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Dec 6 2017, 1:24 PM (110 w, 2 d)

# Thu, Jan 16

Hi! Since this is the last commit in Instructions.cpp, you can maybe help?

Thu, Jan 16, 8:09 AM · Restricted Project

Thu, Jan 16, 6:01 AM · Restricted Project, Restricted Project

# Wed, Jan 15

Hi @tycho ! Sorry for not getting back earlier.
I implemented an alternate approach last year, which proved to be better (in terms of build times) than what I proposed in this demo patch. That is, using a thread pool instead of the process pool as implemented here. This makes compilation with /MP considerably faster, and allows for neat optimizations like file caching, re-using allocated memory pages, and possibly other things down the line. But before getting there, it requires somehow making cl::opt and the CommandLineParser thread-safe, thus revive this RFC thread. In essence, we want a mode where cl::opts have their data optionally stored in a stack context, so that we can safely call a CC1Command in each thread. I'll write a proposal to revive the RFC.

Wed, Jan 15, 7:29 PM · Restricted Project, Restricted Project
aganea added a comment to D72769: Replace CLANG_SPAWN_CC1 env var with a driver mode flag.

I guess CLANG_SPAWN_CC1 is/was mostly for debugging purposes. We have otherwise no use for that env var in production, other than for occasional testing.

I'm glad you're fixing this, this problem has came up in our profile traces as well.

Wed, Jan 15, 7:00 AM · Restricted Project

# Tue, Jan 14

Fix NetBSD bot after b4a99a061f517e60985667e39519f60186cbb469 ([Clang][Driver]…

Fixed NetBSD as suggested in rG88b8cb7215d4333ab990c99f21c7f92262ef02ef

Tue, Jan 14, 11:32 AM · Restricted Project, Restricted Project

# Mon, Jan 13

aganea added a comment to D71040: [ThinLTO/WPD] Fix index-based WPD for alias vtables.

Ping @evgeny777 @steven_wu!
Do you think you can take a look at this please? It'd be nice if it could land before the 10.0 branch. Thanks!

Mon, Jan 13, 10:16 AM · Restricted Project

Attention Apple maintainers: after this patch, do not forget to add -DCLANG_SPAWN_CC1=ON to your release scripts, to retain your previous crash reporting behavior (see discussion above). @dexonsmith @arphaman

Mon, Jan 13, 7:53 AM · Restricted Project, Restricted Project
[Clang][Driver] Re-use the calling process instead of creating a new process…
Mon, Jan 13, 7:44 AM · Restricted Project, Restricted Project

# Sun, Jan 12

aganea committed rGde797ccdd74f: [NFC] Fix compilation of CrashRecoveryContext.cpp on mingw (authored by zero9178).
[NFC] Fix compilation of CrashRecoveryContext.cpp on mingw
Sun, Jan 12, 11:47 AM · Restricted Project
Sun, Jan 12, 11:47 AM · Restricted Project, Restricted Project

Thanks for the fix Markus! I can commit on your behalf.

Sun, Jan 12, 9:08 AM · Restricted Project

# Sat, Jan 11

aganea added a comment to D72310: [mlir][VectorOps] Implement strided_slice conversion.

