Binary subdivision

Nira Dyn, John Gregory and David Levin Analysis of Uniform Binary subdivision schemes for curve design. Constructive Approximation 7 ppl27-147 1991... 

N.Dyn and D.Levin Analysis of Asymptotically Equivalent Binary Subdivision Schemes. Journal of Mathematical Analysis and Applications 193, pp594-621, 1995... 

J.Warren Binary Subdivision Schemes for Functions over Irregular Knot Sequences. pp543-562 in Mathematical Methods for Curves and Surfaces (eds Daehlen, Lyche and Schumaker), Vanderbilt University Press 1995 ISBN 0-8265-1268-2... 

J.Warren Sparse filter banks for binary subdivision schemes. pp427-438 in Mathematics of Surfaces VII (eds Goodman and Martin) 1997 Leif Kobbelt Using the discrete fourier transform to analyze the convergence of subdivision schemes. Applied and Computational Harmonic Analysis, Volume 5(1), pp68-91, 1998... 

D. Levin Using Laurent polynomial representation for the analysis of non-uniform binary subdivision schemes. Adv. Comput. Math 11, pp41-54, 1999... 

There have been several attempts at models incorporating breakup and coalescence. Two concepts underlie many of these models binary breakup and a flow subdivision into weak and strong flows. These ideas were first used by Manas-Zloczower, Nir, and Tadmor (1982,1984) in modeling the dispersion of carbon black in an elastomer in a Banbury internal mixer. A similar approach was taken by Janssen and Meijer (1995) to model blending of two polymers in an extruder. In this case the extruder was divided into two types of zones, strong and weak. The strong zones correspond to regions... 

Figure 5.14. Compound formation capability in the binary alloys of Sc, Y, light trivalent lanthanides (as exemplified by La), heavy trivalent lanthanides (exemplified by Gd) and of the actinides (exemplified by Th, U and Pu). The different partners of the 3rd group metals are identified by their position in the Periodic Table. Notice that a sharper subdivision between compound-forming and not forming metals will result from a shifting of Be and Mg from their position in the 2nd group towards the 12th group (see 5.12.3). The behaviour of the divalent lanthanides Eu and Yb is shown in Fig. 5.7 where it is compared with that of the alkaline earth metals.

The subdivision matrix of a binary uniform scheme has each column a copy of the mask, shifted down two rows for each step to the right. Every row (stencil) sums to 1, but the mask entries sum to 2. 

The following subdivisions will be considered (i) binary oxides (ii) spinel oxides (iii) other ternary oxides (iv) iron(IV) oxides (v) chalcogenides (vi) silicate minerals and (vii) lunar samples. 

This section deals principally with binary derivatives of the alkali metals ternary compounds are omitted since they are considered, as appropriate, either elsewhere in this Report or in that covering the inorganic chemistry of the transition metals. Included here are subdivisions relating to hydrides, oxides and related species, and halides. Compounds of Group IV and V non-metals are not discussed because of the paucity of data. A separate section, entitled Molten Salts , dealing with the chemistry of molten halides (and nitrates) as solvents, is also included. 

Bit" is an abbreviation of "binary digit", conceived as a unit of information equal to one binary decision involving the two digits (Oand 1) in binary notation. "Byte" is a set of binary digits conceived as a unit and forming a subdivision of a "word"... 

---