text:
Opened 9 years ago

Closed 5 years ago

## #6061 closed defect (worksforme)

Reported by: Owned by: glc.nwl@… aviram highest TicketChartsMacro blocker charts 0.11

Hi,

After copying TicketCharts.py to my project plugins directory, the plugin is NOT listed in Trac Webadmin plugins section.

• I'm running Trac 0.11.5
• restarted Apache
• when I saw this first problem, I didn't tried to go further in the setup process (didn't installed Open Flash Charts 2 and its version 2 python bindings yet)
• enabled in trac.ini with ticketcharts.* = enabled
• Already have AdvParseArgsPlugin and TicketStats plugins installed and both working fine.
• Couldn't find this kind of issue regarding your plugin on the web.

I guess that it should appear at least in WebAdmin plugin's page, even without OFC, and if I try to call the macro through a wiki page, I get the standard Trac error msg :

Error: Failed to load processor TicketChart

No macro or processor named 'TicketChart' found

So it seems that TicketCharts.py isn't taken at all by Trac

Any thoughts ?

I've recently installed about 10 plugins on Trac and this is the first that doesn't appear on Webadmin. As I'm still a little newbie on Unix, I'd prefer to first ensure that the plug-in is at least "recognized" and executed by Trac, before eventually spending some hours to install and setup Open Flash Charts for nothing (if the plugin still doesn't work after that).

So, if seems possible and logical for you to encounter this issue without having Open Flash Charts installed, just tell me, and I would give a try completing the whole setup process.

Could you help ? This would be nice, as your plugin should be perfect for my needs and I would really like to make it work.

### comment:2 Changed 9 years ago by glc.nwl@…

I confirm that after testing with the whole setup process even installing OpenFlash, nothing happens, your macro .py file isn't recognized nor processed by Trac.

I still have (on Trac 0.11.5) :

Error: Failed to load processor TicketChart

No macro or processor named 'TicketChart' found

With  ticketcharts.* = enabled in trac.ini

### comment:3 follow-up:  6 Changed 9 years ago by Lars Stavholm

Ran in to the exact same problem following those exact steps. The Trac log shows the following:

2009-11-27 12:28:31,091 Trac[loader] DEBUG: Loading file plugin TicketCharts from /usr/share/trac/plugins/TicketCharts.py
Traceback (most recent call last):
File "/usr/share/trac/plugins/TicketCharts.py", line 70, in <module>
import openFlashChart
ImportError: No module named openFlashChart

So, the conclusion is that you've got to install all the pieces, otherwise the plugin wont load.

### comment:4 Changed 9 years ago by Lars Stavholm

Turns out that the name is wrong.

class TicketChart(WikiMacroBase):

...should be:

class TicketChartMacro(WikiMacroBase):

Now the macro actually loads in my Trac page, no errors in the log, but still no chart.

### comment:5 Changed 9 years ago by Lars Stavholm

Finally, it works, and it looks absolutely astonishing!

Final tweaks:

http://whatever.host.com/trac
<proj-env>/htdocs
js
OFCDZ.swf

<proj-env>/conf/trac.ini
[ticket-charts]
js_dir = /trac/chrome/site/js
json_dir = /trac/chrome/site/js/json
ofc_file = /trac/chrome/site/OFCDZ.swf

### comment:6 in reply to:  3 ; follow-up:  7 Changed 9 years ago by wawulong@…

... So, the conclusion is that you've got to install all the pieces, otherwise the plugin wont load.

I have the same message, but I don't understand what you mean install all the pieces. Could you describe more details?!

### comment:7 in reply to:  6 ; follow-up:  9 Changed 9 years ago by Lars Stavholm

What I meant was that you should follow the instructions in the wiki about installing Open Flash Chart, AdvParse plugin, etc. That's the pieces.

### comment:8 Changed 8 years ago by Ricky

Hi,

In my trac instance, everything works except that it keeps "loading" data. Any idea why?

### comment:9 in reply to:  7 Changed 8 years ago by Ricky

What I meant was that you should follow the instructions in the wiki about installing Open Flash Chart, AdvParse plugin, etc. That's the pieces.

In my trac instance, everything works except that it keeps "loading" data. Any idea why?

### comment:10 Changed 8 years ago by Ryan J Ollos

Description: modified (diff)

#6267 may be related.

### comment:11 Changed 8 years ago by fimblo

Hi, has anyone gotten this to work on trac 0.11.1?

I'm encountering the same problems as YouLi, with the flash plugin displays the "Loading Data.." forever.

fyi:

• I'm running it under tracd.
• I can see that the js, js/json and open-flash-chart.swf files are loaded.
• I see that the python scripts are compiled and run.

Thanks

### comment:12 Changed 7 years ago by John Lee

Hi, I've got following error saying no module named cjson. Does this requires the prior installation of python-cjson library?

Thanks.

2011-03-17 10:13:49,704 Trac[loader] DEBUG: Loading tracadvparseargs.macro from c:\trac\test\plugins\tracadvparseargsplugin-0.4-py2.5.egg
Traceback (most recent call last):
File "c:\trac\test\plugins\TicketCharts.py", line 70, in <module>
import openFlashChart
File "C:\Program Files (x86)\VisualSVN Server\trac\python\lib\openFlashChart.py", line 17, in <module>
import	cjson
ImportError: No module named cjson

### comment:13 follow-up:  17 Changed 5 years ago by Ryan J Ollos

If OpenFlashCharts is not installed, you'll find an error such as the following in your log (see t:TracLogging for info on setting the log level to DEBUG):

01:06:46 AM Trac[loader] ERROR: Failed to load plugin from /home/user/Workspace/th6061/tracdev/plugins/TicketCharts.py:
Traceback (most recent call last):
File "/home/user/Workspace/th6061/tracdev/plugins/TicketCharts.py", line 70, in <module>
import openFlashChart
ImportError: No module named openFlashChart

wget http://downloads.sourceforge.net/project/openflashchart/open-flash-chart/Version%202%20Lug%20Wyrm%20Charmer/open-flash-chart-2-Lug-Wyrm-Charmer.zip

Following the advice in comment:5 I added to trac.ini:

[ticket-charts]
js_dir = /tracdev/chrome/site/js
json_dir = /tracdev/chrome/site/js/json
ofc_file = /tracdev/chrome/site/open-flash-chart.swf

where tracdev is the name of my Trac environment.

openFlashCharts.py depends on the cjson library. On Ubuntu,

sudo aptitude install python-cjson

or edit openFlashCharts.py to replace cjson with json.

Copy python-ofc-library-2 to lib/python2.7/site-packages and edit lib/python2.7/site-packages/easy_install.pth to add the following entry:

./python-ofc-library-2

Install advparseargsplugin.

Edit trac.ini:

[components]

Make sure that Shockwave flash is installed in your browser.

### comment:14 Changed 5 years ago by Ryan J Ollos

Resolution: → worksforme new → closed

### comment:15 Changed 5 years ago by Ryan J Ollos

Description: modified (diff)

### comment:16 Changed 5 years ago by Ryan J Ollos

It should be apparent from comment:13 that the plugin is too difficult to install. Ticket #11072. has been created to handle this.