Hi,
This patch fails to build with MSVC (here building with latest Visual Studio 2019 16.4.2).
Could you possibly take a look please? Thanks!

```[801/3515] Building CXX object tools\mlir\lib\Conversion\VectorToLLVM\CMakeFiles\MLIRVectorToLLVM.dir\ConvertVectorToLLVM.cpp.obj
FAILED: tools/mlir/lib/Conversion/VectorToLLVM/CMakeFiles/MLIRVectorToLLVM.dir/ConvertVectorToLLVM.cpp.obj
C:\PROGRA~2\MIB055~1\2019\PROFES~1\VC\Tools\MSVC\1424~1.283\bin\HostX64\x64\cl.EXE  /nologo /TP -DGTEST_HAS_RTTI=0 -DUNICODE -D_CRT_NONSTDC_NO_DEPRECATE -D_CRT_NONSTDC_NO_WARNINGS -D_CRT_SECURE_NO_DEPRECATE -D_CRT_SECURE_NO_WARNINGS -D_HAS_EXCEPTIONS=0 -D_SCL_SECURE_NO_DEPRECATE -D_SCL_SECURE_NO_WARNINGS -D_UNICODE -D__STDC_CONSTANT_MACROS -D__STDC_FORMAT_MACROS -D__STDC_LIMIT_MACROS -Itools\mlir\lib\Conversion\VectorToLLVM -ID:\llvm-project\mlir\lib\Conversion\VectorToLLVM -Iinclude -ID:\llvm-project\llvm\include -ID:\llvm-project\mlir\include -Itools\mlir\include /DWIN32 /D_WINDOWS   /Zc:inline /Zi /Zc:strictStrings /Oi /Zc:rvalueCast /W4 -wd4141 -wd4146 -wd4244 -wd4267 -wd4291 -wd4345 -wd4351 -wd4456 -wd4457 -wd4458 -wd4459 -wd4503 -wd4624 -wd4722 -wd4100 -wd4127 -wd4512 -wd4505 -wd4610 -wd4510 -wd4702 -wd4245 -wd4706 -wd4310 -wd4701 -wd4703 -wd4389 -wd4611 -wd4805 -wd4204 -wd4577 -wd4091 -wd4592 -wd4319 -wd4709 -wd4324 -w14062 -we4238 /MT /O2 /Ob2   -UNDEBUG  /EHs-c- /GR- -std:c++14 /showIncludes /Fotools\mlir\lib\Conversion\VectorToLLVM\CMakeFiles\MLIRVectorToLLVM.dir\ConvertVectorToLLVM.cpp.obj /Fdtools\mlir\lib\Conversion\VectorToLLVM\CMakeFiles\MLIRVectorToLLVM.dir\MLIRVectorToLLVM.pdb /FS -c D:\llvm-project\mlir\lib\Conversion\VectorToLLVM\ConvertVectorToLLVM.cpp
D:\llvm-project\mlir\include\mlir/IR/Attributes.h(234): error C2440: '<function-style-cast>': cannot convert from 'mlir::ArrayAttr::iterator' to 'mlir::ArrayAttr::attr_value_iterator<mlir::IntegerAttr>'
D:\llvm-project\mlir\include\mlir/IR/Attributes.h(234): note: No constructor could take the source type, or constructor overload resolution was ambiguous
D:\llvm-project\mlir\lib\Conversion\VectorToLLVM\ConvertVectorToLLVM.cpp(117): note: see reference to function template instantiation 'llvm::iterator_range<mlir::ArrayAttr::attr_value_iterator<mlir::IntegerAttr>> mlir::ArrayAttr::getAsRange<mlir::IntegerAttr>(void)' being compiled
D:\llvm-project\mlir\include\mlir/IR/Attributes.h(235): error C2440: '<function-style-cast>': cannot convert from 'mlir::ArrayAttr::iterator' to 'mlir::ArrayAttr::attr_value_iterator<mlir::IntegerAttr>'
D:\llvm-project\mlir\include\mlir/IR/Attributes.h(235): note: No constructor could take the source type, or constructor overload resolution was ambiguous
D:\llvm-project\mlir\include\mlir/IR/Attributes.h(234): error C2672: 'llvm::make_range': no matching overloaded function found
D:\llvm-project\mlir\include\mlir/IR/Attributes.h(235): error C2780: 'llvm::iterator_range<IteratorT> llvm::make_range(T,T)': expects 2 arguments - 1 provided
D:\llvm-project\llvm\include\llvm/ADT/iterator_range.h(54): note: see declaration of 'llvm::make_range'
[874/2733] Building CXX object lib\Target\AArch64\CMakeFiles\LLVMAArch64CodeGen.dir\AArch64ISelDAGToDAG.cpp.obj
ninja: build stopped: subcommand failed.```
Sat, Jan 11, 12:50 PM · Restricted Project
[Support] Optionally call signal handlers when a function wrapped by the the…
Sat, Jan 11, 12:32 PM · Restricted Project, Restricted Project

# Fri, Jan 10

aganea committed rGde0a22471157: Remove umask tests (authored by aganea).
Fri, Jan 10, 6:09 PM · Restricted Project, Restricted Project
Fri, Jan 10, 5:51 PM · Restricted Project, Restricted Project
Fri, Jan 10, 5:51 PM · Restricted Project, Restricted Project

Thanks for taking the time @hans!

Fri, Jan 10, 8:15 AM · Restricted Project, Restricted Project

# Thu, Jan 9

aganea added inline comments to D71775: [ThreadPool] On Windows, extend usage to all CPU sockets and all NUMA groups.
Thu, Jan 9, 2:19 PM · Restricted Project, Restricted Project

Updated as suggested by @rnk.
I've also removed ThreadPoolStrategy::PinThreads because it wasn't conclusive. In the best case, pinning threads to a core / hyperthread, was similar in performance to that of using a full CPU socket affinity; in the worst case, it was degrading performance. The NT scheduler seems to be doing a pretty good job here, so we'll stick with it :-)

Thu, Jan 9, 2:19 PM · Restricted Project, Restricted Project
Thu, Jan 9, 2:09 PM · Restricted Project

Dropping this, I'll just deal with the existing process launching API.

Thu, Jan 9, 2:09 PM · Restricted Project
aganea added a comment to D71786: RFC: [Support] On Windows, add optional support for rpmalloc.

Am I the only one who is a little bit uncomfortable with including a replacement to the system allocator in LLVM? It seems to me that this is something that is clearly under the responsibility of the C library. Now this might still be worth doing given the large performance improvement, but yuck...

Thu, Jan 9, 9:27 AM · Restricted Project
aganea updated the diff for D71786: RFC: [Support] On Windows, add optional support for rpmalloc.
• Integrated changes as suggested by @russell.gallop - Could you please re-apply the patch on a clean git checkout see if this works?
• Fixed usage of LLVM_RPMALLOC_PAGESIZE -- it seems attribute((unused)) doesn't always prevent the symbol from being evicted by LLD -- maybe using TLS callbacks is an edge case. I extended the usage of /INCLUDE to Clang, like for MSVC.
• Fixed enabling large pages in rpmalloc, when they are provided in the 'config' struct. Previously, AdjustTokenPrivileges wasn't called in this case, and that is required for VirtualAlloc(MEM_LARGEPAGES, ...) to work.
Thu, Jan 9, 7:53 AM · Restricted Project
Thu, Jan 9, 5:59 AM · Restricted Project, Restricted Project
Thu, Jan 9, 5:59 AM · Restricted Project, Restricted Project

Changes as suggested by @hans.

Thu, Jan 9, 5:50 AM · Restricted Project, Restricted Project
Thu, Jan 9, 5:50 AM · Restricted Project, Restricted Project

# Wed, Jan 8

aganea added a comment to D71786: RFC: [Support] On Windows, add optional support for rpmalloc.

Is rpcmalloc using large pages by default if possible ? I have been toying with using large pages for some of the bump-pointer allocators in clang, namely the allocator of ASTContext and the allocator of Sema, and I am getting a ~5% improvement in parsing speed.

Not by default, but you can use set LLVM_RPMALLOC_PAGESIZE=2M or set LLVM_RPMALLOC_PAGESIZE=1G to enable large pages. However I realize that is broken (crashes), I'll investigate and get back.

Wed, Jan 8, 10:21 AM · Restricted Project
aganea added a comment to D71040: [ThinLTO/WPD] Fix index-based WPD for alias vtables.

I've used this patch since you've published it, on different contexts, things look good from my user perspective.

Wed, Jan 8, 10:21 AM · Restricted Project

# Tue, Jan 7

aganea updated the diff for D71786: RFC: [Support] On Windows, add optional support for rpmalloc.
• Changes as suggested by @rnk
• Fixed linking remarks-shlib as reported by @russell.gallop
• Reverted back to default rpmalloc settings (no more unlimited mode), ie. ENABLE_UNLIMITED_CACHE is 0 now.
• Support rpmalloc's ENABLE_STATISTICS - when enabled, allocation statistics will be printed on process exit.
Tue, Jan 7, 11:22 AM · Restricted Project
Fix issues reported by -Wrange-loop-analysis when building with latest Clang…

# Fri, Jan 3

aganea committed rGe19188af0a26: [mlir] Compilation fix: use LLVM_ATTRIBUTE_UNUSED following… (authored by aganea).
[mlir] Compilation fix: use LLVM_ATTRIBUTE_UNUSED following…
aganea added a comment to D71975: [Support] Support MF_HUGE_HINT on Linux and FreeBSD.

So I need to:

• Add a getHugePageSize similar to sys::Process::getPageSize which will do its best to find out about the huge page size(s) on the platform. This needs to be done for Windows too.
Fri, Jan 3, 1:20 PM · Restricted Project

# Thu, Jan 2

aganea added a comment to D71786: RFC: [Support] On Windows, add optional support for rpmalloc.

It fails creating a library

Thu, Jan 2, 8:53 PM · Restricted Project

# Wed, Jan 1

Hi! This patch broke the polly tests (the bot seems down). I wrote a fix here: 92b68c1937cd065a2fc44d18c1099de7da19b356 - it was trivial enough, but please let me know if you don't agree with the fix.

Wed, Jan 1, 2:39 PM · Restricted Project
[polly][Support] Un-break polly tests Previously, the polly unit tests were…
aganea committed rG6656e961c083: [mlir] Fix compilation warnings (authored by aganea).
[mlir] Fix compilation warnings
aganea committed rG316f6003ef2b: [mlir] Fix linking with LLD (authored by aganea).
aganea committed rG2b223bd1c7d5: [mlir] Fix warnings when compiling with Clang 9.0 (authored by aganea).
[mlir] Fix warnings when compiling with Clang 9.0

# Sat, Dec 21

Will it make sense to say "I don't want hyper-threads" ?

Not sure I remember correctly, but I believe one motivation behind avoiding "hyper-threads" and other virtual cores was that while they improve slightly the performance, they also increase the peak memory requirements: using heavyweight_hardware_concurrency() seemed like a good default tradeoff for most end-users.

Sat, Dec 21, 8:28 AM · Restricted Project, Restricted Project
aganea added a comment to D71786: RFC: [Support] On Windows, add optional support for rpmalloc.

Note in the bar charts how the 28-core system is faster, when compared to the 36-core. The 28-core does not suffer from the "processor group" issue fixed in D71775, the 28-cores/56-threads all fit in a single "processor group", so they are all available to the application; while the 36-cores/72-threads are projected to the application as two "processor groups", out of which only one is used by default. After D71775, the 36-core is evidently faster.

Sat, Dec 21, 8:01 AM · Restricted Project
aganea added a comment to D71786: RFC: [Support] On Windows, add optional support for rpmalloc.

Thank @amccarth, fixed!

Sat, Dec 21, 7:52 AM · Restricted Project
aganea updated the summary of D71786: RFC: [Support] On Windows, add optional support for rpmalloc.
Sat, Dec 21, 7:52 AM · Restricted Project

# Fri, Dec 20

aganea updated the summary of D71775: [ThreadPool] On Windows, extend usage to all CPU sockets and all NUMA groups.
Fri, Dec 20, 2:18 PM · Restricted Project, Restricted Project
Fri, Dec 20, 2:18 PM · Restricted Project
aganea updated the summary of D71775: [ThreadPool] On Windows, extend usage to all CPU sockets and all NUMA groups.
Fri, Dec 20, 9:29 AM · Restricted Project, Restricted Project
Fri, Dec 20, 9:20 AM · Restricted Project, Restricted Project

# Thu, Dec 19

aganea added inline comments to D71248: [clangd] Introduce paragraph, the first part of new rendering structs.
Thu, Dec 19, 11:53 AM · Restricted Project

# Dec 18 2019

I looked over this again, and also studied CrashRecoveryContext some more.

I don't really understand why this patch needs to modify the code for how the CRC is enabled and installed, etc.

I thought all we need for in-process-cc1 is to add the DumpStackAndCleanupOnFailure flag and behavior, nothing more.

Do you think this is possible, or am I missing something?

Dec 18 2019, 6:05 AM · Restricted Project, Restricted Project

# Dec 13 2019

aganea added a comment to D71040: [ThinLTO/WPD] Fix index-based WPD for alias vtables.

Strange this assertion probably means, that there are two summaries with external linkage in VTableVI. I tried reproducer out of curiosity, but it worked fine for me (no assertion on stage2 with ninja clang).

Dec 13 2019, 2:41 PM · Restricted Project

# Dec 12 2019

aganea added a comment to D71040: [ThinLTO/WPD] Fix index-based WPD for alias vtables.

I was able to successfully create an ThinLTO-built clang.exe with this patch. However when compiling with assertions on, I'm still getting this:

`Assertion failed: P.VTableVI.getSummaryList().size() == 1 || llvm::count_if( P.VTableVI.getSummaryList(), [&](const std::unique_ptr<GlobalValueSummary> &Summary) { return GlobalValue::isExternalLinkage(Summary->linkage()); }) <= 1, file D:\llvm-project\llvm\lib\Transforms\IPO\WholeProgramDevirt.cpp, line 852`

I simply built a 2-stage clang with the following cmd-line:

`stage 1: cmake -GNinja ../llvm -DCMAKE_BUILD_TYPE=Release -DLLVM_ENABLE_LIBXML2=OFF -DLLVM_ENABLE_PROJECTS="clang;lld;llvm" -DLLVM_ENABLE_ASSERTIONS=ON -DCMAKE_C_COMPILER="C:/Program Files/LLVM/bin/clang-cl.exe" -DCMAKE_CXX_COMPILER="C:/Program Files/LLVM/bin/clang-cl.exe" -DCMAKE_LINKER="C:/Program Files/LLVM/bin/lld-link.exe" -DLLVM_ENABLE_LLD=true -DLLVM_ENABLE_PDB=ON`
Dec 12 2019, 8:22 PM · Restricted Project

# Dec 11 2019

Yes this was added in rG18627115f4d2db5dc73207e0b5312f52536be7dd and rGe08b59f81d950bd5c8b8528fcb3ac4230c7b736c. It looks like it was only there to validate that specific refactoring.
Should I remove these two files, or simply commit the previous diff? (ie. -rw-rw----)

Dec 11 2019, 12:46 PM · Restricted Project, Restricted Project
aganea updated the summary of D70854: [Clang] In tests, do not always assume others permissions are set.
Dec 11 2019, 10:13 AM · Restricted Project, Restricted Project
aganea requested review of D70854: [Clang] In tests, do not always assume others permissions are set.
Dec 11 2019, 10:13 AM · Restricted Project, Restricted Project
aganea updated the diff for D70854: [Clang] In tests, do not always assume others permissions are set.

Ensure the access-rights commands (setfacl and chmod) won't fail the tests if the user doesn't have the appropriate rights to change permissions.

Dec 11 2019, 10:11 AM · Restricted Project, Restricted Project

# Dec 9 2019

Dec 9 2019, 7:57 AM · Restricted Project, Restricted Project

Added CLANG_SPAWN_CC1 cmake flag & environment variable to control whether we want a cc1 process or not. It is disabled by default. I left out the if (APPLE) part in cmake, as suggested by @rnk.

Dec 9 2019, 7:56 AM · Restricted Project, Restricted Project
Dec 9 2019, 7:38 AM · Restricted Project, Restricted Project

• Removed CrashRecoveryContext::HandleCrash() and #pragma clang handle_crash which wasn't covered by any test and most likely deprecated by #pragma clang crash
• Added refcounting to CrashRecoveryContext::Enable/Disable as well as lazy installation of the exception handlers in CrashRecoveryContext.
• Partially reverted rG4624e83ce7b124545b55e45ba13f2d900ed65654/llvm/lib/Support/Unix/Signals.inc to simplify checks for IntSigs (and to fix the issue mentioned here). @vsk

All tests pass on Windows/MSVC2019/Clang9/10 and Linux/Clang9/GCC9.1.

Dec 9 2019, 7:38 AM · Restricted Project, Restricted Project

# Dec 5 2019

I did this in driver.cpp:

```// Whether the cc1 tool should be called inside the current process, or forked
// to a new new process.
bool UseCC1ProcessFork = CLANG_FORK_CC1;```
Dec 5 2019, 11:30 AM · Restricted Project, Restricted Project
aganea added 1 auditor(s) for rG9a3f892d0182: [Signal] Allow one-shot SIGPIPE handler to be reached: rnk.

