Crystal families and systems in higher dimensions, and geometrical symbols of their point groups. II. Cubic families in five- and n-dimensional spaces

This paper is devoted to the study of the crystal families with cubic symmetries and to the mathematical construction of all their point-symmetry groups. The mono cubic crystal families of n-dimensional space (E(n)) are defined and a list of these families is given for spaces E4, E5, E6 and E7 with the Weigel-Phan-Veysseyre (WPV) symbols of their holohedries. The cubic and iso cubic crystal point-symmetry groups of space E(n) are also defined together with their properties and their WPV symbols. Some examples of these point groups are given. The 16 point groups of the three isomorphic mono cubic crystal families, the cubic-al family of space E4 (No. 19), the cube oblique (or cube parallelogram) family of space E5 (No. XVIII) and the triclinic cubic family of space E6 (No. 21) are listed. All the WPV symbols of the point-symmetry groups of all the mono cubic crystal families of space E5, i.e. the cube rectangle family (No. XXII), the cube square family (No. XXVI) and the cube hexagon family (No. XXVII), are given together with an explanation of the mathematical construction of these point-symmetry groups. All the di cubic crystal families of spaces E6, E7 and E8 are predicted and the symbols of their holohedries are given. Finally, some tri cubic crystal families of spaces E9, E10 and E11 are listed

Effluent generation by the dairy industry: preventive attitudes and opportunities

Work aimed to identify the effluent is generating areas in a dairy company for purpose of changing concept pollution prevention. methodology consisted measuring volumes and collecting samples effluents production sectors. analysis was conducted by sector, order those which generated excessive amounts effluents. results show that dry products (powdered milk powdered whey) are greatest generators BOD, nitrogen phosphorus, while fluid form (UHT milk, formulated UHT, pasteurized cream) butter produced large quantities oils grease. solids recovery, waste segregation water reuse can be applied with saving potential as much R$28,000 ($ 11,200) per month only raw materials also environmental gains in pollution prevention