A function $f$ between monoids is a homomorphism if $f$ preserves operations and the identity. Then, there is some function between monoids that preserves operations but does not preserve the identity. I've tried to get it thinking about $(\mathbb N,+)$, $(\mathbb N\backslash\{0\} ,\times)$ and other elementary monoids, but without success. Could someone help me with some hint? Thank you!
I have from Exercise 1 pg 33 - "Algebra - T. W. Hungerford" following:      Question to proof: Show by example that the first conclusione may be false if $G,\, H$ are monoids that are not group.   I thinked:     Proof: let be for example two monoids $(G:=\{\emptyset\}, \bot)$ and $(H:=\{\emptyset, \{\emptyset\}\}, \top)$ with: $$\begin{array}{c|c} \bot &amp; \emptyset \\ \hline \emptyset &amp; \emptyset \end{array} \, \, \, \,\, \,\, \,\, \,\, \,\, \,\, \,\, \,\, \, \begin{array}{c|cc} \top &amp; \emptyset &amp; \{\emptyset\}\\ \hline \emptyset &amp; \emptyset &amp; \emptyset \\ \{\emptyset\} &amp; \emptyset &amp; \{\emptyset\} \end{array}$$ $G$ with $e_G:=\emptyset$ like neutral element and $H$ with $e_H:=\{\emptyset\}$ like neutral element. Let be $f$ a function from $G$ to $H$ with $\emptyset \mapsto \emptyset$ (namely $x \mapsto x$), the function is Homomorphismus in fact $$ \begin{align} {\color{Red}f}{\color{Red}(}{\color{Red}x}{ \color{Red}\bot }{\color{Red}y}{\color{Red})}=&amp;f( \emptyset \bot \emptyset)= {\color{Green}f}{\color{Green}(}{\color{Green}\emptyset}{\color{Green})}= \emptyset \\ {\color{Red}f}{\color{Red}(}{\color{Red}x}{\color{Red})} {\color{Red}\top} {\color{Red}f}{\color{Red}(}{\color{Red}y}{\color{Red})}=&amp;f(\emptyset) \top f(\emptyset)= \emptyset \top \emptyset= \emptyset \\ &amp;\text{with }x,y \in G \end{align}$$ but it means that $$ \begin{align} f(e_G)&amp;\neq e_H \\f(e_G)={\color{Green}f}{\color{Green}(}{\color{Green}\emptyset}{\color{Green})}=\emptyset &amp;\neq \{\emptyset\}= e_H \end{align}$$ Therefore $f$ ist Semigroup-Hom but not Monoid-Hom...   Is it correct?
Java URL encoding of query string parameters Is it possible to switch from one area of graduate study to another in US universities? For example, suppose someone has enrolled in a computer science phd program. Can he switch over to math(or physics) phd program in the same school later?(or say from applied mathematics to pure mathematics?)  What are the steps for doing for doing that? I have to show by induction that this function is a multiple of 8. I have tried everything but I can only show that is multiple of 4, some hints? The function is $$5^{n+1}+2\cdot 3^n+1 \hspace{1cm}\forall n\ge 0$$, because it is a multiple of 8, you can say that$$5^{n+1}+2\cdot 3^n+1=8\cdot m \hspace{1cm}\forall m\in\mathbb{N}$$. How to update to the latest numpy and scipy on Ubuntu 14.04LTS On my Ubuntu 14.04LTS, for python3, I have   &gt;&gt;&gt; import numpy  &gt;&gt;&gt; import scipy  &gt;&gt;&gt; numpy.__version__  '1.8.2'  &gt;&gt;&gt; scipy.__version__  '0.13.3'   I want to update numpy and scipy to the most , I tried with the following commands  sudo pip3 install --upgrade numpy sudo pip3 install --upgrade scipy   both commands ran successfully, but the version numbers didn't change to 1.9.2 and 0.16.0 at all for both python packages (after restarting the computer). Anyone knows how to update to the most version? Thank you very much!! I have installed QGIS3 from the AUR package, as well as all optional dependencies:   However, when launching, I receive the following error:  Couldn't load plugin 'processing'   ModuleNotFoundError: No module named 'osgeo'  Traceback (most recent call last):   File "/usr/share/qgis/python/qgis/utils.py", line 311, in loadPlugin     __import__(packageName)   File "/usr/share/qgis/python/qgis/utils.py", line 664, in _import     mod = _builtin_import(name, globals, locals, fromlist, level)   File "/usr/share/qgis/python/plugins/processing/__init__.py", line 28, in      from processing.tools.dataobjects import *          # NOQA   File "/usr/share/qgis/python/qgis/utils.py", line 664, in _import     mod = _builtin_import(name, globals, locals, fromlist, level)   File "/usr/share/qgis/python/plugins/processing/tools/dataobjects.py", line 51, in      from processing.algs.gdal.GdalUtils import GdalUtils   File "/usr/share/qgis/python/qgis/utils.py", line 664, in _import     mod = _builtin_import(name, globals, locals, fromlist, level)   File "/usr/share/qgis/python/plugins/processing/algs/gdal/GdalUtils.py", line 35, in      from osgeo import gdal   File "/usr/share/qgis/python/qgis/utils.py", line 664, in _import     mod = _builtin_import(name, globals, locals, fromlist, level) ModuleNotFoundError: No module named 'osgeo'   