Is As per our discussion, ... and As per your instructions, ... wrong, and are they poor grammatical constructions?  As per our conversation, I will tender my resignation on Friday.  Per our conversation, I will tender my resignation on Friday.  Do I use Per or As per in these constructions, or is neither preferred? If neither, what are viable, concise substitutes?
I've read and have heard of both 'as per' and 'per' being used conversationally, both with the same connotation of either 'according to' or 'on authority of'  Examples:  "Tell Ron to start molding new rollers for the mecanum wheels, as per me"  "Per Mr. Crane, you need to start the molds for the new rollers."  They both establish the same context by setting that something should be done on the authority of someone else (or the speaker, per the first example (see what I did there?)). Or it acts as a way to cite a source of a statement, directive or fact in conversational speech.  My question is, what is, if any, the functional and syntactical difference between as per and per. If there are no differences, which is apropos to use?
Conditionals in English are usually formed by using if with normal word order; but for the three past (subjunctive) forms were, should, and had, it is also possible to express the conditional through subject–auxiliary inversion alone, with no if in the conditional clause.  Does forming conditionals in this manner differ semantically from if-conditionals? Is some aspect of the conditional statement or the conditionality emphasised more in one version than in the other? Or are there differences in how and when they are used? Or are they simply completely interchangeable?  For example:     If I were you, I would try it again   Were I you, I would try it again      If I had seen it, I would have told you   Had I seen it, I would have told you      If you should drink, don’t get behind the wheel   Should you drink, don’t get behind the wheel Proving replacement theorem? I want to see if I am understanding the proof of the replacement theorem correctly.   Let $V$ be a vector space that is spanned by a set $G$ containing $n$ vectors.  Let $L \subseteq V$ be a linearly independent subset containing $m$ vectors.  Then $m\leq n$ and there exists a subset H of G containing exactly $n-m$ vectors s.t. $L \cup H$ generates $V$.   The proof in the book says to start with $m=0$. In that case $L=\varnothing$, the empty set.        Let's assume this theorem is true for some integer $m \geq 0$.   Let $L = \{v_j\}_{j=1}^{m+1}$ and define it as a linearly independent subset of $V$ consisting of $m+1$ vectors.  Since any subset of a linearly independent set is linearly independent as well ($S_1 \subseteq S_2 \subseteq V$), then $\{v_j\}_{j=1}^m$ is linearly independent also.   It then says to use the induction hypothesis to say that $m \geq n$. Well, ok, but that seems sort of pulled out of nowhere to me. The next step is to say that there is therefore another subset, $\{u_k\}_{k=1}^{n-m}$ of G such that $\{v_j\}_{j=1}^m \cup \{u_k\}_{k=1}^{n-m}$ spans $V$.   That being the case there are scalars $(a_j)_{j=1}^m$ and $(b_k)_{k=1}^{n-m}$ which you can multiply by the vectors $v_j$ and $u_k$. You can then add the two sets of vectors, yielding $$\sum_{j=1}^m a_j v_j + \sum_{k=1}^{n-m} b_k u_k = v_{m+1}$$  At this point I am not sure I understand things. Because we are assuming $n-m&gt;0$ -- otherwise $v_{m+1}$ is linearly dependent. But then it says not only is $n&gt;m $ but $n&gt;m+1$, and that is where I am losing the plot to get to the next step. Let $T$ and $T^{'}$ be topologies on set $X$ such that $T \leq T^{'}$. If $(X,T^{'})$ is path-connected, is $(X,T)$ path connected? Let $T$ and $T^{'}$ be topologies on set $X$ such that $T \leq T^{'}$. If $(X,T^{'})$ is path-connected, is $(X,T)$ path-connected?  I think it is, and I tried to prove it by contradiction, but I got stuck. Any hint helps! Legend in tikzpicture How to get from Nice to Monaco by public transport? What's the simplest and cheapest way to get from central Nice, France to Monaco by public transportation? Let $b>0.$ Evaluate $\lim_{n \to \infty} \int^{b}_{0} \frac{\sin nx}{nx}dx$ I'm stumped at the last part of this problem. Could anyone advise, please? Thank you.  Here is  my  proof.   Define  $f: \mathbb{R} \to \mathbb{R}$ by $$ f(x) = \left\{\begin{aligned} &amp;\frac{\sin nx}{nx}&amp;&amp;, x \neq0 \\ &amp;1 &amp;&amp;, x=0 \end{aligned} \right.