties of the potential theoretic considerations used in some recent approaches. The moments are given in an explicit manner which, at times, allows us to recognize the analytical form of the corresponding distribution.
An interesting application of the aforesaid functions is the fact that, in most cases, the Schr¨ odinger equation –that rules the quantum mechanical systems– for a wide class of potentials can be transformed into the equation (1.1) by an appropriate change of variables (see [20, Section 1]) and therefore, a deep knowledge of the Special Function Theory allow us to obtain several new relationsfor the wave functions (i.e. the solution of the stationary Schr¨ odinger equation) as it is shown in the papers [6, 11].
There are many applications in modern physics that require knowledge of the wavefunctions of hydrogenlike atoms and isotropic harmonic oscillators, especially for finding the corresponding matrix elements (see, e.g., [18, 23] and references therein). There are several methods for generating such wavefunctions among which the so-called factorization method of Infeld and Hull  is of particular significance (for more recent papers see, e.g., [3, 13, 17, 24]). Moreover, the recurrencerelations and the ladder-type operators for these wavefunctions are useful for finding the transition probabilities and evaluation of certain integrals [18, 23]. Methods for obtaining such recurrencerelations have attracted the interest of several authors (see, e.g., [6, 21, 22]), and usually are based on the connection of such functions with the classical Laguerre polynomials. For generating further ‘non-trivial’ relations a Laplace- transform-based method has been developed recently [6, 25] but the calculation is cumbersome and requires inversion formulae.
Figure 3 shows, in the left panel, the kernel distribution estimates computed using (2) with the obtained plug‐in (green line) and boot‐ strap (red line) bandwidths, that is, the estimates of the emergence curves using the nonparametric approach. In contrast to the density case, the effect that the bandwidth has on the behavior of the distri‐ bution estimator is less evident, since slightly different bandwidths produce very similar distribution estimates. As in the density case, the parameter model in the function bw.dist.binned was set to weibull and logistic to fit parametric regression functions following these models to describe seedling emergence. The corre‐ sponding fits are shown in the right panel of Figure 3, using a green line for the Weibull and a blue line for the logistic. The nonparamet‐ ric distribution estimator (2) is also included in this plot (red line). In both figures, the empirical distribution of the grouped sample data is represented with black lines.
The confluent hypergeometric function kind 1 distribution occurs as the distribu- tion of the ratio of independent gamma and beta variables (Gupta and Nagar , Nadarajah and Kotz ). For α = β, the density (1.1) reduces to a gamma density given by
Table 1 shows the execution time, in seconds (s), of both algorithms. A significant reduction in the parallel execution time of the vector-valued DFT is observed. Table 1 shows that Algorithm 1 with hypercomplex kernel for a Wiener CAZAC signal in 𝑙 2 (Z 8192 , C 5 ) produces a time of serial execution 𝑇 ∗ = 13408 s. Using Algorithm 2, however, we obtain 𝑇 1 = 106.7 (0.80% of 𝑇 ∗ ), 𝑇 2 = 80.44 s (0.60% of 𝑇 ∗ ), 𝑇 3 = 57.35 s (0.43% of 𝑇 ∗ ), and 𝑇 4 = 32.67 s (0.24% of 𝑇 ∗ ). This result shows the advantage of using multicore processors and a parallel computing environment to minimize the high execution time in the vector-valued DFT. This is because parallel computing is a form of computation in which many calculations are carried out simultaneously [19, 20], operating on the principle that large problems can often be divided into smaller ones, which are then solved concurrently, and minimize the execution time [20, 21]. The difference between 𝑇 ∗ and 𝑇 𝑝 is because 𝑇 𝑝 is computed with matrices in C 𝑑𝑟×𝑑𝑟
The Event class represents an abstraction of an event. Each one of the events presented in section 4B should be implemented as a class which extends it (Init, Arrival, Run, End and Preempt). These classes must override the actions() method in order to perform the corresponding actions (that is the f v functions listed in section 4G).
for modular Big Data computation that uses a function map to identify and target intermediate data in the mapping phase, and a function reduce to summarize the output of the map function and give a final result. Because inputs for the reduce function depend on the map function’s output to decrease the communication traffic of the output of map functions to the input of reduce functions, MapReduce permits defining combining function for local aggregation in the mapping phase. MapReduce Hadoop solutions do not warrant the combining functioning application. Even though there exist proposals for warranting the combining function execution, they break the modular nature of MapReduce solutions. Because Aspect-Oriented Programming (AOP) is a programming paradigm that looks for the modular software production, this article proposes and apply Aspect- Combining function, an AOP combining function, to look for a modular MapReduce solution. The Aspect-Combining application results on MapReduce Hadoop experiments highlight computing performance and modularity improvements and a warranted execution of the combining function using an AOP framework like AspectJ as a mandatory requisite.
