OpenLLM-France/wikimedia huggingface dataset:
# Transportation Systems Simulation - A Tutorial for Multi-Modal Simulation Using VISSIM/Intersection: Simulation
## Run the Simulation

You have now entered all of the information in VISSIM necessary to run the simulation. You can set your simulation preferences by going to Simulation -> Parameters… Once all of your settings are to your liking, click the Play button to start the simulation. After a moment of loading the simulations will generate vehicles and your traffic signal should cycle through each phase as programmed.
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# Transportation Systems Simulation - A Tutorial for Multi-Modal Simulation Using VISSIM/Macroscopic Simulation
## Fundamental Diagram

https://en.wikipedia.org/wiki/Fundamental_diagram_of_traffic_flow

## The Cell Transmission Model (CTM) model

https://en.wikipedia.org/wiki/Cell_Transmission_Model
# Transportation Systems Simulation - A Tutorial for Multi-Modal Simulation Using VISSIM/Introduction

The scope of this book is a tutorial about the use and practical implications of Vissim’s tools for freeway, signalized intersection, pedestrian, transit, and bicycle simulation. The text is broken down into five sections; Freeway Simulation, Signalized Intersection Simulation, Pedestrian and Bicycle Simulation, Transit simulation, and Parking Simulation. Each section is split into subsection related to geometric network design, traffic data input, and/or simulation evaluation. These subsections explore important characteristics and attributes that contribute to building and validating a model. The Geometric Network Design section discusses the methods and tools that are used to build a spatial arena to represent the existing world or a proposed design with a step by step example. The Traffic Data Input section provides a step by step example on how to manipulate data input, compositions, and routes. The Evaluation section introduces a method to extract data from the model in order to analyze in a spreadsheet.
A simulation is only as accurate as the quality of the model and data input. This can be summarized by the expression “Garbage In, Garbage Out”, and is as true with Vissim as any traffic simulation software. One not must view the quality and smooth interface of Vissim as a reflection of the quality and relevance of their own model. A rigorous approach must be taken and the goal of this text is to provide the framework. Each section introduces basic concepts and procedures that can be used as a starting point for well calibrated sophisticated models.
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# Transportation Systems Simulation - A Tutorial for Multi-Modal Simulation Using VISSIM/Microscopic Simulation
## Car Following Model

https://en.wikipedia.org/wiki/Microscopic_traffic_flow_model Newell's simplified car-following model: https://en.wikipedia.org/wiki/Newell%27s_car-following_model
# Transportation Systems Simulation - A Tutorial for Multi-Modal Simulation Using VISSIM/New VISSIM File

This is an introduction the program’s interface, user preferences and network settings. There are a few key icons and functions within the program’s interface worth mentioning.

## VISSIM Interface

When starting the application for the first time, VISSIM will prompt you to define the right click behavior. This tutorial was written using the first option, where Right Clicking the mouse will open the context menu. Select “opens the context menu” and then Click OK. Some important functions within the VISSIM interface are shown in the image below:

## File Type

The default file type when saving is a “VISSIM Network File”, it has a “.inpx” extension.

## Customizing the Toolbar

Below the menu is the toolbar. To customize your toolbar, Right Click anywhere on the toolbar and select customize. Explore each tab and configure these settings to your preferred style and layout.

## Network Objects

The toolbar located on the left hand side of the screen has 3 tabs: Network Objects, Levels and Background. Network Objects is the default selection. The most fundamental Network Objects needed to create most networks include:
* Links and Connectors
* Stop Signs
* Signal Heads
* Detectors
* Vehicle Inputs
* Vehicle Routes
* Data Collection Points
* Background Images

## Network Settings

To change the Units to Imperial or Metric, select Base Data > Network Setting, then select the Units tab. Click on "All Imperial", then Click OK
The content above is also available as a video. Click the following YouTube link: VISSIM v7 Tutorial Part 1: Introduction
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# Transportation Systems Simulation - A Tutorial for Multi-Modal Simulation Using VISSIM/Improving Results

After the first simulation, you may have encountered unusual behavior. VISSIM v7 has tools to adjust a few driving parameters.