$$   Hence, $$f(x) = \sum^{\infty}_{k=0}(-1)^k\frac{(nx)^{2k}}{(2k+1)!} , \forall x \in \mathbb{R} \mbox{ and } f \in {\mathscr R[0,b]}.$$  $$\int^{b}_{0} \frac{\sin nx}{nx}dx = \int^{b}_{0}f(x)dx=\sum^{\infty}_{k=0}\int^{b}_{0}(-1)^k\frac{(nx)^{2k}}{(2k+1)!}dx= \sum^{\infty}_{n=0}(-1)^k\frac{(n)^{2k}b^{2k+1}}{(2k+1)(2k+1)!}$$  $$\lim_{n \to \infty} \sum^{\infty}_{k=0}(-1)^k\frac{(n)^{2k}b^{2k+1}}{(2k+1)(2k+1)!}=  ?$$ How to determine the size of a package while using apt prior to downloading? When using apt-get install &lt;package_name&gt;, and there are dependencies that need to be downloaded, the terminal outputs names of additional packages and total size, and asks for confirmation before downloading.   But, when dependencies are satisfied and nothing but the named package needs to be downloaded there is no size output and no confirmation.  When using Synaptic, I can see the total size that new packages that will use after installation but no way to see the size that needs to be downloaded, except to go from package to package and use properties to see the compressed size.  I would like to know if there is a way to see the size of a package(s) in terminal and Synaptic prior to downloading and installing it/them? Mcrypt extension is missing in 14.04 server for mysql The php mcrypt extension on ubuntu 14.04 shows that it is installed properly, but phpmyadmin says:   The mcrypt extension is missing. Please check your PHP configuration.   My current php config is . If you need anymore information, please contact me through the comments.  $ sudo apt-get install php5-mcrypt     Reading package lists... Done     Building dependency tree            Reading state information... Done     php5-mcrypt is already the newest version.     0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. Filter bibliography by author? I would like to create a template for a publication list that can then be used by several people. The idea is that there is one bib-file which contains all of the publications. Peer-reviewed entries are marked with the keyword = pr. Then there is the master-file of the type scriptreport in which everyone can integrate their chapter-file in order to merge the publication lists of everybody into one file. The chapter file is the core of everything and should be reusable. It should filter out the entries for the respective author from the bib file and print them out in two lists (peer-reviewed and non-peer-reviewed). My problem is that I don't really know how to filter by author in this case. Here are the rough codes of the two files: Master: \documentclass[a4paper]{scrreprt}  \usepackage{biblatex}  \title{Publication list}  \addbibresource{sample.bib}  \begin{document}     \maketitle          \tableofcontents     \newpage          \include{Researcher}     \newpage \end{document}  chapter: \chapter*{Researcher} \addcontentsline{toc}{chapter}{Researcher}          \nocite{*}     \printbibliography[keyword={pr}, title={Peer-reviewed}]          \nocite{*}     \printbibliography[notkeyword={pr}, title={Non-peer-reviewed}] Fatou's lemma and measurable sets I don't know how can I imply Fatou's lemma for any measurable sets $A_k$, that is, $$\lambda(\liminf A_k)\le\liminf\lambda(A_k).$$ How can I prove it? And is there any example in $\mathbb R$ of sequence of measurable sets $A_k$ such that $A_k\subset[0,1]$, $\lim\lambda(A_k)=1$, but $\liminf A_k=\varnothing$ ? Thanks for your help! Does a shortcode with a single attribute have to use an array? I want to build a shortcode that takes a single attribute.  Everything online is telling me to make it using an array:  // Add Shortcode function bg_comparison_points_shortcode( $atts ) {     // Attributes     $atts = shortcode_atts(         array(             'custom_field' =&gt; '',         ),         $atts,         'comparison_points'     );     return bg_calculate_points($custom_field); } add_shortcode( 'comparison_points', 'bg_comparison_points_shortcode' );   But in my mind something like this would be much simpler  // Add Shortcode function bg_comparison_points_shortcode( $custom_field ) {     return bg_calculate_points($custom_field); } add_shortcode( 'comparison_points', 'bg_comparison_points_shortcode' );   Is there a problem doing this simpler version? No such file or directory but I can see it! I'm trying to run a python script, on a headless Raspberry PI using winSCP and get the following error message:  Command '"./areadetect_movie_21.py"' failed with return code 127 and error message /usr/bin/env: python : No such file or directory.   