Packing r-Cliques in Weighted Chordal Graphs

In 1, we have previously observed that, in a chordal graph G, the maximum number of independent r-cliques (i.e., of vertex disjoint subgraphs of G, each isomorphic to K_r, with no edges joining any two of the subgraphs) equals the minimum number of cliques of G that meet all the r-cliques of G. When r = 1, this says that chordal graphs have independence number equal to the clique covering number. When r = 2, this is equivalent to a result of Cameron (1989), and it implies a well known forbidden subgraph characterization of split graphs. In this paper we consider a weighted version of the above min-max optimization problem. Given a chordal graph G, with a nonnegative weight for each r-clique in G, we seek a set of independent r-cliques with maximum total weight. We present two algorithms to solve this problem, based on the principle of complementary slackness. The first one operates on a graph derived from G, and is an adaptation of an algorithm of Farber (1982). The second one improves the performance by reducing the number of constraints of the linear programs. Both results produce a min-max relation. When the algorithms are specialized to the situation in which all the r-cliques have the same weight, we simplify the algorithms reported in 1, although these simpler algorithms are not as efficient. As a byproduct, we also obtain new elementary proofs of the above min-max result.     

The Speciality Lemma, Rank 2 Bundles and Gherardelli-type Theorems for Surfaces in P 4

In the present paper we give a very short and easy proof of the speciality lemma for codimension 2 subvarieties, even those that are reducible or non-reduced, in P ⁿ . Furthermore we give cohomological conditions that force a subcanonical surface in P ⁴ to be a complete intersection and a rank 2 bundle to split, which generalize the classical First Theorem of Gherardelli.     

Half-Range Expansions for an Astrophysical Problem

Problems of spectral analysis are studied for an indefinite singular boundary value problem coming from astrophysical theory of particle acceleration around shocks. This leads to a nonclassical initial-boundary value problem for a partial differential equation that can bereduced by separation of variables to an indefinite Sturm–Liouville problem for which we establish Riesz basis properties of the eigen- and associated functions and formulate completeness and expansion theorems.     

Generalized Semicontinuity and Existence Theorems for Cone Saddle Points

This paper is concerned with existence theorems for generalized saddle points (cone saddle points) of vector-valued functions. A concept of lower semicontinuity for vector-valued functions is introduced and its properties are investigated. Previous results of the author are extended by using the lower semicontinuity. Accepted 26 April 1996     

InAs/AlAs quantum dots with InGaAs insertion layer: dependence of the indium composition and the thickness

We have systematically studied the effect of an In_xGa_1−xAs insertion layer (IL) on the optical and structural properties of InAs quantum dot (QD) structures. A high density of 9.6×10¹⁰ cm⁻² of InAs QDs with an In_0.3Ga_0.7As IL has been achieved on a GaAs (1 0 0) substrate by metal organic chemical vapor deposition. A photoluminescence line width of 25 meV from these QDs has been obtained. We attribute the high density and high uniformity of these QDs to the use of the IL. Our results show that the InGaAs IL is useful for obtaining high-quality InAs QD structures for devices with a 1.3 μm operation.     

On nonparametric tests for symmetry inRm

This paper considers the problem for testing symmetry of a distribution inR ^m based on the empirical distribution function. Limit theorems which play important roles for investigating asymptotic behavior of such tests are obtained. The limit processes of the theorems are multiparameter Wiener process. Based on the limit theorems, nonparametric tests are proposed whose asymptotic distributions are functionals of a multiparameter standard Wiener process. The tests are compared asymptotically with each other in the sense of Bahadur.     

Merged beam study of the associative ionisation ( C + , N + ? and ? O + )+ O -

Total cross-sections have been measured for the associative ionisation of C ⁺ + O ^- , N ⁺ + O ^- and O ⁺ + O ^- by means of a merged-beam set-up operating with keV beams. These original measurements might be relevant to the understanding of some astrophysical objects or laboratory-made plasmas (flames and etching plasmas). The magnitude of these cross-sections is particularly large whatever the associating system, as these are in the range of 1×10 ^-14 cm² at thermal energies. Their behaviour as a function of energy significantly differs from one system to another, and is characterised by the Wigner law at low energy, and a rapid fall-off at higher energy due to competition with non-associative ionisation processes. Received 10 December 2001 and Received in final form 12 March 2002     

Insertion of Selenium into Zinc Carbon Bond and Applicationin Synthesis of Arylselenoester

Selenium was inserted into the zinc carbon bond of aryl zinc halides to form corresponding zinc selenoates. They rected in THF-HMPA with acylhalides to afford the selenoesters in high yields.     

Minimal Positive Solutions to Some Singular Second-Order Differential Equations

The existence of a minimal C¹[0, 1] positive solution is established for some second-order singular boundary value and initial value problems by new schemes, which are related to x′. Our nonlinearity may be singular at t = 0, 1, x = 0, or x′ = 0.     

Molecular Structure of 1- (Diisopropyl )amino-2-(p-methyl )phenyl-3-methyl-phosphetane 1-oxided

lINTR0DUCTIONThechemistryofstablephospheniumcati0n[Rl-P-R2j hasbeenextensivelyknowntl-3).Wereportedsynthesesandreactions0fthephospheniumcati0nsfeatur-ingwithanS-P-Nlinkage.(4-8)Recentlywefoundthatphospheniumion[i-Pr2N-P-Clj [AlC'j-canregiOselectivelyinsertintophenylcyclopropaneringattwocycliccarbon-carbonb0ndsadjacenttophenylgr0uptogivel-(diisopropyl)amin0-2-(p-methyl)phenyl-3-methyl-phosphetanel-oxide(1).Inordertodisclosetherelativesterelchemistry,itssinglecrystalwasobtainedfromn-he…