text:
# Difference between closed under countable union and arbitrary union

From my research, I am confused in differentiating the difference between closed under arbitrary unions and countable unions.

1. What exactly is the difference between them?

In an example, it states that:

Let $X$ be an uncountable set. Also let $\tau$ = {O $\subseteq X \mid$ O = X or O is at most countable}

For this example, without much explainantion, it states that $\tau$ is closed under finite intersections and under countable unions. But it isn't a topology on X as it isn't closed under arbitrary unions.

1. How this example is not a topology?

My note on this is that since $\tau$ contains $\emptyset$ and $X$ so it has finite number of elements, hence it is countable. Taking their union will still be in $\tau$, so it is closed under countable unions. Why it is not closed under arbitrary unions? What's the difference?

• It's about how many sets you're taking the union of. A countable union has to be, well, a union of countably many sets. An arbitrary union is, well, a union of arbitrarily many sets. E.g. $\mathbb{R}$ is an arbitrary union of singletons - $\mathbb{R}=\bigcup_{r\in\mathbb{R}}\{r\}$ - but not a countably union of singletons (since $\mathbb{R}$ is uncountable). – Noah Schweber Aug 12 '18 at 16:48
• Incidentally, I don't understand what you mean when you say that $\tau$ is countable (finite, even!). It's definitely not: if $X$ is uncountable, it has uncountably many countable sets. E.g. if $X=\mathbb{R}$ then each set of the form $\{r\}$ for $r\in\mathbb{R}$ is in $\tau$, and there are uncountably many of those. – Noah Schweber Aug 12 '18 at 16:49
• Can you please differentiate between term arbitrary and countable here? Because what I am not perceiving here is that $\mathbb{R}$ can not be union of arbitrary sets since it will lose some points. Isn't it? – Wasiq Noor Aug 12 '18 at 17:25
• "Arbitrary" just means "as many as you want." E.g. $\bigcup_{r\in\mathbb{R}}\{r\}$ is an arbitrary union (every union is an arbitrary union) but not a countable union (since the number of sets involved is uncountable - it uses "$\mathbb{R}$-many" sets, and $\mathbb{R}$ is uncountable). – Noah Schweber Aug 12 '18 at 17:47
• To quote my answer: "The difference between countable unions and arbitrary unions is just how many sets we're allowed to "union together." In a countable union, we're taking the union of only countably many sets; in an arbitrary union, we're taking the union of as many sets as we want" – Noah Schweber Aug 12 '18 at 17:48

First of all, I think you have some confusion about what $\tau$ is, based on your claim that $\tau$ is countable (finite, even!). $\tau$ is definitely uncountable: any uncountable set has uncountably many countable subsets - e.g. the set of singleton subsets is uncountable.

I think you may be conflating $\tau$ - which is a set of subsets of $X$ - with individual subsets of $X$.

Now as to the different types of union, it might help to consider a concrete example. Let $X=\mathbb{R}$, and consider the set $[0,1]$. Then:

• $[0,1]$ is a union of sets in $\tau$, namely $$[0,1]=\bigcup_{x\in[0,1]}\{x\},$$ so $[0,1]$ had better be in $\tau$ if $\tau$ is to be a topology.

• But $[0,1]$ isn't all of $X$ and it also isn't countable, so it's not in $\tau$. What's going on here is that while we can write it as a union of a bunch of sets in $\tau$ (as above), we can't write it as a union of only countably many sets in $\tau$.

The difference between countable unions and arbitrary unions is just how many sets we're allowed to "union together." In a countable union, we're taking the union of only countably many sets; in an arbitrary union, we're taking the union of as many sets as we want. For example, a countably union of countable sets is countable (briefly, "$\aleph_0\times\aleph_0=\aleph_0$" if you're familiar with $\aleph$-notation), but an arbitrary union of countable sets can be as big as you want: indeed, any set is an arbitrary union of one-element sets via $$S=\bigcup_{s\in S}\{s\}.$$

As a further exercise, thinking along the lines above we can show:

If $\tau$ is a topology on a set $X$ which contains every one-element subset of $X$, then in fact $\tau$ contains every subset of $X$ (we say $\tau$ is the discrete topology in this case).

Once you're comfortable with the proof of this fact, I think you'll understand the issues above perfectly.

• I understand the example of $[0, 1]$ here. When I relate this to the example given in the question, which denies $\tau$ to be topology, I perceive that: like your example of $[0, 1]$ you can get a topology if $[0, 1]$ is in $\tau$. Since my question allow to have $X$ in the $\tau$, we can have a topology if $X$ is included? – Wasiq Noor Aug 12 '18 at 20:43
• No: just having $X$ isn't enough, you need everything that can be written as a union of arbitrarily many elements of $\tau$. In fact, you'll need every subset of $X$, since any subset of $X$ can be written as a union of countable - indeed, one-element - sets: $$A=\bigcup_{a\in A}\{a\}.$$ – Noah Schweber Aug 12 '18 at 20:45
• Yes, I intended to say that we can get a topology in the case where we have every subset of $X$ including $X$ in $\tau$. But obviously this is not always the case due to the OR in the question statement. – Wasiq Noor Aug 12 '18 at 20:49
• Exactly, that's right. Now you've got it! – Noah Schweber Aug 12 '18 at 20:54
• One more question: If this special case is considered, we are closed under arbitrary unions. Can we also say that we are closed under countable unions? – Wasiq Noor Aug 12 '18 at 20:59

Countable union means the union of countably many sets in the system (has nothing to do with the cardinality of the sets themselves). So this system is clearly closed under countable unions by the following case distinction: Case 1: If $X$ is in the family of subsets whose union is taken, then the union is $X$, which is in $\tau$. Case 2: If $X$ is not in the family of subsets whose union is taken, then you take the union of countably many countable subsets of $X$, which yields a countable subset of $X$, which is in $\tau$.

However, $\tau$ is not closed under arbitrary unions. E.g., if $X=\mathbb{R}$, then the set of positive numbers is the union of singleton sets. Singleton sets are countable, so the set of positive numbers can be written as a union of sets in $\tau$, but it is not in $\tau$. (There are uncountably many positive real numbers, and the set of positive real numbers is not $X$ itself.)

• Why do we need to consider 2 scenarios here? Why do we explicitly include $X$ here to prove our point? – Wasiq Noor Aug 12 '18 at 20:22
• The set $\tau$ is also given by a case distinction: a set is in it either because it is countable or because it is equal to the whole underlying set $X$. So it is not very surprising that when proving something about $\tau$, you need to make a case distinction along these line. Of course, there are ways to reformulate the proof, but essentially, you need to distinguish between these two cases somehow. – A. Pongrácz Aug 12 '18 at 20:26
• In case 1: we are taking uncountable union of many countable sets to get $X$. Do we still name this as colosed under countable unions? – Wasiq Noor Aug 12 '18 at 21:03
• @WasiqNoor I don't understand what you're asking. We're not taking the union of uncountably many countable sets; rather, in case 1 we're considering a countable union of sets, one of which is $X$. Do you understand why this is a countable union, and is all of $X$? – Noah Schweber Aug 12 '18 at 21:21
• Consider the case when $\tau$ has all the subsets of $X$ as well as $X$ in it. Now since $X$ has uncountable subsets, when we union all of these subsets from $\tau$, we get $X$ which is in $\tau$. Now actually we have union uncounably many countable subsets. Right? So aren't we violating by considering it a countable union? – Wasiq Noor Aug 12 '18 at 21:31

You’re given that $X$ is an uncountable set. For every $x\in X$, set $O_x = {x}$. Certainly, $O_x$ is a finite set thus $O_x\in\tau$. Now, let $A\subset X$ be any subset. Therefore, the set

$$O_A = \bigcup_{x\in A} O_x$$

is exactly equal to $A$, but it is not always the case that $A\in\tau$. Therefore, it is not true that $\tau$ is closed under arbitrary unions.

Note that this breaks down exactly when $A$ is uncountable, i.e. when we take an uncountable union!


text:
when quoting this document, please refer to the following
DOI:
URN: urn:nbn:de:0030-drops-23067
URL:

; ;

### On the Memory Consumption of Probabilistic Pushdown Automata

 pdf-format:

### Abstract

We investigate the problem of evaluating memory consumption for systems modelled by probabilistic pushdown automata (pPDA). The space needed by a runof a pPDA is the maximal height reached by the stack during the run. Theproblem is motivated by the investigation of depth-first computations that playan important role for space-efficient schedulings of multithreaded programs. We study the computation of both the distribution of the memory consumption and its expectation. For the distribution, we show that a naive method incurs anexponential blow-up, and that it can be avoided using linear equation systems.We also suggest a possibly even faster approximation method.Given~$\varepsilon>0$, these methods allow to compute bounds on the memoryconsumption that are exceeded with a probability of at most~$\varepsilon$. For the expected memory consumption, we show that whether it is infinite can be decided in polynomial time for stateless pPDA (pBPA) and in polynomial space for pPDA. We also provide an iterative method for approximating theexpectation. We show how to compute error bounds of our approximation methodand analyze its convergence speed. We prove that our method convergeslinearly, i.e., the number of accurate bits of the approximation is a linear function of the number of iterations.

### BibTeX - Entry

@InProceedings{brazdil_et_al:LIPIcs:2009:2306,
author =	{Tomas Brazdil and Javier Esparza and Stefan Kiefer},
title =	{{On the Memory Consumption of Probabilistic Pushdown Automata}},
booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages =	{49--60},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-13-2},
ISSN =	{1868-8969},
year =	{2009},
volume =	{4},
editor =	{Ravi Kannan and K. Narayan Kumar},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},

format: plain


text:
# How to animate 2D fields¶

In this post, we will be discussing how to animate a 2D field with Python

In this case we're animating the surface temperature from a dataset provided by the xarray tutorial.

In [1]:
# Numpy and xarray are always necessary
import numpy as np
import xarray as xr

# pyplot needed to plot the dataset, but animation only needed much further down.
from matplotlib import pyplot as plt, animation
%matplotlib inline

# This is needed to display graphics calculated outside of jupyter notebook
from IPython.display import HTML, display

# Also, in case we haven't created it yet, make sure that we have a directory for images and videos
! test -d ../images/Python_Animation && rm -rf ../images/Python_Animation/* || mkdir -p ../images/Python_Animation

In this case, we'll be using the North-American Air Temperature data provided by xarray in the github directory https://github.com/pydata/xarray-data

In [2]:
ds = xr.tutorial.open_dataset('air_temperature')
ds

Out[2]:
<xarray.Dataset>
Dimensions:  (lat: 25, lon: 53, time: 2920)
Coordinates:
* lat      (lat) float32 75.0 72.5 70.0 67.5 65.0 ... 25.0 22.5 20.0 17.5 15.0
* lon      (lon) float32 200.0 202.5 205.0 207.5 ... 322.5 325.0 327.5 330.0
* time     (time) datetime64[ns] 2013-01-01 ... 2014-12-31T18:00:00
Data variables:
air      (time, lat, lon) float32 ...
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...

