f(f(x)-f(y)) £ f(x+y) + f(f(x-y)) -f(x) - f(y), f(f(x)-f(y)) £ f(f(x+y)) + f(x-y) -f(x) - f(y), f(f(x)-f(y)) £ f(f(x+y)) + f(f(x-y)) -f(f(x)) - f(y),\begin{gathered}f(f(x)-f(y)) \leq f(x+y) + f(f(x-y)) -f(x) - f(y), \hfill \\ f(f(x)-f(y)) \leq f(f(x+y)) + f(x-y) -f(x) - f(y), \hfill \\ f(f(x)-f(y)) \leq f(f(x+y)) + f(f(x-y)) -f(f(x)) - f(y),\end{gathered} 相似文献
7.
Let C( f), Q( f), E( f) and A( f) be the sets of all continuity, quasicontinuity, upper and lower quasicontinuity and cliquishness points of a real function
f: X → ℝ, respectively. The triplets ( C( f), Q( f), A( f)), ( C( f), E( f), A( f) and ( Q( f), E( f), A( f)are characterized for functions defined on Baire metric spaces without isolated points. 相似文献
8.
Let f be a holomorphic self-map of the punctured plane ℂ *=ℂ\{0} with essentially singular points 0 and ∞. In this note, we discuss the sets I
0( f)={ z ∈ ℂ *: f
n
( z) → 0, n → ∞} and I
∞( f)={ z ∈ ℂ *: f
n
( z) → 0, n → ∞}. We try to find the relation between I
0( f), I
∞( t) and J( f). It is proved that both the boundary of I
0( f) and the boundary of I
∞) f) equal to J( f), I
0( f) ∩ J( f) ≠ θ and I
∞( f) ∩ J( f) ≠ θ. As a consequence of these results, we find both I
0( f) and I
∞( f) are not doubly-bounded.
Supported by the National Natural Science Foundation of China 相似文献
9.
Let f be a transcendental meromorphic function and g(z)=f(z+c1)+f(z+c2)-2f(z) and g2(z)=f(z+c1)·f(z+c2)-f2(z).The exponents of convergence of zeros of differences g(z),g2(z),g(z)/f(z),and g2(z)/f2(z) are estimated accurately. 相似文献
10.
We consider the family f
a,b
( x, y)=( y,( y+ a)/( x+ b)) of birational maps of the plane and the parameter values ( a, b) for which f
a,b
gives an automorphism of a rational surface. In particular, we find values for which f
a,b
is an automorphism of positive entropy but no invariant curve. The Main Theorem: If f
a,b
is an automorphism with an invariant curve and positive entropy, then either (1) ( a, b) is real, and the restriction of f to the real points has maximal entropy, or (2) f
a,b
has a rotation (Siegel) domain.
Research supported in part by the NSF. 相似文献
11.
Let f be a transcendental entire function and let I( f) denote the set of points that escape to infinity under iteration. We give conditions which ensure that, for certain functions,
I( f) is connected. In particular, we show that I( f) is connected if f has order zero and sufficiently small growth or has order less than 1/2 and regular growth. This shows that, for these functions,
Eremenko’s conjecture that I( f) has no bounded components is true. We also give a new criterion related to I( f) which is sufficient to ensure that f has no unbounded Fatou components. 相似文献
12.
Let k be a positive integer, let M be a positive number, let F be a family of meromorphic functions in a domain D, all of whose zeros are of multiplicity at least k, and let h be a holomorphic function in D, h ≢ 0. If, for every f ∈ F, f and f
(k) share 0, and | f( z)| ≥ M whenever f
(k)( z) = h( z), then F is normal in D. The condition that f and f
(k) share 0 cannot be weakened, and the condition that | f( z)| ≥ M whenever f
(k)( z) = h( z) cannot be replaced by the condition that | f( z)| ≥ 0 whenever f
(k)( z) = h( z). This improves some results due to Fang and Zalcman [ 2] etc. 相似文献
13.
Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced. It is proved that: (1) fhas zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f^5 has a division; (2) If f has zero topological entropy,then for any xECR(f)--P(f) the w-limit set of x is an infinite minimal set. 相似文献
14.
