It is shown that the growth of the hyperbolic derivative of an analytic self-map phi of the unit disc naturally restricts the behaviour of its modulus yielding new integral growth estimates for z bar right arrow log 1-vertical bar phi(0)vertical bar(2)/1-vertical bar phi(z)vertical bar(2). function is used to derive a kind of embedding theorem involving hyperbolic derivative. This result is further used to characterize weighted hyperbolic Dirichlet classes in terms of hyperbolic oscillation. Certain inclusion relations related to hyperbolic Besov classes are also briefly discussed.
We give necessary and sufficient conditions for the existence and finiteness of absolutely continuous conservative and ergodic a-finite invariant measures for a Markov operator, via the induced operator and the (Thaler) jump operator with respect to an appropriate sweep-out set. The key of our characterisation is mean constrictivity, introduced in [3], for the induced/jump operator. As an example, a one-parameter family of random maps on the unit interval with a uniformly contraction property is concerned. For those random maps, further statistical laws, such as the Darling-Kac law, are established through the asymptotics of their a-finite and infinite invariant measures.
In this paper, we prove a stability result for a simple mathematical model that describes virus dynamics as well as predator-prey-substrate interaction in a chemostat. Our model consists of ordinary differential equations with general functional forms. We assume that the functions satisfy some conditions, such as monotonicity and signatures at zero and infinity. Employing the general forms makes the relation among the basic reproduction number, the existence of equilibria and the stability switch clear.
This paper aims to solve the so-called realization problem of J. H. C. Whitehead in the category CW51 of 1-connected and 5-dimensional CW-complexes X such that Tor(H2(X), Z2) = 0. For this purpose we define the notion of Fhomomorphisms which are graded homomorphisms f : H (X) - H (Y ) satisfying a certain algebraic condition. We prove that if f is F-homomorphism, then there exists a map a : X - Y such that H (a)= f .
In this paper, we provide an explicit formula for the twisted Alexander polynomial of a once-punctured torus bundle over the circle with tunnel number one associated with a curve of irreducible representations into GL4(C). Consequently, we can derive the Reidemeister torsion on the curve by using this formula.
Redundancy of frames plays an important role in the context of erasures, as one might be able to reconstruct signals even if information is lost. The purpose of the paper is to present two results on overcomplete polynomially-generated frames. In the first part we show that bandlimited wavelet frames, for which the Fourier transform of the window / has polynomial behavior in a neighborhood of zero, are remarkably stable towards erasures: given such a frame and any N E N, there exists an ordering of the frame elements having the property that for any N E N the subfamily obtained by selecting each Nth element itself a frame. The result is surprising, because it is known that band-limited wavelets for which /psi vanishes on a neighborhood of zero never has this property. We illustrate the results with a number of concrete constructions, e.g., showing that it is even possible to construct a Parseval frame with the subsampling property. No such example has been identified in the literature so far. In the second part of the paper we introduce a method that allows to construct an overcomplete frame for Hilbert spaces of the form L2(-r, r) or L2(0, r), starting with a Riesz basis for the same space. When applied to standard orthogonal polynomials the construction yields nonorthogonal polynomial frames with attractive features: the frames are linearly independent, have infinite excess, the frame decomposition is simple, and the functions in the frame are "very close" to the functions in the given orthogonal system.
Let a be an ideal of a Noetherian ring R such that the R-modules H2a(M) and Ha3 (M) are a-cofinite, for all finitely generated R-modules M. In this paper, it is shown that the R-modules Hia(M) are a-cofinite, for all finitely generated R-modules M and all integers i E N0.
Studying geometric properties of geodesic spheres of sufficiently small radii in a complex hyperbolic space CHn(c) of constant holomorphic sectional curvature c (< 0), we present examples of Riemannian manifolds which are diffeomorphic to Euclidean spheres and are not so called Berger spheres. These manifolds are closely related to the redefinition of Berger spheres given in [9]. We next characterize these manifolds considered as real hypersurfaces in CHn(c) from the viewpoint of submanifold geometry.
We construct representation formulas for local null curves in the four-dimensional pseudo-Euclidean space of index two and derive corresponding parametrizations for local minimal timelike surfaces without integration. As a special case of the representation formula, we construct a representation formula for local null curves in the three-dimensional pseudo-Euclidean space of index one that involves integration. Our results provide examples of minimal timelike surfaces.
