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# Energy conservation in different reference frames

Suppose, I'm on top of a hill, and I drop a ball from some height. As there are no external forces acting on the Earth-ball system, I can safely claim that the total energy is conserved. I know that, as the ball falls from a certain height, it (the system) loses potential energy and gains kinetic energy.

Depending on where I took my reference frame level, the value of the potential energy at all the different points would change. However, the change of potential energy is independent of my reference level. Similarly, the velocity doesn't depend on where I'm standing. So I can say $$K_f+U_f=K_i+U_i$$. More generally, I can say $$\Delta K+\Delta U=0$$.

At any point along the fall, the total energy is the kinetic energy at that point added to the potential energy to that point. This creates a small problem. Even though the change in total energy is $$0$$, the value of the total energy depends on where I took my reference level. In this case, it is the value of the potential energy that depends on my choice of reference.

Another case is, suppose I, the observer, jump with the ball, such that I'm moving with some speed. In this frame the ball moves at a different speed as compared to the first one. Since the work done by gravity remains the same, I can argue that the potential energy of the system remains the same (depending on our reference level).

The problem now is that the ball has some kinetic energy different from the kinetic energy in the first example. So, even though the total change in energy is $$0$$, the value of the total energy is not the same anymore.

Another example, consider a car moving in the $$x$$ direction. The total energy is equal to the kinetic energy and that is $$E$$ suppose. With respect to some observer in the car, the kinetic energy and by extension, the total energy is $$0$$. So, as we move from one frame to the other, the total energy seems to have changed.

What does energy conservation mean exactly?

Does it mean total mechanical energy remains exactly the same in all inertial frames. For example if it is $$E_1$$ in one frame, it must be $$E_1$$ in all other frames?

Or does it mean that if the total energy is conserved in one inertial frame, i.e. the change in total energy is $$0$$ in one frame, then the change in total energy must also be $$0$$ in all other inertial frames?

Thus the value of the total energy at a point, seems to depend upon, the speed of the observer's inertial frame (kinetic energy depends on this), and the reference level where the observer assumes potential is $$0$$ (the potential energy at a point depend on this).

• The end of your post asks about inertial frames, but one of the examples is falling with the ball, which is not an inertial reference frame in classical physics. Did you mean to include a different inertial reference frame at moves relative to the first one? Dec 7, 2021 at 2:31
• @BioPhysicist yes, that is exactly what I meant. I'm so sorry I completely forgot about the fact that the ball is accelerating downward, and so my frame must be non-inertial. I'll edit that right away. Dec 7, 2021 at 2:49
• consider the definition of potential energy, it's an integral from one point to the other point. so it doesn't matter where you put the coordinate. same as $\Delta U$. Dec 7, 2021 at 3:01
• @leave2014 but I can add an arbitrary constant to the potential energy, which would change it's value. For example if I take the ground as reference, then potential energy at height $h$ is $mgh$. If I take the height at reference, then the potential energy there is $0$. However the difference doesn't change. The integral describes this difference. I suppose it would be useless to talk about the potential energy at a point. It would be more useful to talk about $\Delta U$ instead. Dec 7, 2021 at 3:08
• @RayPalmer $mgh$ is a simplified formula for using, it's a result of a definite integral between $h=h$ and $h=0$ by putting the coordinate on the ground where the gravity force cannot do more work say "$U=0$". Dec 7, 2021 at 3:21

What does energy conservation mean exactly?

It means $$\Delta E = 0$$, or if you know calculus $$\frac{d}{dt}E=0$$. The total energy is constant, it does not change as time goes on.

Does it mean total mechanical energy remains exactly the same in all inertial frames. For example if it is 𝐸1 in one frame, it must be 𝐸1 in all other frames?

What you are describing is called frame invariance. Energy is conserved, but it is not invariant. Different inertial frames will disagree on the value of energy, but they will all agree that it is constant over time.

Or does it mean that if the total energy is conserved in one inertial frame, i.e. the change in total energy is 0 in one frame, then the change in total energy must also be 0 in all other inertial frames?

Yes.

Most of your examples are based on this misunderstanding of energy and are simply resolved by recognizing that your analysis is correct, but does not contradict the conservation of energy. However, there is one small error here:

suppose I, the observer, jump with the ball, such that I'm moving with some speed. In this frame the ball moves at a different speed as compared to the first one. Since the work done by gravity remains the same, I can argue that the potential energy of the system remains the same (depending on our reference level).

The work done by gravity on the ball does not remain the same in different reference frames. This problem does demonstrate energy conservation, but neither energy nor work is invariant. To show energy conservation requires using the conservation of momentum also, and careful accounting for the change in the KE of the earth.


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# Questions about Laplacian Surface Editing

I read the paper called Laplacian Surface Editing, but I'm confused about how does the author solve the formula (4). The paper says that 'Solving this quadratic minimization problem results in a sparse linear system of equations', so I have tried to use the quadprog function in matlab, but when the size of the nodes is growing up, my result is becoming messy. And I read the 'MATLAB 2D demo' code of this paper (http://igl.ethz.ch/projects/Laplacian-mesh-processing/Laplacian-mesh-editing/), it seems that they solve the question just by solving a linear system instead of using method such like 'interior-point' or 'active-set'. If someone has read this paper, Could you please tell me how on earth they solve the formula(4) ? Thanks a lot!

• Welcome to SciComp! In the future, please type in full the formula you refer to in your question. Forcing users to visit an external link to get essential information to answer your question is discouraged. – Geoff Oxberry Jan 27 '14 at 19:39

I'll state this in terms of an analogous problem in a domain where you are looking for a function $u(x)$ (namely the Laplace equation): If you are looking to minimize the problem $$\min_{u \in H^1} \frac 12 \|\nabla u\|^2_{L_2(\Omega)} - \int f\; u \; dx$$ then this is equivalent to solving the partial differential equation $$-\Delta u = f.$$ This is because the PDE are the optimality conditions for the optimization problem and, because they are linear, allows for the direct solution.

In the same way, the minimization problem given by equation (4) of the paper leads to a partial differential equation -- here posed on the surface of a body -- as the optimality conditions, and this is what the authors solve.

• Thank you very much! I understand the principle with your help, by the way, if you have seen the code for this paper, could you please tell me what the meaning of 'Tdelta' and why can they calculate the pseudo inverse of 'C' to get 'Tdelta'? It seems that they want to get 's' and 'a' subject to that s1*x1 + s2*x2+ s3*x3 + s4*y1 + s5*y2 + s6*y3 = 1 and s1*y1 + s2*y2 + s3*y3 - s4*x1 - s5*x2 - s6*x3 = 0 and s1 + s2 + s3 = 0 and s3 + s4 + s5 = 0 and the condition for 'a' is similar, where s = [s1, s2, s3, s4, s5, s6], and C = [x1, y1, 1, 0; x2, y2, 1, 0; x3, y3, 1, 0; y1, -x1, 0, 1; ...]; – Monkey D Bear Jan 27 '14 at 3:34
• I haven't looked at the code, so can't help -- sorry. – Wolfgang Bangerth Jan 27 '14 at 3:48

To add to Wolfgang's answer, the PDE that they come up with in the paper arises as the optimality condition for an unconstrained optimization problem. You mention using the quadprog function in MATLAB and methods like interior point and active set; these are more appropriate for optimization problems with inequality constraints. This would be a problem like

$\min\frac{1}{2}\int_\Omega |\nabla u|^2 dx - \int_\Omega u\cdot f dx$, over all $u$: $u \ge 0$.

The addition of the constraint $u \ge 0$ is what makes quadratic programming problems with inequality constraints so much harder than unconstrained QP, which boils down to just solving a linear system. By using the interior point method, you would be applying a method normally used for problems with inequality constraints to an unconstrained problem. Hope this clarifies matters!

• Box constraints like $u(x)\ge 0$ are actually not all that difficult to treat with quadratic objective functions such as the one you mention here. They are efficiently solved with active set methods. It becomes much more complicated if you have constraints of the kind $|\nabla u(x)|\le \gamma$ as you have in plasticity, for example. – Wolfgang Bangerth Jan 28 '14 at 4:01
• Cool, I thought inequality constraints make everything a total nightmare. By efficient, do you mean that the run-time of the solver scales as the number of non-zeros, like for AMG? – Daniel Shapero Jan 28 '14 at 4:14
• I don't know enough about the theory of optimization, but typically box constraints are not overly expensive to deal with because they concern only individual variables. – Wolfgang Bangerth Jan 29 '14 at 2:01

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## How deep is the well?

In one episode of the television series Time Team, the indefatigable archaeologists want to measure the depth of a mediaeval well. They drop something into it and time its fall, which takes an amazingly long six seconds. You hear it clattering its way down for ages. They come dangerously close to calculating the depth using Newton’s laws of motion, but cop out at the last moment and use three very long tape measures joined together instead.

The formula they very nearly state is

$s=\frac{1}{2}gt^{2}$

where s is the distance travelled under gravity, falling from rest, and g is the acceleration due to gravity. It applies when air resistance can be ignored. This formula was discovered experimentally by Galileo Galilei and later generalized by Isaac Newton to describe motion under the influence of any force.

Taking $g= 10 m s^{-2}$how deep is the well?

You’ve got three days to do it.

Ref: Prof Ian Stewart’s Cabinet of Mathematical Curiosities.

