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Page "Competitive Lotka–Volterra equations" ¶ 1
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For and competition
For some squads the level of competition on the weekends can equal that of an all-star squad.
For the first time this placed the Maritime manufacturers in direct competition with those of Central Canada.
: For a complete list of Ferrari racing cars, see List of Ferrari competition cars.
For more than one hundred years, English and French trading companies had fought one another for supremacy, and by the middle of the 18th century competition between the British and the French had heated up.
For a time, Boniface served as Pope in competition with the Antipope Dioscorus, who had been elected by most of the priests of Rome.
For instance, when advertisements claim that their product is 37 % more effective than the competition, they are making a logical appeal.
For the entire two months life for many islanders is one big party with a major feature of crop over being the calypso competition.
For example, it has also been said that competition law in the European Union ( EU ) tends to protect the competitors in the marketplace, even at the expense of market efficiencies and consumers.
For example, during a debate over the act in 1890, Representative William Mason said " trusts have made products cheaper, have reduced prices ; but if the price of oil, for instance, were reduced to one cent a barrel, it would not right the wrong done to people of this country by the trusts which have destroyed legitimate competition and driven honest men from legitimate business enterprise.
For a long time, this had been thought to be intermale competition, but closer observation has revealed it is usually a female hitting a male to prevent copulation.
For example, the horse's straightness going across the diagonal may be assessed by judges at M and H. Judges in the United States are licensed by the USEF for different levels of competition, depending on the judge's experience and training.
For example, Darwinian evolution points to the competition of a variety of species, each with heterogeneous members, within a given environment.
For centuries, Taiwan's aboriginal peoples experienced economic competition and military conflict with a series of colonizing peoples.
For centuries, Taiwan's aboriginal peoples experienced economic competition and military conflict with a series of colonizing peoples.
For example, they indicate that investors could diversify their stock investments, efficiently managing the risk of a few catastrophic corporate failures, whether due to fraud or competition.
For example, according to an entry in the Parian Marble, Simonides died in 468 / 7 BC at the age of ninety yet, in another entry, it lists a victory by his grandfather in a poetry competition in Athens in 489 / 8 BC — this grandfather must have been over a hundred years old at that time if the birth dates for Simonides are correct.
Shiva's focus on water has seen her appear in a number of related films: " Ganga from the ground up " a documentary on water issues in the river Ganges ,, Blue Gold: World Water Wars by Sam Bozzo, Irena Salina's documentary Flow: For Love of Water ( in competition at the 2008 Sundance Film Festival ) and the PBS NOW documentary On Thin Ice.
For high scorers on the final competition for the team selection, there also is a summer camp, like that of China.
For example, the British had been fascinated by Edgar Wallace's ( 1875 – 1932 ) crime novels ever since the author set up a competition offering a reward to any reader who could figure out and describe just how the murder in his first book, The Four Just Men ( 1906 ), was committed.
For the tournament's second season in 1961 – 62, UEFA took over the running of all aspects of the competition and this time all the clubs eligible to enter accepted the opportunity.
For example, the annual sporting competition between Lancaster University and the University of York is called the Roses Tournament. This is also carried over into cricket with the cricket matches between Lancashire andvYorkshire cricket clubs which are called ' The War of The Roses '.
For architects, the competition was an important event ; not only was it for one of the largest building projects of its time, but it was only the third opportunity to build an Anglican cathedral in England since the Reformation in the 16th century ( St Paul's Cathedral being the first, rebuilt from scratch after the Great Fire of London in 1666, and Truro Cathedral being the second, begun in the 19th century ).
For 31 years, Imperial Beach played home to the U. S. Open Sand Castle competition, the largest sand castle competition in the United States, drawing in approximately 325, 000 people.
For the first time in the competition, the group-stages were expanded from 24 teams to 32, with eight groups of four.

For and equations
For atoms with two or more electrons, the governing equations can only be solved with the use of methods of iterative approximation.
For the mathematical formulation of the model, is also assumed to be twice continuously differentiable, so that differential equations describing the motion may be formulated.
For a certain class of Green functions coming from solutions of integral equations, Schmidt had shown that a property analogous to the Arzelà – Ascoli theorem held in the sense of mean convergence — or convergence in what would later be dubbed a Hilbert space.
For a fully relativistic treatment, the equation of state used will interpolate between the equations for small ρ and for large ρ.
For example, the expanding profile of a laser beam, the beam shape of a radar antenna and the field of view of an ultrasonic transducer can all be analysed using diffraction equations.
For other ways to solve this kind of equations, see below, System of linear equations.
For fluids which are sufficiently dense to be a continuum, do not contain ionized species, and have velocities small in relation to the speed of light, the momentum equations for Newtonian fluids are the Navier-Stokes equations, which is a non-linear set of differential equations that describes the flow of a fluid whose stress depends linearly on velocity gradients and pressure.
For him, the fact that his theory gave a straightforward explanation of the anomalous perihelion shift of the planet Mercury, discovered earlier by Urbain Le Verrier in 1859, was important evidence that he had at last identified the correct form of the gravitational field equations.
For simple diatomic molecules, the obtained wavefunctions are represented mathematically by the equations
For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences ; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science ; they are used in calculus and numerical analysis to approximate other functions.
For a set of polynomial equations in several unknowns, there are algorithms to decide if they have a finite number of complex solutions.
For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations
For example, classical thermodynamics is characterized by its study of materials that have equations of state or characteristic equations.
For a two-dimensional situation with horizontal and vertical forces, the sum of the forces requirement is two equations: ΣH
For vector wave equations, such as the ones describing electromagnetic radiation or waves in an elastic solid, the solution for a homogeneous medium is similar: the scalar amplitude A < sub > o </ sub > is replaced by a constant vector A < sub > o </ sub >.
For a lossless transmission line, the second order steady-state Telegrapher's equations are:
For example, S < sub > 5 </ sub >, the symmetric group in 5 elements, is not solvable which implies that the general quintic equation cannot be solved by radicals in the way equations of lower degree can.
For example, equations used to develop models of the origin do not in themselves explain how the conditions of the universe that the equations model came to be in the first place.
For example, application of quantum " fuzziness " ( per the Wheeler – DeWitt application of subatomic position and momentum equations to universal radius and expansion ) avoids boundary issues, as developed in the Hartle – Hawking wave function.
For example, in a coherent system the units of force, energy and power are chosen so that the equations

1.004 seconds.