We open the dataset and select the temperature field, change it to Celsius, and give it a shorter "long name".

In [3]:
tas=ds.air
tas = tas - 273.15
tas.attrs['units'] = 'degC'
tas.attrs['long_name'] = "Air Temperature"

Any animation is practically a succession of frames, or still images. What we have to do is generate all frames independently and then stitch them together.

But for a start, we're first looking at the initial images to see what we get:

In [4]:
for i in range(5):
tas[i,:,:].plot(figsize=(6,4))
plt.show()
plt.close()

The first thing we notice is the title. At each frame for midnight, it shows only the date, but any other time, it also adds the hours, minutes, and seconds. This makes the title quite jittery, and will not look good in the animation. We need to set the title manually.

In [5]:
for i in range(5):
tas[i,:,:].plot(figsize=(6,4))
plt.title("Time = " + str(tas.coords['time'].values[i])[:13])
plt.show()
plt.close()

Now that we have a constant width title, and everything else seems fine, we can start working on the animation.

## Animated Gif¶

If we want to create an animated Gif, we'll start by creating the frames and save them to PNG files independently.

In [6]:
for i in range(40):
tas[i,:,:].plot(
figsize = (12,6)      # We'll make it a bit bigger
)
plt.title("Time = " + str(tas.coords['time'].values[i])[:13])
plt.savefig(f"../images/Python_Animation/Python_Animation_01_frame_{i:04}.png")
plt.close()

In the savefig command, we're using an "f-string", that is a litteral f followed by a string. This means that inside the string, any braces will indicate where it should replace something.

In this case, {i:04} means replace this with the value of i, zero-padded on the left to 4 digits.

We can see the files with the ls command:

In [7]:
!ls ../images/Python_Animation/

Python_Animation_01_frame_0000.png Python_Animation_01_frame_0020.png
Python_Animation_01_frame_0001.png Python_Animation_01_frame_0021.png
Python_Animation_01_frame_0002.png Python_Animation_01_frame_0022.png
Python_Animation_01_frame_0003.png Python_Animation_01_frame_0023.png
Python_Animation_01_frame_0004.png Python_Animation_01_frame_0024.png
Python_Animation_01_frame_0005.png Python_Animation_01_frame_0025.png
Python_Animation_01_frame_0006.png Python_Animation_01_frame_0026.png
Python_Animation_01_frame_0007.png Python_Animation_01_frame_0027.png
Python_Animation_01_frame_0008.png Python_Animation_01_frame_0028.png
Python_Animation_01_frame_0009.png Python_Animation_01_frame_0029.png
Python_Animation_01_frame_0010.png Python_Animation_01_frame_0030.png
Python_Animation_01_frame_0011.png Python_Animation_01_frame_0031.png
Python_Animation_01_frame_0012.png Python_Animation_01_frame_0032.png
Python_Animation_01_frame_0013.png Python_Animation_01_frame_0033.png
Python_Animation_01_frame_0014.png Python_Animation_01_frame_0034.png
Python_Animation_01_frame_0015.png Python_Animation_01_frame_0035.png
Python_Animation_01_frame_0016.png Python_Animation_01_frame_0036.png
Python_Animation_01_frame_0017.png Python_Animation_01_frame_0037.png
Python_Animation_01_frame_0018.png Python_Animation_01_frame_0038.png
Python_Animation_01_frame_0019.png Python_Animation_01_frame_0039.png

The easiest way to convert this to an animated gif is to use the command line tool convert, which is part of "ImageMagick":

In [8]:
!convert ../images/Python_Animation/Python_Animation_01_frame*png ../images/Python_Animation/Python_Animation_01.gif
display(HTML(""))

The display(HTML()) part includes the image as part of the output of the cell. Unfortunately this also means that the image will probably be cached by the browser, so don't be too surprised if it doesn't seem to change even if you make changes to the code.

Because we're going one directory up, jupyter notebook needs to be started at least one directory up from where this Notebook is actually located, otherwise it won't find the image file.

In the following, we will be using higher numbers in the file names to distinguish between animations.

In the above animation, we see that the colorbar at the side is flickering widely. The ticks are always going from -40 to 40, but they are not stationary at all. So let's fix them.

In [9]:
for i in range(40):
tas[i,:,:].plot(
figsize = (12,6),
vmin=-40, vmax=40  # Minimum and Maximum values
)
plt.title("Time = " + str(tas.coords['time'].values[i])[:13])
plt.savefig(f"../images/Python_Animation/Python_Animation_02_frame_{i:04}.png")
plt.close()

In [10]:
!convert ../images/Python_Animation/Python_Animation_02_frame*.png ../images/Python_Animation/Python_Animation_02.gif
display(HTML(""))

Now we see that two things have changed. One is the colormap. We liked the old one better, so we need to change that. Also, in some frames, the minimum temperature in some places is below -40 degrees Celsius, which causes the colorbar to get an arrow end pointing down, which causes flickering.

Now we could change the minimum value, but for this example, I'll be using the kwargs to disable these arrows.

In [11]:
for i in range(40):
tas[i,:,:].plot(
figsize = (12,6),
vmin=-40, vmax=40,
cmap='coolwarm',    # Change the colormap back to 'bwr'
cbar_kwargs={
'extend':'neither' # Don't extend the colorbar in either direction. Other possibilities
# would be 'both', 'min', or 'max'
}
)
plt.title("Time = " + str(tas.coords['time'].values[i])[:13])
plt.savefig(f"../images/Python_Animation/Python_Animation_03_frame_{i:04}.png")
plt.close()

In [12]:
!convert ../images/Python_Animation/Python_Animation_03_frame*.png ../images/Python_Animation/Python_Animation_03.gif
display(HTML(""))

And this is a perfectly good animated gif to use in any presentation or website.

## Animation within Python¶

This is where the animation import from the beginning comes in.

The animation is trickier, because we need to interact with the module, the figures, even the axes explicitly, but it's also a lot shorter to write, as we only update the data, not the whole figure.

This is still a bit confusing even to me, but it seems as if this part doesn't work if we don't execute all the code in a single cell.

In [13]:
# Get a handle on the figure and the axes
fig, ax = plt.subplots(figsize=(12,6))

# Plot the initial frame.
cax = tas[0,:,:].plot(
cmap='coolwarm',
vmin=-40, vmax=40,
cbar_kwargs={
'extend':'neither'
}
)

# Next we need to create a function that updates the values for the colormesh, as well as the title.
def animate(frame):
cax.set_array(tas[frame,:,:].values.flatten())
ax.set_title("Time = " + str(tas.coords['time'].values[frame])[:13])

# Finally, we use the animation module to create the animation.
ani = animation.FuncAnimation(
fig,             # figure
animate,         # name of the function above
frames=40,       # Could also be iterable or list
interval=200     # ms between frames
)

Now that we have the animation object, we can either display it as a JavaScript App:

In [14]:
HTML(ani.to_jshtml())

Out[14]:

Once Loop Reflect


text:
## Functions preserving 2-series strict orders

• In recent years a considerable attention was paid to an investigation of finite orders relative to different properties of their isotone functions [2,3]. Strict order relations are defined as strict asymmetric and transitive binary relations. Some algebraic properties of strict orders were already studied in [6]. For the class K of so-called 2-series strict orders we describe the partially ordered set EndK of endomorphism monoids, ordered by inclusion. It is obtained that EndK possesses a least element and in most cases defines a Boolean algebra. Moreover, every 2-series strict order is determined by its n-ary isotone functions for some natural number n.

$Rev: 13581$


text:
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# Soil salinity and matric potential interaction on water use, water use efficiency and yield response factor of bean and wheat

### Subjects

An Author Correction to this article was published on 31 August 2018

## Abstract

We studied the effects of soil matric potential and salinity on the water use (WU), water use efficiency (WUE) and yield response factor (Ky), for wheat (Triticum aestivum cv. Mahdavi) and bean (Phaseoulus vulgaris cv. COS16) in sandy loam and clay loam soils under greenhouse conditions. Results showed that aeration porosity is the predominant factor controlling WU, WUE, Ky and shoot biomass (Bs) at high soil water potentials. As matric potential was decreased, soil aeration improved, with Bs, WU and Ky reaching maximum value at −6 to −10 kPa, under all salinities. Wheat WUE remained almost unchanged by reduction of matric potential under low salinities (EC ≤ 8 dSm−1), but increased under higher salinities (EC ≥ 8 dSm−1), as did bean WUE at all salinities, as matric potential decreased to −33 kPa. Wheat WUE exceeds that of bean in both sandy loam and clay loam soils. WUE of both plants increased with higher shoot/root ratio and a high correlation coefficient exists between them. Results showed that salinity decreases all parameters, particularly at high potentials (h = −2 kPa), and amplifies the effects of waterlogging. Further, we observed a strong relationship between transpiration (T) and root respiration (Rr) for all experiments.

## Introduction

Soil aeration is an important factor affecting water uptake and growth in plants1. In wet soils (h > −10 to −30 kPa) aeration is limited, gas diffusion and transfer are insufficient, plants respiration is impeded and consequently water not absorbed efficiently2. As the frequency and connectivity of air filled pores increase, so does the soil matric suction, intensifying the uptake of water2. Oxygen deficiency symptoms occur below the critical value of air content, depending on plant and soil types. Thus, under flood irrigation, plants tolerant to lack of aeration such as the tomato, and a variety of forage species, commence water uptake within a few hours of irrigation, while species sensitive to aeration, such as the pea and potato, may take a few days, particularly in fine-textured soils1.

In addition to soil water content, soil salinity also influences the soil available water range, and subsequently the water use of plants. Salinity, via reduction of soil water potential and ionic toxicity, dramatically reduces the photosynthetic rate, transpiration rate (T), stomata conductance and root hydraulic conductance. Thus, plant water uptake and productivity decrease significantly3.

