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1.
Jerzy Jezierski 《Journal of Fixed Point Theory and Applications》2016,18(3):609-626
There are two algebraic lower bounds of the number of n-periodic points of a self-map \({f : M \rightarrow M}\) of a compact smooth manifold of dimension at least 3:andIn general NJD n (f) may be much greater than NF n (f). In the simply connected case, the equality of the two numbers is equivalent to the sequence of Lefschetz numbers satisfying restrictions introduced by Chow, Mallet-Parret and Yorke (1983). The last condition is not sufficient in the non-simply connected case. Here we give some conditions which guarantee the equality when \({\pi_{1}M = \mathbb{Z}_{2}}\).
相似文献
$$NF_{n}(f) = min\{\#Fix(g^{n}); g ~ f; g continuous\}$$
$$NJD_{n}(f) = min\{\#Fix(g^{n}); g ~ f; g smooth\}.$$
2.
In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM~k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M~j(s), M~k(t)) for s, t ≤ n, M~j, M~k are g-twisted V modules, if V is g-rational. 相似文献
3.
Let f(n) be the largest integer such that every poset on n elements has a 2-dimensional subposet on f(n) elements. What is the asymptotics of f(n)? It is easy to see that f(n) = n 1/2. We improve the best known upper bound and show f(n) = O (n 2/3). For higher dimensions, we show \(f_{d}(n)=\O \left (n^{\frac {d}{d + 1}}\right )\), where f d (n) is the largest integer such that every poset on n elements has a d-dimensional subposet on f d (n) elements. 相似文献
4.
We investigate the equiconvergence on TN = [?π, π)N of expansions in multiple trigonometric Fourier series and in the Fourier integrals of functions f ∈ Lp(TN) and g ∈ Lp(RN), p > 1, N ≥ 3, g(x) = f(x) on TN, in the case where the “partial sums” of these expansions, i.e., Sn(x; f) and Jα(x; g), respectively, have “numbers” n ∈ ZN and α ∈ RN (nj = [αj], j = 1,..., N, [t] is the integral part of t ∈ R1) containing N ? 1 components which are elements of “lacunary sequences.” 相似文献
5.
Jerzy Jezierski 《Topology and its Applications》2006,153(11):1825-1837
Boju Jiang introduced a homotopy invariant NFn(f), for a natural number n, which is a lower bound for the cardinality of periodic points, of period n, of a self-map of a compact polyhedron. In [J. Jezierski, Wecken theorem for periodic points, Topology 42 (5) (2003) 1101-1124] and [J. Jezierski, Wecken theorem for fixed and periodic points, in: Handbook of Topological Fixed Point Theory, Kluwer Academic, Dordrecht, 2005] we prove that any self-map of a compact PL-manifold (dimM?3) is homotopic to a map g satisfying #Fix(gn)=NFn(f) i.e. NFn(f) is the best such homotopy invariant. Here we give an alternative, simpler proof of these results. 相似文献
6.
We give all solutions of the equation f(n) = g(n) + h(n) for every n ∈ ?, where f is a completely multiplicative, g is a 2-additive, and h is a 3-additive function. We also determine all completely multiplicative functions f and all q-additive functions g for which f(n) = g 2(n) for every n ∈ ?. 相似文献
7.
V. M. Badkov 《Proceedings of the Steklov Institute of Mathematics》2009,264(1):39-43
Let {p n (t)} n=0 t8 be a system of algebraic polynomials orthonormal on the segment [?1, 1] with a weight p(t); let {x n,ν (p) } ν=1 n be zeros of a polynomial p n (t) (x x,ν (p) = cosθ n,ν (p) ; 0 < θ n,1 (p) < θ n,2 (p) < ... < θ n,n (p) < π). It is known that, for a wide class of weights p(t) containing the Jacobi weight, the quantities θ n,1 (p) and 1 ? x n,1 (p) coincide in order with n ?1 and n ?2, respectively. In the present paper, we prove that, if the weight p(t) has the form p(t) = 4(1 ? t 2)?1{ln2[(1 + t)/(1 ? t)] + π 2}?1, then the following asymptotic formulas are valid as n → ∞:
相似文献
$$\theta _{n,1}^{(p)} = \frac{{\sqrt 2 }}{{n\sqrt {\ln (n + 1)} }}\left[ {1 + {\rm O}\left( {\frac{1}{{\ln (n + 1)}}} \right)} \right],x_{n,1}^{(p)} = 1 - \left( {\frac{1}{{n^2 \ln (n + 1)}}} \right) + O\left( {\frac{1}{{n^2 \ln ^2 (n + 1)}}} \right).$$
8.
