Search results for "Complete"

Indefinite integrals of Lommel functions from an inhomogeneous Euler–Lagrange method

2015

ABSTRACTA method given recently for deriving indefinite integrals of special functions which satisfy homogeneous second-order linear differential equations has been extended to include functions which obey inhomogeneous equations. The extended method has been applied to derive indefinite integrals for the Lommel functions, which obey an inhomogeneous Bessel equation. The method allows integrals to be derived for the inhomogeneous equation in a manner which closely parallels the homogeneous case, and a number of new Lommel integrals are derived which have well-known Bessel analogues. Results will be presented separately for other special functions which obey inhomogeneous second-order linear…

An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations

2020

In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces.

Theoretical studies on the spectroscopy of the 7-azaindole monomer and dimer

2001

The absorption and the emission spectra, both fluorescence and phosphorescence, of the 7-azaindole molecule have been studied by means of the complete active space (CAS) SCF method and multiconfigurational second-order perturbation theory (CASPT2). Excitation energies, oscillator strengths, dipole moments, transition dipole moments, and their directions have been computed and the results compared to those of analogous molecules such as indene, indole, and benzimidazole, to get a homogeneous picture of the photophysics of the systems. The absorption and emission of the 7-azaindole dimer and its related tautomer have also been computed in order to get further insight into the double fluoresce…

A Theoretical Study of the Electronic Spectra of N9 and N7 Purine Tautomers

1999

The complete active space (CAS) SCF method and multiconfigurational second-order perturbation theory (CASPT2) have been used to study electronic spectra of the N(9)H and N(7)H tautomers of purine. The calculations include vertical excitation energies, oscillator strengths, dipole moments, and transition moment directions in gas phase. In accord with experiment in nonpolar solvents, the two lowest π → π* excited singlet valence states are predicted to be located at 4.7 and 5.1 eV. The latter is expected to shift to the red in aqueous solutions. A satisfactory interpretation of the electronic spectra above 5.5 eV is obtained if the experimental data are assumed to consist of the superposition…

The overlap algebra of regular opens

2010

Abstract Overlap algebras are complete lattices enriched with an extra primitive relation, called “overlap”. The new notion of overlap relation satisfies a set of axioms intended to capture, in a positive way, the properties which hold for two elements with non-zero infimum. For each set, its powerset is an example of overlap algebra where two subsets overlap each other when their intersection is inhabited. Moreover, atomic overlap algebras are naturally isomorphic to the powerset of the set of their atoms. Overlap algebras can be seen as particular open (or overt) locales and, from a classical point of view, they essentially coincide with complete Boolean algebras. Contrary to the latter, …

Basic Sequences in the Dual of a Fréchet Space

2001

Some fixed point theorems for generalized contractive mappings in complete metric spaces

2015

We introduce new concepts of generalized contractive and generalized alpha-Suzuki type contractive mappings. Then, we obtain sufficient conditions for the existence of a fixed point of these classes of mappings on complete metric spaces and b-complete b-metric spaces. Our results extend the theorems of Ciric, Chatterjea, Kannan and Reich.

Set-Valued Generalizations of Baire′s Category Theorem

1995

Abstract We prove some generalizations of Baire′s category theorem for chains of iterates of multifunctions defined on Cech-complete spaces. In particular, we extend Lennard′s results stated for functions on complete metric spaces.

A note on best approximation in 0-complete partial metric spaces

2014

We study the existence and uniqueness of best proximity points in the setting of 0-complete partial metric spaces. We get our results by showing that the generalizations, which we have to consider, are obtained from the corresponding results in metric spaces. We introduce some new concepts and consider significant theorems to support this fact.

Common Fixed Points in a Partially Ordered Partial Metric Space

2013

In the first part of this paper, we prove some generalized versions of the result of Matthews in (Matthews, 1994) using different types of conditions in partially ordered partial metric spaces for dominated self-mappings or in partial metric spaces for self-mappings. In the second part, using our results, we deduce a characterization of partial metric 0-completeness in terms of fixed point theory. This result extends the Subrahmanyam characterization of metric completeness.