Here, we present detailed proofs of all theorems in the main paper, as well as some observations and experiments which we had to exclude from the main paper owing to paucity of space. 1 Model and definitions Here, we provide the proof of Lemma 1 from Section 2 of the main paper. Restatement of Lemma 1. For a two-ouctome forecasting problem where an expert’s report can be specified in terms of a...

ing from the latter exemplary viewpoint, in general we obtain a multilinear transition function f : F2 ×F2 ×F2 → F2 f (x[k+1],x[k],u[k]) = 0 = ∑ S1∈2In ∑ S2∈2In ∑ S3∈2Im δS1,S2,S3 ( ∏ j∈S1 x j[k+1] )( ∏ l∈S2 xl[k] )( ∏ m∈S3 um[k] ) , (21) with x ∈ F2 and u ∈ F2 , where the sets In = {1,2, . . . ,n}, Im = {1,2, . . . ,m} are index sets, 2In denotes the (possibly empty) power set of In and δS1,S2...

|f1(z)| + |f2(z)| ≥ |f(z)| ∀z ∈ D, and such, that f2 does not belong to the ideal I generated by f1, f2, i. e. f2 cannot be represented as f2 ≡ f1g1 + f2g2, g1, g2 ∈ H∞. This gives a negative answer to an old question by T. Wolff. Note, that it was well known before that under the same assumptions f belongs to the ideal if p > 2, but a counterexample can be constructed for p < 2, so our case p ...

Set F = F2 and K = F2k . Let

We consider cubic boolean bent functions, each cubic monomial of which contains the same variable. We investigate canonical forms of these functions under affine transformations of variables. In particular, we refine the affine classification of cubic bent functions of 8 variables. 1 Preliminaries Let Vn be an n-dimensional vector space over the field F2, and Fn be the set of all boolean functi...

A matrix is simple if it is a (0,1)-matrix and there are no repeated columns. Given a (0,1)-matrix F , we say a matrix A has F as a configuration, denoted F ≺ A, if there is a submatrix of A which is a row and column permutation of F . Let |A| denote the number of columns of A. Let F be a family of matrices. We define the extremal function forb(m,F) = max{|A| : A is an m−rowed simple matrix and...

Using the high resolution laser photoelectron attachment method, we demonstrate that the cross section for F- formation due to electron capture by F2(X{1}Sigma{g}{+}) molecules at very low energies exhibits p-wave threshold behavior. This finding confirms the theoretical expectation that low-energy attachment to F2 proceeds through the F2{-}(2Sigma{u}{+}) p-wave shape resonance in contrast with...

T;2 EXAM )B)(2& ") % 5#&8.2(2 #+C."+2 2D%& (%E"+F 8#4(%.G T2%5;24) %+0 )(/02+() %42 %))")(20 "+ (;2 H;#.2 84#52)) #9 %))2))&2+( (2)( '/".0"+F, 2D%& (%E"+F, %+0 (2)( 5#4425("#+G O+2 #9 (;2 &#)( "+(242)("+F 92%(/42) #9 (;2 8#4(%. ") (;2 8#))"'"."(B (# %/(#&%("5%..B F2+24%(2 %))2))&2+( (2)() '%)20 #+ /)24 02+20 5#+)(4%"+()G A (2%5;24 ") &%02 %'.2 (# '/".0 /8 %+ %))2))&2+( (2)( (2&8.%(2 /)"+F % )"...

INT~ODUCTION ................................................................... Hypothesis of heterogametism ..................................................... Equivalence, within strain C, of pollen of Oenothera pratincola f. typica and mut. latifolia. . The Fa and F, generations of the cross mut. formosa from strain E X mut. latifolia from strainc ............................................