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1.
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. 相似文献
2.
M. Zayed 《Archiv der Mathematik》2002,78(5):345-349
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. 相似文献
3.
Mohamed Hilmy Elnagdi Ramadan Maawad Abdel-Motaleb Mona Mustafa Mohamed Foad Zayed Eman Moustafa Kamel 《Journal of heterocyclic chemistry》1987,24(6):1677-1681
The behaviour of several 2-amino-3-cyano-4H-pyran derivatives toward a variety of nucleophilic reagents is reported. 相似文献
4.
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.
5.
Ahmed I. Zayed 《Journal of Fourier Analysis and Applications》1995,2(3):303-314
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 tn = an + b if n = 0, 1, 2, ... and tn = 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. 相似文献
6.
Maher Zayed 《Monatshefte für Mathematik》1988,105(2):165-170
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:
- For any positive integern, there are at most finitely many indecomposable right modules of lengthn; or
- There is an infinite number of integersd such that, for eachd, A has infinitely many indecomposable right modules of lengthd.
7.
8.
9.
2-Amino-and 2-hydrazino-5-(3 or 4-pyridyl)-1, 3, 4-oxadiazoles [IIi-k] have been prepared by racting 2-chloro derivatives with the corresponding amines or hydrazines, the 2-hydrazino (IIi-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 (IIIa-c) were obtained, the given structures were biologically screened. 相似文献
10.
Zayed MA Fahmey MA Hawash MF 《Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy》2005,61(5):799-805
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. 相似文献