Our simulations in general suggest that FTR-based cost functions remain piecewise continuous —as well as piecewise differentiable— over the entire FTR range. Regions with negative marginal costs could cause concern. However, they seem to shrink, as one moves to more realistic (multi-node) networks and includes changes in reactances in the model. This then provides support for applications of mechanisms that use FTRs to promote network expansion. More specifically, our results showed that compared with the fixed-network case the introduction of variable line reactances significantly changes the possible outcomes. In particular, the introduction of a link between capacity and reactance appears to reduce the impact of loop-flows in terms of significant kinks. Therefore, one general result is that smoothness of non-lumpy cost functions is gained with variable reactances. In a lumpy environment, this result translates to variable reactances, implying increasing stepwise functions.
Abstract. The interchange of ontologies across the World Wide Web (WWW) and the cooperation among heterogeneous agents placed on it is the main reason for the development of a new set of ontology specification languages, based on new web standards such as XML or RDF. These languages (SHOE, XOL, RDF, OIL, etc) aim to represent the knowledge contained in an ontology in a simple and human-readable way, as well as allow for the interchange of ontologies across the web. In this paper, we establish a common framework to compare the expressiveness and reasoning capabilities of „traditional“ ontology languages (Ontolingua, OKBC, OCML, FLogic, LOOM) and „web-based“ ontology languages, and conclude with the results of applying this framework to the selected languages.
Background. Liver transplantation is the only therapy for end-stage liver disease. Cirrhosis secondary to autoimmune hepatitis (AIH) is an indication in 4-6% of adult transplants. Aims. To describe the outcomes and recurrence of AIH in liver transplant patients. Material and methods. Twenty patients were retros- pectively studied. Results. The female/male ratio was 3:1, the median age was 36.7 years (range, 16 to 39 years), and the median MELD score was 18.5. According to serological analysis, 19 patients were AIH type 1 and one patient was AIH type 2. AIH was associated with human leukocyte antigen (HLA) DR13+ and DR4+. The overall 5-year patient and graft survival rates were 94 and 85%, respectively. Three (15.7%) cases of re- current AIH were diagnosed based on histological evidence. Clinical and histological features of acute and chronic rejection were present in four (20%) and three (16.6%) patients, respectively. Conclusion. AIH frequently affected young women, was the most frequent indication for liver transplantation. Rejection and recurrence were commonly associated with AIH, but did not affect patient survival. No significant relationship between HLA-DR type and recurrence was found. Rapid progression to cirrhosis should be considered in severe recurrences.
In this subsection, the estimation of f on the grid points is carried out using Kernel Non-parametric Local Polynomial Regression ( KNPL henceforth; see Appendix A ) and we can obtain the coef ﬁ cients using a nonlinear MM that is also easy to implement. For the particular problem described in Section 2.1, we consider the 1000 samples already mentioned and we carry out computations to calculate the coef ﬁ cients of the development for each sample, then we obtain the mean and the standard deviation. More speci ﬁ cally, we use a KNPL of 6th order considering the formulation given by Wand & Jones ( 1995 ) , where the integrals have been computed using the Simpson rule. These values appear in bold in Table 1. We can remark that, in our MM, the coef ﬁ cients have been computed one by one, independently of each other, and with no selection a priori of the order of the development. On the contrary, in the DLS we have considered successive orders of development and all the coef ﬁ cients had to be recalculated for each new higher order.
For the infinite horizon case we incorporate the time parameter to the state obtaining a stationary model, in which the discount varies with the state. We define appropriate dynamic operators, and characterize the value function as its unique bounded fixed point. We also show in this enlarged model the existence of deterministic stationary optimal strategies. We obtain results for the origi- nal problem noting that stationary policies in the stationary model traduces in Markov policies in the non-stationary one.