The purpose of this paper is to use indefinite theta functions to explain and generalize an example of a Maass waveform which was constructed by Cohen from two functions σ and σ∗, studied by Andrews, Dyson and Hickerson. For this, we construct certain functions attached to an indefinite binary quadratic form and show that they are “nearly” Maass waveforms. In certain special cases we obtain act...

One of Greenberg’s claims concerning the appearance of numerals as modifiers concerns the order of the elements, suggesting that post-nominal numerals are “favored in indefinite and approximate constructions”. Examining a small but representative body of data from a variety of languages, and one of the common grammaticalisation targets of singular numerals, the indefinite article, we conclude t...

In this paper we introduce the notion of screen pseudo-slant lightlike submanifolds of indefinite Kaehler manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions D1, D2 and RadTM on screen pseudo-slant lightlike submanifolds of an indefinite Kaehler manifold have been obtained. Further, we obtain necessary and suff...

The notions of totally indefinite and weakly isotropic algebras with involution are introduced and a proof is given of the fact that a field satisfies the Effective Diagonalization Property (ED) if and only if it satisfies the following weak Hasse principle: every totally indefinite central simple algebra with involution of the first kind over the given field is weakly isotropic. This generaliz...

To solve variational indefinite problems, one uses classically the Banach–Nečas–Babuška theory. Here, we study an alternate theory to solve those problems: T-coercivity. Moreover, we prove that one can use this theory to solve the approximate problems, which provides an alternative to the celebrated Fortin lemma. We apply this theory to solve the indefinite problem div σ∇u = f set in H1 0 , wit...

the significance of error analysis for the learner, the teacher and the researcher is now widely recognized. earlier studies of error analysis concentrated on intersystematic comparison of the “native language” and the “target language” and drew the required data largely from intuitions and impressionistic observations. this study was conducted on the basis of the following observations: (1) to...

This paper introduces and studies a declarative framework for updating views over indefinite databases. An indefinite database is a database with null values that are represented, following the standard database approach, by a single null constant. The paper formalizes views over such databases as indefinite deductive databases, and defines for them several classes of database repairs that real...

A linear quadratic optimal stochastic control problem with random coefficients and indefinite state/control weight costs is usually linked to an indefinite stochastic Riccati equation (SRE), which is a matrix-valued quadratic backward stochastic differential equation along with an algebraic constraint involving the unknown. Either the optimal control problem or the SRE is solvable only if the g...