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981.
José Carlos Díaz-Ramos Miguel Domínguez-Vázquez Cristina Vidal-Castiñeira 《Annals of Global Analysis and Geometry》2018,53(2):205-216
We show that an isoparametric submanifold of a complex hyperbolic plane, according to the definition of Heintze, Liu and Olmos’, is an open part of a principal orbit of a polar action. We also show that there exists a non-isoparametric submanifold of the complex hyperbolic plane that is isoparametric according to the definition of Terng’s. Finally, we classify Terng-isoparametric submanifolds of two-dimensional complex space forms. 相似文献
982.
We present two new Ramanujan-type congruences modulo 5 for overpartitions. We also give an affirmative answer to a conjecture of Dou and Lin, which includes four congruences modulo 25 for overpartition. 相似文献
983.
Let D be a subset of a finite commutative ring R with identity. Let \(f(x)\in R[x]\) be a polynomial of degree d. For a nonnegative integer k, we study the number \(N_f(D,k,b)\) of k-subsets S in D such that In this paper, we establish several bounds for the difference between \(N_f(D,k, b)\) and the expected main term \(\frac{1}{|R|}{|D|\atopwithdelims ()k}\), depending on the nature of the finite ring R and f. For \(R=\mathbb {Z}_n\), let \(p=p(n)\) be the smallest prime divisor of n, \(|D|=n-c \ge C_dn p^{-\frac{1}{d}}\,+\,c\) and \(f(x)=a_dx^d +\cdots +a_0\in \mathbb {Z}[x]\) with \((a_d, \ldots , a_1, n)=1\). Then answering an open question raised by Stanley (Enumerative combinatorics, 1997) in a general setting, where \(\delta (n)=\sum _{i\mid n, \mu (i)=-1}\frac{1}{i}\) and \(C_d=e^{1.85d}\). Furthermore, if n is a prime power, then \(\delta (n) =1/p\) and one can take \(C_d=4.41\). Similar and stronger bounds are given for two more cases. The first one is when \(R=\mathbb {F}_q\), a q-element finite field of characteristic p and f(x) is general. The second one is essentially the well-known subset sum problem over an arbitrary finite abelian group. These bounds extend several previous results.
相似文献
$$\begin{aligned} \sum _{x\in S} f(x)=b. \end{aligned}$$
$$\begin{aligned} \left| N_f(D, k, b)-\frac{1}{n}{n-c \atopwithdelims ()k}\right| \le {\delta (n)(n-c)+(1-\delta (n))\left( C_dnp^{-\frac{1}{d}}+c\right) +k-1\atopwithdelims ()k}, \end{aligned}$$
984.
Xavier Bonnefond Pierre Maréchal Walter Cedric Simo Tao Lee 《Set-Valued and Variational Analysis》2018,26(2):265-275
Considering a general linear ill-posed equation, we explore the duality arising from the requirement that the discrepancy should take a given value based on the estimation of the noise level, as is notably the case when using the Morozov principle. We show that, under reasonable assumptions, the dual function is smooth, and that its maximization points out the appropriate value of Tikhonov’s regularization parameter. The numerical relevance of our approach is established by means of an illustrative example from nonparametric instrumental regression, a standard problem in statistics. 相似文献
985.
Let U be an open subset of the Riemann sphere \(\hat {\mathbb{C}}\). We give sufficient conditions for which a finite type map f: U → \(\hat {\mathbb{C}}\) with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-?wi?tek. We also give sufficient conditions for which, instead, Δ has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-?wi?tek. 相似文献
986.
Let k be an integer with k ≥ 6: Suppose that λ1, λ2,..., λ5 be nonzero real numbers not all of the same sign, satisfying that λ1/λ2 is irrational, and suppose that η is a real number. In this paper, for any ε > 0; we consider the inequality |λ1p1 + λ2p 2 2 + λ3p 3 3 + λ4p 4 4 + λ5p 5 k + η | < (max pj)-σ(k)+ε has infinitely many solutions in prime variables p1, p2,...,p5, where σ(k) depends on k. Our result gives an improvement of the recent result. Furthermore, using the similar method in this paper, we can refine some results on Diophantine approximation by unlike powers of primes, and get the related problem. 相似文献
987.
We derive a new special case C(q) of a general continued fraction recorded by Ramanujan in his Lost Notebook. We give a representation of the continued fraction C(q) as a quotient of Dedekind eta-function and then use it to prove modular identities connecting C(q) with each of the continued fractions \(C(-q)\), \(C(q^{2})\), \(C(q^{3})\), \(C(q^{5})\), \(C(q^{7})\), \(C(q^{11})\), \(C(q^{13})\) and \(C(q^{17})\). We also prove general theorems for the explicit evaluation of the continued fraction C(q) by using Ramanujan’s class invariants. 相似文献
988.
We are concerned with the non-stationary Stokes system with non-homogeneous external force and non-zero initial data in \({\mathbb {R}}^n_+ \times (0,T)\). We obtain new estimates of solutions including pressure in terms of mixed anisotropic Sobolev spaces. As an application, some anisotropic Sobolev estimates are presented for weak solutions of the Navier–Stokes equations in a half-space in dimension three. 相似文献
989.
Luciana Mafalda Elias de Assis Malay Banerjee Ezio Venturino 《Annali dell'Universita di Ferrara》2018,64(2):259-283
In this paper two mathematical models are proposed and analyzed to elucidate the influence on a generalist predator of its hidden and explicit resources. Boundedness of the system’s trajectories, feasibility, local and global stability of the equilibria for both models are established, as well as possible local bifurcations. The findings indicate that the relevant behaviour of the system, including switching of stability, extinction and persistence of the involved populations, depends mainly on the reproduction rate of the favorite prey. To achieve full ecosystem survival some balance between the respective grazing pressures exerted by the predator on the prey populations needs to be maintained, while higher grazing pressure just on one species always leads to its extinction. 相似文献
990.
In this paper, we study the theory of a Kantorovich version of the multivariate neural network operators. Such operators, are activated by suitable kernels generated by sigmoidal functions. In particular, the main result here proved is a modular convergence theorem in Orlicz spaces. As special cases, convergence theorem in \(L^p\)-spaces, interpolation spaces, and exponential-type spaces can be deduced. In general, multivariate approximations by constructive neural network algorithms are useful for applications to neurocomputing processes involving high dimensional data. At the end of the paper, several examples of activation functions of sigmoidal-type for which the above theory holds have been described. 相似文献