text:
### Writing a thesis with LaTeX

##### [ Monday, 21 January 2008, TLu ]

A dissertation is composed of two elements: the content and the form. The author is certainly the person best qualified to speak about the content. We, however, will focus on the form. We are going to see how to get a fine composition with low time expenditure using LaTeX.

Author: Tomasz Łuczak

### Is writing in LaTeX really worth it?

Certain universities, faculties or departments ventured to formalize the typesetting requirements of a thesis. Writing a dissertation in LaTeX enables us to adjust the graphical composition to the requirements irrespective of the content. The separation of form and content notably facilitates the task of working on the matter of the thesis. The graphical composition can be defined immediately with a shipped class (there are premade dissertation classes available) or chosen at the end.

The table of contents, figures or literature will all be created by the computer. The automatic numbering of annotations and quotations or sorting the references is also a task for the program. All that is left for us is to write the content since we will satisfy the remaining requirements at the end.

### Structure

Every dissertation has a similar layout:

Title page
Acknowledgments and dedications
Statement of authorship
Table of contents
Introduction with the following chapters
Table of figures
Table of charts
Bibliography

The first few pages are usually precisely defined and that is where we shall need to adjust the composition to the requirements.

As we have mentioned before, we do not have to bother with creating the indexes. We just need to choose or define our own style sheet to be used to generate the bibliography.

LaTeX provides us with some ready-made commands to divide the text into logical structures like chapters, sections, paragraphs, enumerations or footnotes. Taking advantage of these commands enables us to change the form of each structure globally, in the entire document.

### Let’s start writing

Our advisors usually expect us to present the progress of our work in the subsequent chapters. Let’s begin with the content.

For our convenience it is advisable to divide the text into several separate files: the title page and preliminary pages, the introduction, chapters and conclusion. Consequently, we will be working on a smaller part of the text at a time. If our chapters are voluminous we may want to divide them into subchapters as well.

The resulting main document includes the above files via the \include{file} command. A change in any of the separate files will be reflected in the main document every time it is compiled.

If, however, our text is not especially long or if we do not find working on a large file particularly troublesome we may decide to keep it as a single file.

### The main document

The thesis will presumably contain several chapters and therefore the most suitable class for our case will be ‘book’. The title page and preliminary pages will be left for the dessert in the title.tex file.

For a start all we need is a table of contents, which can be inserted with the \tableofcontents command.

If we use charts in the text and a list of tables is required then we can insert it with the \listoftables command.

The main document will have the following structure:

% set sans-serif headings, paper format,
% font size and the main class
\\documentclass{sfheadings,a4paper,11pt}{book}
% set encoding
\\usepackage{latin1}{inputenc}
\\begin{document} % Let's go!
\\include{title}
\\tableofcontents
% \\lisoftables
\\include{introduction}
\\include{chapter1}
\\include{chapter2}
\\include{conclusion}

### Introduction and the following chapters

Introduction is the part that is being read the most often, so obviously it should be well written. As for the typesetting, it is one of the easiest sections, since it usually contains just plain text without charts or figures.

Sections and chapters can be numbered or not numbered. The default is numbered, so if we want to exclude a section from the numbering we need to add an asterisk to the command.

For example, the introduction is an un-numbered chapter comprised of one or more paragraphs. We can insert it with the \chapter*{Introduction} command.

The chapters of our thesis, on the other hand, should be numbered, so we should begin our chapter’s file with, for example, the \chapter{Mathematical Model}command

The text in chapters can be divided into sections and subsections with the \section, \subsection and \subsubsection commands respectively, for example: \section{Process Identification}.

### Spacing

Monosyllable conjunctions at the end of a line are generally not desired and should be gotten rid of. LaTeX does not move them to the next line automatically so we need to instruct it by inserting non-braking spaces between the conjunction and the following word. A non-braking space is simply a tilde “~”, for example “so~it”.

Double spaces are not particularly appealing, either. In this case, however, TeX knows what to do and no matter how many spaces we type it will render just one. A mark ending a line is also considered to be a space.

The feature of adding a comment is also remarkable. A line beginning with “%” is treated as a comment and is not being processed. Therefore

We can write	as we like
no matter what TeX will
compile the text %look! a comment!
the right way
with~one character   spacing between the words.

An empty line — that is, two newline characters — marks an ending of a paragraph and a beginning of a new one.

### Enumerations

LaTeX supports three kinds of enumerations: numbered, not numbered and description. The first two are the ‘enumerate’ and ‘itemize’ environments which we know already. The last one is a variant of the not numbered enumeration. In this case, a description is used instead of a symbol. Each enumeration begins with the item command.

Numbered enumeration:
\\begin{enumerate}
\\item One
\\item Two
\\item Three
\\end{enumerate}

Not numbered enumeration:
\\begin{itemize}
\\item One
\\item Two
\\item Three
\\end{itemize}

Description enumeration:
\\begin{description}
\\item[Iron] -- an element
\\item[Steel] -- an alloy
\\item[Caffe latte] -- a mixture
\\end{description}

### Horizontal lines.

The keyboard allows us to enter only two types of dashes directly — a hyphen and an underscore. LaTeX, however, delivers the following horizontal lines:

hyphen: "-" to join words, i.e daughter-in-law
en-dash: "--" to join digits, i.e 1937--2007
em-dash: "---" to denote a pause, i.e yes --- or no?
underscore to join file names: "_"

In practice, we use just the hyphen and en-dash; mathematical expressions are a good material for a separate article.

