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Read through the article, you will get a lot of information. Feel free to google words you don't know. In short, in milk, the main spoilage is driven by gram-negative bacteria. They are able to grow a little better than other bacteria in cold temperatures and over time their concentration is high enough where they start changing the chemical make-up of the milk. Mainly, it seems that they release enzymes that break up the fats in milk (not entirely sure about non-fat milk) to other fats whose taste we don't like.

Measuring different kinds of fats, or bacterial concentrations is possible, but to do so cheaply with a simple readout on a carton or bottle is very hard. You will have to go for something that can have an easy read-out but is still indicative of the bacterial concentration. As you guessed, a good metric may be pH. It turns out, many bacteria like to make lactic acid as they grow, especially without too much oxygen, which lowers the pH of the milk.

Again, there are studies already available on the change of pH of spoiling milk, but this is where the fun part comes in. You can do these test yourself very easily. All you have to do is get a couple of cartons of milk (preferably different makes, and different fat% milk). Then measure their pH over time. Probably once per day for the 2 or so weeks it takes the milk to spoil. Each time you measure the pH, write it down and then taste the milk to see if it has spoiled. Try to find a pH value below which you would say the milk is spoiled.

Don't worry, having a little spoiled milk will not hurt you. Especially if you spit it out. Then make sure to take a couple more readings a few days after you know the milk is spoiled (don't taste that stuff) and make sure that the trend of lowering pH is still there.

As for how to measure pH. You can use pH strips. It's important to find ones that have a good change in color in the range you need (6.4-6.8 for fresh milk and lower for spoiled). This might be a good option.

Ideally, then you would need to find a dispenser design that would allow for a pH strip to be subjected to the milk without leaking the dye back into the container. Have fun coming up with some ideas!

Good luck and make sure you talk to your science teacher or any scientists in your community to help you plan experiments. This will help you learn how good experiments are done and in turn make your project all that much better.

The topics you list are certainly worth writing on, but you need to get much more focused. Some of the worst student essays I've read start with some large topic and wander all over the place. In the end, these essays accomplish nothing.

As an example, consider political developments. A great question might be "Did American democracy expand or contract from 1776 to 1865?" This is a very interesting and important question, and answering it should only take 1104 single-spaced pages. Surely this is do-able by the average undergrad. Or maybe not.

Instead, take your question and get micro. For example, maybe you live in Pennsylvania. Maybe Pittsburgh. Focus your question narrowly to something like "Did voting expand in Pittsburgh from 1800-1860?" You can look at old voter rolls, election records and whatnot to determine if voters, as a percentage of total citizens, expanded or not during those years. And then, you can write a page or so showing how this was or was not a part of the larger national trend.

Done well, this would be a solid paper. Interesting, part of a much larger question, and probably not the same thing your TA has read half a million times. (Trust me, that's important.)

Anyway, that's just a bit of general advice. Find something interesting (Do you care enough to write on the subject?,) do-able (is there source material? Most likely secondary if you're an undergrad.,) and if at all possible, not the same paper everyone else is doing.

From the topics you list, I'd go with 19th C US economic developments. Lots of stuff out there. Consider a paper on a particular union or guild, an industry as it developed, local banking laws, currency developments, or railroad or transportation changes. All of these have good secondary source material and are probably not overdone.

What this expressions says

First of all let's specify that the domain over which these statements operate is the set of all people say.
Let us give the two place predicate P(x,y) a concrete meaning. Let us say that P(x,y) signifies the relation x loves y.

This allows us to translate the statement:
∀x∀yP(x,y) -> ∀xP(x,x)

What does ∀x∀yP(x,y) mean?

This is saying that For all x, it is the case that For all y, x loves y.
So you can interpret it as saying something like everyone loves everyone.

What does ∀xP(x,x) mean?

This is saying that For all x it is the case that x loves x. So you can interpret this as saying something like everyone loves themselves.

So the statement is basically saying:
Given that it is the case that Everyone loves Everyone, this implies that everyone loves themselves.
This translation gives us the impression that the statement is true. But how to prove it?