## Adjusting Driving Behavior

Every link and connector can have a unique Behavior Type. Under “Network Objects” Right Click “Links” and Select “Show List” (see Figure below). A new window will appear below the network editor. All Links and Connectors by default should be “Urban (motorized)” as the “LinkBehavType”.
TIP: VISSIM uses two types of models: Wiedemann 74 and Wiedemann 99.
       Wiedemann 74 is suitable for urban traffic and merging
       Wiedemann 99 is suitable freeway traffic with no merging
       You may need to change the “LinkBehavType” for some or all links/connectors
WARNING: Run the simulation first with default values. Only make the following adjustments if the first simulation does not accurately represent highway traffic behavior.

## Wiedemann Model (Following)

* To adjust specific parameters for each Wiedemann model, Select Base Data > Driving Behaviors from the top toolbar (see Figure below)
* A new “Driving Behavior” window will appear below the Network Editor
* Right Click your desired CarFollowModType and select “Edit…”
* A new window will appear and only adjust the following parameters
“Following” tab and Car following model: Wiedemann 74
* Look ahead distance
* Look back distance
* Average standstill distance
“Following” tab and Car following model: Wiedemann 99 (Figure 44)
* Look ahead distance
* Look back distance
* CC0 (Standstill Distance)
* CC1 (Headway Time)
* CC2 (‘Following’ Variation)
TIP: Only change parameter values in small increments if necessary. The table below shows the default value and the Suggested Range for each parameter.
CC0 (Standstill Distance): the average desired standstill distance between two vehicles or the desired rear-bumper to front-bumper distance (feet) between stopped vehicles, as shown in the Figure below.
CC1 (Headway Time): is the gap (seconds) which a driver wants to maintain at a certain speed. The higher the value, the more cautious the driver is as shown in Figure 46. Desired Safety Distance = CC1 +CCO.
CC2 (Following Variation): is the longitudinal oscillation during following conditions. It defines the additional distance (feet) from the desired safety distance a driver allows before he intentionally moves closer to the car in front. (see Figure below)

## Wiedemann Model (Lane Change)

* “Lane Change” tab and General behavior: “Free lane selection” or “Slow lane rule”
* Check the “Cooperative lane change” box (see Figure below)
WARNING: It is not recommended to adjust Lane Change parameters until all previous steps have been attempted.
After adjusting a few Driving Behavior Parameters, run the simulation again and calculate the GEH with your new Simulation volumes. Only adjust Driving Behavior Parameters one at a time and by 10% to 25%.
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# Thai Civilization/Socio-Political Background of the Thai Society

| Socio-Political Background | of the Thai Society |
The king is the head of state. The prime minister or premier is the head of government.
The premier and other members of the Cabinet make the Government's policies and carry out the operations of the government.
Thailand is divided into 76 provinces. The capital city is Bangkok. In terms of its administrative divisions, the provinces are divided into 795 districts (amphoe), 81 subdistricts (king amphoe), 7,255 rural administrative subdistricts (tambon), and 69,866 villages (muban).

## Social Structure of the Thai Society

‘ village’ or ‘Moo Ban’ is the most basic unit of the structure. In the past, it was a self-contained community in terms of economy and basic needs.
In general, Thai people's ways of life and customs are based mainly on agricultural activities and religious activities. Most villages had a wat (Buddhist monastery). Most villages have a shrine for a village deity. Wats have been the spiritual and educational centers.

## The Sakdina System

Prai Sakdina System of the Ayudthaya Period
The Prai-Sakdinal system was a form of social system during the Ayudthaya period. It was established to serve the state as well as to function as a means to balance the power of the administration of the kingdom/government.
The Prai (commoners) Sakdina system was invented to support the power of the rulers. During that time, Thai society divided its Prais or commoners into three groups:
1) Prai Som, 2) Prai Suai, and 3) Prai Luang
1) Prai Som worked for the lords. Their wellbeings depended on their masters or lords. During the Ayudthaya period, this category of people worked for the state every other month (one month for the state - one month for the self). This system, perhaps, has created the concept of 'Nai' (Master) in Thai society (even today).
2) Prai Suai were war captives or labor given to the state by its vassal states.
3) Prai Luang served the king.
# Thai Arts (Painting, Sculpture, and Architecture)
## Painting

Prehistoric painting Thai painting Mural Paintings

## Sculpture

* The Mon Dvaravati and Haripunjaya Period
* Srivijaya Art
* Lop Buri Art
* The Sukhothai Era
* The Ayudthaya Period
* The Rattanakosin Era

## Architecture

* Srivijaya Architecture
* The Sukhothai Era
* Ayudthaya Period
# Thai Civilization/Education
## Historical development