Thanks Vedant! Minor: there's still an unexpected side-effect when InitLLVM is called with InstallPipeSignalExitHandler=false or if sys::SetOneShotPipeSignalFunction is used to clear the default function. In that case, the test will fall through, and will go and call llvm::sys::RunSignalHandlers(). Whereas before it used raise the signal again, and return. What do you think?
I'm wondering if the code shouldn't read more like:

```if (llvm::is_contained(IntSigs, Sig) || Sig == SIGPIPE) {
if (auto OldInterruptFunction = InterruptFunction.exchange(nullptr))
return OldInterruptFunction();```

# Dec 4 2019

aganea added inline comments to D70277: [Signal] Allow llvm clients to opt into one-shot SIGPIPE handling.
Dec 4 2019, 3:26 PM · Restricted Project, Restricted Project
aganea added inline comments to D69452: [ThinLTO/WPD] Fix index-based WPD for available_externally vtables.
Dec 4 2019, 9:14 AM · Restricted Project

@aganea Please disable the new behavior for the Darwin platform. We rely on the fact that Clang -cc1 processes crash to report crashes using system's crash reporting infrastructure.

Dec 4 2019, 7:03 AM · Restricted Project, Restricted Project
aganea updated the diff for D70854: [Clang] In tests, do not always assume others permissions are set.

Just after I hit Submit last night, I found a better way, by disabling ACL for that folder.
Ping @tstellar @Meinersbur in case they have an opinion.
Please let me know which solution you think is better.

Dec 4 2019, 5:57 AM · Restricted Project, Restricted Project

# Dec 3 2019

aganea added inline comments to D70854: [Clang] In tests, do not always assume others permissions are set.
Dec 3 2019, 3:14 PM · Restricted Project, Restricted Project
aganea added inline comments to D70854: [Clang] In tests, do not always assume others permissions are set.
Dec 3 2019, 2:55 PM · Restricted Project, Restricted Project
[LLDB] Disable MSVC warning C4190: 'LLDBSwigPythonBreakpointCallbackFunction'…
Dec 3 2019, 6:59 AM · Restricted Project

# Dec 2 2019

Dec 2 2019, 3:25 PM · Restricted Project, Restricted Project

You're right indeed Russell, my bad, this gain is not as important as I initially claimed -- however there's a gain.

Dec 2 2019, 3:21 PM · Restricted Project, Restricted Project

# Nov 29 2019

aganea updated subscribers of D67463: [MS] Warn when shadowing template parameters under -fms-compatibility.
Nov 29 2019, 2:33 PM · Restricted Project, Restricted Project

You probably already know this, but the behavior between MSVC & Clang is different as to the value of the constant (testcase for PR43265).
See: https://godbolt.org/z/y4uvgp
Clang gives 0, while MSVC gives 5. This incompatibility is a potential source of failure, one of our tests broke because of that.

Nov 29 2019, 2:33 PM · Restricted Project, Restricted Project
On Windows, fix fuse-ld.c test when lld is provided explictly in -DCMAKE_LINKER
[CIndex] Fix annotate-deep-statements test when using a Debug build
Nov 29 2019, 7:53 AM · Restricted Project
Nov 29 2019, 6:38 AM · Restricted Project, Restricted Project
aganea retitled D70854: [Clang] In tests, do not always assume others permissions are set from [Clang] Do not always assume others permissions are set to [Clang] In tests, do not always assume others permissions are set.
Nov 29 2019, 6:38 AM · Restricted Project, Restricted Project

Thanks for analyzing this!

Nov 29 2019, 6:03 AM · Restricted Project, Restricted Project

# Nov 28 2019

aganea committed rG1abd4c94d757: [Clang] Bypass distro detection on non-Linux hosts (authored by aganea).
[Clang] Bypass distro detection on non-Linux hosts
Nov 28 2019, 2:08 PM · Restricted Project
aganea committed rGbdad3ec75ab3: [LLDB] On Windows, force error message formatting to English (authored by aganea).
[LLDB] On Windows, force error message formatting to English
Nov 28 2019, 11:24 AM · Restricted Project
[LLDB] Fix wrong argument in CommandObjectThreadStepWithTypeAndScope
Nov 28 2019, 11:01 AM · Restricted Project
aganea updated the diff for D70830: [LLDB] Disable MSVC warning C4190.
Nov 28 2019, 11:01 AM · Restricted Project
Nov 28 2019, 9:28 AM · Restricted Project

# Nov 26 2019

Do I understand correctly that the main point is to get a stack trace when CrashRecoveryContext::RunSafely() fails, instead of just returning an error?

Nov 26 2019, 10:21 AM · Restricted Project, Restricted Project

It looks like the git apply didn't work, but the script continued so this was a duff experiment, please ignore. I'll try to fix this and run it again.

Nov 26 2019, 9:35 AM · Restricted Project, Restricted Project

# Nov 25 2019

Thanks for the feedback Russell!

Nov 25 2019, 8:55 AM · Restricted Project, Restricted Project
Nov 25 2019, 8:55 AM · Restricted Project, Restricted Project

# Nov 21 2019

Nov 21 2019, 2:03 PM · Restricted Project, Restricted Project


text:
## Transform a vector from Cartesian to Cylindrical coordinates

1. The problem statement, all variables and given/known data

Transform the vector below from Cartesian to Cylindrical coordinates:

$$Q\,=\,\frac{\sqrt{x^2\,+\,y^2}}{\sqrt{x^2\,+\,y^2\,+\,z^2}}\,\hat{x}\,-\,\frac{y\,z}{x^2\,+\,y^2\,+\,z^2}\,\hat{z}$$

2. Relevant equations

Use these equations:

$$A_{\rho}\,=\,\hat{\rho}\,\cdot\,\overrightarrow{A}\,=\,A_x\,cos\,\phi\, +\,A_y\,sin\,\phi$$

$$A_{\phi}\,=\,\hat{\phi}\,\cdot\,\overrightarrow{A}\,=\,-A_x\,sin\,\phi\,+\,A_y\,cos\,\phi$$

$$A_z\,=\,A_z$$

$$x\,=\,\rho\,cos\,\phi$$

$$y\,=\,\rho\,sin\,\phi$$

3. The attempt at a solution

$$Q_{\rho}\,=\,\frac{\sqrt{\left(\rho\,cos\,\phi\right)^2\,+\,\left(\rho\ ,\sin\,\phi\right)^2}}{\sqrt{\left(\rho\,cos\,\phi\right)^2\,+\,\left(\ rho\,\sin\,\phi\right)^2\,+\,z^2}}\,cos\,\phi$$

$$Q_{\rho}\,=\,\frac{\rho}{\sqrt{\rho^2\,+\,z^2}}\,cos\,\phi$$

$$Q_{\phi}\,=\,-\,\frac{\rho}{\sqrt{\rho^2\,+\,z^2}}\,sin\,\phi$$

$$Q_z\,=\,-\,\frac{z\,\rho\,sin\,\phi}{\rho^2\,+\,z^2}$$

Does the above look correct?

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Hi VinnyCee!
 Quote by VinnyCee $$A_{\rho}\,=\,\hat{\rho}\,\cdot\,\overrightarrow{A}\,=\,A_x\,cos\,\phi\, +\,A_y\,sin\,\phi$$ $$A_{\phi}\,=\,\hat{\phi}\,\cdot\,\overrightarrow{A}\,=\,-A_x\,sin\,\phi\,+\,A_y\,cos\,\phi$$
No … these are the equations for an ordinary rotation of the x and y axes through an angle phi.
 $$Q_{\rho}\,=\,\frac{\rho}{\sqrt{\rho^2\,+\,z^2}}\,cos\,\phi$$ $$Q_{\phi}\,=\,-\,\frac{\rho}{\sqrt{\rho^2\,+\,z^2}}\,sin\,\phi$$
hmm … you want polar coordinates of a vector along the x-axis … so what will its phi coordinate be?

 Really? The equations for transforming from Cartesian to Cylindrical were given in the notes for the class in a matrix form and then solved out to a formula, the one below. Here is a more detailed version for the $\rho$ coordinate transformation only: $$A_{\rho}\,=\,\hat{\rho}\,\cdot\,\overrightarrow{A} \,=\,\left(\hat{\rho}\,\cdot\,\hat{x}\right)\,A_x\,+\,\left(\hat{\rho}\ ,\cdot\,\hat{y}\right)\,A_y\,+\,\left(\hat{\rho}\,\cdot\,\hat{z}\right) \,A_z\,=\,A_x\,cos\,\phi\,+\,A_y\,sin\,\phi$$ Is that incorrect? If so, what is the correct way to transform from Cartesian to Cylindrical? I think the $\phi$ coordinate would be zero in this case since there is no y-component, right?

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## Transform a vector from Cartesian to Cylindrical coordinates

 Quote by VinnyCee $$A_{\rho}\,=\,\hat{\rho}\,\cdot\,\overrightarrow{A}\,=\,A_x\,cos\,\phi\, +\,A_y\,sin\,\phi$$ $$x\,=\,\rho\,cos\,\phi$$ $$y\,=\,\rho\,sin\,\phi$$ 3. The attempt at a solution $$Q_{\rho}\,=\,\frac{\sqrt{\left(\rho\,cos\,\phi\right)^2\,+\,\left(\rho\ ,\sin\,\phi\right)^2}}{\sqrt{\left(\rho\,cos\,\phi\right)^2\,+\,\left(\ rho\,\sin\,\phi\right)^2\,+\,z^2}}\,cos\,\phi$$

Here you've included the Ax cos(phi) term, but forgot the Ay sin(phi) term

 $A_y$ is zero, so it need not be included, right?
 Mentor Blog Entries: 10 Oops, I was confusing Ay and Az. My bad. Your results from post #1 look okay to me. My understanding is the dot product of the vector Q with the coordinate unit-vector is the component of Q in that coordinate direction, which is exactly what you did. On the other hand I'm hesitant to disagree with tiny-tim, since he knows this stuff pretty well also.

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 Quote by VinnyCee $A_y$ is zero
That's right! for x > 0 and y = 0, phi must be zero.
 , so it need not be included, right?
No!

A three-dimensional vector needs three coordinates …

if one coordinate is 0, you have to say so!
 Quote by VinnyCee Here is a more detailed version for the $\rho$ coordinate transformation only: $$A_{\rho}\,=\,\hat{\rho}\,\cdot\,\overrightarrow{A} \,=\,\left(\hat{\rho}\,\cdot\,\hat{x}\right)\,A_x\,+\,\left(\hat{\rho}\ ,\cdot\,\hat{y}\right)\,A_y\,+\,\left(\hat{\rho}\,\cdot\,\hat{z}\right) \,A_z\,=\,A_x\,cos\,\phi\,+\,A_y\,sin\,\phi$$ Is that incorrect?
No, that is correct … the other one is wrong.

 Mentor Blog Entries: 10 Isn't that the same expression as in post #1 for Aρ ?

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 Quote by Redbelly98 Isn't that the same expression as in post #1 for Aρ ?
ah … I meant the phi-coordinate $$A_{\phi}\,=\,\hat{\phi}\,\cdot\,\overrightarrow{A}\,=\,-A_x\,sin\,\phi\,+\,A_y\,cos\,\phi$$ is wrong.

 Mentor Blog Entries: 10 Um, if we use the convention that φ's unit vector points counterclockwise, and φ is taken counterclockwise from the positive x-axis, then I agree with VinnyCee's formula.
 So, does that mean that the original post contains the correct answer? Or is the $Q_{\phi}$ variable still going to be zero even though the formulas given produce the expression I wrote in the first post? The expression written from a matrix in class is: $$A_{\phi}\,=\,\hat{\phi}\,\cdot\,\overrightarrow{A} \,=\,\left(\hat{\phi}\,\cdot\,\hat{x}\right)\,A_x\,+\,\left(\hat{\phi}\ ,\cdot\,\hat{y}\right)\,A_y\,+\,\left(\hat{\phi}\,\cdot\,\hat{z}\right) \,A_z\,=\,-A_x\,sin\,\phi\,+\,A_y\,cos\,\phi$$ Since... $$\hat{x}\,\cdot\,\hat{\phi}\,=\,-\,sin\,\phi$$ $$\hat{y}\,\cdot\,\hat{\phi}\,=\,cos\,\phi$$ $$\hat{z}\,\cdot\,\hat{\phi}\,=\,0$$ Right?

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 Quote by Redbelly98 Um, if we use the convention that φ's unit vector points counterclockwise, and φ is taken counterclockwise from the positive x-axis, then I agree with VinnyCee's formula.
 Quote by VinnyCee So, does that mean that the original post contains the correct answer?
Hi VinnyCee and Redbelly98!

Yes, I completely mis-read the original question.

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Dynamics of epidemic models with asymptomatic infection and seasonal succession

1. School of Mathematical Science, Shanghai Jiao Tong University, Shanghai 200240, China
2. Yangtze Center of Mathematics and Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

## Abstract    Full Text(HTML)    Figure/Table    Related pages

In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and evaluated directly for this model, and uniform persistence of the disease and threshold dynamics are obtained. Specially, global dynamics of the model without seasonal force are studied. It is shown that the model has only a disease-free equilibrium which is globally stable if $\mathcal{R}_0≤ 1$, and as $\mathcal{R}_0>1$ the disease-free equilibrium is unstable and there is an endemic equilibrium, which is globally stable if the recovering rates of asymptomatic infectives and symptomatic infectives are close. These theoretical results provide an intuitive basis for understanding that the asymptomatically infective individuals and the seasonal disease transmission promote the evolution of the epidemic, which allow us to predict the outcomes of control strategies during the course of the epidemic.

