Proof of the bieberbach conjecture for a certain class of univalent functions

In the following we prove that for a given univalent function such that |a ₂| <0.867, |a _n |≦n for eachn. The method of proof is closely related to Milin’s method.     

Facile Debromination by Potassium-Graphite Intercalate

The dehalogenation of vic-dihalides can be performed with the easily accessible potassium-graphite intercalate C₈K. The reaction is a convenient one, the yields are good, and the workup us simple.     

A charged particle in bimetric general relativity

The gravitational field of a charged particle is investigated on the basis of the bimetric general relativity theory. It is found that the field differs from the Reissner-Nordström field only very close to the sphereR=m+(m ² –Q ²)^1/2. This sphere is impenetrable, and its interior is unphysical.     

Model‐based guidelines for user‐centric satellite control software development

Three persistent common problems in satellite ground control software are obsolescence, lack of desired features and flexibilities, and endless software bug fixing. The obsolescence problem occurs when computer and ground equipment hardware become obsolete, usually after only one‐third into the satellite mission lifetime. The software needs to be updated to accommodate changes on the hardware side, requiring significant work of satellite operators to test, verify, and validate these software updates. Trying to help solve these problems, we have proposed an object‐process methodology model and guidelines for developing satellite ground control software. The system makes use of a database‐driven application and concepts of object‐process orientation and modularity. In the new proposed framework, instead of coding each software function separately, the common base functions will be coded, and combining them in various ways will provide the different required functions. The formation and combination of these base functions will be governed by the main code, definitions, and database parameters. These design principles will make sure that the new software framework would provide satellite operators with the flexibility to create new features and enable software developer to find bugs quicker and fix them more effectively. Copyright © 2015 John Wiley & Sons, Ltd.     

Basic phononic diagnostic measurements in fluid columns

A pre-selected 21 MHz ultrasonic transducer was used to produce characteristic pulses, arbitrarily similar to the quantum-mechanical concept of a phonon, describable as having a single-frequency modulated Gaussian shape. The propagation of such pulses in water-acoustic channels was studied in conjunction with nonlinear regression analysis and an Erlangian model for size distribution of molecular aggregates. Experimental results obtained distinguish between surface and bulk phenomena and provide quantitative measures of an average molecular cluster size in water. The relevance of the Erlangian model, in studying the near front of the channel, provides a significant distinction between the behavior of pure water and Ringer's solution of water. The inherent consistency between the various results re-enforces the theoretical approach, implying new venues for future research.     

On students’ conceptions of arithmetic average: the case of inference from a fixed total

There is more to understanding the concept of mean than simply knowing and applying the add-them-up and divide algorithm. In the following, we discuss a component of understanding the mean – inference from a fixed total – that has been largely ignored by researchers studying students understanding of mean. We add this component to the list of types of reasoning needed to understand mean and discuss student responses to tasks designed to elicit this component of reasoning. These responses reveal that inference from a fixed total reasoning is rare even in advance high school students.     

Synthesis of N-substituted aziridine-2-carboxylates

The synthesis of the methyl esters of N-methoxycarbonyl- and N-benzyloxycarbonylaziridine-2-carboxylic acid 2 by reacting methyl 2-chloro-N-carbalkoxyglycinate 1 with diazomethane is described. The aziridines were readily converted to derivatives of O-methylserine 5 and S-methylcysteine 6.