The development of education in Thailand has stretched back along her history for nearly eight hundred years. It can be now divided into four main periods:
(1) traditional education, (2) education during the early Rattanakosin period (foundation of formal education), (3) education after the political reform of AD 1932(modernized education for national development), and (4) education in he early 21st century.
# Economic Foundation of the Thai Society

Thailand has recognized itself as a country with agriculture-based society. In the past, most Thais were farmers.
The stone inscription says that Thailand is a fertile land --- there are fish in water and rice in the field pr "Nai Nam Mi Pla, Nai Na Mi Khao." Thailand has been a rice-growing society for many centuries. The Thai word for 'rice' is 'khao.'
Gradually, Thailand has developed into an industrialized state like many other countries in the world.
However, agriculture remains its back-bone of the economy. Its exports include rice, rubber, sugar, bananas, pineapples, and other agricultural products. In fact, the Thai government has branded Thailand as 'a great kitchen of the world.'
# The Legend of Zelda: Link's Awakening/Walkthrough/Catfish's Maw

Catfish's Maw is the fifth dungeon in "The Legend of Zelda: Link's Awakening." This dungeon is known for its complex layout and the presence of multiple mini-boss battles, which adds a unique challenge compared to other dungeons in the game. Catfish's Maw in "The Legend of Zelda: Link's Awakening" is a dungeon that emphasizes exploration, combat, and the strategic use of the Hookshot.

## Location and Access

* Underwater Entrance: Catfish's Maw is located in Martha's Bay. Link must swim underwater to find and enter the dungeon through the mouth of a giant catfish statue.
* Requirement: The Flippers, obtained in the previous dungeon (Angler's Tunnel), are needed to dive underwater and access the dungeon.

## Dungeon Layout

* Complex Navigation: The dungeon features a multi-layered, labyrinthine layout with numerous rooms and passageways that often require backtracking and careful exploration.
* Puzzles and Obstacles: The puzzles in Catfish's Maw often involve moving blocks, hitting switches, and using the Hookshot to traverse gaps or pull items closer.

## Key Item

* Hookshot: The primary item found in Catfish's Maw. It allows Link to:
** Grapple across gaps.
** Pull enemies and objects towards him.
** Hit distant switches.
** Cross large bodies of water and chasms.The Hookshot significantly expands Link's mobility and combat options, making it one of the most important tools in his arsenal.

## Post-Dungeon

* Wind Marimba: Upon defeating Slime Eel, Link receives the Wind Marimba, one of the eight Instruments of the Sirens needed to awaken the Wind Fish.
# The Legend of Zelda: Link's Awakening (2019 video game)

This is a strategy guide for the 2019 remake of the Game Boy classic, The Legend of Zelda: Link's Awakening.
A separate guide for the original Game Boy and Game Boy Color releases can be found in the Wikibook for The Legend of Zelda: Link's Awakening.

## Table of Contents
### Main Game

* Getting Started
* Wake Up!
* Exploring Mabe Village
* Hitting the Beach
* Toadstool Trek
* Tail Cave Exploration
* Walk the Dog
* Bottle Grotto Exploration
* Storming the Castle
* Key Cavern Exploration
* Dream Shrine
* Ancient Ruins Exploration
* Exploring Animal Village
* Journey with Marin

### Gameplay

* Controls
* Inventory
* Pieces of Heart
* Secret Seashells
* Stand locations
* Trendy Game Shop
* Town Tool Shop
* Fishing Pond
* Dampé
* Trading Sequence

### Story

* Characters

### Meta

* Challenges
* Easter Eggs
* About
# The Legend of Zelda: Link's Awakening (2019 video game)/About
## Book History

Work on this Wikibook began on June 14th, 2021.

