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.     

Finite element modal solutions of planar photonic crystal fibers with rectangular air-holes

Modal solutions of planar photonic crystal waveguides with rectangular air-holes are presented by using a rigorous full-vectorial finite element-based approach. The effective indices, mode field profiles, spot-sizes, power confinements, modal hybridness, beat lengths and group velocity dispersions are shown for the fundamental and higher order modes of the quasi-TE and TM polarizations.     

Selected action density to speed up the computation of the nonlinear wave-wave interactions

This paper deals with the development of a numerical method to study the non-linear wave-wave interactions in oceans. Based on works from Webb-Tracy-Resio, the Hasselmann’s non-linear mathematical model is reviewed numerically. With this theory and the selection of action density domain, a program to reduce time of computation has been developed. Results from new computation are displayed graphically and compared with previous program. This work augments our understanding better about the non-linear process of wave-wave interactions and it improves the numerical computations to obtain efficiency in operational forecast.     

The convex hull property and topology of hypersurfaces with nonnegative curvature

We prove that, in Euclidean space, any nonnegatively curved, compact, smoothly immersed hypersurface lies outside the convex hull of its boundary, provided the boundary satisfies certain required conditions. This gives a convex hull property, dual to the classical one for surfaces with nonpositive curvature. A version of this result in the nonsmooth category is obtained as well. We show that our boundary conditions determine the topology of the surface up to at most two choices. The proof is based on uniform estimates for radii of convexity of these surfaces under a clipping procedure, a noncollapsing convergence theorem, and a gluing procedure.     

Synthesis and characterization of isotopically enriched methylmercury (CH3201Hg+)

A simple procedure for the synthesis of an important standard, isotopically enriched methylmercury, which is not commercially available, has been established successfully. The isotopically enriched standard synthesized is utilized in conventional isotope dilution mass spectrometry (IDMS), as well as in speciated IDMS (SIDMS), for determination of the true concentration of methylmercury in environmental samples. The CH₃²⁰¹Hg⁺ standard has been synthesized from commercially available ²⁰¹HgO and tetramethyltin. The synthesis time required is 1 h at 60°C. The product is highly pure, yielding more than 90% as ²⁰¹Hg in CH₃²⁰¹Hg⁺. Hazardous dimethylmercury does not occur during this synthesis procedure. The product synthesized was analyzed using high‐performance liquid chromatography coupled with inductively coupled plasma mass spectrometry (ICP‐MS) and ICP‐MS alone in order to determine its concentration, isotopic composition and purity. The stability of the product was also evaluated for over 6 months and found to be stable at 4°C in the dark. The isotopically enriched methylmercury synthesized can be used in SIDMS and IDMS analyses as a standard. Copyright © 2003 John Wiley & Sons, Ltd.