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.     

Novel model of FM-noise conversion in a UMZI using RF external phase modulation of lasers: Theoretical and experimental results

In this paper, we propose and demonstrate a new and original model for theoretical calculation and experimental measurement of the noise power spectral density (NPSD) in phase-modulated optical links. The phase modulation is operated in the RF frequency range by an external phase modulator. The NPSD is derived for the first time in interferometric systems, by considering all effects such as the 1/f FM noise of the laser and white noise applied to light from a 1550 nm DFB laser, with phase modulation. The results show for the first time the influence of the phase modulation index, modulation frequency and interferometric delay in the phase-to-intensity noise conversion. The experimental and simulation results of conversion of FM-noise to intensity noise in an optical link by considering the external RF phase modulation are shown with good agreement.     

An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss

A subclass of the scale-parameter exponential family is considered and for the rth power of the scale parameter, which is lower bounded, an admissible minimax estimator under scale-invariant squared-error loss is presented. Also, an admissible minimax estimator of a lower-bounded parameter in the family of transformed chi-square distributions is given. These estimators are the pointwise limits of a sequence of Bayes estimators. Some examples are given.     

Synthesis of Highly Functionalized Isoxazolinediones from One-pot Reaction of Alkylidene Meldrum ’s Acid with Alkyl Isocyanides in the Presence of Arylhydroxylamines

Alkyl isocyanides undergo a smooth reaction with alkylidene Meldrum’s acids in the presence of arylhydroxylamines to produce N ¹-alkyl-2-(3,5-dioxo-2-aryltetrahydro-4-isoxazolyl)alkanamides in high yields.     

Silver(I)-selective coated-wire electrode based on an octahydroxycalix[4]arene derivative.

The performance of octahydroxycalix[4]arene derivative used as a neutral carrier for silver polymeric membrane electrode was studied. The sensor gave a good Nernstian response of 58 +/- 1 mV per decade for silver ion in the activity range 3.3 x 10(-6) to 3.3 x 10(-2) M Ag+. The limit of detection reached 2.1 x 10(-6) M Ag+ and exhibited high selectivity for silver ion against the alkali, alkaline earth and transition metal ions. The sensor can be used in wide pH range from 1.5 to 6.5. The response time of the sensor is less than 20 s. The potentiometric sensor was used as the indicator electrode in the titration of Ag+ ions by sodium chloride solution.     

Constructing a new optical sensor for monitoring ammonia in water samples using bis(acetylacetoneethylendiamine)-tributylphosphin cobalt(III) tetraphenylborate complex-coated triacetylcellulose.

A new ammonia optical sensor was designed using bis(acetylacetoneethylendiamine)tributylphosphin cobalt(III) tetraphenylborate complex, coated on transparent triacetylcellulose film as membrane. The change in the absorbance of the optode at the maximum wavelength of 408 nm was related to ammonia concentration in aqueous samples. A buffer solution with a pH of 9 (sodium borate-HCl) was used. The optode was fully regenerated in pH 2. The linear dynamic range for determination of ammonia was 3.3 x 10(-4) to 6.9 x 10(-3) mol l(-1) with a detection limit of 5.0 x 10(-5) mol l(-1) and a response time range of 4 - 6 min. This membrane was successfully applied for determination of ammonia in drinking water.     

Coated wire silver-ion selective electrode based on a N,N'-bis(2-thienylmethylene)-1,2-diaminobenzene.

A novel membrane coated platinum-wire electrode (MCPWE) based on N,N'-bis(2-thienylmethylene)-1,2-diaminobenzene (BTMD) for highly selective determination of Ag+ ion has been developed. The influences of membrane composition and pH on the potentiometric responses of electrode were investigated. The potentiometric responses are independent of the pH of the test solution in the range of 5.0 - 9.0. The electrode shows a linear response for Ag+ ion over the concentration range of 1.0 x 10(-60 to 1.0 x 10(-1) M with a lower detection limit of 6.0 x 10(-7) M. The electrode possesses a Nernstian slope of 59.7 mV decade(-1) and a fast response time of < or = 17 s and can be used for at least 2 months without any observable deviation. The proposed electrode displayed very good selectivity for Ag+ ion with respect to NH4+ and alkali, alkaline earth and some common transition metal ions. The practical utility of the electrode has been demonstrated by its use as the indicator electrode in the potentiometric titration of an AgNO3 solution with a NaI solution and in determination of the silver content of a developed radiological film.     

Some inequalities for the polar derivative of a polynomial

LetP(z) be a polynomial of degreen which does not vanish in |z|<1. In this paper, we estimate the maximum and minimum moduli of thekth polar derivative ofP(z) on |z|=1 and thereby obtain compact generalizations of some known results, which among other results, yields interesting refinements of Erdos-Lax theorem and a theorem of Ankeny and Rivlin.