More treasures coming from Prof Stewart’s cabinet for us later,

Nalin Pithwa

### One Comment

1. Anubhav Clancy Singh


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# [Dev-luatex] bug with \ifcsname, ttf font spacing problems, and catcode initialisation for utf8 beyond ascii

Hans Hagen pragma at wxs.nl
Fri Sep 14 11:52:56 CEST 2007

```Arthur Reutenauer wrote:
>> I tried Yannis Haralambous's code sample to load a ttf font :
>
>   Redde Cæsari quæ sunt Cæsaris: the code is actually mine :-) I
> exchanged mail with Yannis and sent him the code, which he later
> edited a bit. But Hans, you must remember having seen that code too,
> since you looked over my shoulder when I wrote it in Münster ;-)
>
>   I remember having modified it later on, especially for the mag problem
> (you probably have to replace the test around size with
> “if size < 0 then size = -size * 655360 end”, and “mag = size / 2048”
> with “mag = size / ttfont.units_per_em”). The setting of vertical must
> be an even later addition by Yannis.
>
>   Anyway, I will test the code with the latest revision of LuaTeX and
> update the wiki as needed.

why not kick out the mag, after all it's an example and using mag
complicates matters

Hans

-----------------------------------------------------------------


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## Thomas' Calculus 13th Edition

$\dfrac{2}{3}x^{3/2}+\dfrac{3}{4}x^{4/3}+C$
As we know $\int x^n dx=\dfrac{x^{n+1}}{n+1}+C$ Re-write $\int (\sqrt x+\sqrt [3] x) dx$ as $\int (\sqrt x+\sqrt [3] x) dx=\int (x^{1/2}+ x^{1/3}) dx$ Thus, $\int (x^{1/2}+ x^{1/3}) dx=\dfrac{x^{3/2}}{3/2}+\dfrac{x^{4/3}}{4/3}+C=\dfrac{2}{3}x^{3/2}+\dfrac{3}{4}x^{4/3}+C$


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# Show that the measure is equal to zero

Let $\mu$ be a Borel measure in $\mathbb{R}$ such that $\mu(I) \leq v^a(I)$ for each bounded interval $I$, where $a>1$. Show that $\mu=0$.

($v(R)$ is the volume of $R$)

Do we maybe use the following to show that?

For each rectangle $R$, $m^*(R)=v(R)$.

Or do I have to do it otherwise?? Could you give me some hints??

• Could you say what is $v$? – Petite Etincelle Oct 14 '14 at 23:09
• It should be $\mu(I) \le (v(I))^a$, where $v(\cdot)$ is the Lebesgue measure. – Orest Bucicovschi Oct 14 '14 at 23:13
• @LiuGang $v(R)$ is the volume of $R$ – Mary Star Oct 14 '14 at 23:22

For every interval $I =[x,y)$ and every $n \in \mathbb{N}$ we have that $$I= [x,y)= \bigcup_{k = 0}^{n-1} \underbrace{\left[ x + (y-x)\frac{k}{n},x + (y-x)\frac{k+1}{n}\right)}_{I_k}$$ Then $$\mu(I_k) \leq \nu(I_k)^a = \left(\frac{y-x}{n}\right)^a$$ Now by additivity we have $$\mu(I) = \sum_{k=0}^{n-1} \mu(I_k) \leq \sum_{k=0}^{n-1}\left(\frac{y-x}{n}\right)^a = (y-x)^a n^{1-a} \stackrel{n \to \infty}{\longrightarrow} 0$$ Hence $\mu(I)=0$ for every interval so $\mu = 0$.
Hint: Notice that $[a,a+b)=[a,a+b/2)\cup [a+b/2,a+b)$. Use this to show that $\mu([a,a+b))$ is smaller than any $\varepsilon>0$.


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Homework Help: Show limit does not exist

1. Nov 22, 2011

Hwng10

1. The problem statement, all variables and given/known data
Show limit 1/x^2 when x approaches zero does not exist.

2. Relevant equations

3. The attempt at a solution
What I do is suppose the limit exists,say L.Then I show that for all real number L, the limit does not approaches L. In this case, I separate L into different cases. Can anyone help me to check is this a valid prove.

2. Nov 22, 2011

HallsofIvy

Yes, that is a valid approach.

3. Nov 22, 2011

Staff: Mentor

$$\lim_{x \to 0}\frac{1}{x^2} = \infty$$

Since ∞ is not a real number the limit above is said not to exist. This limit means that for any large, positive number M, there is some interval around 0 such that if x is in that interval, 1/x2 > M.


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# Simpson’s 1/24 Rule for Numerical Integration

by admin in on April 29, 2019

This code calculates the Numerical Integration of a given equation on a predefined interval using Simpson’s 1/24 Rule. This codes uses variable step size so it gives accurate results. This method used in case of narrow picks.  The method is comparable in accuracy and fastness with Simpson’s 1/3 and 3/8 rules.

### Code Outputs:

• Chart of Integration History
• Chart of Residuals
• Printed values of Final Iteration value, Accuracy and Number of Iterations.

Result is: 0.99718, Accuracy: 2.0449e-05, NO Iterations: 28

### Input Requirements:

• The equation you intended to integrate
• Integration interval [a b].
• predefined error (default 0.0001).
• Maximum number of iterations (default 50000).

For Simpson’s voting rule, see Minimax Condorcet. For Simpson’s rules used in ship stability, see Simpson’s rules (ship stability). Simpson’s rule can be derived by approximating the integrand (x) (in blue) by the quadratic interpolant P(x) (in red).

### Simpson’s 1/24 Rules:

In the task of estimation of full area of narrow peak-like functions, Simpson’s rules are much less efficient than trapezoidal rule. Namely, composite Simpson’s 1/3 rule requires 1.8 times more points to achieve the same accuracy[7] as trapezoidal rule. Composite Simpson’s 3/8 rule is even less accurate. Integral by Simpson’s 1/3 rule can be represented as a sum of 2/3 of integral by trapezoidal rule with step h and 1/3 of integral by rectangle rule with step 2h. No wonder that error of the sum corresponds lo less accurate term. Averaging of Simpson’s 1/3 rule composite sums with properly shifted frames produces following rules:

where two points outside of integrated region are exploited and

Those rules are very much similar to Press’s alternative extended Simpson’s rule. Coefficients within the major part of the region being integrated equal one, differences are only at the edges. These three rules can be associated with Euler-MacLaurin formula with the first derivative term and named Euler-MacLaurin integration rules. They differ only in how the first derivative at the region end is calculated.

### References:

[1] Atkinson, Kendall E. (1989). An Introduction to Numerical Analysis (2nd ed.). John Wiley & Sons. ISBN 0-471-50023-2.

[2] Burden, Richard L.; Faires, J. Douglas (2000). Numerical Analysis (7th ed.). Brooks/Cole. ISBN 0-534-38216-9.

[3] Pate, McCall (1918). The naval artificer’s manual: (The naval artificer’s handbook revised) text, questions and general information for deck. United States. Bureau of Reconstruction and Repair. p. 198.

[4] Matthews, John H. (2004). ‘Simpson’s 3/8 Rule for Numerical Integration’. Numerical Analysis – Numerical Methods Project. California State University, Fullerton. Archived from the original on 4 December 2008. Retrieved 11 November 2008.

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## Simple LRU Cache

For a bit of fun, I wanted to implement a simple LRU cache in Python. Here’s a short walk-through of my thought processes and general steps. This LRU cache is not a full implementation for anything you’d want to use in production, but just the core functionality. I may add more to it in the future though.

If you are looking for a complete LRU cache, consider the following:

Others are also available.

## What is an LRU cache?

LRU stands for ‘least recently used’. An LRU cache is a cache which discards its least recently used items when it becomes full.

Some examples are with an LRU cache of size 2 applied to a function called add which simply adds two numbers together:

## Setting up the function decorator

First step is to define how the end-user will interact with the LRU cache.

Typically, this is done via a function decorator. Here’s an example:

So we expect the LRU cache to be used in the following way:

## First iteration

Here we perform the initial setup of our LRUCache class which is consistent with how we intend to use it. We also stub out an incredibly simple (and incomplete) call method; it just returns a cached value if the same arguments are used.

The underlying data structure of this LRU cache is a dictionary.

## Adding the notion of orderedness

To ensure only a maximum of N items are cached, we need to add a check after retriving the value.

At the same time, we can switch from using a dictionary to an ordered dictionary. This will allow us to remove the value of the earliest entry.

Note that this is still incorrect - it does not follow the definition of ‘least recently used’.

## Removing the correct cached value

Here we pop any already cached value or compute a new value given the arguments. This saves us a few lines of code for the earlier if statement.

We then re-insert the value so that the OrderedDict can update the order internally. This means the popitem(last=False) will remove the oldest used cache value, thus keeping only the most recently used items.

## Supporting kwargs

The eagle-eyed amoungst us will have spotted that we only supported positional arguments earlier; the kwargs dictionary is not hashable so cannot be used as a dictionary key.

In order to create a key, we convert the dictionary into a list of sorted tuples.

We then use this key when getting and setting values in the cache.

Note this is just an extremely naive way of supporting kwargs. It is quite easy to construct test cases which break this.

## Final implementation

Here we present the full implementation of a basic LRU cache.

As previously mentioned, this was just for some fun so its best to use a more fully-featured implementation.


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main-content

