从含Sn,Zn,Cu,Pb,In的盐酸溶液中用TBP萃取Sn

文题的最佳工艺条件为:25%TBP-10%癸醇-65%煤油,3mol/LHCl,20～30℃。负载有机相中的杂质离子Zn~(2+),Cu~(2+),In~(3+),Pb~(2+)用约5mol/L盐酸洗涤除去。负载有机相中的Sn~(4+)用0.24mol/L HCl反萃。萃取及反萃取的理论级数分别为2和7级。     

The index of a critical point for densely defined operators of type in Banach spaces

The purpose of this paper is to demonstrate that it is possible to define and compute the index of an isolated critical point for densely defined operators of type acting from a real, reflexive and separable Banach space into This index is defined via a degree theory for such operators which has been recently developed by the authors. The calculation of the index is achieved by the introduction of a special linearization of the nonlinear operator at the critical point. This linearization is a new tool even for continuous everywhere defined operators which are not necessarily Fréchet differentiable. Various cases of operators are considered: unbounded nonlinear operators with unbounded linearization, bounded nonlinear operators with bounded linearization, and operators in Hilbert spaces. Examples and counterexamples are given in 2,$"> illustrating the main results. The associated bifurcation problem for a pair of operators is also considered. The main results of the paper are substantial extensions and improvements of the classical results of Leray and Schauder (for continuous operators of Leray-Schauder type) as well as the results of Skrypnik (for bounded demicontinuous mappings of type Applications to nonlinear Dirichlet problems have appeared elsewhere.

     

Sets of uniqueness for spherically convergent multiple trigonometric series

A subset of the -dimensional torus is called a set of uniqueness, or -set, if every multiple trigonometric series spherically converging to outside vanishes identically. We show that all countable sets are -sets and also that sets are -sets for every . In particular, , where is the Cantor set, is an set and hence a -set. We will say that is a -set if every multiple trigonometric series spherically Abel summable to outside and having certain growth restrictions on its coefficients vanishes identically. The above-mentioned results hold also for sets. In addition, every -set has measure , and a countable union of closed -sets is a -set.

     

N,N′-双{双[4-(二甲氨基)苯基]甲基}尿素合成的反应机理

由对二甲氨基苯甲醛(A)和N,N′-二甲基苯胺(B)在盐酸存在下与尿素反应,合成题示化合物。研究了它的反应机理。结果表明,在强酸存在下,该反应是分两步进行的。首先是A和B缩合形成米氏醇(4,4′-二甲氨基二苯甲醇)中间物,然后再与尿素作用得到尿素衍生物。同时证明,该类取代苯甲醛与取代芳胺,在强酸介质中与尿素作用合成相应的尿素衍生物,都是按上述两步机理进行的。     

On linearly Lindelöf and strongly discretely Lindelöf spaces

We prove that the cardinality of every first countable linearly Lindelöf Tychonoff space does not exceed , and every strongly discretely Lindelöf Tychonoff space of countable tightness is Lindelöf.

     

Homogeneity and the disjoint arcs property

Some previous results of the author towards a classification of homogeneous metric continua are improved. The disjoint arcs property is fully revealed in this context. In particular, closed -manifolds, , are characterized as those homogeneous continua which do not have the disjoint arcs property.

     

En">Characters and Composition Factor Multiplicities for the Lie Superalgebra $${\mathfrak{g}}{\mathfrak{l}}$$ ( m / n )

The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra (m/n ) were described by Serganova, leading to her solution of the character problem for (m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed.     

On the quintuple product identity

In this note we present a new proof of the quintuple product identity which is based on our study of order theta functions with characteristics and the identities they satisfy. In this context the quintuple product identity is another example of an identity which when phrased in terms of theta functions, rather than infinite products and sums, has a simpler form and is much less mysterious.

     

Some rapidly converging series for

For a natural number , the author derives several families of series representations for the Riemann Zeta function . Each of these series representing converges remarkably rapidly with its general term having the order estimate:

Relevant connections of the results presented here with many other known series representations for are also pointed out.