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By and solving
By solving this equation, one arrives at the " equations of motion " of the field.
By trading optimality, completeness, accuracy, and / or precision for speed, a heuristic can quickly produce a solution that is good enough for solving the problem at hand, as opposed to finding all exact solutions in a prohibitively long time.
By using heuristics, time can be reduced when solving problems.
By the first decades of the eleventh century, Chinese ironworkers in the Yellow River valley began to fuel their furnaces with coke, solving their fuel problem in that tree-sparse region.
By forming a partnership with the community through Community Policing Initiatives we will work together to protect the lives and property of the citizens through fair, honest and professional enforcement of the laws, crime prevention and community problem solving.
By solving this problem, online auctions reduce the transaction costs for bidders, increase the number of bidders, and increase the average bid price.
By differentiating both equations one more time and solving them with proper initial conditions
By solving for the fixed point of the system:
By solving the theory in one space and one time dimension ,'t Hooft was able to derive a formula for the masses of mesons.
By using receivers and transmitters tuned to different frequencies, and solving the problems introduced by operation of a receiver immediately next to a transmitter, simultaneous transmission and reception was possible at each end of a radio link, in so-called " full duplex " mode.
By solving the quantum mechanical system of two electrons as harmonic oscillators at some finite distance from one another, being displaced about their respective rest positions and interacting with each others fields, London showed that the energy of this system is given by:
By substituting for y < sup > 2 </ sup > into the equation for triangle BHC and solving for x:
By employing positive group dynamic tools and a rigorous problem solving infrastrucure ( guided by a facilitator ) the team harnesses its multiplicative potential to problem solve.
If housing services ( X4 ) is separated into the components that comprise it ( Z1, Z2, Z3, Z4 ,... Zn ), then the utility function can be rewritten as U = U ( X1, X2, X3 ,( Z1, Z2, Z3, Z4 ,... Zn )... Xn ) By varying the price of housing services ( X4 ) and solving for points of optimal utility, that household's demand schedule for housing services can be constructed.
By his fundamental approach and his inner understanding of human nature, Ohayon succeeds in breaking the ring of silence and solving the murder mystery on his way to the next book.
By solving subproblems one time and reusing these solutions many times, we can drastically reduce the time required.
By solving quests or defeating opponents the player is awarded experience points, which can be used to improve attributes, skills, and weapon proficiencies to further develop the character.
By substituting V < sub > 1 </ sub > to the first equation and solving in respect to V2, we get:
By inducing participants to generate language samples in the context of solving an actual task ( using a computer that they believed actually understood what they were typing ), the variety and complexity of the lexical structures gathered was greatly reduced and simple keyword matching algorithms could be developed to address the actual language collected.

By and calculating
By calculating the maximum time that electrical signals can move in various branches of a CPU's many circuits, the designers can select an appropriate period for the clock signal.
By calculating the area under the relevant portion of the graph for 50 trials, the archaeologist can say that there is practically no chance the site was inhabited in the 11th and 12th centuries, about 1 % chance that it was inhabited during the 13th century, 63 % chance during the 14th century and 36 % during the 15th century.
By calculating in the frame of reference of the moving lithosphere ( velocity v ), which have spatial coordinate x '
By 1872 Lord Kelvin devised an analogue computer to predict the tides, and by 1875 Frank Stephen Baldwin was granted the first US patent for a practical calculating machine that performs four arithmetic functions.
By calculating the product of all six redenominations, it is seen that a pre-1921 ruble is equal to.
Consider two waveforms f and g. By calculating the convolution, we determine how much a reversed function g must be shifted along the x-axis to become identical to function f. The convolution function essentially reverses and slides function g along the axis, and calculates the integral of their ( f and the reversed and shifted g ) product for each possible amount of sliding.
By calculating the area of the peak using the mathematical function of integration, the concentration of an analyte in the original sample can be determined.
By calculating the energies for monomers, dimers, trimers, etc., in an N-object system, a complete set of two -, three -, and up to N-body interaction energies can be derived.
By carrying out this quantization and calculating the eigenvalues of the Casimir operator for the Kepler problem, Wolfgang Pauli was able to derive the energy levels of hydrogen-like atoms ( Figure 6 ) and, thus, their atomic emission spectrum.
By calculating these amounts after every time step the simulation can be programmed to increase the stepsize Δt if they do not change significantly, and to reduce it if they start to do so.
By counting and calculating, Taylor wanted to transform management, which was essentially an oral tradition, into a set of calculated and written techniques.
By calculating the time differential in the passage of a particle from one sensor to the other, the speed of the hull through the water can be calculated directly.
By calculating the ideal digital signal and then subtracting it from the actual analog signal, it is possible to amplify the signal remaining after subtraction and use it to determine what had previously been written on the disk.
By calculating the sequence of Mills primes, one can approximate Mills ' constant as
By keeping track of the sum current, one can recover information about the local oscillator ’ s intensity, since this is usually an unknown quantity, but an important quantity for calculating the quadrature component.
By calculating the tide table for 12 October 1216 and given travel in the usual daylight hours, it is possible to deduce that King John's treasure was lost in crossing the Welland in the vicinity of the site of the much later Fosdyke Bridge.
By definition, only Na < sup >+</ sup >, Cl < sup >−</ sup > and HCO < sub > 3 </ sub >< sup >−</ sup > (+/- K ) are used when calculating the anion gap.

