Sampling with a String

Kramer's sampling theorem forms a bridge between the Whittaker-Shannon-Kotel'nikov sampling theorem and boundary-value problems. It has been shown that sampling expansions associated with Sturm-Liouville boundary-value problems are Lagrange-type sampling series, i.e., Lagrange series with infinitely many terms converging to entire functions. String theory as developed by Feller, Kac, and Krein, is a generalization of the Sturm-Liouville theory. We investigate sampling series associated with strings and compare them with those associated with Sturm-Liouville problems. We show that unlike sampling series associated with Sturm-Liouville problems, those associated with strings include not only Lagrange-type sampling series, but also Lagrange polynomial interpolation.     

On f-injective modules

In this paper, the notions of f-injective and f^*-injective modules are introduced. Elementary properties of these modules are given. For instance, a ring R is coherent iff any ultraproduct of f-injective modules is absolutely pure. We prove that the class S^* \Sigma^* of f^*-injective modules is closed under ultraproducts. On the other hand, S^* \Sigma^* is not axiomatisable. For coherent rings R, S^* \Sigma^* is axiomatisable iff every c₀ \chi_0 -injective module is f^*-injective. Further, it is shown that the class S \Sigma of f-injective modules is axiomatisable iff R is coherent and every c₀ \chi_0 -injective module is f-injective. Finally, an f-injective module H, such that every module embeds in an ultraprower of H, is given.     

Studies on heterocyclic enamines: New syntheses of 4H-pyranes,pyranopyrazoles and pyranopyrimidines

The behaviour of several 2-amino-3-cyano-4H-pyran derivatives toward a variety of nucleophilic reagents is reported.     

Sinc-Galerkin method for solving linear sixth-order boundary-value problems

There are few techniques available to numerically solve sixth-order boundary-value problems with two-point boundary conditions. In this paper we show that the Sinc-Galerkin method is a very effective tool in numerically solving such problems. The method is then tested on examples with homogeneous and nonhomogeneous boundary conditions and a comparison with the modified decomposition method is made. It is shown that the Sinc-Galerkin method yields better results.

     

A Generalized Sampling Theorem with the Inverse of an Arbitrary Square Summable Sequence as Sampling Points

In this article a generalized sampling theorem using an arbitrary sequence of sampling points is derived. The sampling theorem is a Kramer-type sampling theorem, but unlike Kramer's theorem the sampling points are not necessarily eigenvalues of some boundary value problems. The theorem is then used to characterize a class of entire functions that can be reconstructed from their sample values at the points t_n = an + b if n = 0, 1, 2, ... and t_n = an + c if n = 0, -1, -2, ..., where a, b, c are arbitrary constants. The reconstruction formula is derived explicitly in the form of a sampling series expansion. When a = 1, b = 0 = c, the famous Whittaker-Shannon-Kotel'nikov sampling theorem is obtained as a special case.     

Indecomposable modules over right pure semisimple rings

The aim of this paper is to prove the following result. IfA is a right pure semisimple ring, then it satisfies one of the two following statements:

1. For any positive integern, there are at most finitely many indecomposable right modules of lengthn; or
2. There is an infinite number of integersd such that, for eachd, A has infinitely many indecomposable right modules of lengthd.

The result is derived with the aid of ultraproduct-technique.     

Some Reactions of 5-(3 or 4-Pyridyl)-1,3,4-Oxadiazoles with Amines and Hydrazines

2-Amino-and 2-hydrazino-5-(3 or 4-pyridyl)-1, 3, 4-oxadiazoles [II_i-k] have been prepared by racting 2-chloro derivatives with the corresponding amines or hydrazines, the 2-hydrazino (II_i-k) compounds that obtained were heated with carbon disulphide and alcoholic potassium hydroxide where 5-(3 or 4-pyridyl)-1,3,4-oxadiazolo (2,3-C)-1,2,4-triazole 5-thione (III_a-c) were obtained, the given structures were biologically screened.     

Investigation of diazepam drug using thermal analyses, mass spectrometry and semi-empirical MO calculation

In the present work diazepam (Dz) drug was investigated using thermal analyses (TA) measurements (TG/DTG) in comparison with EI mass spectral (MS) fragmentation at 70 and 20 eV. Semi-empirical MO calculations, MNDO procedure, have been carried out on diazepam both as neutral molecule and the corresponding positively charged molecular ion. These include molecular geometry, bond order, charge distribution, heats of formation and ionization energy. Thermogravimetric and kinetic analysis, reveal a high response of the drug to the temperature variation with very fast rate. It is completely decomposed in the temperature range between 204 and 340 degrees C with average kinetic energy (KE) at 164.69 kJ mol(-1). On the other hand, diazepam can easily fragmented at low energy after ionization by electron energy at 9.56 eV. The losses of CO gas molecules followed by chlorine gas from the entity of diazepam (both neutral and charged molecular ion) as the best selected pathway were observed in both mass spectra (MS) and thermal analyses (TA). MNDO calculation was applied to declare both TA and MS observations.     

Microdetermination of some xylenols via investigation of their catalyzed reactions with iodine

The oxidation of some xylenols with iodine in aqueous ethanolic solutions in the presence of silver ions as a catalyst was investigated and used for microdetermination of these reductants. The study of these redox reactions and the microdetermination of these phenols were performed by volumetric and spectrophotometric methods. These methods were compared. The spectrophotometric method was more accurate at very low concentrations (60–488 μg). The volumetric methods used silver ions as catalyst. The potentiometric method is more accurate than the visual method. Possible schemes for the course of these redox reactions were suggested. One electron processes for oxidation of xylenols have been indicated.     

Reactivity of 4-bromomethylquinoline derivatives towards glycine and thioglycolic acid. A new ring system

Condensation of 4-bromomethylquinoline derivatives1 a-1 c with glycine and thioglycolic acid gave the corresponding quinolylmethylglycine and quinolylmethylthioacetic acid derivatives2 a-2 c and2 d-2 f, respectively. Cyclization of2 a-2 f was affected either by polyphosphoric acid or concentrated sulphuric acid to give3 a-3 f. Chlorination of2 a-2 f and3 a-3 f were also accomplished.

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Die Reaktivität von 4-Brommethylchinolin-Derivaten gegenüber Glycin und Thioglycolsäure. Ein neues Ringsystem

Zusammenfassung Die Reaktion von 4-Brommethylchinolin-Derivaten1 a-c mit Glycin und Thioglycolsäure gab die entsprechenden Kondensationsprodukte2 a-c und2d-f.2 a-f konnten mit Polyphosphorsäure bzw. mit konzentrierter Schwefelsäure zu Benzo[c]-2,6-naphthyridinen3 a-f zyklisiert werden.2 a-f und3 a-f waren einer Chlorierung (POCl₃) zugängig.