Plant productivity is dependent on the availability of soil water, in terms of both quantity and quality, as well as on water use efficiency (WUE = yield/water use)4. WUE is an important subject in agriculture, due to the increase in areas under irrigation and the high water requirements of crops, which consume around 70% of water available to humans5. WUE is considered an expression factor of yield value under stress conditions and can illustrate crop tolerance to drought stress. The yield production level is highly dependent on the transpiration rate. Effective use of water improves soil water uptake and subsequently transpiration rate and crop yield, so WUE significantly augments yield6. Increased water use efficiency can improve productivity and reduce stresses caused by environmental conditions7. This parameter is an expression of the relationship between crop yield and water use (evapotranspiration) during a growing season and is critically affected by soil available water and its limiting parameters8. In saturated and near-saturated soils, due to reduction of the oxygenation parameters such as air permeability, gas diffusion coefficient and air filled porosity1, the water uptake by plant roots decreases, leading to significant reductions in yield and WUE9. The association between WUE and soil moisture has been well researched for many crops, under different production systems, especially in waterlogged soils10. Dasila et al.11 showed that WUE in flooded irrigation conditions is very low, due to serious water and nutrient losses. A further complication is that an excess of soil water may not immediately exit the system, but may remain in the B horizon of texture-contrast soils as a perched water table12. This can lead to transient anoxia, stomata closing, yield and WUE reduction, and eventually root death, depending on the duration of waterlogging12. Létourneau et al.13 revealed that the best yield and WUE are obtained with a soil matric potential (based on irrigation thresholds) of −8 kPa in silty clay loam soil, or −10 to −15 kPa in clay loam soil, and suggested that WUE could be further improved by implementing high frequency irrigation.

Soil water salinity also affects WUE due to the ion specific toxicity and the decrease in available water, as well as the photosynthetic activity and crop yield. Semiz et al.14 stated that WUE response to salinity is very similar to the yield response to salinity. At optimal soil condition, WUE initially increases with salinity to threshold EC, and then decreases. At suboptimal condition, WUE is initially almost constant then sharply reduces with high salinity levels14. Similar results have been confirmed by Bompy et al.15.

Another factor affected by soil water quantity and quality is yield response factor (Ky), which represents the yield response where soil water uptake is restricted. The Ky factor describes the reduction in relative yield, according to the reduction in ET16. Lovelli et al.17 corroborated validity of Ky as a synthesis parameter, in the quantification of the level of tolerance of crops, in terms of water stress. In the case of safflower, a Ky value below 1 indicates tolerance of water deficiency, with minimal impacts on production and overall stability, in terms of water use efficiency. Thus, the species has the mechanism to adapt to limited irrigation and can offer economic sustainability in such irrigation regimes. Conversely, eggplant with a Ky value exceeding 1 shows sensitivity under conditions that include water stress17. These results confirm the interactivity of the Ky and WUE parameters18, and thus Ky, as an empirical parameter that requires further research testing, may have a value in the estimation of water scheduling needs of specific crops. Zonta et al.16 rated factor Ky as 0.53 and 0.82, for irrigation of 70% and 40% ETc, respectively. Similarly, Singh et al.19 rated Ky as 0.28, 0.98 and 1.02 for cotton yields in semi-arid regions of India, for irrigation levels of 90%, 60% and 50% ETc, respectively.

With an increase in demand for irrigation in many global regions, as well as extensive subsidies and restrictive regulations, leading to greater stress on freshwater resources20, increases in WUE and reductions in Ky will be required to maintain maximum agricultural productivity with minimum water use21. Hence, estimations of WUE and Ky values of specific crops, at a variety of levels of soil salinity and matric potential, are useful for the specification of ideal soil salinity and soil water levels, in terms of available water sources (qualitative and quantitative). Based on these results, practical solutions can be proposed for optimal management, such that crop yields and WUE reach the highest possible levels, without soil salinity increases. Despite the importance of this issue in terms of global sustainability, the effects of soil moisture and salinity interactions on Ky, WUE and WU have rarely been investigated for wet soil (near-saturated to the FC). The purposes of this study are: i) to evaluate the interaction effects of soil aeration and salinity on Ky, WUE, and WU, at FC and higher moisture contents, ii) to investigate the relationship between T and root respiration (Rr) of bean and wheat under salinity and waterlogging, and iii) to estimate critical aeration porosity, according to mentioned parameters and to investigate the accuracy of the hypothesis ‘critical aeration porosity of 10% is not representative for all soils and plants’.

## Materials and Methods

The experiments were undertaken in a research greenhouse (20 ± 5 °C and relative air humidity between 55–80%), using a completely randomized factorial design with three replicates.

### Soil properties

Clay loam and sandy loam soils were selected from 0–0.3 m layers of non-saline, agricultural lands in Zanjan, Iran. Sand particles percentage was measured by a sieve series with diameters of 0.05–2 mm and percentage of silt and clay particles were evaluated based on the Stokes law and hydrometer method22. The soils were sampled using cylinders with 100 cm3 volume and then soil water characteristics curve (SWCC) was measured by hanging water column at −0.1 to −15 kPa matric potentials (h), using a pressure plate at −33 to −100 kPa matric potentials and by pressure membrane at matric potentials of −150 to −1500 kPa2. The van Genuchten-Mualem (VG-M) model was fitted to the SWCC data (θs, α, n) with the RETC program.

Soil electrical conductivity (EC) and reaction (pH) were specified in saturation extract of soils by EC meter (Jenway 4510) and pH meter (Jenway 3505), respectively23. The soils were oxidized with sulfuric acid and their nitrogen were measured by Kjeldahl device24. Also soils phosphor was determined using Olsen method and Spectrophotometer device (UV/VIS Perkin elmetr- lambada 25-USA)25. Finally soils potassium was assessed by ammonium acetate and Flame photometer device (Jenway, PFP-7, UK).

### Plant materials

The soils were collected with an initial field bulk density into plastic pots (0.27 m height and 0.26 m diameter) and an opaque, polyethylene closed chamber, with cross section of 36 × 10−4 m2 and volume of 5 × 10−4 m3, was set in each pot26. The closed chamber system is a technique which measures the soil respiration rate27 (greater detail can be found in Mohammadi et al.26. A chemical fertilizer solution was added to the soil in each pot, according to soil analysis (Table 1), nutrients leaching and plant type, to enhance growth through the stages of planting, flowering and grain filling28 (Table 2). Foliar sprays of micro and macro elements (N = 110 mgl−1, P2O5 = 40 mgl−1, K2O5 = 80 mgl−1, Mg = 0.5 mgl−1, Mn = 1 mgl−1, Cu = 0.2 mgl−1, Zn = 3 mgl−1, B = 0.2 mgl−1, Fe = 2 mgl−1, Mo = 0.03 mgl−1) were applied during the growth season, for frequently leached pots. Bean (Phaseoulus vulgaris cv. COS16) and wheat (Triticum aestivum cv. Mahdavi), were planted in the pots. Once the plants had established, eight wheat and four bean plants were subjected to the experimental treatments (soil moisture and salinity). For blank treatment of root respiration (as microbial respiration, Mr) and transpiration experiments, forty pots were prepared without any plants26.

### Salinity treatments

The irrigation water solutions with salinity levels of 0.7, 2, 4, 6 and 8 dSm−1 for bean, and 2, 4, 8, 16 and 20 dSm−1 for wheat, were prepared using CaCl2 and NaCl (3:1). The salinity treatments levels were determined, according to the FAO report on the ranges of bean and wheat tolerance to salinity29.

### Moisture treatments

The −2, −6, −10 and −33 kPa matric potentials were applied as soil moisture treatments for both plants. The matric potentials were conducted using the negative pressure water circulation technique26,30. This method authorized us to regulate levels of salinity with high drainage volumes. At treatments of high matric potential (h ≥ −10 kPa), an intensive leaching rate was applied to avoid solute accumulation. At treatments of lower matric potential (h < − 10 kPa), levels of soil salinity were adjusted before seed sowing and de-ionized water was used for irrigation without drainage. Throughout the experiment, the quantities of irrigation and drainage water were recorded accurately for each pot.

$$(2\,{\rm{soils}}\times 2\,{\rm{plants}}\times 5\,{\rm{salinity}}\,{\rm{levels}}\times 4\,{\rm{matric}}\,{\rm{potential}}\,{\rm{levels}}\times 3\,{\rm{replicates}})+(40\,{\rm{blanks}})=280\,{\rm{pots}}$$

### Measurement of root respiration rate

CO2 accumulation in the closed chamber, per 0.5 hour (Soil respiration, Sr), was measured31, using Lambada device (Lambada, U. K. ADC Company) every 3 days, for 45 days after the plant establishment stage. Root respiration rate, Rr, (μ mol m−3 s−1) was estimated by26:

$$Rr=Sr-Mr$$
(1)

### Calculation of water use, water use efficiency and yield response factor

At the end of the plant growth (~4 months) after grain filling, shoots (shoot material and grain) and roots were harvested separately. All samples were oven-dried at 70 °C for at least 72 hours, after which they were weighed and the biomass of shoots (Bs) and roots (Br) were measured.

Volume of water use (WU, m3/pot) or ET (evapotranspiration) during the experiment was calculated as follows:

$$WU=Wi-Wd$$
(2)

where, Wi and Wd are the total amounts of irrigation and drainage water in the planted pots, respectively.

Evaporation (E) was estimated by Eq. (3)

$${\rm{E}}={\rm{Wi}}({\rm{b}})-{\rm{Wd}}({\rm{b}})$$
(3)

where, Wi(b) and Wd(b) are the total amounts of irrigation and drainage water in non-planted pots, respectively.

Transpiration (T) was calculated as follows:

$${\rm{T}}={\rm{WU}}-{\rm{E}}$$
(4)

WUE (kgm−3) of shoot was obtained by mass of shoot biomass divided by volume of water use32:

$$WUE=Bs/WU$$
(5)

Finally Ky was calculated by32:

$$(1-Bs/B{s}_{max})={K}_{y}(1-ET/E{T}_{max})$$
(6)

where Bs and Bsmax are the actual biomass and maximum biomass of shoots, and ET and ETmax are the evapotranspiration and maximum evapotranspiration, respectively.

The statistical analyses were performed using SAS 9.1.3 statistics software. The effect of the treatments and the interactive effects between them were investigated using the Duncan multiple range test.

## Results

Physical and chemical properties of the soils used in the greenhouse experiment are given in Table 1.