### comment:17 in reply to:  13 Changed 5 years ago by Ivanelson Nunes

If OpenFlashCharts is not installed, you'll find an error such as the following in your log (see t:TracLogging for info on setting the log level to DEBUG): ...

Make sure that Shockwave flash is installed in your browser.

In my log does not appear this error. Even entered my dir <my trac-env>/plugins and >>did:

import TicketCharts

Without error. I do not understand why these settings:

[ticket-charts]
js_dir = /tracdev/chrome/site/js
json_dir = /tracdev/chrome/site/js/json
ofc_file = /tracdev/chrome/site/open-flash-chart.swf

I need to create these folders or do something related?

### comment:18 Changed 5 years ago by Ivanelson Nunes

I found(HttpNotFound) in my Trac log.

2013-05-13 17:48:52,322 Trac[main] WARNING: [200.ZZ.ZZ.ZZZ] HTTPNotFound: 404 Not Found (No handler matched request to /site/js/swfobject.js)

I've tried several ways:

[ticket-charts]
height = 300
js_dir = /site/js
json_dir = /site/js/json
ofc_file = /site/OFC.swf
width = 500

[ticket-charts]
height = 300
js_dir = /chrome/site/js
json_dir = /chrome/site/js/json
ofc_file = /chrome/site/OFC.swf
width = 500

[ticket-charts]
height = 300
js_dir = site/js
json_dir = site/js/json
ofc_file = /chrome/site/OFC.swf
width = 500

My dir <Env/plugins>:

bkp:/var/trac/projects/mybase/plugins$ls -l total 948 -rw-r--r-- 1 www-data www-data 47670 May 9 10:45 EstimationTools-0.4.6-py2.7.egg -rwxr-xr-x 1 www-data www-data 263109 May 13 15:06 OFCDZ.swf -rwxr-xr-x 1 www-data www-data 263109 May 13 15:05 OFC.swf -rwxr-xr-x 1 www-data www-data 263109 May 13 15:03 open-flash-chart.swf -rwxr-xr-x 1 www-data www-data 56035 Apr 23 18:15 SimpleMultiProject-0.0.3dev-py2.7.egg -rwxrwxrwx 1 www-data www-data 17722 May 13 14:13 TicketCharts.py -rw-r--r-- 1 www-data www-data 17501 May 13 14:14 TicketCharts.pyc -rw-r--r-- 1 www-data www-data 20626 Mar 18 18:32 TracSubTicketsPlugin-0.2.0.dev_20130318-py2.7.egg bkp:/var/trac/projects/mybase/plugins$

My dir Python packages:

bkp:/usr/local/lib/python2.7/site-packages\$ ls -l
total 32
-rw-r--r-- 1 root staff   990 May 13 15:23 easy-install.pth
-rw-r--r-- 1 root staff  4456 May 13 15:38 openFlashChart_elements.py
-rw-r--r-- 1 root staff  3627 May 13 15:38 openFlashChart.py
-rw-r--r-- 1 root staff 10587 May 13 15:38 openFlashChart_varieties.py
drwxr-sr-x 2 root staff  4096 May 13 13:42 python-ofc-library-2

### comment:19 follow-up:  20 Changed 5 years ago by Ryan J Ollos

Please standby and I'll push some changes shortly that will eliminate the need to deal with those settings on your end :)

### comment:20 in reply to:  19 ; follow-up:  21 Changed 5 years ago by Ivanelson Nunes

Please standby and I'll push some changes shortly that will eliminate the need to deal with those settings on your end :)

Sorry! I'm anxious. I'm going home. Later come back here.

### comment:21 in reply to:  20 Changed 5 years ago by Ryan J Ollos

Sorry! I'm anxious. I'm going home. Later come back here.

A new version has been pushed against #11072. The manual setup steps are eliminated. You only need to install an egg, using one of the methods described on t:TracPlugins.


text:
# Locally compact subspace is an intersection of an open and closed set

Let X be a locally compact topological space. I need to prove that if $M\subset X$ is a locally compact subspace of X then there exist $U,F\subset X$ such that U is open and F is closed, and $M=U\cap F$. It can be assumed that for every open $x\in V$ there exist an open subset U such that $x \in U \subset \overline U \subset V$ and $\overline U$ is compact.

My thoughts about the problem are that for every $x\in M$ and for every neighborhood $x\in V_x$ there exist an open neighborhood $U_x$ in M such that $x\in U_x\subset \overline U_x \subset V_x$ and $\overline U_x$ is compact and closed in M. So there exist an open subset $Z_x\subset X$ such that $U_x = Z_x\cap M$. I can take $U = \bigcup _{x\in M}Z_x$, then U is open in X, but i was having trouble finding the closed set F. I thought to take $F = \overline {\bigcup _{x\in M}U_x}$, that is closure in X. Now $M\subset U\cap F$, but I haven't succeeded in showing that $M\supset U\cap F$, maybe that's not even true.

Thanks!

Without assuming that $X$ is Hausdorff (and using the definition of local compactness given) the result is not true.

Let $X$ be any set with at least two elements, and consider the trivial (anti-discrete) topology on $X$. Clearly this space has the property that the nonempty open sets with compact closures form a base (indeed, there is only one nonempty open set, and it's closure is clearly compact), and so this space is locally compact. Note, too, that any nonempty proper $M \subseteq X$ is also locally compact (another anti-discrete space), but will not be the intersection of an open and a closed subset of $X$.

However, the result does follow if we assume that $X$ is Hausdorff. (Then local compactness is equivalent to every point having an open neighbourhood with compact closure.)

To wit: given $x \in M$, let $V_x$ be a neighbourhood of $x$ in $M$ such that $\mathrm{cl}_M ( V_x ) = \overline{V_x} \cap M$ is compact. Now $\overline{V_x} \cap M$ is also a compact subset of $X$, so by Hausdorffness $\overline{V_x} \cap M$ is closed (in $X$). Fix an open $W_x \subseteq X$ such that $W_x \cap M = V_x$. Clearly we have that $$\overline{ W_x \cap M } \cap M = \mathrm{cl}_M (V_x).$$ Note, now, that as $W_x \cap M \subseteq \overline{ W_x \cap M } \cap M$, we have that $$W_x \cap \overline{M} \subseteq \overline{ W_x \cap \overline{M} } = \overline{ W_x \cap M } \subseteq \overline{ W_x \cap M } \cap M \subseteq M,$$ (and clearly $x \in W_x \cap \overline{M}$).

Setting $U = \bigcup_{x \in M} W_x$, it follows that $U$ is open in $X$, and $M = U \cap \overline{M}$, as desired.

