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# New 3D model format and single header SDK

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Dear All,

I'd like to introduce you a new model format. It is simple, well-defined and well-documented, and has the best data density of all formats. Suzanne with normals, UVs and materials require less than 12K using this format.

I'm not good with names, so it's just simply called Model 3D and has the extension ".m3d". I'd like to get some feedback and hear your opinion about it.

Provided implementations

For compatibility, it is implemented with Assimp. Unfortunately according to my findings Assimp fails to live up to it's promise "Loads 40+ 3D file formats into one unified and clean data structure.", as its data structure is neither unified nor clean. But I managed it, so here it is, libassimp can load M3D files with vertex colors, materials, textures, and skeletal animations.

A new model format is no good if you can't use it with your favorite modeler software, so I have provided Blender plugin to export objects and their animations into M3D. The exporter is fully functional and supports all features of the M3D format, however the importer is WIP. You can export vertex lists with colors, normals, UVs, PBR materials (PrincipledBSDF), textures, armature, and several model actions too using the Blender Animation's timeline markers feature.

And finally, it's native SDK is an stb-style, totally dependency-free, single header file ANSI C89/C++11 SDK. It can load and save files, supports the binary M3D format (and if included with the M3D_ASCII define then it's ASCII counterpart, A3D too). It is MIT licensed, written in ANSI C and with the provided C++ wrapper class it should be straightforward to integrate into any new or existing projects. It compiles to about 70K, which includes the built-in PNG texture decompressor.

Features of the format

A few words on why does it worth it to use this format:

• it is Open Source and free. Not only its SDK, but the format itself is MIT licensed and expandable.
• it can store big models in very little files. Blender's cube can be saved in about 100 bytes. An usual Blitz3D animated model (.b3d) in .m3d saves 70%-80% storage space.
• exactly one model per file, but with all properties: materials, skeleton, textures, skeletal animations. No complex scene parsing involved. (Lightning and camera setups are NOT properties of the model!)
• but if needed, engine specific data can be embedded in a way that it won't break the model compatibility with other software.
• the same model can be read by different software with different levels. The same file is compatible with more applications, for example: one can only load the static mesh from it, while another can also utilize the bone information and the animations.
• it has a human readable ASCII variant, which can be easily loaded with a slightly modified Wavefront OBJ loader (however the SDK can handle).
• it's SDK is simple, fast and painless to use (according to the K.I.S.S. has only 5 functions altogether).
• it's in-memory format is efficient and fast (uses indices in contrast to recursive node parsing matching strings), and well-specified (for example it makes it clear that right-handed coordinate system is used with the coordinates, and how the coordinate system is oriented. No surprises when you load a model from M3D).

I've provided a command line utility (m3dconv) which loads any Assimp-supported format and converts it into Model 3D. A simple, portable GL-based viewer (m3dview) is also included in the repository to demonstrate how to display the animated models once you loaded them (whole thing less than 500 SLoC :-) ). You can compile the latter with GLFW, GLUT and SDL2 (the interface is autodetected, just run "make").

Cheers,
bzt

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13 hours ago, bzt said:

A new model format is no good if you can't use it with your favorite modeler software, so I have provided Blender plugin

I won't call Blender to be favorite but if you really want to push your stuff, Maya, Houdini, 3D Max and ZBrush are must haves for you because those are the industry leading ones for games.

13 hours ago, bzt said:

it has a human readable ASCII variant

How fast is parsing performed? High compressionratio most of the time leads to slow processing performance so I'm corious if it can be as fast as FBX or OBJ (as you mentioned).

13 hours ago, bzt said:

it's SDK is simple, fast and painless to use

How complex is the code for processing the file and what about flexibility? Do I have to integrate Assimp into our engine just to use your file format or do you also provide code that can easily be grabbed and placed in our source without the need to make huge adaptions for us to work?

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Hi,

5 hours ago, Shaarigan said:

I won't call Blender to be favorite but if you really want to push your stuff, Maya, Houdini, 3D Max and ZBrush are must haves for you because those are the industry leading ones for games.

Well, are they Open Source? Until then you can use the m3dconv utility to convert their formats into M3D in your build system automatically.

5 hours ago, Shaarigan said:

How fast is parsing performed? High compressionratio most of the time leads to slow processing performance so I'm corious if it can be as fast as FBX or OBJ (as you mentioned).

Actually a LOT faster than any FBX or OBJ loaders out there. However the ASCII variant A3D is for debugging purposes. For your game, you should use the binary variant, M3D which loads as fast as possible. There are no unecessarry string conversions, everything is read right from binary and all chunk sizes are known in advance (so it allocates memory as few times as possible). Profiling showed that the slowest part is performing the post-processing phase, calculating the transformation matrices for the bones, but a) that's still pretty fast, b) you can avoid that if you include the SDK with the M3D_NOANIMATION define. That way only the file format decoder will run.

For small file sizes, the binary format is compressed. To further speed up your game loading for the price of bigger storage, you can avoid that compression (see m3dconv), and store only the binary chunks (which are still pretty small compared to OBJ, FBX, .glF or any other XML or JSON based formats.) The m3d_load() autodetects if the binary is compressed or not, and what's more, if it's not then it does not allocate extra memory and uses pointers directly into the uncompressed image.

5 hours ago, Shaarigan said:

How complex is the code for processing the file and what about flexibility?

Both questions are answered on the project's main README.md file. You can load a colored static mesh in 80 SloC if you don't want to use the SDK (which you should, it's a single header file with only one function for loading). The format is also flexible, supports engine-specific chunks (you have to parse those on your own of course).

5 hours ago, Shaarigan said:

Do I have to integrate Assimp into our engine

Most definitely NOT. You only have to include an stb-style single header library if you don't want to parse the files on your own. The Assimp support is only there in case if you already have integrated Assimp, but that's all.

5 hours ago, Shaarigan said:

do you also provide code that can easily be grabbed and placed in our source without the need to make huge adaptions for us to work?

I'm starting to have a feeling that you haven't read my post, nor have you checked the repo.

Of course I provide code:

• an example how to parse the files without the SDK (80 SLoC)
• tests directory contains examples
• m3dconv also uses the API and provides example
• m3dview was written to showcase how to use the API and display an animated model (500 SLoC)
• plus there's the API usage manual, full with examples.

Cheers,
bzt

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A few numbers to satisfy your curiousity:

The WusonBlitz.b3d file (provided in the Assimp repo test/models/B3D) is a binary format, 87k. Converted into M3D it's only 29k. Loading the same file using

Assimp: 581,017 bytes in 4,088 blocks
M3D SDK (m3d.h): 229,534 bytes in 4 blocks

As you can see, Assimp requires more than twice the RAM, and it uses more than 4 thousand blocks. That means at least more than 4 thousand memory allocation calls. The M3D SDK on the other hand not just loads the same model into less RAM, but it only calls memory allocation 4 times only. Also the native SDK's memory is less fragmented, meaning less memory wasted. (FYI: fewer memory allocation calls => faster loading time.)

Also M3D SDK stores the model in a more compact way and provides faster access (indices instead of recursive node-walking with string comparititons). The native in-memory format resembles VBOs and EBOs so you can display them with fewer conversions (actually a non-animated mesh can be directly fed into a VBO/EBO).  (FYI: simpler structure with direct indices instead of look-ups loops => faster rendering time.)

All the differences in the Assimp's and M3D's philosophy is explained in the repo, assimp/README.md and the M3D SDK API usage manual is here with both C and C++ examples.

Cheers,
bzt

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17 hours ago, bzt said:

Well, are they Open Source?

Defintely not but they provide plugins and are the industry standard. If I have to parse their formats into something you provide, I can on the same track parse it directly into something our engine supports by native so I don't see any benefits of your file format here especially in a real production case.

There might be benefits for indie games that really have to take watch of the space they have for assets on an online share for example but those people won't use a file format not supported by their major engines Unity and Unreal so, im corious what your statement is 🙂

17 hours ago, bzt said:

Actually a LOT faster than any FBX or OBJ loaders out there

Did you see/ test against this very popular implementation on GitHub? I implemented similar code in our engine which makes use of our streaming API and came up with round about 800 ms for the file the person provides on GitHub on a Win7 maschine Intel i7 hexa core x64 OS. Would be corious if you can provide some benchmarks

17 hours ago, bzt said:

if you don't want to use the SDK (which you should, it's a single header file with only one function for loading)

As you make use of the STL, especially in the model wrapper, this is against our engine policy, so no I would prefer to not use the SDK, the same for the sprintf's I saw in your code. This makes it difficult to integrate it in our existing systems.

So if I would decide to integrate your file format in our workflow, I would need to rewrite it from scratch to play well with our existing systems and API. This should not value your work (I feel I have to write it into each of my posts when providing a personal opinion today), just a notice from my all-day industry perspective 🤐

18 hours ago, bzt said:

I'm starting to have a feeling that you haven't read my post, nor have you checked the repo

I have carefully read the post because it might propably be of interest but you wrote about Assimp and the SDK. I don't had checked the repo and still didn't browse through it entirely. If you post it in a forum, you have in my opinion to somehow work with questions 🤷♂

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5 hours ago, Shaarigan said:

Defintely not but they provide plugins and are the industry standard. If I have to parse their formats into something you provide, I can on the same track parse it directly into something our engine supports

First, you don't have to parse their formats into something I provide, because there's already a tool to do that for you.
Second, you don't have to parse anything into your engine, you just include one header file and there you go. Are you familiar with stb-style headers? This is what my m3d.h provides for C and C++.

5 hours ago, Shaarigan said:

Did you see/ test against this very popular implementation on GitHub? I implemented similar code in our engine which makes use of our streaming API and came up with round about 800 ms

Yes of course. 800ms that's laughable 🙂 I also got a similar value repeating the test 32 times. Here's a comparition for you.