The variance analysis table shows that soil matric potential has a significant influence on bean and wheat Bs, WU, WUE and Rr (p < 0.01). The statistical analysis also confirms the influence of soil salinity on bean and wheat Bs, WU and WUE (p < 0.01). The effect of salinity on wheat Rr (p < 0.01) is more significant than on bean (p < 0.05). The interaction effects of soil salinity and matric potential on all parameters of wheat, and WU and Rr of bean, are significant (p < 0.01). However, there was no effect on bean Bs and WUE (Table 3).

### Biomass of shoot

The variations of Bs (kg/plant), as a function of soil salinity for the planted wheat and bean, are shown in Fig. 1. The results show that at −2 kPa matric potential, wheat Bs is lower than −6 kPa potential under EC ≤ 8 dSm−1 and is lower than other potentials (h < − 2 kPa) under EC > 8 dSm−1. The bean Bs is the minimum at −2 kPa potential, under all salinity levels, in sandy loam and clay loam soils. As the soil matric potential decreases slightly, the wheat and bean Bs increase, reaching maximum value at −6 to −10 kPa potentials in both soils. At matric potentials lower than −10 kPa, and under salinities lower than 8 dsm−1 for wheat and 4 dsm−1 for bean, Bs decreases with reduction of potential (especially for wheat), while under higher salinities it remains nearly constant (Fig. 1).

Salinities lower than 8 dSm−1 for wheat, and 4 dSm−1 for bean, do not significantly affect Bs (Table 4). Under higher salinities, the Bs of both plants decrease in sandy loam and clay loam soils. The highest effect of salinity on wheat and bean Bs is at −2 kPa potential. As matric potential decreases, the salinity effect reduces and at −33 kPa potential is minimized in sandy loam and clay loam soils (Fig. 1). The minimum Bs of both plants was observed at −2 kPa potential under EC = 20 dsm−1 for wheat, and EC = 8 dsm−1 for bean, in clay soil (Fig. 1).

Comparing sandy loam and clay loam soils shows that the variations of Bs in terms of salinity and matric potential are almost identical in both soils, indicating that soil texture does not affect Bs dramatically.

The results show that reduction of wheat and bean shoot biomass with increasing of one salinity unit (b) is the maximum value at −2 kPa potential, especially for wheat in sandy loam and clay loam soils. As soil matric potential decreases from −2 to −33 kPa, b decreases, with lowest values in sandy loam and clay loam soils obtained at −33 kPa potential (Fig. 1).

### Volume of water use

The results shows that variations of water use (WU) for wheat and bean, in terms of soil matric potential and salinity, are similar to those for Bs. The wheat WU at −2 kPa matric potential is lower than −6 to −10 kPa potential, and bean WU reaches minimum value at −2 kPa potential, rather than other potentials (h < −2 kPa) in both sandy loam and clay loam soils (Table 4). As matric potential decreases from −2 to −6 or −10 kPa, wheat and bean WU reach their maximum values and then collapse at −33 kPa in sandy loam and clay loam soils (Fig. 2).

Salinities lower than 4 dSm−1 for bean and 8 dSm−1 for wheat do not seriously affect WU (Table 4). Under higher salinities, wheat and bean WU reduces significantly, particularly at −2 kPa potential, in both soils (Table 5). The minimum WU is 0.004 m3/pot under EC = 20 dSm−1 and −33 kPa potential for wheat, and 0.002 m3/pot under EC = 8 dSm−1 and −2 kPa potential for bean, in clay loam soil (Fig. 2).

Figure 2 shows that wheat WU is higher than bean under all salinities, particularly under anoxia condition (−2 kPa potential).

### Water use efficiency

Figure 3 shows that the wheat WUE remains almost constant with reductions of matric potential under EC = 2–8 dSm−1, while when EC > 8 dSm−1, it increases with reduction of matric potential in sandy loam and clay loam soils. The bean WUE also increases with reductions of matric potential under all salinities and in both soils (Fig. 3). The maximum WUE of wheat and bean are 3.7 and 2.9 kgm−3, respectively at −33 kPa potential, while their minimum values are 1.1 and 1.5 kgm−3, respectively at −2 kPa potential, in clay loam soil (Fig. 3). At −33 kPa potential, wheat WUE is 20% and bean WUE is 41% greater than their WUE at −2 kPa potential (Table 4).

Salinities lower than 8 dSm−1 for wheat, and 4 dSm−1 for bean, do not significantly affect WUE (Table 4). Under higher salinities, WUE decreases severely with a minimum value under EC = 20 dSm−1 for wheat, and EC = 8 dSm−1 for bean, at all potentials and in both soils. Under these salinities, wheat WUE drops by 39% (rather than EC = 2 dSm−1) and bean by 26% (rather than EC = 0.7 dSm−1) (Table 4). The effect of salinity on wheat WUE is more pronounced at higher potentials and minimizes at −33 kPa potential (Fig. 3).

Figure 3 shows that the variations of WUE, in terms of salinity, are almost the same in both soils, as well as the variations of WUE according to matric potential. The results reveal that wheat WUE exceeds bean WUE in sandy loam and clay loam soils.

Figure 4 shows a significant relationship between WUE and the shoot/root ratio for wheat and bean, and the strong correlation coefficient indicates the considerable effect of the shoot/root ratio on WUE. The wheat correlation coefficient (0.83–0.73) is higher than bean (0.71–0.64) in sandy loam and clay loam soils. The wheat slope of regression line in sandy loam soil (0.17) is lower than in clay loam soil (0.67), while for bean it is the same in both soils (0.2).

### Yield response factor

Since Ky is crop specific and is not influenced by soil type, Ky (for both soils) as a function of soil salinity and matric potential is given in Figs 5 and 6, respectively.

The Ky is the maximum value and equals 1.65 under EC = 2 dSm−1 for wheat and 1.30 under EC = 0.7 dSm−1 for bean. Wheat and bean Ky decrease with salinity and the high regression coefficient (0.78–0.84, respectively) demonstrates the significant effect of salinity on both crops. Figure 5 shows that bean Ky reduces more than wheat, in terms of salinity, and its slope of regression line (3.4%) is more than that of wheat (1.6%). Further, wheat Ky values are higher than bean under all salinities (Fig. 5).

The results reveal that under waterlogging (−2 kPa potential), wheat and bean Ky values are minimum and equal 1.1 and 0.9, respectively. As matric potential decreases, Ky increases and reaches a maximum value at −10 kPa potential for wheat (1.8) and at −6 kPa potential for bean (1.3) (Fig. 6). The increment of bean Ky with reduction of potential is greater than in the case of wheat. At lower potentials (h < −10 kPa for wheat and h < −6 kPa for bean), Ky decreases significantly, especially for wheat (Fig. 6).

### Relationships between rate of root respiration and transpiration

The variations of transpiration (T) as a function of root respiration (Rr, μ mol m−3 s−1) and soil matric potential, under salinities lower and higher than threshold, for wheat (EC = 2 and 20 dSm−1) and bean (EC = 0.7 and 8 dSm−1) are shown in Figs 7 and 8, respectively. The results show that T is affected by soil potential and Rr.

In sandy loam and clay loam soils, under salinities lower than threshold, wheat T decreases with decreasing potential and Rr, reaching a minimum value at −33 kPa. Under higher salinities, wheat T lowest value is at −2 kPa potential (Fig. 7). Bean T is minimum at −2 kPa potential, and increases with decreasing potential and increasing Rr under all salinity levels (Fig. 8). A comparison of the two plants illustrates that wheat Rr and T values exceed those for bean in both soils (Figs 7 and 8).

## Discussion

### The effects of soil matric potential

This study has shown that Bs, WU, WUE, Rr and Ky are strongly influenced by soil aeration and decrease at −2 kPa potential (Figs 1 and 2). At high matric potential (−2 kPa), or high soil water content, pores are blocked by water and oxygen deficit results in stomata closure and restricted water uptake. Subsequently, the decline of the photosynthetic rate and root permeability lead to decreased growth and impeded plant activities, such as transpiration and root respiration33. Wheat adapts somewhat to soil anoxia34 by developing aerenchyma tissues35 and adventitious roots36. Thus, wheat WU and WUE values are higher than those for bean under anoxia condition (−2 kPa potential), confirming the high tolerance of wheat to stresses (Figs 2 and 3).

As the soil matric potential decreases (to −6 or −10 kPa), soil aeration and root uptake of water and nutrients improves, such that wheat and bean Bs and WU increase, reaching maximum values at −6 to −10 kPa potential, in both soils (Figs 1 and 2). Consequently, Ky also increases to a maximum value at −10 kPa potential for wheat, and at −6 kPa potential for bean (Fig. 6). It seems that these matric potentials correspon d with optimum soil moisture conditions, which can be considered as the critical aeration porosity (0.18–0.16 m3m−3 in sandy loam and clay loam, respectively), in which there is equilibrium between the quantities of water and air, resulting in both reasonable respiration and water uptake. This result supports the hypothesis that 10% critical aeration porosity is not sufficient for all plants and soils.

Wheat and bean WUE also increases with aeration improvement (Fig. 3), due to the fact that increases of Bs (numerator) with decreasing potential exceed WU (denominator), and their ratio which is defined as WUE, thus increases. The increase of WUE with reduction of soil potential has been observed by many researchers (e.g. see Ghamarnia et al.37). Markandya et al. concluded that flood irrigation WUE is nearly 35%, and equivalent to half and one third of the sprinkler and drip irrigation systems38, respectively. Flood irrigation can result in decreasing water uptake and inefficient use of fertilizer, ultimately decreasing WUE39. The flooding effect on WUE depends on the type of plant. Fahong et al.39 showed that wheat WUE increased 30% by changing from flood to furrow irrigation, while rice WUE under field capacity is lower than that under flooding40. At potentials lower than −6 to −10 kPa, because of deviation from optimum moisture condition and decreasing of soil non-limiting water, hydraulic conductivity and salt mass flow, water uptake by root reduces, leading to decreased Bs, WU (or evapotranspiration) and Ky (Figs 1, 2 and 6). The WU decline can be also attributed to a decrease in shoots and surface leaves that affect wheat and bean transpiration adversely (Fig. 1). Further, at these lower potentials, evaporation of soil water content decreases, strongly affecting WU. This result is comparable with the results observed by Kiani41.