• I don't see how you got that $\overline{W_x\cap M}\subset\overline{W_x\cap M}\cap M$. How did you get that? – Anonymous Jul 25 '18 at 17:46

Let us assume that $X$ is a KC space, that is a space where all compact sets are closed (In particular, each Hausdorff space is KC). Then $M$, as a subspace, is also KC. Now it suffices if every point in $M$ has a compact neighborhood, as then we can assume that this compact neighborhood is the closure of some open neighborhood. With these hypotheses, let's show that $M$ is the intersection of an open and a closed subset of $X$:
Each $x\in M$ has an open neighborhood $N$ in $M$, whose closure relative to $M$ is compact and a subset of $M$. But that implies, as $X$ is KC, that this relative closure is closed in $X$, hence $$\overline N^M=\overline N\subseteq M$$ Since $N$ was open in $M$, there is an open $N'$ such that $N=M\cap N'$. Now $$\overline M∩N'=\overline{M∩N'}^{N'}=\overline N^{N'}=\overline N∩N'\subseteq M∩N'=N$$ This means that $N=\overline M∩N'$ is also a neighborhood of $x$ in $\overline M$. Since $x\in M$ was arbitrary, and $N\subseteq M$, this shows that $M$ is open in $\overline M$. In particular, $M$ is the intersection of some open set with $\overline M$.

Edit (06/12/2015): The proof becomes shorter using the notion of local closedness and assuming that you have proven that a locally closed subset is open in its own closure. Here a set $Y$ of a space is locally closed if each $y\in Y$ has a neighborhood $U$ such that $Y\cap U$ is closed in $U$.
Now if $Y$ is a locally compact subspace of the KC space $X$, then each $y\in Y$ has a neighborhood $K'$ in $X$ such that the relative neighborhood $K=Y\cap K'$ is compact. But that means that $Y\cap K'$ is closed, so $Y$ is locally closed.

format: plain


text:
Temperature Dependency on Conformational Sampling of 12-Crown-4 by Simulated Annealing

• Journal title : Journal of the Chosun Natural Science
• Volume 6, Issue 1,  2013, pp.8-11
• Publisher : The Research Institute of Chosun Natural Science
• DOI : 10.13160/ricns.2013.6.1.008
Title & Authors
Temperature Dependency on Conformational Sampling of 12-Crown-4 by Simulated Annealing
Gadhe, Changdev G.; Cho, Seung Joo;

Abstract
In this manuscript, we report a protocol to determine most of the lowest energy conformations from the ensemble of conformations. 12-crown-4 was taken as study compound to get the most of energy minima conformations. Molecular dynamic (MD) simulation for 1 nanosecond (ns) was performed at 300, 500, 700, 900 and 1100 K temperature. At particular interval conformations were sampled. Then Gaussian program was used to minimize compounds using PM6 energy levels. Duplicates were removed by checking energy as well as mirror image conformations, and only unique conformations were retained for the next $\small{6-31+G^*}$ level minimization. It was observed that upto certain increment in temperature the number of unique conformations were increased, but afterword it decreased.
Keywords
Molecular Dynamics;Simulated Annealing;Conformational Sampling;PM6;$\small{6-31^*}$;
Language
English
Cited by
References
1.
R. Elber and M. Karplus, "Enhanced sampling in molecular dynamics: use of the time-dependent Hartree approximation for a simulation of carbon monoxide diffusion through myoglobin", J. Am. Chem. Soc., Vol. 112, pp. 1961-1975, 1990.

2.
A. E. Garcia and K.Y. Sanbonmatsu, "Exploring the energy landscape of a beta hairpin in explicit solvent", Proteins, Vol. 42, pp. 345-354, 2001.

3.
K. Tai, "Conformational sampling for the impatient", Biophys. Chem., Vol. 107, pp. 213-220, 2004.

4.
R. E. Bruccoleri and M. Karplus, "Prediction of the folding of short polypeptide segments by uniform conformational sampling", Biopolymers, Vol. 26, pp. 137-168, 1987.

5.
M. Saunders, "Stochastic exploration of molecular mechanics energy surface: hunting for the global minimum", J. Am. Chem. Soc., Vol. 109, pp. 3150-3152, 1987.

6.
D. M. Ferguson and D. J. Raber, "A new approach to probing conformational space with molecular mechanics: random incremental pulse search", J. Am. Chem. Soc., Vol. 111, pp. 4371-4378, 1989.

7.
Z. Q. Li and H. A. Scheraga, "Monte-carlo-minimi-zation approach to the multiple-minima problem in protein folding", Proc. Natl. Acad. Sci. U. S. A. Vol. 84, pp. 6611-6615, 1987.

8.
S. H. R. SYBYL8.1; Tripos Inc., St. Louis, MO 63144 USA (2008).

9.
D. A. Case, T. A. Darden, T. E. Cheatham, III, C. L. Simmerling, J. Wang, R. E. Duke, R. Luo, R. C. Walker, W. Zhang, K. M. Merz, B. Roberts, S. Hayik, A. Roitberg, G. Seabra, J. Swails, A. W. Goetz, I. Kolossvary, K. F. Wong, F. Paesani, J. Vanicek, R. M. Wolf, J. Liu, X. Wu, S. R. Brozell, T. Steinbrecher, H. Gohlke, Q. Cai, X. Ye, J. Wang, M.-J. Hsieh, G. Cui, D. R. Roe, D. H. Mathews, M. G. Seetin, R. Salomon-Ferrer, C. Sagui, V. Babin, T. Luchko, S. Gusarov, A. Kovalenko, and P. A. Kollman, AMBER 12, University of California, San Francisco (2012).

10.
A. Jakalian, B. L. Bush, B. D. Jack, and C. I. Bayly, "Fast, efficient generation of high-quality atomic charges. AM1-BCC Model: I. Method", J. Comp. Chem., Vol. 21, pp. 132-146, 2000.

11.
J. Wang, R. M. Wolf, J. W. Caldwell, P. A. Kollman, and D. A. Case, "Development and testing of a general amber force field", J. Comp. Chem., Vol. 25, pp. 1157-1173, 2004.

12.
S. J. Cho, "Meaning and definition of partial charge", J. Chosun Natural Sci., Vol. 3, pp. 231-236, 2010.

13.
S. J. Cho, "Calculation and application of partial charge". J. Chosun Natural Sci., Vol. 3, pp. 226-230, 2010.


text:
# Consistent with this hypothesis is the observation of HLA-DR-positive microglial cells containing A in the vicinity of A-positive extracellular NFTs

