Using the notation that is sometimes used to concisely describe diagonal matrices, we can write:

Using the diagonal sled-type leg press machine.

Using the above notation, and the diagonal function arises quite naturally as.

Using close textual analysis means rhetorical critics use the tools of classical rhetoric and literary analysis to evaluate the style and strategy used to communicate the argument.

Using a counting argument one can show that there exist transcendental numbers which have bounded partial quotients and hence are not Liouville numbers.

Using this argument, Weinberg predicted that the cosmological constant would have a value of less than a hundred times the currently accepted value.

Using a complicated combinatorial argument, they demonstrated that for every odd number n with n > 4381, there exist infinite, finitely generated groups of exponent n. Adian later improved the bound on the odd exponent to 665.

Using the characters of Clarissa and Rezia, she makes the argument that people can only interpret Septimus ' shell-shock according to their cultural norms.

Using logical terminology and applying it to the argument from free will, there is a marked distinction between the statement " It is impossible ( for God to know a future action to be true and for that action to not occur )" and the statement " If God knows that a future action is true, then it is impossible for that action to not occur.

Using strong critical thinking we might evaluate an argument, for example, as worthy of acceptance because it is valid and based on true premises.

Using this style, the debate is finished with a closing argument by each of the first speakers from each team and new evidence may not be introduced.

Using an argument first articulated by the late American rabbinical leader Joseph Soloveitchik, Yosef claims that the Arab-Israeli conflict endangers human lives, thereby meeting the above criteria and overruling the priority of commandments pertaining to settling the land of Israel.

where e is the identity of G. Though the f ″ defined a couple of paragraphs back is only defined for G-irreducible representations, and though A ⊗ B is not a G-irreducible representation in general, we claim this argument could be made correct since A ⊗ B is simply the direct sum of copies of Bs, and we have shown that each copy all maps to the same G × G-irreducible subrepresentation of C, we have just showed that as an irreducible G × G-subrepresentation of C is contained in A ⊗ B as another irreducible G × G-subrepresentation of C. Using Schur's lemma again, this means both irreducible representations are the same.

Using a drama with interviews from experts, then a discussion of the programme with a panel of experts from both sides of an argument.

Using Jensen's argument this could then be taken as evidence that the Flynn effect is substantially due to genetic causes, which is absurd.

Using a static replication argument

Using the same Thermal Wind argument, the strongest part of the jet stream should be in proximity where temperature gradients are the largest.

Using this argument Ritter contended, e. g., that Frederick the Great's invasion of Silesia in 1740 was a necessary act to allow the Prussian state to live, regardless of international laws against aggression.

Using this biological argument, anything that decreased chances of reproductive success would thus be seen as unethical or deviant, while anything that increased the chance of reproductive success would be seen as ethical.

Using Edgerton's method, the fast-closing action is obtained from the blackening of a window by exploding a series of parallel lead wires.

Using the F-distribution is a natural candidate because the test statistic is the ratio of two scaled sums of squares each of which follows a scaled chi-squared distribution.

Using visual imagery of a soroban, one can arrive at the answer in the same time as, or even faster than, is possible with a physical instrument.

Using a byte-oriented approach, it is possible to combine the < tt > SubBytes </ tt >, < tt > ShiftRows </ tt >, and < tt > MixColumns </ tt > steps into a single round operation.

Using two anchors set approximately 45 ° apart, or wider angles up to 90 °, from the bow is a strong mooring for facing into strong winds.

Using the same techniques they calculated the length of the Nile as, which is longer than previous estimates but still shorter than the Amazon.

Using the biblical Book of Revelation as a point of departure, Caesar Antichrist presents a parallel world of extreme formal symbolism in which Christ is resurrected not as an agent of spirituality but as an agent of the Roman Empire that seeks to dominate spirituality.

Using archery to take game animals is known as bow hunting.

Using a bow and arrow to take fish is known as bow fishing.

Using this criterion of falsifiability, astrology is a pseudoscience.

Using the formula, the overall speed boost is 1 / 0. 4575

Using this binding mechanism, an antibody can tag a microbe or an infected cell for attack by other parts of the immune system, or can neutralize its target directly ( for example, by blocking a part of a microbe that is essential for its invasion and survival ).

* Using a suitable catalyst ( e. g. Wilkinson's catalyst ), it is possible to reduce just one of the double bonds of an allene.

Using Zorn's lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K.

Using the above theorem it is easy to see that the original Borsuk Ulam statement is correct since if we take a map f: S < sup > n </ sup > → ℝ < sup > n </ sup > that does not equalize on any antipodes then we can construct a map g: S < sup > n </ sup > → S < sup > n-1 </ sup > by the formula

Using an existing language to bootstrap a new language is one way to solve the " chicken or the egg " causality dilemma.

Using ballpoint pens to create artwork is not without limitations.

Using the familiar cartesian basis, a vector A is written ;

Using programs or proofs of bounded lengths, it is possible to construct an analogue of the Berry expression in a formal mathematical language, as has been done by Gregory Chaitin.

Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.

Using numeric references that refer to permanently undefined characters and control characters is forbidden, with the exception of the linefeed, tab, and carriage return characters.

Using a three-digit Julian day number saves one byte of computer storage over a two-digit month plus two-digit day, for example, " January 17 " is 017 in Julian versus 0117 in month-day format.

Using color this way, the darkness and intensity ( or value ) of the color is evaluated by the eye as a measure of intensity or concentration.