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COEFFICIENT DISCS AND GENERALIZED CENTRAL FUNCTIONS FOR THE CLASS OF CONCAVE SCHLICHT FUNCTIONS
Bhowmik, Bappaditya,Wirths, Karl-Joachim Korean Mathematical Society 2014 대한수학회보 Vol.51 No.5
We consider functions that map the open unit disc conformally onto the complement of an unbounded convex set with opening angle ${\pi}{\alpha}$, ${\alpha}{\in}(1,2]$, at infinity. We derive the exact interval for the variability of the real Taylor coefficients of these functions and we prove that the corresponding complex Taylor coefficients of such functions are contained in certain discs lying in the right half plane. In addition, we also determine generalized central functions for the aforesaid class of functions.
What We Have Learned from PISA so far: A German Educational Psychology Point of View
Detlev Leutner,Joachim Wirth 한국교육개발원 2005 KEDI Journal of Educational Policy Vol.2 No.2
After publication of the PISA 2000 results, the German newspapers were talking about the “PISA shock”. The competencies of German students in reading, mathematics, and science ranged below the OECD average. Although the PISA 2003 results showed small improvements in mathematics and science and above-average achievements in problem solving, the discussion continues. Not only are the unexpectedly low competencies of German students worrying, particularly alarming is the high correlation between students’ socio-economic/cultural background and students’ competencies, which indicates missing equity in the distribution of learning opportunities in Germany. As a consequence, the ministers of education of the 16 German federal states decided on measures for moving their education systems from an inputcontrolled to a more output-controlled format that is based on empirical research. Germany added national extensions to the international PISA test materials (a subscale of a German cognitive ability test, a computer-based test on dynamic problem solving, and a metacognitive nowledge test on reading strategies) for controlling, among others, the curricular validity of the tests and for developing when-and-why hypotheses. Over and above, members of the German PISA consortium received funding from the German National Research Association (DFG) for additional studies on testing those hypotheses.Thus, PISA not only caused intense political debates in Germany, but also a quantum advance in empirical educational research for justifying future political decisions based on empirical evidence.
Coefficient discs and generalized central functions for the class of concave schlicht functions
Bappaditya Bhowmik,Karl-Joachim Wirths 대한수학회 2014 대한수학회보 Vol.51 No.5
We consider functions that map the open unit disc confor- mally onto the complement of an unbounded convex set with opening angle πα, α ∈ (1, 2], at infinity. We derive the exact interval for the vari- ability of the real Taylor coefficients of these functions and we prove that the corresponding complex Taylor coefficients of such functions are con- tained in certain discs lying in the right half plane. In addition, we also determine generalized central functions for the aforesaid class of functions.