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Citation: Yilei Tang, Dongmei Xiao, Weinian Zhang, Di Zhu. Dynamics of epidemic models with asymptomatic infection and seasonal succession. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1407-1424. doi: 10.3934/mbe.2017073

References

• [1] M. E. Alexander,S. M. Moghadas, Bifurcation analysis of SIRS epidemic model with generalized incidence, SIAM J. Appl. Math., 65 (2005): 1794-1816.
• [2] R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, New York, 1991.
• [3] J. Arino,F. Brauer,P. van den Driessche,J. Watmoughd,J. Wu, A model for influenza with vaccination and antiviral treatment, J. Theor. Biol., 253 (2008): 118-130.
• [4] L. Bourouiba,A. Teslya,J. Wu, Highly pathogenic avian influenza outbreak mitigated by seasonal low pathogenic strains: insights from dynamic modeling, J. Theor. Biol., 271 (2011): 181-201.
• [5] F. Brauer and C. Castillo-Chávez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, New York, 2001.
• [6] J. M. Cushing, A juvenile-adult model with periodic vital rates, J. Math. Biol., 53 (2006): 520-539.
• [7] O. Diekmann,J. A. P. Heesterbeek,J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in themodels for infectious disease in heterogeneous populations, J. Math. Biol., 28 (1990): 365-382.
• [8] K. Dietz, The incidence of infectious diseases under the influence of seasonal fluctuations, Lecture Notes in Biomath, 11 (1976): 1-15, Berlin-Heidelberg-New York: Springer.
• [9] D. J. D. Earn,P. Rohani,B. M. Bolker,B. T. Grenfell, A simple model for complex dynamical transitions in epidemics, Science, 287 (2000): 667-670.
• [10] Z. Guo,L. Huang,X. Zou, Impact of discontinuous treatments on disease dynamics in an SIR epidemic model, Math. Biosci. Eng., 9 (2012): 97-110.
• [11] H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000): 599-653.
• [12] Y. Hsieh,J. Liu,Y. Tzeng,J. Wu, Impact of visitors and hospital staff on nosocomial transmission and spread to community, J. Theor. Biol., 356 (2014): 20-29.
• [13] W. O. Kermack,A. G. McKendrick, Contributions to the mathematical theory of epidemics, Proc. R. Soc. London A: Math., 115 (1927): 700-721.
• [14] I. M. Longini,M. E. Halloran,A. Nizam,Y. Yang, Containing pandemic influenza with antiviral agents, Am. J. Epidemiol., 159 (2004): 623-633.
• [15] R. Olinky,A. Huppert,L. Stone, Seasonal dynamics and thresholds governing recurrent epidemics, J. Math. Biol., 56 (2008): 827-839.
• [16] I. B. Schwartz, Small amplitude, long periodic out breaks in seasonally driven epidemics, J. Math. Biol., 30 (1992): 473-491.
• [17] H. L. Smith, Multiple stable subharmonics for a periodic epidemic model, J. Math. Biol., 17 (1983): 179-190.
• [18] H. L. Smith and P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge Univ. Press, 1995.
• [19] L. Stone,R. Olinky,A. Huppert, Seasonal dynamics of recurrent epidemics, Nature, 446 (2007): 533-536.
• [20] Y. Tang,D. Huang,S. Ruan,W. Zhang, Coexistence of limit cycles and homoclinic loops in a SIRS model with a nonlinear incidence rate, SIAM J. Appl. Math., 69 (2008): 621-639.
• [21] S. Towers,Z. Feng, Social contact patterns and control strategies for influenza in the elderly, Math. Biosci., 240 (2012): 241-249.
• [22] S. Towers,K. Vogt Geisse,Y. Zheng,Z. Feng, Antiviral treatment for pandemic influenza: Assessing potential repercussions using a seasonally forced SIR model, J. Theor. Biol., 289 (2011): 259-268.
• [23] P. Van den Driessche,J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002): 29-48.
• [24] W. Wang,S. Ruan, Bifurcation in an epidemic model with constant removal rate of the infectives, J. Math. Anal. Appl., 291 (2004): 775-793.
• [25] W. Wang,X. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Diff. Equ., 20 (2008): 699-717.
• [26] D. Xiao, Dynamics and bifurcations on a class of population model with seasonal constant-yield harvesting, Discrete Contin. Dynam. Syst. -B, 21 (2016): 699-719.
• [27] D. Xiao,S. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate, Math. Biosci., 208 (2007): 419-429.
• [28] F. Zhang,X. Zhao, A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007): 496-516.
• [29] X. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.


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# cohomology group theorem

## Primary tabs

Defines:
conjugacy class or representation of $\pi_1$ into $\pi$,set of based homotopy classes of based maps
Keywords:
Abelian and non-Abelian groups, the cohomology group theorem, cohomology group, homotopy group, theorem on the equivalence of homology and homotopy groups, natural isomorphisms,fundamental cohomology theorem
Synonym:
fundamental cohomology theorem
Type of Math Object:
Theorem
Major Section:
Reference


text:
# Calculus Why read Spivak's Calculus?

Tags:
1. Mar 30, 2015

### Daniel Wqw

I'm currently an A-Level Maths and Physics student looking to get ahead before university maths/ physics. Looking on the internet I see people making a big deal of Spivak's Calculus but on looking thought it I can't see how it could possibly be useful for future maths and physics. To me it seems in a way like learning geometry using euclids elements. Sure it's quite interesting and satisfies extreme skepticism but if you just want to learn about it you can get lost in the details. I feel like I might come out from reading it thinking 'why am I learning all this stuff?!'. And that's what I'd really like to know. What will I get out of reading Spivak's Calculus book? If I work my way through it what advantage would I have over the me in a parallel universe who didn't work through it? Thanks :)

2. Mar 30, 2015

### micromass

You read it because it interests you. If it doesn't interest you to read a book like that, then don't read it. You will certainly not miss much.

Personally, I enjoy getting "lost in the details" and to "satisfy extreme skepticisim". If you don't, then you probably shouldn't go into math. There is no real other reason to go into math besides that.

3. Mar 30, 2015

### Daniel Wqw

The main reason I like to learn something is because it is a bridge to solving an interesting problem of some sort. I mean I can see the purpose of learning integration because I like that it can tell you the area under a graph between two intervals and I like combinations because I can tell tell what number of arrangements of objects I can have. And then I can see you can use this knowledge to go to something else and something else etc. But when I see a proof of 'for a<c<b integral of f from a to b equals the integral of f from a to c plus the integral of f from c to b' with extravagant notation and such when it's obvious to start with! And after you've finished with all that stuff what was the point? Does it help you to solve more difficult problems and what kind of problems does it help you solve. Or does the style in some way prepare you for something later on?

4. Mar 30, 2015

### micromass

Yes. But it depends on what kind of problems you want to solve. If you want to solve problems in physics, then you don't need all that math. But if you want to do math, then Spivak is very necessary. But if you already don't see the point of Spivak, then you'll likely won't see the point of abstract math. However, if you want to go deeper into math and know the deep reasons of why something is true, then Spivak is necessary.

Yes, more abstract math. Whether you want that or not is up to you.

But it is true, many things in Spivak are trivial to see geometrically, but with difficult proofs. So I know why you find it useless. However, the further you go in physics, you'll see math that isn't trivial to see and is in fact quite subtle. For example, you'll find functions $\delta$ such that $\int_{-\infty}^{+\infty} \delta(x)dx = 1$ but such that $\delta(x)=0$ for nonzero $x$. Such a function obviously does not exist. But in physics we often pretend that it does. So either you can go on and pretend it exists, which is ok. But you can also try to find the deeper reasons why it works. In that case, you need to study the difficult proofs of math. And then Spivak is a necessary first step.

5. Apr 4, 2015

### verty

Here is my take; I'll use the example of riding a bicycle. Riding a bicycle certainly seems difficult in the beginning, partly because one doesn't innately know that slower is more hazardous. One might think that one should start off slow and master it before speeding up, but actually it works the other way round. The intuition is wrong and makes it seems much more difficult than it is.

If we extract this wisdom, any new thing will seem difficult at first because our intuition is wrong, but by the simple fact that many other people succeed at it, there must be a way to succeed and we just need to correct our mistaken intuitions.

I'll say the same about Spivak's book, it is difficult because our intuition is wrong. Our intuition is that a person should start at page 1, read everything carefully, answer every question, never turn a page without understanding what it contains, etc, a linear approach. And it is appealing that we can learn every definition and prove every theorem and then know the subject completely, so it seems that this is how one should proceed.

But there is a philosophical problem here. What one is trying to do is learn the subject, and sticking to one particular method of learning can only be a hindrance, it can never be a help. So that's the first point: don't be limited to any one method. Hopefully this quells your worry about it being like learning from Euclid's Elements. It would still be learning, you wouldn't need to learn in any one particular way.

Why this book? Because it contains rigorous calculus and is known for having challenging problems.

Why rigorous calculus? I want to defer to Micromass's answer on this point.

What I will say is, I like to think of math as a language. To be philosophical, words are just words, what is important is the things that they refer to. And mathematical symbols are just symbols, what is important is what they refer to, what they are about.

Calculus, rigorous or not, is about a language of symbols to talk about rates of change, slopes or areas and volumes. Rigorous caclulus is careful to define those symbols rigorously, in excruciating detail so as to make the meaning very clear, and that is interesting of course, but really I find the use of the symbols to be more interesting.

One can ask, what is a continuous function? And if one is being precise, one must use the rigorous definition. But why was it defined that way? Because we want it to define what was non-rigorous before. Because if continuity was anything else, it wouldn't be called continuity. If you understand that, that the definition is meant to define something that is intuitively obvious, that it is meant to be somehow simple, and the proofs themselves, although complicated, have simple start and end points because they connect ideas that should be simple, you should start to see that there is a simplicity criterion to the theorems and the complication is buried in the proofs.

But realize that the theorems are chosen so that the proofs have a simplicity criterion as well. Proofs that are too complicated will make use of lemmas to make them easier to understand. So proving any particular lemma or theorem will be to some degree simple or elementary as well. That said, the simplicity criterion for proofs applies only to how the proof looks, not to how easy it was to find the proofs. So any particular proof could be difficult to find.

