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 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.

For example, in crystalline solids, these correspond to phonons, which are quantized versions of lattice vibrations.

For anisotropic multicomponent diffusion coefficients one needs 4-index quantities, for example,, where i, j are related to the components and α, β = 1, 2, 3 correspond to the space coordinates.

For example, the English verbs " to know " ( the state of knowing ) and " to find out " ( knowing viewed as a " completed action ") correspond to the imperfect and perfect of the French verb " savoir ".

For this rule to be applicable, each element y ∈ Y must correspond to no more than one x ∈ X ; a function ƒ with this property is called one-to-one, or information-preserving, or an injection.

For example, there are many common lasers ( e. g., dye lasers, carbon dioxide lasers ) where the laser medium consists of complete molecules, and energy states correspond to vibrational and rotational modes of oscillation of the molecules.

For example, a human voice can be sent as a radio wave or microwave by making the wave vary to correspond variations in the voice.

For example, a patient might present a set of symptoms which correspond to a number of different distinct diagnoses each with a different probability.

For instance, half of the velocity goal could correspond to a quarter as long of a tunnel needing to be constructed, for the same acceleration.

For the most part these groups do not correspond to any formal taxonomic groupings or phylogeny and many species and hybrids have characteristics of more than one group, or do not fit well in any of them.

For example, if one wishes to concentrate on a god, one might memorize a system of correspondences ( perhaps chosen arbitrarily, as this would not affect its usefulness for mystical purposes ) and then make every object that one sees " correspond " to said god.

The rows correspond to the dimensions, and t, and the columns to the dimensional variables D, T, V. For instance, the 3rd column, ( 1, − 1 ), states that the V ( velocity ) variable has units of.

( The rows correspond to the dimensions t, m, and l, and the columns to the dimensional variables T, M, L and g. For instance, the 4th column, (− 2, 0, 1 ), states that the g variable has units of.

For unary features to be fully specified, it is necessary to include binary subfeatures that correspond to them.

For example, in some interpretations of quantum mechanics ( such as the many-worlds interpretation ) the ket vector associated to the system state is said to correspond to an element of physical reality, while in other interpretations it is not.

For example, he correctly trusted the faithful Lu Xun and Zhuge Jin, so much so that he made a duplicate imperial seal and left it with Lu Xun ; whenever he would correspond with Shu's emperor Liu Shan or regent Zhuge Liang, he would deliver the letter to Lu Xun first ( as Lu's post was near the Shu border ), and then if, in Lu's opinion, changes were needed, he would revise the letter and then restamp it with Sun's imperial seal.

For example, the coefficients for BK7 above correspond to two absorption resonances in the ultraviolet, and one in the mid-infrared region.

For example in mathematical physics, the homogeneous equation may correspond to a physical theory formulated in empty space, while the inhomogeneous equation asks for more ' realistic ' solutions with some matter, or charged particles.

For a flexible polymer, low temperature may correspond to poor quality and high temperature makes the same solvent good.

Although this definition implies a series of identical temporal waveforms, it is more helpful to define the SSEP in terms of the frequency components that are an alternative description of the time-domain waveform, because different frequency components can have quite different properties For example, the properties of the high-frequency flicker SSEP ( whose peak amplitude is near 40 – 50 Hz ) correspond to the properties of the subsequently discovered magnocellular neurons in the retina of the macaque monkey, while the properties of the medium-frequency flicker SSEP ( whose amplitude peak is near 15 – 20 Hz ) correspond to the properties of parvocellular neurons.

* For σ < sub > 1 </ sub >, these eigenvalues correspond to the eigenvectors

* For σ < sub > 3 </ sub >, they correspond to the eigenvectors

In the image to the right, the solid lines correspond to real particles ( of momentum p < sub > 1 </ sub > and so on ), while the dotted line corresponds to a virtual particle carrying momentum k. For example, if the solid lines were to correspond to electrons interacting by means of the electromagnetic interaction, the dotted line would correspond to the exchange of a virtual photon.