Since the extension principles of constructing wavelet frames were presented, a lot of symmetric and compactly supported wavelet frames with high vanishing moments have been constructed. However the problem of constructing periodic wavelet frames with the help of extension principles is open. In this paper, we will construct tight periodic wavelet frames using the unitary extension principle an...

Let X be a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristic p big enough. Given a local ring OP,X at a rational singular point P of X, we attached a universal zeta function which is a rational function and admits a functional equation if OP,X is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincaré se...

A new simple model is introduced for a liquid and an equation of state is derived based on this model and the statistical mechanical calculations. This equation of state works well for the non-polar and slightly polar liquids. The important conclusion that may be deduced from this equation of state is that if the reduced variables of state are chosen and defined appropriately, then, the pri...

Defining the standard Boolean operations on fuzzy Booleans with the compositional rule of inference (CRI) or Zadeh's extension principle gives counter-intuitive results. We introduce and motivate a slight adaptation of the CRI, which only effects the results for non-normal fuzzy sets. It is shown that the adapted CRI gives the expected results for the standard Boolean operations on fuzzy Boolea...