The Monitoring of Exponentially Weighted Forecasts

By considering equivalences between various forecasting systems, the exact stochastic process followed by the one-step-ahead errors may be found. This process, the error process, is important for any monitoring scheme, and is a function of the forecasting system and the underlying data process. The error process is obtained for the most general form of exponential smoothing systems used in optimal conditions. The statistical properties are derived. In particular, the approximate variance of Trigg's smoothed error tracking signal is obtained explicitly for several exponential smoothing systems, and a procedure is given for obtaining it numerically for any such system. The use of different smoothing constants in the forecasting system and the tracking signal is discussed and it is found that suitable choice of the tracking signal constant greatly improves the performance of the signal, making it more comparable with CUSUM schemes.     

Silicon in synthesis: use of the highly nucleophilic trimethylsilyallyl anion for the synthesis of steroidal 17-spiro-γ-lactones

Trimethylsilylallylzinc chloride $\text{2}$ (M  ZnCl) reacts with 17-ketosteroids to give adducts $\text{4}$ that can be converted into 17-spirolactones.     

High school students’ understanding of the function concept

This paper is a study of part of the Algebra Project's program for underrepresented high school students from the lowest quartile of academic achievement, social and economic status. The study focuses on students’ learning the concept of function. The curriculum and pedagogy are part of an innovative, experimental approach designed and implemented by the Algebra Project. The instructional treatment took place over 7 weeks during the Junior Year of 15 students from our target population. Immediately after instruction, a written instrument was administered followed, several weeks later, by in-depth interviews. The results are that many of our participants achieved a level of knowledge and understanding of functions on a par with beginning college students, including preservice teachers, as reported in the literature. Many conceptual difficulties that have been reported in the research literature were not as prevalent for our participants and some of them were capable of solving difficult problems involving composition of functions. We conclude that, with appropriate pedagogy, it is possible for students in the Algebra Project's target population to learn substantial and non-trivial mathematics at the high school level, and that the Algebra Project approach is one example of such a pedagogy.     

Existence of Generalized Inverse of Linear Transformations over Finite Fields

Relationships between the orthogonal direct sum decomposition of a vector space over a finite field and the existence of the generalized inverses of a linear transformation over the finite field are analyzed. Necessary and sufficient conditions for judging the existence of the generalized inverses of a linear transformation over a finite field are presented.     

Ueber einige Reactionen des Kobalts

Ohne Zusammenfassung     

Zur Bestimmung des Titans

Analytical and Bioanalytical Chemistry -     

Notiz zur F?llung einiger Metallsulfide mit Thiosulfat

Ohne Zusammenfassung