scholarly journals Powers of paths in tournaments

2021 ◽  
pp. 1-5
Author(s):  
Nemanja Draganić ◽  
François Dross ◽  
Jacob Fox ◽  
António Girão ◽  
Frédéric Havet ◽  
...  
Keyword(s):  
Complete Solution ◽  
Short Note ◽  
Directed Path

Abstract In this short note we prove that every tournament contains the k-th power of a directed path of linear length. This improves upon recent results of Yuster and of Girão. We also give a complete solution for this problem when k=2, showing that there is always a square of a directed path of length , which is best possible.

A NOTE ON A COMPLETE SOLUTION OF A PROBLEM POSED BY K. MAHLER

2018 ◽  
Vol 98 (1) ◽  
pp. 60-63
Author(s):  
DIEGO MARQUES ◽  
CARLOS GUSTAVO MOREIRA
Keyword(s):  
Recent Result ◽  
Real Number ◽  
Complete Solution ◽  
Short Note ◽  
Radius Of Convergence ◽  
Complex Conjugation ◽  
Exceptional Set ◽  
Exceptional Sets ◽  
Transcendental Functions

Let $\unicode[STIX]{x1D70C}\in (0,\infty ]$ be a real number. In this short note, we extend a recent result of Marques and Ramirez [‘On exceptional sets: the solution of a problem posed by K. Mahler’, Bull. Aust. Math. Soc.94 (2016), 15–19] by proving that any subset of $\overline{\mathbb{Q}}\cap B(0,\unicode[STIX]{x1D70C})$, which is closed under complex conjugation and contains $0$, is the exceptional set of uncountably many analytic transcendental functions with rational coefficients and radius of convergence $\unicode[STIX]{x1D70C}$. This solves the question posed by K. Mahler completely.

scholarly journals Vertex Turán problems for the oriented hypercube

2021 ◽  
Vol 13 (2) ◽  
pp. 356-366
Author(s):  
Dániel Gerbner ◽  
Abhishek Methuku ◽  
Dániel T. Nagy ◽  
Balázs Patkós ◽  
Máté Vizer
Keyword(s):  
Short Note ◽  
Oriented Graph ◽  
Directed Path ◽  
Maximum Cardinality ◽  
Directed Tree ◽  
Induced Subgraph ◽  
Asymptotic Value ◽  
Turan Problem ◽  
Turan Problems ◽  
Turán Problem

Abstract In this short note we consider the oriented vertex Turán problem in the hypercube: for a fixed oriented graph F → \vec F , determine the maximum cardinality e x v ( F → , Q → n ) e{x_v}\left( {\vec F,{{\vec Q}_n}} \right) of a subset U of the vertices of the oriented hypercube Q → n {\vec Q_n} such that the induced subgraph Q → n [ U ] {\vec Q_n}\left[ U \right] does not contain any copy of F → \vec F . We obtain the exact value of e x v ( P k , →   Q n → ) e{x_v}\left( {\overrightarrow {{P_k},} \,\overrightarrow {{Q_n}} } \right) for the directed path P k → \overrightarrow {{P_k}} , the exact value of e x v ( V 2 → ,   Q n → ) e{x_v}\left( {\overrightarrow {{V_2}} ,\,\overrightarrow {{Q_n}} } \right) for the directed cherry V 2 → \overrightarrow {{V_2}} and the asymptotic value of e x v ( T → , Q n → ) e{x_v}\left( {\overrightarrow T ,\overrightarrow {{Q_n}} } \right) for any directed tree T → \vec T .

Introduction

2018 ◽  
Author(s):  
Peter Hopkins
Keyword(s):  
Final Section ◽  
Short Note ◽  
Current Situation ◽  
Research Projects ◽  
Everyday Lives ◽  
Early Settlement ◽  
The Everyday ◽  
Initial Research

The chapters in this collection explore the everyday lives, experiences, practices and attitudes of Muslims in Scotland. In order to set the context for these chapters, in this introduction I explore the early settlement of Muslims in Scotland and discuss some of the initial research projects that charted the settlement of Asians and Pakistanis in Scotland’s main cities. I then discuss the current situation for Muslims in Scotland through data from the 2011 Scottish Census. Following a short note about the significance of the Scottish context, in the final section, the main themes and issues that have been explored in research about Muslims in Scotland.

