Suggest the following twenty-first-century amendment: By moving the term `` Republic '' to lower case, substituting the modern phrase, `` move ahead '' for the stodgy `` keep '', and by using the Postmaster's name on every envelope ( in caps, of course, with the `` in spite '' as faded as possible ), the slogan cannot fail.

By using the appropriate version any one of these factors can be determined for any combination of the other three.

By using instruments of gradually increasing size, the vagina is gently, and with minimum pain at each stage, taught to yield to an object of the appropriate shape.

By 1827 Laplace was using least

By comparing the form of several yupanas, researchers found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20 and 40 as place values for the different fields in the instrument.

By night, an aardwolf can consume up to 200, 000 harvester termites using its sticky, long tongue.

By using the palette to mask the top area of the display and taking care about when it changes mode it can shift the continuous graphics at the bottom of the display down in two pixel increments because the internal display counter is not incremented on blank scanlines during non-continuous graphics modes.

By using the formula

By the Roman period brass was being deliberately produced from metallic copper and zinc minerals using the cementation process and variations on this method continued until the mid 19th century.

By comparison to biotechnology, bioengineering is generally thought of as a related field with its emphasis more on higher systems approaches ( not necessarily altering or using biological materials directly ) for interfacing with and utilizing living things.

By the late 1920s, New York writers other than Fitz Gerald were starting to use " Big Apple " and were using it outside of a horse-racing context.

By the mid-1980s at least 500 courses in business ethics reached 40, 000 students, using some twenty textbooks and at least ten casebooks along supported by professional societies, centers and journals of business ethics.

By 1000 BC ancient civilizations were using technologies that formed the basis of the various branches of chemistry such as ; extracting metal from their ores, making pottery and glazes, fermenting beer and wine, making pigments for cosmetics and painting, extracting chemicals from plants for medicine and perfume, making cheese, dying cloth, tanning leather, rendering fat into soap, making glass, and making alloys like bronze.

By using custom formatting and load / save routines ( sometimes included in third-party DOSes, see below ), all of the mechanically possible 40 tracks could be used.

By the early 1990s, the performance of microprocessor-based computers reached the point that real-time generation of computer music using more general programs and algorithms became possible.

By using the commutator as a Lie bracket, every associative algebra can be turned into a Lie algebra.

By a strange twist of their respective fates, this foursome ends up partnering together, using their unique talents to become a ragtag team of bounty hunters, although their fortunes as such are at best mixed.

By 1970, a calculator could be made using just a few chips of low power consumption, allowing portable models powered from rechargeable batteries.

By reducing the number of tracks used ( and thus the capacity ), Commodore could further reduce cost-in contrast to the double-density drives used e. g. in IBM PCs of the day which saved 180 KB on one side ( by using a 40-track format ).

By the time of the Vietnam War, IDs spelled out the broad religious choices such as PROTESTANT and CATHOLIC, rather than using initials, and also began to show individual denominations such as " METHODIST " or " BAPTIST.

By 1695 he was back in England, now formally using the name " Defoe ", and serving as a " commissioner of the glass duty ", responsible for collecting taxes on bottles.

By contrast, non-digital ( or analog ) systems represent information using a continuous function.

By using doublespeak in advertisements, aspirin production rose by almost 50 percent from over 23 million pounds in 1960 to over 35 million pounds in 1970.

By the 12th to 13th centuries A. D., monks were preparing illuminated manuscripts on vellum and parchment in monasteries throughout Europe and were using lead styli to draw lines for their writings and for the outlines for their illuminations.

By direct substitution, the solution to this equation can be readily shown to be the scalar Green's function, which in the spherical coordinate system ( and using the physics time convention ) is:

* By whether the same key is used for both encryption and decryption ( symmetric key algorithms ), or if a different key is used for each ( asymmetric key algorithms ).

By the late 1990s new research building on Mack's insights was beginning to mature, and after 2004, the U. S. military began once again to seriously consider the problems associated with asymmetric warfare.