A. Lins Neto presented in [LN02] a 1-dimensional family of degree four foliations on the complex projective plane FtEC with non-degenerate singularities of fixed analytic type, whose set of parameters t for which Ft is an elliptic pencil is dense and countable. In [Mc01] and [Gu02], M. McQuillan and A. Guillot showed that the family lifts to linear foliations on the abelian surface E & times; E, where E = C/P, P = (1, r) and r is a primitive 3rd root of unity. The parameters for which Ftare elliptic pencils being t E Q(T) U co, in [Pu13] the second author gave a closed formula for the degree of the elliptic curves of Ft as function of t E Q(T). In this work we determine degree, positions and multiplicities of singularities of the elliptic curves of Ft, for any given t E Z(T), algorithmically implemented in Python. And also we obtain the explicit expressions for the generators of the elliptic pencils, using the Singular software. Our constructions depend on the effect of quadratic Cremona maps on the family of foliations Ft.
We study the analytic structure of the double and triple point spaces M2(f) and M3(f) of finite multi-germs f : (X, S)- (Cn+1, 0), based on results of Mond and Pellikaan for the mono-germ case. We show that these spaces are Cohen-Macaulay, provided that certain dimensional conditions are satisfied, and give explicit expressions for their defining ideals in terms of those of their mono-germ branches.
The Perron-Frobenius theorem in infinite-dimensional Hilbert spaces can be breifly stated as follows: Given a Hilbert cone in a real Hilbert space, a bounded positive self-adjoint operator A is ergodic with respect to this cone if and only if the maximum eigenvalue parallel to A parallel to of A is simple, and the corresponding eigenvector is strictly positive with respect to this cone. This paper addresses the inverse problem of the Perron-Frobenius theorem: Does there exist a Hilbert cone such that a given bounded positive self-adjoint operator A becomes ergodic when its maximum eigenvalue parallel to A parallel to is simple? We provide an affirmative answer to this question in this paper. Furthermore, we conduct a detailed analysis of a specialized Hilbert cone introduced to obtain this result. Additionally, we provide an illustrative example of an application of the obtained results to the heat semigroup generated by the magnetic Schro & uml;dinger operator.
In this paper, sharp bounds for the first nonzero eigenvalues of different type have been obtained. Moreover, when those bounds are achieved, related rigidities can be characterized. More precisely, first, by applying the Bishop-type volume comparison proven in [8,11] and the Escobar-type eigenvalue comparisons for the first nonzero Steklov eigenvalue of the Laplacian proven in [22], for manifolds with radial sectional curvature upper bound, under suitable preconditions, we can show that the first nonzero Wentzell eigenvalue of the geodesic ball on these manifolds can be bounded from above by that of the geodesic ball with the same radius in the model space (i.e., spherically symmetric manifolds) determined by the curvature bound. Besides, this upper bound for the first nonzero Wentzell eigenvalue can be achieved if and only if these two geodesic balls are isometric with each other. This conclusion can be seen as an extension of eigenvalue comparisons in [7,22]. Second, we prove a general Reilly formula for the drifting Laplacian, and then use the formula to give a sharp lower bound for the first nonzero Steklov eigenvalue of the drifting Laplacian on compact smooth metric measure spaces with boundary and convex potential function. Besides, this lower bound can be achieved only for the Euclidean ball of the prescribed radius. This conclusion gives a partial answer to the famous Escobar's conjecture proposed in [6].
In this paper, we study some quantity equivalent to the norm of Bloch to A(alpha)(p) composition operator on one condition, where 'Bloch' is the Bloch space on the unit ball of Cm, A(alpha)(p) is the weighted Bergman space on the unit ball of C-n, (0 < p < infinity and-1 < alpha < infinity).
We study the Grassmann geometry of surfaces in the reducible Riemannian symmetric space H2 x R.
We investigate contact of cross caps and cuspidal edges with (right circular) cylinders. We introduce cylindrical directions of cross caps and cuspidal edges which are defined by the kernel field of A A3-contact of the surfaces with cylinders.