Model Format File Size Library Required Time
WusonOBJ.obj text OBJ 258k tinyobjloader real 0m0.748s
WusonOBJ.obj text OBJ 258k libassimp real 0m2.716s
WusonBlitz.b3d binary Blitz 87k libassimp real 0m0.414s
WusonBlitz.m3d uncompressed M3D 33k libassimp real 0m6.906s
WusonBlitz.a3d ASCII Model 3D 141k M3D SDK real 0m0.258s
WusonBlitz.m3d uncompressed M3D 33k M3D SDK real 0m0.073s
WusonCompr.m3d deflated M3D 42k M3D SDK real 0m0.162s

As you can see my SDK is 10 times faster than your beloved tinyobjloader. Even with deflated chunks it is still 4 times faster. But let's be fair, compare only text formats, so tinyobjloader vs A3D: my SDK is still 2.5 times faster (but this is irrelevant because you should not use the debug format in your engine). Feel free to repeat the test on your machine.

Believe me, if I say my implementation is a LOT faster, then I know what I'm talking about, I've done my homework and I had performed my tests 😉

I kindly ask you to read the README.md, and comment only when you have a clue what my repository is about. Thank you.

Cheers,

bzt

5 hours ago, Shaarigan said:

As you make use of the STL, especially in the model wrapper

Again, NO, I do not use STL. You would know that should you have read the API documentation. You can configure the SDK not to use zlib inflate at all, but then you won't have textures either, because that's needed for PNGs too. (You'll have to use your own image decoder in this case.)

5 hours ago, Shaarigan said:

I have carefully read the post

Then why are you asking questions like "do you provide code examples"? Just askin'.

Cheers,
bzt

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Oh and two more things:

5 hours ago, Shaarigan said:

the same for the sprintf's I saw in your code

That's only needed for the A3D writer. So IF you specify M3D_EXPORTER and IF you specify M3D_ASCII. By default only the binary M3D importer gets included. Why on earth would you want a model dumper in your engine????

5 hours ago, Shaarigan said:

So if I would decide to integrate your file format in our workflow, I would need to rewrite it from scratch to play well with our existing systems and API.

If ANSI C89 and C++11 standards WITHOUT ANY DEPENDENCY is a problem for your existing systems, then the problem is in your existing systems. No offense, that's the truth.

But if you want to rewrite it from scratch, feel free to do so, go ahead, check out the repository's main page README.md, which has a 80 SLoC example how to read a colored static mesh. The file format is well-defined and well-documented in every little detail, up to the last bit, see m3d_format.md.

Cheers,
bzt

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Hi,

As I said, the code does not use STL, std::string and std::vector are merely containers, only initialized in "return" statements (you won't find any push_back calls in my code). But to ease your mind, I made the M3D::Model wrapper class optional, now it's only included if M3D_CPPWRAPPER is defined. Without you're free to implement your own wrapper, but there's still no need to start from scratch, just call the C API m3d_load() and convert the struct arrays to whatever C++ object you want.

About sprintf, I see no reason why do you ever want to export a model in ASCII format from an engine. Or why would you ever want to use the ASCII format at all other than debugging. But let's say for a moment, that you need it. Could you elaborate what is your issue with the use of sprintf? If you are concerned about buffer overflows, check the code again. All buffers are accurately measured and allocated before any sprintf use. If I made a mistake in that, I'd like to know so that I can fix it.

Cheers,
bzt

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If you want your file format to get adopted by someone, you should give a good reason to take the effort to support it. First of all, you have to think about when it's used in the entire development cycle.

• During Content Creation
• Between Creation and Integration
• in the built game

Not every engine/game/developer is differentiating strictly between these steps, e. g. because the artists store and export using the same file format, or because the engine/build system doesn't process the assets.

In general, during content creation, the file format has to support everything the tool used for creation is supporting, without altering the data to much. (If you create models by placing primitives, this format has to support these primitives.)
After creation, the format should still support a lot of features (e. g. include not only the model, but also material information, a rig, animations, ...).
The format used in the built game has on the other hand to target performance, either small size or (what most will prefer nowadays) fast load times. This format might also have to rely inside a container file format, so the loader has to be able to handle the memory as a source, and not just files. Maybe there could be a special "batch mode" if there are multiple consecutive modles in memory/in a container file.

Since you emphasize a lot on the fast load time, maybe the last is most suitable for your file format. If that's the case, only the engine developers are your target audience.

Another use case might be any model file that's handled using a Version Control System (SVN, Git, ...). For all of these, a text format is easier to handle (e. g. detecting conflicts), but on the other hand, this would also require the file content to be predictable (e. g. if I change something over here, this section in the file changes and nothing else). Since I don't think this would be the case for 3D Models in general, I don't think it's worth spending to much time thinking about it (and didn't include it above).

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17 hours ago, Sacaldur said:

The format used in the built game has on the other hand to target performance, either small size or (what most will prefer nowadays) fast load times.

It is fast load times in nearly any case, especially when developing a console game. Companies Sony and Microsoft have strict guidelines how long a game is allowed to load until it first shows up to the player or become rejected from the platform

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# Balls matching boxes question

#### Usagi

##### Member
Hi guys, really simple question but...

I'm not quite sure on how they ended up with the expression for P(exactly one match). I would have done it in a more straight forward way, simply define A: matching the colour red in the red box only. B: matching the colour blue in the blue box only and C: matching the colour white in the white box only.

So P(exactly one match) = P(A)+P(B)+P(C) = $$\frac{3}{6} = \frac{1}{2}$$

How exactly did they get their expression?

Thanks

MHB Math Scholar

format: plain


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zbMATH — the first resource for mathematics

Generalized simulated annealing for function optimization. (English) Zbl 0609.65045
The authors describe a heuristic approach to find the global minimizer of an arbitrary real-valued function, where constraints may be included. A search direction is determined randomly and a new iterate is accepted, if the function value is improved or if at least a test of the form $$V<\exp (-\beta f(x_ k)^ g(f(x_{k+1})-f(x_ k)))$$ is satisfied, V randomly chosen. Numerical results obtained by an academic example indicate that the algorithm is quite sensitive to the choice of parameters. A more detailed investigation of a practical optimization problem (concentration of a neurotransmitter) and a comparison with existing results are presented.
Reviewer: K.Schittkowski

MSC:
 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming
Full Text:


text:
# Penetration depth limits of in vivo confocal reflectance imaging

### Abstract

We present experiments to predict the maximum penetration depth at which typical biological structures in amelanotic tissue can be detected with confocal microscopy. The detected signal is examined as the signal source strength (index of refraction mismatch), the source depth, and the medium scattering coefficient are varied. The detected background produced by scattering outside the focal volume is examined as the medium scattering coefficient, the depth in the medium, the dimensionless pinhole radius, $\nu_p$, and the shape of the scattering phase function are varied. When the system approaches ideal confocal performance ($\nu_p \simeq 3$), the penetration depth is limited by the signal-to-noise ratio to approximately 3–4 optical depths (OD’s) for a 0.05 index mismatch. As $\nu_p$ increases to 8, the penetration depth is limited by the signal-to-background ratio and is dependent on the scattering coefficient. At $\mu_s$ = 100 cm$^{-1}$ ($l_s$ = 100 µm) and an index mismatch of 0.05, the maximum penetration depth is approximately 2 OD.

Type
Journal article
Publication
Applied Optics


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## Which indent marker controls all the lines except first line?

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JMU CS280 SP18 WK08

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# Problem BRhyming Slang

Rhyming slang involves replacing a common word with a phrase of two or three words, the last of which rhymes with the original word. For example,

• replacing the word “stairs” with the rhyming phrase “apples and pears”,

• or replacing “rotten” with the phrase “bales of cotton”.

English has such a wide variety of spellings and pronunciations that for any non-native speaker telling what rhymes isn’t always easy. Perhaps you can help?

Typically, two words rhyme (or can be forced to rhyme) if both of their endings can be found on the same list of word endings that sound the same.

Given a common word, a number of lists, each containing word endings that sound the same, and a number of phrases, determine if those phrases could be rhyming slang.

## Input

• One line containing the single common word $S$ ($1 \le |S| \le 20$).

• One line containing an integer $E$ ($1 \le E \le 10$), the number of lists of word endings that sound the same.

• $E$ lines, each no more than $100$ characters long. Each a list of space-separated word endings.

• One line containing an integer $P$ ($1 \le P \le 10$), the number of phrases to test.

• $P$ lines, each no more than $100$ characters long, containing a phrase $p_ i$ of two or three words that might rhyme with the common word.

All words and letters will be in lower case. The common word’s ending will appear in at least one ending list.

## Output

• $P$ lines, each consisting of either:

• YES’: The phrase $p_ i$ rhymes with the common word.

• NO’: The phrase $p_ i$ does not rhyme with the common word.