## Purpose

The primary purpose of this book is to inform the reader.
However this book also exists as an experiment to create a new strategy guide for Wikibooks from scratch, not relying on old undeleted Wikibooks from before the period in which they were banned (~2006-2021), or from imports from StrategyWiki. While a book on StrategyWiki existed for this game, it was only partially developed at the time of writing. This meant this was an ideal game to try writing about from scratch, rather then attempt an import. The one exception is the page Controls.
A walkthrough was included hesitantly - since they are not needed in a pure strategy guide and significantly increase the amount of upfront work required in the creation of the guide. However a walkthrough can also help organize the chronology of a game, a handy tool for scholars of media. Thus this walkthrough also pays special attention to plot and subplot developments.
Many guides leverage nonfree media to assist the reader. A goal during the writing of this Wikibook was to see if this could successfully be avoided. If you, the reader, feel this guide is an insufficient aid without such media, please feel free to add fair use screenshots per the Wikibooks policy.
# The Legend of Zelda: Link's Awakening (2019 video game)/Challenges

Some gamers will want a more challenging experience. Here are some Challenges, mostly self imposed, used commonly among gamers in the Zelda community to increase challenge. To increase the difficulty, select one or more of these challenges.
| Challenge | Description |
| Hero Mode | Do a Hero Mode playthrough. |
| 0 Game Overs | Restart the entire game on a game over. |
| 3 Heart | Never increase heart capacity above the starting 3 hearts. |
# Traditional Chinese Medicine/Purgative Prescriptions

Prescriptions for Relieving Exterior Syndromes | Prescriptions for Clearing Away Heat | Prescriptions for Warming the Interior | Purgative Prescriptions |
* Da Cheng Qi Tang
* Da Huang Fu Zi Tang
* Wen Pi Tang
back to:
# Traditional Chinese Medicine/Qi-Regulating Herbs

* Chen Pi (Pericarpium Citri Reticulatae)
** Ju Hong (Exocarpium Citri Rubrum)
** Ju Luo (Fibra Citri Rubrum)
** Ju Ye (Folium Citri Rubrum)
** Ju He (Semen Citri Rubrum)
* Hua Ju Hong (Exocarpium Citri Grandis)
* Qing Pi (Pericarpium Citri Reticulatae Viride)
* Zhi Shi (Fructus Aurantii Immaturus)
* Zhi Ke (Fructus Aurantii)
* Xiang Yuan (Fructus Citri)
* Fo Shou (Fructus Citri Sarcodactylis)
* Fo Shou Hua (Flos Citri Sarcodactylis)
* Po Bu Zi Ye (Folium Cordia Dichotoma)
* Da Fu Pi (Pericarpium Arecae)
* Wan Dian Jin (Radix Ilicis Asprellae)
* Mu Xiang (Radix Aucklandiae)
* Xiang Fu (Rhizoma Cyperi)
* Wu Yao (Radix Linderae)
* Wu Teng (Ramulus Linderae)
* Xie Bai (Bulbus Allii Macrostemonis)
* Tan Xiang (Lignum Santali Albi)
* Chen Xiang (Lignum Aquilariae Resinatum)
* Chuan Lian Zi (Fructus Toosendan)
* Ku Lian Zi (Fructus Meliae)
* Qing Mu Xiang (Radix Aristolochiae)
* Li Zhi He (Semen Litchi)
* Suo Luo Zi (Semen Aesculi)
* Ba Yue Zha (Fructus Akebiae)
* Gan Song (Radix seu Rhizoma Nardostachys)
* Jiu Ceng Ta (Herba Ocimi Basilici)
* Tian Xian Tiang (Herba Aristolochiae)
* Dao Dou (Semen Canavaliae)
* Shi Di (Calyx Kaki)
back to : Traditional Chinese Herbology And Pharmacology
# Traditional Chinese Medicine/Qi-Regulating Prescriptions

Qi-regulating prescriptions have been classified as follows:

## Qi-Moving Prescriptions

* Yue Ju Wan (Escape Restraint Pill)
** Xiang Fu Wan (Cyperus Pill)
* Jin Ling Zi San (Melia Toosendan Powder)
** Yan Hu Suo San (Corydalis Powder)
** Yan Hu Yi Hao (Corydalis Formula One)
** Yan Hu Er Hao (Corydalis Formula Two)
* Ban Xia Hou Po Tang (Pinellia and Magnolia Bark Decoction)
* Zhi Shi Xie Bai Gui Zhi Tang (Immature Bitter Orange, Chinese Chive, and Cinnamon Twig Decoction)
** Gua Lou Xie Bai Bai Jiu Tang (Trichosanthes Fruit, Chinese Chive, and Wine Decoction)
** Gua Lou Xie Bai Ban Xia Tang (Trichosanthes Fruit, Chinese Chive, and Pinellia Decoction)
** Jia Wei Gua Lou Xie Bai Tang (Augmented Trichosantbes Fruit and Chinese Chive Decoction)
* Ju He Wan (Tangerine Seed Pill)
* Tian Tai Wu Yao San (Top-Quality Lindera Powder)
** San Ceng Hui Xiang Wan (Fennel Seed Pill with Three Levels)
** Dao Qi Tang (Conduct the Qi Decoction)
* Nuan Gan Tang (Warm the Liver Decoction)
* Hou Po Wen Zhong Tang (Magnolia Bark Decoction for Warming the Middle)
** Liang Fu Wan (Galangal and Cyperus Pill)

