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.     

Periodicity and convergence for xn+1=|xn−xn−1|

Each solution {x_n} of the equation in the title is either eventually periodic with period 3 or else, it converges to zero—which case occurs depends on whether the ratio of the initial values of {x_n} is rational or irrational. Further, the sequence of ratios {x_n/x_n−1} satisfies a first-order difference equation that has periodic orbits of all integer periods except 3. p-cycles for each p≠3 are explicitly determined in terms of the Fibonacci numbers. In spite of the non-existence of period 3, the unique positive fixed point of the first-order equation is shown to be a snap-back repeller so the irrational ratios behave chaotically.     

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.     

Spectrophotometric and AAS determination of trace amounts of cobalt after preconcentration by using alpha-benzilmonoxime-microcrystalline naphthalene.

The formed cobalt-a-benzilmonoxime complex was adsorbed onto microcrystalline naphthalene. Then it was determined by zero and first derivative spectrophotometry and by atomic absorption spectrophotometry (AAS) after dissolving into chloroform and methylisobutylketone (MIBK), respectively. Under optimum conditions, cobalt in the range of 1.0 - 20.0, 0.4 - 30.0 and 2.5 - 50.0 microg could be determined by spectrophotometry, first derivative spectrophotometry and AAS method, respectively. By the method, a preconcentration factor equal to approximately 30 for cobalt was obtained. The effect of diverse ions on the determination of 5.0 microg cobalt was also studied. The method was successfully applied to some pharmaceuticals and synthetic alloy samples.     

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.     

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.     

Convergence analysis of perturbed hemivariational inequalities

We consider the rate of convergence for a class of perturbed hemivariational inequalities in reflexive Banach Spaces. Our results can be viewed as an extension and refinement of some previous known results in this area.