## Über dieses Buch

This IMA Volume in Mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAVES. We are grateful to the Scientific Commit tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the Work shop Organizers, Andrew Majda and James Glimm, for bringing together many of the major figures in a variety of research fields connected with multidimensional hyperbolic problems. A vner Friedman Willard Miller PREFACE A primary goal of the IMA workshop on Multidimensional Hyperbolic Problems and Computations from April 3-14, 1989 was to emphasize the interdisciplinary nature of contemporary research in this field involving the combination of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation, and experiments. The twenty-six papers in this volume span a wide cross-section of this research including some papers on the kinetic theory of gases and vortex sheets for incompressible flow in addition to many papers on systems of hyperbolic conservation laws. This volume includes several papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves.

## Inhaltsverzeichnis

### Macroscopic Limits of Kinetic Equations

Abstract
The connection between kinetic theory and the macroscopic equations of fluid dynamics is described. In particular, our results concerning the incompressible Navier-Stokes equation are compared with the classical derivation of Hilbert and Chapman-Enskog. Some indications of the validity of these limits are given. More specifically, the connection between the DiPerna-Lions renormalized solution for the Boltzmann equation and the Leray-Hopf solution for the Navier-Stokes equation is considered.
Claude Bardos, François Golse, David Levermore

### The Essence of Particle Simulation of the Boltzmann Equation

Abstract
We describe the mathematical structure of recently developed family of consistent and convergent particle simulation methods for the Boltzmann equation.
H. Babovsky, R. Illner

### The Approximation of Weak Solutions to the 2-D Euler Equations by Vortex Elements

Abstract
It is shown that the Euler equations of two-dimensional incompressible flow, with initial vorticity in L p , p > 1, possess weak solutions which may be obtained as a limit of vortex “blobs”; i.e., the vorticity is approximated by a finite sum of cores of prescribed shape which are advected according to the corresponding velocity field. If the vorticity is instead a finite measure of bounded support, such approximations lead to a measure-valued solution of the Euler equations in the sense of DiPerna and Majda [7]. The analysis is closely related to that of [7].
J. Thomas Beale

### Limit Behavior of Approximate Solutions to Conservation Laws

Abstract
We are concerned with the limit behavior of approximate solutions to hyperbolic systems of conservation laws. Several mathematical compactness theories and their role are described. Some recent and ongoing developments are reviewed and analyzed.
Chen Gui-Qiang

### Modeling Two-Phase Flow of Reactive Granular Materials

Abstract
In this study, we examine a two-phase model proposed by Baer and Nunziato to describe the modes of combustion from deflagration to detonation in reactive granular materials. The model treats all phases in nonequilibrium and fully compressible. A compaction evolutionary equation, describing changes in volume fraction, provides model closure. In contrast to a pressure equilibrium model that has elliptic regions, the system of equations is hyperbolic except at points where the relative flow is locally sonic.
Pedro F. Embid, Melvin R. Baer

### Shocks Associated with Rotational Modes

Abstract
Many interesting systems of conservation laws in several space variables are isotropic in the sense of equivariance under rotations acting on the spatial components of the independent variable and on appropriate components of the state variable (e.g. the velocity vector in gas dynamics, or the velocity vector and the magnetic field vector in magnetohydrodynamics). As consequences of the isotropy, the conservation law which governs the propagation of plane waves in a given direction is not only independent of this direction, but also inherits a rotational symmetry, where now rotations act only on the transverse parts of the said components of the state variable. Generically — e.g. in magnetohydrodynamics, but not in gas dynamics — these transverse parts exhibit an interesting wave pattern including isolated linearly degenerate rotational modes. The talk is especially on the following three facts: These modes have not only contact discontinuities, but also shocks associated with them; for an arbitrarily given strictly stable and rotationally equivariant viscosity many of these shocks have viscous profiles; for an arbitrary choice of the four viscosity parameters in the usual dissipative version of magnetohydrodynamics there exist intermediate magnetohydrodynamic shocks which have a viscous profile.
Heinrich Freistühler

### Self-Similar Shock Reflection in Two Space Dimensions

Abstract
Self-similar oblique shock wave reflection for the equations of unsteady inviscid gas dynamics is among the outstanding unsolved problems in nonlinear PDE. This is so due not only to its’ standing as the simplest possible nontrivial shock wave interaction problem for these equations and the importance of the problem in engineering applications, but to the tantalizingly large amount of experimental and computational data which is available after half a century of intensive research since WW II.
Harland M. Glaz

### Nonlinear Waves: Overview and Problems

Abstract
The subject of nonlinear hyperbolic waves is surveyed, with an emphasis on the discussion of a number of open problems.
James Glimm

### The Growth and Interaction of Bubbles in Rayleigh-Taylor Unstable Interfaces

Abstract
The dynamic behavior of Rayleigh-Taylor unstable interfaces may be simplified in terms of dynamics of fundamental modes and the interaction between these modes. A dynamic equation is proposed to capture the dominant behavior of single bubbles and spikes in the linear, free fall and terminal velocity stages. The interaction between bubbles, characterized by the process of bubble merger, is studied by investigating the motion of the outer envelope of the bubbles. The front tracking method is used for simulating the motion of two compressible fluids of different density under the influence of gravity.
James Glimm, Xiao Lin Li, Ralph Menikoff, David H. Sharp, Qiang Zhang

### Front Tracking, Oil Reservoirs, Engineering Scale Problems and Mass Conservation

Abstract
A critical analysis is given of the mechanisms for mass conservation loss for the front tracking algorithm of the authors and co-workers in the context of two phase incompressible flow in porous media. We describe the resolution to some of the non-conservative aspects of the method, and suggest methods for dealing with the remainder.
James Glimm, Brent Lindquist, Qiang Zhang

### Collisionless Solutions to the Four Velocity Broadwell Equations

Abstract
In this note we shall examine special collisionless solutions to the four velocity Broadwell equations. These solutions are new and seem to have gone unnoticed by other investigators who have worked in this area1. These solutions are apparently stable; that is in numerical simulations they appear as the asymptotic state of the evolving system.
J. M. Greenberg, Cleve Moler

### Anomalous Reflection of a Shock Wave at a Fluid Interface

Abstract
Several wave patterns can be produced by the interaction of a shock wave with a fluid interface. We focus on the case when the shock passes from a medium of high to low acoustic impedance. Curvature of either the shock front or contact causes the flow to bifurcate from a locally self-similar quasi-stationary shock diffraction, to an unsteady anomalous reflection. This process is analogous to the transition from a regular to a Mach reflection when the reflected wave is a rarefaction instead of a shock. These bifurcations have been incorporated into a front tracking code that provides an accurate description of wave interactions. Numerical results for two illustrative cases are described; a planar shock passing over a bubble, and an expanding shock impacting a planar contact.
John W. Grove, Ralph Menikoff

### An Application of Connection Matrix to Magnetohydrodynamic Shock Profiles

Abstract
In this note we shall summarize how to use the connection matrix to show the existence of a viscous profile to the magnetohydrodynamic (MHD) equations. Although Freistuhler [1] has obtained various intermediate shock profiles in a different parameter regime, our technique is different and interesting to know. This is a technique based on algebraic topology and an extension of Con-ley’s index. As the detailed version will be appearing elsewhere [2], in this note we concentrate on how to use the connection matrix.
Harumi Hattori, Konstantin Mischaikow

### Convection of Discontinuities in Solutions of the Navier-Stokes Equations for Compressible Flow

Abstract
We report here on results concerning the existence, uniqueness, and continuous dependence on initial data of discontinuous solutions of the Navier-Stokes equations for one-dimensional compressible fluid flow:
$$\left\{ \begin{gathered} {\upsilon_t} - {u_x} = 0 \hfill \\ {u_t} + p{(\upsilon, e)_x} = {\left( {\frac{{ \in {u_x}}}{\upsilon }} \right)_x} \hfill \\ {\left( {\frac{{{u^2}}}{2} + e} \right)_t} + {(up(\upsilon, e))_x} = {\left( {\frac{{ \in u{u_x} + \lambda T{{(\upsilon, e)}_x}}}{\upsilon }} \right)_x} \hfill \\ \end{gathered} \right.$$
(1)
with Cauchy data
$$\left[ \begin{gathered} \upsilon \hfill \\ u \hfill \\ e \hfill \\ \end{gathered} \right](x,0) = \left[ \begin{gathered} {\upsilon_0} \hfill \\ {u_0} \hfill \\ {e_0} \hfill \\ \end{gathered} \right](x)$$
(2)
Here v, u, e, p, and T represent respectively the specific volume, velocity, specific internal energy, pressure, and temperature in a fluid; x is the Lagrangian coordinate, so that x = constant corresponds to a particle path; and and λ are fixed positive viscosity parameters.
David Hoff

### Nonlinear Geometrical Optics

Abstract
Using asymptotic methods, one can reduce complicated systems of equations to simpler model equations. The model equation for a single, genuinely nonlinear, hyperbolic wave is Burgers equation. Reducing the gas dynamics equations to a Burgers equation, leads to a theory of nonlinear geometrical acoustics. When diffractive effects are included, the model equation is the ZK or unsteady transonic small disturbance equation. We describe some properties of this equation, and use it to formulate asymptotic equations that describe the transition from regular to Mach reflection for weak shocks. Interacting hyperbolic waves are described by a system of Burgers or ZK equations coupled by integral terms. We use these equations to study the transverse stability of interacting sound waves in gas dynamics.