By utilizing two different monolayers in Langmuir-Blodgett deposition or a combination of Langmuir-Blodgett and vesicle rupture deposition it is also possible to synthesize an asymmetric planar bilayer.

By dynamically adjusting the number of timeslots used for downlink and uplink, the system can more easily accommodate asymmetric traffic with different data rate requirements on downlink and uplink than FDD schemes.

The active metabolite ( top right ) has E-Z notation | Z configuration at the double bond C3 – C16 and possibly Chirality ( chemistry )# By configuration: R-and S-| R configuration at the newly asymmetric C4.

By 1963 – 4 Gödel would disavow Herbrand – Gödel recursion and the λ-calculus in favor of the Turing machine as the definition of " algorithm " or " mechanical procedure " or " formal system ".

By the completeness theorem of first-order logic, a statement is universally valid if and only if it can be deduced from the axioms, so the can also be viewed as asking for an algorithm to decide whether a given statement is provable from the axioms using the rules of logic.

By reversing the steps in the Euclidean algorithm, the GCD can be expressed as a sum of the two original numbers each multiplied by a positive or negative integer, e. g., 21 = × 105 + × 252.

By far the most commonly used FFT is the Cooley – Tukey algorithm.

By hand as well as with a computer, this division can be computed by the polynomial long division algorithm.

By comparison, a quantum computer could efficiently solve this problem using Shor's algorithm to find its factors.

By means of this computer Grover's algorithm for four variants of search has generated the right answer from the first try in 95 % of cases.

On the other hand, if T is written as a unary number ( a string of n ones, where n = T ), then it only takes time n. By writing T in unary rather than binary, we have reduced the obvious sequential algorithm from exponential time to linear time.

By repeated random selection of a possible witness, the large probability that a random string is a witness gives an expected polynomial time algorithm for accepting or rejecting an input.

By tuning the three parameters in the PID controller algorithm, the controller can provide control action designed for specific process requirements.

By analogy with this physical process, each step of the SA algorithm attempts to replace the current solution by a random solution ( chosen according to a candidate distribution, often constructed to sample from solutions near the current solution ).

By comparison, if PCA ( a linear dimensionality reduction algorithm ) is used to reduce this same dataset into two dimensions, the resulting values are not so well organized.

By using a data structure such as a doubly linked list to maintain the set of unused edges incident to each vertex, to maintain the list of vertices on the current tour that have unused edges, and to maintain the tour itself, the individual operations of the algorithm ( finding unused edges exiting each vertex, finding a new starting vertex for a tour, and connecting two tours that share a vertex ) may be performed in constant time each, so the overall algorithm takes linear time.

By the LU decomposition algorithm, any invertible matrix may be written as the product of a lower triangular matrix L by an upper triangular matrix U.

By applying the extended Euclidean algorithm, we wish to find and such that.

By an application of Markov's inequality, a Las Vegas algorithm can be converted into a Monte Carlo algorithm via early termination ( assuming the algorithm structure provides for such a mechanism ).

By performing the above algorithm with this pairwise multiplication, even fewer temporary results need to be held.

By shaving 3 milliseconds off the previously fastest fiber optic connection between these two trading centers, Barksdale built the " Ultimate Trading Weapon " and, according to some industry insiders, can charge 8 to 10 times the going rate because any HFT algorithm not operating on his network is at a significant speed disadvantage.

In other words, the higher-dimensional, multi-player, n-in-a-row generalization of game of tic-tac-toe cannot end in a draw, no matter how large n is, no matter how many people c are playing, and no matter which player plays each turn, provided only that it is played on a board of sufficiently high dimension H. By a standard strategy stealing argument, one can thus conclude that if two players alternate, then the first player has a winning strategy when H is sufficiently large, though no constructive algorithm for obtaining this strategy is known.

Let denote the complement of L. By the definition of PP there is a polynomial-time probabilistic algorithm A with the property that and.