Sample Input 1 Sample Output 1
stairs
2
erres airs ears ares aires
eet eat
2
apples and pears
plates of meat

YES
NO

Sample Input 2 Sample Output 2
drought
2
aught ought aut acht
ought oubt outte out oute
5
tasty sprout
difficult route
worried and fraught
forever in doubt
apples and pears

YES
YES
YES
YES
NO

Sample Input 3 Sample Output 3
listen
1
issen isten ison
2
glisten
listen

YES
YES


text:
# American Institute of Mathematical Sciences

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September  2016, 21(7): 2293-2319. doi: 10.3934/dcdsb.2016048

## Kolmogorov-type systems with regime-switching jump diffusion perturbations

 1 School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China 2 Department of Mathematics, Wayne State University, Detroit, Michigan 48202 3 Centre for Actuarial Studies, Department of Economics, The University of Melbourne, VIC 3010, Australia

Received  August 2015 Revised  November 2015 Published  August 2016

Population systems are often subject to various different types of environmental noises. This paper considers a class of Kolmogorov-type systems perturbed by three different types of noise including Brownian motions, Markovian switching processes, and Poisson jumps, which is described by a regime-switching jump diffusion process. This paper examines these three different types of noises and determines their effects on the properties of the systems. The properties to be studied include existence and uniqueness of global positive solutions, boundedness of this positive solution, and asymptotic growth property, and extinction in the senses of the almost sure and the $p$th moment. Finally, this paper also considers a stochastic Lotka-Volterra system with regime-switching jump diffusion processes as a special case.
Citation: Fuke Wu, George Yin, Zhuo Jin. Kolmogorov-type systems with regime-switching jump diffusion perturbations. Discrete and Continuous Dynamical Systems - B, 2016, 21 (7) : 2293-2319. doi: 10.3934/dcdsb.2016048
##### References:
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Yuan, Stochastic population dynamics driven by Lévy noise, Journal of Mathematical Analysis and Applications, 391 (2012), 363-375. doi: 10.1016/j.jmaa.2012.02.043. [8] N. H. Dang, N. H. Du and G. Yin, Existence of stationary distributions for Kolmogorov systems of competitive type under telegraph noise, Journal of Differential Equations, 257 (2014), 2078-2101. doi: 10.1016/j.jde.2014.05.029. [9] A. Dembo and O. Zeitouni, Large Deviation Techniques and Applications, $2^{nd}$, Jones and Bartlett, Boston, 1998. doi: 10.1007/978-1-4612-5320-4. [10] J. D. Deuschel and D. W. Stroock, Large Deviations, Academic Press, Boston, 1989. [11] M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, I, Communications on Pure and Applied Mathematics, 28 (1975), 1-47. [12] M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, II, Communications on Pure and Applied Mathematics, 28 (1975), 279-301. [13] M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, III, Communications on Pure and Applied Mathematics, 29 (1976), 389-461. doi: 10.1002/cpa.3160290405. [14] M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, IV, Communications on Pure and Applied Mathematics, 36 (1983), 183-212. doi: 10.1002/cpa.3160360204. [15] N. H. Du and N. H. Dang, Dynamics of Kolmogorov systems of competitive type under the telegraph noise, Journal of Differential Equations, 250 (2011), 386-409. doi: 10.1016/j.jde.2010.08.023. [16] N. H. Du, D. H. Nguyen and G. Yin, Conditions for permanence and ergodicity of certain stochastic predator-prey models,, to appear in Journal of Applied Probability., ().  doi: 10.1017/jpr.2015.18. [17] T. Faria and J. J. Oliveira, Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks, Journal of Differential Equations, 244 (2008), 1049-1079. doi: 10.1016/j.jde.2007.12.005. [18] B. M. Gary, A functional equation characterizing monomial functions used in permanence theory for ecological differential equation, Universitatis Iagellonicae acta mathematica, 42 (2004), 69-76. [19] T. C. Gard, Persistence in stochastic food web models, Bulletin of Mathematical Biology, 46 (1984), 357-370. doi: 10.1007/BF02462011. [20] T. C. Gard, Stability for multispecies population models in random environments, Nonlinear Analysis, 10 (1986), 1411-1419. doi: 10.1016/0362-546X(86)90111-2. [21] T. C. Gard, Introduction to Stochastic Differential Equations, Dekker, New York, 1988. [22] K. Gopalsamy, Global asymptotic stability in a periodic Lotka-Volterra system, The Journal of the Australian Mathematical Society. Series B, Applied Mathematics, 27 (1985), 66-72. doi: 10.1017/S0334270000004768. [23] X. Han, Z. Teng and D. Xiao, Persistence and average persistence of a nonautonomous Kolmogorov system, Chaos Solitons Fractals, 30 (2006), 748-758. doi: 10.1016/j.chaos.2006.04.026. [24] O. Kallenberg, Foundations of Modern Probability, $2^{nd}$ Edition, Springer, 2002. [25] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic press, Bosten, 1993. [26] Y. Li and Y. Kuang, Periodic solutions of periodic delay Lotka-Volterra equations and systems, Journal of Mathematical Analysis and Applications, 255 (2001), 260-280. doi: 10.1006/jmaa.2000.7248. [27] M. Liu and K. Wang, Stochastic Lotka-Volterra systems with Lévy noise, Journal of Mathematical Analysis and Applications, 410 (2014), 750-763. doi: 10.1016/j.jmaa.2013.07.078. [28] Q. Luo and X. Mao, Stochastic population dynamics under regime switching, Journal of Mathematical Analysis and applications, 334 (2007), 69-84. doi: 10.1016/j.jmaa.2006.12.032. [29] Q. Luo and X. Mao, Stochastic population dynamics under regime switching II, Journal of Mathematical Analysis and Applications, 355 (2009), 577-593. doi: 10.1016/j.jmaa.2009.02.010. [30] E. Lungu and B. Øksendal, Optimal harvesting from a population in a stochastic crowded environment, Mathematical Biosciences, 145 (1997), 47-75. doi: 10.1016/S0025-5564(97)00029-1. [31] E. Lungu and B. Øksendal, Optimal Harvesting from Interacting Populations in a Stochastic Environment, Bernoulli, 7 (2001), 527-539. doi: 10.2307/3318500. [32] X. Mao, G. Marion and E. Renshaw, Environmental noise supresses explosion in population dynamics, Stochastic Processes and their Applications, 97 (2002), 95-110. doi: 10.1016/S0304-4149(01)00126-0. [33] X. Mao, Delay population dynamics and environmental noise, Stochastics and Dynamics, 5 (2005), 149-162. doi: 10.1142/S021949370500133X. [34] X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, Imperial College Press, Londen, 2006. doi: 10.1142/p473. [35] X. Mao, Stochastic Differential Equations and Applications, $2^{nd}$ Edition, Horwood, Chichester, UK, 2008. doi: 10.1533/9780857099402. [36] J. D. Murray, Mathematical Biology, I. an Introduction, $3^{rd}$ Edition, Springer, 2002. [37] H. D. Nguyen, N. H. Du and G. Yin, Existence of stationary distributions for Kolmogorov systems of competitive type under telegraph noise, Journal of Differential Equations, 257 (2014), 2078-2101. doi: 10.1016/j.jde.2014.05.029. [38] S. Pang, F. Deng and X. Mao, Asymptotic properties of stochastic population dynamics, Dynamics of Continuous Discrete and Impulsive Systems Series A, 15 (2008), 603-620. [39] P. E. Protter, Stochastic Integration and Differential Equations, $2^{nd}$ Edition, Springer, 2004. [40] M. Slatkin, The dynamics of a population in a Markovian environment, Ecology, 59 (1978), 249-256. doi: 10.2307/1936370. [41] Y. Takeuchi, Global Dynamical Properties of Lotka-Volterra Systems, World Scientific, Singapore, 1996. doi: 10.1142/9789812830548. [42] Y. Takeuchi, N. H. Du, N. T. Hieu and K. Sato, Evolution of predator-prey systems described by a Lotka-Volterra equation under random environment, Journal of Mathematical Analysis and applications, 323 (2006), 938-957. doi: 10.1016/j.jmaa.2005.11.009. [43] B. Tang and Y. Kuang, Permanence in Kolmogorov-type systems of nonautonomous functional differential equations, Journal of Mathematical Analysis and Applications, 197 (1996), 427-447. doi: 10.1006/jmaa.1996.0030. [44] Z. Teng, The almost periodic Kolmogorov competitive sysems, Nonlinear Analysis, 42 (2000), 1221-1230. doi: 10.1016/S0362-546X(99)00149-2. [45] F. Wu and S. Hu, Stochastic functional Kolmogorov-type population dynamics, Journal of Mathematical analysis and applications, 347 (2008), 534-549. doi: 10.1016/j.jmaa.2008.06.038. [46] F. Wu and S. Hu, Suppression and stabilisation of noise, International Journal of Control, 82 (2009), 2150-2157. doi: 10.1080/00207170902968108. [47] F. Wu and Y. Xu, Stochastic Lotka-Volterra population dynamics with infinite delay, SIAM Journal on Applied Mathematics, 70 (2009), 641-657. doi: 10.1137/080719194. [48] F. Wu, S. Hu and Y. Liu, Positive solution and its asymptotic behaviour of stochastic functional Kolmogorov-type system, Journal of Mathematical Analysis and Applications, 364 (2010), 104-118. doi: 10.1016/j.jmaa.2009.10.072. [49] F. Wu and G. Yin, Environmental noise impact on regularity and extinction of population systems with infinite delay, Journal of Mathematical Analysis and Applications, 396 (2012), 772-785. doi: 10.1016/j.jmaa.2012.07.017. [50] G. Yin and F. Xi, Stablity of regime-switching jump diffusions, SIAM Journal on Control and Optimization, 48 (2010), 4525-4549. doi: 10.1137/080738301. [51] G. Yin and C. Zhu, Hybrid Switching Diffusions: Properties and Applications, Springer, New York, 2010. doi: 10.1007/978-1-4419-1105-6. [52] G. Yin, G. Zhao and F. Wu, Regularization and stabilization of randomly switching dynamic systems, SIAM Journal on Applied Mathematics, 72 (2012), 1361-1382. doi: 10.1137/110851171. [53] C. Zhu and G. Yin, On hybrid competitive Lotka-Volterra ecosystems, Nonlinear Analysis: Theory, Methods & Applications, 71 (2009), e1370-e1379. doi: 10.1016/j.na.2009.01.166. [54] C. Zhu and G. Yin, On competitive Lotka-Volterra model in random environments, Journal of Mathematical Analysis and Applications, 357 (2009), 154-170. doi: 10.1016/j.jmaa.2009.03.066. [55] X. Zong, F. Wu, G. Yin and Z. Jin, Almost sure and $p$th-moment stability and stabilization of regime-switching jump diffusion systems, SIAM Journal on Control and Optimization, 52 (2014), 2595-2622. doi: 10.1137/14095251X.