John K. Hunter

### Geometric Theory of Shock Waves

Abstract
Substantial progresses have been made in recent years on shock wave theory. The present article surveys the exact mathematical theory on the behavior of nonlinear hyperbolic waves and raises open problems.
Tai-Ping Liu

### An Introduction to front Tracking

Abstract
In fluid flows one can often identify surfaces that correspond to special features of the flow. Examples are boundaries between different phases of a fluid or between two different fluids, slip surfaces, and shock waves in compressible gas dynamics. These prominent features of fluid dynamics present formidable challenges to numerical simulations of their mathematical models. The essentially nonlinear nature of these waves calls for nonlinear methods. Here we present one such method which attempts to explicitly follow (track) the dynamic evolution of these waves (fronts). Most of this exposition will concentrate on one particular implementation of such a front tracking algorithm for two space, where the fronts are one-dimensional curves. This is the code associated with J. Glimm and many co-workers.

### One Perspective on Open Problems in Multi-Dimensional Conservation Laws

Abstract
It is evident from the lectures at this meeting that the subject of systems of hyperbolic conservation laws is flourishing as one of the prototypical examples of the modern mode of applied mathematics. Research in this area often involves strong and close interdisciplinary interactions among diverse areas of applied mathematics including
(1)
Large (and small) scale computing

(2)
Asymptotic modelling

(3)
Qualitative modelling

(4)
Rigorous proofs for suitable prototype problems

combined with careful attention to experimental data when possible. In fact, the subject is developing at such a rapid rate that new predictions of phenomena through a combination of theory and computations can be made in regimes which are not readily accessible to experimentalists. Pioneering examples of this type of interaction can be found in the papers of Grove, Glaz, and Colella in this volume as well as the recent work of Woodward, Artola, and the author ([1], [2], [3], [4], [5], [6]). In this last work, novel mechanisms of nonlinear instability in supersonic vortex sheets have been documented and explained very recently through a sophisticated combination of numerical experiments and mathematical theory.
Andrew J. Majda

### Stability of Multi-Dimensional Weak Shocks

Abstract
In this paper we discuss the stability of weak shocks for a class of multi-dimensional systems of conservation laws, containing Euler’s equations of gas dynamics; we study the well-posedness of the linearized problem, and study the behaviour of the L 2 estimates when the strength of the shock approaches zero.
Guy Métivier

### Nonlinear Stability in Non-Newtonian Flows

Abstract
In this paper, we discuss recent results on the nonlinear stability of discontinuous steady states of a model initial-boundary value problem in one space dimension for incompressible, isothermal shear flow of a non-Newtonian fluid between parallel plates located at x = ±1, and driven by a constant pressure gradient. The non-Newtonian contribution to the shear stress is assumed to satisfy a simple differential constitutive law. The key feature is a non-monotone relation between the total steady shear stress and steady shear strain rate that results in steady states having, in general, discontinuities in the strain rate. We explain why every solution tends to a steady state as t → ∞, and we identify steady states that are stable; more details and proofs will be presented in [8].
J. A. Nohel, R. L. Pego, A. E. Tzavaras

### A Numerical Study of Shock Wave Refraction at a CO2/CH4 Interface

Abstract
This paper describes the numerical computation of a shock wave refracting at a gas interface. We study a plane shock in carbon dioxide striking a plane gas interface between the carbon dioxide and methane at angle of incidence α i . The primary focus here is the structure of the wave system as a function of the angle of incidence for a fixed (weak) incident shock strength. The computational results agree well with the shock polar theory for regular refraction including accurately predicting the transition between a reflected expansion and a reflected shock. They also yield a detailed picture of the transition from regular to irregular refraction and the development of a precursor wave system. In particular, the computations indicate that for the specific case studied the precursor shock weakens to become a band of compression waves as the angle of incidence increases in the irregular regime.
Elbridge Gerry Puckett

### An Introduction to Weakly Nonlinear Geometrical Optics

Abstract
Many natural phenomenae are governed by systems of nonlinear conservation laws that are — in a first approximation — hyperbolic. In this context, the understanding of the laws governing the propagation and interaction of small but finite amplitude high frequency waves in hyperbolic P.D.E.’s, and their interactions with “large scale” phenomenae (mean flows, shear layers, shock and detonation waves, etc.) is very important. Weakly Nonlinear Geometrical Optics (W.N.G.O.) is an asymptotic formal theory whose objective is precisely to do this.
In this paper we review the theory of W.N.G.O. as it stands currently. An important point is that W.N.G.O. is not (yet?) a complete theory. It fails at caustics, singular rays, etc. Since these are frequently regions of physical interest, a good theory for what happens there is important — and mostly nonexistent. The current status of these important open problems will also be (briefly) reviewed.
Rodolfo R. Rosales

### Numerical Study of Initiation and Propagation of One-Dimensional Detonations

Abstract
In this paper we briefly review some recent work centered on numerical simulation of initiation and propagation of reactive shock waves. This work is a joint project with A. Majda [1–3] with some very recent contributions by Majda’s Ph.D. student A. Bourlioux.
Victor Roytburd

### Richness and the Classification of Quasilinear Hyperbolic Systems

Abstract
Rich quasilinear hyperbolic systems are those which possess the largest possible set of entropies. Such systems have a property of global existence of weak solutions, whatever large is the bounded initial data. Although the full gas dynamics is not rich, many physically meaningful systems are. One gives below new examples and properties of the fully linearly degenerate case.
Denis Serre

### A Case of Singularity Formation in Vortex Sheet Motion Studied by a Spectrally Accurate Method

Abstract
Moore’s asymptotic analysis of vortex sheet motion predicts that the Kelvin-Helmholtz instability leads to the formation of a weak singularity in the sheet profile at a finite time. The numerical studies of Meiron, Baker & Orszag, and of Krasny, provide only a partial validation of his analysis. In this work, the motion of periodic vortex sheets is computed using a new, spectrally accurate approximation to the Birkhoff-Rott integral. As advocated by Krasny, the catastrophic effect of round-off error is suppressed by application of a Fourier filter, which itself operates near the level of the round-off. It is found that to capture the correct asymptotic behavior of the spectrum, the calculations must be performed in very high precision. The numerical calculations proceed from the initial conditions first considered by Meiron, Baker & Orszag. For the evolution of a large amplitude initial condition, the results indicate that Moore’s asymptotic analysis is valid only at times well before the singularity time. Near the singularity time the form of the singularity departs significantly away from that predicted by Moore. Convergence of the numerical solution beyond the singularity time is not observed.
M. J. Shelley

### The Goursat-Riemann Problem for Plane Waves in Isotropic Elastic Solids with Velocity Boundary Conditions

Abstract
The differential equations for plane waves in isotropic elastic solids are a 6 × 6 system of hyperbolic conservation laws. For the Goursat-Riemann problem in which the initial conditions are constant and the constant boundary conditions are prescribed in terms of stress, the wave curves in the stress space are uncoupled from the wave curves in the velocity space and the equations are equivalent to a 3 × 3 system. This is not possible when the boundary conditions are prescribed in terms of velocity. An additional complication is that, even though the system is linearly degenerate with respect to the c 2 wave speed, the c 2 wave curves cannot be decoupled from the c 1 and c 3 wave curves. Nevertheless, we show that many features and methodology of obtaining the solution remain essentially the same for the velocity boundary conditions. The c and c 3 wave curves are again plane polarized in the velocity space although the plane may not contain a coordinate axis of the velocity space. Likewise, the c 2 wave curves are circularly polarized but the center of the circle may not lie on a coordinate axis of the welocity space. Finally, we show that the c 2 wave curves can be treated separately of the c 1 and c 3 wave curves in constructing the solution to the Goursat-Riemann problem when the boundary conditions are prescribed in terms of velocity.
T. C. T. Ting, Tankin Wang
Weitere Informationen


text:
# Limit of a series

#### hedi

Hi,
Prove that the attached series converges to 1

#### Attachments

• 97.3 KB Views: 24

#### Plato

MHF Helper
Prove that the attached series converges to 1
There is a major mistake in your attachment. What is the $\Large k~?$

