# on 10-Dec-2023 (Sun)

#### Flashcard 7604161875212

Question
For specific weight funciton $$w(x)=1$$ and domain $$x\in(-L,L)$$, then: [Important inner products]

- $$\displaystyle\left\langle \cos\left(\frac{n\pi x}{L}\right), \cos\left(\frac{m\pi x}{L}\right)\right\rangle=\int^{L}_{-L}\cos\left(\frac{n\pi x}{L}\right)\ \cos\left(\frac{m\pi x}{L}\right)\cdot1dx=L\cdot\delta_{nm}$$
- $$\displaystyle\left\langle \sin\left(\frac{n\pi x}{L}\right), \sin\left(\frac{m\pi x}{L}\right)\right\rangle=\int^{L}_{-L}\sin\left(\frac{n\pi x}{L}\right)\ \sin\left(\frac{m\pi x}{L}\right)\cdot1dx=L\cdot\delta_{nm}$$
- $$\displaystyle\left\langle \cos\left(\frac{n\pi x}{L}\right), \sin\left(\frac{m\pi x}{L}\right)\right\rangle=\int^{L}_{-L}\cos\left(\frac{n\pi x}{L}\right)\ \sin\left(\frac{m\pi x}{L}\right)\cdot1dx=0$$

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Important Inner Products
For specific weight funciton $$w(x)=1$$ and domain $$x\in(-L,L)$$, then - $$\displaystyle\left\langle \cos\left(\frac{n\pi x}{L}\right), \cos\left(\frac{m\pi x}{L}\right)\right\rangle=\int^{L}_{-L}\cos\left(\frac{n\pi x}{L}\right)\ \cos\left(\frac{m\pi x}{L}\right)\cdot1dx=L\cdot\delta_{nm}$$ - $$\displaystyle\left\langle \sin\left(\frac{n\pi x}{L}\right), \sin\left(\frac{m\pi x}{L}\right)\right\rangle=\int^{L}_{-L}\sin\left(\frac{n\pi x}{L}\right)\ \sin\left(\frac{m\pi x}{L}\right)\cdot1dx=L\cdot\delta_{nm}$$ - $$\displaystyle\left\langle \cos\left(\frac{n\pi x}{L}\right), \sin\left(\frac{m\pi x}{L}\right)\right\rangle=\int^{L}_{-L}\cos\left(\frac{n\pi x}{L}\right)\ \sin\left(\frac{m\pi x}{L}\right)\cdot1dx=0$$

#### Annotation 7604560858380

 The key to the answer is to be found in adistinction between operations overtly performed (or imagined to be performed) and operations symbolically executed. When we act overtly, consequences ensue ;if we do not like them, they are nevertheless there in existence. We are entangled in the outcome of what we doj we have to stand its consequences. We shall put aquestion that is so elementary that it may seem silly. How can we have an end in view with- out having an end, an existential result, in fact?

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#### Annotation 7604562431244

 The failure of empiricism to account for mathematical ideas is due to its failure to connect them with acts performed. In accord with its sensationalistic character, traditional em- piricism sought their origin in sensory impressions, or at most in supposed abstraction from properties antecedently character- izing physical things. Experimental empiricism, has none of the difficulties of Hume and Mill in explaining the origin of math- ematical truths. It recognizes that experience, the actual expe- rience of men, is one of doing acts, performing operations, cutting, marking off, dividing up, extending, piecing together, joining, assembling and mixing, hoarding and dealing outj in general, selecting and adjusting things as means for reaching consequences. Only the peculiar hypnotic effect exercised by exclusive preoccupation with knowledge could have led think- ers to identify experience with reception of sensations, when five minutes' observation of achild would have disclosed that sensations count only as stimuli and registers of motor activity expended in doing things.

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#### Annotation 7604564004108

 the difficulties and paradoxes which have been found to attend the logic of number disappear when instead of their being treated as either essences or as proper- ties of things in existence, they are viewed as designations of potential operations. Mathematical space is not akind of space distinct from so-called physical and empirical space, but is a name given to operations ideally or formally possible with respect to things having spacious qualities: it is not amode of Being, but away of thinking things so that connections among them are liberated from fixity in experience and implication from one to another is made possible.