### Fonts and sizes

To write in bold font we need to use the \textbf{text-in-bold} command; to write in sans-serif font there is the \textsf{sans-serif-text} command; italics can be enabled with the \textit{text-in-italics} command, and finally \textsl{caps} renders the text in small caps.

A word of advice: underlining text should be avoided because it makes the text more difficult to read by crossing the parts of glyphs descending below the baseline. The custom of underlining text dates back to the times of typewriters which had just one typeface. Likewise, the text should not be highlighted with bald font since a black element in a grey rectangle of text draws readers’ attention and disturbs the rhythm of reading.

### References in the text

Frequently in a thesis we refer to some other part of it, for example a chart or a figure. In order to refer to any place, we need to label it. In labels’ names, spaces and diacritical marks should not be used. Preferably, a label should contain only Latin letters, digits and dashes. A label can be inserted with the \label{fig_1} command.

A label inherits the information from the environment that precedes it. Placing a label just behind the name of a section or chapter will show its number in the reference. Analogically, placing it behind a caption of a figure will show the figure’s number in the reference. A reference to a label can be inserted with the \ref{fig_1} command.

TeX processes our file sequentially, so in order to get the references rendered properly we need to compile the document twice. During the first processing TeX will generate the numbers of all the chapters and captions; in the second one it will place correct references where necessary. Rendering a table of contents also requires double compilation.

### Footnotes

Frequently we need to place a footnote under the main flow of text or at the end of the document. In that case, we need to place a footnote with \footnote{footnote-content} command.

### Summary

The number of “spells” needed to write a thesis, excluding figures, charts, bibliography and mathematical expressions, is just a few commands. It is not much work, considering that a text created with LaTeX can be given directly to our advisor and the time expenditure to create a visually appealing composition is minimal.

In the next article we will finish writing the dissertation and we will describe how to insert tables, figures, a bibliography and how to prepare the preliminary pages of our work.

You can download an example dummy thesis from our server: Thesis in LaTeX [examples, tar.gz]. It is properly divided into small tex files for better granularity.

This text is based on the article published in Dragonia Magazine, a Polish online magazine about Free and Open-Source Software. You can download the latest Dragonia issue (first one in English from our mirror). The article has been slightly modified compared with the original version by the PolishLinux team.

Translated by Jan Misiak, Proof-read by Jake Conroy

## About the Author

#### Tomasz Łuczak

TeaM-TL developer, Dragonia Magazine's editor, TeX and Tcl/Tk enthusiast. Lives in Katowice, Poland.

## RSS: Comments

You can follow the comments to this article through a special channel RSS 2.0 .

more »


text:
Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English version of the page.

# drift

Drift-rate model component

## Description

The `drift` object specifies the drift-rate component of continuous-time stochastic differential equations (SDEs).

The drift-rate specification supports the simulation of sample paths of `NVARS` state variables driven by `NBROWNS` Brownian motion sources of risk over `NPERIODS` consecutive observation periods, approximating continuous-time stochastic processes.

The drift-rate specification can be any `NVARS`-by-`1` vector-valued function F of the general form:

`$F\left(t,{X}_{t}\right)=A\left(t\right)+B\left(t\right){X}_{t}$`

where:

• `A` is an `NVARS`-by-`1` vector-valued function accessible using the (t, Xt) interface.

• `B` is an `NVARS`-by-`NVARS` matrix-valued function accessible using the (t, Xt) interface.

And a drift-rate specification is associated with a vector-valued SDE of the form

`$d{X}_{t}=F\left(t,{X}_{t}\right)dt+G\left(t,{X}_{t}\right)d{W}_{t}$`

where:

• Xt is an `NVARS`-by-`1` state vector of process variables.

• dWt is an `NBROWNS`-by-`1` Brownian motion vector.

• A and B are model parameters.

The drift-rate specification is flexible, and provides direct parametric support for static/linear drift models. It is also extensible, and provides indirect support for dynamic/nonlinear models via an interface. This enables you to specify virtually any drift-rate specification.