Consistent with this hypothesis is the observation of HLA-DR-positive microglial cells containing A in the vicinity of A-positive extracellular NFTs. Caspase activation detected as caspase-cleaved fragments of tau (tau-CCP) may suggest that activation of apoptosis pathways may mediate cell death in DP, as has been reported for other tauopathies (Gamblin et al., 2003; Newman PJ 34 hydrochloride et al., 2005; Rissman et al., 2004). of glial tau inclusions (astrocytes and oligodendroglia). Cerebrovascular pathology was minimal with patchy amyloid angiopathy. Inflammation was another important feature, including microglial activation and significant C1q labeling of neurons, along with NFTs. TDP-43-positive pathology was also observed. Inflammation may be a key inciting as well as propagating feature of DP neuropathology. studies (Moseley, 2000; Scully et al., 1999; Spillane, 1962; Zhang et al., 2003,2006). Often there is scarring of the cerebellum and pronounced Purkinje cell loss (Corsellis et al., 1973). Significant loss of pigmented neurons in the substantia nigra may cause extrapyramidal motor indicators in affected subjects (Corsellis et al., 1973; Forstl et al., 2010). Basal forebrain cholinergic neurons are also affected (Uhl et al., 1982). The purpose of the current study EN-7 was to statement on an interesting DP patient who was thoroughly evaluated clinically and neuropathologically. Although severe concussions can cause permanent neurologic damage, in boxing the acute neurologic injury is usually more often transient (Forstl et al., 2010; Gavett et al., 2011; Heilbronner et al., 2009). On the other hand, repetitive concussive and subconcussive blows to the brain over many years have been identified as the primary cause of neurologic symptoms, and can occur many years and even decades after the individual has retired from boxing. While the exact mechanisms involved in the significant long-term delayed sequelae associated with sports-related CTE are poorly understood (DeKosky et al., 2010), the clinical presentation PJ 34 hydrochloride is consistent with a slowly progressive tauopathy (McKee et al., 2009). In the current study we focused on the frontal cortex, given the clinical signs, and comparisons were made with patients of similar age who had clinical features suggestive of FTD, but who proved pathologically PJ 34 hydrochloride to have Alzheimer’s disease (AD; imaging (Cagnin et al., 2004), and by immunohistochemistry (Arnold et al., 2000; Schofield et al., 2003). Microglial PJ 34 hydrochloride cell activation may result in the release of proinflammatory cytokines and chemokines and exacerbate neuronal dysfunction (Lucas et al., 2006; Nguyen et al., 2002). As a second marker for upregulation of the inflammatory cascade, we immunostained the brain of the DP case with anti-C1q antibodies. The complement (C) system is critically involved with humoral and cellular immunity and inflammatory responses, and has been implicated in several neurodegenerative diseases (van Beek et al., 2003). C1q was primarily neuronal in our case and seen on extracellular NFTs, in contrast to both neuronal- and plaque-associated C1q in the AD cases (Afagh et al., 1996; Fonseca et al., 2004). This may suggest that C1q may be increased in DP in response to the disruption of NFT-bearing neuronal membranes that may stimulate an immune response. A role for A accumulation on extracellular NFTs as another C1q activator is also possible, because in AD, fibrillary forms of A can bind and activate C1, the first component of the classical C pathway (Jiang, 1994; McGeer and Rogers, 1992; Webster, 1997). Complement-mediated generation of proinflammatory factors can initiate or induce the recruitment and activation of glial cells, which in turn may contribute to neuronal degeneration. Consistent with PJ 34 hydrochloride this hypothesis is the observation of HLA-DR-positive microglial cells containing A in the vicinity of A-positive extracellular NFTs. Caspase activation detected as caspase-cleaved fragments of tau (tau-CCP) may suggest that activation of apoptosis pathways may mediate cell death in DP, as has been reported for other tauopathies (Gamblin et al., 2003; Newman et al., 2005; Rissman et al., 2004). We extend previous reports of the accumulation of tau-CCP and a possible role in DP-associated neurodegeneration. We observed significant tau-CCP immunostaining in both the frontal cortex and hippocampus of our patient. Tau-CCP was preferentially distributed within NFT-bearing neurons, but was also observed on extracellular NFTs. In contrast.

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text:
Current Location:home > Detailed Browse

# Decipher the short-distance component of $X(3872)$ in $B_c$ decays

## Abstracts

 A foremost task in understanding the nature of the?X(3872)?involves the discrimination of the two-quark and multiquark configurations. In this work, we propose a method to probe the short-distance component of the?X(3872)?by measuring the ratio between the?Bc?semileptonic and nonleptonic decays into the?X(3872). We demonstrate that if the?X(3872)?production mechanism is through the?c?c?component, the ratios would be universal and could be reliably predicted in theory. Measurements of these ratios at LHC and the next-generation electron-positron colliders are capable of validating/invalidating this production mechanism and providing deeper insights into the nature of the?X(3872).
Keywords: short-distance ; X(3872);
Recommended references： Wei Wang,Qiang Zhao.(2016).Decipher the short-distance component of $X(3872)$ in $B_c$ decays.[ChinaXiv:201609.01052] (Click&Copy)
Version History
Related Paper


text:
### JEE Mains Previous Years Questions with Solutions

4.5
star star star star star
1

### AIEEE 2005

MCQ (Single Correct Answer)
A magnetic needle is kept in a non-uniform magnetic field. It experiences
A
neither a force nor a torque
B
a torque but not a force
C
a force but not a torque
D
a force and a torque

## Explanation

A magnetic needle kept in non uniform magnetic field experience a force and torque due to unequal forces acting on poles.
2

### AIEEE 2005

MCQ (Single Correct Answer)
Two concentric coils each of radius equal to $2$ $\pi$ $cm$ are placed at right angles to each other. $3$ ampere and $4$ ampere are the currents flowing in each coil respectively . The magnetic induction in Weber / ${m^2}$ at the center of the coils will be
$\left( {\mu = 4\pi \times {{10}^{ - 7}}Wb/A.m} \right)$
A
${10^{ - 5}}$
B
$12 \times {10^{ - 5}}$
C
$7 \times {10^{ - 5}}$
D
$5 \times {10^{ - 5}}$

## Explanation

The magnetic field due to circular coil $1$ and $2$ are

${B_1} = {{{\mu _0}{i_1}} \over {2r}} = {{{\mu _0}{i_1}} \over {2\left( {2\pi \times {{10}^{ - 2}}} \right)}}$

$= {{{\mu _0} \times 3 \times {{10}^2}} \over {4\pi }}$

${B_2} = {{{\mu _0}{i_2}} \over {2\left( {2\pi \times {{10}^{ - 2}}} \right)}} = {{{\mu _0} \times 4 \times {{10}^2}} \over {4\pi }}$

$B = \sqrt {B_1^2 + B_2^2} = {{{\mu _0}} \over {4\pi }}.5 \times {10^2}$

$\Rightarrow B = {10^{ - 7}} \times 5 \times {10^2}$

$\Rightarrow B = 5 \times {10^{ - 5}}\,Wb/{m^2}$
3

### AIEEE 2005

MCQ (Single Correct Answer)
Two thin, long, parallel wires, separated by a distance $'d'$ carry a current of $'i'$ $A$ in the same direction. They will
A
repel each other with a force of ${\mu _0}{i^2}/\left( {2\pi d} \right)$
B
attract each other with a force of ${\mu _0}{i^2}/\left( {2\pi d} \right)$
C
repel each other with a force $_0{i^2}/\left( {2\pi {d^2}} \right)$
D
attract each other with a force of ${\mu _0}{i^2}/\left( {2\pi {d^2}} \right)$

## Explanation

${F \over \ell } = {{{\mu _0}{i_1}} \over {2\pi d}} = {{{\mu _0}{i^2}} \over {2\pi d}}$

(attractive as current is in the same direction)
4

### AIEEE 2004

MCQ (Single Correct Answer)
The materials suitable for making electromagnets should have
A
high retentivity and low coercivity
B
low retentivity and low coercivity
C
high retentivity and high coercivity
D
low retentivity and high coercivity

## Explanation

NOTE : Electro magnet should be amenable to magnetization & demagnetization.

