Intrinsic carrier concentration in Hg1−xCdxTe

The effective mass of heavy holes has been determined on the basis of simultaneous analysis of the Hall coefficient and conductivity data obtained in the temperature region 100–300 K on well characterized p-type Hg_1–x Cd_xTe (x0·2) samples. Its value is 0·7m₀. The calculation of intrinsic carrier concentration for 0·19 x0·3 and 50 Kg T 300 K has been carried out using the above value of the effective mass of holes, Hansen's expression for the band gap and momentum matrix element from magneto-optical measurements.     

On the structure of modules of vector-valued modular forms

If \(\rho \) denotes a finite-dimensional complex representation of \(\mathbf {SL}_{2}(\mathbf {Z})\), then it is known that the module \(M(\rho )\) of vector-valued modular forms for \(\rho \) is free and of finite rank over the ring M of scalar modular forms of level one. This paper initiates a general study of the structure of \(M(\rho )\). Among our results are absolute upper and lower bounds, depending only on the dimension of \(\rho \), on the weights of generators for \(M(\rho )\), as well as upper bounds on the multiplicities of weights of generators of \(M(\rho )\). We provide evidence, both computational and theoretical, that a stronger three-term multiplicity bound might hold. An important step in establishing the multiplicity bounds is to show that there exists a free basis for \(M(\rho )\) in which the matrix of the modular derivative operator does not contain any copies of the Eisenstein series \(E_6\) of weight six.     

Stein domains in complex surfaces

Let S be a closed connected real surface and π: S→X a smooth embedding or immersion of S into a complex surface X. We denote by I(π) (resp. by I_±(π) if S is oriented) the number of complex points of π (S)∪X counted with algebraic multiplicities. Assuming that I(π)≤0 (resp. I_±(π)≤0 if S is oriented) we prove that π can be C⁰ approximated by an isotopic immersion π₁: S→X whose image has a basis of open Stein neighborhood in X which are homotopy equivalents to π₁ (S). We obtain precise results for surfaces in and find an immersed symplectic sphere in with a Stein neighborhood.     

Oka properties of ball complements

Let $n>1$ be an integer. We prove that holomorphic maps from Stein manifolds $X$ of dimension ${<}n$ to the complement $\mathbb {C}^n{\setminus } L$ of a compact convex set $L\subset \mathbb {C}^n$ satisfy the basic Oka property with approximation and interpolation. If $L$ is polynomially convex then the same holds when $2\dim X \le n$ . We also construct proper holomorphic maps, immersions and embeddings $X\rightarrow \mathbb {C}^n$ with additional control of the range, thereby extending classical results of Remmert, Bishop and Narasimhan.     

Stein compacts in Levi-flat hypersurfaces

We explore connections between geometric properties of the Levi foliation of a Levi-flat hypersurface and holomorphic convexity of compact sets in , or bounded in part by . Applications include extendability of Cauchy-Riemann functions, solvability of the -equation, approximation of Cauchy-Riemann and holomorphic functions, and global regularity of the -Neumann operator.

     

Nonlinear mapping and distance geometry

Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well established questions: DGP is about finding a Euclidean realization of an incomplete set of distances in a Euclidean space, whereas Nonlinear Mapping is a weighted Least Square Scaling (LSS) method. We show how all these methods (LSS, NLM, DGP) can be assembled in a common framework, being each identified as an instance of an optimization problem with a choice of a weight matrix. We study the continuity between the solutions (which are point clouds) when the weight matrix varies, and the compactness of the set of solutions (after centering). We finally study a numerical example, showing that solving the optimization problem is far from being simple and that the numerical solution for a given procedure may be trapped in a local minimum.

     

Efficient stabilization of copper(III) in tetraaza pseudo-macrocyclic oxime-and-hydrazide ligands with adjustable cavity size

Substitution of the amide donors in open-chain {2N(oxime), 2N(amide)} ligands by hydrazide donors gives new pseudo-macrocyclic copper complexes that show a significant decrease of the Cu(3+/2+) redox potentials in both mono- and polynuclear systems, thus demonstrating a pronounced capacity of such ligand systems to efficiently stabilize the trivalent copper.