From basic functional analysis we know that any ket can be written as

From Nial manual: " An operation is a functional object that is given an argument array and returns a result array.

From the point of view of functional analysis, calculus is the study of two linear operators: the differential operator, and the indefinite integral operator.

From a diagnostic standpoint, organic disorders were those held to be caused by physical illness affecting the brain ( that is, psychiatric disorders secondary to other conditions ), while functional disorders were considered to be disorders of the functioning of the mind in the absence of physical disorders ( that is, primary psychological or psychiatric disorders ).

From early on in his account of language, Halliday has argued that it is inherently functional.

From subdivision, styling, and Class A surfaces to mechanical functional surfaces.

From an evolutionary perspective, a convoluted structure such as the inverted retina can generally come about as a consequence of two alternative processes ; ( a ) an advantageous " good " compromise between competing functional limitations, or ( b ) as a historical maladaptive relic of the convoluted path of organ evolution and transformation.

From a functional point of view, therefore, non-Orthodox rabbis are valid leaders of Jewish religious communities, and it is both fatuous and self-defeating not to acknowledge this openly and draw the necessary consequences -- for example, establishing friendly and harmonious and respectful relationships and working together, all of us, towards those Jewish communal and global goals that we share and that unite us inextricably and indissolubly ....

From 2003 until 2008, the Gentoo Reference Platform ( GRP ) was a snapshot of prebuilt packages that users could quickly install during the Gentoo installation process, to give faster access to fully functional Gentoo installation.

* From a functional perspective, the focus is on how entities like businesses or state authorities are used.

From the ENCODE project, scientists have found about 20 % of the TARS were produced from previously unidentified ‘ potential unborn genes ’ which says that there are functional pseudogenes inside these regions.

From a genetic point of view, aversion to breeding with close relatives results in fewer congenital diseases, because, where one gene is faulty, there is a greater chance that the other-being from a different line-is of another functional type and can take over.

From the mid-19th century through the mid-20th, the neighborhood served as the functional equivalent of both a " railroad suburb " and a " streetcar suburb " of Center City ; although it was part of Philadelphia, and not a suburb, it was a leafy outlying part functioning much like a commuter town.

From this, one immediately has the functional equation of the zeta function also, as well as another means to extend the definition of eta to the entire complex plane.

From this quote it is clear that Hobbes contended that people in a state of nature ceded their individual rights to create sovereignty, retained by the state, in return for their protection and a more functional society.

From a functional perspective, throw pillows may provide back, neck and head support, although some throw pillows are very uncomfortable.

From this density, the functional action can be constructed by integrating over spacetime

From the beginning, the process of appointing NMPs has been weighted towards functional representation of discrete interests.

From this study, it is suggested that the " true " action of the supraspinatus is to hold the capsule in position to allow greater functional strength and stamina of the deltoid muscle.

From these two sites, only one was functional.

From a technical standpoint, the string playing is good, but the Pro Arte people fail to enter into the spirit of things here.

) From the technical standpoint, records differ from live music to the degree that they fail to convey the true color, texture, complexity, range, intensity, pulse, and pitch of the original.

From the volume standpoint, the total market represented by the sign industry is impressive.

From the standpoint of the army of duffers, however, this was easily the most heartening exhibition they had had since Ben Hogan fell upon evil ways during his heyday and scored an 11 in the Texas open.

From a baroque standpoint it is a moment of divine intervention in the affairs of man.

From an engineering and service standpoint, the Phoenix could be said to be a notable success.

From a monetary standpoint, governments control just how much money is in circulation worldwide, which plays an immense role on how money is spent in one's own country.

From the standpoint of an observer in an inertial frame, the effects can be explained as results of inertia without invoking the centrifugal force.

From a qualitative standpoint, the path can be approximated by an arc of a circle for a limited time, and for the limited time a particular radius of curvature applies, the centrifugal and Euler forces can be analyzed on the basis of circular motion with that radius.

From a rigorous theoretical standpoint, the expected value is the integral of the random variable with respect to its probability measure.

From a psychological standpoint, the ELIZA effect is the result of a subtle cognitive dissonance between the user's awareness of programming limitations and their behavior towards the output of the program.

Eppig, Fincher, and Thornhill ( 2009 ) argue that " From an energetics standpoint, a developing human will have difficulty building a brain and fighting off infectious diseases at the same time, as both are very metabolically costly tasks " and that " the Flynn effect may be caused in part by the decrease in the intensity of infectious diseases as nations develop.

From the standpoint of group theory, isomorphic groups have the same properties and need not be distinguished.

From a political standpoint, the Whig Party had been in decline in the South because of the effectiveness with which the Democrats had hammered Whigs over slavery issues.

From the Mings ' standpoint, the Portuguese were ultimately responsible for the massacre, since it was they who provoked the Chinese through " rapaciousness ".

From a geological standpoint, the Ohio River is young.

From Stroessner's standpoint, there were ominous similarities between Somoza and himself.

From this standpoint, Pantheism is the view that everything is part of an all-encompassing, immanent God.

From the standpoint of radiation protection, radiation is often separated into two categories, ionizing and non-ionizing, to denote the level of danger posed to humans.

From the standpoint of the doctrine of the Trinity — one Divine Being existing in three Persons — patripassianism is considered heretical because it denies the distinct personhood of the Members of the Trinity.

" From his standpoint, he could now threaten the entire Crusader coast.

From a military standpoint, historian John Keegan notes exaggerations and myths that surround Shaka, but nevertheless maintains:

For them, ' primitive ' denotes irrational use of resources and absence of the intellectual and moral standards of ' civilised ' human societies .... From the standpoint of anthropological knowledge, both these views are equally one-sided and simplistic.

From a rhetorician's standpoint, an effective scheme of omission that Poe employs is diazeugma, or using many verbs for one subject ; it omits pronouns.