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1.
In this paper, based on existing symmetric multiwavelets, we give an explicit algorithm for constructing multiwavelets with high approximation order and symmetry. Concretely, suppose Φ(x) := (φ1(x), . . . , φr(x))T is a symmetric refinable function vectors with approximation order m. For an arbitrary nonnegative integer n, a new symmetric refinable function vector Φnew(x) := (φn1 ew(x), . . . , φrn ew(x))T with approximation order m + n can be constructed through the algorithm mentioned above. Additionally,...  相似文献   

2.
Let T(Δ) and B(Δ) be the Teichmüller space and the infinitesimal Teichmüller space of the unit disk Δ respectively. In this paper, we show that [ν] B(Δ) being an infinitesimal Strebel point does not imply that [ν] T(Δ) is a Strebel point, vice versa. As an application of our results, problems proposed by Yao are solved. This work was supported by the National Natural Science Foundation of China (Grant No. 10571028)  相似文献   

3.
On total chromatic number of planar graphs without 4-cycles   总被引:5,自引:0,他引:5  
Let G be a simple graph with maximum degree A(G) and total chromatic number Xve(G). Vizing conjectured thatΔ(G) 1≤Xve(G)≤Δ(G) 2 (Total Chromatic Conjecture). Even for planar graphs, this conjecture has not been settled yet. The unsettled difficult case for planar graphs isΔ(G) = 6. This paper shows that if G is a simple planar graph with maximum degree 6 and without 4-cycles, then Xve(G)≤8. Together with the previous results on this topic, this shows that every simple planar graph without 4-cycles satisfies the Total Chromatic Conjecture.  相似文献   

4.
Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order p~r,i.e.,a finite homocyclic abelian group.LetΔ~n (G) denote the n-th power of the augmentation idealΔ(G) of the integral group ring ZG.The paper gives an explicit structure of the consecutive quotient group Q_n(G)=Δ~n(G)/Δ~(n 1)(G) for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.  相似文献   

5.
Bernstein-Kantorovich quasi-interpolants K^(2r-1)n(f, x) are considered and direct, inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω^2rφ(f, t)p (1 ≤ p ≤+∞) are obtained.  相似文献   

6.
Consider the Poisson's equation ψ" (x) = -ev-ψ eψ-v-N(x) with the Dirichlet boundary data, and we mainly investigate the inverse problem of determining the unknown function N(x) from a parameter function family. Some uniqueness and stability results in the inverse problem are obtained.  相似文献   

7.
In this paper the following theorem is proved: Every group L3(q) for q = 3^(2m-1)(m≥2) is characterized by its set of element orders.  相似文献   

8.
A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a′(G), is the least number of colors in an acyclic edge coloring of G. Alon et al. conjectured that a′(G) ⩽ Δ(G) + 2 for any graphs. For planar graphs G with girth g(G), we prove that a′(G) ⩽ max{2Δ(G) − 2, Δ(G) + 22} if g(G) ⩾ 3, a′(G) ⩽ Δ(G) + 2 if g(G) ⩾ 5, a′(G) ⩽ Δ(G) + 1 if g(G) ⩾ 7, and a′(G) = Δ(G) if g(G) ⩾ 16 and Δ(G) ⩾ 3. For series-parallel graphs G, we have a′(G) ⩽ Δ(G) + 1. This work was supported by National Natural Science Foundation of China (Grant No. 10871119) and Natural Science Foundation of Shandong Province (Grant No. Y2008A20).  相似文献   

9.
Let (Γ,I) be the bound quiver of a cyclic quiver whose vertices correspond to the Abelian group Zd. In this paper, we list all indecomposable representations of (Γ,I) and give the conditions that those representations of them can be extended to representations of deformed preprojective algebra Πλ(Γ,I). It is shown that those representations given by extending indecomposable representations of (Γ,I) are all simple representations of Πλ(Γ,I). Therefore, it is concluded that all simple representa-tions of rest...  相似文献   

10.
A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of the graph G is the smallest number of colors in a linear coloring of G. In this paper, we prove that every graph G with girth g(G) and maximum degree Δ(G) that can be embedded in a surface of nonnegative characteristic has lc(G) = Δ(2G )+ 1 if there is a pair (Δ, g) ∈ {(13, 7), (9, 8), (7, 9), (5, 10), (3, 13)} such that G s...  相似文献   

