Electronic structure of a thermoelectric material: CsBi4Te6

We have calculated the electronic structure of CsBi₄Te₆ by means of first-principles self-consistent total-energy calculations within the local-density approximation using the full-potential linear-muffin-tin-orbital method. From our calculated electronic structure we have calculated the frequency dependent dielectric function. Our calculations shows that CsBi₄Te₆ a semiconductor with a band gap of 0.3 eV. The calculated dielectric function is very anisotropic. Our calculated density of state support the recent experiment of Chung et al. [Science 287 (2000) 1024] that CsBi₄Te₆ is a high performance thermoelectric material for low temperature applications.     

On a low intensity <Superscript>241</Superscript>Am Compton spectrometer for measurement of electron momentum density

In this paper, a new design and construction of a low intensity (100 mCi) ²⁴¹Am γ-ray Compton spectrometer is presented. The planar spectrometer is based on a small disc source with the shortest geometry. Measurement of the momentum density of polycrystalline Al is used to evaluate the performance of the new design. The measured profile is in good agreement with the existing theoretical data and our density functional calculations.      

Probability-one homotopy maps for mixed complementarity problems

Probability-one homotopy algorithms have strong convergence characteristics under mild assumptions. Such algorithms for mixed complementarity problems (MCPs) have potentially wide impact because MCPs are pervasive in science and engineering. A probability-one homotopy algorithm for MCPs was developed earlier by Billups and Watson based on the default homotopy mapping. This algorithm had guaranteed global convergence under some mild conditions, and was able to solve most of the MCPs from the MCPLIB test library. This paper extends that work by presenting some other homotopy mappings, enabling the solution of all the remaining problems from MCPLIB. The homotopy maps employed are the Newton homotopy and homotopy parameter embeddings.     

A composite very large-scale neighborhood structure for the capacitated minimum spanning tree problem

The capacitated minimum spanning tree (CMST) problem is to find a minimum cost spanning tree in a network where nodes have specified demands, with an additional capacity constraints on the subtrees incident to a given source node s. The capacitated minimum spanning tree problem arises as an important subproblem in many telecommunication network design problems. In a recent paper, Ahuja et al. (Math. Program. 91 (2001) 71) proposed two very large-scale neighborhood search algorithms for the capacitated minimum spanning tree problem. Their first node-based neighborhood structure is obtained by performing multi-exchanges involving several trees where each tree contributes a single node. Their second tree-based neighborhood structure is obtained by performing multi-exchanges where each tree contributes a subtree. The computational investigations found that node-based multi-exchange neighborhood gives the best performance for the homogenous demand case (when all nodes have the same demand), and the tree-based multi-exchange neighborhood gives the best performance for the heterogeneous demand case (when nodes may have different demands). In this paper, we propose a composite neighborhood structure that subsumes both the node-based and tree-based neighborhoods, and outperforms both the previous neighborhood search algorithms for solving the capacitated minimum spanning tree problem on standard benchmark instances. We also develop improved dynamic programming based exact algorithms for searching the composite neighborhood.     

Finding minimum-cost flows by double scaling

Several researchers have recently developed new techniques that give fast algorithms for the minimum-cost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm(log logU) log(nC)) time on networks withn vertices,m edges, maximum arc capacityU, and maximum arc cost magnitudeC. The major techniques used are the capacity-scaling approach of Edmonds and Karp, the excess-scaling approach of Ahuja and Orlin, the cost-scaling approach of Goldberg and Tarjan, and the dynamic tree data structure of Sleator and Tarjan. For nonsparse graphs with large maximum arc capacity, we obtain a similar but slightly better bound. We also obtain a slightly better bound for the (noncapacitated) transportation problem. In addition, we discuss a capacity-bounding approach to the minimum-cost flow problem.Research partially supported by an NSF Presidential Young Investigator Fellowship, Contract 8451517ECS, and grants from Analog Devices, Apple Computer Inc., and Prime Computer.On leave from Indian Institute of Technology, Kanpur, India.Research partially supported by an NSF Presidential Young Investigator Award.Research at Princeton University partially supported by National Science Foundation Grant DCR-8605962 and Office of Naval Research Contract N00014-87-K-0467.     

On extremal properties for the polar derivative of polynomials

If p(z) is a polynomial of degree n having all its zeros on |z| = k, k ≤ 1, then it is proved[5] that max |z|=1 |p′(z)| ≤ kn1n + kn m|z|=ax1 |p(z)|. In this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type p(z) = cnzn + ∑n j=μ cn jzn j, 1 ≤μ≤ n. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.     

Changing the variable in convolution of distributions

In this paper the author has extended the concept of changing the variables in distributions to the convolution of distributions. For an infinitely differentiable functionh(x), he has first defined the convolution of two distributions f(h(x)) and g(h(x)) and then proved some of its properties. Finally, he has applied his results to the fractional integral and fractional differential operators