Python version: 3.6.4 (default, Jan  5 2018, 02:35:40) [GCC 7.2.1 20171224]  QGIS version: 3.0.0-Girona Girona, exported   Python Path: /usr/share/qgis/python /home/thiago/.local/share/QGIS/QGIS3/profiles/default/python /home/thiago/.local/share/QGIS/QGIS3/profiles/default/python/plugins /usr/share/qgis/python/plugins /usr/lib/python36.zip /usr/lib/python3.6 /usr/lib/python3.6/lib-dynload /usr/lib/python3.6/site-packages /home/thiago/.local/share/QGIS/QGIS3/profiles/default/python   It seems to be a path issue, but I am not sure how to solve it. Pacman shows gdal and python-gdal both as installed. I tried sudo yum update but it just keeps java "1.7.0_75". I need 1.8 for it to work with another application but can't figure out how to upgrade it. Do I need to manually install it somehow? There's not much information on this on the internet as far as I can see. Specs:   java version "1.7.0_75" OpenJDK Runtime Environment (amzn-2.5.4.0.53.amzn1-x86_64 u75-b13) OpenJDK 64-Bit Server VM (build 24.75-b04, mixed mode)   When I try update now:     [ec2-________]$ sudo yum update Loaded plugins: priorities, update-motd, upgrade-helper amzn-main/latest                                         | 2.1 kB     00:00 amzn-updates/latest                                      | 2.3 kB     00:00 No packages marked for update   Is there anything else I need to do? Thanks. My Father passed away - next test(s) on what remains of his DNA sample? I posted this general question over at the forum on FamilyTreeDNA. Though I received a reply, there is still no answer to my question, so I thought I'd try my luck at posting here.  Anyhow, in early 2009 I bought two kits for the Genographic Project and dutifully had my father do his cheek swabs: one kit for his Y-Chromosome, and one for his mtDNA. Once that was completed, I had his samples transferred to Family Tree DNA.  Then, late in 2009 I paid to have an mtFullSequence done on his mtDNA sample.  My father passed away in 2015. In early 2016, I phoned FTNDA to discuss. The first thing they did was arrange to merge his two original samples into one kit. Then, they suggested doing Family Finder. I did that and recently obtained the interesting results.  So, all told what I have done on my father is:   Y-12 (originally done for the Genographic Project) mtFullSequence Family Finder   My father's Y Haplogroup is R-M269 and I am being presented with the M343 SNP pack on FTNDA.  My question is, what now? My father is gone so the sample that remains with FTDNA is old and finite (their customer service says they still have "one container" of his DNA). His siblings have all passed away -- unfortunately, with no samples taken. What is the best way to make use of the sample of my father's DNA that is left?  Should I refine the Y-Chromosome to Y-111? That seems the most natural (though I'm a male and carry it too). Should any SNP tests best be done on his remaining sample as opposed to on me? Or, should I do nothing and just let his 2009 samples continue to sit at FTDNA?  By phone, FTDNA said that they should have enough left to do the Y-111 and a SNP pack which is great, but I'd love to know independent of their customer service if that is the wisest way to make use of the remaining DNA sample which they have?  Full disclosure: I did have my father do 23andMe in 2010 and I did have his blood drawn and sent to a DNA Bank. I hope to never touch his banked DNA (except maybe to do a full sequence someday), but at least it does exist. My question now is solely how to best make use of my father's remaining sample at Family Tree DNA? I am trying to (partially) reproduce the algorithm displayed in Figure 4 from   My problem is with the multi-line conditions present in the "IFs". I want them to be indented, but \Indp does not seem to take effect if a new line \\ is not present in the same line.  This is what I tried:  \begin{algorithm}[htb]     \SetAlgoNoLine%     \SetNoFillComment     \SetKwIF{If}{ElseIf}{Else}{if}{:}{elif}{else:}{}%      \If{(SYNs from both hosts and \\             \Indp SYNs in earliest NFs of both hosts and \\             \Indp hosts' earliest packets differ)}{         Host with earliest NF is originator      }     \If{(SYN only from one host and \\         \Indp SYN is in connection's earliest NF)}{     Host is originator     }     \If{one host uses port 20 (ftp-data)}{     Host is originator     }     \If{only one host uses a well-known port}{     Host is responder     }     \If{start of hosts' first packets differ}{     Host with earliest NF is originator     }     Arbitrarily choose originator     \caption{Pseudo code for determining connection server side}     \label{algo:serverside2} \end{algorithm}   For instance, the line "SYNs in earliest NFs of both hosts and" is indented correctly, but "hosts' earliest packets differ" is not. How can I run Maniac Mansion through ScummVM? Day of the Tentacle Remastered Edition includes Maniac Mansion as a .  