Báo cáo toán học: "A generalization of generalized Paley graphs and new lower bounds for R(3, q)" pot

... have used the cyclic graphs of prime order to study the lower bounds for classical Ramsey numbers to the effect of improvements and generalizations of the method of Paley graphs. For example, in [7] ... constructed cyclic graphs by using higher residues of finite fields and obtained new lower bounds such like R(3, 3, 1 2)  182, R(3, 3, 13)  212, R(3, 28...

Ngày tải lên: 08/08/2014, 11:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

... electronic journal of combinatorics 3 (1996), #R19 16 [4] G. Gasper and M. Rahman, An indefinite bibasic summation formula and some quadratic, cubic, and quartic summation and transformation formulas,Canad.J.Math.,42 ... gcd p,q (P ∗ ,R ∗ ) and gcd p,q (Q ∗ , j R ∗ )= 1for all j ≥ 1, and (b) let a x , b x , a y ,andb y denote the coefficients of the lowest occurring powers of...

Ngày tải lên: 07/08/2014, 06:20

... upper-right corner of the array, and travels along the boundary of the connected component of the diagram squares of rank zero. (It follows from the lower bound for the rank of diagram squares ... 10, 7). As discussed in the proof of Proposition 2, the equality of the diagram squares of rank at most m − 3 for π and σ =Φ m (π)meansthatσ i = π i for all i for which...

Ngày tải lên: 07/08/2014, 07:21

... ∈ A it takes value of 1. Hence f ≡ 1 and the coefficient of x |A|−1 equals 0. But it is also the same as the the left hand side of the asserted equality. Theorem 3. (Coefficient Formula) Let f be ... F-linear and holds for f ′ , it is enough to prove it for the polynomial h = f −1 α 1 , ,α n · (f − f ′ ) = n  i=1  b∈A i \{a i } (x i − b). Now h α 1 , ,α n = 1, and the right hand...

Ngày tải lên: 08/08/2014, 11:20

... L(S). Since P and π are the unique point and the unique plane of P of weight 2 and 5 in L(S), respectively, and since the elements of G commute with ⊥, we have that the weights of P , π, P ⊥ and π ⊥ in ... of type II and III are extended to new infinite families of semifields of order q 6 , existing for every prime power q. ∗ This work was supported by the Research...

Ngày tải lên: 08/08/2014, 12:23

... and Triebel-Lizorkin spaces, which is a characterization of Morrey-type Besov and Triebel-Lizorkin spaces. Before stating it, we recall some notations and the definition of Morrey-type Besov and ... denotes the Fourier transform of ϕ, and ϕ ∨ denotes the inverse Fourier transform of ϕ. Definition 1. If 0 <q p<∞ and f ∈ L q Loc (R n ),wesayf ∈ M p q (R n ) provided tha...

Ngày tải lên: 06/08/2014, 05:20

... the first term. 4.4 Dissimilar forests Fix a class T of rooted trees. An unordered forest is a multiset of trees in T , and we let F be the class of all forests. A forest is said to be dissimilar ... 7 2 ) represents the profile of any permutation of size 25 that has three cycles of length 2, one cycle of length 5, and two cycles of length 7. The probability a π that a rando...

Ngày tải lên: 07/08/2014, 13:21

... with e an idempotent of M. Notice that eMe is a monoid with identity e. The group of units of eMe is denoted G e and is called the maximal subgroup of M at e. The set of idempotents of M shall be ... 7.7. The dimension of the space of M-invariant K-bil i near forms o n KΩ is the number of weak orbitals of (Ω, M). Let Ω {2} denote the subset of P (Ω) consisting of all...

Ngày tải lên: 08/08/2014, 12:23