Báo cáo toán học: "Translational tilings of the integers with long periods" ppt

... our construction for the proof of Theorem 2 the tile X has constant cardinality 15. 2. There is nothing magical about the choice of the primes 2, 3 and 5 in the proof of Theorem 2. Any three ... 9 y z Q 3p 5q 2 A x Figure 1: The group Z 3p × Z 5q × Z 2 and (0, 0, 1). Then, in the bottom level of the tiling shift one of the columns along the x direction, say the...

Ngày tải lên: 07/08/2014, 07:21

... under the map given by the Chinese Remainder Theorem (whereby the coefficient of x n becomes the value of the entry (n mod 2,n mod 3,n mod 5)). Thus the a a a a a a Figure 8: A 2 ×3 × 5 inflate of the ... running the full length of the array. Call a fiber any array consisting of a single line of 1’s running parallel to one of the co- ordinate axes and running th...

Ngày tải lên: 07/08/2014, 13:21

... to the expression in Theorem 1, so the proof of Theorem 1 is complete. The proof of Theorem 2 is given in Section 9. Analogously to the proof of The- orem 1, it is enough to count the rhombus tilings ... Outline of the proofs of Theorems 1 and 2 Outline of the proof of Theorem 1: 10 the electronic journal of combinatorics 6 (1999), #R30 G − correspond bijec...

Ngày tải lên: 07/08/2014, 06:20

... reflection group. The purpose of this paper is to study the isotypic components of C with respect to the action of B n rather then that of B n × B n . This is to say that we are restricting the action to ... ±x σ(i) , with the sign equal to the sign of β(i), and σ(i) equal to its absolute value. The B n - invariant polynomials are thus simply the usual symmetric p...

Ngày tải lên: 07/08/2014, 13:21

... g m (ζ)) b a+deg z,∞ a r m {b a+deg z,∞ a r m 1 m 2 qk−p(r) m ρ m } m 1 m 2 qk−p(r) M r [g m ](ζ). (3.11) 11 3. Proof of the results Proof of Theorem 1.4 Suppose that the conclusion of theorem is not true, then there exists an entire solution w(z) satisfies the equation [Q(w(z))] n = ... C, if ζ is not the zero of g(ζ), by (3.4) then we can get g (k) (ζ) = 0 from (3.5). By the...

Ngày tải lên: 20/06/2014, 20:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 15:21

... in the theory of differential equations and in mathematical physics. Krupka [5] studied the sheaves of differential forms on finite r-jet prolonga- tions J r Y . Then he constructed the sequence of ... [5]. The variational bi- complex was mainly studied on the infinite jet prolongation J ∞ Y of the fibered manifold Y with the base X and the projection π : Y → X, where dim...

Ngày tải lên: 06/08/2014, 05:20

... similarly. The proof is complete.  Now we are in a position to proof a version of the well known minimax theorem due to Neumann-Sion [11, 15] in the case of hyperconvex metric spaces. Theorem 3.5. ... at the Seminar ”Geometry of Banach spaces and Fixed point theory”, organized jointly by the Hanoi Institute of Mathematics and Hanoi University of Education. The author wo...

Ngày tải lên: 06/08/2014, 05:20