A Comparative Overview of the Fair Wear and Tear Exception: the Duty of Holders of Temporary Interests to Preserve Property

2002 ◽  
Vol 6 (1) ◽  
pp. 85-100
Author(s):  
Raffaele Caterina
Keyword(s):  
Common Core ◽  
Complete Solution ◽  
Roman Law ◽  
Private Ownership ◽  
Legal Systems ◽  
Personal Rights ◽  
Wear And Tear ◽  
Long Life ◽  
The Law ◽  
The Relationship

“A system of private ownership must provide for something more sophisticated than absolute ownership of the property by one person. A property owner needs to be able to do more than own it during his lifetime and pass it on to someone else on his death.”1 Those who own things with a long life quite naturally feel the urge to deal in segments of time. Most of the owner's ambitions in respect of time can be met by the law of contract. But contract does not offer a complete solution, since contracts create only personal rights. Certain of the owner's legitimate wishes can be achieved only if the law allows them to be given effect in rem—that is, as proprietary rights. Legal systems have responded differently to the need for proprietary rights limited in time. Roman law created usufruct and other iura in re aliena; English law created different legal estates. Every system has faced similar problems. One issue has been the extent to which the holder of a limited interest should be restricted in his or her use and enjoyment in order to protect the holders of other interests in the same thing. A common core of principles regulates the relationship between those who hold temporary interests and the reversioners. For instance, every system forbids holder of the possessory interest to damage the thing arbitrarily. But other rules are more controversial. This study focuses upon the rules which do not forbid, but compel, certain courses of action.

Short Note: A Record of Twin Fetuses in a Harbor Porpoise (Phocoena phocoena) Stranded on the Dutch Coast

2014 ◽  
Vol 40 (4) ◽  
pp. 394-397 ◽  
Author(s):  
Lonneke L. IJsseldijk ◽  
Andrea Gröne ◽  
Sjoukje Hiemstra ◽  
Jeroen Hoekendijk ◽  
Lineke Begeman
Keyword(s):  
Short Note ◽  
Phocoena Phocoena ◽  
Harbor Porpoise ◽  
Dutch Coast

Short Note: Predation of Harbour Porpoises (Phocoena phocoena) by Grey Seals (Halichoerus grypus) in Wales

2015 ◽  
Vol 41 (2) ◽  
pp. 188-191 ◽  
Author(s):  
Thomas Stringell ◽  
Dave Hill ◽  
Dafydd Rees ◽  
Ffion Rees ◽  
Padrig Rees ◽  
...  
Keyword(s):  
Short Note ◽  
Halichoerus Grypus ◽  
Phocoena Phocoena

Impact of Optimal Cropping Patterns on Incomes in a Punjab District

1976 ◽  
Vol 15 (2) ◽  
pp. 218-221
Author(s):  
M. Arshad Chaudhry
Keyword(s):  
Developing Countries ◽  
Linear Programming ◽  
Short Note ◽  
Cropping Pattern ◽  
Small Farms ◽  
Cropping Patterns ◽  
Punjab Province ◽  
Optimal Cropping

To improve farm incomes in developing countries, the foremost question that the farmer must address himself to is: what cropping pattern best uses the fixed resources in order to get the highest returns? During the last decade, the agricultural economists have shown great interest in applying the tools of linear programming to individual farms. Most of the studies conducted elsewhere have shown that, under existing cropping pattern, farm resources were not being utilized optimally on the small farms.[l, 4]. We conducted a survey in the canal-irrigated areas of the Punjab province of Pakistan1 to investigate into the same problem. This short note aims at identifying the opti¬mal cropping pattern and to estimate the increase in farm incomes as a result of a switch towards it on the sampled farms.

Diagnostic Fault Simulation for the Failure Analyst

2004 ◽  
Author(s):  
Dan Bodoh ◽  
Anthony Blakely ◽  
Terry Garyet
Keyword(s):  
Fault Diagnosis ◽  
Failure Analysis ◽  
Complete Solution ◽  
Fault Simulation ◽  
Building Blocks ◽  
Physical World ◽  
Design For Test ◽  
Fault Diagnosis System ◽  
Diagnosis Algorithm ◽  
Diagnosis Tool

Abstract Since failure analysis (FA) tools originated in the design-for-test (DFT) realm, most have abstractions that reflect a designer's viewpoint. These abstractions prevent easy application of diagnosis results in the physical world of the FA lab. This article presents a fault diagnosis system, DFS/FA, which bridges the DFT and FA worlds. First, it describes the motivation for building DFS/FA and how it is an improvement over off-the-shelf tools and explains the DFS/FA building blocks on which the diagnosis tool depends. The article then discusses the diagnosis algorithm in detail and provides an overview of some of the supporting tools that make DFS/FA a complete solution for FA. It also presents a FA example where DFS/FA has been applied. The example demonstrates how the consideration of physical proximity improves the accuracy without sacrificing precision.

Short Note Chromosomal Homology between the Human and the Bovine DMRT1 Genes

2008 ◽  
Vol 57 (1) ◽  
pp. 29-32
Author(s):  
Anna Bratuś ◽  
Monika Bugno ◽  
Jolanta Klukowska-Rötzler ◽  
Małgorzata Sawińska ◽  
Andre Eggen ◽  
...  
Keyword(s):  
Short Note ◽  
Chromosomal Homology
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