$\therefore$ retentivity should be low & coercivity should be low

### Joint Entrance Examination

JEE Advanced JEE Main

### Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE ME GATE PI GATE EE GATE CE GATE IN

NEET

Class 12


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# How can efficiently I edit my 2D tile-based maps?

I've been developing a very basic 2D tile-based game for my own experience. I read what must be hundreds of tutorials on what I found on Google with "tile based maps".

Almost every tutorial I see is an engine that reads a text file and loads tiles based on the numbers in the file, such as:

0,0,0,0
3,0,0,3
2,0,2,2
2,0,2,2

But what if I were making a map that contained several 100 tiles?

surely there's an easier way to make a map than by writing a ton of numbers into a text file? How can this be done quicker?

An idea I had was making the world a single layered image: A layer for the objects/sprites/characters and another on top of that for tiles that should be under you like walls, trees, etc.

Is this possible/worthwhile?

• Almost all tiled maps are created with special editors that let you "paint" with tiles as brushes, and have lots of built in helpers to make the job easier. There's definitely not a lot of writing text files except for very small test maps. Search google on "tile map editor" for a good overview and lots of examples of these kinds of editors! – Patrick Hughes Jun 19 '13 at 2:38
• thanks for your reply mate, yeah right now i'm currently using tiled. but most loaders i've looked at have very little explanation of how they work and i gave up figuring them out, right now i use Tiled to make the map, save it as a image and add it onto XNA.. that way i just use a single image as the entire map, ill be putting a grid over the top, add invisible collision tiles and then a layer on the top of that for eg top of trees and walls that the character goes under when moving over the top of the tile.. is this possible and/or a viable way of mapping? – kraze Jun 19 '13 at 2:50
• You seem to be concerned with the by the size of your text file. Don't, just have something working and see if there is anything to improve ( regardless though, your map size will always grow the bigger your level is ) – Sidar Jun 19 '13 at 7:13
• Your idea of the image is one that pops up often, and is useful, because if you do it right, you've instantly got the map for your game already coded! The catch is, that if you're writing pixel data with RGB values, then essentally all you're doing is saving a 6 digit hex number instead of a single "Index" number as you've been finding. The principle is identical, with many of the same hurdles. Both are useful. Most maps for 2D games are going to be one or more layers of ID numbers as you've found. You can shrink them using compression such as Run-length encoding or LZH or anything else. – Phil Jul 19 '13 at 11:48
• @kraze The image idea scales incredibly poorly. The maximum size of a texture is around 8k by 8k and most cards can only handle 2k by 2k. Whats wrong with saving it as a .tmx file and loading that in? bitbucket.org/vinull/xtiled – ClassicThunder Jul 19 '13 at 15:27


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Application Domains
New Software and Platforms
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Bibliography
 PDF e-Pub

## Section: Research Program

### Perspectives in Stochastic Analysis

#### Optimal transport and longtime behavior of Markov processes

The dissipation of general convex entropies for continuous time Markov processes can be described in terms of backward martingales with respect to the tail filtration. The relative entropy is the expected value of a backward submartingale. In the case of (non necessarily reversible) Markov diffusion processes, J. Fontbona and B. Jourdain [71] used Girsanov theory to explicit the Doob-Meyer decomposition of this submartingale. They deduced a stochastic analogue of the well known entropy dissipation formula, which is valid for general convex entropies, including the total variation distance. Under additional regularity assumptions, and using Itô's calculus and ideas of Arnold, Carlen and Ju [47], they obtained a new Bakry-Emery criterion which ensures exponential convergence of the entropy to 0. This criterion is non-intrinsic since it depends on the square root of the diffusion matrix, and cannot be written only in terms of the diffusion matrix itself. They provided examples where the classic Bakry Emery criterion fails, but their non-intrinsic criterion applies without modifying the law of the diffusion process.

With J. Corbetta, A. Alfonsi and B. Jourdain have studied the time derivative of the Wasserstein distance between the marginals of two Markov processes [11]. The Kantorovich duality leads to a natural candidate for this derivative. Up to the sign, it is the sum of the integrals with respect to each of the two marginals of the corresponding generator applied to the corresponding Kantorovich potential. For pure jump processes with bounded intensity of jumps, J. Corbetta, A. Alfonsi and B. Jourdain [41] proved that the evolution of the Wasserstein distance is actually given by this candidate. In dimension one, they showed that this remains true for Piecewise Deterministic Markov Processes. They applied the formula to estimate the exponential decrease rate of the Wasserstein distance between the marginals of two birth and death processes with the same generator in terms of the Wasserstein curvature.

#### Mean-field systems: modeling and control

- Mean-field limits of systems of interacting particles. In [77], B. Jourdain and his former PhD student J. Reygner have studied a mean-field version of rank-based models of equity markets such as the Atlas model introduced by Fernholz in the framework of Stochastic Portfolio Theory. They obtained an asymptotic description of the market when the number of companies grows to infinity. Then, they discussed the long-term capital distribution, recovering the Pareto-like shape of capital distribution curves usually derived from empirical studies, and providing a new description of the phase transition phenomenon observed by Chatterjee and Pal. They have also studied multitype sticky particle systems which can be obtained as vanishing noise limits of multitype rank-based diffusions (see [76]). Under a uniform strict hyperbolicity assumption on the characteristic fields, they constructed a multitype version of the sticky particle dynamics. In [78], they obtain the optimal rate of convergence as the number of particles grows to infinity of the approximate solutions to the diagonal hyperbolic system based on multitype sticky particles and on easy to compute time discretizations of these dynamics.

In [72], N. Fournier and B. Jourdain are interested in the two-dimensional Keller-Segel partial differential equation. This equation is a model for chemotaxis (and for Newtonian gravitational interaction).

- Mean field control and Stochastic Differential Games (SDGs).To handle situations where controls are chosen by several agents who interact in various ways, one may use the theory of Stochastic Differential Games (SDGs). Forward–Backward SDG and stochastic control under Model Uncertainty are studied in [84] by A. Sulem and B. Øksendal. Also of interest are large population games, where each player interacts with the average effect of the others and individually has negligible effect on the overall population. Such an interaction pattern may be modeled by mean field coupling and this leads to the study of mean-field stochastic control and related SDGs. A. Sulem, Y. Hu and B. Øksendal have studied singular mean field control problems and singular mean field two-players stochastic differential games [75]. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some assumptions, the optimality conditions for singular mean-field control are reduced to a reflected Skorohod problem. Applications to optimal irreversible investments under uncertainty have been investigated. Predictive mean-field equations as a model for prices influenced by beliefs about the future are studied in [86].

