混合Bitsadze-Lavrentév-Tricomi边值问题

It is well known that F. G. Tricomi (1923) is the originator of the theoryof boundary value problems for mixed type equations by establishing the Thicomi equation: y·u_xx+u_yy=0 which is hyperbolic for y < 0, elliptic for y=0. and parabolic for y= 0 and then applied it in the theory of transonic flows.Then A.V.Bitsadze together with M. A . Lavrent′ev (1950) established the Bitsadze Lavre nt′ev equation: sgn( y ) ·u_xx+u_yy=0 where sgn(y) = 1 for y > 0, = -1 for y<0, 0 for y=0 with the discontinuous coefficient sgn( y ) of u_xx, while in the case of Tricomi equation the corre sponding coefficient y is continuous. In this paper we establish the mixed Bitsadze Lavrent′ev Tricomi equation. Lu=K(y)·u_xx+sgn(x) ·u_yy+r(x,y)·u=f(x,y), where the coefficient K=K(y) of u_xx is increasing continuous and coefficient M=sgn(x) of u_yy discontinuous, r=r(x,y) is once continuously differentiable, f=f(x,y) continuous. Finally we prove the uniqueness of quasi regular solutions and observe that these new results can bbe applied in fluid dynamics.     

On the Reaction of Triaryl Trithioarsenites, (ArS)3As,with Octasulfur

para‐Substituted with electron donating or electron withdrawing groups triphenyl trithioarsenites, (ArS)₃As, and octasulfur in refluxing carbon disulfide or chloroform do not give the triaryl tetrathioarsenates, (ArS)₃As=S, as was claimed in the literature for tris(4‐methylphenyl) tetrathioarsenate. In some cases oxidative decomposition to As₂O₃ and disulfides ArSSAr was found. When equivalent amounts of the same esters and octasulfur were heated at 105 or 150 °C no As^V compound was detected or isolated and again some esters decomposed to As₂O₃ and disulfides. These experiments demonstrated that the aromatic trithioarsenites do not react with octasulfur, probably because they cannot open the octasulfur ring. These esters in solution react with octasulfur in the presence of a catalytic (10—20 mol%) amount of triethylamine giving disulfides, As₂O₃ and colored solids which could not be characterized.     

Production of antibodies from chicken egg yolk to phenyl- N -methylcarbamate insecticides for analytical purposes

With the aim of developing polyclonal antibodies binding as many phenyl-N-methylcarbamate insecticides (PNMCs) as possible, IgY antibodies were produced in laying hens. Two haptens (3-(2,6-dimethyl-4-(methylcarbamoyl)phenylaminocarbonyl)propanoic acid and 4-((2,6-dimethyl-4-(methylcarbamoyl)phenylaminocarbonyl)-3,3-dimethyl)butanoic acid) were synthesized preserving the major structural features of PNMCs, by a novel synthetic pathway. These haptens differed only in the spacer arm incorporated. Immunizing antigen and coating antigen were prepared by coupling the first hapten with bovine serum albumin and the second with thyroglobulin, from porcine thyroid glands, respectively. The titre and maturation increase in the developed antibodies, in the egg yolk, were assessed by non-competitive ELISA. Avidity and cross-reactivity of the antibodies with selected pesticides were estimated by means of competitive ELISA. The produced IgYs exhibited a high binding capacity to carbaryl, trimethacarb, metolcarb, aminocarb, and promecarb. These antibodies can be used for immunosorbent preparation for analytical purposes.     

A Comparative Study of Various Pretreatment Approaches for Bio-Ethanol Production from Willow Sawdust,Using Co-Cultures and Mono-Cultures of Different Yeast Strains

The effect of different pretreatment approaches based on alkali (NaOH)/hydrogen peroxide (H₂O₂) on willow sawdust (WS) biomass, in terms of delignification efficiency, structural changes of lignocellulose and subsequent fermentation toward ethanol, was investigated. Bioethanol production was carried out using the conventional yeast Saccharomyces cerevisiae, as well as three non-conventional yeasts strains, i.e., Pichia stipitis, Pachysolen tannophilus, Wickerhamomyces anomalus X19, separately and in co-cultures. The experimental results showed that a two-stage pretreatment approach (NaOH (0.5% w/v) for 24 h and H₂O₂ (0.5% v/v) for 24 h) led to higher delignification (38.3 ± 0.1%) and saccharification efficiency (31.7 ± 0.3%) and higher ethanol concentration and yield. Monocultures of S. cerevisiae or W. anomalus X19 and co-cultures with P. stipitis exhibited ethanol yields in the range of 11.67 ± 0.21 to 13.81 ± 0.20 g/100 g total solids (TS). When WS was subjected to H₂O₂ (0.5% v/v) alone for 24 h, the lowest ethanol yields were observed for all yeast strains, due to the minor impact of this treatment on the main chemical and structural WS characteristics. In order to decide which is the best pretreatment approach, a detailed techno-economical assessment is needed, which will take into account the ethanol yields and the minimum processing cost.     

A Class of Projection Methods for General Variational Inequalities

In this paper, we consider and analyze a new class of projection methods for solving pseudomonotone general variational inequalities using the Wiener-Hopf equations technique. The modified methods converge for pseudomonotone operators. Our proof of convergence is very simple as compared with other methods. The proposed methods include several known methods as special cases.     

Pexider type operators and their norms in <Emphasis Type="Italic">X</Emphasis><Subscript><Emphasis Type="Italic">λ</Emphasis></Subscript> spaces

In this paper, we introduce Pexiderized generalized operators on certain special spaces introduced by Bielecki-Czerwik and investigate their norms.     

Controlling thiiranium intermediates—a new route to an iNOS inhibitor

Our synthetic efforts towards an iNOS (inducible isoform of the nitric oxide synthase) inhibitor led us to the relatively unexplored field of generating and controlling the reactivity of chiral, unsymmetrical thiiranium species. We found that product regiochemistry depends on a tunable equilibrium, the understanding of which proved pivotal in defining a new route to a drug substance. The development of a new amidination method is also discussed.     

On the stability of the linear functional equation in a single variable on complete metric groups

In this paper we obtain a result on Hyers–Ulam stability of the linear functional equation in a single variable $f(\varphi (x)) = g(x) \cdot f(x)$ on a complete metric group.     

Low temperature,high pressure Raman study of SbSBr

Abstract

We have measured the Raman spectra of the quasi-one-dimensional crystal SbSBr as a function of pressure at 295, 70, 37 and 25 K.

The pressure coefficients of the observed Raman modes have been determined and used to distinguish inter-from intrachain modes. Spectral features characteristic of the ferroelectric phase have been attributed to impurities or lattice imperfections and not to the presence of the ferroelectric phase, providing indication that the para-to ferroelectric phase transition occurs below 25 K.     

On the Ulam stability of Jensen and Jensen type mappings on restricted domains

In 1941 Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 Bourgin was the second author to treat this problem for additive mappings. In 1982-1998 Rassias established the Hyers-Ulam stability of linear and nonlinear mappings. In 1983 Skof was the first author to solve the same problem on a restricted domain. In 1998 Jung investigated the Hyers-Ulam stability of more general mappings on restricted domains. In this paper we introduce additive mappings of two forms: of “Jensen” and “Jensen type,” and achieve the Ulam stability of these mappings on restricted domains. Finally, we apply our results to the asymptotic behavior of the functional equations of these types.