Using the standard method for solving a diffusion equation we have

Using a DC pulse as the electrical current, spark plasma, spark impact pressure, joule heating, and an electrical field diffusion effect would be created.

Using that mathematical tool Hambardzumyan resolved a number of nonlinear problems of the light diffusion.

Using the equivalence principle, this tensor is readily generalized to curved space-time.

Using conditions 1 and the symmetry of the metric tensor g we find:

Using index notation, the Hodge dual is obtained by contracting the indices of a k-form with the n-dimensional completely antisymmetric Levi-Civita tensor.

Using tensor calculus, proper time is more rigorously defined in general relativity as follows: Given a spacetime which is a pseudo-Riemannian manifold mapped with a coordinate system and equipped with a corresponding metric tensor, the proper time experienced in moving between two events along a timelike path P is given by the line integral

Using these properties, the Navier – Stokes equations of motion, expressed in tensor notation, are ( for an incompressible Newtonian fluid ):

Using Newton's identities, this condition can be re-expressed in terms of the traces of the powers of the Einstein tensor as

Using analysis of one nDNA and 2 mtDNA sequences, Moyle & Marks ( 2006 ) found one largely Asian lineage and one African group of greenbuls and bristlebills ; the Golden Greenbul seemes to be very distinct and form a group of its own.

Using 12S ribosomal DNA sequences, Houde et al.

Using the commonalities among sequences and hydropathy plot analyses, it was predicted that there are 12 hydrophobic membrane spanning regions in the ‘ Classical ’ transporter family.

Using this idea, a context-specific extension of the popular BLAST program has been demonstrated to achieve a twofold sensitivity improvement for remotely related sequences over BLAST at similar speeds ( CS-BLAST ).

Using a heuristic method, BLAST finds similar sequences, not by comparing either sequence in its entirety, but rather by locating short matches between the two sequences.

Using the Tor functor's long exact sequences, one can then easily prove facts about a short exact sequence

Using recombinant DNA techniques genetic sequences coding for epitopes that are recognized by common antibodies can be fused to the gene.

Using ANSI escape code SGR sequences, compatible terminals can print out colored text:

Using cryptographic hashes inside the port knock sequence can mean that even sniffing the network traffic in and out of the source and target machines is ineffective against discovering the port knock sequence or using traffic replay attacks to repeat prior port knock sequences.

Using percent-encoding, reserved characters are represented using special character sequences.

Using HIV-1 sequences preserved in human biological samples along with estimates of viral mutation rates, scientists calculate that the jump from chimpanzee to human probably happened during the late 19th or early 20th century, a time of rapid urbanisation and colonisation in equatorial Africa.

Using this framework, brief nude scenes of women appeared in Maniac ( 1934 ) and Sex Madness ( 1937 ), and nude swimming sequences in Damaged Lives ( 1933 ), Marihuana ( 1936 ) and Child Bride ( 1938 ).

Using sequences of reduction functions changes how lookup is done: because the hash value of interest may be found at any location in the chain, it's necessary to generate k different chains.

Using this method, copy number changes at a level of 5 – 10 kilobases of DNA sequences can be detected.

Using a steering system that controlled the modified rocket's tail surfaces and wings equipped with ailerons, Fiedler was to land the missile on a skid especially bolted under the fuselage.

: Using * to denote a binary operation performed on a set

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 these tools, one can write a more complex text editor, and a simple compiler for a higher-level language and so on, until one can have a graphical IDE and an extremely high-level programming language.

Using pharmacogenomics, pharmaceutical companies can create drugs based on the proteins, enzymes and RNA molecules that are associated with specific genes and diseases.

Using the language of category theory, many areas of mathematical study can be cast into appropriate categories, such as the categories of all sets, groups, topologies, and so on.

Using ClearType on these display configurations will actually reduce the display quality.

Using the Cartesian coordinate system, geometric shapes ( such as curves ) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape.

Using to denote the size of the original grammar, the size blow-up in the worst case may range from to, depending on the transformation algorithm used.

Using pioneering film-looping technology, Enoch J. Rector presented the entirety of a famous 1897 prize-fight on cinema screens across the country.

* International Good Practice: Guidance on Project Appraisal Using Discounted Cash Flow, International Federation of Accountants, June 2008, ISBN 978-1-934779-39-2

Using the civil unrest in India as an excuse to move troops to the Durand Line, Afghan troops crossed the border at the western end of the Khyber Pass on 3 May 1919 and occupied the village of Bagh, the scene of an earlier uprising in April.

Using his favorite model in his last painting of her, a fellow painter, Victorine Meurent, also the model for Olympia and the Luncheon on the Grass, sits before an iron fence holding a sleeping puppy and an open book in her lap.

Using digital computers, on the other hand, both FIR and IIR filters are straightforward to implement in software.

Using humanist techniques for working on texts, he prepared important new Latin and Greek editions of the New Testament.

* Using Java, and based very closely on Weizenbaum's published description of the program: http :// www. chayden. net / eliza / Eliza. html

* Using Z80 assembly language on the TI-83 Plus: ticalc. org

Using this method, the customer does not need to authenticate his or her identity by PIN entry or signature, as on a regular machine.

Using mathematical rules and procedures based on properties of reducible configurations, Appel and Haken found an unavoidable set of reducible configurations, thus proving that a minimal counterexample to the four-color conjecture could not exist.

Using FProxy, a user can browse freesites ( web sites that use normal HTML and related tools, but whose content is stored within Freenet rather than on a traditional web server ).

Using whatever equipment the vassal could obtain by virtue of the revenues from the fief, the vassal was responsible to answer calls to military service on behalf of the lord.

Using the submarine, Akatsuki, they hope to gather information on the robot's builders, the alien simians.

Using the notion of covering provided by a Grothendieck topology, it becomes possible to define sheaves on a category and their cohomology.

Using their data on the time occupied by travel to work, Table 2 below shows the absolute number of people who responded with travel times " at least 15 but less than 20 minutes " is higher than the numbers for the categories above and below it.

Using the Emergency-era Internal Security Act ( ISA ), the new government suspended Parliament and political parties, imposed press censorship and placed severe restrictions on political activity.