## Creation

### Syntax

``DriftRate = drift(A,B)``

### Description

example

````DriftRate = drift(A,B)` creates a default `DriftRate` model component.Specify required input parameters `A` and `B` as one of the following types: A MATLAB® array. Specifying an array indicates a static (non-time-varying) parametric specification. This array fully captures all implementation details, which are clearly associated with a parametric form.A MATLAB function. Specifying a function provides indirect support for virtually any static, dynamic, linear, or nonlinear model. This parameter is supported via an interface, because all implementation details are hidden and fully encapsulated by the function. NoteYou can specify combinations of array and function input parameters as needed. Moreover, a parameter is identified as a deterministic function of time if the function accepts a scalar time `t` as its only input argument. Otherwise, a parameter is assumed to be a function of time t and state X(t) and is invoked with both input arguments. The `drift` object that you create encapsulates the composite drift-rate specification and returns the following displayed parameters: `Rate` — The drift-rate function, F. `Rate` is the drift-rate calculation engine. It accepts the current time t and an `NVARS`-by-`1` state vector Xt as inputs, and returns an `NVARS`-by-`1` drift-rate vector.`A` — Access function for the input argument `A`.`B` — Access function for the input argument `B`. ```

### Input Arguments

expand all

`A` represents the parameter A, specified as an array or deterministic function of time.

If you specify `A` as an array, it must be an `NVARS`-by-`1` column vector of intercepts.

As a deterministic function of time, when `A` is called with a real-valued scalar time `t` as its only input, `A` must produce an `NVARS`-by-`1` column vector. If you specify `A` as a function of time and state, it must generate an `NVARS`-by-`1` column vector of intercepts when invoked with two inputs:

• A real-valued scalar observation time t.

• An `NVARS`-by-`1` state vector Xt.

Data Types: `double` | `function_handle`

`B` represents the parameter B, specified as an array or deterministic function of time.

If you specify `B` as an array, it must be an `NVARS`-by-`NVARS` two-dimensional matrix of state vector coefficients.

As a deterministic function of time, when `B` is called with a real-valued scalar time `t` as its only input, `B` must produce an `NVARS`-by-`NVARS` matrix. If you specify `B` as a function of time and state, it must generate an `NVARS`-by-`NVARS` matrix of state vector coefficients when invoked with two inputs:

• A real-valued scalar observation time t.

• An `NVARS`-by-`1` state vector Xt.

Data Types: `double` | `function_handle`

## Properties

expand all

Composite drift-rate function, specified as F(t,Xt). The function stored in `Rate` fully encapsulates the combined effect of `A` and `B`, where `A` and `B` are:

• `A`: The intercept term, A(t,Xt), of F(t,Xt)

• `B`: The first order term, B(t,Xt), of F(t,Xt)

Data Types: `struct` | `double`

## Examples

collapse all

Create a drift-rate function `F`:

`F = drift(0, 0.1) % Drift rate function F(t,X)`
```F = Class DRIFT: Drift Rate Specification ------------------------------------- Rate: drift rate function F(t,X(t)) A: 0 B: 0.1 ```

The `drift` object displays like a MATLAB® structure and contains supplemental information, namely, the object's class and a brief description. However, in contrast to the SDE representation, a summary of the dimensionality of the model does not appear, because the `drift` class creates a model component rather than a model. `F` does not contain enough information to characterize the dimensionality of a problem.

expand all

## Algorithms

When you specify the input arguments `A` and `B` as MATLAB arrays, they are associated with a linear drift parametric form. By contrast, when you specify either `A` or `B` as a function, you can customize virtually any drift-rate specification.

Accessing the output drift-rate parameters `A` and `B` with no inputs simply returns the original input specification. Thus, when you invoke drift-rate parameters with no inputs, they behave like simple properties and allow you to test the data type (double vs. function, or equivalently, static vs. dynamic) of the original input specification. This is useful for validating and designing methods.

When you invoke drift-rate parameters with inputs, they behave like functions, giving the impression of dynamic behavior. The parameters `A` and `B` accept the observation time t and a state vector Xt, and return an array of appropriate dimension. Specifically, parameters `A` and `B` evaluate the corresponding drift-rate component. Even if you originally specified an input as an array, `drift` treats it as a static function of time and state, by that means guaranteeing that all parameters are accessible by the same interface.

## References

[1] Ait-Sahalia, Y. “Testing Continuous-Time Models of the Spot Interest Rate.” The Review of Financial Studies, Spring 1996, Vol. 9, No. 2, pp. 385–426.

[2] Ait-Sahalia, Y. “Transition Densities for Interest Rate and Other Nonlinear Diffusions.” The Journal of Finance, Vol. 54, No. 4, August 1999.

[3] Glasserman, P. Monte Carlo Methods in Financial Engineering. New York, Springer-Verlag, 2004.

[4] Hull, J. C. Options, Futures, and Other Derivatives, 5th ed. Englewood Cliffs, NJ: Prentice Hall, 2002.

[5] Johnson, N. L., S. Kotz, and N. Balakrishnan. Continuous Univariate Distributions. Vol. 2, 2nd ed. New York, John Wiley & Sons, 1995.

[6] Shreve, S. E. Stochastic Calculus for Finance II: Continuous-Time Models. New York: Springer-Verlag, 2004.

format: plain


text:
## Homework 2 forum

Hey everyone,

I have a strange bug since the begining of my tests, that I wanted to carry alone but it stays unresolved and I really don't understand what it means.

While the test for IndexShares passes, TestGossiper-Download-Parallel-Multiple has an issue for the file of peer B. The Chunk 0 is requested by A, B sends it to A without any issue (B Marshal the packet and send it via its UDP Port, like any other packet sent in the project). But when the packet arrives at A, I can't unmarshal it. It says :
unexpected end of JSON input
Did anyone experienced this error, and have a hint of how it can be resolved ? I know we should not ask for debugging here but since I can transfer large files locally, and as the test for IndexShare passes, I wonder if it is not a specificity of the test case that anyone can explain.

Thanks a lot !

Hi,

My guess is that the buffer that you initialize for reading from a UDP socket is too small (i.e., something like buf = make([]byte, X)). X has to be bigger than the default chunk size + other headers. Otherwise, your gossiper reads only a part of a data reply gossip packet and hence it ends up with an incorrect json encoding (since the end is missing).

Does it help?

Kirill


text:
# Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

## Uniform decompositions of polytopes

### Tom 33 / 2006

Applicationes Mathematicae 33 (2006), 243-252 MSC: 65D18, 60-08. DOI: 10.4064/am33-2-7

#### Streszczenie

We design a method of decomposing convex polytopes into simpler polytopes. This decomposition yields a way of calculating exactly the volume of the polytope, or, more generally, multiple integrals over the polytope, which is equivalent to the way suggested in Schechter, based on Fourier–Motzkin elimination (Schrijver). Our method is applicable for finding uniform decompositions of certain natural families of polytopes. Moreover, this allows us to find algorithmically an analytic expression for the distribution function of a random variable of the form $\sum_{i=1}^{d}c_{i}X_{i}$, where $(X_{1},\ldots ,X_{d})$ is a random vector, uniformly distributed in a polytope.

#### Autorzy

• Daniel BerendDepartments of Mathematics and Computer Science
Ben-Gurion University of the Negev
Beer-Sheva 84105, Israel
e-mail
• Luba BrombergDepartment of Mathematics
Ben-Gurion University of the Negev
Beer-Sheva 84105, Israel

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek


text:
# making of a language

## Recommended Posts

dkx187    100
I am currently making a language with xml but sometimes I wan't to make commands in other languages.Is there any way I could do this?If you know a web page I could visit then please link. Thank you

##### Share on other sites
rip-off    10979
Why XML? It is terribly verbose for such a task.

If by "make commands in other languages" you mean use types or functions defined by other languages, then it is possible. How is pretty much up to you, after all you are writing the language.

##### Share on other sites
ToohrVyk    1596
You can do this pretty easily. For instance, I could do like XSLT does and use:
<xsl:value-of select="php:frobnicate(@content)"/>
This calls the "frobnicate" PHP function.

Of course, the hard part is getting your compiler or interpreter to actually handle this. For instance, when running XSLT from PHP, you can register PHP functions to be run from XSLT. In the general case, you can use any technique available to the interpreter (or compiler target) for calling external functions.

But there are so many possible interpreters or compiler targets that I'm not going to give you a complete list of how to do it, nor will you find a complete list online. However, if you told us your interpreter technology or compiler target technology, we would be able to help.


text:
J. Meteor. Res.  2018, Vol. 32 Issue (1): 60-68 PDF
http://dx.doi.org/10.1007/s13351-018-7068-z
The Chinese Meteorological Society
0

#### Article Information

LYU, Lihui, Yunsheng DONG, Tianshu ZHANG, et al., 2018.
Vertical Distribution Characteristics of PM2.5 Observed by a Mobile Vehicle Lidar in Tianjin, China in 2016 . 2018.
J. Meteor. Res., 32(1): 60-68
http://dx.doi.org/10.1007/s13351-018-7068-z

### Article History

in final form September 8, 2017
Vertical Distribution Characteristics of PM2.5 Observed by a Mobile Vehicle Lidar in Tianjin, China in 2016
Lihui LYU1,2, Yunsheng DONG1, Tianshu ZHANG1, Cheng LIU1,2, Wenqing LIU1,2, Zhouqing XIE1,2, Yan XIANG1,2, Yi ZHANG1,4, Zhenyi CHEN1, Guangqiang FAN1, Leibo ZHANG3, Yang LIU1,2, Yuchen SHI1,2, Xiaowen SHU5
1. Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031;
2. University of Science and Technology of China, Hefei 230026;
3. Tianjin Academy of Environmental Sciences, Tianjin 300191;
4. Chinese Academy of Sciences Wuxi Photonics Co.,Ltd., Wuxi 214135;
5. The Air Force Military Representative's Office in Beijing, Beijing 100086
ABSTRACT: We present mobile vehicle lidar observations in Tianjin, China during the spring, summer, and winter of 2016. Mobile observations were carried out along the city border road of Tianjin to obtain the vertical distribution characteristics of PM2.5. Hygroscopic growth was not considered since relative humidity was less than 60% during the observation experiments. PM2.5 profile was obtained with the linear regression equation between the particle extinction coefficient and PM2.5 mass concentration. In spring, the vertical distribution of PM2.5 exhibited a hierarchical structure. In addition to a layer of particles that gathered near the ground, a portion of particles floated at 0.6–2.5-km height. In summer and winter, the fine particles basically gathered below 1 km near the ground. In spring and summer, the concentration of fine particles in the south was higher than that in the north because of the influence of south wind. In winter, the distribution of fine particles was opposite to that measured during spring and summer. High concentrations of PM2.5 were observed in the rural areas of North Tianjin with a maximum of 350 μg m–3 on 13 December 2016. It is shown that industrial and ship emissions in spring and summer and coal combustion in winter were the major sources of fine particles that polluted Tianjin. The results provide insights into the mechanisms of haze formation and the effects of meteorological conditions during haze–fog pollution episodes in the Tianjin area.
Key words: mobile vehicle lidar     vertical concentration profile     fine particle
1 Introduction