1 person

#### topsquark

Forum Staff
Hi,
Prove that the attached series converges to 1

Here's the sum in question:
$$\displaystyle \sum_{n}^{\infty} \dfrac{(-1)^k}{(k!)^2 {n \choose k}}$$

-Dan

#### hedi

the series should be

#### Attachments

• 90 KB Views: 5
1 person

#### Plato

MHF Helper
the series should be
Now is this correct: $$\displaystyle \Large\mathop {\lim }\limits_{n \to \infty } \sum\limits_{k = 0}^n {\frac{{{{( - 1)}^k}}}{{{{(k!)}^2}\dbinom{2n}{k}}}}~?$$

1 person

#### hedi

Sorry, it is my mistake.in the denominator there is n,not 2n

#### Plato

MHF Helper
Sorry, it is my mistake.in the denominator there is n,not 2n
Hedi. Why can't you get this right?
I have no appetite for spending time on something that you may change on the next post.

1 person

#### topsquark

Forum Staff
So is this (finally) what the question is asking you to calculate?
$$\displaystyle \lim_{n \to \infty} \sum_{k = 0}^m \dfrac{(-1)^k}{(k!)^2 {n \choose k}}$$

Note that $$\displaystyle {n \choose k} = \dfrac{n!}{k! ~ (n - k)!}$$

$$\displaystyle \lim_{n \to \infty} \sum_{k = 0}^m \dfrac{(-1)^k}{(k!)^2 {n \choose k}} = \lim_{n \to \infty} \sum_{k = 0}^n \dfrac{(-1)^k}{(k!)^2 \dfrac{n!}{k! ~ (n - k)!}}$$

$$\displaystyle = \lim_{n \to \infty} \sum_{k = 0}^n \dfrac{(-1)^k k! ~ (n - k)!}{ (k!)^2 n!}$$

$$\displaystyle = \lim_{n \to \infty} \sum_{k = 0}^n \dfrac{(-1)^k (n - k)!}{ k! ~ n!}$$

What's next?

-Dan

#### Idea

Let

$$\displaystyle s_n=\sum _{k=0}^n \frac{(-1)^k(n-k)!}{k!n!}$$

expanding we get

$$\displaystyle s_n=1-\frac{1}{n}+\frac{1}{2!n(n-1)}-\frac{1}{3!n(n-1)(n-2)}+\text{...}$$

the terms are decreasing in absolute value so

$$\displaystyle 1-\frac{1}{n}\leq s_n\leq 1$$

1 person


text:
The intersection of the set of even integers and the set of prime integers is {2}, the set that contains the single number 2. A Theorem of Volterra Vito 15 9. What makes this thing a continuum? The real number field â, with its usual topology and the operation of addition, forms a second-countable connected locally compact group called the additive group of the reals. De ne T indiscrete:= f;;Xg. Cite this chapter as: Holmgren R.A. (1994) The Topology of the Real Numbers. Compact Spaces 21 12. Open sets Open sets are among the most important subsets of R. A collection of open sets is called a topology, and any property (such as â¦ Typically, a discrete set is either finite or countably infinite. I mean--sure, the topology would have uncountably many subsets of the reals, but conceptually a discrete topology on the reals is possible, no? Therefore, the closure of $(a,b)$ is â¦ Product Topology 6 6. Perhaps the most important infinite discrete group is the additive group â¤ of the integers (the infinite cyclic group). Quotient Topology â¦ discrete:= P(X). Then T indiscrete is called the indiscrete topology on X, or sometimes the trivial topology on X. I think not, but the proof escapes me. TOPOLOGY AND THE REAL NUMBER LINE Intersections of sets are indicated by ââ©.â Aâ© B is the set of elements which belong to both sets A and B. Subspace Topology 7 7. In nitude of Prime Numbers 6 5. The real number line $\mathbf R$ is the archetype of a continuum. Universitext. For example, the set of integers is discrete on the real line. If $\tau$ is the discrete topology on the real numbers, find the closure of $(a,b)$ Here is the solution from the back of my book: Since the discrete topology contains all subsets of $\Bbb{R}$, every subset of $\Bbb{R}$ is both open and closed. Homeomorphisms 16 10. Closed Sets, Hausdor Spaces, and Closure of a Set 9 8. 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text:
# No output for N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]]

Is my input below correct? I've received no response from Mathematica.

N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]]

-
The answer (output) should be $\pi/4$. –  Chris's sis Feb 20 '13 at 9:32
The result of the integral seems to be Pi/4 for any n. –  b.gatessucks Feb 20 '13 at 10:39
@b.gatessucks: Right. This is straightforward by letting $x=\pi/2-y$. –  Chris's sis Feb 20 '13 at 10:52
so problem solved ? –  b.gatessucks Feb 20 '13 at 11:03
@b.gatessucks: I'm trying to learn to deal with such things by using Mathematica. –  Chris's sis Feb 20 '13 at 11:07

Not an answer, just will not fit in the comment.

Mathematica can't seem to be able to integrate Sin[x]^n/(Sin[x]^n + Cos[x]^n analytically. I tried using the formulas for Sin[x]^n and Cos[x]^n for odd n with the hope it will help. But still no luck. Using Wiki, the formulas are from here

mysin[x_,n_] := (2/(2^n)) Sum[(-1)^((n - 1)/2 - k) Binomial[n, k]*
Sin[(n - 2 k) x], {k, 0, (n - 1)/2}];

mycos[x_,n_] := (2/(2^n)) Sum[Binomial[n, k]*Cos[(n - 2 k) x], {k, 0, (n - 1)/2}];

integrand =
Assuming[Element[n, Integers] && n > 0 && Element[x, Reals],
FullSimplify[mysin[x, n]/(mysin[x, n] + mycos[x, n])]];

res = ComplexExpand[integrand];
Integrate[res, {x, 0, Pi/2}]

Its been running for 30 minutes.

But doing numerical integration

Table[
NIntegrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], {n, 0, 10}]

(*Out[1]= {0.785398, 0.785398, 0.785398, 0.785398, 0.785398, 0.785398, \
0.785398, 0.785398, 0.785398, 0.785398, 0.785398}*)

So may be you do not not need to do analytical integration after all? Are you sure this integrand can be integrated analytically?

-


text:
# Overview

At the 3rd Blueprint @ MIT, I created Math Maze, a two-player game about finding your way through a maze faster than the other player. The trick? There are no walls in the maze—you have to find a path that adds up to the specified target number.

Since I had already created another math-related game, the real project here wasn’t as so much as the gameplay as figuring out how to develop a maze generation algorithm that worked as quickly as possible as to not interrupt gameplay.

# Implementation

In “Math Maze”, each puzzle starts with a “Start” point and an “End” point displayed on a 4 x 5 grid of numbers. The “End” point displays the target number for the current puzzle. Players trace a path of numbers from the “Start” point to the end point that adds up to the target number. As the players trace the path, the “End” point updates with the current value of their path so far.

## Puzzle Generation

To generate a path, I first select a random “Start” point on the 4 x 5 grid and decide on a random length for the path. (The funky typecasting seen here is necessary to properly convert the random UInt32 given to a higher-level CGFloat.)

From there, I randomly decide on a direction to head from that point, and continually append new points to a storage array. Path generation stops once the pathLength has been reached.

However, the path is not allowed to intersect itself nor land outside of the edges of the grid, so we first check to see if the current path already contains the given point or if it lands outside a boundary. If so, we then check to see if the current path is completely “boxed-in”—that is, it has no possible point to head towards in its current state. If so, maze generation immediately stops there.

From there, all we have to do is randomly populate the grid with numbers and calculate an answer from the numbers that fall in the specified path.

Finally, even though we know the desired path, I add up the numbers for every solution the player comes up with just in case unexpected solutions come up from the numbers we generate. This guarantees that there always is at least one possible answer to every puzzle. Perfect!

Math Maze was developed at MIT Blueprint in February 2016.


text:
# Does the integral of PDF of multi-normal distribution over quarter planes have a closed form?

I am interested in finding a closed form solution (wich I suspect does not exist) to the following integral

$$\displaystyle \int _a^{\infty }\int _b^{\infty } \frac{\exp \left(-\frac{x^2+y^2-2 c x y}{2 \left(1-c^2\right)}\right)}{2 \pi \sqrt{1-c^2}} dy dx$$

which corresponds to the integral of the PDF$(x,y)$ of a multiNormalDistribution (of covariance coefficient $c$) over the quarter plane $x>a$ and $y>b$. Here $a$ and $b$ are positive and $0<c<1$ (and I know a solution exists for $a=b=0$, but this is not sufficient for my purpose).

More generally I would be interested in the $3$D generalization of this problem.

I have tried in Mathematica to no avail.

Regards,

-

## 1 Answer

Generically, cumulative distribution function of multivariate Gaussian vector is not expressible in terms of cdf of standard normal random variable $\Phi(x)$. The book by Alan Genz and Frank Brentz, "Computation of multivariate Normal and t Probabilities" is good reference on the subject.

For a standard 2D Gaussian vector $(X,Y)$ with correlation coefficient $-1 < \rho <1$, the probability $\mathbb{P}(X>a,Y>b)$ can be expressed in terms of Owen's T-function.

By the way Mathematica v8 has a built-in support for multi-normal distribution with special efficient cases for 2D and 3D Gussian random vectors, see BinormalDistribution (ref-page), and MultinormalDistribution (ref-page), and OwenT (ref-page).

-
 Is it correct to assume there is no generalization of the Owen's T function which would be applicable to the 3D case? – chris Jun 4 '12 at 8:41 @chris Of course there is. The generalization is called the multinormal probability. Generically it does not reduce to lower-dimensional probability functions though. – Sasha Jun 4 '12 at 13:44 Nor does its cumulative distribution reduces to any analytic form? – chris Jun 4 '12 at 14:00 No, I am afraid it does not – Sasha Jun 4 '12 at 15:11


text:
# objective question exam!!

Algebra Level 1

a man got a objective question paper ! if he give a right ans he will get 1 mark , if he give a wrong ans he will loose 0.5 mark .he gave all answer... ! after exam he got 29.5 mark . so how many ans was wrong and how many was wright??????

×


text:
# Fossil Fuels for Transport

The three most common types of fossil fuel used for transportation are as follows:

• Gasoline (cars, trucks)
• Diesel (cars, trucks, buses, rail locomotives, ships)