### The effects of soil salinity

The results have shown that high salinities (EC > 8 dSm−1 for wheat and EC > 4 dSm−1 for bean) decrease Bs, WU, WUE and Rr in both plants, and the effects are greater in wheat rather than bean (Figs 1, 2, 3, 7 and 8). In addition, Ky decreases significantly with salinity (Fig. 5). Similar results were obtained for corn (Azizian and Sepaskhah, 2014), while Shabani et al.42 reported that rapeseed Ky increases with salinity to threshold salinity, and then decreases under higher salinities. Ion toxicity (especially sodium), ion balance disorder and restricted uptake of water and nutrient are the most important reasons for yield reduction, and related factors, under high salinities43. This result has been confirmed by many researchers14,44,45.

### The interaction effects of soil salinity and matric potential

Oxygen deficit can intensify the effects of salinity stress. This synergic effect results in major decreases of Bs, WU and WUE at high potentials (−2 kPa) under high salinities (Figs 1, 2 and 3). As soil potential decreases from −2 to −33 kPa, the adverse effect of salinity on wheat and bean diminishes, and reduced soil moisture becomes the major controlling factor of plant growth and development (Fig. 1). Based on this result, it can be stated that at the upper limit of the water range (high soil moistures or high matric potentials), salinity affects plant growth significantly, while at the lower limit (low soil moistures or low matric potentials), the effect of salinity is minimal and plant water uptake and growth are barely impacted by matric potential.

Figures 5 and 6 confirm that Ky value is minimum under stress conditions (waterlogging and salinity). Since biomass decline (numerator) by stresses is lower than that of evapotranspiration, or WU (denominator), their ratio (Ky) reduces under waterlogging and salinity. In other words, under suitable environmental conditions (at optimum matric potential and low salinity), plant sensitivity to stresses is very high42.

Ky values for bean and wheat are higher than 1 (Ky > 1) for all salinities and matric potentials. These values are reported by FAO as 1.15 for both plants18. This indicates that neither plant adapts well to waterlogging and salinity.

Under low salinities, wheat can extend its root system and adapt to anoxia that its Rr increases at −2 kPa potential. Subsequently, due to enhanced water and nutrient uptake, shoots are extended, leading to increased T. Since salinity intensifies waterlogging, under high salinities wheat roots and shoots decrease severely and Rr and T decline to a minimum value at −2 kPa potential (Fig. 7). Bean is very sensitive to waterlogging, so its minimum Rr and T are remain −2 kPa potential, for all salinity levels (Fig. 8).

### The relation between root respiration and transpiration

Figures 7 and 8 show that wheat and bean Rr affects T and that there is a significant relationship between these factors in sandy loam and clay loam soils. With treatments of matric potential and salinity, the wheat and bean T variations are almost similar to those of Rr (Figs 7 and 8). Under stress conditions, shoot and root growth and plant activities such as photosynthesis and root respiration decrease, leading to decreased T46. These results confirm that T, and subsequently WUE, can be controlled by Rr regulation. The Rr rate depends on environmental factors and plant type, age and activity33. In the case of the two study plants, due to the extensive root system of wheat, its mean Rr (5.79 μ mol m−3 s−1) is higher than that of bean (5.69 μ mol m−3 s−1) (Figs 7 and 8). Although their values are closed, this difference is considerable biologically.

### The relation between shoot/root ratio and water use efficiency

WUE increases with shoot/root ratio, indicating a significant relationship between them (Fig. 4). An higher shoot /root ratio causes an increase in transpiration and photosynthesis rate, and consequently WUE improves under irrigated conditions. Ma et al.47 reported similar results and showed that controlling the root/shoot ratio can affect WUE.

## Conclusions

This study was conducted to investigate variations in water use, water use efficiency and yield response factor in bean and wheat, as a function of soil matric potential and salinity in sandy loam and clay loam soils. The results showed firstly that in wet soil, soil aeration porosity is the principal factor determining these parameters and that secondly, the effects of soil salinity, soil texture and crop type are significant. At high matric potentials, and under waterlogging, the parameters referred to are very low and reach maximum values at optimum matric potentials (−6 to −10 kPa). These matric potentials correspond with aeration porosities of 0.16–0.18m3m−3. This result demonstrates that a critical aeration porosity of 10% does not hold for different plants and soils. The low to medium salinities do not significantly affect water use, water use efficiency and yield response factor. Conversely, high salinities decrease all parameters significantly, and intensify the effect of oxygen deficit at high potentials. Thus, in the absence of a quality water source, in order to minimize the effect of salinity and improve WUE, it is more expedient to control soil potential in critical aeration porosity (according to soil and plant). Comparing our two study plants indicates the greater ability of wheat as regards water uptake and growth under stress conditions. The results also showed that root respiration affects transpiration, and that a significant relationship exists between these two functions. Thus, by regulating root respiration and transpiration rate, WUE can be effectively controlled48.

## Change history

• ### 31 August 2018

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has been fixed in the paper.

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Moud, A. & Maghsoudi, K. Salt stress effects on respiration and growth of germinated seeds of different wheat (Triticum aestivum L.) cultivars. World J. Agric. Sci 4, 351–358 (2008).

47. 47.

Ma, S., Li, F., Xu, B. & Huang, Z. Effect of lowering the root/shoot ratio by pruning roots on water use efficiency and grain yield of winter wheat. Field Crops Research 115, 158–164 (2010).

48. 48.

Dane, J. & Hopmans, J. 3.3. 1 Introduction. Methods of Soil Analysis: Part 4 Physical Methods, 671–973 (2002).

## Author information

Authors

### Contributions

Conceived and designed the experiments: M.K., M.M. Performed the experiments: M.K., M.M. Analysed the data: M.K., M.M. Contributed reagents/materials/analysis tools: M.K., M.M., F.S. Wrote the paper: M.K., M.M., F.S.

## Ethics declarations

### Competing Interests

The authors declare no competing interests.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions

Khataar, M., Mohammadi, M. & Shabani, F. Soil salinity and matric potential interaction on water use, water use efficiency and yield response factor of bean and wheat. Sci Rep 8, 2679 (2018). https://doi.org/10.1038/s41598-018-20968-z

• Accepted:

• Published:

### Keywords

• Yield Response Factor
• Potential Mates
• Matric Potential Decreases
• Clay Loam Soil
• Aeration Porosity


text:
# Math Help - How do I solve when A fraction is involved?

1. ## How do I solve when A fraction is involved?

Solve

w - 2w 1/2 - 15 = 0

2. Treat the fraction as any other constant, except if your equation is:

$w-2w\frac{1}{2}-15=0$

then it's false since:

$w-2w\frac{1}{2}-15=0$

$w-w-15=0$

$-15=0$

which is obviously not true.


text:
## The Webster scalar curvature and sharp upper and lower bounds for the first positive eigenvalue of the Kohn-Laplacian on real hypersurfaces.(English)Zbl 1404.32071

The authors study upper and lower bounds for the first positive eigenvalue $$\lambda_1$$ of the Kohn-Laplacian on compact strictly presudoconvex hypersurfaces $$(M,\Theta)$$ in $$\mathbb C^{n+1}$$.
In particular, they provide a sharp upper bound for $$\lambda_1$$ given explicitly in terms of the defining function $$\rho$$ under a technical assumption on $$\rho$$. As a corollary, a Reilly-type estimate follows when $$M$$ is embedded into the unit sphere.
Also, when the structure $$\Theta$$ on $$M\subset\mathbb C^{n+1}$$ is (the unique) volume-normalized with respect to $$dz^1\wedge dz^2\wedge\cdots\wedge dz^{n+1}$$, they establish a lower bound for $$\lambda_1$$ given explicitly in terms of the Webster scalar curvature of $$(M,\Theta)$$.

### MSC:

 32V20 Analysis on CR manifolds 32W10 $$\overline\partial_b$$ and $$\overline\partial_b$$-Neumann operators
Full Text:

### References:

 [1] Boutet de Monvel, L., Intégration des équations de Cauchy-Riemann induites formelles (French), 1-13, (1975), Paris · Zbl 0317.58003 [2] Burns, D. M.; Epstein, C. L., Embeddability for three-dimensional CR manifolds, J. Amer. Math. Soc., 3, 809-841, (1990) · Zbl 0736.32017 [3] Chanillo, S.; Chiu, H. L.; Yang, P., Embeddability for 3-dimensional Cauchy-Riemann manifolds and CR Yamabe invariants, Duke Math. J., 161, 2909-2921, (2012) · Zbl 1271.32040 [4] Case, J. S.; Chanillo, S.; Yang, P., The CR paneitz operator and the stability of CR pluriharmonic functions, Adv. Math., 287, 109-122, (2016) · Zbl 1327.32050 [5] Farris, F., An intrinsic construction of fefferman’s CR metric, Pacific J. Math., 123, 33-45, (1986) · Zbl 0599.32018 [6] Graham, C. R.; Lee, J. M., Smooth solutions of degenerate Laplacians on strictly pseudoconvex domains, Duke Math. J., 57, 697-720, (1988) · Zbl 0699.35112 [7] Hammond, C., Variational problems for Fefferman hypersurface measure and volume-preserving CR invariants, J. Geom. Anal., 21, 372-408, (2011) · Zbl 1219.32022 [8] Kohn, J. J., The range of the tangential Cauchy-Riemann operator, Duke Math. J., 53, 525-545, (1986) · Zbl 0609.32015 [9] Lee, J. M., The Fefferman metric and Pseudohermitian invariants, Trans. Amer. Math. Soc., 296, 411-429, (1986) · Zbl 0595.32026 [10] Lee, J. M.; Melrose, R., Boundary behavior of the complex Monge-Ampère equation, Acta Math., 148, 159-192, (1982) · Zbl 0496.35042 [11] Li, S. Y.; Luk, H. S., An explicit formula for the Webster pseudo-Ricci curvature on real hypersurfaces and its application for characterizing balls in C\^{}{n}, Comm. Anal. Geom., 14, 673-701, (2006) · Zbl 1113.32008 [12] Li, S. Y., On characterization for a class of pseudo-convex domains with positive constant pseudoscalar curvature on their boundaries, Comm. Anal. Geom., 17, 17-35, (2009) · Zbl 1194.32021 [13] Li, S. Y., Plurisubharmonicity for the solution of the Fefferman equation and applications, Bull. Math. Sci., 6, 287-309, (2016) · Zbl 1383.32010 [14] Li, S. Y.; Son, D. N.; Wang, X., A new characterization of the CR sphere and the sharp eigenvalue estimate for the Kohn Laplacian, Adv. Math., 281, 1285-1305, (2015) · Zbl 1319.53032 [15] Li, S. Y.; Lin, G. J.; Son, D. N., The sharp upper bounds for the first positive eigenvalue of the Kohn- Laplacian on compact strictly pseudoconvex hypersurfaces, Math. Z., 288, 949-963, (2018) · Zbl 1396.32017 [16] Lin, G. J.: Lichnerowicz-Obata type theorem for Kohn-Laplacian on the real ellipsoid. Acta Mathematica Scientia (Series B), to appear · Zbl 1438.32031 [17] Reilly, R., On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space, Comment. Math. Helvet., 52, 525-533, (1977) · Zbl 0382.53038 [18] Webster, S. M., Pseudo-Hermitian structures on a real hypersurface, J. Diff. Geom., 13, 25-41, (1978) · Zbl 0379.53016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
# DAVIDSTUTZ