## Qi-Descending Prescriptions

* Su Zi Jiang Qi Tang (Perilla Fruit Decoction for Directing Qi Downward)
** San Zi Jiang Qi Tang (Three-Seed Decoction for Directing Qi Downward)
* Ding Chuan Tang (Arrest Wheezing Decoction)
* Shen Mi Tang (Mysterious Decoction)
* Si Mo Tang (Four Milled-Herbs Decoction)
** Wu Mo Yin Zi (Five Milled-Herbs Decoction)
* Xuan Fu Dai Zhe Shi Tang (Inula and Hematite Decoction)
** Gan Jiang Ren Shen Ban Xia Wan (Ginger, Ginseng, and Pinellia Pill)
* Ju Pi Zhu Ru Tang (Tangerine Peel and Bamboo Shaving Decoction)
** Ju Pi Zhu Ru Tang (Tangerine Peel and Bamboo Shaving Decoction)
** Xin Zhi Ju Pi Zhu Ru Tang (Newly-Formulated Tangerine Peel and Bamboo Shaving Decoction)
* Ding Xiang Shi Di Tang (Clove and Persimmon Calyx Decoction)
** Shi Di Tang (Persimmon Calyx Decoction)
* Sheng Yang San Huo Tang (Raise the Yang and Disperse the Fire Decoction)
back to:
* Classification Of Prescriptions
Reference: John K Chen and Tina Chen: "Chinese Herbal Formulas and Applications". Art of Medicine Press Inc. 2009. ISBN-10: 0-9740635-7-6
# Traditional Chinese Medicine/Qi Bao Mei Ran Dan

The formula Qi Bao Mei Ran Dan, designed to invigorate the kidney, nourish essence, darken graying hair, promote kidney yin, consists of the following:
| No. | Pinyin | Simplified Chinese |
| 1 | He Shou Wu | 何首乌 |
| 2 | Bai Fu Ling | 白茯苓 |
| 3 | Niu Xi | 牛膝 |
| 4 | Dang Gui | 当归 |
| 5 | Gou Qi Zi | 枸杞子 |
| 6 | Tu Si Zi | 菟丝子 |
| 7 | Po Gu Zhi (Bu Gu Zhi) | 破故纸 (补骨脂) |
back to :
* Formula Design
* Glossaries
* Prescriptions
# Traditional Chinese Medicine/Qi Xian Dan

The formula Qi Xian Dan, designed to nourish the liver and kidney, enrich blood and darken hair, consists of the following:
| No. | Pinyin | Simplified Chinese |
| 1 | He Shou Wu | 何首乌 |
| 2 | Ren Shen | 人参 |
| 3 | Sheng Di Huang | 生地黄 |
| 4 | Shu Di Huang | 熟地黄 |
| 5 | Mai Men Dong | 麦门冬 |
| 6 | Tian Men Dong | 天门冬 |
| 7 | Fu Ling | 茯苓 |
| 8 | Chao Hui Xiang | 炒茴香 |
back to :
* Formula Design
* Glossaries
* Prescriptions
# Traditional Chinese Medicine/Qian Zheng San

The formula Qian Zheng San, designed to expel and remove phlegm, dredge the collaterals and relieve convulsion, consists of the following:
| No. | Pinyin | Simplified Chinese | Grams |
| 1 | Bai Fu Zi | 白附子 | 9 |
| 2 | Jiang Can | 僵蚕 | 9 |
| 3 | Quan Xie | 全蝎 | 9 |
back to:
* Relieving Convulsion By Stopping Endogenous Wind
* Formula Design
* Prescriptions
# Traditional Chinese Medicine/Qian Jin Wei Jing Tang