• Jet fuel (aviation)

Although these fuels differ greatly in how they are used and handled, for the purposes of energy and GHG calculations, they are all more-or-less the same.

Gasoline is the most common liquid fuel for internal combustion engines. Its chemical composition is complicated and variable, but a simple approximation removes all these uncertainties and allows to make sufficiently accurate energy and CO$_2$ production calculations.

The most important characteristics of gasoline for the purposes of our calculations are:

1. Enthalpy of combustion (“energy content”) in terms of MJ/kg and MJ/L. These two quantities are linked via the density in kg/L.

Engineering Toolbox[1]Engineering Toolbox https://www.engineeringtoolbox.com/fuels-higher-calorific-values-d_169.html [2019-09-13] gives an enthalpy value of 46.4 MJ/kg noting that this value may vary either way by 5-10%. The density of 737 kg/m$^3$ (0.737 kg/L) thus gives an enthalpy of 34.2 MJ/L.

2. Hydrogen to carbon ratio (H/C): the three main components of gasoline are isooctane, butane and 3-ethyltoluene [2]Gasoline: chemical analysis and production, https://en.wikipedia.org/wiki/Gasoline#Chemical_analysis_and_production [2019-09-13], whose H/C ratios are 18/8, 12/9 and 12/5 respectively. In other words, H/C $\approx$ 2.

Using H/C = 2, we can calculate the CO$_2$ production for a given quantity of fuel burned.

CH$_2$ + 3/2 O$_2 \rightarrow$ CO$_2$ + H$_2$O $\tag{1}$

Taking the molar masses of CH$_2$ to be 14 and CO$_2$ to be 44, this means that 14 kg of gasoline (14/0.737 = 19.0 L) burns to 44 kg of CO$_2$. Thus 1 L of gasoline burns to 44/14 = 2.3 kg of CO$_2$. This is the generally accepted value[3] “How much carbon dioxide is produced by burning gasoline and diesel fuel?”. U.S. Energy Information Administration (EIA). [2013-10-27], i.e. H/C = 2 is a perfectly usable approximation.

Diesel

Diesel fuel is a heavier fraction of crude oil and consists of a mixture of different hydrocarbons with an average chemical composition of C$_{12}$H$_{24}$[4]Diesel, chemical analysis, https://en.wikipedia.org/wiki/Diesel_fuel#Chemical_analysis [2019-09-16].. Thus H/C = 2 is as good an assumption as for gasoline, and CO$_2$ emissions in terms of kg/kg will be the same.

The enthalpy of combustion is 45.6 MJ/kg, 38.6 MJ/L with a density of 846 kg/m$^3$[5]Engineering Toolbox https://www.engineeringtoolbox.com/fuels-higher-calorific-values-d_169.html [2019-09-13].

Jet Fuel

Jet fuel, a.k.a. aviation kerosene or Jet-A, has a mean chemical composition of C$_{12}$H$_{26}$[6]Kerosene, https://en.wikipedia.org/wiki/Kerosene#Engines [2019-09-16]., i.e. H/C = 2.17 or a little larger than 2. The CO$_2$ emissions in terms of kg/kg will be a few % less than for gasoline or diesel.

The enthalpy of combustion is 43 MJ/kg, 35 MJ/L with a density of around 800 kg/m$^3$[7]Jet Fuel, https://en.wikipedia.org/wiki/Jet_fuel [2019-09-13].

 Fuel C:H ratio Enthalpy MJ/kg Enthalpy MJ/L Density kg/L kg(CO$_2$)/L Gasoline CH$_2$ 46.4 34.2 0.74 2.3 Diesel CH$_2$ 45.6 38.6 0.85 2.7 Jet A CH$_{2.17}$ 43 35 0.80 2.5

Table 1. Summary of liquid fossil fuels used in transportation.

The values shown in the summary Table 1 are typical, not definitive. The bottom line is that they are all about the same. If you assume that any given liquid fuel has an enthalpy of combustion of 35 MJ/L, a density of 0.8 kg/L and produces when burnt 2.5 kg of CO$_2$/L, you will not be far wrong.

Updated (CEW) 2019-10-03

Footnotes   [ + ]

 1, 5. ↑ Engineering Toolbox https://www.engineeringtoolbox.com/fuels-higher-calorific-values-d_169.html [2019-09-13] 2. ↑ Gasoline: chemical analysis and production, https://en.wikipedia.org/wiki/Gasoline#Chemical_analysis_and_production [2019-09-13] 3. ↑ “How much carbon dioxide is produced by burning gasoline and diesel fuel?”. U.S. Energy Information Administration (EIA). [2013-10-27] 4. ↑ Diesel, chemical analysis, https://en.wikipedia.org/wiki/Diesel_fuel#Chemical_analysis [2019-09-16]. 6. ↑ Kerosene, https://en.wikipedia.org/wiki/Kerosene#Engines [2019-09-16]. 7. ↑ Jet Fuel, https://en.wikipedia.org/wiki/Jet_fuel [2019-09-13]


text:
# Select string of text between quotes

## Recommended Posts

Hello,

I am interested in looking at a chunk of text, selecting the string that is in quotes, and copying it to the clipboard. It will always have quotes at the beginning and end, start with https:// and will always contain .mp3 . But everything else is pretty random. This is an example of a piece of text

 Quote   suhfiushifuhrifuei file: "https://d1gwazgugjenv6.net/after/bef0re/062316.mp3?Expires=1470376621&Signature=h06vK9xR0mbXaMPKO0eQpBSUJX6hvK7l~AgQgCRMcd6DPJmbuMNOaD8P52pnvaGYrQUZUjBUlTfxXACtGyzgP-AdJZkcUlprGUtL47PAqLeiuu-JEomk2Y13qRB7eWjVVl3v0CfjXvgxQXVlwNob2HrmglVFKkusSJRdOTjuwAAZP89Pf~l3w2p6RFy9gL3E1nq3DQowa9NGIQYEdExLPDOYu5jLPI5lhuH8t8vTAZRCwq6YuJtIQ5vJgrQHkk4q7aECn8T8pGvwmossGjrcz-Ga0KlZiefBwFe7XXV66Xor5SVPkaoN3DTQ07ZuAqEtV5ccd6PyOM0iVLFfYjw__&Key-Pair-Id=APKAJ5GT74YAYAGA4KAA",   APKAJ5GT74YAYAGA4KAA   I tried doing something like this but it didn't like the quotes.  $sStart = "file: ""$sEnd = ""," $aExtract = _StringBetween($sStart, $sEnd) ClipPut($aExtract)   Or is there a better/easier way to do this?

##### Share on other sites

Working with quotes in a string can get hairy fast and _StringBetween returns an array, try this code and see if it doesn't help...

#include <Array.au3>
#include <String.au3>
$string = 'suhfiushifuhrifuei file: "https://d1gwazgugjenv6.net/after/bef0re/062316.mp3?Expires=1470376621&Signature=h06vK9xR0mbXaMPKO0eQpBSUJX6hvK7l~AgQgCRMcd6DPJmbuMNOaD8P52pnvaGYrQUZUjBUlTfxXACtGyzgP-AdJZkcUlprGUtL47PAqLeiuu-JEomk2Y13qRB7eWjVVl3v0CfjXvgxQXVlwNob2HrmglVFKkusSJRdOTjuwAAZP89Pf~l3w2p6RFy9gL3E1nq3DQowa9NGIQYEdExLPDOYu5jLPI5lhuH8t8vTAZRCwq6YuJtIQ5vJgrQHkk4q7aECn8T8pGvwmossGjrcz-Ga0KlZiefBwFe7XXV66Xor5SVPkaoN3DTQ07ZuAqEtV5ccd6PyOM0iVLFfYjw__&Key-Pair-Id=APKAJ5GT74YAYAGA4KAA", APKAJ5GT74YAYAGA4KAA'$sStart = 'file: "'
$sEnd = '",'$aExtract = _StringBetween($string,$sStart, $sEnd) ;ClipPut($aExtract)
_ArrayDisplay(aExtract) #### Share this post ##### Link to post ##### Share on other sites ## Create an account or sign in to comment You need to be a member in order to leave a comment ## Create an account Sign up for a new account in our community. It's easy! Register a new account ## Sign in Already have an account? Sign in here. Sign In Now • ### Similar Content • Good morning, I am trying to align a two-line text in a button so that it would be centered in the button but can't succeed to do it for the vertical part. Can someone tell me what I do wrong ? Here is my code:btn3 = GUICtrlCreateButton("Execute " & @LF & " file 1", 100, 65, 60, 50, _ BitOr($BS_CENTER,$BS_BOTTOM,$BS_MULTILINE)) and here is the resulting layout I get in my window. I tried to follow the help, made a lot of different parameter combinations (here it's $BS_BOTTOM, but I tried $BS_VCENTER and $BS_TOP), still get the same result : vertical alignement is a no go for me.
Can someone help ?
TIA
Gilles

• So basically need to pull text from a .txt file or .sql and use that text to replace something within a different file.

First File:
jumps

Or:
Text1 = jumps
Text2 = fence
Second File:
My Dog XXXXX over the YYYYY.

After Script:
My Dog jumps over the fence

I have found a good start, I'm basic programmer at best, I have some experience but this gets out of my wheel house.

Any help is appreciated.

• By misioooo
Hi!

I am writing some GUI and i need to use images as buttons, but with text on them (text is from INI file).
Part with button looks like this:
$ankieta1 = GUICtrlCreateButton($txtAnk1, 100,350,765,164) GUICtrlSetFont(-1, 22, 800, -1, "Arial") ;GUICtrlSetColor(-1,0xffffff) $hImageBtn_1 = _GUIImageList_Create(765, 164) _GUIImageList_AddBitmap($hImageBtn_1, "c:\path\to\ankieta_clean.bmp") _GUICtrlButton_SetImageList($ankieta1,$hImageBtn_1, 4) GUICtrlSetOnEvent(-1, "On_Ankieta1") The problem - if i uncomment GUICtrlSetColor, color of text changes, but button is just plain gray (no image). How i can change text color not touching image on a button here?
• By vin1
i have a script that selects  a text file and deletes a line (text input required) in the text file selected
i have to make it remove all lines found on a file i name, toRemoveLines.txt
it has to remove lines from all text files found in a folder
this is the script that has to be modified
where it says "select file" it has to be "select folder"
where it says "line text input" it has to be all lines from a text file
#Include <File.au3> Global $success = False$file_name = FileOpenDialog("Select file", @ScriptDir, "All files (*.*)", 1+4) $line_text_input = InputBox("Line's text", "Line must contain following text:", "line contains this text")$file_count_lines = _FileCountLines($file_name) for$i = 0 to $file_count_lines$Lines_text_output = FileReadLine($file_name,$i) if StringInStr($Lines_text_output,$line_text_input) then _FileWriteToLine($file_name,$i, "", 1) $success = True ExitLoop EndIf Next if$success = True Then MsgBox(0, "Success", "Line has been deleted") Else MsgBox(0, "Failure", "Line wasn't found") EndIf
• By Epic007
Hey guys I'm stuck with a program.....I need a make an automation which copies text from a chat bot app and paste it in notepad to log the replies of my chat bot and to analyse stuff....a lil help pls

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text:
Note: Due to technical difficulties, the Archives are currently not up to date. GMANE provides an alternative service for most mailing lists.
c.f. bug 424647
List Archive: gentoo-pms