When I try and run from terminal, I get:  : No such file or directory.   I try a similar python script, in the same directory, with the same python shebang, the same permissions and using the same user pi, and it works.  I also do a ls and I can see the file, so I don't know why it will not run. Compile Views in ASP.NET MVC Please stop bounties from turning off community moderation Possible Duplicate:                tl;dr: Please get rid of "This question has an open bounty and cannot be closed"  Questions with bounties on them can't be closed:    This is by design, and the recommended course of action is to flag for moderator attention, at which point they'll decide whether to refund the bounty and close the question or not.   But why should a bounty disable regular community moderation?  We should be able to cast close votes on bountied questions as usual, and if a question gets enough, the bounty's refunded and the question closed.  An obvious benefit would be reduced burden on moderators, but I doubt that this is really a significant part of their workload.  More important is allowing the entire community's wisdom to be brought to bear.  Consider this question:      Having a simple MFC application with web browser controller that navigates to some site and then to another one on and on.      Using a powerfull machine (16 cores and lots of memory) OS is Server 2008 R2. I can see when launching my app over 30 instances I'm getting the OS UI (each window including my app, mspaint, taskmgr etc..) become very sluggish and slow.      I have monitored the machine resources (CPU, memory and GDI objects) but it seems that all of them are not even close to be in some level of stress.      What is the problematic resource that influence the machine in such way?      10x, Guy   It doesn't look like a good question: somewhat poorly written, vague, not a ton of information, etc.  I would vote to close this question.  However, I don't do much work with MFC and maybe there's something I'm missing.  (I can readily imagine a similarly bad looking question with the extremely concrete answer: .)  I'm comfortable casting a vote to close, not closing unilaterally.  Flagging for a moderator just passes the buck to them, when the correct action is letting the community weigh in. When trying to deploy the converted metadata using VS code sfdx force:mdapi:deploy deploy to my Production Org and I get the error Property 'itemInstances' not valid in version 48.0 and Property 'processOrder' not valid in version 48.0. But when I go to Developer Console and open a class, even though it says 48.0, I have the option to select 49.0, so I am assuming I have 49.0. Yet I get this error. Pretty much all my classes, trigger and components are version 48.0, but I am not sure how that affects flexipages and Approval processes. Why do airplanes experience negligible Coriolis force while bullets experience the Coriolis force in long range shooting, even though the mass of airplane is much bigger than a bullet? By default  indents with a hard tab character. How do I change it to spaces? How would one write object-oriented code in C? I am recording videos on iPhone and uploading them to my Linux server. Users can see these videos on website. If users are seeing videos on mac or iDevices the video is looking fine but when users are seeing that video on windows systems these videos are getting rotated.   I am assuming this is because of some apple's flag in the recorded video which Windows systems are not able to read. Can I record videos in some way so they don't get rotated on Windows systems? Or is there any way I can re-encode videos with proper interface orientation using FFmpeg?  I am open to both FFmpeg or iOS way. What hash is concatenating with the data to be signed in TLS 1.3 CertificateVerify message? According to specification, to create data that will be signed with server private key for CertificateVerify message, we need to concatenate 64 space characters, the string &quot;TLS 1.3, server CertificateVerify&quot;, null and the hash of all handshake messages to this point. During the handshake process, we choosing the cipher suite and signature scheme... So, if the cipher suite is, for example, TLS_AES_256_GCM_SHA384 and the signature scheme is rsa_pss_rsae_sha256 (different hash algorithms), hash of which algorithm should be used as handshake hash in data to sign, SHA-384 or SHA-256?