China has been suffering from severe haze pollution in recent years, especially in megacity clusters such as the Beijing–Tianjin–Hebei area [called Jing–Jin–Ji (JJJ) in Chinese], Yangtze River Delta (YRD), and Pearl River Delta (PRD) (Parrish and Zhu, 2009), because of the ra-pid economic growth and urbanization. Fine particles (PM2.5), which are the main contributor of haze pollution, have attracted worldwide attention. Fine particles in the boundary layer exert significant direct and indirect effects on human lives and activities. Therefore, determining the distribution characteristics of fine particles is essential. Extensive studies were conducted to detect the concentration of fine particles near the ground using particulate matter samplers (Pu et al., 2015; Zhang et al., 2017). However, particulate matter samplers do not effectively measure the vertical distribution of particles in the boundary layer. Only a few researchers obtained the vertical profile of fine particles. Yang et al. (2005) obtained the PM2.5 profiles in Beijing by putting some PM2.5 monitors on different altitudes of a 325 m–high meteorological tower. Tao et al. (2016) profiled the vertical distribution of the PM2.5 mass concentration in the boundary layer with a charge-coupled device (CCD) side-scattering lidar. The feasibility of the observation of fine particle profile based on lidar was suggested. However, most haze pollution occurs on a regional scale, and point measurements based on a lidar site or a lidar network cannot be adequate representatives. To conduct regional observations on this phenomenon, a vehicle-based mobile lidar system was developed and applied in atmospheric monitoring (Lyu et al., 2016). The mobile lidar can obtain the vertical distribution of fine particles quickly on a regional scale.

Most previous studies focused on the haze pollution in Beijing, China (Che et al., 2015a; Jing et al., 2015; Wu et al., 2016; Ma et al., 2017), while some concerned about the haze pollution in the JJJ area (Che et al., 2014, 2015b; Sun et al., 2014; Wu et al., 2017). Considerable results have shown that urban or industrial aerosols and regionally transported pollutants from the southwest pathway under some particular meteorological conditions were significant factors in haze formation in Beijing (Chen et al., 2015; Zhang et al., 2017). However, relevant observations in Tianjin are rare, and the mechanisms of haze formation and the effect of meteorological conditions are not well understood there. Thus, observations in Tianjin are strongly needed to access the distribution characteristics of fine particles, the formation mechanism of haze, and the effect of meteorological conditions. In this paper, fine particles profile were observed by using a vehicle-based mobile lidar system during different seasons in Tianjin in 2016. In that same period, the SO2, NO2, and PM2.5 data were obtained by local monitoring stations. Furthermore, an in-depth study [composite analysis with Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) model] was also performed to discuss the source and characteristic of fine particles in Tianjin.

2 Methodology 2.1 Experiment

Mobile lidar measurements were conducted in Tianjin in 2016 to obtain the distribution characteristics of fine particles under different seasons. Tianjin, one of the metropolises in North China, is located east of the Bohai Sea and north of the Yanshan Mountain. It has an approximate population of 15 million and an area of around 12,000 km2. The city is characterized by high population density, heavy traffic, and enhanced industrial activities. Thus, it has a variety of fine particle sources, e.g., marine particles from the Bohai Sea, anthropogenic particles (transportation emissions, industrial emissions, and coal burning emissions) from highly populated urban centers, industrial areas, and rural areas, etc. In addition, regional transportation is also an important source of pollution particles in Tianjin. In this paper, observations in different seasons, spring, summer, and winter, are presented and discussed. Figure 1 shows the mobile lidar measurement path in Tianjin during the experiment.

 Figure 1 Mobile lidar measurement path (black line) in Tianjin.
2.2 Lidar system

The vehicle-based mobile lidar system was developed at the Anhui Institute of Optics and Fine Mechanics. The sub-units of the mobile lidar system include a laser emitting unit, a receiving unit, a signal acquisition unit, and a global positioning system (GPS). The laser source is a pulsed Nd:YAG laser that emits short pulses at 532 and 355 nm in 20 Hz. The receiving telescope of the lidar system is based on a Cassegrain design. The range resolution of the lidar is 7.5 m. The full overlap height of the lidar is about 100 m. Detailed specifications of the mobile lidar were provided in a previous study (Lyu et al., 2016). The mobile lidar can detect atmospheric aerosols and indicate the stereoscopic distribution properties of aerosols.

The formulas for aerosol extinction coefficient (Fernald, 1984) and depolarization ratio are:

 (1)
 (2)

where αa and αm are the particle extinction and molecular extinction coefficients, respectively. The particle extinction-to-backscatter ratio Sa = 50 Sr, the corresponding ratio for the molecular Sm = 8π/3, and P(z) is the received power at height z in Formula (1). δ is the linear depolarization ratio, k is a calibration factor, and P and $P_{//}$ are cross-polarized and co-polarized signals, respectively, in Formula (2). The vertical profiles of extinction coefficient are retrieved by using Formula (1). The profiles of fine particles can also be derived from particle extinction coefficient with the following formula:

 (3)

where $M P M 2.5$ is the PM2.5 mass concentration, α is the particle extinction coefficient, and ξ is a specific coefficient independent of altitude, which can be considered a constant when aerosol hydrophilic growth is negligible (Tao et al., 2016). Considering the unstable factors in the measurement, constant c is included in the formula, as shown in Formula (4). Parameters ξ and c can be obtained by use of linear regression analysis (Han et al., 2006).

 (4)
2.3 Back trajectory model

The paths of air masses were determined by the National Oceanic and Atmospheric Administration Hybrid Signal Particle Lagrangian Integrated Trajectory model (http://ready.arl.noaa.gov/HYSPLIT_traj.php). In the following analysis, we set 500 m as the starting height to obtain information on particle sources and types. The backward trajectories of air masses at Tianjin were calculated to study the effect of meteorological conditions and regional transport.

3 Results and discussion

During the experiment, the atmosphere environment monitoring vehicle, which is equipped with mobile lidar, moved clockwise along the border road of Tianjin under different seasons. The main route of the monitoring vehicle passed over seven districts of Tianjin, from as far north as Jizhou District to as far south as Binhai District. The route had a length of approximately 400 km, which took approximately eight hours to finish. In the following analysis, four examples are presented to show the comparative results in different seasons. In the following experimental cases, the relative humidity was less than 60%. Therefore, hygroscopic growth was negligible (Chen et al., 2014).