Let L be a Schrdinger operator of the form L =-? + V acting on L~2(R~n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R~n) denote the BMO space associated to the Schrdinger operator L on R~n. In this article, we show that for every f ∈ BMO_L(R~n) with compact support, then there exist g ∈ L~∞(R~n) and a finite Carleson measure μ such that f(x) = g(x) + S_(μ,P)(x) with ∥g∥∞ + |||μ|||c≤ C∥f∥BMO_L(R~n), where S_(μ,P)=∫(R_+~(n+1))Pt(x,y)dμ(y, t),and Pt(x, y) is the kernel of the Poisson semigroup {e-~(t(L)~(1/2))}t0 on L~2(R~n). Conversely, if μ is a Carleson measure, then S_(μ,P) belongs to the space BMO_L(R~n). This extends the result for the classical John-Nirenberg BMO space by Carleson(1976)(see also Garnett and Jones(1982), Uchiyama(1980) and Wilson(1988)) to the BMO setting associated to Schrdinger operators. 相似文献
9.
W. R. Lü F. Lü L. Wu J. Yang 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2018,53(5):260-265
In this note, we study the admissible meromorphic solutions for algebraic differential equation fnf' + Pn?1(f) = R(z)eα(z), where Pn?1(f) is a differential polynomial in f of degree ≤ n ? 1 with small function coefficients, R is a non-vanishing small function of f, and α is an entire function. We show that this equation does not possess any meromorphic solution f(z) satisfying N(r, f) = S(r, f) unless Pn?1(f) ≡ 0. Using this result, we generalize a well-known result by Hayman. 相似文献
10.
Let M be an n-dimensional complete Riemannian manifold with Ricci curvature n- 1. By developing some new techniques, Colding(1996) proved that the following three conditions are equivalent: 1)dGH(M, S~n) → 0; 2) the volume of M Vol(M) → Vol(S~n); 3) the radius of M rad(M) →π. By developing a different technique, Petersen(1999) gave the 4th equivalent condition, namely he proved that the n + 1-th eigenvalue of M, λ_(n+1)(M) → n, is also equivalent to the radius of M, rad(M) →π, and hence the other two.In this paper, we use Colding's techniques to give a new proof of Petersen's theorem. We expect our estimates will have further applications. 相似文献
11.
Alain Escassut Ta Thi Hoai An 《P-Adic Numbers, Ultrametric Analysis, and Applications》2018,10(1):12-31
Let IK be an algebraically closed field of characteristic 0 complete for an ultrametric absolute value. Following results obtained in complex analysis, here we examine problems of uniqueness for meromorphic functions having finitely many poles, sharing points or a pair of sets (C.M. or I.M.) defined either in the whole field IK or in an open disk, or in the complement of an open disk. Following previous works in C, we consider functions fn(x)fm(ax + b), gn(x)gm(ax + b) with |a| = 1 and n ≠ m, sharing a rational function and we show that f/g is a n + m-th root of 1 whenever n + m ≥ 5. Next, given a small function w, if n, m ∈ IN are such that |n ? m|∞ ≥ 5, then fn(x)fm(ax + b) ? w has infinitely many zeros. Finally, we examine branched values for meromorphic functions fn(x)fm(ax + b). 相似文献
12.
Let(T, d) be a dendrite with finite branch points and f be a continuous map from T to T. Denote byω(x,f) and P(f) the ω-limit set of x under f and the set of periodic points of,respectively. Write Ω(x,f) = {y| there exist a sequence of points x_k E T and a sequence of positive integers n_1 n_2 … such that lim_(k→∞)x_k=x and lim_(k→∞)f~(n_k)(x_k) =y}. In this paper, we show that the following statements are equivalent:(1) f is equicontinuous.(2) ω(x, f) = Ω(x,f) for any x∈T.(3) ∩_(n=1)~∞f~n(T) = P(f),and ω(x,f)is a periodic orbit for every x ∈ T and map h : x→ω(x,f)(x ET)is continuous.(4) Ω(x,f) is a periodic orbit for any x∈T. 相似文献
13.
V. Z. Grines E. Ya. Gurevich V. S. Medvedev 《Proceedings of the Steklov Institute of Mathematics》2008,261(1):59-83
Let M n be a closed orientable manifold of dimension greater than three and G 1(M n ) be the class of orientation-preserving Morse-Smale diffeomorphisms on M n such that the set of unstable separatrices of every f ∈ G 1(M n ) is one-dimensional and does not contain heteroclinic orbits. We show that the Peixoto graph is a complete invariant of topological conjugacy in G 1(M n ). 相似文献
14.
V. A. Bykovskii 《Doklady Mathematics》2016,94(2):527-528
Given any nonzero entire function g: ? → ?, the complex linear space F(g) consists of all entire functions f decomposable as f(z + w)g(z - w)=φ1(z)ψ1(w)+???+ φn(z)ψn(w) for some φ1, ψ1, …, φn, ψn: ? → ?. The rank of f with respect to g is defined as the minimum integer n for which such a decomposition is possible. It is proved that if g is an odd function, then the rank any function in F(g) is even. 相似文献
15.