#### Stochastic control and optimal stopping (games) under nonlinear expectation

M.C. Quenez and A. Sulem have studied optimal stopping with nonlinear expectation ${ℰ}^{g}$ induced by a BSDE with jumps with nonlinear driver $g$ and irregular obstacle/payoff (see [83]). In particular, they characterize the value function as the solution of a reflected BSDE. This property is used in [67] to address American option pricing in markets with imperfections. The Markovian case is treated in [64] when the payoff function is continuous.

In [8], M.C. Quenez, A. Sulem and R. Dumitrescu study a combined optimal control/stopping problem under nonlinear expectation ${ℰ}^{g}$ in a Markovian framework when the terminal reward function is only Borelian. In this case, the value function $u$ associated with this problem is irregular in general. They establish a weak dynamic programming principle (DPP), from which they derive that the upper and lower semi-continuous envelopes of $u$ are the sub- and super- viscosity solution of an associated nonlinear Hamilton-Jacobi-Bellman variational inequality.

The problem of a generalized Dynkin game problem with nonlinear expectation ${ℰ}^{g}$ is addressed in [65]. Under Mokobodzki's condition, we establish the existence of a value function for this game, and characterize this value as the solution of a doubly reflected BSDE. The results of this work are used in [9] to solve the problem of game option pricing in markets with imperfections.

A generalized mixed game problem when the players have two actions: continuous control and stopping is studied in a Markovian framework in [66]. In this work, dynamic programming principles (DPP) are established: a strong DPP is proved in the case of a regular obstacle and a weak one in the irregular case. Using these DPPs, links with parabolic partial integro-differential Hamilton-Jacobi- Bellman variational inequalities with two obstacles are obtained.

With B. Øksendal and C. Fontana, A. Sulem has contributed on the issues of robust utility maximization [85], [86], and relations between information and performance [70].

#### Generalized Malliavin calculus

Vlad Bally has extended the stochastic differential calculus built by P. Malliavin which allows one to obtain integration by parts and associated regularity probability laws. In collaboration with L. Caramellino (Tor Vegata University, Roma), V. Bally has developed an abstract version of Malliavin calculus based on a splitting method (see [49]). It concerns random variables with law locally lower bounded by the Lebesgue measure (the so-called Doeblin's condition). Such random variables may be represented as a sum of a "smooth" random variable plus a rest. Based on this smooth part, he achieves a stochastic calculus which is inspired from Malliavin calculus [6]. An interesting application of such a calculus is to prove convergence for irregular test functions (total variation distance and more generally, distribution distance) in some more or less classical frameworks as the Central Limit Theorem, local versions of the CLT and moreover, general stochastic polynomials [53]. An exciting application concerns the number of roots of trigonometric polynomials with random coefficients [15]. Using Kac Rice lemma in this framework one comes back to a multidimensional CLT and employs Edgeworth expansions of order three for irregular test functions in order to study the mean and the variance of the number of roots. Another application concerns U statistics associated to polynomial functions. The techniques of generalized Malliavin calculus developed in [49] are applied in for the approximation of Markov processes (see [56] and [55]). On the other hand, using the classical Malliavin calculus, V. Bally in collaboration with L. Caramellino and P. Pigato studied some subtle phenomena related to diffusion processes, as short time behavior and estimates of tubes probabilities (see [51], [52], [50]).


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# JEE Novice - (23)

Algebra Level 3

$\large \begin{cases} \log_{30} 3 & = & a \\ \log_{30} 5 & = & b \\ \log_{30} 16 & = & ? \end{cases}$

Give your answer in terms of $a$ and $b$.

###### This question is a part of JEE Novices.
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• --Your father’s never visited to Hainan, __________ he?
--__________. How he wishes to go there again! A．has, Yes, he has.5 C8 h1 G.  I, c% Z B．is, Yes, he is9 h! f& ?; ?- b0 T# b C．hasn’t, No, he hasn’t./ f7 @4 _% Z- a D．has, No, he hasn’t.5 S: S3 _8 K; A0 A6 Y/ _

• 写出划线字母的音标
【小题1】wait /    /
【小题2】silk /    /
【小题3】snake /    /
【小题4】pink /    /
【小题5】light /   /
【小题6】change /    /
【小题7】yellow/   /
【小题8】usually /   /
【小题9】quiet /    /
【小题10】couch /    /

• 现代化的世界里,广告无处不在。有人喜欢广告,有人讨厌。请你来当评论家，谈谈自己的高见,说说广告的优点与不足。 (词数为80词左右。)

• 根据短文内容和所给汉语提示，写出短文空白处各单词的正确形式。每空限填一词。
At school many things happen to us. We may feel   1 （激动的）when we succeed in a school play. We may feel sorry if we lose an important   2 （比赛）. We want to keep the memory in our lives. How to keep memories? Our teacher, Mr. Smith, has taught us how to   3 （记住）things to make our own yearbook. A yearbook is a  4 （种） of book which is used to memory wonderful moments. It’s usually made at the end of year. Last  5 （十二月）, we began to make our yearbook.  6 (首先) we chose the persons that had done something   7 （特殊的）, then some   8  （学生） interviewed them, some   9 （写）down their stories, others took photos of them. Finally our teacher helped us to put the things   10 （一起）. Then we had our first yearbook.

• 同学们，经过多年的学习，你一定积累了很多良好学习方法，现请你介绍五种成功的学习方法。

• _____________ your grandfather live? He lives next to the library. A．What does3 H+ G$U9 j0 J B．How is 8 K& ?0 e9 C1 R6 h3 A C．Where does' A) \. I# @$ c4 h4 @9 T\$ F*  D．How old is6 ^+ O: X" ?& ^5 B5 E8 C4 J

• Now，please look at this picture．This girl is my sister．Her name is Sally! She is l3 years old．She is in Class Two，Grade Seven．This boy is aunt’s son．He is my cousin．His name is Jeff．He is an English boy．He is 12 years old．His mother is my aunt．My aunt and uncle are both teachers．This jacket is Jeff’s．Its color is black．You Can see a green pencil case，a blue notebook on the chair．My sister, Jeff and I and in the same school．
【小题1】How old is Sally?
【小题2】将划线部分句子译成汉语：
【小题3】What color is Jeff's jacket?
【小题4】Are Jeff’s mother and father teachers?
【小题5】Where are the green pencil case and the blue notebook?

• 根据所给汉语或英语首字母写出短文中所缺英语单词的正确形式。
Last week, my friends and I talked about the rules in our school. Here are some of our ideas.
At our school, we have to wear uniforms every 【小题1】d______. The problem is that all my classmates think the uniforms are 【小题2】丑的______.We think young people should【小题3】l______ smart and so we would like to wear our own clothes. Our teachers believe that if we did that, we would concentrate more on our clothes than our studies. We don’t【小题4】同意________.We would feel more comfortable and that is 【小题5】g______ for studying. If we can’t do that, we should be【小题6】允许__________to design our own uniforms. That would be a good way to keep both teachers and 【小题7】学生___________ happy.
Besides, vacations should be longer. At present they’re too【小题8】s______. Longer vacations would give us time to do things like volunteering. Last summer I had a(n) 【小题9】机会_________ to volunteer at the local hospital, 【小题10】b________ I couldn’t because I had to go back to school.

