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As we will later see, a crucial role in model building is played by symmetries. You are already familiar with symmetries and with some of their consequences. For example, Nature seems to have the symmetry of the Lorentz group which implies conservation of energy, momentum and angular momentum. In order to understand the interplay between symmetries and interactions, we need a mathematical tool ...

In this research, zeolite Na-Y was synthesized from Kaolin without an organic template under the non-hydrothermal condition to adsorb sulfur compound. Model fuel desulfurization was optimized by employing the Box-Behnken experimental design with 2 center points, the three parameters, and one response value. The objective was to find how sorption capacity is related to alkali fusion temperat...

The grain yield (Y) of crops is determined by several Y components that reflect positive or negative effects. Conventionally, ordinary Y components are screened for the highest direct effect on Y. Increasing one component tends to be somewhat counterbalanced by a concomitant reduction in other component (s) due to competition for assimilates. Therefore, it has been suggested that components...

In this paper we investigate the generalized Hyers-Ulamstability of the following Cauchy-Jensen type functional equation$$QBig(frac{x+y}{2}+zBig)+QBig(frac{x+z}{2}+yBig)+QBig(frac{z+y}{2}+xBig)=2[Q(x)+Q(y)+Q(z)]$$ in non-Archimedean spaces

Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let X and Y be Banach spaces such that X is weakly compactly generated Asplund space and X has the approximation property (respectively Y is weakly compactly generated Asplund space and Y ∗ has the approximation property). Suppose that L(X, Y ) 6= K(X,Y ) and let 1 < λ < 2. Then X (respective...

Boron carbide phases exist over a widely varying compos-itional range B(12+x)C(3-x) (0.06 < x < 1.7). One idealized structure corresponds to the B(13)C(2) composition (space group R-3m) and contains one icosa-hedral B(12) unit and one linear C-B-C chain. The B(12) units are composed of crystallographically distinct B atoms B(P) (polar, B1) and B(Eq) (equatorial, B2). Boron icosa-hedra are inter...