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Abstract

In [4], Császár has introduced the notions of weak structures and the structures α(w), π(w), σ(w), β(w). The main aim of this paper is to introduce and study properties of the structures r(w), α(w), π(w), σ(w) and β(w).

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Abstract

We define weak structures and show that these structures can replace in many situations generalized topologies or minimal structures.

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], (2) u = w c o s θ ,   v = w s i n θ ,   d u d v = w d w d θ . By using Eqs (1) and (2) , the inverse Fourier transform can be defined as, (3) f ( x ,   y ) = ∫ 0 2 π ∫ 0 ∞ F ( w ,   θ ) e j 2 π w ( x c o s θ + y s i n θ ) w d w d θ + ∫ 0 π ∫ 0 ∞ F

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≦ ( 0 ) > 0 . The definition of Eq. (11) indicates that a greater Arrow – Pratt index of absolute risk aversion generates a greater curvature of the indifference curve near (0, 0) the bi-dimensional space of y c / y e . Therefore, let π w be

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relates to irreversibility. Clearly, Q → Π , W e ′ → W e , and Δ H □ ′ → Δ H □ , and Eq. 16 reduces to Eq. 15 when i → 0. Equation 16 is very useful in the experimental data processing. For a set of experimental data at a given concentration

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