The mean-square end-to-end distance of the polyisobutylene chain has been calculated in reasonable agreement with values deduced from viscosity data.

** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.

Colored plastic inserts on a modern anchor chain show the operator how much chain has been paid out.

Any player may declare the game over at any time during his turn if either of two conditions is true: one chain has 41 or more tiles, or there is at least one chain on the board and every chain on the board has 11 or more tiles.

This leaves the last two boxes in the chain for their opponent, but then the opponent has to open the next chain.

Against a player who doesn't understand the concept of a sacrifice, the expert simply has to make the correct number of sacrifices to encourage the opponent to hand him the first chain long enough to ensure a win.

It is the smallest of the four islands and has a central mountain chain reaching 860 meters at its highest.

Several competing models, although correctly dealing with the conformation of each individual peptide chain, gave way to the triple-helical " Madras " model, which provided an essentially correct model of the molecule's quaternary structure although this model still required some refinement .< ref > The packing structure of collagen has not been defined to the same degree outside of the fibrillar collagen types, although it has been long known to be hexagonal or quasi-hexagonal.

In this situation, the chain rule represents the fact that the derivative of is the composite of the derivative of f and the derivative of g. This theorem is an immediate consequence of the higher dimensional chain rule given above, and it has exactly the same formula.

The word has nautical resonances: the tasks involved in operating a ship, particularly a sailing ship, providing numerous specialities within a ship's crew, often organised with a chain of command.

An underlying principle is that the chain may be considered a rigid body once it has attained equilibrium.

Let w denote the weight per unit length of the chain, then the weight of the chain has magnitude

If a reaction results in a small energy release making way for more energy releases in an expanding chain, then the system will typically collapse explosively until much or all of the stored energy has been released.

In 1963 Friedman and Schwartz proposed a positive feedback loop as a mechanism for catastrophic failures in economics: “ It happens that a liquidity crisis in a unit fractional reserve banking system is precisely the kind of event that trigger-and often has triggered-a chain reaction.

In a lightweight implementation such as described here, the project manager has not accumulated cost nor defined a detailed project schedule network ( i. e., using a critical path or critical chain methodology ).

Furthermore, the exchange would not be expected to be sensitive to trace amounts of impurities because it would not be apt to be a chain reaction since the activation energy for abstraction of chlorine by a chlorine atom would be expected to be too high ; ;

Dioxins from Agent Orange have persisted in the Vietnamese environment since the war, settling in the soil and sediment and entering into food chain through the animals and fish that feed in the contaminated areas.

There may be a Kempe chain joining the red and blue neighbors, and there may be a Kempe chain joining the green and yellow neighbors, but not both, since these two paths would necessarily intersect, and the vertex where they intersect cannot be colored.

In Europe Center Parcs might be considered a chain of resort hotels, since the sites are largely man-made ( though set in natural surroundings such as country parks ) with captive trade, whereas holiday camps such as Butlins and Pontin's are probably not considered as resort hotels, since they are set at traditional holiday destinations which existed before the camps.

These machines are mechanically similar since all three types use a handle connected to a flywheel by rope, chain, or strap to provide resistance to the user – the types differ only in braking mechanism.

This was a workable solution but made it nearly impossible to develop on the Unix machines since the power of the Mesa compiler and associated tool chain was lost using this approach.

This implementation of the factorial function is not guaranteed to terminate, since a negative argument causes an infinite descending chain of recursive calls.

One 1941 property from the Waco, Texas-based Alamo Plaza Courts chain, the first US motel chain ( founded 1929, expansion stopped with the departure of the chain's founders in the 1950s ), still stands on U. S. Route 190 in Baton Rouge, Louisiana, but has been declining steadily since a change of ownership in the mid-1980s.

In-situ plutonium production also contributes to the neutron chain reaction in other types of reactors after sufficient plutonium-239 has been produced, since plutonium-239 is also a fissile element which serves as fuel.

Szilárd, however, did not propose fission as the mechanism for his chain reaction, since the fission reaction was not yet discovered or even suspected.

Leonard Goldenson, who had headed the chain since 1938, remained as the new company's president.

The lower mountains in the extreme west are wooded, but the extent of forest declines eastwards, and the eastern Pyrenees are peculiarly wild and barren, all the more since it is in this part of the chain that granitic masses prevail.

Cap and ball type revolvers were also prone to chain fire, which again was more of a problem for rifles since the rifleman's arm was in front of the cylinder.

He had suffered from duodenal ulcers as far back as 1960, and had been a chain smoker since adolescence.

Tools are the most important items that the ancient humans used to climb to the top of the food chain ; by inventing tools, they were able to accomplish tasks that human bodies could not, such as using a spear or bow and arrow to kill prey, since their teeth were not sharp enough to pierce many animals ' skins.

This chain of events lead to Operation Praying Mantis, the largest US Naval surface engagement since the Second World War.

Any version of Snakes and Ladders can be represented exactly as an absorbing Markov chain, since from any square the odds of moving to any other square are fixed and independent of any previous game history.

Helium-4 is very stable and is nearly the end of this chain if it runs for only a short time, since helium neither decays nor combines easily to form heavier nuclei ( since there are no stable nuclei with mass numbers of 5 or 8, helium does not combine easily with either protons, or with itself ).

She kills, among other villainous characters, Jabba the Hutt, choking him with the very chain that bound her to him ; Leia is also responsible for Grand Admiral Thrawn's death, since she turns the Noghri against him.

Dioxins enter the general population almost exclusively from ingestion of food, specifically through the consumption of fish, meat, and dairy products since dioxins are fat-soluble and readily climb the food chain.

originally combined many of the franchises ' locations with its chain of A & W Restaurants, and most new Long John Silver's locations in the first few years after the acquisition were co-branded with A & W.

the chain also has a co-branded location with a a & w in dickson city pa.

In late 2010, drug store chain Rite Aid became a licensed Save-A-Lot operator when it converted ten of its existing pharmacy locations in the Greenville, South Carolina, market to " Save-A-Lot / Rite Aid " co-branded stores.

While such locations usually have two counters set up for each chain ( much like the Wendy's / Tim Hortons co-branded locations ), depending on business that day, both products can be bought at the same counter ( usually the Dunkin ' counter ), much like the Yum!

Her preferred medium is acrylic on canvas or wood and her designs appear on many lines of licensed merchandise, notably through the chain stores Hot Topic and collectibles through the Bradford Group including co-branded Disney projects.

At one time, some were co-branded with Mid-Atlantic convenience store chain Uni-Mart, which now sells its own brand of gasoline.

Originally, Ontario stores were co-branded with the local Loblaw banner ( i. e. " Loblaws-The Real Canadian Superstore "), but most shortened their name to reduce confusion and allow separate weekly specials for each chain.

In 1999 the company launched Pasta Central, a franchised chain within the " home meal replacement " category featuring Italian-style pasta and pizza ; the concept was exclusively a vehicle for co-branded Blimpie / Pasta Central outlets.