Twisted Semigroup Crossed Products and Twisted Toeplitz Algebras of Ordered Groups

Let г^＋ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г＋ as endomorphisms of C^＊-algebras, and use this to generalize the theorem of Ji.     

Dependence of viscosity of polystyrene solutions on molecular weight and concentration

Viscosities of solutions of polystyrene in toluene were measured for concentrations up to 400 kg m^?3 at 298 K. Polymers of molecular weights ranging from 8.7 × 10³ to 2.4 × 10⁶ were used. It is observed that viscosity of the polymer solution increases with increasing concentration and molecular weight; the rate of increase is greater at higher values of the two parameters. A master curve for the system is constructed by using the experimental data for viscosity, concentration and molecular weight of the polymer. Regions of various polymer interactions in solution are identified.     

Moufang Loops of Odd Orderpq1 ··· qnr1 ··· rm

LetLbe a Moufang loop of odd orderpαqα11···qnαnwherepandqiare primes with 3 ≤ p < q1 < ··· < qnand αi ≤ 2. In this paper, we prove thatLis a group ifpandqiare primes with 3 ≤ p < q1 < ··· < qn: (i) α ≤ 3, or (ii) α ≤ 4,p ≥ 5.     

Molal volumes of sucrose in aqueous solutions of NaCl,KCl, or urea at 25°C

The apparent molal volume _v of sucrose in water has been measured at 25°C in the concentration range 0.04–4.4m from precise density measurements. The same property was also determined for dilute solutions of sucrose in mixed aqueous solvents containing NaCl, KCl, or urea. The limiting values _v ^° and the slopesS _v ^* were obtained in each case, and their significance has been discussed briefly. The mean apparent molal volumes _v of the ternary systems were also calculated, and the predictive accuracy of Ward and Millero's modified Young's rule for _v was found to be comparable to that for other electrolyte-nonelectrolyte solutions. For the system H₂O-sucrose-urea, an additivity rule based simply on total molality predicted _v with similar accuracy.Deceased January 15, 1976.     

Symmetric Weighing Matrices Constructed using Group Matrices

A weighing matrix of order n and weight m² is a square matrix M of order n with entries from {-1,0,+1} such that MM^T=m²I where I is the identity matrix of order n. If M is a group matrix constructed using a group of order n, M is called a group weighing matrix. Recently, group weighing matrices were studied intensively, especially when the groups are cyclic and abelian. In this paper, we study the abelian group weighing matrices that are symmetric, i.e.M^T=M. Some new examples are found. Also we obtain a few exponent bounds on abelian groups that admit symmetric group weighing matrices. In particular, we prove that there is no symmetric abelian group weighing matrices of order 2p^r and weight p² where p is a prime and p≥ 5.Communicated by: K.T. Arasu     

Density,viscosity, conductance,and transference number of concentrated aqueous magnesium chloride at 25°C

The density, viscosity, conductance, and transference number of aqueous magnesium chloride at 298.15°K are reported for the concentration range 0 to 5.7m. The transference numbers were determined using the emf method. It was found that the viscosity, conductance, and transference number of aqueous magnesium chloride are similar to those for aqueous nickel chloride. It was therefore tentatively concluded that incomplete dissociation and complex formation was unlikely to be of importance in nickel chloride solutions.     

Effect of cloud on atmospheric ozone formation over Kolkata (22°34′N, 88°24′E), India

The paper presents the nature of variations of clouds and total ozone over Kolkata (22°34′N, 88°24′E), India. The low-level cloud over Kolkata has been noticed to occur for many days and nights, particularly in the months from June to September. The low level cloud occurrences were minimum in winter months. The effect of cloud occurrence on ozone concentration has been critically analyzed and explained. It has been observed that the concentration of ozone increased with the increase of cloud occurrence. The related possible chemical explanation for ozone production processes has been offered.     

Effect of nanoporous GaN templates with different pore diameters on the subsequent thick GaN layers by HVPE

A set of GaN films were overgrown by hydride vapor phase epitaxy (HVPE) on nanoporous GaN templates with different pore diameters. These samples have various properties as seen from the measurements of X-ray diffraction (XRD) and photoluminescence (PL). Cross-sectional observations under a scanning electron microscopy (SEM) reveal that the overgrowth mechanism and process are strongly related to the dimension of nanopores, indicating that an optimum diameter exists for the properties of subsequent HVPE–GaN layers. When the diameters of nanopores are less than the optimum value, the pores on top of GaN templates can be left, and the properties of HVPE–GaN films show significant improvement. In contrast, the pores are almost stuffed with HVPE–GaN films, which obviously limit the improvement degree of HVPE–GaN films.     

Optimization designs and performance comparison of two CUSUM schemes for monitoring process shifts in mean and variance

In statistical process control (SPC), when dealing with a quality characteristic x that is a variable, it is usually necessary to monitor both the mean value and variability. This article proposes an optimization algorithm (called the holistic algorithm) to design the CUSUM charts for this purpose. It facilitates the determination of the charting parameters of the CUSUM charts and considerably or significantly increases their overall detection effectiveness. A single CUSUM chart (called the ABS CUSUM chart) has been developed by the holistic algorithm and fully investigated. This chart is able to detect two-sided mean shifts and increasing variance shifts by inspecting the absolute value of sample mean shift. The results of performance studies show that the overall performance of the ABS CUSUM chart is nearly as good as an optimal 3-CUSUM scheme (a scheme incorporating three individual CUSUM charts). However, since the ABS CUSUM chart is easier for implementation and design, it may be more suitable for many SPC applications in which both mean and variance of a variable have to be monitored.     

Using one EWMA chart to jointly monitor the process mean and variance

Two control charts are usually used to monitor the process mean and variance separately. The mean is monitored using the [`(X)]{\bar{{X}}} chart while the variance using either the standard deviation, S chart, or the range, R chart. Recently, numerous single variable charts are proposed to jointly monitor the mean and variance. Most approaches transform the sample mean and sample variance into two statistics, each having a standard scale, and either plotting them on the same chart or combining them into a single statistic to be plotted on a chart. The R chart is more widely used than the S chart but no attempt is made to combine the [`(X)]{\bar{{X}}} and R charts in the construction of a single variable chart and to study its properties and performance. In this paper, we transform the [`(X)]{\bar{{X}}} and R statistics into two standard normal random variables, used in the computation of two corresponding exponentially weighted moving average (EWMA) statistics, which are then merged into a single plotting statistic for the proposed chart, called the EWMA [`(X)]-R{\bar{{X}}-R} chart.