The common notation for the divergence ∇· F is a convenient mnemonic, where the dot denotes an operation reminiscent of the dot product: take the components of ∇ ( see del ), apply them to the components of F, and sum the results.

A fairly simple proof of the lemma, reminiscent of one of the simplest proofs of Fermat's little theorem, can be obtained by evaluating the product

For millennia, cow's milk has been processed into dairy products such as cream, butter, yogurt, kefir, ice cream, and especially the more durable and easily transportable product, cheese.

The most common UHT product is milk, but the process is also used for fruit juices, cream, soy milk, yogurt, wine, soups, and stews.

Frozen yogurt ( also spelled frozen yoghurt ; also known by the tradenames Frogurt and FroYo ) is a frozen dessert made with the cultured, fermented milk product called yogurt and sometimes other dairy products.

Around this same time, another packaged frozen yogurt product, called " Danny " debuted from Dannon.

This variation was a raspberry yogurt product on a stick and covered with dark chocolate.

When a sufficient amount of air has been incorporated into the product, the yogurt is rapidly frozen to prevent the formation of large ice crystals, and stored in a cold place to be shipped.

You can choose a mix with high fat or low fat content and you can choose how much air you introduce into the soft serve frozen yogurt, The higher the level of fat the more air the soft serve frozen yogurt can absorb, and the more air that is mixed or pumped into the soft serve frozen yogurt mix as it freezes the creamier the product will taste.

* Frozen yogurt, the cultured, frozen milk product, with a tart flavor

* Frozen yogurt, the cultured and frozen milk product

Filmjölk ( also known as fil or the older word surmjölk ) is a Nordic dairy product, similar to yogurt, but using different bacteria which give a different taste and texture.

The fiber in TCBY's product also serves as a prebiotic, or food for the healthful bacteria in the yogurt, which boosts the benefit that live-and-active cultures bring to the digestive system.

On January 10, 2012, USA Today reported that TCBY would launch a Greek frozen yogurt product.

Skyr () is an Icelandic cultured dairy product, similar to strained yogurt.

common to yogurt to the final product, to increase its appeal.

The self-service buffet generally consists of common breakfast offerings, including cereal, a hot meat product, a hot egg product, pancakes, biscuits and gravy, bagels and muffins, fruit, yogurt, and the brand's exclusive cinnamon roll.

During the 1970s, when dieting and fitness became more popular, Carvel began offering a low-fat frozen dessert called Thinny-Thin and a frozen yogurt product called Lo-Yo.

Their product had been endorsed by Good Housekeeping, the A.M.A., and the Veterinary Journal, among other repositories of higher wisdom, and before much longer if you didn't have a cake of their soap in the john, even your best friends would think you didn't bathe.

The finished -- and drastically cut -- product would begin with a hazy longshot of Joyce entering the suds, then bursting above the pool's surface clad in layers of lavender lather, and I had a hunch this item was going to sell tons and tons of soap ; ;

This would be reduced by multiplying 8 times 6 and then dividing the product by 12.

The principal potential advantage would be that the finished product could be transported and stored at lower cost under refrigeration instead of being frozen.

Several companies also saw possibilities in using the technique for extruding or molding vinyl products with a slight cellular core that would reduce costs yet would not affect physical properties of the end product to any great extent.

A single craftsman or team of craftsmen would create each part of a product.

They would then assemble them into the final product, making cut-and-try changes in the parts until they fit and could work together ( craft production ).

However, many important and interesting operations are non-associative ; one common example would be the vector cross product.

Token Ring would eventually be supported with the similar TokenTalk product, which also used the same Network control panel and underlying software.

Apple had considered the problem, and AppleTalk included the possibility for a low-cost LocalTalk-to-Ethernet bridge, but they felt it would be a low-volume product and left it to 3rd parties.

where θ < sub > r, p </ sub > is the angle between r and p measured from r to p ; an important distinction because without it, the sign of the cross product would be meaningless.

When assured by Mersenne that it was, indeed, the product of the son not the father, Descartes dismissed it with a sniff: " I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients ," adding, " but other matters related to this subject can be proposed that would scarcely occur to a sixteen-year-old child.

In addition, it was believed that Canion's consensus-style management slowed the company's ability to react in the market, whereas Pfeiffer's autocratic style would be suited to price and product competition.