Proof by contradiction

We can prove this statement with a technique called proof by contradiction. That is, let us assume that the conclusion is false, and show that this leads to a contradiction, which implies that the conclusion must be true.

So let's assume:
∀x∀yP(x,y) -> not ∀xP(x,x)

not ∀xP(x,x) is equivalent to ∃x not P(x,x).
In words this means It is not the case that For all x P(x,x) is true, is equivalent to saying there exists x such P(x,x) is false.

So let's instantiate this expression with something from the domain, let's call it a. Basically let's pick a person for whom we are saying a loves a is false.

not P(a,a)

Using the fact that ∀x∀yP(x,y) we can show a contradiction exists.

Let's instantiate the expression with the object a we have used previously (as a For all statement applies to all objects by definition) ∀x∀yP(x,y)

This happens in two stages:

First we instantiate y
∀xP(x,a)

Then we instantiate x
P(a,a)

The statements P(a,a) and not P(a,a) are contradictory, therefore we have shown that the statement:

∀x∀yP(x,y) -> not ∀xP(x,x) leads to a contradiction, which implies that
∀x∀yP(x,y) -> ∀xP(x,x) is true.

Hopefully that makes sense.

Recommended Resources

Wilfred Hodges - Logic

Peter Smith - An Introduction to Formal Logic

Chiswell and Hodges - Mathematical Logic

Velleman - How to Prove It

Solow - How to Read and Do Proofs

Chartand, Polimeni and Zhang - Mathematical Proofs: A Transition to Advanced Mathematics

I use [this book]http://www.amazon.com/Statistics-Manual-Edwin-L-Crow/dp/048660599X) as a reference. It's very small and inexpensive (you may have to buy it direct from Dover, though). It won't go through any derivations, but it covers most of the very important, basic, topics. I also have my old textbook on backup as well. Old editions of textbooks are cheaper, and all the information is the same.

Looking through amazon, this one looks pretty good as well, especially for an inexpensive text. A reviewer said it ends with what we just talked about! Any book that lays down the foundations well enough should be fine. See if you can find one that does correlation analysis, since you'll probably use that later.

Getting more advanced than this may depend on your field. If you're in biology, I'd recommend a book on designing and analyzing scientific experiments. I can't recommend a good title, though, because I'm only familiar with computer experiments (which tend to be easier).

I hope this helps!

No problem--I'm happy to help! If you get the chance (but I certainly understand a heavy work load), the book [But Is It Art?] (http://www.amazon.com/But-Is-It-Art-Introduction/dp/0192853678) is a really good introduction to a lot of critical theory that you will run into when dealing with 20th century art. Also, I don't think you can really use it as a true source for your paper, but I would also recommend [Postmodernism for Beginners] (http://www.amazon.com/Postmodernism-For-Beginners-Jim-Powell/dp/1934389099). We used it in an undergrad seminar when I was just starting to learn theory, and it was absolutely invaluable--very, very easy to read, and you really get a good overview of the major ideas and philosophers in Postmodernism. Good Luck!

I'd pick up an instrumental analysis textbook. If you're at a university, their library may have one in circulation, saving you a few bucks. I've used Skoog's text.

That said, I'll give a few pointers to get you started. Of course, a little context on the details of the separation you're trying to accomplish would focus this discussion some. Maybe this is just a classroom exercise. That is, maybe you're not actually trying to perform a separation in the lab. Regardless, I'd follow TurkFebruary's advice and google it. Wikipedia has some good info, too.

• Column/stationary phase type. Depending on the nature of the analytes you're separating, the choice of column packing material is an important one. It seems that reverse-phase is becoming the standard, as it takes advantage of relatively polar mobile phases, in which case water is one of your components. Anyway, you can get polar (normal phase) and nonpolar (reverse phase) columns. Further, if your analytes can be easily separated by size, you may choose a size exclusion column. Also, ion exchange columns are particularly useful for separating charged species or species with charged moieties.
  
  
• Column size. HPLC columns generally fit into 2 categories depending on the scale of the separation to be performed: analytical and prep scales. Analytical columns are shorter, narrower, and as such, contain a smaller volume of stationary phase. Analytical columns provide higher resolution, but have low sample loading capacities (micrograms or even nanograms of solute). Preparative columns are used for larger-scale separations, are greater in length and diameter, and are may effect up to gram-scale separations. The terms are not mutually exclusive, and there are grades between, sometimes called semi-prep.
  
