2018美赛O奖论文B题合集.pdf

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2.1 Notations and Symbol Description . . . . . . . . . . . . . . . . . . . . . . . 2

2.2 General Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3 Analysis of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.4 Calculating and Simplifying the Model . . . . . . . . . . . . . . . . . . . . 6

2.5 The Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Modified Model 9

3.1 Notations and Symbool Description . . . . . . . . . . . . . . . . . . . . . . 9

3.6 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4 Application of Our Model 17

4.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.2 Symbol Descrption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3 Calculating and Simplifying . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Appendix B Figures 26

1 Introduction

There are about 6,900 languages spoken on Earth nowadays. About half of the world’s

population take one of ten languages as their native language and much of the world

population also speaks a second language. However, because of a variety of influences,

the population of speakers of a language may increase or decrease over time. Our target

is to investigate trends of global languages and location options for new offices.

In part I, we compared our problem with the idea of Markov chain, and add transition

matrix to describe the population transition from native speakers of a language to second

language speakers of another language to native speakers of another language. Consid-

2.1.1 Symbol Description

Symbol Descrption

N The number of languages in consideration

year of n

The annual proportion of non-native speakers of

language i giving birth to native speakers of this

language

The annual death rate of native speakers of language i

The annual death rate of non-native speakers of

language i

The annual proportion (learning rate) of native speakers

A as a foreign language (Implying that the individual possesses advanced skills of

language A and is fluent in both speaking and writing).

1. Speakers of any particular language can be categorized into two groups: native

speakers and non-native speakers.

2. The number of native speakers only increases out of natural birth, and all new-

born babies remain native speakers at the year of their birth (Leaving out rare cases

of prodigies who can instantly learn to speak foreign languages); The number of

native speakers is only reduced by death (Leaving out rare cases of postnatal first

language disability).

of this language, but can become non-native speakers of other languages.

6. Once an individual has mastered a new language, he becomes a non-native speaker

of this language, while remaining all previous identities.

7. No radical and unpredicted events will occur, causing utter shifting in the popula-

tion structure.

It is apparent that native speakers and non-native speakers of the same language are

more closely related, which mainly reflects in:

1. Parents usually raise their children to have the same first languages, or at least

languages they master. Therefore, we can assume that new native speakers can only