On 26 April 2016, a clear day in spring, the vehicle-based mobile lidar system operated from 0700 to 1600 local time (LT). Figure 2 shows the time series of particle extinction coefficient observed by lidar for this case. The particle was accumulated almost below 2.5 km from the ground. The vertical distribution of fine particles exhibited a hierarchical structure with a particle layer concentrated near the ground and a thick particle layer suspended at the height of 0.6–2.5 km. A relatively clean layer existed between the two pollution layers. Figure 3 presents a particle extinction profile at 0806 LT and the corresponding depolarization ratio profile. Figure 3 shows that the major difference between the two layers was the depolarization ratio. The depolarization ratio of the floating layer was significantly higher than that of the surface layer below 0.5 km. The result indicated that the particles of the two layers may come from different sources.

 Figure 2 Time series of particle extinction coefficient profiles on 26 April 2016.
 Figure 3 Profiles of (a) particle extinction coefficient and (b) depolarization ratio at 0806 local time (LT) 26 April 2016.

The combination of in-situ PM2.5 sampler data and particle extinction coefficient retrieved by lidar was found to be a valid method to obtain PM2.5 profile with lidar. In Fig. 4, the in-situ measured PM2.5 data were compared with the particle extinction coefficient near the ground. The correlation coefficient between the particle extinction and PM2.5 data was roughly 0.85. A linear regression equation was established to convert lidar data to PM2.5 data.

 Figure 4 Linear fitting of the extinction coefficient and mass concentration of PM2.5.
3.1 Case I: Spring

Using the real-time latitude and longitude data obtained by GPS, we overlaid the profiles of PM2.5 mass concentration on Google Earth map, as shown in Fig. 5a. The maximum value of PM2.5 appeared near the port in the southeast of Tianjin. The fine particles mainly concentrated at heights lower than 0.5 km at the southeast of the route. The PM2.5 mass concentrations ranged from 10 to 200 μg m–3. The air mass at 500 m was mainly from the southeast in spring, as indicated in Fig. 5b. The air mass came from the southeast, passed through the port, and arrived at Tianjin. The air mass was likely to bring pollutants from the port (emissions from ships), particularly from high-sulfur fuel. Yao and Wang (2016) determined that the Bohai gulf area was one of the main potential source areas of SO2 during spring based on potential source contribution function analysis. Liu et al. (2017) demonstrated that ship emissions substantially contributed to the air pollution in Shanghai. The port city in North China is busy, and ship emissions are deciding factors that cannot be neglected in Tianjin. Therefore, the southeast part near the port had a high concentration of PM2.5 during the observational experiment.

 Figure 5 (a) Spatial distribution of PM2.5 mass concentration along the experiment path measured by the mobile lidar and (b) backward trajectories at 500-m height determined by the HYSPLIT model on 26 April 2016.
3.2 Case II: Summer

To obtain the distribution characteristics, potential sources, and meteorological conditions effects of fine particles in other seasons, more observations based on the mobile lidar were conducted on the same route. Figures 68 show the typical examples in the summer (3 July 2016) and winter (13–14 December 2016) to indicate the spatial distributions of PM2.5 mass concentration and corresponding backward trajectories, respectively.

On 3 July, the distribution of fine particles was the same as that in spring. Figure 6a shows that the fine particles mainly concentrated at the heights lower than 0.5 km in southeast of the measurement path. The north area had lower PM2.5 data (with a mean of 35 μg m–3), and the southeast sections had a relatively high value with an average of 104 μg m–3 near the ground. Figure 6b presents the density distributions of SO2, NO2, and PM2.5 obtained by monitoring sites along the measurement path of the mobile lidar. The sampling data obtained by the monitoring sites indicate that the concentration of PM2.5 in the south was higher than that in the north. The distributing characteristics of PM2.5 (data obtained by mobile lidar and sampling data obtained by monitoring sites) were consistent. On 3 July, the air mass was mainly from the south instead of the southeast, as shown in Fig. 6c. Thus, the ship emission effect was not apparent under the southeast wind field. Hence, in addition to ship emission effects from the southeast, pollution sources existed in the south of the high-value region.

 Figure 6 (a) Spatial distribution of PM2.5 mass concentration along the experiment path measured by the mobile lidar, (b) distributions of SO2, NO2, and PM2.5 obtained by monitoring sites along the path of the mobile lidar, and (c) backward trajectories at 500-m height determined by the HYSPLIT model on 3 July 2016.
3.3 Case III: Winter

As shown in the previous examples, when the wind mainly came from the southeast or south in spring and summer, higher concentrations of PM2.5 were detected in the south. In the following two typical examples in winter, as shown in Figs. 7, 8, the air mass was mainly from the north and higher concentrations of PM2.5 always appeared in the north of Tianjin. On 13 December 2016, the wind blew from the northwest with wind speed of 2 m s–1 near the ground. The maximum value of PM2.5 obtained by lidar was 350 μg m–3, indicating heavy pollution in the north of Tianjin. The fine particles mainly concentrated at the heights lower than 1 km in the northern part of the route. Figure 7b presents the distributions of SO2, NO2, and PM2.5 obtained at the monitoring sites along the measurement path of the mobile lidar. As mentioned above, the concentrations of PM2.5 during summer were higher in the south than that in the north. By contrast, the concentrations of PM2.5 during winter in the north were higher than that in the south. Figure 7b also shows that both SO2 and NO2 were higher than that in summer, particularly in the north of Tianjin. The phenomenon was always attributed to coal combustion in winter. In addition, a strong positive correlation existed between the gaseous pollutants (SO2 and NO2) and PM2.5 in winter. Thus, the heavy haze in the north of Tianjin was caused by coal combustion. The results of the observations in winter showed that coal combustion was the chief source in the north of Tianjin.