23thAPRIL2020

Marchisio et al. propose a black-box adversarial attack on Capsule Networks. The main idea of the attack is to select pixels based on their local standard deviation. Given a window of allowed pixels to be manipulated, these are sorted based on standard deviation and possible impact on the predicted probability (i.e., gap between target class probability and maximum other class probability). A subset of these pixels is then manipulated by a fixed noise value $\delta$. In experiments, the attack is shown to be effective for CapsuleNetworks and other networks.


text:
## [0705.4311] The Likely Cause of the EGRET GeV Anomaly and its Implications

 Authors: F. W. Stecker, S. D. Hunter, D. A. Kniffen (NASA/GSFC) Abstract: Analysis of data from the EGRET gamma-ray detector on the Compton Gamma Ray Observatory indicated an anomaly in the form of an excess diffuse galactic flux at GeV energies over that which was theoretically predicted. Various explanations for this anomaly have been put forth, including the invocation of supersymmetric dark matter annihilation. We reexamine these explanations here, including a new discussion of the possible systematic errors in the sensitivity determination of the EGRET detector. We conclude that the most likely explanation of the EGRET GeV anomaly'' was an error in the estimation of the of the EGRET sensitivity at energies above ~1 GeV. We give reasons why such a situation could have occurred. We find evidence from our new all-sky analysis which is inconsistent with the assumption that the anomaly can be a signal of supersymmetric dark matter annihilation. We also reconfirm the original results of the EGRET team on the extragalactic gamma-ray background spectrum. There are important implications of our analysis for the upcoming Gamma Ray Large Area Telescope (GLAST) mission. [PDF]  [PS]  [BibTex]  [Bookmark]

Discussion related to specific recent arXiv papers
Syksy Rasanen
Posts: 119
Joined: March 02 2005
Affiliation: University of Helsinki

### [0705.4311] The Likely Cause of the EGRET GeV Anomaly and i

What do people familiar with the EGRET anomaly think of this paper? Is it indeed likely that it would be just a calibration error, as the authors claim?

Andy Strong
Posts: 5
Joined: June 17 2007
Affiliation: Max-Planck-Institut für extraterrestrische Physik
Contact:

### [0705.4311] The Likely Cause of the EGRET GeV Anomaly and

At present we really don't know for sure, but up to now it was always stated as unlikely by the instrumentalists. In this paper the view is taken that a particular diffuse emission model is reliable and hence EGRET can be renormalized to it. However no physical basis is given for the instrumental effect, as the authors admit. In fact a recent paper (0706.0503), which does an extensive Monte-Carlo of EGRET, actually finds the excess is underestimated. There are several astrophysical explanations - as referenced in their paper - including, plausibly, cosmic-ray spectra different from local in the Galaxy at large (while their's is based just on the local cosmic-ray spectrum). Another possibility is populations of unresolved sources (astro-ph/0609359). Still, with GLAST to be launched early next year, it is probably best just to wait and see. A more extensive discussion can be found at http://galprop.stanford.edu/forum/viewtopic.php?t=43 .


text:
Functiones et Approximatio Commentarii Mathematici

Primes in Certain Arithmetic Progressions

Abstract

We discuss to what extent Euclid's elementary proof of the infinitude of primes can be modified so as to show infinitude of primes in arithmetic progressions (Dirichlet's theorem). Murty had shown earlier that such proofs can exist if and only if the residue class (mod $k$) has order 1 or 2. After reviewing this work, we consider generalizations of this question to algebraic number fields.

Article information

Source
Funct. Approx. Comment. Math. Volume 35, Number 1 (2006), 249-259.

Dates
First available in Project Euclid: 16 December 2008

http://projecteuclid.org/euclid.facm/1229442627

Digital Object Identifier
doi:10.7169/facm/1229442627

Mathematical Reviews number (MathSciNet)
MR2271617

Zentralblatt MATH identifier
05784932

Citation

Murty, Ram; Thain, Nithum. Primes in Certain Arithmetic Progressions. Funct. Approx. Comment. Math. 35 (2006), no. 1, 249--259. doi:10.7169/facm/1229442627. http://projecteuclid.org/euclid.facm/1229442627.


text:
View Single Post
2020-03-11, 11:33   #1945
kar_bon

Mar 2006
Germany

54048 Posts

Quote:
 Originally Posted by Cruelty Solid 11 years This is quite "heavy" k.
It's quite more than 11 years now: I've included the primes found from the older primes thread with post links in the Wiki and your first found for k=25 was in 2006!

Last fiddled with by kar_bon on 2020-03-11 at 11:35


text:
# Operator theory

## Operator theory Topics

Sort by:

### Operator

An operator assigns to every function a function . It is therefore a mapping between two function spaces. If the range is on the real line or in the complex plane, the mapping is usually called a functional instead.

### Hermitian operator

A second-order linear Hermitian operator is an operator that satisfies(1)where denotes a complex conjugate. As shown in Sturm-Liouville theory, if is self-adjoint and satisfies the boundary conditions(2)then it is automatically Hermitian.Hermitian operators have real eigenvalues, orthogonal eigenfunctions, and the corresponding eigenfunctions form a complete biorthogonal system when is second-order and linear.Note that the concept of Hermitian operator is somewhat extended in quantum mechanics to operators that need be neither second-order differential nor real. Simply assuming that the boundary conditions give sufficiently strongly vanishing near infinity or have periodic behavior allows an operator to be Hermitian in this extended sense if(3)which is identical to the previous definition except that quantities have been extended to be complex (Arfken 1985, p. 506).In order to prove that eigenvalues must be..

### Operator extension

Let and be linear operators from domains and , respectively, into a Hilbert space . It is said that extends if and if for any vector .

### Cyclic vector

A vector on a Hilbert space is said to be cyclic if there exists some bounded linear operator on so that the set of orbitsis dense in . In this case, the operator is said to be a cyclic operator.

### Unitary

An operator satisfying (1)(2)where is the adjoint.

### Cyclic operator

A bounded linear operator on a Hilbert space is said to be cyclic if there exists some vector for which the set of orbitsis dense in . In this case, the vector is said to be a cyclic vector.

### Conjugate transpose

The conjugate transpose of an matrix is the matrix defined by(1)where denotes the transpose of the matrix and denotes the conjugate matrix. In all common spaces (i.e., separable Hilbert spaces), the conjugate and transpose operations commute, so(2)The symbol (where the "H" stands for "Hermitian") gives official recognition to the fact that for complex matrices, it is almost always the case that the combined operation of taking the transpose and complex conjugate arises in physical or computation contexts and virtually never the transpose in isolation (Strang 1988, pp. 220-221).The conjugate transpose of a matrix is implemented in the Wolfram Language as ConjugateTranspose[A].The conjugate transpose is also known as the adjoint matrix, adjugate matrix, Hermitian adjoint, or Hermitian transpose (Strang 1988, p. 221). Unfortunately, several different notations are in use as summarized in the..

### Closed operator

A linear operator from its domain into a Hilbert space is closed if for any sequence of vectors such that and as , it follows that and .

### Closable operator

A linear operator from its domain into a Hilbert space is closable if it has a closed extension where . Closable operators are sometimes called preclosed (Takesaki 1970), and the extension of is sometimes called the closure of .

### Antiunitary

An operator is said to be antiunitary if it satisfies:(1)(2)(3)where is the inner product and is the complex conjugate of .

### Separating vector

Given a subalgebra of the algebra of bounded linear transformations from a Hilbert space onto itself, the vector is a separating vector for if the only operator satisfying is the zero operator .

### Antilinear

An antilinear operator satisfies the following two properties:(1)(2)where is the complex conjugate of .

### Linear operator

An operator is said to be linear if, for every pair of functions and and scalar ,and


text:
Why use hooks?

The goal of pre-commit hooks is to improve the quality of commits. This is achieved by making sure your commits meet some (formal) requirements, e.g:

• that they comply to a certain coding style (with the hook style-files).

• that you commit derivatives such as README.md or .Rd files with their source instead of spreading them over multiple commits.

• and so on.

As all changes enter a repository history with a commit, we believe many checks should be performed at that point, and not only later on a CI service. For example, creating auto-commits at a CI service for styling code creates unnecessary extra commits, as styling can be checked at the time of committing and is relatively inexpensive.

Why use the pre-commit framework?

Implementing hooks in a framework such as pre-commit.com has multiple benefits compared to using simple bash scripts in .git/hooks:

• Easily use hooks other people have created, in bash, R, python and other languages. There are a wealth of useful hooks available, most listed here. For example, check-added-large-files prevents you from committing big files, other hooks validate json or yaml files and so on.

• No need to worry about dependencies, testing, different versions of hooks, file filtering for specific hooks etc. It’s all handled by pre-commit.

• Hooks are maintained in one place, and you just need a .pre-commit-config.yaml file. No need to c/p hooks from one project to another.

Have an idea for a hook? Please file an issue.


text:
skewNormal {EvidenceSynthesis} R Documentation

The skew normal function to approximate a log likelihood function

Description

The skew normal function to approximate a log likelihood function

Usage

skewNormal(x, mu, sigma, alpha)

Arguments

 x The log(hazard ratio) for which to approximate the log likelihood. mu The position parameter. sigma The scale parameter. alpha The skew parameter.

Details

The skew normal function. When alpha = 0 this function is the normal distribution.

Value

The approximate log likelihood for the given x.

References

Azzalini, A. (2013). The Skew-Normal and Related Families. Institute of Mathematical Statistics Monographs. Cambridge University Press.