So hopefully this is a bit of a road map. The theorems themselves, if you don't prove them, are still interesting to know, I believe. And because the proofs have a simplicity criterion, it can be worthwhile to just look them up because they will usually be short and easy to memorize. Why spend hours when you can spend minutes?

As a strange peculiar example, one of the things I wanted to learn from Spivak was how to do limit proofs. I devised a strategy that always worked, a universal procedure to tackle any limit proof (of the type that was in the book). It seems magical but facing a bunch of those questions, I was like, how can I make this more efficient?

Consider this, limit proofs should be similar, very similar; if the function is suitably continuous, why wouldn't the proof be almost identical? So here again, intuition has led us wrong. What seemed magical, that there could be a universal procedure, now perhaps seems even obvious, of course, each problem is the same in a sufficiently small interval (unless the function is strange but no problem was of that sort).

My point is, if you want to read it, it doesn't need to be some kind of pilgrimage to the Mecca of Math, you could read it just to learn about the theorems, to have a more structured knowledge, to reinforce what you know. That said, it is a definition-theorem-proof book so you would need to be able to handle that.

6. Apr 4, 2015

### lurflurf

Spivak is a modern book and Euclid is not. If you want to learn calculus Spivak is a good book, but it is not necessary or sufficient to read it. Most people would read an easier book before Spivak and some other books because Spivak does not cover all topics, covers some topics in a strange way, and it not general enough. For example Spivak often hides the topology in his arguments, leaves out many methods, does not cover differentials and so forth. So read Spivak or don't who cares. Your question really seems to be if it necessary to learn calculus well. Sure you can learn to calculate some things without really understanding what you are doing. Sometimes you will get wrong answers and not know why. Spivak is an introductory calculus books (though among the harder ones). If you want calculus as a tool you will in practice cut your study of it off at some point. I do not see why you would choose such a low bar as Spivak though. That would be very limiting.


text: dc.creator Kisiel, Zbigniew en_US dc.creator Kraśnicki, Adam en_US dc.date.accessioned 2011-07-12T17:39:45Z dc.date.available 2011-07-12T17:39:45Z dc.date.issued 2011 en_US dc.identifier 2011-MH-06 en_US dc.identifier.uri http://hdl.handle.net/1811/49681 dc.description Author Institution: Institute of Physics, Polish Academy of Sciences, Al. Lotnikow; 32/46, 02-668 Warszawa, Poland en_US dc.description.abstract Previous determinations of the electric dipole moment of acrylonitrile, while in agreement on the total dipole moment, showed an appreciable difference in the value of the smaller $\mu_b$ component., {\bf 22}, 516 (1954)}$^,$, {\bf 40a}, 998 (1985)} The value of this component is important for intensity considerations in the THz spectrum of this molecule, which is dominated by $b$-type transitions. {\bf 258}, 26 (2009).} \vspace{0.2cm} We decided to update the dipole moment determination of acrylonitrile, and also of propionitrile (ethyl cyanide) by making Stark measurements in supersonic expansion. We used the Stark electrode arrangement developed in our laboratory and the program QSTARK for fitting Stark measurements on resolved nuclear quadrupole hyperfine structure. {\bf 325}, 523 (2000).} The results for acrylonitrile show a further, significant difference in the value of $\mu_b$, while those for propionitrile, while more precise, are essentially consistent with previous values., {\bf 29a}, 1345 (1974)} The evidence from $ab~initio$ calculations and from relative intensity measurements supporting the current dipole moment determinations is presented. en_US dc.language.iso en en_US dc.publisher Ohio State University en_US dc.title IMPROVED DIPOLE MOMENTS FOR ACRYLONITRILE AND PROPIONITRILE en_US dc.type Article en_US dc.type Image en_US dc.type Presentation en_US


text:
# NCERT Solutions for Class 3 Maths Rupees and Paise

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NCERT Solutions for Class 3 Maths Rupees and Paise book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 3 Maths Rupees and Paise and chapter wise NCERT solution for Maths Book all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

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## NCERT Solutions for Class 3 Maths Rupees and Paise

CHAPTER 14 Class 3 Maths Rupees and Paise

Ans. Rs. 22.

Ans. Rs. 10.

Ans. Rs. 7.50.

Ans. Rs. 15.50.

Ans. Rs. 9.

Ans. Rs. 12.

Ans. Rs. 8.50.

### 8. What can you buy if you have a twenty-rupee note?

Ans. 1 toy car, 1 lemon juice, 1 banana.

1 ball, 1 doll, 1 notebook.

1 toy car, 1 banana, 1 glass milk.

1 toy car, 1 packet of biscuit, 1 toffee.

1 toy car, 1 toy giraffe, 1 glass milk.

### 9. Monu prepared the following cash memos:

Check the cash memos and correct them if you find a mistake.

Ans. Corrected cash memo are given below:

 Cash MemoSelf Service Store Item Rate Rs Paise 1 Ball 7 7 00 2 Pencil 2.50 5 00 5 Toffees 1.50 2 50 Total 14 50
 Cash MemoSelf Service Store Item Rate Rs Paise 1 Toy car 15 15 00 3 Glass milk 3.50 10 50 4 Notebooks 5 20 00 Total 45 50
 Cash MemoSelf Service Store Item Rate Rs Paise 1 Toy car 15 15 00 3 Pencils 2.50 7 50 7 Toffees 0.50 3 50 1 Biscuits 4.50 4 50 Total 30 50

(a)

 Rs. 12. 50 Rs. +13. 00 Rs.

Ans.

 Rs. 12 50 Rs. 13 00 Rs. 25 50

(b)

 Rs. 55. 50 Rs. +14. 00 Rs.

Ans.

 Rs. 55 50 Rs. 14 00 Rs. 69 50

(c)

 Rs. 30. 00 Rs. +31. 50 Rs.

Ans.

 Rs. 30 00 Rs. 31 50 Rs. 61 50

### 11. Subtract the following:

(a)

 Rs. 15. 50 Rs. -11. 50 Rs.

Ans.

 Rs. 15 50 Rs. -11 50 Rs. 14 00

(b)

 Rs. 103. 50 Rs. -62. 00 Rs.

Ans.

 Rs. 103 50 Rs. -62 00 Rs. 41 50

(c)

 Rs. 19. 50 Rs. – 7. 00 Rs.

Ans.

 Rs. 19. 50 Rs. – 7. 00 Rs. 12. 50

### 12. You have 30 rupees with you. Find out how much money will be left after buying the following items: One ball, one doll and one toy giraffe. Total cost of Rs. 21.50. Money left Rs. 8.50.

Ans. Cost of 1 ball = Rs. 7

Cost of 1 doll = Rs. 8

Cost of 1 toy giraffe = Rs. 6.50

So, Total cost = Rs. 7 + Rs. 8 + Rs. 6.50 = Rs. 21.50

Money left = Total Money – Money Spent = Rs. 30 – Rs. 12.50 = Rs. 8.50.

### 13. Two bananas, one pack of biscuits and two glasses of lemon juice. Total cost Rs. 13.50. Money left Rs. 16.50.

Ans. Cost of 2 bananas = Rs. 1.502 = Rs. 3

Cost of 1 pack of biscuits = RS. 4.50

Cost of 2 glasses of lemon juice = Rs. 32 = Rs. 6

So, Total cost = Rs. 3 + Rs. 4.50 + Rs. 6 = Rs. 13.50

Money left = Total money – Money spent

= Rs. 30 – Rs. 13.50 = Rs. 16.50.

### 14. Three notebooks, two pencils and two erasers. Total cost Rs. 22. Money left Rs. 8.

Ans. Cost of 3 notebooks = Rs. 5 3 = Rs. 15

Cost of 2 pencils = Rs. 2.502 = Rs. 5

Cost of 2 erasers = Rs. 12 = Rs. 2

Total cost = Rs. 15 + Rs. 5 + Rs. 2 = Rs. 22

Money left = Total money – Money spent = Rs. 30 – Rs. 22 = Rs. 8

### 15. Three friends wanted to buy a cricket bat and ball. Bina had Rs. 48.50, Raman had Rs. 55. 50 and Venu had Rs. 38.00. How much money did they have in all?

Ans. Money with Bina = Rs. 48.50

Money with Raman = Rs. 55.50

Money with Venu = Rs. 38.00

Total money = Rs. 142.00

### 16. Hari booked a railway ticket for Rs. 62.50. He gave a 100 rupee note. How much money will he get back with the ticket?

Ans. Total money with Hari = Rs. 100

Money spent on ticket = Rs. 62.50

Money left = Rs. 100 – Rs. 62.50

= Rs. 37.50

### 17. Gita and her friends went shopping. She bought things for Rs. 58, Rs. 37 and Rs. 22. Gita had a hundred-rupee note. How much money should she borrow from her friends to pay the bill?

Ans. Total money with Geeta = Rs. 100

Money spent by Geeta = Rs. 58 + Rs. 37 + Rs. 22 = Rs. 117

Money to be borrowed = Rs. 117 – Rs. 110 = Rs. 17.

Class 3 Maths Rupees and Paise

### 18. Find the cost of tickets:

(a) Bhupen is going from New Jalpaiguri to Alipurduar. That is the cost of his ticket?

Ans.  Cost of ticket from New Jalpaiguri to Alipurduar is Rs. 28.00.

(b) Indira has to go from New Jalpaiguri to Goalpara. How much does she pay for the ticket?

Ans.  Cost of ticket from New Jalpaiguri to Goalpara is Rs. 49.50.

(c) Debu, Shoma and Gobind are going from New Jalpaiguri to New Mal. What amount will they pay for tickets?

Ans. Fare from New Jalpaiguri to New Mal = Rs. 12. 50

Amount of fare from debu, Shoma and Gobind = Rs. 12. 503 = Rs. 37.50

Money given for tickets = Rs. 50

Money spent on tickets = Rs. 37.50

Money got back = Rs. 50 – Rs. 37.50 = Rs. 12.50.

## NCERT solutions for Class 3 Mathematics Chapter 14 Rupees and Paise

NCERT Solutions Class 3 Maths Rupees and Paise PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 3 Maths includes text book solutions from Class 3 Maths Book . NCERT Solutions for CBSE Class  Maths have total 14 chapters. 3 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 3 solutions PDF and solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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<meta http-equiv="refresh" content="1; url=/nojavascript/"> Multiplication and Division of Radicals ( Activities ) | Algebra | CK-12 Foundation

# Multiplication and Division of Radicals

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# I forgot How to do these

I forgot How to do these....

## Homework Statement

y = x^2 - 8x + 10
change into y = (x[plus or minus]A)*(x[plus or minus]B)

I just forgot how to do these.... real fast could someone solve w/ showing work?

Thanks. I just don't remember how to do it.....

Related Precalculus Mathematics Homework Help News on Phys.org
You need to find 2 numbers that give you the difference of -8 and the product of positive 10.

Since you won't be able to find it by simple factorization, you have to use the quadratic formula.

Oh ok thanks.

yea, i was just running factors over and over in my head and i wasn't coming up with anything, I'm kind of brain dead, so i wasn't sure if it was just me. Thanks.

1 and 10
2 and 5

:(

You need to find 2 numbers that give you the difference of -8 and the product of positive 10.

Since you won't be able to find it by simple factorization, you have to use the quadratic formula.

when i type in on Google quadratic formula, then i plug the equations in, it tells me x=16 and x = 8

?????? not the answer i need.

also those were wrong, i did it wrong. hold on

Nope ... try it again.

ok i think i got it, is it just (x - [8+$$\sqrt{24}$$/2]) * (x - [8-$$\sqrt{24}$$/2])?

ok i think i got it, is it just (x - [8+$$\sqrt{24}$$/2]) * (x - [8-$$\sqrt{24}$$/2])?
Yes, but don't forget to reduce!

by that, you just mean plugging it into a calculator and finding the answer, correct?

which happens to be 6.5505 & 1.4495 correct?

by that, you just mean plugging it into a calculator and finding the answer, correct?

which happens to be 6.5505 & 1.4495 correct?
No. $$\frac{8 \pm \sqrt{4 \cdot 6}}{2}$$ can reduce.

so 4 $$\pm \sqrt{2*3}$$?

Yeppp.


text:
Journal of Complexity ( IF 1.338 ) Pub Date : 2019-08-20 , DOI: 10.1016/j.jco.2019.101426
Zhiying Fang; Zheng-Chu Guo; Ding-Xuan Zhou

