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E. B. Christoffel pp 728-730 | Cite as

Chapter

Abstract

Christoffel’s paper [1] deals with the complete solution of determining the infinitely small oscillations of a system of particles distributed in space according to a periodic pattern and submitted to attractive and repulsive internal forces. Cauchy had studied extensively this problem, with the hope of using it as a new mathematical background for analytical optics. His approach consisted in first searching the movements of the particles which consist in plane waves, and then using Fourier’s theorem to obtain the general solution. Christoffel criticizes it somewhat by observing that, in this method, the initial state of the system was described in terms of continuous functions on the whole space, giving initial positions and velocities not only for the positions of the particles in the lattice, but also for all other points. As a consequence, the corresponding solution contains irrelevant elements which have to be eliminated later. Christoffel proposes and develops a more natural approach in which initial conditions are only given at those points occupied by the particles.

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[1]
Christoffel, E.B.: . J. Reine Angew. Math. (1864), 273–288. CrossRef Google Scholar
[2]
Butzer, P.L.: . In: Elwin Bruno Christoffel; Gedenkschrift zur 150. Wiederkehr des Geburtstages. Heimatblätter des Kreises Aachen 34/35, no. 3/4 (1978) — no. 1 (1979), p. 18. Google Scholar
[3]
Brillouin, L.: in . Second edition, Dover, New York 1953. Google Scholar
©Springer Basel AG1981

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If you’re on the other side, however – the losing side – it’s a horror movie in slow motion.

The only way out? Invest in your own destruction. In this context, the FANG stocks are not a gimmick or a fad, they’re a f***ing life raft. Market commentators rhetorically ask aloud what multiple should investors pay to own the technology giants. That’s the wrong question when people feel like they’re drowning.

What multiple would you pay to survive? Grab a raft.

Here’s the “Robotics and Automation ETF” over the last two years:

There’s panic in this chart.A much more sustained kind of panic than can be sown by the pronouncements of Trump or the bellicosity of North Korea.

There’s a great joke about an automated carplant in Japan, where the machines work in the dark (no need for light, they don’t have eyes) and there are only two living things authorized to be on the factory floor – a man and a dog.

What’s the man there for?

His job is to feed the dog.

What’s the dog for?

The dog keeps theman from touching any of the machines.

Matt Levine at Bloomberg View has an interesting way of thinking about Bridgewater, a gigantic hedge fund overseeing almost $200 billion in assets:

if you had to describe in two words what Bridgewater’s 1,500 employees do, “not investing” would be a pretty good fit. They have a computer to do the investing! Bridgewater runs on algorithms, and famouslyfew of itsemployees have much visibility into how the algorithms actually work. They instead spend their time marketing the firm, doing investor relations, and — crucially — evaluating and critiquing one another. I once explained my theory of Bridgewater : “One stylized model for thinking about Bridgewater is that it is run by the computer with absolute logic andefficiency; in this model, the computer’s main problem is keeping the 1,500 human employees busy so that they don’t interfere with its perfect rationality.”

This heuristic – a room full of geniuses playing mind games with each other while computers keep the profits rolling in – is definitely silly, but Vonnegut would have loved it. And it works really well symbolically, even if it’s a distortion. You don’t get a better educated, more highly pedigreed workforce than the folks at Bridgewater. So theimage of them looking for ways to fill their days – even though untrue – could only increase the dread ofpeople working in firmsfurther down in the Knowledge Economy food chain.

“Specialize” the displaced workers are being told. “Up your eduction and increase your skills! Move to a different city! Find a niche where technology can’t replace you! Learn to code!” They’re trying, but this doesn’t seem to be a long-term solution. We’re in an age where we’re being told AI is about to start writing its own software. Machines are going to be trying legal cases and diagnosing illnesses, writing songs and architecting buildings, giving financial advice and driving our vehicles. Every day more articles about this or that breakthrough. There are no limits, there are no protections. It’s bordering on lawlessness.

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If others are to be believed, cows are major contributors to greenhouse gases. Thus, many advocate a reduction in livestock production to combat global warming. Climate change (aka global warming) is a real phenomenon. To date, May 2016 was the hottest month ever recorded. 1 Scientists have also recently attributed the first mammalian extinction (Bramble Cay melomys) to climate change. 2 This is a real serious issue that is changingour world. Therefore,who are the main providers ofglobal greenhouse gas emissions? Also,is there any truth in livestock being a major contributor?

To first understand how grazing cattle can be considered carbon neutral, a background in climate change science is helpful. For a full explanationon climate change I suggest you visit NASA’s Climate Change website. Onemeasurement of what is causing the climate to rapidly shift is carbon, or more specifically carbon dioxide (greenhouse gases). Thus, governments around the world have been investigatingcarbon contributors to the environment.

The graph to the right is from the US Environmental Protection Agency, and shows theUnited States carbon contributors. 3 Methane, the major gasattributed to livestock, only contributes 16% to our total global emissions. Within this 16% includes other agriculture activities, biomass burning or other energy sources.

According to the EPA, agriculture alone contributes only 9% to the United States total global greenhouse emissions. This directly contradicts popular media that claims agriculture is the #1 contributor to greenhouse gas emissions. The data proves otherwise.The EPA website report can be found .

Of this 9%, a third can be attributed to methane production from cattle or other ruminants (sheep, goats). So roughly you can conclude 3% of total greenhouse emissions from the United States can be attributed to livestock. It is also worth notingthe United States produces ~20%of the world’s beef supply.

What drew my interest to write about this topic was a recent article I came across. Teague and others recently published an article titled ‘ The role of ruminants in reducing agriculture’s carbon footprint in North America ’ in the Journal of Soil and Water Conservation. 4 In this article, the scientists discuss the impact agriculture has on the environment and global greenhouse emissions. These authors come from many different fieldsto include: Ecology, Animal Science, Environment and Natural Resources, Engineering, Sustainable Agriculture, and Economics.

The authors’ state current crop production contributes to greenhouse gas emissions by:

The authors conclude “production of food to meet global demand comes at considerable environmental and social cost.” These scientists state even if all livestock production were to cease, there would be no impact to greenhouse gas emissions. They explain the greenhouse gas emissions from the production of food needed to replace animal protein in dietswould be the same (or greater).

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