 >>>>> On Tue, 26 Apr 2011, Ciaran McCreesh wrote: >> Portage ignores self-blockers both in DEPEND and RDEPEND. > Even strong blockers? No, strongs blockers are honoured in this case. (Which is fine, since the spec says "A strong block must not be ignored.") Updated patch (I've added the word "weak") is included below. > Also, what happens for packages that can't be rebuilt once they're > installed (e.g. because they screw up and use stuff on / if it's > there)? Such packages should be fixed. But if someone really needs a DEPEND blocker on the ebuild's version itself, he can use EAPI 2 or later and a strong blocker. > We've got this weird situation where DEPEND=!!self would prevent you > from upgrading or downgrading, but wouldn't stop you from rebuilding > the exact same version. That doesn't seem right. > It seems weird that we're mandating that a package manager should > just outright ignore bits of dependency variables. Maybe it would be > better to mark it as undefined as to whether or not the package > manager honours such a block (and tell people not to do it), and > then for the next EAPI figure out the logical meaning and specify > that? I don't like adding such "undefined" bits in cases where portage behaviour is well-defined. Ulrich From 5935aa87d46a97a72c8c032728f50a6ecbdf864d Mon Sep 17 00:00:00 2001 From: Ulrich Mueller Date: Tue, 26 Apr 2011 19:10:51 +0200 Subject: [PATCH] Clarify wording on self-blockers. --- dependencies.tex | 2 +- 1 files changed, 1 insertions(+), 1 deletions(-) diff --git a/dependencies.tex b/dependencies.tex index 362f6cc..f6318d8 100644 --- a/dependencies.tex +++ b/dependencies.tex @@ -187,7 +187,7 @@ following exceptions: \begin{compactitem} \item Blocks on a package provided exclusively by the ebuild do not count. \label{provided-blocks} -\item Blocks on the ebuild itself do not count. +\item Weak blocks on the package version of the ebuild itself do not count. \end{compactitem} \featurelabel{bang-strength} There are two strengths of block: weak and strong. A weak block may be -- 1.7.5.rc1


text:
# Wrap page number in colored box in footer

I a looking for a way to achieve the following outcome for the page numnbers in my footer created using fancyhdr:

My current code in a stand-alone example looks like this:

\documentclass[12pt,a4paper,parskip=full]{scrartcl}

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{lipsum}
\usepackage{fancyhdr}

\fancyhf{}
\pagestyle{fancy}
\renewcommand{\sectionmark}[1]{\markboth{\thesection.\ #1}{}}
\renewcommand{\footrulewidth}{0.3pt}
\lfoot{\small{Author name}}
\rfoot{\small{\thepage}}

\begin{document}

\pagestyle{fancy}

\section{Section One}

\lipsum

\clearpage

\section{Section Two}

\lipsum

\end{document}

This of course leads to a pretty much standard outcome:

The closest thing I found in the fancyhdr documenatation are the thumb-indexes however I am not sure how to adapt them for this.

Is there an easy way to do this or would it require a lot of custom drawing with tikz?

I appreciate all hints.

Because of you are using the KOMA-Script class scrartcl I would suggest to use scrlayer-scrpage instead fancyhdr. Then you can define and insert a new layer for the background of the pagenumber.

\documentclass[12pt,numbers=enddot,parskip=full]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{blindtext}
\usepackage{xcolor}

\clearpairofpagestyles
\ifoot{Author name}

\newcommand\pagenumberwidth{1cm}% <- width of the black box
\ofoot{\makebox[\pagenumberwidth]{\pagemark}}

% new layer for the pagenumber background:
\DeclareNewLayer[
clone=scrheadings.foot.oneside,% <- clone the foot layer
contents={\parbox{\layerwidth}{\raggedleft\rule{\pagenumberwidth}{\baselineskip}}}%<- black rule
]{pagenumber.bg}
% add the new layer to the pagestyle before the foot layer:

% fonts

\begin{document}
\Blinddocument
\Blinddocument
\end{document}

Or you could add the black box to the layer of the headsepline and move this layer to the background:

\documentclass[12pt,numbers=enddot,parskip=full]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{blindtext}
\usepackage{xcolor}

\clearpairofpagestyles
\ifoot{Author name}

\newcommand\pagenumberwidth{1cm}% <- width of the black box
\ofoot{\makebox[\pagenumberwidth]{\pagemark}}
\ModifyLayer[
background,
\nobreak\makebox[0pt][r]{\smash{\raisebox{-\height}{%
\parbox{\layerwidth}{\raggedleft\rule{\pagenumberwidth}{\baselineskip}}%
}}}}

% fonts

\begin{document}
\Blinddocument
\Blinddocument
\end{document}

The result is the same as above.

Note, that the option addcontents was implemented in KOMA-Script version 3.16 (2015/02/07). So you need this or a newer version to run the second example.

• In the first version your request a specific version for scrlayer-scrpage. Why? – user3783960 May 25 '15 at 11:48
• Oh, sorry: The first example does not need a specific scrlayer-scrpage version. But the second example needs version 3.16 or newer because addcontents was implemented in this version. – esdd May 25 '15 at 21:10

My first thought would be to use TikZ, but you don't need TikZ if you're willing to load the xcolor package.

Here's my poor man's version:

\documentclass{article}

\usepackage{xcolor}
\usepackage{fancyhdr}
\fancyhf{}
\pagestyle{fancy}
\renewcommand{\sectionmark}[1]{\markboth{\thesection.\ #1}{}}
\renewcommand{\footrulewidth}{0.3pt}
\lfoot{\small{Author name}}
\rfoot{\mypage}

\usepackage{lipsum}

\newcommand\mypage{%%
\raisebox{2 pt}[0pt][0pt]{%%
\rule[-1ex]{1cm}{3.5ex}%%
\hspace*{-0.5cm}%%
\makebox[0pt]{\textcolor{white}{\small\thepage}}%%
\hspace*{0.5cm}}%%
}

\begin{document}

\lipsum[1-140]

\end{document}

• @A. Ellett I'm not a tikz expert can you put the code of how will you do the same thing using tikz Thanks!!! – Very23 May 31 '15 at 19:05


text:
# A Matrix for the New HPL-AI Benchmark

My colleagues are looking for a matrix to be used in a new benchmark. They've come to the right place.

### Contents

#### Email

A couple of weeks ago I got this email from Jack Dongarra at the University of Tennessee.

For this new HPL-AI benchmark, I'm looking for a matrix that is not symmetric, is easily generated (roughly O(n^2) ops to generate), is dense, doesn’t require pivoting to control growth, and has a smallish condition number (<O(10^5)).

There are two steps for the benchmark:

1) do LU on the matrix in short precision and compute an approximation solution x. (On Nvidia this is 6 times faster in half precision then in DP.)

2) do GMRES on with L and U as preconditions with x as the starting point (this usually takes 3-4 iterations to converge.)

The benchmark details are here: http://bit.ly/hpl-ai.

Any ideas for a matrix?

#### Symmetric Hilbert Matrix

One of the first matrices I ever studied was the Hilbert matrix. With the singleton expansion features now in MATLAB, the traditional symmetric Hilbert matrix can be generated by

  format rat
n = 5;
i = 1:n
j = i'
H = 1./(i+j-1)

i =
1              2              3              4              5
j =
1
2
3
4
5
H =
1              1/2            1/3            1/4            1/5
1/2            1/3            1/4            1/5            1/6
1/3            1/4            1/5            1/6            1/7
1/4            1/5            1/6            1/7            1/8
1/5            1/6            1/7            1/8            1/9

When you add the row vector i to the column vector j, the resulting i+j is a matrix. Compare this with the inner product, i*j, which produces a scalar, and the outer product, j*i, which produces another matrix. The expression i+j can be thought of as an "outer sum".

Two more scalar expansions complete the computation; i+j-1 subtracts 1 from each element of the sum and 1./(i+j-1) divides 1 by each element in the denominator. Both of these scalar expansions have been in MATLAB from its earliest days.

The elements of Hilbert matrices depend only on the sum i+j, so they are constant on the antidiagonals. Such matrices are known as Cauchy matrices. There are fast algorithms for solving system of equations involving Cauchy matrices in $O(n^2)$ time.

#### Nonsymmetric Hilbert Matrix

Some years ago, I wanted a nonsymmetric test matrix, so I changed the plus sign in the denominator of the Hilbert matrix to a minus sign. But this created a division by zero along the subdiagonal, so I also changed the -1 to +1/2. I call this the "nonsymmetric Hilbert matrix."

   H = 1./(i-j+1/2)

H =
2              2/3            2/5            2/7            2/9
-2              2              2/3            2/5            2/7
-2/3           -2              2              2/3            2/5
-2/5           -2/3           -2              2              2/3
-2/7           -2/5           -2/3           -2              2

The elements depend only on i-j and so are constant on the diagonals. The matrices are Toeplitz and, again, such systems can be solved with $O(n^2)$ operations.

I was astonished when I first computed the singular values of nonsymmetric Hilbert matrices -- most of them were nearly equal to $\pi$. Already with only the 5-by-5 we see five decimal places.

   format long
sigma = svd(H)

sigma =
3.141589238341321
3.141272220456508
3.129520593545258
2.921860834913688
1.461864493324889

This was a big surprise. The eventual explanation, provided by Seymour Parter, involves a theorem of Szego from the 1920's relating the eigenvalues of Toeplitz matrices to Fourier series and square waves.

#### Benchmark Matrix

I have been working with Jack's colleague Piotr Luszczek. This is our suggestion for the HPL-AI Benchmark Matrix. It depends upon two parameters, n and mu. As mu goes from 1 to -1, the core of this matrix goes from the symmetric to the nonsymmetric Hilbert matrix. Adding n in the denominator and 1's on the diagonal produces diagonal dominance.

   A = 1./(i + mu*j + n) + double(i==j);

   clear A
type A

function Aout = A(n,mu)
% A(n,mu).  Matrix for the HPL-AI Benchmark.  mu usually in [-1, 1].
i = 1:n;
j = i';
Aout = 1./(i+mu*j+n) + eye(n,n);
end

If mu is not equal to +1, this matrix is not Cauchy. And, if mu is not equal to -1, it is not Toeplitz. Furthermore, if mu is greater than -1, it is diagonally dominant and, as we shall see, very well-conditioned.

#### Example

Here is the 5x5 with rational output. When mu is +1, we get a section of a symmetric Hilbert matrix plus 1's on the diagonal.

   format rat
mu = 1;
A(n,mu)

ans =
8/7            1/8            1/9            1/10           1/11
1/8           10/9            1/10           1/11           1/12
1/9            1/10          12/11           1/12           1/13
1/10           1/11           1/12          14/13           1/14
1/11           1/12           1/13           1/14          16/15

And when mu is -1, the matrix is far from symmetric. The element in the far southwest corner almost dominates the diagonal.

   mu = -1;
A(n,mu)

ans =
6/5            1/6            1/7            1/8            1/9
1/4            6/5            1/6            1/7            1/8
1/3            1/4            6/5            1/6            1/7
1/2            1/3            1/4            6/5            1/6
1              1/2            1/3            1/4            6/5

#### Animation

Here is an animation of the matrix without the addition of eye(n,n). As mu goes to -1 to 1, A(n,mu)-eye(n,n) goes from nonsymmetric to symmetric.

#### Gaussian elimination

If mu > -1, the largest element is on the diagonal and lu(A(n,mu)) does no pivoting.

   format short
mu = -1
[L,U] = lu(A(n,mu))

mu = 1
[L,U] = lu(A(n,mu))

mu =
-1
L =
1.0000         0         0         0         0
0.2083    1.0000         0         0         0
0.2778    0.1748    1.0000         0         0
0.4167    0.2265    0.1403    1.0000         0
0.8333    0.3099    0.1512    0.0839    1.0000
U =
1.2000    0.1667    0.1429    0.1250    0.1111
0    1.1653    0.1369    0.1168    0.1019
0         0    1.1364    0.1115    0.0942
0         0         0    1.1058    0.0841
0         0         0         0    1.0545
mu =
1
L =
1.0000         0         0         0         0
0.1094    1.0000         0         0         0
0.0972    0.0800    1.0000         0         0
0.0875    0.0729    0.0626    1.0000         0
0.0795    0.0669    0.0580    0.0513    1.0000
U =
1.1429    0.1250    0.1111    0.1000    0.0909
0    1.0974    0.0878    0.0800    0.0734
0         0    1.0731    0.0672    0.0622
0         0         0    1.0581    0.0542
0         0         0         0    1.0481

#### Condition

Let's see how the 2-condition number, $\sigma_1/\sigma_n$, varies as the parameters vary. Computing the singular values for all the matrices in the following plots takes a little over 10 minutes on my laptop.

#### sigma_1

   load HPLAI.mat s1 sn n mu

surf(mu,n,s1)
view(25,12)
xlabel('mu')
ylabel('n')
set(gca,'xlim',[-0.9 1.0], ...
'xtick',[-0.9 -0.5 0 0.5 1.0], ...
'ylim',[0 2500])
title('\sigma_1')

The colors vary as mu varies from -0.9 up to 1.0. I am staying away from mu = -1.0 where the matrix looses diagonal dominance. The other horizontal axis is the matrix order n. I have limited n to 2500 in these experiments.

The point to be made is that if mu > -0.9, then the largest singular value is bounded, in fact sigma_1 < 2.3.

#### sigma_n

   surf(mu,n,sn)
view(25,12)
xlabel('mu')
ylabel('n')
set(gca,'xlim',[-0.9 1.0], ...
'xtick',[-0.9 -0.5 0 0.5 1.0], ...
'ylim',[0 2500])
title('\sigma_n')

If mu > -0.9, then the smallest singular value is bounded away from zero, in fact sigma_n > .75.

#### sigma_1/sigma_n

   surf(mu,n,s1./sn)
view(25,12)
xlabel('mu')
ylabel('n')
set(gca,'xlim',[-0.9 1.0], ...
'xtick',[-0.9 -0.5 0 0.5 1.0], ...
'ylim',[0 2500])
title('\sigma_1/\sigma_n')

If mu > -0.9, then the condition number in the 2-norm is bounded, sigma_1/sigma_n < 2.3/.75 $\approx$ 3.0 .

#### Overflow

The HPL-AI benchmark would begin by computing the LU decomposition of this matrix using 16-bit half-precision floating point arithmetic, FP16. So, there is a signigant problem if the matrix order n is larger than 65504. This value is realmax, the largest number that can be represented in FP16. Any larger value of n overflows to Inf.

Some kind of scaling is going to have to be done for n > 65504. Right now, I don't see what this might be.

The alternative half-precision format to FP16 is Bfloat16, which has three more bits in the exponent to give realmax = 3.39e38. There should be no overflow problems while generating this matrix with Bfloat16.

#### Thanks

Thanks to Piotr Luszczek for working with me on this. We have more work to do.

Published with MATLAB® R2019b

|

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text:
# beamer not showing bibliography

I would like to show the bibliography on a frame of a beamer. But I have not been able to achieve it. This is a short example of the code I have employed.

\documentclass[10pt,t]{beamer}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{graphicx}%insertar fotos pdf etc... (pdf,png,ps,eps)

\title{Neurohard}
\date[2016]{2016}

\begin{document}

\begin{frame}
Hi \cite{158511}
\end{frame}

\begin{frame}
\frametitle{References}
\bibliography{bibliography}
\end{frame}

\end{document}

Where the bibliography.bib item is:

@ARTICLE{158511,
journal={IEEE Circuits and Devices Magazine},
title={Analog implementation of neural networks},
year={1992},
volume={8},
number={5},
pages={36-41},
keywords={MOS integrated circuits;analogue computer circuits;multiplying circuits;neural nets;MOS components;adjustable weights;analog control signal;analogue implementation;electrically tunable synapses;integrated-circuit analog multiplier;neural networks;neural processing algorithms;neurocomputers;synaptic connections;Arithmetic;Artificial neural networks;Computer networks;Computer vision;Concurrent computing;Embedded computing;Neural network hardware;Neural networks;Neurons;Very large scale integration},
doi={10.1109/101.158511},
ISSN={8755-3996},
month={Sept},}

To compile it, I have followed the instructions given in other forums: pdflatex, bibtex, pdflatex, pdflatex.

I have also try with this:

\documentclass[10pt,t]{beamer}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{graphicx}%insertar fotos pdf etc... (pdf,png,ps,eps)
\usepackage[backend=bibtex]{biblatex}

\title{Neurohard}
\date[2016]{2016}

\begin{document}

\begin{frame}
Hi \cite{158511}
\end{frame}

%\begin{frame}
%\frametitle{References}
%\bibliography{bibliography}
%\end{frame}

\begin{frame}
\printbibliography
\end{frame}

\end{document}

But none of them worked.

• any error messages? – naphaneal Nov 15 '16 at 15:24
• You are missing some style like \bibliographystyle{plain} in the first example. – user36296 Nov 15 '16 at 15:32
• You second example works out of the box for me. – user36296 Nov 15 '16 at 15:36
• Offtopic, you don't need \usepackage{graphicx} as beamer already provides this functionality. – user36296 Nov 15 '16 at 15:37

Here is an example using Biblatex, which works with the example bibliography you provided:

\documentclass{beamer}
\usepackage[natbib=true,style=authoryear,backend=bibtex,useprefix=true]{biblatex}
\begin{document}

\begin{frame}
Here is a reference: \citet{158511}
\end{frame}

\begin{frame}[t,allowframebreaks]
\frametitle{References}
\printbibliography
\end{frame}

\end{document}

The resulting bibliography looks like this:

From here you can set about changing the style to your needs. For example,

\documentclass{beamer}
\usepackage[natbib=true,style=authoryear,backend=bibtex,useprefix=true]{biblatex}
\setbeamercolor*{bibliography entry title}{fg=black}
\setbeamercolor*{bibliography entry location}{fg=black}
\setbeamercolor*{bibliography entry note}{fg=black}
\setbeamertemplate{bibliography item}{}
\renewcommand*{\bibfont}{\scriptsize}
\begin{document}

\begin{frame}
Here is a reference: \citet{158511}
\end{frame}

\begin{frame}[t,allowframebreaks]
\frametitle{References}
\printbibliography
\end{frame}

\end{document}

In the bibtex example, the style is missing, e.g. something like \bibliographystyle{plain}

\documentclass[10pt,t]{beamer}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}

\title{Neurohard}
\date[2016]{2016}

\begin{document}

\begin{frame}
Hi \cite{158511}
\end{frame}

\begin{frame}
\frametitle{References}
\bibliographystyle{plain}
\bibliography{test}
\end{frame}

\end{document}

You second example compiles fine for me. But remember that you have to clean your auxiliary files, if you make the switch from bibtex to biblatex.


text:
Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01q237hv27r
 Title: Sequence Alignment and Parsimony Analysis for Constructing Language Phylogenies Authors: Shen, Qinlan Advisors: Fellbaum, Christiane Department: Computer Science Class Year: 2015 Abstract: The standard approach for determining whether languages are related is to manually detect regular sound correspondences in words between languages. This procedure, however, has been criticized for being subjective and does not take full advantage of available computational resources and techniques. To address these concerns, this thesis presents a method of extending sequence alignment techniques for constructing phylogenies in computational biology to language data by encoding phonetic transcriptions of words across different languages as three-character sequences reflecting the phonetic features of sounds. In addition, we propose a technique for using parsimony to measure the accuracy of generated trees against well-attested linguistic subgroups. Additional experiments were run to see whether the mean column score from an alignment could be correlated with tree parsimony to see if alignment scores could be used to estimate the accuracy of a generated phylogeny. Preliminary experiments on applying our alignment-based phylogeny construction method to the Indo-European and Austronesian language families suggest that an alignment-based method for constructing language phylogenies can accurately reconstruct well-known subgroups for Indo-European but performs poorly on Austronesian languages. Preliminary results also suggest that mean column score is not correlated with tree parsimony, making mean column score a poor estimator for the accuracy of a generated language tree. Extent: 59 pages URI: http://arks.princeton.edu/ark:/88435/dsp01q237hv27r Type of Material: Princeton University Senior Theses Language: en_US Appears in Collections: Computer Science, 1988-2016

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text:
## Algebra 2 Common Core

$x^2+24x+100+44=-46+44$ $x^2+24x+144=-2$ $Factor$ $to$ $get$ $(x+12)^2=-2$, which is A.