show all references

##### References:
 [1] W. J. Anderson, Continuous-Time Markov Chains, Springer-Verlag, New York, 1991. doi: 10.1007/978-1-4612-3038-0. [2] D. Applebaum, Levy Processes and Stochastic Calculus, $2^{nd}$ Edition, Cambridge University Press, New York, 2009. doi: 10.1017/CBO9780511809781. [3] D. Applebaum and M. Siakalli, Asymptotic stability properties of stochastic differential equations driven by Lévy noise, Journal of Applied Probability, 46 (2009), 1116-1129. [4] A. Bahar and X. Mao, Stochastic delay Lotka-Volterra model, Journal of Mathematical Analysis and Applications, 292 (2004), 364-380. [5] A. Bahar and X. Mao, Stochastic delay population dynamcis, International Journal of pure and applied mathematics, 11 (2004), 377-400. [6] J. Bao, X. Mao, G. Yin and C. Yuan, Competitive Lotka-Volterra population dynamics with jumps, Nonlinear Analysis: Theory, Methods & Applications, 74 (2011), 6601-6616. doi: 10.1016/j.na.2011.06.043. [7] J. Bao and C. Yuan, Stochastic population dynamics driven by Lévy noise, Journal of Mathematical Analysis and Applications, 391 (2012), 363-375. doi: 10.1016/j.jmaa.2012.02.043. [8] N. H. Dang, N. H. Du and G. Yin, Existence of stationary distributions for Kolmogorov systems of competitive type under telegraph noise, Journal of Differential Equations, 257 (2014), 2078-2101. doi: 10.1016/j.jde.2014.05.029. [9] A. Dembo and O. Zeitouni, Large Deviation Techniques and Applications, $2^{nd}$, Jones and Bartlett, Boston, 1998. doi: 10.1007/978-1-4612-5320-4. [10] J. D. Deuschel and D. W. Stroock, Large Deviations, Academic Press, Boston, 1989. [11] M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, I, Communications on Pure and Applied Mathematics, 28 (1975), 1-47. [12] M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, II, Communications on Pure and Applied Mathematics, 28 (1975), 279-301. [13] M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, III, Communications on Pure and Applied Mathematics, 29 (1976), 389-461. doi: 10.1002/cpa.3160290405. [14] M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, IV, Communications on Pure and Applied Mathematics, 36 (1983), 183-212. doi: 10.1002/cpa.3160360204. [15] N. H. Du and N. H. Dang, Dynamics of Kolmogorov systems of competitive type under the telegraph noise, Journal of Differential Equations, 250 (2011), 386-409. doi: 10.1016/j.jde.2010.08.023. [16] N. H. Du, D. H. Nguyen and G. Yin, Conditions for permanence and ergodicity of certain stochastic predator-prey models,, to appear in Journal of Applied Probability., ().  doi: 10.1017/jpr.2015.18. [17] T. Faria and J. J. Oliveira, Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks, Journal of Differential Equations, 244 (2008), 1049-1079. doi: 10.1016/j.jde.2007.12.005. [18] B. M. Gary, A functional equation characterizing monomial functions used in permanence theory for ecological differential equation, Universitatis Iagellonicae acta mathematica, 42 (2004), 69-76. [19] T. C. Gard, Persistence in stochastic food web models, Bulletin of Mathematical Biology, 46 (1984), 357-370. doi: 10.1007/BF02462011. [20] T. C. Gard, Stability for multispecies population models in random environments, Nonlinear Analysis, 10 (1986), 1411-1419. doi: 10.1016/0362-546X(86)90111-2. [21] T. C. Gard, Introduction to Stochastic Differential Equations, Dekker, New York, 1988. [22] K. Gopalsamy, Global asymptotic stability in a periodic Lotka-Volterra system, The Journal of the Australian Mathematical Society. Series B, Applied Mathematics, 27 (1985), 66-72. doi: 10.1017/S0334270000004768. [23] X. Han, Z. Teng and D. Xiao, Persistence and average persistence of a nonautonomous Kolmogorov system, Chaos Solitons Fractals, 30 (2006), 748-758. doi: 10.1016/j.chaos.2006.04.026. [24] O. Kallenberg, Foundations of Modern Probability, $2^{nd}$ Edition, Springer, 2002. [25] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic press, Bosten, 1993. [26] Y. Li and Y. Kuang, Periodic solutions of periodic delay Lotka-Volterra equations and systems, Journal of Mathematical Analysis and Applications, 255 (2001), 260-280. doi: 10.1006/jmaa.2000.7248. [27] M. Liu and K. Wang, Stochastic Lotka-Volterra systems with Lévy noise, Journal of Mathematical Analysis and Applications, 410 (2014), 750-763. doi: 10.1016/j.jmaa.2013.07.078. [28] Q. Luo and X. Mao, Stochastic population dynamics under regime switching, Journal of Mathematical Analysis and applications, 334 (2007), 69-84. doi: 10.1016/j.jmaa.2006.12.032. [29] Q. Luo and X. Mao, Stochastic population dynamics under regime switching II, Journal of Mathematical Analysis and Applications, 355 (2009), 577-593. doi: 10.1016/j.jmaa.2009.02.010. [30] E. Lungu and B. Øksendal, Optimal harvesting from a population in a stochastic crowded environment, Mathematical Biosciences, 145 (1997), 47-75. doi: 10.1016/S0025-5564(97)00029-1. [31] E. Lungu and B. Øksendal, Optimal Harvesting from Interacting Populations in a Stochastic Environment, Bernoulli, 7 (2001), 527-539. doi: 10.2307/3318500. [32] X. Mao, G. Marion and E. Renshaw, Environmental noise supresses explosion in population dynamics, Stochastic Processes and their Applications, 97 (2002), 95-110. doi: 10.1016/S0304-4149(01)00126-0. [33] X. Mao, Delay population dynamics and environmental noise, Stochastics and Dynamics, 5 (2005), 149-162. doi: 10.1142/S021949370500133X. [34] X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, Imperial College Press, Londen, 2006. doi: 10.1142/p473. [35] X. Mao, Stochastic Differential Equations and Applications, $2^{nd}$ Edition, Horwood, Chichester, UK, 2008. doi: 10.1533/9780857099402. [36] J. D. Murray, Mathematical Biology, I. an Introduction, $3^{rd}$ Edition, Springer, 2002. [37] H. D. Nguyen, N. H. Du and G. Yin, Existence of stationary distributions for Kolmogorov systems of competitive type under telegraph noise, Journal of Differential Equations, 257 (2014), 2078-2101. doi: 10.1016/j.jde.2014.05.029. [38] S. Pang, F. Deng and X. Mao, Asymptotic properties of stochastic population dynamics, Dynamics of Continuous Discrete and Impulsive Systems Series A, 15 (2008), 603-620. [39] P. E. Protter, Stochastic Integration and Differential Equations, $2^{nd}$ Edition, Springer, 2004. [40] M. Slatkin, The dynamics of a population in a Markovian environment, Ecology, 59 (1978), 249-256. doi: 10.2307/1936370. [41] Y. Takeuchi, Global Dynamical Properties of Lotka-Volterra Systems, World Scientific, Singapore, 1996. doi: 10.1142/9789812830548. [42] Y. Takeuchi, N. H. Du, N. T. Hieu and K. Sato, Evolution of predator-prey systems described by a Lotka-Volterra equation under random environment, Journal of Mathematical Analysis and applications, 323 (2006), 938-957. doi: 10.1016/j.jmaa.2005.11.009. [43] B. Tang and Y. Kuang, Permanence in Kolmogorov-type systems of nonautonomous functional differential equations, Journal of Mathematical Analysis and Applications, 197 (1996), 427-447. doi: 10.1006/jmaa.1996.0030. [44] Z. Teng, The almost periodic Kolmogorov competitive sysems, Nonlinear Analysis, 42 (2000), 1221-1230. doi: 10.1016/S0362-546X(99)00149-2. [45] F. Wu and S. Hu, Stochastic functional Kolmogorov-type population dynamics, Journal of Mathematical analysis and applications, 347 (2008), 534-549. doi: 10.1016/j.jmaa.2008.06.038. [46] F. Wu and S. Hu, Suppression and stabilisation of noise, International Journal of Control, 82 (2009), 2150-2157. doi: 10.1080/00207170902968108. [47] F. Wu and Y. Xu, Stochastic Lotka-Volterra population dynamics with infinite delay, SIAM Journal on Applied Mathematics, 70 (2009), 641-657. doi: 10.1137/080719194. [48] F. Wu, S. Hu and Y. Liu, Positive solution and its asymptotic behaviour of stochastic functional Kolmogorov-type system, Journal of Mathematical Analysis and Applications, 364 (2010), 104-118. doi: 10.1016/j.jmaa.2009.10.072. [49] F. Wu and G. Yin, Environmental noise impact on regularity and extinction of population systems with infinite delay, Journal of Mathematical Analysis and Applications, 396 (2012), 772-785. doi: 10.1016/j.jmaa.2012.07.017. [50] G. Yin and F. Xi, Stablity of regime-switching jump diffusions, SIAM Journal on Control and Optimization, 48 (2010), 4525-4549. doi: 10.1137/080738301. [51] G. Yin and C. Zhu, Hybrid Switching Diffusions: Properties and Applications, Springer, New York, 2010. doi: 10.1007/978-1-4419-1105-6. [52] G. Yin, G. Zhao and F. Wu, Regularization and stabilization of randomly switching dynamic systems, SIAM Journal on Applied Mathematics, 72 (2012), 1361-1382. doi: 10.1137/110851171. [53] C. Zhu and G. Yin, On hybrid competitive Lotka-Volterra ecosystems, Nonlinear Analysis: Theory, Methods & Applications, 71 (2009), e1370-e1379. doi: 10.1016/j.na.2009.01.166. [54] C. Zhu and G. Yin, On competitive Lotka-Volterra model in random environments, Journal of Mathematical Analysis and Applications, 357 (2009), 154-170. doi: 10.1016/j.jmaa.2009.03.066. [55] X. Zong, F. Wu, G. Yin and Z. Jin, Almost sure and $p$th-moment stability and stabilization of regime-switching jump diffusion systems, SIAM Journal on Control and Optimization, 52 (2014), 2595-2622. doi: 10.1137/14095251X.
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text:
# Effusion and speed of molecules

## Homework Statement

Part(a): Find rate of incidence of gas molecules.
Part(b): Find v1 and v2.
Part (c): Find mean free path for faster molecules.
Part (d): Find mean free path of 10m/s molecules.