We study a learning algorithm for distribution regression with regularized least squares. This algorithm, which contains two stages of sampling, aims at regressing from distributions to real valued outputs. The first stage sample consists of distributions and the second stage sample is obtained from these distributions. To extract information from samples, we embed distributions to a reproducing kernel Hilbert space (RKHS) and use the second stage sample to form the regressor by a tool of mean embedding. We show error bounds in the ${L}^{2}$-norm and prove that the regressor is a good approximation to the regression function. We derive a learning rate which is optimal in the setting of standard least squares regression and improve the existing work. Our analysis is achieved by using a novel second order decomposition to bound operator norms.

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2018-09-27

# Model Predictive Control for DAEs from an ODE perspective

## Jun.-Prof. Dr. Karl Worthmann, TU Ilmenau

26 Nov 2018, 16:15–17:45; Location: S2|17-103

Differential Algebraic Equations (DAEs) combine Ordinary Differential Equations (ODEs) with algebraic constraints. Hence, even for linear systems both the initial condition and the control input cannot be arbitrarily chosen. We present a framework for linear regular systems, which allows to characterise the space of consistent initial conditions and the set of admissible controls from an ODE point of view. Then, based on an augmented system, we design a Model Predictive Control (MPC) scheme such that asymptotic stability of the origin w.r.t. the MPC closed loop is guaranteed.

Category: CE Seminar


text:
# perfect-numbers

• The Ideal Generated by a Non-Unit Irreducible Element in a PID is Maximal Let $R$ be a principal ideal domain (PID). Let $a\in R$ be a non-unit irreducible element. Then show that the ideal $(a)$ generated by the element $a$ is a maximal ideal.   Proof. Suppose that we have an ideal $I$ of $R$ such that $(a) \subset I \subset […] • Group of Order pq is Either Abelian or the Center is Trivial Let G be a group of order |G|=pq, where p and q are (not necessarily distinct) prime numbers. Then show that G is either abelian group or the center Z(G)=1. Hint. Use the result of the problem "If the Quotient by the Center is Cyclic, then the Group is […] • Vector Space of Polynomials and a Basis of Its Subspace Let P_2 be the vector space of all polynomials of degree two or less. Consider the subset in P_2 \[Q=\{ p_1(x), p_2(x), p_3(x), p_4(x)\},$ where \begin{align*} &p_1(x)=1, &p_2(x)=x^2+x+1, \\ &p_3(x)=2x^2, &p_4(x)=x^2-x+1. \end{align*} (a) Use the basis $B=\{1, x, […] • Quiz 1. Gauss-Jordan Elimination / Homogeneous System. Math 2568 Spring 2017. (a) Solve the following system by transforming the augmented matrix to reduced echelon form (Gauss-Jordan elimination). Indicate the elementary row operations you performed. […] • Elements of Finite Order of an Abelian Group form a Subgroup Let$G$be an abelian group and let$H$be the subset of$G$consisting of all elements of$G$of finite order. That is, $H=\{ a\in G \mid \text{the order of a is finite}\}.$ Prove that$H$is a subgroup of$G$. Proof. Note that the identity element$e$of […] • The Center of a p-Group is Not Trivial Let$G$be a group of order$|G|=p^n$for some$n \in \N$. (Such a group is called a$p$-group.) Show that the center$Z(G)$of the group$G$is not trivial. Hint. Use the class equation. Proof. If$G=Z(G)$, then the statement is true. So suppose that$G\neq […]
• Find Values of $a$ so that Augmented Matrix Represents a Consistent System Suppose that the following matrix $A$ is the augmented matrix for a system of linear equations. $A= \left[\begin{array}{rrr|r} 1 & 2 & 3 & 4 \\ 2 &-1 & -2 & a^2 \\ -1 & -7 & -11 & a \end{array} \right],$ where $a$ is a real number. Determine all the […]
• The Range and Null Space of the Zero Transformation of Vector Spaces Let $U$ and $V$ be vector spaces over a scalar field $\F$. Define the map $T:U\to V$ by $T(\mathbf{u})=\mathbf{0}_V$ for each vector $\mathbf{u}\in U$. (a) Prove that $T:U\to V$ is a linear transformation. (Hence, $T$ is called the zero transformation.) (b) Determine […]


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# Angle in Semicircle is Right Angle

Consider the equation of the circle with centre at the origin $O\left( {0,0} \right)$ is given by the equation

Let $AOB$ be nay diameters of the circle and $P\left( {{x_2},{y_2}} \right)$ be any point on the given circle.
We shall show that $m\angle APB = {90^ \circ }$.
Suppose that coordinates of $A$ is $\left( {{x_1},{y_1}} \right)$, then $B$ has coordinates $\left( { - {x_1}, - {y_1}} \right)$.
Slope of $AP = \frac{{{y_1} - {y_2}}}{{{x_1} - {x_2}}} = {m_1}$
Slope of $BP = \frac{{{y_1} + {y_2}}}{{{x_1} + {x_2}}} = {m_2}$
Now multiplying the slopes ${m_1}$and ${m_2}$, we get
${m_1}{m_2} = \frac{{{y_1}^2 - {y_2}^2}}{{{x_1}^2 - {x_2}^2}}\,\,\,\,{\text{ - - - }}\left( {\text{i}} \right)$
Since points $A\left( {{x_1},{y_1}} \right)$ and $P\left( {{x_2},{y_2}} \right)$ lies on the circle, we have

Substituting the values of ${x_1}^2$ and ${x_2}^2$ from equation (ii) into equation (i), we get

This is the condition of perpendicular lines.
Thus $AP \bot BP$ and so $m\angle APB = {90^ \circ }$.


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# A Search for B -> K(*) nu nubar and Invisible Quarkonium Decays

Abstract : We search for the flavor-changing neutral-current decays B->K(*)\nu\nu, and the invisible decays J/psi->\nu\nu\ and psi(2S)->\nu\nu\ via B->K(*)J/psi and B->K(*)psi(2S) respectively, using a data sample of 471 x10^6 BB pairs collected by the BaBar experiment. We fully reconstruct the hadronic decay of one of the B mesons in the Upsilon(4S)->BB decay, and search for the B->K(*)\nu\nu\ decay in the rest of the event. We observe no significant excess of signal decays over background and report branching fraction upper limits of BR(B+->K+\nu\nu)<3.7 x10^-5, BR(B0->K0\nu\nu)< 8.1 x10^-5, BR(B+->K*+\nu\nu)<11.6 x10^-5, BR(B0->K*0\nu\nu)<9.3 x10^-5, and combined upper limits of BR(B->K\nu\nu)<3.2 x10^-5 and BR(B->K*\nu\nu)<7.9 x10^-5, all at the 90% confidence level. For the invisible quarkonium decays, we report branching fraction upper limits of BR(J/psi->\nu\nu)<3.9 x10^-3 and BR(psi(2S)->\nu\nu)<15.5 x10^-3 at the 90% confidence level. Using the improved kinematic resolution achieved from hadronic reconstruction, we also provide partial branching fraction limits for the B->K(*)\nu\nu\ decays over the full kinematic spectrum.
Document type :
Journal articles

http://hal.in2p3.fr/in2p3-00806650
Contributor : Sabine Starita <>
Submitted on : Tuesday, April 2, 2013 - 10:21:36 AM
Last modification on : Tuesday, December 8, 2020 - 1:46:06 PM

### Citation

J.P. Lees, V. Poireau, V. Tisserand, N. Arnaud, M. Davier, et al.. A Search for B -> K(*) nu nubar and Invisible Quarkonium Decays. Physical Review D, American Physical Society, 2013, 87, pp.112005. ⟨10.1103/PhysRevD.87.112005⟩. ⟨in2p3-00806650⟩

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text:
# feynmf: colour flow lines

I would like to add colour flow lines to Feynman diagrams as in this example:

Is there a convenient way to have such a functionality?

The code is the following:

\documentclass[class=minimal,border=20pt]{standalone}
\usepackage{feynmf}
\begin{document}
\begin{fmffile}{diagram}
\begin{fmfgraph*}(150, 150)
\fmfleft{i}
\fmfright{o1,o2}
\fmf{fermion}{i,v,o1}
\fmf{gluon}{v,o2}
\end{fmfgraph*}
\end{fmffile}
\end{document}

This is a code which produces something rather similar to what you want:

 \documentclass[class=minimal,border=20pt]{standalone}
\usepackage{feynmp}

\newcommand{\LFermionFlow}[7][X]
% Usage: see \LFermionFlow[Deformation]{Node1}{Node2}{Length}{Shift x}{Shift y}{color}
{
\fmffreeze
\fmf{phantom}{#2,#2FFNode#3}
\fmf{phantom,tension=#4}{#2FFNode#3,#3FFNode#2}
\fmf{phantom}{#3FFNode#2,#3}
\fmffreeze
\fmfshift{#5,#6}{#2FFNode#3,#3FFNode#2}
\fmffreeze
\if X#1 {
\fmf{fermion,width=0.5,fore=#7,left=0.3}{#2FFNode#3,#3FFNode#2}
}
\else
{
\fmf{fermion,width=0.5,fore=#7,left=#1}{#2FFNode#3,#3FFNode#2}
}
\fi
}

\newcommand{\RFermionFlow}[7][X]
% Usage: see \RFermionFlow[Deformation]{Node1}{Node2}{Length}{Shift x}{Shift y}{color}
{
\fmffreeze
\fmf{phantom}{#2,#2FFNode#3}
\fmf{phantom,tension=#4}{#2FFNode#3,#3FFNode#2}
\fmf{phantom}{#3FFNode#2,#3}
\fmffreeze
\fmfshift{#5,#6}{#2FFNode#3,#3FFNode#2}
\fmffreeze
\if X#1 {
\fmf{fermion,width=0.5,fore=#7,right=0.3}{#2FFNode#3,#3FFNode#2}
}
\else
{
\fmf{fermion,width=0.5,fore=#7,right=#1}{#2FFNode#3,#3FFNode#2}
}
\fi
}
\begin{document}
\begin{fmffile}{diagram}
\begin{fmfgraph*}(150, 150)
\fmfleft{i}
\fmfright{o1,o2}
\fmf{fermion,label=$~$}{i,v,o1}
\fmf{gluon,label=$~$}{v,o2}
\fmffreeze
\RFermionFlow{i}{o2}{0.5}{0.5}{0}{blue}
\RFermionFlow{o2}{o1}{0.5}{0.5}{0}{red}
\end{fmfgraph*}
\end{fmffile}
\end{document}

I removed the corners from the flow lines.

Of course, here this is not a fermion flow (for which the command originally was designed), but it can perhaps also serve as a `color flow'.


text:
# Applied elasticity: matrix and tensor analysis of elastic continua

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Elasticity and Continuum Mechanics Texts in Rutgers Libraries last updated Jan 2011 (A.J. Nagy/ A. N. Norris [email protected] Elasticity texts: General 1. Mathematical theory of elasticity, I. S. Sokolnikoff, New York, McGraw-Hill, 1956.

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Sketching in Adversarial Environments Implicit Runge–Kutta Methods for Lipschitz Continuous Ordinary Differential Equations

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Applied elasticity : matrix and tensor analysis of elastic continua. J.D. Renton （Ellis Horwood series in mechanical engineering） E. Horwood , Halsted Press, 1987

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### Introduction to Elasticity/Tensors - Wikiversity

en.wikiversity.org/wiki/Introduction_to_Elasticity/Tensors

A second order tensor is a linear operator that sends vectors to vectors. According to Simmonds, "the name tensor comes from elasticity theory where in a loaded elastic body the stress tensor acting on a unit vector normal to a plane through a point delivers the tension (i.e., the force per unit area) acting across the plane at that point."


text:
design – How should I handle complex class construction?

I’m making a naval warfare strategy game, based on a boardgame, in C# and having difficulty finding a good way to construct my complex ship objects (I am a beginner in the language and OOP).

Currently, each ship class inherits from an abstract base `Ship` class that implements the interface `IShip` (code below). This interface defines the properties and behaviours common to all ships. I have attempted to reduce complexity by grouping related properties into their own objects (e.g., one models the crew, another models the rigging, etc.). As these properties are required for a given ship to function properly, I would like to initialise them in the ship constructor. I have reduced the number of constructor parameters to just a single `ShipProperties` object, which gets passed into a simple ship factory method to simplify ship construction and reduce code repetition. Ultimately, this property object will be set, using object initialisers for clarity, by reading game scenarios from a JSON file.

I feel there must be a better solution to this issue, however, so would appreciate feedback on my design.

Ship interface:

``````public interface IShip
{
Identifiers Identifiers { get; }
Stats Stats { get; }
Crew Crew { get; }
Rigging Rigging { get; }
Armaments Armaments { get; }
MovementAbilities MovementAbilities { get; }

void MoveTo(Coordinates coordinates);
void GrappleWith(IShip ship);
void UngrappleFrom(IShip ship);
void Board(IShip ship);
void Unfoul();
}
``````

Abstract base ship class, with default implementations of ship interface:

``````public abstract class Ship : IShip
{
public Identifiers Identifiers { get; }
public Stats Stats { get; }
public Crew Crew { get; }
public Rigging Rigging { get; }
public Armaments Armaments { get; }
public MovementAbilities MovementAbilities { get; }

public Ship(ShipProperties shipProperties)
{
Identifiers = shipProperties.Identifiers;
Stats = shipProperties.Stats;
Crew = shipProperties.Crew;
Rigging = shipProperties.Rigging;
Armaments = shipProperties.Armaments;
MovementAbilities = shipProperties.MovementAbilities;
}

public void MoveTo(Coordinates coordinates) { }
public void GrappleWith(IShip ship) { }
public void UngrappleFrom(IShip ship) { }
public void Board(IShip ship) { }
public void Unfoul() { }
}
``````

Ship properties record:

``````public record ShipProperties
{
public Identifiers Identifiers { get; init; }
public Stats Stats { get; init; }
public Crew Crew { get; init; }
public Rigging Rigging { get; init; }
public Armaments Armaments { get; init; }
public MovementAbilities MovementAbilities { get; init; }
}
``````

Ship property objects:

``````public class Identifiers
{
public string Name { get; }
public ShipClass Class { get; } // is an enum
public Nationality Nationality { get; } // is an enum
public int ID { get; }

public Identifiers(string name, ShipClass @class, Nationality nationality) // not every ship has an ID in every scenario
{
Name = name;
Class = @class;
Nationality = nationality;
}

public Identifiers(string name, ShipClass @class, Nationality nationality, int id)
: this(name, @class, nationality)
{
ID = id;
}
}

public class Stats
{
public int PointValue { get; }
public int HullHP { get; private set; }
public int HullDepth { get; }

public Stats(int pointValue, int hullHP, int hullDepth)
{
PointValue = pointValue;
HullHP = hullHP;
Depth = hullDepth;
}
}

public class Crew
{
public CrewQuality Quality { get; } // is an enum
public int() SectionStrengths { get; set; }

public Crew(CrewQuality quality, params int() sectionStrengths)
{
Quality = quality;

SectionStrengths = new int(sectionStrengths.Length);
for (int i = 0; i < sectionStrengths.Length; i++)
{
SectionStrengths(i) = sectionStrengths(i);
}
}
}

public class Rigging
{
public int() RiggingHPPerMast { get; set; }
public Rigging(params int() riggingHPPerMast)
{
RiggingHPPerMast = new int(riggingHPPerMast.Length);
for (int i = 0; i < riggingHPPerMast.Length; i++)
{
RiggingHPPerMast(i) = riggingHPPerMast(i);
}
}
}

public class Armaments
{
public ShotType ShotType { get; private set; } // is an enum
public Guns Guns {get; private set;}

public Armaments(Guns guns)
{
Guns = guns;
}

{
}
}

public class MovementAbilities
{
public int TurningAbility { get; private set; }
public int BattleSailSpeed { get; private set; }
public int FullSailSpeed { get; private set; }

public MovementAbilities(int turningAbility, int battleSailSpeed) // for basic game rules
{
TurningAbility = turningAbility;
BattleSailSpeed = battleSailSpeed;
}

public MovementAbilities(int turningAbility, int battleSailSpeed, int fullSailSpeed)
: this(turningAbility, battleSailSpeed)
{
FullSailSpeed = fullSailSpeed;
}
}
``````

Ship factory:

``````public class ShipFactory
{
public IShip CreateShip(ShipProperties shipProperties)
{
return shipProperties.Identifiers.Class switch
{
ShipClass.ShipOfTheLine      => new ShipOfTheLine(shipProperties),
ShipClass.LargeShipOfTheLine => new LargeShipOfTheLine(shipProperties),
ShipClass.Frigate            => new Frigate(shipProperties),
ShipClass.LargeFrigate       => new LargeFrigate(shipProperties),
ShipClass.Corvette           => new Corvette(shipProperties),
ShipClass.Brig               => new Brig(shipProperties),
ShipClass.Sloop              => new Sloop(shipProperties),
ShipClass.Schooner           => new Schooner(shipProperties),
ShipClass.Gondola            => new Gondola(shipProperties),
ShipClass.Galley             => new Galley(shipProperties),
ShipClass.Gunboat            => new Gunboat(shipProperties),
ShipClass.Privateer          => new Privateer(shipProperties),
ShipClass.Merchantman        => new Merchantman(shipProperties),
ShipClass.FireShip           => new FireShip(shipProperties),
ShipClass.BombKetch          => new BombKetch(shipProperties),
_                            => throw new NotImplementedException()
};
}
}
``````

real analysis – Question about construction of \$mathbb{R}\$

I hope this question is not naïve, but I’ve stumbled across it and now it’s really bugging me. If we define the real numbers as the completion of the rationals, isn’t the statement that every Cauchy sequence converges a tautology? In what sense is it a theorem?

japan – Are there any Japanese castles currently under construction?

Many once destroyed or demolished Japanese castles were later erected anew in order to boost local tourism. For example, reconstruction of Osaka Castle was finished in 1997.

Are there any castles that are currently being built? I am only aware of on-going restoration of Kumamoto Castle after it was damaged in 2016 earthquake.

differential equations – Construction of Navigation Function: Error

https://www.sciencedirect.com/science/article/abs/pii/S0921889015302451

https://arxiv.org/pdf/1605.00638.pdf – Paragraph III

I am trying to create a navigation function for a 2D system.

$$begin{cases} dot{x}=-x \ dot{y}=-y end{cases}$$

It is built, according to sources, in the following way.

In the end, I want to get something like this

Well. I am trying to do it according to the following algorithm:

1.$$X=(x,y)$$ – vector of states and $$x_{goal}=(0,0)$$ – vector of goal states;

1. $$x_{obs}=(1,1)$$ – obstacles position;

2. $$gamma_d(x)=||X-x_{goal}||^2$$

3. $$beta(x)=(X-x_{obs})^T(X-x_{obs})$$

4. Construct navigation function like: $$frac{gamma_d(x)}{(gamma_d(x)^k+beta(x))^{1/k}}$$

Well, this is the code in Mathematica and I get utter nonsense. Instead of an area of attraction in the region of the target state, I get uncertainty, and the obstacles are not visible at all.

``````Clear("Derivative")

ClearAll("Global`*")

k = 5

X = {x, y}

xgoal = {0, 0}

xobs = {1, 1}

(Gamma)d = Sqrt((X - xgoal).(X - xgoal))^2

(Beta) = (X - xobs).(X - xobs)

(CapitalPhi) = (Gamma)d/(((Gamma)d^k + (Beta))^(1/k))

ParametricPlot3D({x, y, (CapitalPhi)}, {x, -4, 4}, {y, -4, 4},
PlotPoints -> 50)
``````

Problem: What did I go wrong in designing the navigation function?

nt.number theory – Construction of maximal abelian extensions of totally real fields complex-analytically

So Hilbert’s 12th problem has finally been solved for totally real fields (https://arxiv.org/abs/2103.02516), although $$p$$-adic analytically. There is an explicit construction of maximal abelian extensions of totally real fields through adjunction of Brumer-Stark units along with certain other elements.

The question is: what insights does this $$p$$-adic construction provide into how this might be accomplished complex analytically as was the original vision of Hilbert, already realized for the rational field, its imaginary quadratic extensions and a few other fields using division points on abelian varieties?

Dasgupta and Kakde mention that just as in their work integration might be required rather than just special values of complex analytic functions.

Construction of the Hilbert Scheme

I am reading the book "Rational Curves on Algebraic Varieties" of János Kollár. Definition-Proposition 1.2, begin like this:

Let $$g:Yrightarrow Z$$ be a projective morphism and $$mathcal{O}(1)$$ a $$g$$-ample line bundle. I would like to know what is a "$$g$$-ample line bundle".

Thank you a lot!

circle packing – trigonometry- Construction Profession needs help

Architect designed floor layout with a radius that is outside of the building and too far away to see the vertex. Normally we would pull a string the length of the radius but that is not an option. Is there a way to calculate the height of an arc from different points along the chord?

Example- I know where the arc starts and ends, the radius is 300′ and not visible from inside the building but we also know the chord length is 50′. How can I plot the curve of this circle every 3′?
The intention is to draw the arc on the floor as close as possible.

nt.number theory – Construction of Genus class fields

Given a finite extension $$K/mathbb{Q}$$, the genus class field $$G$$ is defined to be the maximal abelian extension of $$mathbb{Q}$$ that is a subfield of the Hilbert class field $$H$$ of $$K$$. I am trying to understand the proof of an alternative construction of $$G$$ in the case when $$K$$ is a cyclic extension with prime degree $$l$$ as follows.

Let $$p_1, p_2, …, p_n$$ be the primes in $$mathbb{Q}$$ that ramify in $$K$$. Suppose $$G_1, G_2, …, G_n$$ be cyclic extensions of degree $$l$$ over $$mathbb{Q}$$ such that $$G_i$$ ramify only at $$p_i$$. Then $$G = G_1 G_2…G_n$$.

I was reading the proof in “Construction of Class Fields – Cael Herz“. The basic strategy is to associate $$K$$ and the $$G_i$$‘s to norm subgroups of $$K$$ using Class field theory and relate them. But I find it hard to comprehend and justify certain crucial claims in the proof one of which I posted on MO earlier (Norm groups of number fields).

Can someone refer me to an alternate proof of this fact or provide some light into Cael’s proof if possible?


text:
# Car Friction problem

1. Mar 21, 2005

### stupidpig

Hi, I've been working on this problem for a while and I keep on getting same answer! Can someone please tell me what I'm doing wrong.

Problem:
A circular curve is banked so that a car travelling with uniform speed rounding the curve usually relies on friction to keep it from slipping to this left or right.
What is the maximum velocity the car can maintain in order that the car does not move up the plane.(Answer in km/hr).

Mass of car = 2.3kg
Angle = 34 degree
Coefficient of kinetic friction = 0.41

My work:
N = mgcos(34) = 18.68
Fp = mgsin(34) = 12.6
Fr = (0.41)N = 7.66
Fc = centripetal force = mv^2/r

so here's my final equation to get v:
mv^2/r-Fr = Fp
(2.3)(v^2)/(56.4)-(7.66) = 12.6
v = 22.28m/s = 82.08km/hr

82.08km/hr is so unrealistic for 2.8kg car to bank such a turn.
Heck, even my puny vw golf cant even do it at 82.08km/hr

I must be doing something wrong!

Thanks

2. Mar 22, 2005

### Clausius2

Given the notation above, the force of friction must balance the centripetal force and weight:

$$\mu Mgcos \alpha=\frac{Mv^2}{R}cos\alpha+Mgsen\alpha$$

SURPRISE! the problem has no dependence on the mass M!!!. Is it true in real world???

$$v=\sqrt{gR\frac{\mu+tan\alpha}{1-\mu tan \alpha}}$$

For velocities greater than this, the equilibrium is broken and car would be rejected on the tangent way.

I wish there were some road with $$\mu=1/tan\alpha$$ !!!


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text:
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