 Figure 7 (a) Spatial distribution of PM2.5 mass concentration along the path measured by the mobile lidar, (b) distributions of SO2, NO2, and PM2.5 obtained by monitoring sites along the measurement path of the mobile lidar, and (c) backward trajectories at 500-m height determined by the HYSPLIT model on 13 December 2016.
 Figure 8 (a) Spatial distribution of PM2.5 mass concentration along the path measured by the mobile lidar and (b) backward trajectories at 500-m height determined by the HYSPLIT model on 14 December 2016.
4 Conclusion

Observations of pollutants based on a mobile lidar were carried out in spring, summer, and winter seasons to study the distribution characteristics of PM2.5 in Tianjin. According to the measurement results, the fine particles mainly concentrated near the ground. The distribution characteristics of PM2.5 obtained by the mobile lidar and from the monitoring sites were consistent. The combined results obtained by mobile lidar, sampling data obtained by monitoring sites, and air mass trajectories in the observation period, indicated that the distribution of PM2.5 and wind direction were connected. The concentration of fine particles in the south was higher than that in the north because of the influence of the south (south and southeast) wind in spring and summer, suggesting the existence of emission sources in the south and southeast of Tianjin. The fine particles were probably from the local sources (such as industrial emissions and ship emissions) in the upwind region. In winter, the concentration of fine particles in the north was higher than that in the south because of the prevailing north wind. High concentrations of PM2.5 were observed in the rural areas of North Tianjin. The high concentrations of PM2.5 in the north were mainly from coal combustion during the heating season in Tianjin, suggesting the substantial contribution of coal combustion in North China.

Acknowledgments

The authors gratefully acknowledge the NOAA Air Resources Laboratory for providing the HYSPLIT mo-del and the Google Earth for providing the map used in this study. We also thank Chinese Academy of Sciences Wuxi Photonics Co.,Ltd. for providing part of the lidar data measured in April 2016 and their help during the experiment.

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# Failure load of hollow tube under transverse compression

How would one analytically calculate the maximum force a tube under transverse compression can withstand? I am specifically looking for a general equation to model the yield strength of a hollow tube being compressed on its sides between two platforms, given any values for its geometric and material properties (e.g. inner/outer diameter, length, yield stress, modulus of elasticity, etc.). I am particularly uncertain about where plastic deformation and/or fracturing would first occur, either at the points of contact with the plates or along the plane midway between the plates. I cannot calculate this using FEA as I need to include an analytical equation in an optimization code I'm writing. Any insight into how to analytically calculate this would be much appreciated.

For thin ring ($$R/d \ge 8$$):

For a thick ring, you shall use formulas for "Arch Beam" to account for additional deformations. A good reference will be "Roark's Formulas for Stress and Strain" by Warren Young.

what I'd do is take advantage of the symmetry and investigate this as a curved beam.

One reference I can think of that has a separate section on curved beams is Robert D. Cook and Warren Young's "Advanced mechanics of materials". (ISBN-10  :  0133969614, ISBN-13  :  978-0133969610)

I would say as a quick approximation it will fail by developing plastic hinges at the mid-distance between the two plates. That is because the contact lines along plates have the support of the plates.

The cylinder will deform to an ellipse, widening at free edges until develops plastic hinges.

Imagine a typical cross-section of the cylinder at point F, if it starts to flatten in competition with the section through the free midspan which wants to bend, its strain which will be trying to compress it at the contact point will be constrained by the friction of the supports and the section through free span will deform and develop a plastic hinge mechanism. This as well as a small widening of the cylinder will affect large deformations on the free midspan lines.

This is assuming the thickness of the cylinder is much less than its radius.

$$t<


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Equation of a circle 3 points [duplicate]

How does one solve the equation of a circle through three given points?...

(81,45) (81,-45) (85,0)

What is the solution to this???

I'm at a loss

Assume the equation to be of the form $$(x-x_0)^2 + (y-y_0)^2 = r^2$$ for some unknowns $$x_0$$, $$y_0$$ and $$z_0$$.
Plug in those three points for $$(x, y)$$ and solve for the unknowns.
• I have told you the procedure, you should substitute your points for $x$ and $y$. For example, $(81-x_0)^2+(45-y_0)^2 = r^2$ and similarly others. The symmetry will give you $y_0 = 0$ easily as pointed out in the other comment. You should be able to carry out the computations. – Aryaman Maithani Jan 6 at 13:20
The general equation of a circle is $$(x-a)^2+(y-b)^2=r^2,$$ with $$(a,b)$$ being the center of the circle, and $$r$$ being the radius.
Note that the first 2 points are symmetric about the $$x-$$axis, telling you that the y coordinate of the center is zero. So you get 2 equations with 2 unknowns $$(81-a)^2+45^2=r^2$$ $$(85-a)^2+0^2=r^2$$ You can subtract one equation from the other to solve for $$a$$, and then $$r$$ should be simple from there.


