Ultramicro determination of organic halogens using sealed tube dry combustion method

A sealed tube dry combustion method that is simple, accurate, and precise for ultramicro determination of halogens in organic compounds has been developed. Samples below 1 mg are heated at 580 °C for 1 h in an electric furnace. After the combustion and absorption of the gaseous halogen, the interior of the tube is rinsed. Subsequent titration is carried out potentiometrically with silver nitrate and yielded standard deviations of 0.21% for chlorine, 0.17% for bromine, and 0.25% for iodine.     

Studies on the synthesis of condensed pyridazine derivatives. IV. Synthesis and anxiolytic activity of 2-aryl-5,6-dihydro-(1)benzothiepino[5,4- c]pyridazin-3(2H)-ones and related compound.

A series of 2-aryl-5,6-dihydro-(1)benzothiepino[5,4-c]pyridazin-3(2H)- ones and related compounds were synthesized and evaluated for their ability to displace 3H-diazepam from rat brain membranes in vitro, and to prevent bicuculline induced convulsions in mice in vivo. Compounds with a 4'-methoxyphenyl (36) or 4'-chlorophenyl group (37, 39--42) as 2-aryl substituents showed prominent activities in both the in vitro and in vivo tests. Among them, 2-(4'-chlorophenyl)-5,6-dihydro- (37) and 2-(4'-chlorophenyl)-5,6-dihydro-10-fluoro-(1)benzothiepino[5,4-c]+ ++pyridazin- 3(2H)-one 7-oxides (41) showed activity twice as potent as diazepam in an anticonflict test (Vogel type, rats) while exhibiting less muscle relaxation (rotarod test, mice) and augmentation of gamma-aminobutyric acid-induced chloride current (Icl) in isolated frog sensory neurones than diazepam. Compound 37 (Y-23684) was selected from this series as a candidate for further development. The structure-activity relationships are discussed.     

Pharmacokinetics of brain natriuretic peptide in rats.

The pharmacokinetics of rat brain natriuretic peptide (rBNP) was compared with that of alpha-rat atrial natriuretic peptide (alpha-rANP) in rats. After intravenous infusion in rats (600 pmol min-1kg-1 for 2 min), the disappearance of plasma rBNP was 4-fold slower than that of alpha-rANP. The estimated mean plasma clearance rates for rBNP and alpha-rANP were 45.9 ml min-1kg-1 and 74.4 ml min-1kg-1, respectively. The affinity of rBNP for the clearance receptor or degradation enzyme was considered to be lower than that of alpha-rANP.     

Neumann initial–boundary value problem for Benjamin–Ono equation

We consider the Neumann initial–boundary value problem for Benjamin–Ono equation on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial–boundary value problem and the asymptotic behavior of solutions for large time.     

Asymptotics for Fractional Nonlinear Heat Equations

The Cauchy problem is studied for the nonlinear equations withfractional power of the negative Laplacian where (0,2), with critical = /n and sub-critical (0,/n)powers of the nonlinearity. Let u₀ L^1,a L C, u₀(x) 0 in Rⁿ, = . The case of not small initial data is of interest. It is proved that the Cauchy problemhas a unique global solution u C([0,); L L^1,a C) and the largetime asymptotics are obtained.     

Asymptotics of solutions for sub critical non‐convective type equations

We study the Cauchy problem for non‐linear dissipative evolution equations (1) where ?? is the linear pseudodifferential operator and the non‐linearity is a quadratic pseudodifferential operator (2) û ≡ ?_x→ξ u is the Fourier transformation. We consider non‐convective type non‐linearity, that is we suppose that a(t,0,y) ≠ 0. Let the initial data , are sufficiently small and have a non‐zero total mass , where is the weighted Sobolev space. Then we give the main term of the large time asymptotics of solutions in the sub critical case. Copyright © 2004 John Wiley & Sons, Ltd.     

Global existence of small solutions for the fourth-order nonlinear Schrödinger equation

We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation

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where \(n=1,2\). We prove global existence of small solutions under the growth condition of \(f\left( u\right) \) satisfying \(\left| \partial _{u}^{j}f\left( u\right) \right| \le C\left| u\right| ^{p-j},\) where \(p>1+\frac{4}{n},0\le j\le 3\).

     

Asymptotics of solutions to the generalized Ostrovsky equation

We consider the Cauchy problem for the generalized Ostrovsky equation

_utx=u+_(f(u))xx,$u_{tx}=u+{(f(u))}_{xx},$

where f(u)=|u|^ρ−1u$f(u)={|u|}^{\rho -1}u$ if ρ   is not an integer and f(u)=u^ρ$f(u)=u^{\rho }$ if ρ   is an integer. We obtain the L^∞${\mathbf{L}}^{\infty }$ time decay estimates and the large time asymptotics of small solutions under suitable conditions on the initial data and the order of the nonlinearity.     

Comparison of Bartlett-type adjusted tests in the multiparameter case

Considering some Bartlett-type adjusted tests for a simple hypothesis about a multidimensional parameter, this paper clarifies similarities and dissimilarities with the one-parameter case developed in the 1990s, where a major emphasis is put on the issue posed by Rao and Mukerjee [C.R. Rao, R. Mukerjee, Comparison of Bartlett-type adjustments for the efficient score statistic, J. Statist. Plann. Inference 46 (1995) 137-146] on the power under a sequence of local alternatives. Not surprisingly, there is an infinite number of adjustments which extend Chandra-Mukerjee and Taniguchi approaches to the multiparameter case. Revisiting their ideas, this paper presents four specific cases (type K, K=0,1,2,3) and gives a sufficient condition under which our generalized adjustment for each case is uniquely determined, where type 0 is a counterpart of Chandra and Mukerjee’s original proposal for Rao’s test statistic, whereas the latter three types are introduced as double adjustments related to the Cordeiro and Ferrari approach. If the adjustment of type 1 is made instead of type K, K=0,2,3, it is shown that Chandra and Mukerjee’s approach is equivalent to Taniguchi’s approach in terms of the third-order local power. The same is partially true for type 0, depending on the model under consideration. However, the adjustments of type K, K=2,3, reveal, in general, the non-equivalence of these two approaches in terms of the third-order local power.     

Global existence to the initial–boundary value problem for a system of nonlinear diffusion and wave equations

We prove the global existence of weak solution pair to the initial boundary value problem for a system of m-Laplacian type diffusion equation and nonlinear wave equation. The interaction of two equations is given through nonlinear source terms $f(u,v)$ and $g(u,v)$.