Examples

skewNormal(x = 0:3, mu = 0, sigma = 1, alpha = 0)

[Package EvidenceSynthesis version 0.3.0 Index]


text:
7:56 AM
@JosephWright Seems a bit of mod attention is needed. tex.stackexchange.com/users/116472/amorris
Thanks

8:41 AM
Morning @DavidCarlisle

@JosephWright morning, hope you didn't mind my etex change;-)

@DavidCarlisle Enjoying the UK-TUG spam?

@JosephWright I shall be asking for money later:-)

@DavidCarlisle Did wonder

@JosephWright I think to support tex education we should get a pound per tick:-)

8:51 AM
Quakc. :)

9:04 AM
@PauloCereda Morning

@JosephWright Hi! :)

9:44 AM
@PauloCereda @JosephWright How was the meeting?

@egreg I did well, except the part I answered questions. :)

9:58 AM
@PauloCereda “Any questions?" says the chairperson. “I have one,” says an esteemed member of the audience, “When will you finish your thesis?”
6

@egreg LOL
@egreg I did mentioned my thesis. :)

@PauloCereda Assuming the esteemed member I'm referring to was not fast asleep.

@egreg :)

@PauloCereda along with Schrödinger's cat and other mythical objects

@DavidCarlisle awww you were watching! <3

10:01 AM
@DavidCarlisle Were there unicorns?

@egreg There was a beagle and Scooby Doo.

@egreg no but apparently the highlight of 30 years of tex contributions is a recursive macro to typeset x^{x^x} :(

@DavidCarlisle Indeed, the best you can provide.

@DavidCarlisle oh no
@David: @egreg was mentioned too!

@egreg apparently, but now at least after the last checkin to the latex sources, lualatex can keep up with my linguistic abilities

10:04 AM
@PauloCereda About forgotten %?

@egreg xpatch :)

@egreg l3 regex patch thing
-\def\newlanguage  {\e@alloc\language \chardef{\count19}\m@ne\@cclvi}
\let\newfam\new@mathgroup
+%    \end{macrocode}
+%
+% \changes{v2.3a}{2016/10/16}{Allow languages up to 16383 in luatex}
+%    \begin{macrocode}
+\ifx\directlua\@undefined
+  \def\newlanguage  {\e@alloc\language \chardef{\count19}\m@ne\@cclvi}
+\else
+  \def\newlanguage  {\e@alloc\language \chardef{\count19}\m@ne{16384}}
+\fi

@DavidCarlisle Still fewer languages than you master.

@egreg Tra cui l'italiano, naturalmente.

10:29 AM
First video (@PauloCereda's) uploaded: vimeo.com/187525063
I'm going to have to re-record my own one, but that should also be done today

10:50 AM
PANIC: unprotected error in call to Lua API ((null))
Aborted (core dumped)
@JosephWright ^^ :-)

@DavidCarlisle Ooops
@DavidCarlisle Run away?

@JosephWright actually it might be a documented feature
"Messing too much can push LuaTEX into panic mode."

11:13 AM
@PauloCereda At the 9:00 mark you could have written “This is not a dog” à la Magritte. ;-)

11:28 AM
The review comments are sometimes ridiculous. As a new user, i would probably be startled. tex.stackexchange.com/a/334331/37907

12:20 PM
@JosephWright oh no! :)
@egreg ooh :)
@egreg: there's a ragtime background sound. :)

well-[5]be-[100]ing baby-[5]sit-[100]ter bank-[5]roll carry-[5]all com-[100]mon-[5]place dish-[5]wa-[100]ter
@JosephWright ^^^ showhyphens with varying penalties:-)

@DavidCarlisle Oooh

@JosephWright I only made luatex dump core about 50 times (it's not very forgiving in this area:-)

@DavidCarlisle Odd that

12:48 PM
@PauloCereda Going a bit further; how many levels can you interpret this at? VVVV

1:45 PM
My talk's ready to upload, but the license I've got for the recording software seems to be not working :(
@DavidCarlisle, @StefanKottwitz, @PauloCereda Forgot to press 'record' actually during the meeting, so I've had to re-record!

@JosephWright faking records of meetings is probably a criminal offence

@DavidCarlisle Thanks a lot!

2:40 PM
@DavidCarlisle I am thinking about asking the committee for some cash to get a better set up (VGA capture, etc.)

@PauloCereda I just watched your talk. It was very good :-)

@DavidCarlisle Seen mails from Chris?

Hi @JosephWright. Any chance I could ask you a quick question about biblatex? Or anyone else? 😊

@AdamLiter You can ask ...

2:47 PM
It's about this comment:
Thanks for the help! I am not sure but should the behaviour of biblatex be regarded as a bug? — maetra Dec 29 '13 at 13:47

@JosephWright no, looking...

In authoryear-comp.cbx, the delimiter for citations from the same author with the same year is hard coded as a comma.
But this seems like what \compcitedelim is supposed to do, based on my understanding of the manual (which may well be wrong).

@AdamLiter Certainly \compcitedelim is there: I'd have to work on it a bit to be sure what exactly is 'expected'

But it is hard coded on line 36 of authoryear-comp.bx and on line 58 and on line 75 (and maybe others that I'm missing).
Do you think it's worth opening a bug report on GitHub? At the very least, it might help to clarify in the manual what \compcitedelim is supposed to do, if this is the intended behavior.

@AdamLiter Ah, the cases are different: a comma is forced when you get the 'a,b' business but not if you are compressing more complex situations

2:52 PM
Yes.
So \compcitedelim occurs between the same author but with different years.

@AdamLiter Yes

And you get \addcomma with the same author and the same year.
It just seems odd that that is hard coded.

@AdamLiter I think the argument is that a space or similar would be out-and-out misleading with the 'a,b' case

And the description of \compcitedelim in the manual is "Similar to \multicitedelim, but used by certain citation styles when ‘compressing’ multiple citations. The default definition is a comma plus an interword space."

@AdamLiter The labels are 'XXXXa' and 'XXXb' being compressed to 'XXXXa,b', so there is no logical place for a space

2:54 PM
@JosephWright That's a fair point, but it still seems odd that you cannot change it to a semicolon very easily, for example.

@JosephWright replied:-)

@DavidCarlisle :)

3:15 PM
I love the authors, they are sometimes "very clever". This attitude so annoys me.
Dear Tom,

I have made some observation while using your document class.

I noticed that I had some accented letters in the references of my document and so I need the \RequirePackage[utf8]{inputenc}, which I included for seamless typesetting.

I have included the following packages in your document class for improved typeseting of scientific articles:
\RequirePackage[version=4]{mhchem} for chemical symbols and equation
\RequirePackage{siunitx} for SI units
\RequirePackge{multirow} for float environment.
I mean, what the f%^&* he thinks he is?! Especially with multirow?!

Anybody interested in the wikibook and LaTeX is invited to leave an opinion. en.wikibooks.org/wiki/Talk:LaTeX/…

3:33 PM
@DavidCarlisle Trying to draft a reply to the latest team list mail ...

(sorry, I had to vent the anger so that my reply to his mail is not too rude)

@yo' Many people conflate 'what I do/think is useful' and 'what everyone needs'
3

@JosephWright ... and 'what is right'

Thanks for the help and discussion, @JosephWright. I appreciate it! I'm heading out. Hope everyone has a great day. :)

@JosephWright ptex....

3:41 PM
@DavidCarlisle Yes, but that's OK as there is e-pTeX

@JosephWright hmm, presumably there is a reason for having two versions (why isn't there an ejtex? i suppose we should ask...)

@DavidCarlisle I have a feeling the bit where it last went to CTAN about 1995 and isn't in TeX Live or MiKTeX might be a giveaway
@DavidCarlisle I see David K has put things in his own style

@JosephWright yes but If it's in Akira's builds I'd have thought it was pretty well maintened, or perhaps he just compiles teh source unseen

@DavidCarlisle You might enjoy JF's post to the EduTeX list today

@JosephWright :-)
@JosephWright I doubt it

3:46 PM
@DavidCarlisle That is true, and suggests there's a reason it's not in TeX Live (as he does the Win binaries)
> By nature, I might be more a visionary than a pragmatist.

draft of my reply (hope it's not too offensive):
Dear professor ABC,
thanks for your observations. However, packages used only by people from a specific scientific community shan't be included in a general class like this one. As for multirow, I consider its usage a deadly sin. As for inputenc, the class works without it for many people.

I would like to ask you not to distribute any modified copy of actapoly.cls.

Sincerely,

@yo' Not if you know LaTeX. I would be offended as well.
@yo' What you really should include is that one package only linguistics needs. Thought would be necessary.

@yo' “The choice of the packages automatically loaded by the class was well pondered and we decided not to include packages that only benefit a specific scientific community. For other packages the situation is different: we recommand, for stylistic reasons, not to use multirow; inputenc should instead always be a document-specific choice.”

@yo' Imho the main problem with inputenc would be that the class will no longer work for people who use another encoding.

@egreg Sounds good.

4:00 PM
@yo' On the other hand, I use to say that I've never seen a table using \multirow that cannot be improved by removing it to begin with.

@JosephWright Will the workshop talk Jonathan mentioned on Edutex be available as well? Can you ping me when it is available?

@egreg well, that why I use stronger language when speaking about multirow
@egreg another thing is, I try to limit the number of loaded packages to the bare minimum required to make the class work smoothly

4:19 PM
@Johannes_B I have the audio: I'll need to listen back and make a decision (@PauloCereda's talk is online, I'll do mine and @StefanKottwitz's during the week)

@JosephWright Take your time. I already watched @Paulo's talk. It was good.

@yo' That's taken care of by “well pondered”.

4:33 PM
@Johannes_B The discussion is quite easy for me to do: probably later today

@JosephWright not much of it was on topic though

@DavidCarlisle True
@DavidCarlisle Thought I stayed on-topic :)

4:57 PM
@yo' Yes, this is really the key. The class shouldn't load any packages that aren't required for providing the functionality of the class.
@egreg Too subtle... :)
@Johannes_B And the best one for that would be gb4e which makes _ and ^ active in text mode. Much fun will ensue.

@AlanMunn :-)

5:32 PM
@egreg ooh
@JosephWright oh no
@Johannes_B ooh <3

@PauloCereda Just need to sort out a Camtasia license to do the export (we have one at work but apparently it doesn't work with the latest release!)

@JosephWright Oh my!

@DavidCarlisle For once Chris is not the most opaque person on the list :)
@PauloCereda I might simply do it at work: on my desktop I have got it working

@JosephWright you can send a clarifying overview:-)

1 hour later…
6:46 PM
User pings me asking for help, i write a comment. Question is deleted while typing. That's new.