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# Import an image using Matex without the path of the image inserted in the output

I am playing with MaTeX to include an image. It works but it also displays the path of the image in the output which messes things out.

Here is a MWE (on windows with 11.3)

<< MaTeX
SetOptions[MaTeX, "Preamble" -> {"\\usepackage{graphicx}"}];
MaTeX["This is a test \\includegraphics[width=.5\\textwidth]{C:/Program Files/Wolfram Research/Mathematica/11.3/Documentation/English/System/ExampleData/pearls.png} with data"]

which gives

I'd like the path of the images not to show in the text output.

Is there a way to do that?

MaTeX Version 1.7.4, Mathematica 11.3 on windows 10.

Could someone on windows 10 please try to see if they can reproduce this?

Updated

I also tried using \text{}

<<MaTeX
MaTeX["\\text{Test \\includegraphics[width=.5\\textwidth]{C:/Program Files/Wolfram Research/Mathematica/11.3/Documentation/English/System/ExampleData/pearls.png} image}","Preamble"->{"\\usepackage{graphicx}"}]

• I just tried this on macOS with MacTeX 2018 and I cannot reproduce the problem. I see only the images, not the path. I don't know why the path appears for you. i.stack.imgur.com/U8Bw2.png – Szabolcs Jan 27 '19 at 18:39
• @Szabolcs thanks for trying. It might be a Platform related then? There are no errors or warning generated also. – Nasser Jan 27 '19 at 18:49
• Can you try putting it in \text{}? Does it work then? – Szabolcs Jan 27 '19 at 19:19
• @Szabolcs I did. I tried exactly your example. It did not work. I will now post that as well. – Nasser Jan 27 '19 at 19:24
• I suggest you create a TeX-only minimal example and ask on TeX.SE. Do let me know if you found out why it happens or if you have a solution! To create a minimal example, do ClearMaTeXCache[] before the MaTeX call and add the option "TeXFileFunction" -> Print. This will show you the TeX source that MaTeX generates. As a first simplification, replace the \MaTeX{ ... } with simply $...$. Then you can remove most of the preamble (which just serves to define \MaTeX). – Szabolcs Jan 27 '19 at 19:43

"Preamble" -> {"\\usepackage{graphicx}", "\\usepackage{grffile}"}


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# Since the monitoring beam diameter is less than 3 mm, we assume t

Since the monitoring beam diameter is less than 3 mm, we assume that the I exp value is constant across the whole monitoring beam in the middle of the cuvette. This assumption may not be completely valid for the sample with membranes due to scattering effects. Because of this, scattering effects within membrane bound samples were investigated further. Table 3 Photoexcitation intensities measured at the surface of incidence and estimated at the middle of the sample

cuvette for isolated and membrane-bound RCs 4EGI-1 concentration Parameter I exp at the surface of the cuvette, mW cm−2 Estimated I exp in the middle of the cuvette with isolated RCs, mW cm−2 Estimated I exp in the middle of the cuvette with membrane-bound RCs, mW cm−2 I exp_1 18.07 9.16 0.92 SRT2104 clinical trial I exp_2 9.51 4.82 0.48 I exp_3 7.70 3.91 0.39 I exp_4 5.38 2.76 0.27 I exp_5 3.02 1.52 0.15 I exp_6 AZD8931 ic50 1.59 0.81 0.08 I exp_7 1.29 0.65 0.07 I exp_8 0.69 0.35 0.04 I exp_9 0.39 0.2 0.02 The type and amount of scattering in the membrane samples was estimated by fitting the absorption curve of a membrane sample to the sum of a scaled, previously measured isolated RC absorption spectrum and the scattering formula $$A_\textscatter = C_S \cdot \lambda^K_S$$, where C S is a constant and K S characterizes the scattering. For small particles with respect to the wavelength, K S  = −4 and is representative of Rayleigh scattering.

Values of K S above −4 and approaching zero are more characteristic of Mie scattering (Cavatorta et al. 1986; Hudson 1969). Figure 5 shows the resulting least squares fit of the membrane absorption spectrum and PI-1840 the corresponding curve for A scatter. From the analysis, the values log[C S ] = 8 ± 0.05 and K S  = −2.95 ± 0.02 were obtained. The value of K S indicates that the scattering is more

like that of Mie scattering, or Rayleigh–Debye–Gans scattering, in which case the dimension of the scattering particle was large and could not be treated as a single dipole (Cavatorta et al. 1986; Hudson 1969). The absorption at 802 nm, after subtracting the scatter curve A scatter from the membrane absorption, was used to determine the concentrations to be ~1 µM. This analysis, however, does not address possible multiple scattering effects fully, which were found to play a large role in RC photoexcitation dynamics (Goushcha et al. 2004) and are discussed further below. Fig. 5 Effects of multiple light scattering in membrane-bound RCs. Solid line is membrane absorption curve. Dotted line is the scaled isolated RC spectrum + A scatter. The dashed line below these curves is the contribution due to scattering, A scatter, in the absorption spectrum Figure 6 shows a simplified schematic of the cuvette compartment. The monitoring beam propagates along the x-axis, and CW excitation is applied along the y-axis. Since the scattering is pronounced in membrane samples, the actual CW excitation beam intensity in the middle of the cuvette (the hatched region of the cuvette in Fig.