Abstract. Using a simple classical method we derive bilateral series identities from terminating ones. In particular, we show how to deduce Ramanujan’s 1ψ1 summation from the q-Pfaff–Saalschütz summation. Further, we apply the same method to our previous q-Abel–Rothe summation to obtain, for the first time, Abel–Rothe type generalizations of Jacobi’s triple product identity. We also give some r...

Most formal approaches to argumentative reasoning under uncertainty focus on the analysis of qualitative aspects. An exception is the framework of probabilistic argumentation systems. Its philosophy is to include both qualitative and quantitative aspects through a simple way of combining logic and probability theory. Probabilities are used to weigh arguments for and against particular hypothese...

We use both Abel’s lemma on summation by parts and Zeilberger’s algorithm to find recurrence relations for definite summations. The role of Abel’s lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger alg...

The assessment of sexual arousal and sexual interest patterns have become significant elements in the detection and treatment of sexual disorders. This study investigated whether there was a relationship between sexual interest (utilizing viewing time) and sexual arousal (utilizing plethysmography) in a clinical sample of sexual offenders with diagnosed pedophilic interests. Thirty nine partic...

PURPOSE To translate and adapt the ABEL--Auditory Behavior in Everyday Life--questionnaire into Brazilian Portuguese, and to establish the profile of auditory behavior in a group of children who use hearing aids. METHODS The ABEL questionnaire was translated and back translated. This version was compared to the original version regarding semantic equivalence, generating a new version in Portu...

Introduction 2 1. Preliminaries 6 1.1. Algebraic modular forms 6 1.2. Modular forms over C 9 1.3. p-adic modular forms 11 1.4. Elliptic curves with complex multiplication 12 1.5. Values of modular forms at CM points 14 2. Generalised Heegner cycles 15 2.1. Kuga-Sato varieties 15 2.2. The variety Xr and its cohomology 18 2.3. Definition of the cycles 19 2.4. Relation with Heegner cycles and L-se...

The inversion of electron density from total electron content (TEC) measurements of GPS radio occultation is investigated by means of simulated data from the International Reference Ionosphere IRI-2001 and observations by the GPS/MET satellite experiment. In both cases a meridional slice of electron density is derived for northern summer solstice June/July 1995 from the midnight to the noon sec...

We find a large class of integral operators which allow a systematic and explicit diagonalization. These operators generalize Abel’s integral operator, for which such a diagonalization has recently been found.