7:04 PM
@DavidCarlisle Not new anymore. And i didn't even read the messages. :-)

7:48 PM
The default page numbering in footer is like "125". But I want to make it "-125-". How to do that?

@manetsus it depends how you defined the footer, if using fancyhdr just define the foot to be ---\thepage---

@JosephWright Oh, in what context?

@DavidCarlisle how to do that? I just wrote \pagenumbering{Roman}.

@manetsus why don't you give any clues over what you have eg at the very least what document class you are using with \usepackage{fancyhdr} probably just \cfoot{---\thepage---}

@DavidCarlisle again I am sorry, I just forget this. \documentclass[a4paper,oneside,11pt]{report}

8:00 PM
@manetsus that should work then, see the fancyhdr package doc for more options

@DavidCarlisle unfortunately it is not working.

@manetsus you did something wrong then, but since only you have seen the code impossible to guess perhaps you are using plain style see section 7 the example there is
\fancypagestyle{plain}{%
\fancyhf{} % clear all header and footer fields
\fancyfoot[C]{\textbf{\thepage}} % except the center
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}}
but you just want ---\thepage--- not \textbf

@DavidCarlisle Thanks for the snippet. but it is working for some pages and for some other pages, it is not working. I added the snippet in preamble

8:15 PM
@manetsus aren't the pages where it doesn't work pages where chapters start? (just a guess, I can't even dig into the problem as I got to go)
night, everybody!

@yo' Actually it is working for pages where chapters started!

@manetsus well in that case it's because you have only defined the plain style (which is the default page style) but you are using a different page style on other pages, probably headings but why make us guess

@DavidCarlisle I see normal service with Chris is resumed

@manetsus naturally, David's code is changing plain-style, you should also change the fancy style for the other pages. And you should learn to show complete examples -- you will get better and faster solutions.

@UlrikeFischer \cleardoublepage\pagenumbering{arabic} could it change the plain-style?
or this '\setlength{\footskip}{28mm}
\setcounter{secnumdepth}{5}'?

8:25 PM
@manetsus I won't help you unless you give a complete example.

@manetsus what is the point of doing a gradual reveal? just make a small 6-line document that has the problem and ask a question on site with a complete example document

@DavidCarlisle okay, I understood. Thanks.
This has the same problem:
\documentclass[a4paper,oneside,11pt]{report}

\usepackage{fancyhdr}
\fancypagestyle{plain}{%
\fancyhf{} % clear all header and footer fields
\fancyfoot[C]{---\thepage---} % except the center
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}}
\usepackage{lipsum}

\begin{document}
\pagenumbering{gobble}
\lipsum[0]
\pagenumbering{Roman}
\addcontentsline{toc}{section}{Abstract}
\lipsum[1]
\newpage
\addcontentsline{toc}{section}{Acknowledgement}
\lipsum[2]

adding
\pagestyle{fancy}
\cfoot{---\thepage---}
@manetsus will put you on the right track, probably

@DavidCarlisle but it brings the chapter names etc in the header

8:43 PM
@manetsus You have to restate \pagestyle{plain}, so the style is updated to the new definition.
\documentclass[a4paper,oneside,11pt]{report}

\usepackage{fancyhdr}
\usepackage{lipsum}

\fancypagestyle{plain}{%
\fancyhf{}% clear all header and footer fields
\fancyfoot[C]{---\thepage---}% except the center
\renewcommand{\headrulewidth}{0pt}%
\renewcommand{\footrulewidth}{0pt}%
}
\pagestyle{plain}

\begin{document}
\pagenumbering{gobble}
\lipsum[0]
\clearpage
\pagenumbering{Roman}
\addcontentsline{toc}{section}{Abstract}
\lipsum[1]
\clearpage
\addcontentsline{toc}{section}{Acknowledgement}
@manetsus Remember to add \clearpage before any \pagenumbering command; in general \clearpage is better than \newpage.

@egreg oh, it works, thanks a lot for all of your effort.
@egreg could I safely remove \newpage adding \clearpage instead?

@manetsus You see, it needs someone who knows LaTeX.
@manetsus Yes, I changed all of them, I believe.

@egreg Obviously. I owed to you people a lot :)

@egreg who could that be?

@egreg the new one is bringing an extra "-" in pages where I did not start numbering. I meant gobble pages

8:55 PM
@manetsus Of course it will. In general I discourage \pagenumbering{gobble}. Just use \pagestyle{empty} for the part where you want nothing added and \pagenumbering{Alph} (which will keep hyperref happy, in case you load it).

@egreg do you know where this pagenumbering{gobble} comes from, i seem to see it all the time in examples?
@egreg That is I know where it's defined but there must be some tutorial suggesting it.

@egreg There are a lot of thing to learn from you people. Respect. It is working exactly as I wanted. I have no word to express thanks.
@DavidCarlisle I did it in march. So, I found the tutorial at that time.

@DavidCarlisle I happened to see it without really having seen it in guides.

@manetsus it's a trick definition that was never intended: it just works by accident due to details of the implementation,

9:13 PM
@DavidCarlisle I blame the Britons

Nov 26 '15 at 12:44, by Joseph Wright
@egreg Blame Robin
@egreg @manetsus "use the rather delightful \pagenumbering{gobble};" is UK english for I shouldn't be telling you to do this!!! :-)


text:
chapter 05 - 1 CHAPTER FIVE CONSUMER THEORY The consumer is one of the main economic decision-making units in an economy Consumer theory is an attempt

# chapter 05 - 1 CHAPTER FIVE CONSUMER THEORY The consumer is...

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CHAPTER FIVE CONSUMER THEORY The consumer is one of the main economic decision-making units in an economy. Consumer theory is an attempt to give an explanation of consumer’s behaviour when faced with the problem of choice, i.e. it is an explanation as to why the consumer chooses to spend his income as he does 1 . This chapter among other things will rationalise the downward sloping demand curve. Two theories have been advanced in an attempt to explain consumer’s behaviour; Cardinalist or Marginal Utility Approach Ordinal or Indifference Curve Approach A more recent theory is the theory of revealed preference None of these theories presents a complete picture of consumer’s behaviour. Definitions Utility : this is the satisfaction derived by a consumer from the consumption of a commodity 2 . Marginal Utility : this is that extra or additional utility derived from the consumption of one more unit of a commodity (the consumption of all other commodities held constant) Cardinalist (Marginal utility) approach This approach is based on the following assumptions Rationality The consumer 3 is assumed to be rational, i.e. he aims at maximising utility subject to his income and commodity prices. 4 Utility is measurable The utility from each commodity is measurable cardinally, i.e. using cardinal numbers. The unit of measurement can be in subjective units known as utils 5 or in monetary units, which 1 Blue print of consumers’ behaviour 2 Utility is subjective and thus different from usefulness. E.g. Drugs give the user some satisfaction but are harmful. 3 It is assumed also that the consumer has complete knowledge of all the relevant information to make decisions. I.e. he has complete knowledge of all commodities available, their prices and his income. 4 In reality subject also to other things, morals, legislation etc. rationality means use of reason. 5 Subjective because others in this case cannot verify this measurement unlike meters, Celsius etc 1
are more convenient i.e., the amount of money the consumer is willing to sacrifice for another unit of the commodity 6 Constant marginal utility of money The marginal utility of money 7 is assumed to be constant, and this is necessary if the monetary unit is used as a measure of utility. The essential feature of a standard unit of measure is that it be constant. Total utility Total utility of a basket (or combination) of goods depends on the quantities of individual commodities consumed. If there are n commodities in the basket with quantities q 1 , q 2 … q n the total utility is U = f (q 1 , q 2 …q n ) 8 Diminishing marginal utility Central to the Cardinalist theory is the axiom or hypothesis of diminishing marginal utility. To illustrate this hypothesis consider an individuals’ consumption of commodity X over a given period of time. The table below shows what happens to the consumer’s total utility and marginal utility (both measured in utils) as he consumes more and more units of the commodity during the week.

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• Fall '14
• kimond
• Utility


text:
How to use LaTex(1)

5 (100%) 1 vote

WHAT IS LATEX(1)

LaTex is a widely used tool for scientific documents, like mathematics, computer science, physics and so on. For us students, we may use it when we write some papers.  Latex uses Tex typesetting program for formatting its output, and is itself written in the TeX macro language.

How To Install Latex

Until now, Latex has lots of distributions, like TexLive for three platforms, CTex for windows and MaxTex for Mac. You can choose any distribution you like, just like choosing one distribution of Linux. I will show you the demo with TexLive

Then, choosing an editor. Ctex has a default editor WinEdt, and mac, TexShop. Here I will use TeXworks.

Starting TeXworks

It is quite simple, <Win> + R and enter texworks, and then enter again.

If it doesn’t show up, then you can go to the start menu or the path Tex System installed.

Once you start, you will see something like this.

By default, Texworks will use UTF8 coding. TeXworks provide lots of typesetting tools for us, like pdfTex, pdfLaTex, XeTex and so on. As we are beginners now, we can ignore this, and use pdfLaTex by default.

Try first

hello world!

In the editing area, we enter:

 1 2 3 4 5 \documentclass{article} \begin{document} Hello, world! \end{document}

After compilation, the result is:

It is easy to find that five lines of text entered in the edit box and only 1 lines are displayed in the final output PDF file. Now, let me explain these code.

A control sequence (or a command / tag) is included in the first line of \\documentclass{article} here. The so-called control sequence that begins with a backslash \, a string of text to end the first blank or non alphanumeric characters, they are not output, but they will affect the effect of the output document. The control sequence here is documentclass. The {article} behind it represents a necessary parameter for the control sequence, and the value of the parameter is article. The function of this control sequence is to call a document class named “article”.

Attention: LaTex is case sensitive when we are talking about control sequence.

The second line here begins with%. In the TeX style document, from “%” to the end of the line, all characters at the end of the line will be ignored by the TeX system, only as an annotation for human reading. So if you want print a ‘%’， then you should add a ‘\’, that is ‘\%’.

Then the control sequence begin appeared, and the control sequence always appeared in pairs. The two control sequences and their middle contents are called the “environment”; the first necessary parameters after them are always consistent and are called environmental names.

Only content in the “document” environment can be normally exported to a document or as a control sequence to influence the document. In other words, it is not valid to insert anything after \end{document}.

The part between the \begin{document} and the \documentclass{article} is called the introduction area. The control sequence in the introduction usually affects the entire output document.

Above is the basic information of LaTex.