Tests for covariance matrices, particularly for high dimensional data

Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can be larger than the sample size, n. The statistics, derived under very general conditions, follow an approximate normal distribution for large p, also when p >> n. Simulation results, particularly emphasizing the case when p can be much larger than n, show that the proposed statistics are accurate for both size control and power. A discussion of the commonly used assumptions for high dimensional set up is also given, with the conclusions applicable in general as well as in the special case of high dimensional covariance testing

Spatial Distribution of Jack Pine Cones and Those Attacked by Insects

The middle crown and south quadrant of 6-m-tall jack pines, Pinus banksiana Lamb., produced significantly more cones than the rest of the tree. The number of cones attacked by Eucosma monitorana Heinrich was also highest in the middle crown and south quadrant. Laspeyresia toreuta (Grote) attacked the most cones in the middle crown. A positive, linear correlation existed between the number of cones attacked by inseets and cone abundanee per tree, indicating a response of the insect population to inereased food supply

Price-setting for Residential Water: Estimation of Water Demand in Lahore

The Water and Sewerage Agency (WASA) of Lahore is facing soaring demand and rising costs. But while massive investments are made to augment supply, tariffs remain low and are not adjusted in line with growing expenses. This has resulted not only in heavy and increasingly unsustainable reliance on loans and subsidies, but also in consumers undervaluing the resource, resulting in its inefficient utilisation. In this scenario, water tariffs badly need to be reformed. This study explores the potential of a pricing policy to regulate residential water demand in order to achieve the objectives of cost recovery, efficient water use, and equitable allocation of water resources. To this end, a demand function is estimated using household level data about water consumption and socio-economic characteristics of 156 households supplied by WASA, Lahore, for the period 2004-2006. Under block-rate tariffs the price variable is endogenously determined and a system of simultaneous equations emerges, solved here using two-stage least squares method. The estimated model explains 57 percent variation in water demand. The study finds water demand to be inelastic to price and, considering WASA’s exceedingly low tariffs, recommends up to 50 percent increase in the current tariff structure. Further computations show that a 50 percent increase will not endanger lifeline water supply. However, tariff increases may not be felt uniformly across all income groups, and absence of income data remains a limitation of this study. The study also recommends linking the non-volumetric part of tariffs to wealth-determined variables, such as property value and income.Water Demand; Price-setting

1-(2,6-Dichlorobenzoyl)-3-(3-methoxyphenyl)thiourea

The two aromatic rings in the title compound, C15H12Cl2N2O2S, enclose a dihedral angle of 37.49 (6)°. The molecule exists in the solid state in its thione form with typical thiourea C-S and C-O bonds lengths, as well as shortened C-N bonds. An intramolecular N-H...O hydrogen bond stabilizes the molecular conformation. In the crystal, molecules are connected by N-H...O and N-H...S hydrogen bonds, forming chains running along the alpha axis. Key indicators: single-crystal X-ray study; T = 173 K; mean σ (C–C) = 0.002 Å; disorder in main residue; R factor = 0.035; wR factor = 0.087; data-to-parameter ratio = 18.9

1-(3-Chloro­phen­yl)-3-(2,6-dichloro­benzo­yl)thio­urea

The structure of the title compound, C14H9Cl3N2OS, is composed of discrete mol­ecules with bond lengths and angles quite typical for thio­urea compounds of this class. The plane containing the thio­carbonyl and carbonyl groups subtends dihedral angles of 48.19 (3) and 87.51 (3)° with the planes formed by the 3-chloro and 2,6-dichloro­phenyl rings, respectively; the dihedral angle between the two benzene ring planes is 45.32 (3)°. An intra­molecular N—H⋯O hydrogen bond stabilizes the mol­ecular conformation and the mol­ecules form inter­molecular N—H⋯S and N—H⋯O hydrogen bonds, generating a sheet along the a axis

1-(4-Chloro­benzo­yl)-3-(2,4,6-trichloro­phen­yl)thio­urea hemihydrate

The asymmetric unit of the title compound, C14H8Cl4N2OS·0.5H2O, contains two independent mol­ecules with different conformations with respect to the aromatic ring planes, and one water mol­ecule. The bond lengths and angles are typical of thio­urea compounds of this class. The mol­ecule exists in the solid state in its thione form with typical thio­urea C—S and C—O bonds lengths, as well as shortened C—N bonds. The dihedral angles between the two aromatic planes are 66.93 (8) and 60.44 (9)° in the two independent mol­ecules. An intra­molecular N—H⋯O hydrogen bond stabilizes the mol­ecular conformation and the crystal packing is characterized by N—H⋯O, O—H⋯S and O—H⋯Cl hydrogen bonds

1-(3-Chloro­benzo­yl)-3-(2,3-dimethyl­phen­yl)thio­urea

The title mol­ecule, C16H15ClN2OS, exists in the solid state in its thione form with typical thio­urea C—S and C—O bonds lengths, as well as shortened C—N bonds. An intra­molecular N—H⋯O hydrogen bond stabilizes the mol­ecular conformation and inter­molecular N—H⋯S hydrogen bonds link the mol­ecules into centrosymmetric dimers. The dihedral angle between the aromatic rings is 50.18 (5)°

Molecular-dynamics simulations of stacking-fault-induced dislocation annihilation in pre-strained ultrathin single-crystalline copper films

We report results of large-scale molecular-dynamics (MD) simulations of dynamic deformation under biaxial tensile strain of pre-strained single-crystalline nanometer-scale-thick face-centered cubic (fcc) copper films. Our results show that stacking faults, which are abundantly present in fcc metals, may play a significant role in the dissociation, cross-slip, and eventual annihilation of dislocations in small-volume structures of fcc metals. The underlying mechanisms are mediated by interactions within and between extended dislocations that lead to annihilation of Shockley partial dislocations or formation of perfect dislocations. Our findings demonstrate dislocation starvation in small-volume structures with ultra-thin film geometry, governed by a mechanism other than dislocation escape to free surfaces, and underline the significant role of geometry in determining the mechanical response of metallic small-volume structures.Comment: 28 pages, 3 figure

1-(2,6-Dichloro­benzo­yl)-3-(2,3,5,6-tetra­chloro­phen­yl)thio­urea trichloro­methane hemisolvate

The title compound, C14H6Cl6N2OS·0.5CHCl3, crystallizes with four 1-(2,6-dichloro­benzo­yl)-3-(2,3,5,6-tetra­chloro­phen­yl)thio­urea mol­ecules and two trichloro­methane mol­ecules in the asymmetric unit. The thiourea molecules exist in the solid state in their thione forms with typical thio­urea C—S and C—O bonds lengths, as well as shortened C—N bonds. The —NH—C(=S)—NH—C(=O)— plane is almost perpen­dicular to the benzene ring in each thiourea molecule. Intra­molecular N—H⋯O hydrogen bonds stabilize the mol­ecular conformation and inter­molecular N—H⋯S hydrogen bonds stabilize the packing arrangement