Baker's conjecture for functions with real zeros

Baker's conjecture states that a transcendental entire functions of order less than 1/2 has no unbounded Fatou components. It is known that, for such functions, there are no unbounded periodic Fatou components and so it remains to show that they can also have no unbounded wandering domains. Here we introduce completely new techniques to show that the conjecture holds in the case that the transcendental entire function is real with only real zeros, and we prove the much stronger result that such a function has no orbits consisting of unbounded wandering domains whenever the order is less than 1. This raises the question as to whether such wandering domains can exist for any transcendental entire function with order less than 1. Key ingredients of our proofs are new results in classical complex analysis with wider applications. These new results concern: the winding properties of the images of certain curves proved using extremal length arguments, growth estimates for entire functions, and the distribution of the zeros of entire functions of order less than 1

Raskaiden ajoneuvoyhdistelmien vaatimukset Suomessa ja Pohjoismaissa

Tiivistelmä. Tämän kandidaatintyön tavoitteena oli selvittää raskaiden ajoneuvoyhdistelmien vaatimuksia Suomessa ja muissa Pohjoismaissa. Vaatimuksia ovat muun muassa akseli-, teli- ja kokonaismassat, mitat sekä rengasmääräykset. Lisäksi pyrittiin selvittämään, minkälaisia moduuliyhdistelmiä saa ajaa missäkin Pohjoismaassa. Tutkimuksessa hyödynnettiin eri maiden tieliikennelainsäädäntöä sekä viranomaisten ja muiden alan toimijoiden julkaisuja. Selvisi, että Suomen enintään 76-tonniset ja 34,5-metriset ajoneuvoyhdistelmät ovat tällä hetkellä Pohjoismaiden raskaimpia ja pisimpiä. Pohjoismaiden välillä on jonkin verran hajontaa vaatimuksissa erityisesti yhdistelmien enimmäismittojen ja kokonaismassojen osalta. Ruotsi on sallimassa liikennekäyttöön enintään 74-tonniset yhdistelmät vuonna 2023 ja Tanska suunnittelee aloittavansa lähitulevaisuudessa testiajot enintään 34-metrisillä 72-tonnisilla yhdistelmillä.Requirements for combined vehicles in Finland and the Nordic countries. Abstract. The aim of this thesis is to investigate the requirements for combined vehicles in Finland and other Nordic countries. The requirements include axle masses, bogie masses and total masses, dimensions, and tire regulations. In addition, the aim is to find out which types of modular combinations are allowed to be driven in which Nordic countries. The study drew on road transport legislation in the various countries, as well as publications by the authorities and other stakeholders. It was found that Finnish vehicle combinations of up to 76 tons and 34.5 meters are currently the heaviest and longest in the Nordic countries. There is some divergence between the Nordic countries in terms of vehicle requirements, particularly as regards maximum dimensions and total masses of vehicle combinations. Sweden plans to allow up to 74-tonne combinations to enter service in 2023 and Denmark plans to start driving up to 34-metre 72-tonne combinations soon

On critical values of polynomials with real critical points

Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′ are real. We show that there is a zero ζ of f′ such that {pipe} f(ζ)/ζ{pipe} ≤ 2/3, and that this inequality can be taken to be strict unless f is of the form f(z)=z+cz3. © 2009 Springer Science+Business Media, LLC

Smales problem for critical points on certain two rays

Let f be a polynomial of degree n ≥ 2 with f(0)= 0 and f′(0)= 1. We prove that there is a critical point ζ of f with |f(ζ)/ζ| ≤ 1/2 provided that the critical points of f lie in the sector {re iθ:r > 0,|θ| ≤ π/6}, and |f(ζ)/ζ| < 2/3 if they lie in the union of the two rays {1+re±iθ:r ≥ 0}, where 0 < θ ≤ π /2. Copyright © 2010 Australian Mathematical Publishing Association Inc

Framework for evaluating believability of non-player characters in games

Computing Reviews (1998) Categories and Subject Descriptors: I.2.1 Artificial Intelligence: Applications and Expert Systems — games J.4 Social and Behavioral Science — psychology, sociologyWe present a framework for evaluating believability of characters in first-person shooter (FPS) games and look into the development of non-player character’s user-perceived believability. The used framework is composed of two aspects: firstly, character movement and animation, secondly, behavior. Examination of three different FPS games yields that the newer the game was, the better the believability of characters in the game. Moreover, the results from both the aspects of the framework were mutually balanced through all games examined

Properties of the series solution for Painlevé I

We present some observations on the asymptotic behaviour of the coefficients in the Laurent series expansion of solutions of the first Painlevé equation. For the general solution, explicit recursive formulae for the Taylor expansion of the tau-function around a zero are given, which are natural extensions of analogous formulae for the elliptic sigma function, as given by Weierstrass. Numerical and exact results on the symmetric solution which is singular at the origin are also presented

Slow escaping points of quasiregular mappings

This article concerns the iteration of quasiregular mappings on Rd and entire functions on C. It is shown that there are always points at which the iterates of a quasiregular map tend to infinity at a controlled rate. Moreover, an asymptotic rate of escape result is proved that is new even for transcendental entire functions. Let f:Rd→Rd be quasiregular of transcendental type. Using novel methods of proof, we generalise results of Rippon and Stallard in complex dynamics to show that the Julia set of f contains points at which the iterates fn tend to infinity arbitrarily slowly. We also prove that, for any large R, there is a point x with modulus approximately R such that the growth of |fn(x)| is asymptotic to the iterated maximum modulus Mn(R,f)

Analytic functions satisfying Holder conditions on the boundary

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23936/1/0000183.pd

Non-real zeros of derivatives of meromorphic functions

A number of results are proved concerning non-real zeros of derivatives of real and strictly non-real meromorphic functions in the plane

Comparative study of back-stepping controller and super twisting sliding mode controller for indirect power control of wind generator

© 2021 Springer. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1007/s13198-019-00905-7This paper presents the application nonlinear control to regulate the rotor currents and control the active and reactive powers generated by the Doubly Fed Induction Generator used in the Wind Energy Conversion System (WECS). The proposed control strategies are based on Lyapunov stability theory and include back-stepping control (BSC) and super-twisting sliding mode control. The overall WECS model and control scheme are developed in MATLAB/Simulink and the simulation results have shown that the BSC leads to superior performance and improved transient response as compared to the STSMC controller.Peer reviewe