By and all
`` By God '', Waddell said, `` we don't want to upset the boy at this time of all times.
By early June they were a hundred miles off the coast of Ceylon, by which time all four missionaries were hardened seafarers.
By 1783 her legions had managed to annex the Crimea amid scenes of wanton cruelty and now, in this second combat with the Crescent, were aiming at suzerainty over all of the Black Sea's northern shoreline.
By 1965, several or all of these systems will have been fully tested and their reliability established.
By recognizing and helping Juniors get interested in the dog world, all will be helping to create future dog owners.
By this scheme, pulling one signal to clear locks all the other switch and signal levers in safe positions until the first signal is again restored to normal.
By the time the film was released we were three million dollars over-spent, war was imminent and the public apparently had forgotten all about Mother Cabrini.
By the time the child first attacks the actual problem of reading, he is completely familiar and at ease with all of the elements of words.
By 1960 there were such schools in all but 4 states.
By these measures, Congress, so the Court ( in effect ) now decides, gave not only needless but inadequate relief, since it now appears that the federal courts have inherent power to sterilize the Act of 1875 against all proceedings challenging local regulation ''.
By all means the most important distinction is that between those total-cost apportionments which superimpose a distribution of admittedly unallocable cost residues on estimates of incremental or marginal costs, and those other apportionments which recognize no difference between true cost allocation and mere total-cost distribution.
By July 1, six weeks from now, motel-keepers all over the nation will, by 6 p.m., be switching on that bleak -- to motorists -- sign, `` No Vacancy ''.
: By all admired, and by all reverenced ;
By ancient common law it might be required of all persons above the age of 12, and it was repeatedly used as a test for the disaffected.
By October 1993, Armenian forces succeeded in occupying almost all of former NKAO, Lachin and large areas in southwestern Azerbaijan.
By the late 5th century BC, philosophers might separate Aphrodite into two separate goddesses, not individuated in cult: Aphrodite Ourania, born from the sea foam after Cronus castrated Uranus, and Aphrodite Pandemos, the common Aphrodite " of all the folk ," born from Zeus and Dione.
By no means do all Jews today believe in reincarnation, but belief in reincarnation is not uncommon among many Jews, including Orthodox.
Proof: By symmetry, it suffices to prove that there is some constant c such that for all bitstrings s
By " chance ", he means all those particular comprehensible events which the viewer considers possible in accord with their experience.
By 1987 a comprehensive survey of the phylum was completed: in all, 4516 species and 339 genera had been named.
By 2000, all full-time, undergraduate Acadia students were taking part in the initiative.
By decree of pope Leo X they were created papal nobles, ranking as Comes palatinus (' Count Palatine '), familiars and members of the papal household, so that they might enjoy all the privileges of domestic prelates and of prelates in actual attendance on the Pope, as regards plurality of benefices as well as expectives.
By all accounts, AMOS was extremely fast among interpreted languages.
By 1993, all of the fixed-wing aircraft of the original EHV ( with the exception of the two old Nord 262 transports ) had been taken out of service, and either scrapped, sold off, or abandoned.

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