A single name worldwide would increase the possibility that advertising campaigns, brochures, and promotional materials could be used across countries and simplify product design and manufacturing.

Further, potential buyers would be exposed to the name and product when traveling to other countries.

* However, if we think of as the field of real numbers, then the direct product does not exist-naively defining in a similar manner to the above examples would not result in a field since the element does not have a multiplicative inverse.

That is, the higher the price of a product, the less of it people would be prepared to buy of it ( other things unchanged ).

Keynesians argue that in a modern industrial economy, many prices are sticky downward or downward inflexible, so that instead of prices for non-oil-related goods falling in this story, a supply shock would cause a recession, i. e., rising unemployment and falling gross domestic product.

The Flivver was not a flying car at all, but it did get press attention at the time, exciting the public that they would have a mass produced affordable airplane product that would be made, marketed, sold, and maintained just like an automobile.

This Wöhler Myth, as historian of science Peter J. Ramberg called it, originated from a popular history of chemistry published in 1931, which, " ignoring all pretense of historical accuracy, turned Wöhler into a crusader who made attempt after attempt to synthesize a natural product that would refute vitalism and lift the veil of ignorance, until ' one afternoon the miracle happened '".

There was an initial screenplay with the preliminary title All Monsters Attack Directive, which would have many of the same elements used in the final product.

In those disciplines we would write the product as ( the bra-ket notation of quantum mechanics ), respectively ( dot product as a case of the convention of forming the matrix product AB as the dot products of rows of A with columns of B ).

Companies of all types have made great advances in production capabilities and efficiencies -- in modern equipment and new processes, enlarged R & D facilities, faster new product development.

If private brand competition hasn't been felt in your product field as yet, have you thought how you will cope with it if and when it does appear??

If you have a higher-quality product, how can you make it stand out -- justify its premium price -- without the spoken word??

If competition beats you to it, this exciting new product era can have real headaches in store.

While many companies have done fine work in developing sales personnel, much of it has been product rather than sales training.

Where the industry's product price has been kept below the `` profit-maximizing '' and `` entry-limiting '' prices due to fears of public reaction, the profit seeking producers have an interest in offering little real resistance to wage demands.

Whether the democratic failures should be seen as systemic, or as a product of the extreme conditions of the Peloponnesian war, there does seem to have been a move toward correction.

It is often convenient to write this as an infinite product over all the primes, where all but a finite number have a zero exponent.

The case where X is F, and we have a bilinear form, is particularly useful ( see for example scalar product, inner product and quadratic form ).

Because ballpoint pens are low cost alternatives to both fountain pens and roller-ball pens, they have become largely a disposable product.

In these more general contexts, the bracket does not have the meaning of an inner product, because the Riesz representation theorem does not apply.

Conversely if you do have a better product suddenly you have these businesses that grow like topsy.

In November 2004, the manufacturers, Unilever, announced that the composition of Bovril was being changed from beef extract to a yeast extract, claiming it was to make the product suitable for vegetarians and vegans ; at that time fear of bovine spongiform encephalopathy ( BSE ) may have been a factor.

Celebrity endorsements have proven very successful around the world where, due to increasing consumerism, an individual is considered a status symbol when they purchase a celebrity-endorsed product.

Prices of coffee, the other principal export product, have been more variable.

These categories surely have some objects that are " special " in a certain way, such as the empty set or the product of two topologies, yet in the definition of a category, objects are considered to be atomic, i. e., we do not know whether an object A is a set, a topology, or any other abstract concept – hence, the challenge is to define special objects without referring to the internal structure of those objects.

In addition to the traditional compost pile, various approaches have been developed to handle different composting processes, ingredients, locations, and applications for the composted product.

Johnson ) have claimed precedence in this invention, but recent analysis of both his concrete and raw cement have shown that William Aspdin's product made at Northfleet, Kent was a true alite-based cement.

In 1999, Cygnus offered Cygwin 1. 0 as a commercial product of interest in its own right although subsequent versions have not been released, instead relying on continued open source releases.

As volume and manufacturing capability have improved, the monochrome and passive color technologies were dropped from most product lines.

A modern restatement of the theorem in algebraic language is that for a positive integer with prime factorization we have the isomorphism between a ring and the direct product of its prime power parts: