With hinged, fixed or free end support conditions the deflected shape in neutral equilibrium of an initially straight column with uniform cross section throughout its length always follows a partial or composite sinusoidal curve shape, and the critical load is given by

With their customary source of supply cut off, the Fort Garry free traders engaged three men to cart goods to them from the Mississippi country.

With LAFTA in place existing productive capacity could be used more fully to supply regional needs, industries could reduce costs as a result of potential economies through expanded output and regional specialization, and attraction to new investment occurred as a result of the regional market area.

With pyrethrum in short supply, DDT was used extensively during World War II by the Allies to control the insect vectors of typhus — nearly eliminating the disease in many parts of Europe.

With diesel-electric and electric locomotives, the gear ratio between the traction motors and axles is what adapts the unit to freight or passenger service, although a passenger unit may include other features, such as head end power ( also referred to as hotel power or electric train supply ) or a steam generator.

With irrigation, the food supply in Mesopotamia was compabale to the Canadian prairies.

With the advent of castle-building and the extended siege, supply problems had to be solved on a scale seldom seen before, as armies had to stay in one spot for months, or even years.

With many firms in a market, supply of the product remains high.

With modern development, the freshwater springs are no longer enough to supply water to the whole island.

With the advent of printing in the later fifteenth century, the demands of printers far exceeded the supply of animal skins for parchment.

With this model, peers are both suppliers and consumers of resources, in contrast to the traditional client – server model where only the server supply ( send ), and clients consume ( receive ).

With access to three of the world's oceans — the Atlantic, Arctic, and Pacific — Russian fishing fleets are a major contributor to the world's fish supply.

With respect to the issues, Dole promised a 15 % across-the-board reduction in income tax rates and made former Congressman and supply side advocate Jack Kemp his running mate.

With Peugeot supplying the engines for Prost GP, Mugen-Honda decided to supply the Jordan team.

With a seemingly endless supply of food, the Muckleshoots could engage in various crafts, including weaving, wood-carving, and basket-making.

With the advent of widespread electricity generation and power supply lines from the late 19th century on, problems also arose with equipment short-circuit failure affecting the power supply, and with local fire and shock hazard when the power line was struck by lightning.

With his harpoon gun and his diving equipment he is able to spend hours underwater without worrying about oxygen supply or about danger he may encounter at sea.

With laminations, differences are generally caused by cyclic changes in the sediment supply, caused for example by seasonal changes in rainfall, temperature or biochemical activity.

With the advantage of a peculiarly fine climate, for which this part of Asia Minor has been famous in all ages, Ionia enjoyed the reputation in ancient times of being the most fertile of all the rich provinces of Asia Minor ; and even, though very imperfectly cultivated, it produces abundance of fruit of all kinds, and the raisins and figs of Smyrna supply almost all the markets of Europe.

With the capture of the fort, the Patriot forces obtained a large supply of cannons and other armaments, much of which Henry Knox transported to Boston during the winter of 1775 – 1776.

With supply assured, he then received Fraser, who advised him that 21 bills ( including the electoral redistribution bills ) which had been introduced since the last election fulfilled the double dissolution provisions of Section 57.

With industrialisation and urbanisation, the supply of milk became a commercial industry, with specialised breeds of cattle being developed for dairy, as distinct from beef or draught animals.

With the food supply running low, the settlers needed salt to preserve what meat they had, so in January 1778, Boone led a party of 30 men to the salt springs on the Licking River.

With the enlargement of the tunnels and modification of the electrical supply, Standard Stock ( displaced from the Northern line by new 1938 Stock ) was operated, eventually as 8-car trains following platform extensions.

With innate talent, passion, diligence, discipline, self-motivation and tenacity, being the core factors of achieving success to becoming a celebrity, fame and fortune sometimes occurs spontaneously with relatively little effort due to sheer luck, being fortunate with connections, or simply being at the right place during the right time.

With his next venture, Bowie, in the words of biographer David Buckley, " challenged the core belief of the rock music of its day " and " created perhaps the biggest cult in popular culture ".

With a new management team in place, Lycos also began divesting properties that were not core to its new strategy.

With the first generation of the MX-5, the phrase was developed into five specific core design requirements:

With the damage to the core columns, the buckling exterior columns could no longer support the buildings, causing them to collapse.

* Shabbat laws: With the severity of Sabbath violation, namely the death penalty, one would assume that direction would be provided as to how exactly such a serious and core commandment should be upheld.

With Mobile Application Part, UMTS uses the same core network standard as GSM / EDGE.

With the group scattered, communication is maintained primarily through phone calls, and the group leaders ( in particular the core three ) now assume more superheroic positions and parallels than in previous seasons.

With hierarchical routing, only core routers connected to the backbone are aware of all routes.

With the advent of IN, most of these services ( such as toll free numbers and geographical number portability ) were moved out of the core switch systems and into self serving nodes ( IN ), thus creating a modular and more secure network that allowed the services providers themselves to develop variations and value-added services to their network without submitting a request to the core switch manufacturer and wait for the long development process.

With respect to one another, their relative refractive indices are, in order of distance from the core: lowest, highest, lower, higher.

With the addition of frameworks to do state management, load balancing and dynamic HTML generation, NeXT was able to launch the first object-oriented Web application server, WebObjects, in 1996, with EOF at its core.

With these additions and a talented core of players such as Derek King, Ray Ferraro and Patrick Flatley, along with incoming Soviet-bloc players Vladimir Malakhov and Darius Kasparaitis, the Islanders had a new foundation in the early ' 90s.

With a young core of players led by Lecavalier, Richards, Martin St. Louis, and Fredrik Modin, the Lightning were thought to be very close to respectability.

With a young core that included Linden, Bure and McLean still in their twenties after the 1994 playoffs, the Canucks appeared poised to remain contenders in the league.

With traditional core competences in civil engineering, environment, transport, town and regional planning, mechanics, industrial management and logistics, École des Ponts ParisTech offers high-level programmes in an extensive range of fields, from applied mathematics to economics and management.

With regard to coil composition, the core material may be either a magnetically inert substrate ( i. e., the so-called ‘ air-core ’ coil design ), or possess a solid, ferromagnetically active material ( ie, the so-called ‘ solid-core ’ design ).

With extended data paths for efficient DSP processing, special accumulators and a dedicated MAC-type DSP engine, this core was unifying the DSP and the RISC processor world.

With the courthouse at its center, the Stuart Uptown Historic District encompasses the historic core of the county seat and includes government, financial, religious, and commercial buildings dating from the mid-nineteenth to the mid-twentieth centuries.

With the 1973 selection of the Bangor Ammunition Depot northwest of Bremerton as the Pacific home of the new Trident submarine fleet, residential and commercial development began to move closer to Silverdale and farther from the Bremerton downtown core.

With decreased heat loss, the core temperature itself rises.

With both paths, Katarn has a final confrontation with Jerec in the Valley of the Jedi's core.