11.
Thek-dimensional Piatetski-Shapiro prime number problem fork⩾3 is studied. Let π(x 1 c 1,⋯,c k ) denote the number of primesp withp⩽x, , where 1<c 1<⋯<c k are fixed constants. It is proved that π(x;c 1,⋯,c k ) has an asymptotic formula ifc 1 −1 +⋯+c k −1 >kk/(4k 2+2). Project supported by the National Natural Science Foundation of China (Grant No. 19801021) and the Natural Science Foundation of Shandong Province (Grant No.Q98A02110).  相似文献   

12.
The authors study the p(x)-Laplacian equations with nonlinear boundary condition. By using the variational method, under appropriate assumptions on the perturbation terms f1 (x, u), f2(x, u) and h1(x), h2(x), such that the associated functional satisfies the "mountain pass lemma" and "fountain theorem" respectively, the existence and multiplicity of solutions are obtained. The discussion is based on the theory of variable exponent Lebesgue and Sobolev spaces.  相似文献   

13.
Based on the work of Lenstra, a succinct proof of Browkin’s conjecture about the elements of order five in K 2(ℚ) is given. This work was supported by the National Natural Science Foundation of China (Grant No. 10371061).  相似文献   

14.
    
Let (K, M, H) be an upper triangular biomodule problem. Brüstle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K, M, H) is quasi-hereditary, and there is an equivalence between the category of Δ-good modules of A and Mat(K, M). In this note, based on the tame theorem for bimodule problems, we show that if the algebra A associated with an upper triangular bimodule problem is of Δ-tame representation type, then the category F(Δ) has the homogeneous property, i.e. almost all modules in F(Δ) are isomorphic to their Auslander-Reiten translations. Moreover, if (K, M, H) is an upper triangular bipartite bimodule problem, then A is of Δ-tame representation type if and only if F(Δ) is homogeneous. This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10426014, 10501010 and 19331030) and the Foundation of Hubei Provincial Department of Education (Grant No. D200510005).  相似文献   

15.
Let ƒ be a transcendental meromorphic function, a a nonzero finite complex number, and n ⩾ 2 a positive integer. Then ƒ + a(ƒ′) n assumes every complex value infinitely often. This answers a question of Ye for n = 2. A related normality criterion is also given. This work was supported by the National Natural Science Foundation of China (Grant No. 10771076), the Natural Science Foundation of Guangdong Province, China (Grant No. 07006700) and by the German-Israeli Foundation for Scientific Research and Development (Grant No. G-809-234.6/2003)  相似文献   

16.
In this paper, we give weak regularity theorems on P of u~ε(x, P), where u~ε(x, P)is the viscosity solution of the cell problem H_ε(P D_xu~ε, x)=H_ε(P).  相似文献   

17.
Let p be an odd prime, and f(x), g(x) ∈ [x]. Define
where is the inverse of x modulo p with ∈ {1, ..., p − 1}, and R p (x) denotes the unique r ∈ {0, 1, ..., p − 1} with xr(mod p). This paper shows that the sequences {e n } is a “good” pseudorandom binary sequences, and give a generalization on a problem of D.H. Lehmer. Supported by the National Natural Science Foundation of China under Grant No. 60472068 and No. 10671155; Natural Science Foundation of Shaanxi province of China under Grant No. 2006A04; and the Natural Science Foundation of the Education Department of Shaanxi Province of China under Grant No. 06JK168.  相似文献   

18.
Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.  相似文献   

19.
Letμbe a nonnegative Radon measure on R~d which only satisfiesμ(B(x,r))≤C_0r~n for all x∈R~d,r>0,and some fixed constants C_0>0 and n∈(0,d].In this paper,some weighted weak type estimates with A_(p,(log L)~σ)~ρ(μ) weights are established for the commutators generated by Calder■n-Zygmund singular integral operators with RBMO(μ) functions.  相似文献   

20.
Suppose thatx=|x(n)|n∈ℤ is a sequence of real numbers. For eachp∈ℕ,x p =|x p (n)|n∈ℤis the resulting sequence ofx throughp times median filterings with window 2k+1. It is proved that whenp→∞, bothx (2p) andx(2 p}-1) are convergent. Thus the problem of convergence of the median filters of infinite-length sequences is completely solved. Project supported by the National Natural Science Foundation of China (Grant No. 16971047).  相似文献   

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