Enhancement of electron spin coherence by optical preparation of nuclear spins

We study a large ensemble of nuclear spins interacting with a single electron spin in a quantum dot under optical excitation and photon detection. At the two-photon resonance between the two electron-spin states, the detection of light scattering from the intermediate exciton state acts as a weak quantum measurement of the effective magnetic (Overhauser) field due to the nuclear spins. In a coherent population trapping state without light scattering, the nuclear state is projected into an eigenstate of the Overhauser field operator, and electron decoherence due to nuclear spins is suppressed: We show that this limit can be approached by adapting the driving frequencies when a photon is detected. We use a Lindblad equation to describe the driven system under photon emission and detection. Numerically, we find an increase of the electron coherence time from 5 to 500 ns after a preparation time of 10 micros.     

Topological Homology Semi-Biplanes

 Coherent, topological, tactical semi-biplanes are homology semi-biplanes. In particular, semi-biplanes constructed from pairs of non-collinear points in compact antiregular quadrangles are homology semi-biplanes. (Received 7 March 2000; in final form 12 October 2000)     

Finding all essential terms of a characteristic maxpolynomial

Let us denote ab=max(a,b) and ab=a+b for and extend this pair of operations to matrices and vectors in the same way as in linear algebra. We present an O(n²(m+n log n)) algorithm for finding all essential terms of the max-algebraic characteristic polynomial of an n×n matrix over with m finite elements. In the cases when all terms are essential, this algorithm also solves the following problem: Given an n×n matrix A and k{1,…,n}, find a k×k principal submatrix of A whose assignment problem value is maximum.     

Nanoindentation of glass wool fibers

The nanoindentation technique is used to analyze the depth dependence of the hardness and the reduced elastic modulus of bulk glasses and glass wool fibers (4-12 μm in diameter) of calcium aluminosilicate composition. In spite of the fiber geometry and the delicate sample mounting-technique, nanoindentation proves to be a relatively accurate method that provides reproducible data for both hardness (H) and reduced elastic modulus (E_r) of thin glass fibers. It is found that H and E_r are generally lower for the fiber than for the bulk sample. Within a given fiber, both H and E_r are approximately constant with increasing indentation depth. However, both of these parameters decrease with diminishing fiber diameter. This trend is attributed to an increase of the free volume of the fibers with decreasing fiber diameter, i.e. to an increase of the fictive temperature.     

Solvent-Enhanced Conformational Flexibility of Cyclic Tetrapeptides

Solvent and temperature can affect the structural properties of cyclic peptides by controlling their flexibility. Here, we investigate two cyclic peptides, featuring beta turns. Using temperature-dependent NMR and FT-IR, we observed a pronounced temperature effect on the conformation of the cyclic peptide D-1 in CHCl₃ but a much smaller effect in CH₃CN. Almost no effect was observed for its diastereomer L-1 within a similar temperature range and using the same solvents. With the aid of Replica Exchange Molecular Dynamics simulations and Quantum Mechanics/Molecular Mechanics calculations, we were able to explain this behavior based on the increased flexibility of D-1 (in CHCl₃) in terms of intramolecular hydrogen bonding. The largest temperature dependence is observed for D - 1 in CHCl₃, while the temperature effect is less pronounced for L-1 in CHCl₃ and for both peptides in CH₃CN. This work provides new insights into the role of the environment and temperature on the conformations of cyclic peptides.     

Elementary constructions of locally compact affine planes

In this paper we describe several elementary constructions of 4-, 8- and 16-dimensional locally compact affine planes. The new planes share many properties with the classical ones and are very easy to handle. Among the new planes we find translation planes, planes that are constructed by gluing together two halves of different translation planes, 4-dimensional shift planes, etc. We discuss various applications of our constructions, e.g. the construction of 8- and 16-dimensional affine planes with a point-transitive collineation group which are neither translation planes nor dual translation planes, the proof that a 2-dimensional affine plane that can be coordinatized by a linear ternary field with continuous ternary operation can be embedded in 4-, 8- and 16-dimensional planes, the construction of 4-dimensional non-classical planes that admit at the same time orthogonal and non-orthogonal polarities. We also consider which of our planes have tangent translation planes in all their points. In a final section we generalize the Knarr-Weigand criterion for topological ternary fields.This research was supported by a Feodor Lynen fellowship.     

A linear time algorithm for inverse obnoxious center location problems on networks

For an inverse obnoxious center location problem, the edge lengths of the underlying network have to be changed within given bounds at minimum total cost such that a predetermined point of the network becomes an obnoxious center location under the new edge lengths. The cost is proportional to the increase or decrease, resp., of the edge length. The total cost is defined as sum of all cost incurred by length changes. For solving this problem on a network with m edges an algorithm with running time ${\mathcal{O}(m)}$ is developed.     

Inverse median location problems with variable coordinates

Given n points in \mathbbR^d{\mathbb{R}^d} with nonnegative weights, the inverse 1-median problem with variable coordinates consists in changing the coordinates of the given points at minimum cost such that a prespecified point in \mathbbR^d{\mathbb{R}^d} becomes the 1-median. The cost is proportional to the increase or decrease of the corresponding point coordinate. If the distances between points are measured by the rectilinear norm, the inverse 1-median problem is NP{\mathcal{NP}}-hard, but it can be solved in pseudo-polynomial time. Moreover, a fully polynomial time approximation scheme exists in this case. If the point weights are assumed to be equal, the corresponding inverse problem can be reduced to d continuous knapsack problems and is therefore solvable in O(nd) time. In case that the squared Euclidean norm is used, we derive another efficient combinatorial algorithm which solves the problem in O(nd) time. It is also shown that the inverse 1-median problem endowed with the Chebyshev norm in the plane is NP{\mathcal{NP}}-hard. Another pseudo-polynomial algorithm is developed for this case, but it is shown that no fully polynomial time approximation scheme does exist.     

Buchbesprechungen

Ohne Zusammenfassung     

A Note on the Robust 1-Center Problem on Trees

We consider the robust 1-center problem on trees with uncertainty in vertex weights and edge lengths. The weights of the vertices and the lengths of the edges can take any value in prespecified intervals with unknown distribution. We show that this problem can be solved in O(n ³ logn) time thus improving on Averbakh and Berman's algorithm with time complexity O(n ⁶). For the case when the vertices of the tree have weights equal to 1 we show that the robust 1-center problem can be solved in O(nlogn) time, again improving on Averbakh and Berman's time complexity of O(n ² logn).