• My parents usually take a walk ______ dinner to keep healthy. A．at9 H7 Z8 O) C P9 c2 [% B B．of( N! i" I" Q! @+ W M. K C．during9 E9 ]* K& i( [' S D．after3 A% O% D( I% [" J+ H2 V

• Hobo, _____ wake me up ________ you finish building another house for me. A．doesn’t, until ' ?/ S; ?; i W; C B．not, till9 `3 V( G& K9 T) D) M( V C．don’t, until9 I4 e. g& g: H" L1 i% Q' c D．not, until" ?. ]) Y3 j( F E* K


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# Impedance of free space/wave impedance

1. Apr 15, 2010

### fluidistic

If I'm not wrong, empty space (vacuum) has the greatest impedance amongst any material. Because $$\eta = \frac{1}{n} \sqrt {\frac{\mu _0}{\epsilon}}$$ if I'm not wrong and n=1 (smallest value possible) for free space. What does this mean that free space has a big impedance? It makes the greatest opposition to electromagnetic waves? I'm not getting the meaning of impedance in this case.
P.S.: I've searched in wikipedia, also wave impedance but didn't find any explanation about the meaning of it.

2. Apr 15, 2010

### Antiphon

It is not always true. In a material with high mu but not very high epsilon, the impedance would be much higher.

Don't think of it as opposition, that's not correct. Think of it like this: the natural ratio of electric to magnetic fields for waves in that medium is the impedance. It's not a statement about the difficulty of the waves travels.

3. Apr 15, 2010

### fluidistic

Ok I trust you, although I've some doubt since n would/could be big in those materials? I'd appreciate if you have the name of at least 1 material whose impedance is greater than free space; if you don't, no need to lose your time searching this for me, I'll trust you anyway.
Ah ok, so I should only look at the mathematical definition. I wonder why they called this "impedance".

4. Apr 15, 2010

### Antiphon

Impedance is a close cousin to resistance. The names are motivated by the same concepts but impedance is a frequency domain quantity and is complex (R+iX) where the real part is the resistance.

5. Apr 15, 2010

### fluidistic

Ok so there's definitely a relation with the electrical impedance (which I was aware of). It's not obvious to me from the definition of the free space impedance.

6. Apr 15, 2010

### Antiphon

It is the same concept (and units) except for the definition. In a circuit it's the ratio of V to I at a point in a circuit. In the full field problem it's the ratio of certain components of the E and H fields.

A ferrite is an insulating material where mu can be hundreds of times greater than epsilon. These are used as cores in high frequency coils in circuits.

7. Apr 15, 2010

### fluidistic

Thanks once again for this reply.
Does it has any sense to talk about a refractive index in ferrite? I know light gets absorbed (and thus refracted?)/mostly reflected in metals. Although ferrite is a composed material, I think that some light can pass through the ferrite a small distance.
Anyway the refractive index appears in the definition of the impedance (in my class notes, but I didn't find it in wikipedia), hence my question.

8. Apr 15, 2010

### SpectraCat

Refractive index is also a complex quantity:

$$\tilde{n}=n + ik$$

where n is the real part of the refractive index (the "normal" one that we use e.g. in Snell's law), and k is the extinction coefficient, which becomes important when the material is absorbing radiation. This can be resonant absorption, as in a dielectric, or conduction band absorption, as in a semi-conducting or conducting material.

So yes, ferrite has an index of refraction, but the complex index is large, because it is absorbing. With regards to the wave impedance expression, I am fairly sure it is only the real part of the index of refraction that enters in, since that expression is for perfect dielectrics (so it would make sense to apply it to ferrite anyway).

9. Apr 15, 2010

### Antiphon

It is best defined in terms of complex epsilon and mu. The index of refraction is an incomplete description of a medium.

10. Apr 16, 2010

### fluidistic

Ok thanks to both, I get it. Very interesting.


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# American Institute of Mathematical Sciences

2016, 6(4): 413-435. doi: 10.3934/naco.2016018

## A POD projection method for large-scale algebraic Riccati equations

 1 Department of Aeronautics and Astronautics, Massachusetts Institute of Technology,Cambridge, MA 02139, United States 2 Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, United States

Received  February 2016 Revised  September 2016 Published  December 2016

The solution of large-scale matrix algebraic Riccati equations is important for instance in control design and model reduction and remains an active area of research. We consider a class of matrix algebraic Riccati equations (AREs) arising from a linear system along with a weighted inner product. This problem class often arises from a spatial discretization of a partial differential equation system. We propose a projection method to obtain low rank solutions of AREs based on simulations of linear systems coupled with proper orthogonal decomposition. The method can take advantage of existing (black box) simulation code to generate the projection matrices. We also develop new weighted norm residual computations and error bounds. We present numerical results demonstrating that the proposed approach can produce highly accurate approximate solutions. We also briefly discuss making the proposed approach completely data-based so that one can use existing simulation codes without accessing system matrices.
Citation: Boris Kramer, John R. Singler. A POD projection method for large-scale algebraic Riccati equations. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 413-435. doi: 10.3934/naco.2016018
##### References:

show all references

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Errett Bishop
Get Errett Bishop essential facts below. View Videos or join the Errett Bishop discussion. Add Errett Bishop to your PopFlock.com topic list for future reference or share this resource on social media.
Errett Bishop
Errett A. Bishop
BornJuly 14, 1928
DiedApril 14, 1983 (aged 54)
NationalityAmerican
Alma materUniversity of Chicago
Known forBishop set, Constructive analysis
Scientific career
FieldsMathematics
InstitutionsUniversity of California at San Diego

Errett Albert Bishop (July 14, 1928 - April 14, 1983)[1] was an American mathematician known for his work on analysis. He expanded constructive analysis in his 1967 Foundations of Constructive Analysis, where he proved most of the important theorems in real analysis by constructive methods.

## Life

Errett Bishop's father, Albert T. Bishop, graduated from the United States Military Academy at West Point, ending his career as professor of mathematics at Wichita State University in Kansas. Although he died when Errett was less than 4 years old, he influenced Errett's eventual career by the math texts he left behind, which is how Errett discovered mathematics. Errett grew up in Newton, Kansas. Errett and his sister were apparent math prodigies.

Bishop entered the University of Chicago in 1944, obtaining both the BS and MS in 1947. The doctoral studies he began in that year were interrupted by two years in the US Army, 1950-52, doing mathematical research at the National Bureau of Standards. He completed his Ph.D. in 1954 under Paul Halmos; his thesis was titled Spectral Theory for Operations on Banach Spaces.