  
• Mobile phase composition. Generally, whether employing normal or reverse phase, some time must be spent developing a method with regard to mobile phase composition. In either of these 2 phases, you're taking advantage of differences in affinity of solutes to both your stationary and mobile phase. If your mobile phase is too strong, all solutes will elute simultaneously, effecting no separation. If you mobile phase is too weak, you'll get effective separation, but will waste time. In some cases, gradient elution is used, which takes advantage of a a proportioning valve and a time program, and begins a separation with a relatively weak mobile phase, and gradually alters the composition to provide improved resolution of early eluting components, and speed up elution of late eluting components.
  
  
• Analytical wavelength. Most HPLC systems use a UV-Vis absorbance detector. Obviously, you need to select a wavelength at which your analytes absorb. This can usually be determined by gathering a UV-Vis spectrum of standard samples of your analytes before beginning any chromatography. Of course, if you're using a photodiode array detector, you can gather a full spectrum of analytes as they elute from the column, generating much richer data. I should note that other detection methods exist, like fluorescence detection. In some configurations, HPLC eluent feeds directly into a mass spec, which is a powerful method for separation and identification.
  
  
• Flow rate. Generally, this will be determined by your column choice, as columns typically have suggested maximum flow rates. Larger columns can typically handle faster flow rates. The concern here is pressure. Faster flow rates require larger system pressures. High system pressures may overtax the mobile phase pump and lead to shorter pump life. In addition, theoretical plate height, and therefore resolution, depends on flow rate. The Van Deemter equation and plot can be used to determine the optimum flow rate for a given column.
  
  This is what comes to mind off the top of my head.

Here is the Book

Here is the [Film](https://en.wikipedia.org/wiki/Fahrenheit_451_(film)

Here is where you can buy the book

And here is a paragraph I found about elements of postmodernism.

> QUESTION: What are the elements of Postmodernism and Humanism?

ANSWER:

The elements of postmodernism and humanism are varied. Here are some of the more popular topics of interest:
Postmodernists often profess individualism over God and country, desiring the liberty to establish personal truth and allowing each person’s choice to be tolerated.

Many postmodernists promote the ideals of globalization, excluding any traditional moral or civil laws, free enterprise, or governed by a traditional political system.

Many feel that no single person or group should have dominance, special interest, or wealth over another.

The ideals of postmodernism confront and surpass the modern way of thought and lifestyle which relies on science and technology for progress. Postmodernists tend to blame modern capitalism for causing the evil in the modern West.

Many postmodernists ultimately reject Christianity.

I think that's a fair assessment of 'the Absurd'. There isn't really a wrong answer here! In this game it's all about interpretation and supporting yourself logically and coherently. My suggestion to you then, is to take a look at The Myth of Sysiphus (and the [sparknotes won't you here hurt either] (http://www.sparknotes.com/philosophy/sisyphus/summary/)). Find yourself a breakdown of Camus' philosophy somewhere that you can understand. This is sprawling, complicated stuff, and no one in their right mind would expect someone in high school to write a comprehensive paper covering all of Camus' philosophy from source texts. Solomon's 'Existentialism' really is gold. I tried to find a pdf online for you, but it doesn't seem to exist. Since you seem to have an interest in the topic, I'd suggest picking this up at some point (maybe a birthday or Xmas gift?). Solomon also has a short little paperback called 'Introducing The Existentialists' which is worth picking up. Any more questions, ask away! Good luck!

Yes.

Protons (and neutrons) are the main contributors to an atom's mass. Higher mass implies more protons and/or neutrons. Thus, the size of the molecule, which means more protons/neutrons, implies both greater size and greater mass. It is thus implied that increased size affects its speed as described in Graham's Law. But you want to look at mass because it's more accurate and measurable.

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It's full of quirky, unorthodox essays (e.g. one girl wrote her essay about a banana... I did you not). Obviously don't copy anything, but you can get some ideas :)

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