## The Attempt at a Solution

Part (a)

Letting ##\phi## be flux, and ##\Delta p## be change in momentum of rebounding molecule,
$$\phi \Delta p = \left(\frac{4}{3}\pi r^3\right)\rho g$$
$$\phi (2m\overline c) = \left(\frac{4}{3}\pi r^3\right)\rho g$$
$$R = \frac{2}{3}\frac{r\rho g}{m \overline c}$$

Funny how the mass of the molecule is not given. But this make sense as the more massive the atom travelling at a certain speed, the less flux you need to support the weight.

Part (b)

The speed distribution of molecules coming out of the oven is given by ##f = 2\alpha^2 v^3 e^{-\alpha v^2}##.

$$v_2 = \int_0^{\infty} v f dv$$
$$= \frac{3}{4}\sqrt{\frac{\pi}{\alpha}}$$
$$= \sqrt{\frac{9}{8}\frac{\pi kT_1}{m}}$$

For interest, let's calculate the temperature of the Chamber:

$$v_2 = \sqrt{\frac{8kT_2}{\pi m}} = \sqrt{\frac{9}{8}\frac{\pi kT_1}{m}}$$
$$T_2 = \left(\frac{3}{8}\pi\right)^2 T_1\approx 972K$$

To calculate ##v_1##, we use the speed distribution of the chamber (not the one coming out of the oven!)

$$g = 2\alpha_2^2 v^3 exp(-\alpha_2 v^2)$$

$$v_1 = 2\alpha_2^2 \int_0^{\infty} v^4 exp(-\alpha_2 v^2)$$
$$= \sqrt{\frac{9}{8}\frac{\pi kT_2}{m}}$$
$$= \pi \sqrt{\frac{81}{512}\frac{\pi k T_1}{m}} \approx 1112 ms^{-1}$$

Part (c)
I'm not sure whether the mean free path calculated here is correct.

The relative speed is ##v_r = |v_2 - v_1| = 1112 - 944 = 168 ms^{-1}## and ##n = \frac{P}{kT} = 2.47*10^{17}## and ##\sigma = 1.52*10^{-19}##.

Mean free path = (Distance travelled)/(No. of collisions during that distance)

$$\lambda = \frac{v_2t}{v_r n \sigma t} = 176m$$

Part (d)
In this case, ##v_r = |1112 - 10| = 1102##.

$$\lambda = \frac{10t}{v_r n \sigma t} = 0.24 m$$

This is roughly 700 times less than above.

This means that the atoms in the beam have a much larger mean free path than the atoms in the chamber. Thus velocity of the beam reduces much only after 176m into its flight path.


text:
# 5 Best Computer Books

### Top 5 computer books, I chose

This item has been in my blog-to-do list for a while. I am personally not a fan of rankings. However, as I have read a couple of horrible computer books in the past, listing some of the good ones are just natural. There are computer books out there which are so bad and boring that you are not even going to finish reading.

What I found among these “bad” books:

1. Not enough useful examples
2. Long chapters with much concept and explanation. Basically too long.
3. Not well structured - sporadic topics

The books I am about to introduce below are the ones where I enjoyed and was able to apply items in real life. Also, they come with great memorable examples.

### 1. Effective Java - 2nd Edition, by Joshua Bloch

I learned so many rules to follow as a Java Developer from this book and why I need to follow them. It teaches you how to become an overall better Java Developer. There are few memorable things I learned from this book. I really liked how it describes the patterns. It was simple and very easy to understand. Examples shown were precisely to the point. Also, I enjoyed the part where it covers favoring composition over inheritance. I remember I researched to understand that point on the internet to understand better. It also teaches implicitly on the concept, “tight cohesion, loose coupling”. It tells you the benefits of doing loose couplings and why it is necessary on what occasions. The book covers a little bit on Concurrency. It is described for beginners but described very well with concrete examples. It is very important, especially with computer books, to read with code examples discussed in the book. You can git clone github , which covers all the examples covered in this book.

### 2. Clean Code - A Handbook of Agile Software Craftmanship, by Robert Martin

The book showed me to take pride in my programming work. This book gives important basics that you need to know to become a good software developer provided with great explanations and examples. At the end, you would understand how important it is to write “Clean Code”, not just for yourself but for everyone else. You may even feel your ability to write code has been improved. If you are a real beginner of software development, the book might not be suitable. You might even find the examples in the book, not clean. Most of the examples are quite long but I suggest to read one line by line and you will find author’s intention of writing the code in such as way. Well, if you think about how it was written in 2008, it is actually quite well written. I would not recommend writing your code like the examples from the book in modern days since it is quite old, I would skim through it to understand and acknowledge the point the author is trying to make. I would recommend this book to a developer who wants to be a professional developer.

### 3. Cracking the Coding Interview - 5th edition, by Gayle McDowell

When I first read this book, I was shocked. Surprised to the fact how organized the book was toward the interview preparation and it illustrated well how the technical interview is played out. The book had a lot of exercises. The exercises are well linked to chapters in the book. After finishing this book along with exercises, I was a hunger for more programming problem sets which led me to search for online judge sites such as LeetCode, TopCoder, codeforces.com etc. That’s how I began my Algorithm “Playground” Project. It all began with this book, with all the interests toward a piece of the problem set. The book showed me the way to get that awesome feeling after solving that problem set. This book is quite old, there is a 6th edition book available. I did skim through examples from 6th edition. There aren’t many noticeable changes between 5th and 6th. This book is probably great for you to read at least once before you prepare a software developer position interview. It would help you prepare for it both for interviewer and interviewee side. It will make you become a better software developer overall. In the book, it emphasizes the necessity of writing code on the whiteboard. At first, I couldn’t understand the importance of this. But after I actually bought a whiteboard and started writing algorithms on the board, I started to understand why. You will be able to spot problems better and make thorough validations upon writing codes.

### 4. JAVA in a nutshell - 6th edition, Benjamin J Evans, David Flanagan

I read this book just before I switched my role as a full-time Java Developer. I thought I should read at least one Java concentrated book to join a Java Environment team. I am glad I did. Generally, I am not a fan of O’Reilly Media book. Their books are usually matches to “bad-book” points I covered above. Not enough examples + bored with all the concept. However, this book has some of the good examples and the book was well divided into small chunks of chapters with a lot of references. Check out Ben’s (One of the authors) github for all the examples/exercises discussed in the book. I would use this book as a reference for you to come back and read chunks (and repeat). Overall useful book.

### 5. Programming Interviews Exposed, John Mongan, Noah Kindler, Eric Giguere

Here is another great interview guide book which has tons of examples in the book. It covers pages to explain in detail of how to solve given specific problem set. It has many interesting problems which will grab your attention. The area which it covers is similar to “Cracking the Coding Interview”, such as data structures, recursion, sorting, concurrency etc. However, the examples are not exactly same though. I find there are certainly differences between the two. This book focuses on topics such as stable sorting, design patterns, also covers important knowledge-based/non-technical questions. It probably is another great book for preparing for an interview (or for interviewee as well). However, the book does make some assumptions on your knowledge on most of the things like red-black trees, dynamic programming, bit-wise functionalities. You may need to brush up on your algorithm skills and run some extra research on your way to fully understand these terms and how they work. Anyway, another enjoyable book!

### Conclusion

There are so many great computer books out there. For example, I am currently reading a book called Soft Skills by John Sonmez at the moment. I really like the motivation this book feeds in me to become a better software developer. However, I do not particularly like his assertions on how to make money (better) and focus writings about the “money” as a Software Developer. I understand his big dream of becoming a successful entrepreneur, but it didn’t really relate to me at all and I did not like the way he is trying to convince every reader to be such an entrepreneur. Anyways, I only took the advice suitable for me out of this book, which is what you should do for reading any kind of books really. Being able to absorb what is really needed for you is important. Above 5 books may not be in other people’s top 5 computer books. I am not here to advertise on their books. I am just depicting my honest feelings toward these books I read. I cannot guarantee you will enjoy these books but they did at least to me!


text:
# Calculate the pH of the solute in an aqueous solution of 0.0047 M codeine, if the pKa of itsconjugate acid is 8.21. What is the percentage protonation of the solute?

