The second main theorem

Using the second main theorem of value distribution theory and Borel’s lemma, Nevanlinna proved that for two nonconstant meromorphic functions \(f\) and \(g\) on the complex plane C, if they have the same inverse images for five distinct values, then \(f \equiv g\), and that \(g\) is a special type of linear fractional transformation of \(f\) if they have the same inverse images, counted with multiplicities, for four distinct values.

10p runordie5 04-07-2022 3 2   Download

Value distribution theory for holomorphic curves which also known as Nevanlinna-Cartan theory was originated by the work of H. Cartan in 1933. Since that time, it had attracted the attention of many mathematicians and had many important publications and it had many applications in different areas of mathematics.

8p vimarissamayer 02-06-2022 10 3   Download

In this paper, we establish a second main theorem for holomorphic mappings from a disc (R) into Pn(C) and families of hyperplanes in subgeneral position. Our result is an extension the classical second main theorem of Cartan-Nochka and the second main theorem of Fujimoto.

9p tamynhan9 02-12-2020 10 3   Download

In this lecture we will formally define the definite integral and give many of the properties of definite integrals. The main contents of this chapter include all of the following: The definite integra, the second fundamental theorem of calculus.

32p larachdumlanat122 26-11-2020 19 0   Download

In this paper, we establish a second main theorem with a good defect relation for entire curves in a projective variety whose derivatives vanish on inverse image of hypersurface targets. Our method is a combination of the techniques in [7-9].

10p koxih_kothogmih5 04-09-2020 16 2   Download

An extension of Nevanlinna value distribution theory for algebroid functions on annuli is proposed. The main characteristics are one-parameter and possess the same properties as in the classical case. Analogs of the Cartan theorem, the first fundamental theorem, the second fundamental theorem, deficient values, and the uniqueness of algebroid functions on annuli are proved.

20p danhdanh27 07-01-2019 17 2   Download

This paper is concerned with a non-homogeneous multi-point boundary value problem of second order differential equation with one-dimensional p-Laplacian. Using multiple fixed point theorems, sufficient conditions to guarantee the existence of at least three solutions of this kind of BVP are established. Two examples are presented to illustrate the main results.

32p tuongvidanh 06-01-2019 29 2   Download

In this paper, by using the second main theorem for holomorphic curves from annuli ∆ to P n(C) intersecting a collection of fixed hyperplanes in general position with truncated counting functions, we will prove some theorems on unicity for linearly non-degenerate holomorphic curves on annulus ignoring multiplicity with hyperplanes in general position in projective space. This theorems have shown the sufficient conditions for two linearly non-degenerate holomorphic curves being equivalent.

7p doctorstrange1 21-06-2018 25 2   Download

In this lection we will formally define the definite integral and give many of the properties of definite integrals. The main contents of this chapter include all of the following: The definite integra, the second fundamental theorem of calculus.

35p allbymyself_06 26-01-2016 27 2   Download

We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemer´di’s theorem, which ase serts that any subset of the integers of positive density contains progressions of arbitrary length. The second, which is the main new ingredient of this paper, is a certain transference principle. This allows us to deduce from Szemer´di’s e theorem that any subset of a sufficiently pseudorandom set (or measure) of positive relative density contains progressions of arbitrary length. ...

68p dontetvui 17-01-2013 41 6   Download

This text is based on a lecture course developed by the author and given to students in the second year of study in mathematics at Newcastle University. This has been written to provide a typical course (for students with a general mathematical background) that introduces the main ideas, concepts and techniques, rather than a wide-ranging and more general text on complex analysis.

174p sn_buon 29-11-2012 58 2   Download

FINITE DIFFERENCE SCHEMES WITH MONOTONE OPERATORS N. C. APREUTESEI Received 13 October 2003 and in revised form 10 December 2003 To the memory of my mother, Liliana Several existence theorems are given for some second-order difference equations associated with maximal monotone operators in Hilbert spaces. Boundary conditions of monotone type are attached. The main tool used here is the theory of maximal monotone operators. 1. Introduction In [1, 2], the authors proved the existence of the solution of the boundary value problem p(t)u (t) + r(t)u (t) ∈ Au(t) + f (t), u (0) ∈ α u(0) − a , a.e.

12p sting12 10-03-2012 40 3   Download

Chapter 18 THE CENTRAL LIMIT THEOREM FOR STATIONARY PROCESSES 1 . Statement of the problem This chapter contains the main objective of the second part of the book, the investigation of the limiting behaviour of the distributions of sums or integrals of the form

50p dalatngaymua 30-09-2010 76 8   Download