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#### Annotation 7604565839116

 the active and productive character of ideas, of thought, is mani- fest. The motivating desire of idealistic systems of philosophy is justified. But the constructive office of thought is empirical that is, experimental. "Thought" is not aproperty of some- thing termed intellect or reason apart from nature. It is a mode of directed overt action. Ideas are anticipatory plans

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#### Annotation 7604567411980

 They are not innate properties of mind corresponding to ultimate prior traits of Being, nor are they apriori categories imposed on sense in awholesale, once-for-all way, prior to experience so as to make it possible. The active power of ideas is areality, but ideas and idealisms have an operative force in concrete experienced situations j their worth has to be tested by the specified consequences of their operation. Idealism is something experimental not ab- stractly rational jit is related to experienced needs and con- cerned with projection of operations which remake the actual content of experienced objects.

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#### Annotation 7604568984844

 ideas and idealisms are in themselves hypotheses not finalities. Being connected with operations to be performed, they are tested by the consequences of these operations, not by what exists prior to them. Prior experience supplies the conditions which evoke ideas and of which thought has to take account, with which it must reckon. It furnishes both obstacles to attainment of what is desired and the resources that must be used to attain it. Conception and systems of conceptions, ends in view and plans, are constantly making and remaking as fast as those already in use reveal their weak- nesses, defects and positive values. There is no predestined course they must follow. Human experience consciously guided by ideas evolves its own standards and measures and each new experience constructed by their means is an opportunity for new ideas and ideals.

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#### Annotation 7604570557708

 ction is at the heart of ideas. The experimental practice of knowing, when taken to supply the pattern of philosophic doctrine of mind and its organs, elimi- nates the age-old separation of theory and practice. It dis- closes that knowing is itself akind of action, the only one which progressively and securely clothes natural existence with

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#### Annotation 7604582092044

 Unicode® 8.0.0 (whole document)

Unicode 8.0.0
oad) Related Links Unicode Acknowledgements Archive of Unicode Versions About Versions Updates and Errata Glossary of Unicode Terms Unicode Character Name Index Technical Reports Unicode Emoji☺ <span>Unicode® 8.0.0 Released: 2015 June 17 (Announcement) Version 8.0.0 has been superseded by the latest version of the Unicode Standard. This page summarizes the important changes for the Unicode Standar

#### Annotation 7604595723532

 The next step up from a checkbook journal, is a journal that keeps track of all your accounts, not just checking. In such a journal, you record not only who gets paid—in the case of a debit—but where the money came from. In a checkbook journal, it’s assumed that all the money comes from your checking account. But in a general journal, you write postings in two lines: the source account and target account. There must always be a debit from at least one account for every credit made to another account. This is what is meant by “double-entry” accounting: the journal must always balance to zero, with an equal number of debits and credits.

Ledger: Command-Line Accounting
journal, you are recording information about your life and habits, and sometimes that information can start telling you things you aren’t aware of. Such is the aim of all good accounting tools. <span>The next step up from a checkbook journal, is a journal that keeps track of all your accounts, not just checking. In such a journal, you record not only who gets paid—in the case of a debit—but where the money came from. In a checkbook journal, it’s assumed that all the money comes from your checking account. But in a general journal, you write postings in two lines: the source account and target account. There must always be a debit from at least one account for every credit made to another account. This is what is meant by “double-entry” accounting: the journal must always balance to zero, with an equal number of debits and credits. For example, let’s say you have a checking account and a brokerage account, and you can write checks from both of them. Rather than keep two checkbooks, you decide to use one journal fo

#### Annotation 7604597820684

 This is the basis of double-entry accounting: money never pops in or out of existence; it is always a posting from one account to another.

Ledger: Command-Line Accounting
your brokerage account, transferring money to your checking account. There is nothing left over to be accounted for, since the money has simply moved from one account to another in both cases. <span>This is the basis of double-entry accounting: money never pops in or out of existence; it is always a posting from one account to another. Keeping a general journal is the same as keeping two separate journals: One for Pacific Bell and one for Checking. In that case, each time a payment is written into one, you write a cor

#### Annotation 7604599917836

 Most private people consider an account to be something that holds money at an institution for them. Ledger uses a more general definition of the word. An account is anywhere money can go. Other finance programs use “categories”, Ledger uses accounts.

Ledger: Command-Line Accounting
the last time the account was referenced—but it also means having a lot of journal books, if you deal with multiple accounts. Here is a good place for an aside on the use of the word “account”. <span>Most private people consider an account to be something that holds money at an institution for them. Ledger uses a more general definition of the word. An account is anywhere money can go. Other finance programs use “categories”, Ledger uses accounts. So, for example, if you buy some groceries at Trader Joe’s, then more groceries at Whole Food Market, you might assign the transactions like this 2011/03/15 Trader Joe's Expenses:Grocer

#### Annotation 7604602014988

 The purpose of the Ledger program is to make general journal accounting simple, by keeping track of the balances for you. Your only job is to enter the postings. If an individual posting does not balance, Ledger displays an error and indicates the incorrect posting.1 In summary, there are two aspects of Ledger use: updating the journal data file, and using the Ledger tool to view the summarized result of your transactions.

