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Note and associative
Note that while some authors may use the term " algebra " to describe a unital " associative algebra ", this will not be the case for this article.
Note: In this article, all algebras are assumed to be unital and associative.
A central simple algebra ( CSA ) over a field K is a finite-dimensional associative K-algebra A, which is a simple ring, and for which the center is exactly K. Note that CSAs are in general not division algebras, though CSAs can be used to classify division algebras.
Note that exponentiation is not associative, so evaluating the expression in the other order will lead to a different answer:

Note and property
Note that the color red is an objective property of an object.
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 that this is before the effects of round-off error are taken into account ; conditioning is a property of the matrix, not the algorithm or floating point accuracy of the computer used to solve the corresponding system.
Note that completeness is a property of the metric and not of the topology, meaning that a complete metric space can be homeomorphic to a non-complete one.
Note that bias is a property of the estimator, not of the estimate.
Note that, following the property of opposite category,.
Note that this property is itself positive, since it is the conjunction of the ( infinitely many ) positive properties.
Note that the bilinearity and alternating properties imply anticommutativity, i. e., for all elements x, y in, while anticommutativity only implies the alternating property if the field's characteristic is not 2.
Note that the Israeli application of the Immutability Doctrine does not distinguish between personal and real property.
Note that this is not just a property of the set S but one of the set S as subset of P.
Note that this is different from larceny which simply requires that property be taken from the victim ’ s possession, actual or constructive.
Note: historically, a legacy has referred to either a gift of real property or personal property.
Note that this is one of the chief differences between U. S. and EU approach towards Intellectual property rights up till the early 21st century, in that the crystallisation of this modern approach ( the Berne Convention for the Protection of Literary and Artistic Works ) is still only partially put in practice in the U. S., and, where applied, this is done largely outside the legislation regarding IP.
Note that the reference is to the shared Point and not to the SurveyMonument, since any feature object can have more than one geometry object property.
Note that this property holds only as long as other variables on which the intensive variable depends stay constant.
Note that you have to measure the amounts in the same unit that was used to calculate the intensive property from the extensive property.
The promised geometric property of reflexive Banach spaces is the following: if C is a closed non-empty convex subset of the reflexive space X, then for every x in X there exists a c in C such that || x − c || minimizes the distance between x and points of C. ( Note that while the minimal distance between x and C is uniquely defined by x, the point c is not.
Comment: Note that the Recoverability property is needed even if no database failure occurs and no database recovery from failure is needed.
Note that by the unique lifting property, if f is not the identity and C is path connected, then f has no fixed points.
Note that this property is local: there might exist other surfaces that minimize area better with the same global boundary.
Note that if property is falsely obtained for a specific purpose-for example money to buy a car that does not exist-the crime is larceny by trick rather than false pretenses because the victim intended to pass title to the money only upon completion of the transaction ; until such time the victim intended to deliver possession only.
A property called the relativistic mass is defined as the ratio of the momentum of an object to its velocity .< ref > Note that the relativistic mass, in contrast to the rest mass m < sub > 0 </ sub >, is not a relativistic invariant, and that the velocity is not a Minkowski four-vector, in contrast to the quantity, where is the differential of the proper time.

Note and does
Note that though the ideal gas itself contains no additional energy, the compressed gas does exert an increased pressure.
Note that chemists often write H < sup >+</ sup >( aq ) and refer to the hydrogen ion when describing acid-base reactions but the free hydrogen nucleus, a proton, does not exist alone in water, it exists as the hydronium ion, H < sub > 3 </ sub > O < sup >+</ sup >.
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: Botswana does not have a westernmost point as the western section is formed by the 22nd meridian of longitude east of Greenwich.
Note that traditional Berkeley DB also supports a Java API, but it does so via JNI and thus requires an installed native library.
* Note: technically Chad does not have an easternmost point, the northern section of the border being formed by the 24 ° of latitude
Note: in Greek, the term for " consul " is " ypatos ", which translates as " supreme one ", and hence does not necessarily imply a joint office.
Note that the validity of a conditional proof does not require that the CPA is actually true, only that if it is true it leads to the consequent.
Note that in many cases, digital cable telephone service is separate from cable modem service being offered by many cable companies and does not rely on Internet Protocol ( IP ) traffic or the Internet.
Note that this does not require 100 % awareness from the onset of the data warehousing effort, no master plan is required upfront.
Note that a dominatrix does not necessarily dominate a male partner ; a dominatrix may well have female submissives, nor must the role of a dominatrix involve pain toward the submissive ; her domination can be verbal, involving humiliating tasks and servitude.
( Note that anti-trust regulation does take into account cases when only large companies are viable because of the nature of an industry, but favors many participants over few, whenever possible.
Note that materialism does not necessarily imply egoism, as indicated by Karl Marx, and the many other materialists who espoused forms of collectivism.
( Note, chart does not include population statistics.
Note that this derivation does assume that ƒ ( x ) is sufficiently differentiable and well-behaved ; specifically, that ƒ may be approximated by polynomials ; equivalently, that ƒ is a real analytic function of exponential type.
Note that Reynolds does not object to the Marxist use of the term feudalism.
* * Note: Guinea does not have a northern-most point, this section of the border being formed by a straight horizontal line
* * Note: Guinea-Bissau does not have a northern-most point, the border here being formed by a straight horizontal line
Note that chair does not change form between " the chair is here " ( subject ) and " I saw the chair " ( direct object ), a distinction made by word order and context.
Note that ƒ cannot be extended to a homomorphism of rings ( from the complex numbers to the real numbers ), since it does not preserve addition:
Note that this " high temperature " approximation does not distinguish between fermions and bosons.
* * Note: Morocco does not have a southern-most point, the border being formed by a straight horizontal line
Note: In cases where the optical design of a microscope produces an appreciable lateral separation of the two beams we have the case of classical interference microscopy, which does not result in relief images, but can nevertheless be used for the quantitative determination of mass-thicknesses of microscopic objects.
( Note that while Mercury does allow impure functionality, it is not necessary in most software, and serves primarily as a way of calling foreign language code.

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