and Applied Analysis 3 where n α 1, α denotes the integer part of number α, provided that the right side is pointwise defined on 0, ∞ . Definition 2.2 see 20 . The Riemann-Liouville fractional integral of order α > 0 of a function f : 0, ∞ → R is given by I 0 f t 1 Γ α ∫ t 0 t − s α−1f s ds, 2.2 provided that the right side is pointwise defined on 0, ∞ . From the definition of the Riemann-Liouv...

This paper presents an unsupervised discretization method that performs density estimation for univariate data. The subintervals that the discretization produces can be used as the bins of a histogram. Histograms are a very simple and broadly understood means for displaying data, and our method automatically adapts bin widths to the data. It uses the log-likelihood as the scoring function to se...

In this paper we address the issue of research communities in science and engineering and their effects on graduate students and women in particular. We present our observations of graduate student experiences in one particular research community. These observations are considered in the context of research done by national science institutes and feminist theorists about the under-representatio...

Exegesis that includes careful attention to internal matters-theme and development, structure, and features of literary style--can help resolve perennial problems of interpretation. One such difficulty involves the unity and authorship of the book of Nahum. Conclusions reached from the shared contributions of biblical and literary data argue strongly for the unity of the whole prophecy that bea...

Consistent product experience requires congruity between product properties such as visual appearance and sound. Therefore, for designing appropriate product sounds by manipulating their spectral-temporal structure, product sounds should preferably not be considered in isolation but as an integral part of the main product concept. Because visual aspects of a product are considered to dominate t...

I characterize a finite additive utility representation for preferences over menus. The numbers of both positive and negative components in this representation are expressed explicitly in terms of preference. These expressions can be used to characterize models of temptation, perfectionism, context effects, and other phenomena. © 2008 Elsevier Inc. All rights reserved. JEL classification: D81

Consider a database that represents the location of moving objects, such as taxi-cabs (typical query: retrieve the cabs that are currently within 1 mile of 33 Michigan Ave., Chicago), or objects in a battle-eld. Existing database management systems (DBMS's) are not well equipped to handle continuously changing data, such as the position of moving objects, since data is assumed to be constant un...

The physics of charge fractionalization is studied using a simple and physical approach. The normal ordered charge is related to the Atiyah-Patodi-Singer invariant, and the physical interpretation of the spectral asymmetry is clarified in the presence of a continuous spectrum. By introducing the quantity B(E) which is a ratio of Jost-type determinants we relate the asymmetry to the phase and ze...