Ledger: Command-Line Accounting
In both cases the money goes to the ‘Groceries’ account, even though the payees were different. You can set up your accounts in any way you choose. Enter the beauty of computerized accounting. <span>The purpose of the Ledger program is to make general journal accounting simple, by keeping track of the balances for you. Your only job is to enter the postings. If an individual posting does not balance, Ledger displays an error and indicates the incorrect posting.1 In summary, there are two aspects of Ledger use: updating the journal data file, and using the Ledger tool to view the summarized result of your transactions. And just for the sake of example—as a starting point for those who want to dive in head-first—here are the journal transactions from above, formatted as the Ledger program wishes to see

#### Annotation 7604604112140

 The account balances and registers in this file, if saved as ledger.dat

Ledger: Command-Line Accounting

#### Annotation 7604608306444

 1.2 Building the program

Ledger: Command-Line Accounting
that file in any way you prefer, but Ledger is only for analyzing the data, not for altering it. Next: Getting help, Previous: Fat-free Accounting, Up: Introduction to Ledger [Contents][Index] <span>1.2 Building the program Ledger is written in ANSI C++, and should compile on any unix platform. The easiest way to build and install ledger is to use the prepared acprep script, that does a lot of the footwork

#### Annotation 7604610403596

 1.3 Getting help

Ledger: Command-Line Accounting
the ‘INSTALL.md‘ in the source directory for more up to date build instructions. Next: Third-Party Ledger Tutorials, Previous: Building the program, Up: Introduction to Ledger [Contents][Index] <span>1.3 Getting help Ledger has a complete online help system based on GNU Info. This manual can be searched directly from the command-line using info ledger, which will bring up this entire manual in your

### 1.4 Third-Party Ledger Tutorials

There are plenty of people using Ledger for accounting applications. Some have documented how they use Ledger’s features to solve their accounting problems.

One such tutorial, specifically designed for non-profit charities that seek to use Ledger, can be found at https://k.sfconservancy.org/NPO-Accounting/npo-ledger-cli (with a copy on GitHub also available at https://github.com/conservancy/npo-ledger-cli/). If you’re looking for information about how to use Ledger’s tagging system to handle invoicing, track expenses by program targets, and other such concepts, you might find the tutorial useful. (Some of the auditor reporting scripts that relate to the aforementioned Ledger setup can be found contrib/non-profit-audit-reports/ in Ledger’s own source repository.)

Ledger: Command-Line Accounting
http://groups.google.com/group/ledger-cli. You can also find help in the #ledger channel on the IRC server irc.libera.chat. Previous: Getting help, Up: Introduction to Ledger [Contents][Index] <span>1.4 Third-Party Ledger Tutorials There are plenty of people using Ledger for accounting applications. Some have documented how they use Ledger’s features to solve their accounting problems. One such tutorial, specifically designed for non-profit charities that seek to use Ledger, can be found at https://k.sfconservancy.org/NPO-Accounting/npo-ledger-cli (with a copy on GitHub also available at https://github.com/conservancy/npo-ledger-cli/). If you’re looking for information about how to use Ledger’s tagging system to handle invoicing, track expenses by program targets, and other such concepts, you might find the tutorial useful. (Some of the auditor reporting scripts that relate to the aforementioned Ledger setup can be found contrib/non-profit-audit-reports/ in Ledger’s own source repository.) Next: Principles of Accounting with Ledger, Previous: Introduction to Ledger, Up: Overview [Contents][Index] 2 Ledger Tutorial Start a Journal File Run a Few Reports Next: Run a Few Rep

#### Annotation 7604614597900

 2 Ledger Tutorial

Ledger: Command-Line Accounting
p can be found contrib/non-profit-audit-reports/ in Ledger’s own source repository.) Next: Principles of Accounting with Ledger, Previous: Introduction to Ledger, Up: Overview [Contents][Index] <span>2 Ledger Tutorial Start a Journal File Run a Few Reports Next: Run a Few Reports, Previous: Ledger Tutorial, Up: Ledger Tutorial [Contents][Index] 2.1 Start a Journal File A journal is a record of your f

#### Annotation 7604618530060

 go mod init example/user/hello

Open it

#### Annotation 7604628753676

 The writer of a PL/R function must take care that the function cannot be used to do anything unwanted, since it will be able to do anything that could be done by a user logged in as the database administrator. An implementation restriction is that PL/R procedures cannot be used to create input/output functions for new data types.