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Page "Quadratic form" ¶ 8
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Note and quadratic
Note that because all matches are found, there can be a quadratic number of matches if every substring matches ( e. g. dictionary =,,, and input string is ).
Note that the LQ or LQR cost functional can be thought of physically as attempting to minimize the control energy ( measured as a quadratic form ).
Note that since is of degree 4, this conclusion could not have been established by only checking that has no rational roots ( which eliminates possible factors of degree 1 ), since a decomposition into two quadratic factors could also be possible.
Note that a process may be of finite quadratic variation in the sense of the definition given here and its paths be nonetheless a. s. of infinite quadratic variation for every t > 0 in the classical sense of taking the supremum of the sum over all partitions ; this is in particular the case for Brownian Motion.

Note and functions
Note that for any fixed w the function f ( x ) = F ( w x ) is computable ; thus the universality property states that all computable functions of one variable can be obtained in this fashion.
Note, however, that the representation is not complete on the set of square-integrable functions.
Note that different requirements apply to the other related concepts ( cryptographic hash functions, checksums, etc.
Note that continuity is usually considered a fatal flaw for checksums, cryptographic hash functions, and other related concepts.
Note that if you graph the functions the axes represent quantities.
Note that a sample of random variables ( i. e. a set of measurable functions ) must not be confused with the realizations of these variables ( which are the values that these random variables take, formally called random variates ).
Note: Link-level functions provide an interface between the station high-level logic and the data link.
Note: Net operations ( a ) allow participants to conduct ordered conferences among participants who usually have common information needs or related functions to perform, ( b ) are characterized by adherence to standard formats and procedures, and ( c ) are responsive to a common supervisory station, called the " net control station ", which permits access to the net and maintains net operational discipline.
Note that, by convention, sinh < sup > 2 </ sup > x means ( sinh x )< sup > 2 </ sup >, not sinh ( sinh x ), and similarly for the other hyperbolic functions when used with positive exponents.
Note that standalone ICDs do not have any pacemaker functions, but they can be combined with a pacemaker, and modern versions also have advanced features such as anti-tachycardic pacing as well as synchronized cardioversion.
Note that this notion of image may not correspond to the usual notion of image, or range, of a function, even assuming that the morphisms in the category are functions.
Note that although a function is always identified with its graph, they are not the same because it will happen that two functions with different codomain could have the same graph.
Note that many of these are operators which act on functions of the bound variable.
Note that we need two delta functions since there are two roots to
A functional defined on some appropriate space of functions with norm < ref group =" Note "> The dot in this norm expression is a placeholder for an element of V, e. g. .</ ref > is said to have a weak minimum at the function if there exists some such that, for all functions with < math >
Note that is at least n, since smaller functions are never time-constructible.
Note that elements of the Cantor space can be identified with sets of integers and elements of the Baire space with functions from integers to integers.
Note, however, that not all random variables have moment-generating functions.
Note: The functions are allowed to attain the value +∞ and the integrals may also be infinite.
Note that some of these functions are contrary to others.
Note that within the interval the polynomial nature of the basis functions and the linearity of the construction make the curve perfectly smooth, so it is only at the knots that discontinuity can arise.
Note also that the function A ( θ ) or equivalently g ( θ ) is automatically determined once the other functions have been chosen, and assumes a form that causes the distribution to be normalized ( sum or integrate to one over the entire domain ).
Note that, as in the above case of a scalar-valued parameter, the function or equivalently is automatically determined once the other functions have been chosen, so that the entire distribution is normalized.

Note and such
Note that this premise uses the phrase " is not ", a form of " to be "; this and many other examples show that he did not intend to abandon " to be " as such.
Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.
( Note that by designating cardinal directions for 1 ,-1,, and, complex numbers such as are considered constructible.
Note, however, that the fifth article did not completely deny perseverance of the saints ; Arminius, himself, said that " I never taught that a true believer can … fall away from the faith … yet I will not conceal, that there are passages of Scripture which seem to me to wear this aspect ; and those answers to them which I have been permitted to see, are not of such as kind as to approve themselves on all points to my understanding.
Note electrode naming for diodes is always based on the direction of the forward current ( that of the arrow, in which the current flows " most easily "), even for types such as Zener diodes or solar cells where the current of interest is the reverse current.
( Note that " offshoring " is not synonymous with " outsourcing ", which means " to subcontract from an outside supplier or source ", such as when a business outsources its bookkeeping to an accounting firm.
Note that the associative property does not hold for expressions that include non-linear operators, such as the antilinear time reversal operator in physics.
Note: it is reported in the scientific literature that some " shock " features, such as small shatter cones, which are often reported as being associated only with impact events, have been found in terrestrial volcanic ejecta.
* Some waterfowl, such as gulls, penguins, pelicans, storks, and herons ( Note, waterfowl is not being used in the taxonomic sense-e. g.
Note that such engines may not produce their full rated power using 87 octane gasoline under all circumstances due to the delayed ignition timing.
Note: electrode naming for diodes is always based on the direction of the forward current ( that of the arrow, in which the current flows " most easily "), even for types such as Zener diodes or solar cells where the current of interest is the reverse current.
In 1822, Charles Babbage proposed the use of such a machine in a paper to the Royal Astronomical Society on 14 June entitled " Note on the application of machinery to the computation of astronomical and mathematical tables ".
Note that congruences alter some properties, such as location and orientation, but leave others unchanged, like distance and angle s. The latter sort of properties are called invariant ( mathematics ) | invariant s and studying them is the essence of geometry.
Note that the electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together
Alice now discards three of her own cards, and replaces them with three from the top of the deck ( Note: in a player-dealt casino game there is often a rule that the dealer must discard before picking up the deck, but this is a home game so we won't worry about such details ).
Note: the various acronyms in this section are often combined in various ways, such as " TNLNSL, TFTC!
Note that the aspectual systems of certain dialects of English, such as African-American Vernacular English ( see for example habitual be ), and of creoles based on English vocabulary, such as Hawaiian Creole English, are quite different from those of standard English, and often distinguish aspect at the expense of tense.
Note that the ICF and ZAAP are essentially identical to CP, but distinguished for software cost control: they are slightly restricted such they cannot be used to run arbitrary operating systems, and thus do not count in software licensing costs ( which are typically based on the number of CPs ).
( Note: Some older operating systems may handle such values incorrectly ( i. e., signed instead of unsigned ), which would make it impossible to access files larger than 2 GB in size.
Note that while such perfect price discrimination is still a theoretical construct, it is becoming increasingly real with advances of information technology and micromarketing.
Note that these treatments need to be prescribed and monitored carefully to avoid harmful side-effects such as neuroleptic malignant syndrome with the antipsychotic medications.
Note that, although capitalization can aid in recognizing named entities in languages such as English, this information cannot aid in determining the type of named entity, and in any case is often inaccurate or insufficient.
Note that some languages have more such ambiguity than others.
Note that reporting the beliefs of others in a non-fiction format is not necessarily an endorsement of the ultimate veracity of those beliefs, it is simply saying it is true that people believe them ( for such topics as mythology, religion ).

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