The formula Qian Jin Wei Jing Tang, designed to resolve phlegm by clearing away heat, consists of the following:
| No. | Pinyin | Simplified Chinese | Grams |
| 1 | Wei Jing | 苇茎 | 60.0 |
| 2 | Yi Yi Ren | 薏苡仁 | 30.0 |
| 3 | Dong Gua Ren | 冬瓜仁 | 30.0 |
| 4 | Tao Ren | 桃仁 | 9.0 |
back to :
* Resolving Phlegm By Clearing Away Heat
* Formula Design
* Prescriptions
# Traditional Chinese Medicine/Purgative Method With Bitter And Cold Herbs

* Da Cheng Qi Tang
* Ji Jiao Li Huang Wan
* Ma Zi Ren Wan
* Da Huang Gan Cao Tang
back to :
# Traditional Chinese Medicine/Qiang Huo

notopterygium root
(Chinese: 羌活, Pinyin: qiāng huó)
Latin Name: Radix Et Rhizoma Notopterygii
Taste & Temperature:
* Xin-Spicy
* Ku-Bitter
* Wen-Warm
* Xiang-Aromatic
Channels:
* Foot Tai Yang of Urinary Bladder
* Foot Shao Yin of Kidney
Actions & Indications:
* disperse Wind-Cold (Warm & Spicy)
* Expel Wind-Cold-Damp
* stop headache
* Tai Yang headache (occipital)
* Expel Wind-Cold-Damp, especially for upper part of body pain
* guide Qi to Tai Yang & Du channels
Contraindications:
* Qi & Yin deficiency causing excessive sweating
* Blood, Yin and exterior deficiency
* overdose may cause nausea and vomiting
Caution:
* Yin deficiency syndrome
* Blood deficiency
* chronic skin infection
Dosage:
Similar Actions to:
* Gao Ben - Tai Yang headache
* Bai Zhi - Yang Ming headache, toothache, nasal congestion
back to:
* TCM Materia Medica
* Xin Wen Jie Biao

## Notes

* ↑ YEPING SUN, QIANG XU. "AQUEOUS EXTRACT FROM RHIZOMA NOTOPTERYGII REDUCES CONTACT SENSITIVITY BY INHIBITING LYMPHOCYTE MIGRATION VIA DOWN-REGULATING METALLOPROTEINASE ACTIVITY", Pharmacological Research, Volume 46, Issue 4, October 2002, Pages 333-337
# Traditional Chinese Medicine/Qiang Huo Sheng Shi Tang

The formula Qiang Huo Sheng Shi Tang, designed to expel wind and dampness, which may manifest as pain in the shoulders and back causing an inability to look back, consists of the following:
| No. | Pinyin | Simplified Chinese | Grams |
| 1 | Qiang Huo | 羌活 | 6 |
| 2 | Du Huo | 独活 | 6 |
| 3 | Fang Feng | 防风 | 3 |
| 4 | Gao Ben | 藁本 | 3 |
| 5 | Man Jing Zi | 蔓荆子 | 3 |
| 6 | Chuan Xiong | 川芎 | 3 |
| 7 | Zhi Gan Cao | 炙甘草 | 3 |
Source: Liu Gongwang, "Development of Formulas of Chinese Medicine", ISBN: 7-5080-2797-3. Huaxia Publishing House. 2002.
back to :
* Formula Design
* Prescriptions
* Usage Of Prescriptions
# UMD Analysis Qualifying Exam/Jan11 Real
## Problem 1

* Let $f\in AC[0,1]$ be an absolutely continuous function on [0,1] with $f>0$. Prove that $1/f\in AC[0,1]$.

### Solution

Since $f$ is (absolutely) continuous on [0,1] with $f>0$ then there exists some $0<m=\min _{x\in [0,1]}f(x)$.
Since $f\in AC[0,1]$ then for any $\epsilon >0$ there exists some $\delta >0$ such that for any finite collection of disjoint intervals $I_{k}=(x_{k},y_{k}),k=1,...,n$ such that if $\sum _{k=1}^{n}|y_{k}-x_{k}|<\delta$ then $\sum _{k=1}^{n}|f(y_{k})-f(x_{k})|<\epsilon m^{2}$.
Then for any such collection of intervals described above, we have $\sum _{k=1}^{n}|{\frac {1}{f(y_{k})}}-{\frac {1}{f(x_{k})}}=\sum _{k=1}^{n}|{\frac {f(x_{k})-f(y_{k})}{f(y_{k})f(x_{k})}}|\leq \sum _{k=1}^{n}{\frac {1}{m^{2}}}|f(y_{k})-f(x_{k})|<\epsilon$.