Báo cáo toán học: "When are subset sums equidistributed modulo m" doc

... ,q n . Then the subset sums are equidistributed modulo m if and only if h(q) is divisible by (q m − 1)/(q −1). Proof. First, for each i =0, 1, 2, ,leta i be the number of these sums that are equal ... 20 22 24 26 28 30 Figure 1. Dots indicate that t -subset sums from [n] are equidistributed modulo m.Byfixingm and varying t and n, various patterns are revealed. For exam...

Ngày tải lên: 07/08/2014, 06:20

... results on modules with finite hollow dimension are collected in [2]. So for details see [2]. Theorem 2.20. For a COSP-module M the following conditions are equivalent. (1) M has dcc on small s ubmodules. (2) ... statements are true. (1) Every M-small module is semisimple. (2) For every module N ∈ σ[M],Rad(N) ⊆ Soc (N ). Proof. (1) Let N ∈ σ[M]andN  K for some module K ∈ σ[M]. Assume T...

Ngày tải lên: 06/08/2014, 05:20

... following: 1. C(x), H(x), and A(x) all have zero radius of convergence; 2. c n ,a n , and n!h n are positive integers; 3. A(x)=exp(H(x)) = exp   j≥1 C(x j )/j  ; 4. lim inf n→∞ c n /a n = lim ... x j ) −c j and c n =  n!N n if n is even [ N n α−1 ]+1 if n is odd, where α =1/l. Notice N n and c n are positive integers for all n>1. Notice that if n is even, then c n ≥ n!andsoC(x) has...

Ngày tải lên: 07/08/2014, 06:20

... factorization and are therefore equal. Thus p =2 k q=2 m+1 s =2r, proving the claim. Since we are assuming that p =2r, the leading coefficients of a k and b k are different, and we are in Case 1 of ... a k =lcb k ,orequivalently, p p =2 p r r (p−r) p−r ?(1) Claim: All integer solutions 0 <r<pof equation (1) are of the form p =2r. To prove the claim, let p =2 k q,r=2 m s,whereq,s...

Ngày tải lên: 07/08/2014, 06:22

... circular squarefree word if all of its conjugates are squarefree. Example 2.1 The set of conjugates of word 123 is {123, 231, 312}.Eachoftheseis squarefree, so 123 is a circular squarefree word. ... there is an infinite squarefree word, i.e. an infinite sequence not containing any squares. Variations on the problem of finding squarefree words have included finding infinite squarefree tilings [2]...

Ngày tải lên: 07/08/2014, 06:23

... the coefficient of  n i=1 x t i i in f is nonzero. If S 1 , . . . , S n are subsets of F with |S i | > t i then there are s 1 ∈ S 1 , s 2 ∈ S 2 , . . . , s n ∈ S n so that f(s 1 , . . . , s n ) ... coloura- bility of digraphs (Problem 2), but it also yields the following interesting results which are not, at first glance, weight choosability problems. Corollary 4. Every graph G has an...

Ngày tải lên: 08/08/2014, 12:23

... (Figure 4) We computed the visual similarity of characters by 2×(the area of overlap between character A and B)/ (area of character A+area of character B) follow- 375 References Aitchison, J. 1994. ... Japanese. Unlike English, Japanese only has five vowels whose pronunciations are transparently car- ried by the orthography; they are therefore expected to be less prone to cognitive errors....

Ngày tải lên: 19/02/2014, 19:20

... important for the different conformational transitions are highlighted in red, phosphorylation sites on b-RAF with gray. Position of the FxFP linear MAPK docking motif is shown in orange in KSR1 on (C). ... density. Nat Rev Neurosci 10, 87–99. 33 de Arce KP, Varela-Nallar L, Farias O, Cifuentes A, Bull P, Couch BA, Koleske AJ, Inestrosa NC & Alvarez AR (2010) Synaptic clustering of PSD-...

Ngày tải lên: 06/03/2014, 23:20

... if all the conditions in Theorem 5.1 are satisfied, then BVP (5.2) has at least three positive solutions satisfying (5.1). Competing interests The authors declare that they have no competing interests. 20 Existence ... theorems in a cone, the existence of at least one, two, or three positive solutions are obtained. Examples are also given in this article. AMS Subject Classification: 34B10...

Ngày tải lên: 20/06/2014, 20:20

... Algorithm 1. Once the sparse coefficients, α, are obtained, high resolution patches, y, are computed using (39) which are finally merged by averaging in the overlap area to create the resulting image. The ... that the areas which are relatively more structured benefit more from the proposed algorithm as the quality measure used is better at calculating the similarity of structures as comp...

Ngày tải lên: 20/06/2014, 20:20