For a two-dimensional array, the element with indices i, j would have address B + c · i + d · j, where the coefficients c and d are the row and column address increments, respectively.

For example, a similar geometric system was published in 1987 by Kjell Gustafson, whose method represents a rhythm as a two-dimensional graph.

For convenience, pixels are normally arranged in a regular two-dimensional grid.

For example, Girih tiles in a medieval Islamic mosque in Isfahan, Iran, are arranged in a two-dimensional quasicrystalline pattern.

For example, the surface of the Earth is ( ideally ) a two-dimensional sphere, and latitude and longitude provide two-dimensional coordinates on it ( except at the poles and along the 180th meridian ).

For a two-dimensional situation with horizontal and vertical forces, the sum of the forces requirement is two equations: ΣH

For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional ( 2D ) surface.

For two-dimensional signals, e. g., images, the spectrum is reciprocal to f < sup > 2 </ sup >.

For two-dimensional rotational motion, Newton's second law can be adapted to describe the relation between torque and angular acceleration:

For example, is a meromorphic function on the two-dimensional complex affine space.

For a two-dimensional surface, the Bianchi identities imply that the Riemann tensor can be expressed as

For example, atmospheric cyclones are rotational but their substantially two-dimensional shapes do not allow vortex generation and so are not turbulent.

For example, the ordinary generating function of a two-dimensional array a < sub > m, n </ sub > ( where n and m are natural numbers ) is

For instance, a "< big > b </ big >" and a "< big > d </ big >" have a different shape, at least when they are constrained to move within a two-dimensional space like the page on which they are written.

For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.

For convex two-dimensional shapes, the centroid can be found by balancing the shape on a smaller shape, such as the top of a narrow cylinder.

For example, a monatomic gas with a fixed number of particles is a simple case of a two-dimensional system ().

For instance, in the BF model, the spacetime is a two-dimensional manifold M, the observables are constructed from a two-form F, an auxiliary scalar B, and their derivatives.

For a two-dimensional flow the vorticity acts as a measure of the local rotation of fluid elements.

For example, Kahane uses Cantor sets to construct a Besicovitch set of measure zero in the two-dimensional plane.

For such models, economists often use two-dimensional graphs instead of functions.

For example, a two-dimensional real torus has a SL ( 2, Z ) group of large diffeomorphisms by which the one-cycles of the torus are transformed into their integer linear combinations.

For the graph of a two-dimensional function, this corresponds to a point on the graph where the tangent plane is parallel to the xy plane.

For example, the randomization-based analysis results in a small but ( strictly ) negative correlation between the observations.

For example Connecticut applies the following standard to review unpreserved claims: 1. the record is adequate to review the alleged claim of error ; 2. the claim is of constitutional magnitude alleging the violation of a fundamental right ; 3. the alleged constitutional violation clearly exists and clearly deprived the defendant of a fair trial ; 4. if subject to harmless error analysis, the state has failed to demonstrate harmlessness of the alleged constitutional violation beyond a reasonable doubt.

* For a utilitarian analysis of religion, see The ( F ) Utility of Religion: Who Needs God ( s )?– A Prospective Bible for Non-Believers at http :// bradmusil. kramernet. org

For example, the analysis of the debris at the testing site of the first U. S. hydrogen bomb, Ivy Mike, ( 1 November 1952, Enewetak Atoll ), revealed high concentrations of various actinides including americium ; due to military secrecy, this result was published only in 1956.

For an example of its use, analysis of the concentration of elements is important in managing a nuclear reactor, so nuclear scientists will analyze neutron activation to develop discrete measurements within vast samples.

For more rigorous and precise analysis, the numerical approximations must be used.

For theoretical analysis, this approach is more suited for constructing detailed formal proofs and is generally preferred in the research literature.

For the analysis to correspond usefully to the actual execution time, the time required to perform a step must be guaranteed to be bounded above by a constant.

For the same figure, a control volume analysis yields:

For example, promoter analysis involves the identification and study of sequence motifs in the DNA surrounding the coding region of a gene.

For his political writings on doublespeak and hypocrisy, Noam Chomsky received the Orwell Award ( which ' recognizes writers who have made outstanding contributions to the critical analysis of public discourse ') in 1987 and 1989.

: For the theorem of propositional logic which expresses Disjunction elimination, see Case analysis.

( For more on behaviorism's role, see Behavior analysis of child development ).

For the sake of the example ( and this is a gross simplification ), let's assume that he values this particular risk at 5 % per annum ( we could perform a more precise probabilistic analysis of the risk, but that is beyond the scope of this article ).

For the quantitative analysis, ten articles were selected at random – circumcision, Charles Drew, Galileo, Philip Glass, heart disease, IQ, panda bear, sexual harassment, Shroud of Turin and Uzbekistan – and letter grades of A – D or F were awarded in four categories: coverage, accuracy, clarity, and recency.

For a small signal analysis, every non-linear element can be linearized around its operation point to obtain the small-signal estimate of the voltages and currents.

For a summary and analysis of the book itself, see Book of Ezekiel.

For Griffin, fascism is " a genuinely revolutionary, trans-class form of anti-liberal, and in the last analysis, anti-conservative nationalism " built on a complex range of theoretical and cultural influences.

For general nonabelian locally compact groups, harmonic analysis is closely related to the theory of unitary group representations.

In 1991 he was awarded the Balzan Prize for Genetics and Evolution " For his powerful analysis of evolutionary theory and of the role of sexual reproduction as a critical factor in evolution and in the survival of species ; for his mathematical models applying the theory of games to evolutionary problems " ( motivation of the Balzan General Prize Committee ).

For instance, calculus ( in one variable ) generalizes to multivariable calculus, which generalizes to analysis on manifolds.

For economic and social innovation, the city was ranked 15th globally out of 289 cities in 2010, and 5th in Germany by the 2thinknow Innovation Cities Index based on analysis of 162 indicators.

For example, the atomic weight of lithium as found by isotopic analysis of 39 lithium reagents from several manufacturers varied from 6. 939 to 6. 996.

For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model.

For example, constructive proofs in analysis may ensure witness extraction, in such a way that working within the constraints of the constructive methods may make finding witnesses to theories easier than using classical methods.