Summary. Let f : ]0,¥[? \Bbb R f :\,]0,\infty[\to \Bbb R be a real valued function on the set of positive reals. The functional equations¶¶ f( x + y) - f( x) - f( y) = f( x-1 + y-1) f(x + y) - f(x) - f(y) = f(x^{-1} + y^{-1}) ¶and¶ f( xy) = f( x) + f( y) f(xy) = f(x) + f(y) ¶are equivalent to each other. 相似文献
15.
Let M be a smooth compact surface, orientable or not, with boundary or without it, P either the real line ℝ
1 or the circle S
1, and D( M) the group of diffeomorphisms of M acting on C^∞( M, P) by the rule h⋅ f = f ∘ h
−1 for h ∊ D( M) and f ∊ C^∞ ( M, P). Let f: M → P be an arbitrary Morse mapping, Σ
f
the set of critical points of f, D( M,Σ
f
) the subgroup of D( M) preserving Σ
f
, and S( f), S ( f,Σ
f
), O( f), and O( f,Σ
f
) the stabilizers and the orbits of f with respect to D( M) and D( M,Σ
f
). In fact S( f) = S( f,Σ
f
).In this paper we calculate the homotopy types of S( f), O( f) and O( f,Σ
f
). It is proved that except for few cases the connected components of S( f) and O( f,Σ
f
) are contractible, π
k
O( f) = π
k
M for k ≥ 3, π 2 O( f) = 0, and π 1 O( f) is an extension of π 1 D( M) ⊕ Z
k
(for some k ≥ 0) with a (finite) subgroup of the group of automorphisms of the Kronrod-Reeb graph of f.We also generalize the methods of F. Sergeraert to give conditions for a finite codimension orbit of a tame smooth action of a tame Lie group on a tame Fréchet manifold to be a tame Fréchet manifold itself. In particular, we obtain that O( f) and O( f, Σ
f
) are tame Fréchet manifolds.
Communicated by Peter Michor Vienna
Mathematics Subject Classifications (2000): 37C05, 57S05, 57R45. 相似文献
16.
An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v V(G) at most f(v) times. The minimum number of colors needed to f-color G is called the f-chromatic index of G and is denoted by X′f(G). Any simple graph G has the f-chromatic index equal to △f(G) or △f(G) + 1, where △f(G) =max v V(G){[d(v)/f(v)]}. If X′f(G) = △f(G), then G is of f-class 1; otherwise G is of f-class 2. In this paper, a class of graphs of f-class 1 are obtained by a constructive proof. As a result, f-colorings of these graphs with △f(G) colors are given. 相似文献
17.
In this paper, we determine the general solution of the functional equation f1 (2x + y) + f2(2x - y) = f3(x + y) + f4(x - y) + f5(x) without assuming any regularity condition on the unknown functions f1,f2,f3, f4, f5 : R→R. The general solution of this equation is obtained by finding the general solution of the functional equations f(2x + y) + f(2x - y) = g(x + y) + g(x - y) + h(x) and f(2x + y) - f(2x - y) = g(x + y) - g(x - y). The method used for solving these functional equations is elementary but exploits an important result due to Hosszfi. The solution of this functional equation can also be determined in certain type of groups using two important results due to Szekelyhidi. 相似文献
18.
Let f(z) be a Hecke eigenform in the space S 2k(Γ) of holomorphic Γ-cusp forms of even weight 2k, Γ=SL(2,ℤ); let L f(s) be the L-function of f(z). The goal of this paper is to obtain some results on L f(1) as k increases. In particular, we prove an analogue of the classical Landau theorem in the theory of Dirichlet L-functions
and (under a very plausible hypothesis) an analogue of the famous Siegel theorem. Bibliography: 15 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 37–54.
Translated by E. P. Golubeva. 相似文献
19.
Let f be a transcendental meromorphic function. We propose a number of results concerning zeros and fixed points of the difference
g( z) = f( z + c) − f( z) and the divided difference g( z)/ f( z). 相似文献
20.
For a class of analytic functions f( z) defined by Laplace–Stieltjes integrals the uniform convergence on compact subsets of the complex plane of the Bruwier series (B-series) ∑ ∞n=0 λn( f)
, λn( f)= f(n)( nc)+ cf(n+1)( nc), generated by f( z) and the uniform approximation of the generating function f( z) by its B-series in cones |arg z| <
is shown. 相似文献
|