Analytic Renormings of C(K) Spaces

The aim of our present note is to show the strength of the existence of an equivalent analytic renorming of a Banach space, even compared to C∞-Fréchet smooth renormings. It was Haydon who first showed in [8] that C(K) spaces for K countable admit an equivalent C∞-Fréchet smooth norm. Later, in [7] and [9] he introduced a large clams of tree-like (uncountable) compacts K for which C(K) admits an equivalent C∞-Fréchet smooth norm. Recently, it was shown in [3] that C(K) spaces for K countable admit an equivalent analytic norm. Our Theorem 1 shows that in the class of C(K) spaces this result is the best possible.

An Application of Convolution Integral

MSC 2010: 30C45

An Invitation to Additive Prime Number Theory

2000 Mathematics Subject Classification: 11D75, 11D85, 11L20, 11N05, 11N35, 11N36, 11P05, 11P32, 11P55.

An Approach for a more Objective Evaluation of Practical Projects, Used in the Training Process

Well–prepared, adaptive and sustainably developing specialists are an important competitive advantage, but also one of the main challenges for businesses. One option of the education system for creation and development of staff adequate to the needs is the development of pro jects with topics from real economy ("Practical Projects"). The objective assessment is an essential driver and motivator, and is based on a system of well-chosen, well-defined and specific criteria and indicators. An approach to a more objective evaluation of practical projects is finding more objective weights of the criteria. A natural and reasonable approach is the accumulation of opinions of proven experts and subsequent bringing out the weights from the accumulated data. The preparation and conduction of a survey among recognized experts in the field of project-based learning in mathematics, informatics and information technologies is described. The processing of the data accumulated by applying AHP, allowed us to objectively determine weights of evaluation criteria and hence to achieve the desired objectiveness. ACM Computing Classification System (1998): K.3.2.