Let \({\phi : M \to R^{n+p}(c)}\) be an n-dimensional submanifold in an (n + p)-dimensional space form R n+p(c) with the induced metric g. Willmore functional of \({\phi}\) is \({W(\phi) = \int_{M}(S - nH^{2})^{n/2}dv}\) , where \({S = \sum_{\alpha,i, j}(h^{\alpha}_{ij} )^2}\) is the square of the length of the second fundamental form, H is the mean curvature of M. The Weyl functional of (M, g) is \({\nu(g) = \int_{M}|W_{g}|^{n/2}dv}\) , where \({|W_{g}|^{2} = \sum_{i, j,k,l} W^{2}_{ijkl}}\) and W ijkl are the components of the Weyl curvature tensor W g of (M, g). In this paper, we discover an inequality relation between Willmore functional \({W(\phi)}\) and Weyl funtional ν(g). 相似文献
16.
Let (j1,..., jn) be a permutation of the n-tuple (1, ..., n). A system of differential equations \(\dot x = {f_i}\left( {{x_{{j_i}}}} \right),i = 1, \ldots ,n\) in which each function fi is continuous on ? is considered. This system is said to have the property of generation of solutions with a small period if, for any number M > 0, there exists a number ω0 = ω0(M) > 0 such that if 0 < ω ≤ ω0 and hi(t, x1, ..., xn) are continuous functions on ? × ?n ω-periodic in t that satisfy the inequalities |hi| ≤ M the system \(\dot x = {f_i}\left( {{x_{{j_i}}}} \right),i = 1, \ldots ,n\) has an ω-periodic solution. It is shown that a system has the property of generation of solutions with a small period if and only if fi(?) = ? for i = 1,..., n. It is also shown that the smallness condition on the period is essential. 相似文献
17.
Óscar Ciaurri T. Alastair Gillespie Luz Roncal José L. Torrea Juan Luis Varona 《Journal d'Analyse Mathématique》2017,132(1):109-131
It is well known that the fundamental solution of with u(n, 0) = δ nm for every fixed m ∈ Z is given by u(n, t) = e ?2t I n?m (2t), where I k (t) is the Bessel function of imaginary argument. In other words, the heat semigroup of the discrete Laplacian is described by the formal series W t f(n) = Σ m∈Z e ?2t I n?m (2t)f(m). This formula allows us to analyze some operators associated with the discrete Laplacian using semigroup theory. In particular, we obtain the maximum principle for the discrete fractional Laplacian, weighted ? p (Z)-boundedness of conjugate harmonic functions, Riesz transforms and square functions of Littlewood-Paley. We also show that the Riesz transforms essentially coincide with the so-called discrete Hilbert transform defined by D. Hilbert at the beginning of the twentieth century. We also see that these Riesz transforms are limits of the conjugate harmonic functions. The results rely on a careful use of several properties of Bessel functions.
相似文献
$${u_t}\left( {n,t} \right) = u\left( {n + 1,t} \right) - 2u\left( {n,t} \right) + u\left( {n - 1,t} \right),n \in \mathbb{Z},$$
18.
It was proved that the complexity of square root computation in the Galois field GF(3s), s = 2kr, is equal to O(M(2k)M(r)k + M(r) log2r) + 2kkr1+o(1), where M (n) is the complexity of multiplication of polynomials of degree n over fields of characteristics 3. The complexity of multiplication and division in the field GF(3s) is equal to O(M(2k)M(r)) and O(M(2k)M(r)) + r1+o(1), respectively. If the basis in the field GF(3r) is determined by an irreducible binomial over GF(3) or is an optimal normal basis, then the summands 2kkr1+o(1) and r1+o(1) can be omitted. For M(n) one may take n log2nψ(n) where ψ(n) grows slower than any iteration of the logarithm. If k grow and r is fixed, than all the estimates presented here have the form Or (M (s) log 2s) = s (log 2s)2ψ(s). 相似文献
19.
V. P. Maslov 《Mathematical Notes》2016,99(3-4):413-416
In the paper, it is proved that, if f(x1,..., xn)g(y1,..., ym) is a multilinear central polynomial for a verbally prime T-ideal Γ over a field of arbitrary characteristic, then both polynomials f(x1,..., xn) and g(y1,..., ym) are central for Γ. 相似文献
20.
A. G. Chentsov 《Proceedings of the Steklov Institute of Mathematics》2017,296(1):43-59
Let a sequence of d-dimensional vectors n k = (n k 1 , n k 2 ,..., n k d ) with positive integer coordinates satisfy the condition n k j = α j m k +O(1), k ∈ ?, 1 ≤ j ≤ d, where α 1 > 0,..., α d > 0 and {m k } k=1 ∞ is an increasing sequence of positive integers. Under some conditions on a function φ: [0,+∞) → [0,+∞), it is proved that, if the sequence of Fourier sums \({S_{{m_k}}}\) (g, x) converges almost everywhere for any function g ∈ φ(L)([0, 2π)), then, for any d ∈ ? and f ∈ φ(L)(ln+ L) d?1([0, 2π) d ), the sequence \({S_{{n_k}}}\) (f, x) of rectangular partial sums of the multiple trigonometric Fourier series of the function f and the corresponding sequences of partial sums of all conjugate series converge almost everywhere. 相似文献