46,915 questions, page 254
1. ## Chem

Given that 277J of heat are absorbed when 1.12g of sodium nitrate are dissolved in water, calculate the heat of reaction.

asked by Shirley on July 15, 2012
2. ## physics

A 225-kg box is pushed horizontally with a force of 620N. If the coefficient of friction is 0.20, calculate the acceleration of the box.

asked by john on April 23, 2014
3. ## statistics

Calculate SS, variance, and standard deviation for the following population of N _ 7 scores: 8, 1, 4, 3, 5, 3, 4. (Note: The definitional formula works well with these scores.)

asked by Liz on June 22, 2011
4. ## paul

A stock will provide a rate of return of either –20% or +28% . 1. If both possibilities are equally likely, calculate the expected return and standard deviation.

asked by john on April 23, 2010
5. ## statistics

Calculate SS, variance, and standard deviation for the following sample of n _ 4 scores: 3, 1, 1, 1. (Note: The computational formula works well with these scores.)

asked by Liz on June 22, 2011
6. ## Science

A pump is used to lift 500 kg of water from a depth of 80 m in 10 seconds.Calculate the power rating of the pump if it's efficiency is 40% . Take g=10 m/ s*s.

asked by Swati on February 7, 2017
7. ## science

An automobile is pulled by a horizontal tow line, with a force of 900 N. If its acceleration is 1.0 m/s2, calculate the mass of the automobile.

asked by tash on January 30, 2013
8. ## chemistry

How do you calculate deltaHf using the # of moles from a balanced equation? How do you connect the Law of Conservation of Energy to a Thermochemical Equation? Thanks so much!

asked by K on April 29, 2013
9. ## science

Calculate the EMF of the cell CR|Cr3+(0.1M)||Fe2+(0.1M)|Fe Cell reaction- 2Cr(s)+3Fe2+(aq)->2Cr3+(aq)+3Fe(s)

asked by Rasilu on April 26, 2016
10. ## maths /science

A body calling from rest has a velocity of 25m/s at given instant. Calculate 1 the distance the body has fallen 2 the time taken

asked by christina on September 28, 2016
11. ## physics

A 250-kg crate is pushed horizontally with a force of 710 N. If the coefficient of friction is 0.20, calculate the acceleration of the crate.

asked by das on October 18, 2010
12. ## chemistry

a. Determine the density of a cube of copper with a length of 5.00 cm and a mass of 1,112.50 g. b. Calculate the number of atoms in the cube

asked by Mike on July 20, 2014
13. ## math

the total surface of rectangular solid is 130cm^2 .if the solid is 7cm long nd 5cmwide. calculate the height

asked by timi on May 9, 2019
14. ## Chem

A block of metal has a width of 3.2 cm, a length of 17.1 cm, and height of 4.3cm . Its mass is 1.2kg . Calculate the density of the metal.

asked by Cf on September 16, 2013
15. ## chemistry

Help me solve it. Step by step please The value of kp at 20°c for the reaction 2NO(g) +Cl2(g) 2NOCl(g) is 1.9x10^3 atm-1 calculate the value of KC at the same temperature.

asked by john on December 6, 2015

Andrew borrows $79,500 for 5 months on 6.30% interest rate in his saving account. Calculate the simple interest? asked by Anonymous on April 2, 2014 17. ## chemistry When irradiated with a radiation of wavelength 58.4 nm the electron of H atom was ejected with kinetic energy 7.6 eV. Calculate the ionization energy. asked by kamila t arakkal on April 26, 2016 18. ## engineering If faucet is dripping at a rate of one drop per second and each drop contains 0.150 milliliters. Calculate how much water will be lost in 1 year. asked by Maria on January 14, 2011 19. ## physics calculate the total pressure at an ocean depth of 6000 m (the depth at which the wreck of the titanic was found) in both pascals & lb/in^2 asked by john on March 20, 2010 20. ## Physics d1 = 2.53 cm +/- .05 cm d2 = 1.753 m +/- .001 m 0 = 23.5 degrees +/- .5 degrees v1 = 1.55 m/s +/- .15 m/s Using the measured quantities above, calculate the following. Express the uncertainty calculated value. d1 (tan (0)) asked by Joy on November 11, 2013 21. ## Chemistry Calculate the longest wavelength of light that can break a H-O bond. The bond enthalpy of formation is 463 kj/mol asked by Angelina on April 8, 2011 22. ## chemistry Calculate the energy in joules per photon of red light having a wavelength 655 nm. What is the energy of 1 mol of these photons? asked by ashley b on June 23, 2011 23. ## Calculus (Motion with Vector functions) 1. What are the magnitude and direction angle for the vector u= 2. Calculate the speed of a particle in the xy-plane with positive vector r(t)=(4-t^2, 6t) at the point (0,12). asked by Angela on January 22, 2018 24. ## Science A projectile has a range of 50m and reaches a maximum height of 10m. Calculate the angle at which the projectile is fired. asked by Gash on February 6, 2019 25. ## Chem A block of metal has a width of 3.2 cm , a length of 17.1 cm , and height of 5.2cm . Its mass is 1.2kg . Calculate the density of the metal asked by Jillian on September 12, 2013 26. ## physics The surface area and the average depth of the Pacific Ocean are 1.8 x 10 8 km 2 and 3.9 x 10 3 m, respectively. Calculate the volume of water in the ocean in liters. asked by Latrese on September 25, 2011 27. ## chemistry QUESTION 9 The number of moles of the reagent in excess can be used to calculate the moles of the products of the reaction. TRUE FALSE asked by Anonymous on July 11, 2016 28. ## chemistry The heat of vaporization of bromine at its boiling point (59.6 °C) at 1.00 atm is 29.54 kJ/mol. Calculate the vapor pressure of bromine at 37.8 °C. asked by WLP on January 22, 2012 29. ## Chemistry Calculate the mass percent composition of carbon in each the following carbon compounds. C2H2 C3H6 C2H6 C2H6O asked by Amee on March 4, 2013 30. ## SS How often do banks calculate interests on accounts with simple interest? daily weekly monthly yearly yearly? asked by Anonymous on January 31, 2014 31. ## Biochemistry Two molecules of DNA are the same size, but differ in base composition. One molecule contains 20 % (A + T) while the other contains 60 % (A + T). Which molecule has the higher T m? Why?(The m is a subscript of T) I'm not sure what T m is..or how to asked by student on September 17, 2009 32. ## Physics Four equal charges Q=2*10^-8coulumb are placed at the corners of a square of side 60cm.calculate the potential at the centre of the square. asked by Ayodele on April 8, 2010 33. ## Chemistry Given that KH for CO gas at 25 OC is 9.71 x10-4 mol.L-1.atm-1. Calculate the mass of CO that would dissolve in 1.00 L of H2O if the partial pressure of CO is 1.38 atm. asked by Chelsea on February 15, 2011 34. ## geography Calculate the gradient of a road (4km) intervals from a given roundabout the different height between the two end point the road is 400mm? asked by jamilu abubakar sadiq on April 23, 2016 35. ## Chemistry calculate the bond energy for diatomic oxygen O2 given that standard enthalpy of atomization of oxygen (ΔH) = 249.17KJ asked by Solomon on February 29, 2016 36. ## Chemistry A 0.22-caliber handgun fires a 27-{\rm g} bullet at a velocity of 765 {\rm m}/{\rm s}. Part A Calculate the de Broglie wavelength of the bullet. asked by Anonymous on June 30, 2012 37. ## Statistics(Please check) calculate the probability of the following: A four, three, or spade from a single draw from a 52 card deck. there are 4 4's so 4/52, 4 3's so 4/52 and then 13/52 spades so 21/52 but and one 4 and one 3 are from spades so minus 2 = 19/52 Is this correct? asked by Hannah on July 23, 2011 38. ## Please Help! Calculus Calculate the speed of a particle traveling in the xy-plane with position vector r(t)=(4-t^2,6t) at the point (0,12). a)2(sqrt13) b)6 c)4(sqrt13) d)52 e)sqrt2 asked by Tony on January 22, 2018 39. ## chemistry calculate the specific heat (j/g C ) for each of the following: -an 18.5-g sample of tin that absorbs 183 J when its temperature inceases from 35.0 degrees C to 78.6 degrees C asked by kelly on September 14, 2010 40. ## physic Calculate the true mass (in vacuum) of a piece of aluminum whose apparent mass is 4.5000 kg when weighed in air. asked by Ash on August 8, 2010 41. ## physics A reistance thermometer has a resistance of 20w at 0°c and 85w at 100°c if it resistance is 52w in medium calculate the corresponding temperature? asked by poppy on April 26, 2019 42. ## physics the mass of the boy is 70kg. calculate the force in newtons acting on the boy due to his deceleration. how do i work this out asked by evie on March 31, 2012 43. ## chemistry Calculate the wavelength (in nanometers) of a photon emitted by a hydrogen atom when its electron drops from the n = 4 state to the n = 3 state. asked by Tanisha on March 23, 2010 44. ## maths The diagonal of a parallelogram 6cm and 8cm long and they intersect at an angle of 55 degrees. calculate the area of the parallelogram asked by Riliwan on November 22, 2016 45. ## statistics the following sample observations were randomly selected: x: 2,5,6,8,9,11,15 y: 22,23,16,18,19,13,12 a)calculate the correlation coefficient, r b) determine the regression equation c) determine the value of Y when X=20 asked by skitter on November 29, 2010 46. ## Physics A car moves along a circular track at 60 kmph. If the radius of the track is 300 m, calculate the acceleration towards the centre asked by Aditya on August 11, 2011 47. ## Chemistry Calculate the pH when 39.0mL of 0.321 of HA is mixed with 39.0mL of 0.321M NaOH where HA is a monoprotic weak acid with Ka= 7.5x10^-5 M ? asked by Jematormal91 on March 24, 2012 48. ## chemistry A system performs 120J work with no heat supplied to it. Calculate the change in internal energy of the system. asked by jaycab on January 23, 2011 49. ## Physics Particles of charge +65, +48, and −95 μC are placed in a line. The center one is L = 60cm from each of the others.Calculate the net force on the left charge due to the other two. asked by Mary on January 31, 2015 50. ## Chem. N2+3H2 2NH3, The equilibrium constant for the chemical equation is Kp = 0.143 at 225 °C. Calculate the value of the Kc for the reaction at 225 °C. asked by Anonymous!! on March 19, 2014 51. ## Physics Calculate the true mass (in vacuum) of a piece of aluminum whose apparent mass is 1.6000kg when weighed in air. asked by Melissa on November 10, 2012 52. ## Chemistry - equm acid base Calculate [H3O+] 0.100 M NaNO2 and 5.00×10−2 M HNO2 so there's no Ka value for NaNO2, it can be ignored 5.6x10^-4 = x^2 / 5.00x10^-2 x = 5.3x10^-3 the answer is incorrect why? Thanks asked by X on March 8, 2018 53. ## Statistics 1. Consider a population with µ=73.6 and 0 = 5.38 (A) Calculate the z-score for x =72.7 from a sample of size 45. (B) Could this z-score be used in calculating probabilities using Table 3 in Appendix B of the text? Why or why not? asked by jane on October 25, 2011 54. ## community umuokpu. Chemistry if 50cm3 of co3 were put in 40cm3 of O2. Determine the gas that would be in excess and calculate the volume of gas that would be unused asked by Tessy on February 9, 2013 55. ## finance You purchase a stock at a price of$73, and a year later the price increases to $85. You also received a dividend of$2.50. Calculate the rate of return.

