Note that arrows between categories are called functors, subject to specific defining commutativity conditions ; moreover, categorical diagrams and sequences can be defined as functors ( viz.

Note that the axioms are given in terms of the maps ( binary product, unary inverse, and nullary identity ), hence are categorical definitions.

Note also that Peirce held that all deduction can be put into the form of the categorical syllogism Barbara ( AAA ).

Note also that the probability is proportional to the resulting value ; the actual probability must be determined by normalizing across all the possible values that the categorical variable can take ( i. e. adding up the computed result for each possible value of the categorical variable, and dividing all the computed results by this sum ).

Note that, in some fields, such as natural language processing, the categorical and multinomial distributions are conflated, and it is common to speak of a " multinomial distribution " when a categorical distribution is actually meant.

( Note that in many fields, such as in natural language processing, categorical variables are often imprecisely called " multinomial variables ".

Note: This list is limited to linguists who have worked specifically on the Altaic problem since the publication of the first volume of Ramstedt's Einführung in 1952.

Note that quite a few of the plants that were once included in family Alliaceae have been assigned to the subfamily Brodiaeoideae ( rather than the subfamily Allioideae ).

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 that this pressure increase is more than a simple 10: 1 compression ratio would indicate ; this is because the gas is not only compressed, but the work done to compress the gas has also heated the gas and the hotter gas will have a greater pressure even if the volume had not changed.

Note that the officials have one eye, a sign of Odin.

Note the forward wings have not been installed yet ( 2003 )

* Note: Botswana does not have a westernmost point as the western section is formed by the 22nd meridian of longitude east of Greenwich.

* Note: technically Chad does not have an easternmost point, the northern section of the border being formed by the 24 ° of latitude

) Note that the same set of points would not have, as an accumulation point, any point of the open unit interval ; hence that space cannot be compact.

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.

These polar unit vectors can be expressed in terms of Cartesian unit vectors in the x and y directions, denoted i and j respectively :< ref > Note: unlike the Cartesian unit vectors i and j, which are constant, in polar coordinates the direction of the unit vectors u < sub > r </ sub > and u < sub > θ </ sub > depend on θ, and so in general have non-zero time derivatives .</ ref >

Note the changes in subpixel intensity that are used to increase effective resolution when ClearType is enabled — without ClearType, all sub-pixels of a given pixel have the same intensity.

Note that the so-called Kinshasa Highway is not a physical road but a metaphor applied to the route by which AIDS is believed to have been spread east through Uganda and Kenya and neighbouring countries by truck drivers from the Congo.

( Note that, technically, Wisda's damages would be the lost profits only — if Wisda would have had $ 35 per hour in wages, materials and other expenses, its actual damages are only $ 15 per hour

Note: This study only involved male subjects which may be significant as sex steroids may have different effects in the responses to cortisol administration.

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: Many of the essays found in these works have been individually translated and can be found in the English collections.

By Rule 1. 04, Note ( a ), all parks built after 1958 have been required to have foul lines at least long and a center-field fence at least from home plate.

Note: the fasces depicted have no axes, possibly because in the Roman Republic, the blade was always removed from the bundle whenever the fasces were carried inside the city, in order to symbolize the rights of citizens against arbitrary state power ( see above ).

* * 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 with this definition, two elements a and b may very well have several greatest common divisors, or none at all.

Note that not all worlds have the same objects: some objects exist in some worlds and not in others.

Note that due to the reduced number of colors in the image, there are obvious display issues. GIF is palette-based: the colors used in an image ( a frame ) in the file have their RGB values defined in a palette table that can hold up to 256 entries, and the data for the image refer to the colors by their indexes ( 0 – 255 ) in the palette table.

* Historia Augusta, The Life of Antoninus Pius, English version of Historia Augusta Note that the Historia Augusta includes pseudohistorical elements.

Note that the first element in a sequence has the index one and that $ refers to the length ( i. e. total number of elements ) of the sequence.

Note that the end tag's name is preceded by a slash character, "/", and that in empty elements the end tag is neither required nor allowed.

Note that the operators operate on elements from the domain and range, respectively, of the " one-to-one " and " onto " function ƒ.

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 this does not restrict dormant forms of life to these environments, so this argument only contradicts the widest interpretation of panspermia — that life is ongoing and is spread across many different environments throughout the Universe — and presupposes that any life needs those elements, which the proponents of alternative biochemistries do not consider certain.

Note that in this vector dotted with Pauli vector operation the Pauli matrices are treated in a scalar like fashion, commuting with the vector basis elements.

Note that many of the common polyatomic anions are conjugate bases of acids derived from the oxides of non-metallic elements.

Note that elements up to E118 have now been experimentally produced and that there are chemical studies on an increasing number of them.

Note: The principal applications of off-axis optical systems are to avoid obstruction of the primary aperture by secondary optical elements, instrument packages, or sensors, and to provide ready access to instrument packages or sensors at the focus.

Note 1: The PCS switching center represents a collection of one or more network elements.

Note that only the 253 have any claim to stability, but that only 90 nuclides from the first 40 elements are theoretically stable to any process but proton decay.

Note that all elements are written in their standard states, and one mole of product is formed.

Note that this is stated in terms of maps – product and inverse must be maps in the category – and without any reference to underlying " elements " of group – categories in general do not have elements to their objects.

Note: Work function can change for crystalline elements based upon the orientation.

Note for completeness that condition ( 1 ) fails: any map t: B → A must map every two-cycle to the identity because the map has to be a group homomorphism, while the order of a two-cycle is 2 which can not be divided by the order of the elements in A other than the identity element, which is 3 as A is the alternating subgroup of, or namely the cyclic group of order 3.

Note that an iterator performs traversal and also gives access to data elements in a container, but does not perform iteration ( i. e., not without some significant liberty taken with that concept or with trivial use of the terminology ).

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 that while both the elements of the Cantor space ( regarded as sets of integers ) and subsets of the Cantor space are classified in arithmetic hierarchies but these are not the same hierarchy.

Note that not every relation which is not reflexive is irreflexive ; it is possible to define relations where some elements are related to themselves but others are not related to themselves ( i. e., neither all nor none ).

Note that although bulk materials differentiate outward or inward according to their density, the elements that are chemically bound in them fractionate according to their chemical affinities, " carried along " by more abundant materials that they're associated with.