Bishop taught at the University of California, 1954-65. He spent the 1964-65 academic year at the Miller Institute for Basic Research in Berkeley. He was a visiting scholar at the Institute for Advanced Study in 1961-62.[2] From 1965 until his death, he was professor at the University of California at San Diego.

## Work

Bishop's wide-ranging work falls into five categories:

1. Polynomial and rational approximation. Examples are extensions of Mergelyan's approximation theorem and the theorem of Frigyes Riesz and Marcel Riesz concerning measures on the unit circle orthogonal to polynomials.
2. The general theory of function algebras. Here Bishop worked on uniform algebras (commutative Banach algebras with unit whose norms are the spectral norms) proving results such as antisymmetric decomposition of a uniform algebra, the Bishop-DeLeeuw theorem, and the proof of existence of Jensen measures. Bishop wrote a 1965 survey "Uniform algebras," examining the interaction between the theory of uniform algebras and that of several complex variables.
3. Banach spaces and operator theory, the subject of his thesis. He introduced what is now called the Bishop condition, useful in the theory of decomposable operators.
4. The theory of functions of several complex variables. An example is his 1962 "Analyticity in certain Banach spaces." He proved important results in this area such as the biholomorphic embedding theorem for a Stein manifold as a closed submanifold in ${\displaystyle \mathbb {\mathbb {C} } ^{n}}$, and a new proof of Remmert's proper mapping theorem.
5. Constructive mathematics. Bishop became interested in foundational issues while at the Miller Institute. His now-famous Foundations of Constructive Analysis (1967)[3] aimed to show that a constructive treatment of analysis is feasible, something about which Weyl had been pessimistic. A 1985 revision, called Constructive Analysis, was completed with the assistance of Douglas Bridges.

In 1972, Bishop (with Henry Cheng) published Constructive Measure Theory. In the later part of his life Bishop was seen as the leading mathematician in the area of constructive mathematics. In 1966 he was invited to speak at the International Congress of Mathematics on constructive mathematics. His talk was titled "The Constructivisation of Abstract Mathematical Analysis."[4] The American mathematical society invited him to give four hour-long lectures as part of the Colloquium Lectures series. The title of his lectures was "Schizophrenia of Contemporary Mathematics." Robinson wrote of his work in constructive mathematics: "Even those who are not willing to accept Bishop's basic philosophy must be impressed with the great analytical power displayed in his work." (Warschawski 1985) Robinson wrote in his review of Bishop's book that Bishop's historical commentary is "more vigorous than accurate".

## Quotes

• (A) "Mathematics is common sense";
• (B) "Do not ask whether a statement is true until you know what it means";
• (C) "A proof is any completely convincing argument";
• (D) "Meaningful distinctions deserve to be preserved".
(Items A through D are principles of constructivism from his Schizophrenia in Contemporary Mathematics. American Mathematical Society. 1973. (Reprinted in Rosenblatt 1985.)
• "The primary concern of mathematics is number, and this means the positive integers. . . . In the words of Kronecker, the positive integers were created by God. Kronecker would have expressed it even better if he had said that the positive integers were created by God for the benefit of man (and other finite beings). Mathematics belongs to man, not to God. We are not interested in properties of the positive integers that have no descriptive meaning for finite man. When a man proves a positive integer to exist, he should show how to find it. If God has mathematics of his own that needs to be done, let him do it himself." (Bishop 1967, Chapter 1, A Constructivist Manifesto, page 2)
• "We are not contending that idealistic mathematics is worthless from the constructive point of view. This would be as silly as contending that unrigorous mathematics is worthless from the classical point of view. Every theorem proved with idealistic methods presents a challenge: to find a constructive version, and to give it a constructive proof." (Bishop 1967, Preface, page x)
• "Theorem 1 is the famous theorem of Cantor, that the real numbers are uncountable. The proof is essentially Cantor's 'diagonal' proof. Both Cantor's theorem and his method of proof are of great importance." (Bishop 1967, Chapter 2, Calculus and the Real Numbers, page 25)
• "The real numbers, for certain purposes, are too thin. Many beautiful phenomena become fully visible only when the complex numbers are brought to the fore." (Bishop 1967, Chapter 5, Complex Analysis, page 113)
• "It is clear that many of the results in this book could be programmed for a computer, by some such procedure as that indicated above. In particular, it is likely that most of the results of Chaps. 2, 4, 5, 9, 10, and 11 could be presented as computer programs. As an example, a complete separable metric space X can be described by a sequence of real numbers, and therefore by a sequence of integers, simply by listing the distances between each pair of elements of a given countable dense set. . . . As written, this book is person-oriented rather than computer-oriented. It would be of great interest to have a computer-oriented version." (Bishop 1967, Appendix B, Aspects of Constructive Truth, pages 356 and 357)
• "Very possibly classical mathematics will cease to exist as an independent discipline" (Bishop, 1970, p. 54)
• "Brouwer's criticisms of classical mathematics were concerned with what I shall refer to as 'the debasement of meaning'" (Bishop in Rosenblatt, 1985, p. 1)

## Notes

1. ^ UCSD Obituary
2. ^ Institute for Advanced Study: A Community of Scholars
3. ^ Stolzenberg, Gabriel (1970). "Review: Errett Bishop, Foundations of Constructive Analysis". Bull. Amer. Math. Soc. 76 (2): 301-323. doi:10.1090/s0002-9904-1970-12455-7.
4. ^ Bishop, Errett. "The constructivization of abstract mathematical analysis" (PDF). International Mathematical Union. Retrieved 2017.

## References

• Bishop, Errett 1967. Foundations of Constructive Analysis, New York: Academic Press. ISBN 4-87187-714-0
• Bishop, Errett and Douglas Bridges, 1985. Constructive Analysis. New York: Springer. ISBN 0-387-15066-8.
• Bishop, Errett (1970) Mathematics as a numerical language. 1970 Intuitionism and Proof Theory (Proc. Conf., Buffalo, N.Y., 1968) pp. 53-71. North-Holland, Amsterdam.
• Bishop, E. (1985) Schizophrenia in contemporary mathematics. In Errett Bishop: reflections on him and his research (San Diego, Calif., 1983), 1-32, Contemp. Math. 39, Amer. Math. Soc., Providence, RI.
• Bridges, Douglas, "Constructive Mathematics", The Stanford Encyclopedia of Philosophy (Winter 2004 Edition), Edward N. Zalta (ed.), [1] - Online article by Douglas Bridges, a collaborator of Bishop.
• Rosenblatt, M., ed., 1985. Errett Bishop: Reflections on him and his research. Proceedings of the memorial meeting for Errett Bishop held at the University of California-San Diego, September 24, 1983. Contemporary Mathematics 39. AMS.
• Warschawski, S., "Errett Bishop - In Memoriam", in Rosenblatt, M. (ed.), Errett Bishop: Reflections on him and his research, Contemporary Mathematics, 39, American Mathematical Society
• Schechter, Eric 1997. Handbook of Analysis and its Foundations. New York: Academic Press. ISBN 0-12-622760-8 -- Constructive ideas in analysis, cites Bishop.

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