The game appears to be exactly the same as the old DOS release (albeit, the enhanced version).  If possible, how can I run this game through ScummVM?  Pointing ScummVM at my installed game doesn't work.  What do I need to do to play this version of Maniac Mansion? Big tilde in math mode Graphics horribly corrupted on Ubuntu 16.04 in VirtualBox, showing random strips of pixelated colors Is there a way (eg. a binary hack into Finder) to stop it from creating .DS-Stores on LOCAL Volumes?   I am using Leopard, therefore these don't work:    (requires Lion)  (requires Snow Leopard)   Also,  slows down my computer. A specified Include path is not valid. The EntityType does not declare a navigation property with the name * Can I publish without affiliation? In D&amp;D 5e &quot;&quot; is a condition that can affect a creature during the first round of combat, only until the end of their turn:  [... T]he GM compares the Dexterity (Stealth) checks of anyone Hiding with the passive Wisdom (Perception) score of each creature on the opposing side. Any character or monster that doesn’t notice a threat is surprised at the start of the encounter. If you’re surprised, you can’t move or take an action on your first turn of the combat, and you can’t take a reaction until that turn ends. A member of a group can be surprised even if the other members aren’t. - PHB 189  Does the action that causes the surprise count as part of the round, though? Say Renee, a rogue, achieves a stealth check of 22, easily beating an orc sentry's passive perception. She sneaks directly behind him and stabs him in the back. Surely the orc isn't surprised at all until the dagger hits him (or if Renee misses, she fumbles around behind him or something). What I think it really boils down to in the end is: when is initiative rolled? If (in our example) initiative is rolled before Renee's attack hits (or misses) how can we justify the orc recovering from his surprise before the action that triggered said surprise even occurs, should he roll better than Renee on his initiative? I'd like to go with initiative is rolled immediately following whatever event began the encounter (which could be an attack, but is likely to often be something else wherever surprise isn't intended), but I can't find any documentation to support this stance.  Why Does Anyone Care? There are many reasons you might want someone to be surprised while you're attacking - in this example if Renee is over L3 (and took the Assassin archetype) she'll get 'Assassinate' if the orc is surprised, and 'Death Strike' if she's over L17. That's a lot of potential extra damage!  that if the orc is surprised, Renee will be able to retreat and hide, without having to take the disengage action as her bonus action to avoid an attack of opportunity. Of course, there's no way for her to know whether the orc is surprised or not at that stage, so trying this would be a bit of a gamble... Add a note about downvoting on Meta Hello. I was trying to make a bootable flash drive from the startup disk creator, and when I went to erase the flash drive I accidentally erased the wrong drive, a 1TB removable drive. The operation took less than a second and gave no warning. I tried erasing the flash drive and it took about a minute, but it took but a second to erase the 1 TB drive, which is very surprising.  Please help, Gabriel Refused UK Visit visa for lack of sufficient funds - What more can I do? There were so many discussions about an Ubuntu with RR. They were so many pros and contras. At the end ubuntu wont be changed, the 6 month cycle system wont be changed. Thats fine!   But because there are so many people who would like to use an ubuntu with RR Im asking myself why isnt there an Ubuntu Derivate with RR. I couldnt found one, there are a loooot of Ubuntu Derivates but no RR. Is it just impossible? I mean Ubuntu = 6 months cycle, so the derivate have to be a 6 month cycle too? Is there no other option? Or are there already some smart guys trying to solve this problem? Thank you! "An SQL Server database schema" or "a SQL Server database schema"? Possible Duplicate:          I got the following sentence from the book I'm reading:     You can take a database-first approach   by first creating a SQL Server   database schema.   From what I learned, I think it should be "an SQL Server database schema", not "a SQL Server database schema". So which one is correct?