asked by Anonymous on August 1, 2011
56. ## chemistry

Trying to calculate atoms of O in 2.00 moles of H3PO4.I used 2.00 mol h3po4÷4atoms O then × by 6.022 avrogados# My answer 3.011×10^23

asked by jackson on March 25, 2015
57. ## stats - URGENT!!!!

the following sample observations were randomly selected: x: 2,5,6,8,9,11,15 y: 22,23,16,18,19,13,12 a)calculate the correlation coefficient, r b) determine the regression equation c) determine the value of Y when X=20

asked by skitter on November 30, 2010

you invest $2800 in an account that pays an interest of 5.5%, compounded continuously. calculate the balance of your account after 12 years. asked by heidi on August 6, 2013 59. ## Chemistry For the reaction N2O4(g)=2NO2(g), the value of K at 25 degrees XCelsius is 7.19*10^-3. Calculate N2O4 at equilibrium when NO2 =2.20 *10^122 mol/L? asked by Amy on July 14, 2012 60. ## chemistry 130cm3 of a gas excarts a pressure 750mmhg . calculate it pressure if its volume is increase to 150cm3 at 35oc asked by whiskey on August 9, 2017 61. ## statistics Consider a population with µ=93.3 and σ=5.27. (A) Calculate the z-score for x=94.9 from a sample of size 12. (B) Could this z-score be used in calculating probabilities using Table 3 in Appendix B of the text? Why or why not? asked by Dawn on October 17, 2012 62. ## Statistics Consider a population with µ=73.6 and 0 = 5.38 (A) Calculate the z-score for x =72.7 from a sample of size 45. (B) Could this z-score be used in calculating probabilities using Table 3 in Appendix B of the text? Why or why not? asked by jane on October 24, 2011 63. ## chem 1046 Calculate the boiling point a. 10.5 g FeCl3 in 2.11 102 g water b.4.6% KCl by mass (in water) c.0.140 m MgF2 asked by Anonymous on July 6, 2012 64. ## Astronomy Calculate the approximate circumference of Earths orbit around sun, assuming that orbit is a circle with radius of 1.5 X 10 to the eighth. asked by Kandice on June 11, 2014 65. ## Chemistry the question says: Calculate the mass of soap (NaC17H35COO) which contains 1.25 grams of Carbon. Do I use the percentage composition of soap and the mole? asked by Lauren on June 14, 2016 66. ## physics A constant force of 48.7 N, directed at 34.1° from horizontal, pulls a mass of 15.1 kg horizontally a distance of 2.77 m. Calculate the work done by the force. asked by help on November 21, 2010 67. ## Calculus Consider the region in the plane consisting of points (x, y) satisfying x > 0, y > 0, and lying between the curves y=x^2 +1and y=2x^2 −2. (b) Calculate the area of this region. asked by Mary on May 16, 2016 68. ## college chem 2 The enthalpy of vaporization of liquid diethyl ether is 26.0kJ/mol at 35'C calculate the deltaS' for vapor to liquid asked by shel on March 24, 2014 69. ## Chemistry Calculate the mass in grams for a gold sample that absorbs 245J to change its temperature from 19 degrees to 49 degrees asked by Wendy on March 5, 2011 70. ## Maths the acute angles of a rhombus are 76 degrees if the shorter diagonal is of length 8 cm calculate of the sides of the rhombus to the nearest mm asked by Anita on January 9, 2016 71. ## honors chem high school The topic is Changes in energy Level Calculations. calculate energy value for levels n=1 to n=7; given En=-Rh/n2 R=2.180 x 10 -18 J E=hv h=6.626 x 10 -34 J.s I then need to plot them -- I cannot get started. asked by kate on October 3, 2012 72. ## statistics For a normal distribution, explain why we calculate the probability of a range of numbers instead of the probability of a single number on the lines below? asked by rehena on June 9, 2014 73. ## Chemistry Consider the reaction: 2CO2(g)=2CO(g) + O2(g). A reaction mixture in a 5.0 L flask at a certain temperature. At equilibrium there are 85 g of CO2(g), 1.20 g of CO, and 0.688 g of O2(g). Calculate Kc. asked by Ariel on February 27, 2011 74. ## Physics calculate the work required to launch a satellite from the surface of the earth (radius6380km) to orbit 6000 km above the surface asked by Henry on February 16, 2014 75. ## Chemistry 3NO2 + H2O -> 2HNO3 + NO Calculate the percent yield for the following reaction if 76.8 g of H2O reacted and 125 g of NO were produced. asked by Amanda on November 25, 2014 76. ## Physics A car requires velocity of 36 km /h in 10 sec just after the start . It takes 20 sec to stop . Calculate the acceleration in both the cases asked by Srishti on May 31, 2016 77. ## phyics-universal gravity Calculate the force of gravity on a spacecraft 6400 km (1 earth radii) above the Earth's surface if its mass is 1600 kg. asked by DJ on November 3, 2009 78. ## chemistry when one gram of water solidifies to ice 333.33 j of heat is evolved. calculate enthalpy of fusion of ice? asked by gopal on July 30, 2013 79. ## stats - URGENT!!!! the following sample observations were randomly selected: x: 2,5,6,8,9,11,15 y: 22,23,16,18,19,13,12 a)calculate the correlation coefficient, r b) determine the regression equation c) determine the value of Y when X=20 asked by skitter on November 30, 2010 80. ## chemistry The Kw of water varies with temperature. Calculate the pH of water at 46⁰C with a Kw = 1.219 x 10-14. Show all calculations leading to an answer. asked by Ciaria on March 13, 2015 81. ## physics calculate the acceleration of a 2000kg single -engine airplane just before takeoff when the thrust of the airplane ia 500N Using the G.U.E.S.S. method asked by jim on November 2, 2009 82. ## stats - URGENT!!!! the following sample observations were randomly selected: x: 2,5,6,8,9,11,15 y: 22,23,16,18,19,13,12 a)calculate the correlation coefficient, r b) determine the regression equation c) determine the value of Y when X=20 asked by skitter on November 30, 2010 83. ## chemistry A certain rifle bullet has a mass of 6.45 g. Calculate the de Broglie wavelength of the bullet traveling at 1817 miles per hour. asked by brianna on November 1, 2013 84. ## physics two lead spheres whose diameters are 20 cm and 2 cm are placed with centres 100 cm apart. Calculate the force of gravitation between them.(density of lead =11500 kg/m^3 asked by Dhananjay on May 15, 2013 85. ## Physics Calculate the thermal energy required to convert 5kg of ice at 0 Celsius to steam at 100 Celsius asked by Lina on February 19, 2016 86. ## Math A sequence {an} is given by a1=root(3), a n+1 = root(3+an). show that {an} is monotonic and bounded, and calculate lim (n->infinity) an, if it exists. Could someone just tell me what answer they get? asked by Hannah on July 11, 2009 87. ## algebra On average a family of four consums 247.2 gallons of water per day. Calculate the quarterly bill for family of four asked by Anonymous on October 24, 2016 88. ## math How do I calculate value of pi upto 200 decimal places ? Please email me the answer to my email address homework@live.in . asked by I want homework help on December 17, 2007 89. ## Chemistry Consider the reaction: 2CO2(g)=2CO(g) + O2(g). A reaction mixture in a 5.0 L flask at a certain temperature. At equilibrium there are 85 g of CO2(g), 1.20 g of CO, and 0.688 g of O2(g). Calculate Kc. asked by Ariel on February 27, 2011 90. ## Business Math Marcus invests$8,000, at 8% interest, compounded annually for 15 years. Calculate the compound interest for his investment.

asked by Jasmine on March 16, 2019
91. ## chemistry

Consider the galvanic cell constructed from the following metals and their corresponding metal ions: E degrees (V) M^3+^ + 3e^-^ ----> M 0.29 N^2+^ + 2e^-^ ----> N 0.61 calculate the value of K for the cell reaction at 25C

asked by eric on July 13, 2012
92. ## calc

a rectangle is inscribed in the upper half of the circle x^2+y^2=a^2 calculate the area of the largest such rectangle. So A=2xy y=sqrt(a^2-x^2)A what do I do from there?

asked by hannah on August 20, 2014
93. ## Math

The surface area of the moon is 37 832 330 km squared. Calculate the side length of a square with the same area.

asked by KimY on October 1, 2011
94. ## ctu math

calculate the interest charge on a \$5.000 balance with the visa student card annual interest rate of 10.8%

asked by simone on August 3, 2013
95. ## chemistry

Calculate the mass percent composition of carbon in each the following carbon compounds. a) C_4H_10 b) C_6H_10 c) CCl_2F_2 d) C_8H_13O_5N

asked by Mely on September 11, 2010
96. ## chemistry

Calculate the mass percent composition of carbon in the following carbon compound. C_8H_13O_5N I got 0.4729 as an answer but it's wrong. Please help me.

asked by Mely on September 11, 2010
97. ## Chemistry

Consider the reaction: 2CO2(g)=2CO(g) + O2(g). A reaction mixture in a 5.0 L flask at a certain temperature. At equilibrium there are 85 g of CO2(g), 1.20 g of CO, and 0.688 g of O2(g). Calculate Kc.

asked by Ariel on February 27, 2011
98. ## stats - URGENT!!!!

the following sample observations were randomly selected: x: 2,5,6,8,9,11,15 y: 22,23,16,18,19,13,12 a)calculate the correlation coefficient, r b) determine the regression equation c) determine the value of Y when X=20

asked by skitter on November 30, 2010
99. ## Math

The angles of depression of two stones one mile apart on the same side of a tower are 30Â° and 45Â° .calculate height of the tower.

asked by Nisha on March 19, 2017
100. ## Chemistry

A block of metal has a width of 3.2 cm, a length of 17.1 cm, and height of 5.8cm . Its mass is 1.5kg . Calculate the density of the metal.

asked by Jenn on September 2, 2013


text:
Let $f(x,y)=x^2+y^2$ and it is easy to observe that $\operatorname{grad} f(a,b)$ is always perpendicular to the tangent line at point $(a,b)$ and I just can't prove why it would be like that.

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I am a bit puzzled. Are you looking at the surface $\{(x,y,z)\in\mathbb{R}^3: x^2 + y^2 = z\}$, or are you looking at the circle $y = \pm\sqrt{r^2 - x^2}$ for some fixed $r > 0$ and $x\in[-r, r]$? In either case, it doesn't quite matter; in the former case you have a tangent plane, in the latter - a tangent line. For the line case, compute the gradient and take the inner product of the gradient with the tangent vector, and observe that it is zero. –  William Jan 7 '12 at 6:53

So, you are essentially trying to show the following

$(\nabla f) \perp (f=c)$, which is that the gradient of the function is perpendicular to the level surface (f = constant).

Consider in general a curve $r=r(t)$ that stays on the level surface $f=c$. By definition $v = \frac{dr}{dt}$ is tangent to the level curve $f=c$. By the chain rule, the total differential $\frac{df}{dt}$ gives, $$\frac{df}{dt} =\frac{\partial f}{\partial x} \cdot \frac{dx}{dt} + \frac{\partial f}{\partial y} \cdot \frac{dy}{dt} + \frac{\partial f}{\partial z} \cdot \frac{dz}{dt} = \nabla f \cdot \frac{dr}{dt} = \nabla f \cdot v = 0$$ since $f(t)=c$. So, the gradient vector $\nabla f$ is perpendicular to $v$. This is true for any motion on $f=c$, and $v$ can be any vector tangent to $f=c$.

So, given any vector $v$ tangent to the level curve, $\nabla f \perp v$, so $\nabla f \perp$ tangent plane.

Let me know if you need clarification about anything.

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Here, the assumption is that $f(x,y)$ can be parametrized by a continuously differentiable function in a neighborhood $I$ of a point $(x_0,y_0)$ in the domain wrt to a parameter, say $t$ as

$r(t)=x(t)i+jy(t)$ such that it has a non-zero tangent vector, say $r'(t)$ and that If $t\epsilon I,$ $f(r(t))=c$, where c is a constant.

Hence, $\displaystyle\frac{d}{dt} f(r(t))=\nabla{f(r(t)).r'(t)}=0.$

Thus, gradient of $f(r(t))$ i.e. of $f(x,y)$ is perpendicular to the tangent at the level curve at any given point $(x_0,y_0)$.

Take a look at this link

http://poncelet.math.nthu.edu.tw/disk3/cal01/tg.pdf

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text:
zbMATH — the first resource for mathematics

An application of semigroups of locally Lipschitz operators to Carrier equations with acoustic boundary conditions. (English) Zbl 1145.47044
Summary: A generation theorem for semigroups of locally Lipschitz operators on a subset of a real Banach space is given and applied to the problem of the well-posedness of the Carrier equation $$u_{tt} - \kappa (\| u\| ^{2})\Delta u+\gamma | u_t| ^{p - 1}u_t=0$$ in $$\varOmega \times (0,\infty )$$ with acoustic boundary condition, where $$p>2$$ and $$\varOmega$$ is a bounded domain in an arbitrary dimensional space.

MSC:
 47H20 Semigroups of nonlinear operators 35L70 Second-order nonlinear hyperbolic equations
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References:
 [1] Ph. Bénilan, Equations d’évolution dans un espace de Banach quelconque et applications, thesis, Orsay, 1972 [2] Brezis, H., Équations et inéquations non linéaires dans LES espaces vectoriels en dualité, Ann. inst. Fourier, 18, 115-175, (1968) · Zbl 0169.18602 [3] Chambers, J.T.; Oharu, S., Semi-groups of local lipschitzians in a Banach space, Pacific J. math., 39, 89-112, (1971) · Zbl 0232.47080 [4] Crandall, M.G., Nonlinear semigroups and evolution governed by accretive operators, (), Part 1, pp. 305-337 · Zbl 0637.47039 [5] Crandall, M.G.; Evans, L.C., On the relation of the operator $$\partial / \partial s + \partial / \partial \tau$$ to evolution governed by accretive operators, Israel J. math., 21, 261-278, (1975) · Zbl 0351.34037 [6] Crandall, M.G.; Liggett, T.M., Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. math., 93, 265-298, (1971) · Zbl 0226.47038 [7] Frota, C.L.; Goldstein, J.A., Some nonlinear wave equations with acoustic boundary conditions, J. differential equations, 164, 92-109, (2000) · Zbl 0979.35105 [8] Kobayashi, Y., Difference approximation of Cauchy problems for quasi-dissipative operators and generation of nonlinear semigroups, J. math. soc. Japan, 27, 640-665, (1975) · Zbl 0313.34068 [9] Y. Kobayashi, On the generation of nonlinear contraction semigroups, in: Proceedings of the Symposium on Real Analysis and Functional Analysis, 1978, pp. 1-16 (in Japanese) [10] Kobayashi, Y.; Oharu, S., Semigroups of locally Lipschitzian operators in Banach spaces, Hiroshima math. J., 20, 573-611, (1990) · Zbl 0766.47038 [11] Kobayashi, Y.; Matsumoto, T.; Tanaka, N., Semigroups of locally Lipschitz operators associated with semilinear evolution equations, J. math. anal. appl., 330, 1042-1067, (2007) · Zbl 1123.34044 [12] Kobayashi, Y.; Tanaka, N., Semigroups of locally Lipschitz operators, Math. J. okayama univ., 44, 155-170, (2002) · Zbl 1033.47040 [13] Lakshmikantham, V.; Leela, S., Differential and integral inequalities, (1969), Academic Press New York · Zbl 0177.12403 [14] Pazy, A., The Lyapunov method for semigroups of nonlinear contractions in Banach spaces, J. anal. math., 40, 239-262, (1981) · Zbl 0507.47042 [15] Walker, J.A., Dynamical systems and evolution equations, theory and applications, (1980), Plenum Press New York · Zbl 0421.34050
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


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# Problem: Consider the decomposition of liquid hydrogen peroxide (H2O2) to form water and oxygen.What is the heat of formation for gaseous oxygen?

###### FREE Expert Solution

We’re being asked to determine the standard enthalpy change of formation (ΔH˚f) for oxygen. Recall that ΔH˚rxn can be calculated from the enthalpy of formation (ΔH˚f) of the reactants and products involved

$\overline{){\mathbf{∆}}{\mathbf{H}}{{\mathbf{°}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{∆}}{\mathbf{H}}{{\mathbf{°}}}_{\mathbf{f}\mathbf{,}\mathbf{products}}{\mathbf{-}}{\mathbf{∆}}{\mathbf{H}}{{\mathbf{°}}}_{\mathbf{f}\mathbf{,}\mathbf{reactants}}}$

The chemical equation for the reaction is:

H2O2(l)→ O2(g) + H2O(l)

This equation is not yet balanced. To balance it, we have to make sure that the number of elements on both sides is equal.

Balance O: We have 2 O on the reactant side and 3 O on the product side – add a coefficient of 2 to H2O:

H2O2(l)→ O2(g)2 H2O(l)

Balance H: We have 2 H on the reactant side and 4 H on the product side – add a coefficient of 2 to O2:

2 H2O2(l)→ O2(g)2 H2O(l)

97% (237 ratings)
###### Problem Details

Consider the decomposition of liquid hydrogen peroxide (H2O2) to form water and oxygen.

What is the heat of formation for gaseous oxygen?


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# Clay Ford

## Getting Started with Bootstrap Model Validation

Let’s say we fit a logistic regression model for the purposes of predicting the probability of low infant birth weight, which is an infant weighing less than 2.5 kg. Below we fit such a model using the “birthwt” data set that comes with the MASS package in R. (This is an example model and not […]

## Mathematical Annotation in R

In this article we demonstrate how to include mathematical symbols and formulas in plots created with R. This can mean adding a formula in the title of the plot, adding symbols to axis labels, annotating a plot with some math, and so on. R provides a $$\LaTeX$$-like language for defining mathematical expressions. It is documented […]

## Comparing Mixed-Effect Models in R and SPSS

Occasionally we are asked to help students or faculty implement a mixed-effect model in SPSS. Our training and expertise is primarily in R, so it can be challenging to transfer and apply our knowledge to SPSS. In this article we document for posterity how to fit some basic mixed-effect models in R using the lme4 […]

## Comparing the accuracy of two binary diagnostic tests in a paired study design

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## Correlation of Fixed Effects in lme4

If you have ever used the R package lme4 to perform mixed-effect modeling you may have noticed the “Correlation of Fixed Effects” section at the bottom of the summary output. This article intends to shed some light on what this section means and how you might interpret it. To begin, let’s simulate some data. Below […]

## A Beginner’s Guide to Marginal Effects

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Consider the following data from the text Design and Analysis of Experiments, 7 ed (Montgomery, Table 3.1). It has two variables: power and rate. Power is a discrete setting on a tool used to etch circuits into a silicon wafer. There are four levels to choose from. Rate is the distance etched measured in Angstroms […]

## Getting Started with Generalized Estimating Equations

Generalized Estimating Equations, or GEE, is a method for modeling longitudinal or clustered data. It is usually used with non-normal data such as binary or count data. The name refers to a set of equations that are solved to obtain parameter estimates (ie, model coefficients). If interested, see Agresti (2002) for the computational details. In […]