Note that flexural strength is not always improved by simply increasing the density, nor is the change always proportional from one formulation to another.

Note that Q ( x, y ) is simply replaced by.

Note that from the perspective of the smaller-mass object — from the moon, in the preceding example — a spacecraft might appear to orbit in an irregular path about the or point, but from the perspective above the orbital plane, it becomes clear that both the smaller mass and the spacecraft are orbiting the larger mass ( or more precisely, all of the objects are in orbit around the barycenter of the system ); they simply have overlapping orbital paths.

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 ).

Note that most of these verses do not distinguish between the conditional election ( Arminian ) and unconditional election ( Calvinist ), but are simply evidence of some type of election.

Note that because the meaning of binary messages is not hardwired into Smalltalk-80 syntax, all of them are considered to have equal precedence and are evaluated simply from left to right.

Note, however, that a language wishing to index arrays from 1 could simply adopt the convention that every " array address " is represented by a ′ = a – s ; that is, rather than using the address of the first array element, such a language would use the address of an imaginary element located immediately before the first actual element.

Note that searing in no way " locks in " moisture: moisture loss is simply a function of heat and time.

Note that this is different from larceny which simply requires that property be taken from the victim ’ s possession, actual or constructive.

Note that " sweetheart " could also be simply " wee " or the letter " E ", that is, the " heart " ( middle ) of " sweet ".

Note however that the existence of f has to be assumed from the start ; two objects B and B ′ that simply have isomorphic sub-and factor objects need not themselves be isomorphic ( for example, in the category of abelian groups, B could be the cyclic group of order four and B ′ the Klein four-group ).

A principal fractional ideal is one of the form for some nonzero x in K. Note that each principal fractional ideal is invertible, the inverse of being simply.

( Note that Aristotle's actual infinity means simply an actualization of something never-ending in nature, when in contrast the Cantorist actual infinity means the transfinite cardinal and ordinal numbers, that have nothing to do with the things in nature ):

Note, however, that many people with low self-esteem will not be able to improve their view of themselves simply by receiving fame, respect, and glory externally, but must first accept themselves internally.

Note that no money enters or leaves the combined system of endowment principal + accumulated annuity payments, and thus the future value of this system can be computed simply via the future value formula:

Note that the denominator is simply the measure of the set X ( However, this formula cannot be applied if the set X has zero measure, or if either integral diverges.

( Note that Philosophy of Natural Magic: Complete Work on Natural Magic, White & Black Magic, 1569, ISBN 1-56459-160-3, is simply book 1 of De occulta philosophia libri tres.

Note that this definition of entropy can even be viewed as equivalent to the previous one ( unknown information ) if we take a meta-perspective, and say that for observer A to " know " the state of system B means simply that there is a definite correlation between the state of observer A and the state of system B ; this correlation could thus be used by a meta-observer ( that is, whoever is discussing the overall situation regarding A's state of knowledge about B ) to compress his own description of the joint system AB.

Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors ; e. g. 60 = 2 < sup > 2 </ sup > × 3 × 5 has exactly 3 prime factors, but is not sphenic.

( Note that the energy is already being generated elsewhere to provide the high initial gas pressure-this method simply distributes the energy via a different route.

Note that the difference between halfback and tailback is simply the position of the player in the team's offensive formation.

Note: most of the musical is sung, however not all the parts that are sung are titled songs some are simply sung-through scenes with minor amounts of dialogue.

Note that, commonly, 2 < sup > ω </ sup > is referred to simply as the Cantor set, while the term Cantor space is reserved for the more general construction of D < sup > S </ sup > for a finite set D and a set S which might be finite, countable or possibly uncountable.

Note that " logical effort " does not take the load into account and hence we have the term " electrical effort " which takes the load into account. The stage effort is then simply:

Note that the common methods of cooking food do not sterilize food-they simply reduce the number of disease-causing micro-organisms to a level that is not dangerous for people with normal digestive and immune systems.

( Note how strongly the upper lats and serratus are worked in this fine exercise because of the pin-point concentration of force which the dumbbell variation affords ).

Note also that if Af, then Af is divisible by the polynomial p, because Af contains each Af as a factor.

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 most ancient Roman sources are quite critical of Agrippina the Younger, because she was seen as stepping outside the conservative Roman ideals regarding the roles of women in society.

Note: because Solar System bodies are never perfect diffuse reflectors, astronomers use empirically derived relationships to predict apparent magnitudes when accuracy is required.

Note that, because a name translated to an address, which included a socket number as well as a node number, a name in AppleTalk mapped directly to a service being provided by a machine, which was entirely separate from the name of the machine itself.

Note that the 64x16 TRS-80 mode screen uses only a small part of the monitor screen, because the letters are the same size as the 80 × 25 CP / M screen, this was one of the things that was soon after fixed with the redesign to a commercial product

Note that this expression is not well-defined for all time series or processes, because the variance may be zero ( for a constant process ) or infinite.

Note that just because a player is described as being " at bat " in this sense, he will not necessarily be given an at bat in his statistics ; the phrase actually signifies a plate appearance ( assuming it is eventually completed ).

Note that if we regard the product as a vector space, then B is not a linear transformation of vector spaces ( unless or ) because, for example.

The subgroup of generated by all commutators is called the derived group or the commutator subgroup of G. Note that one must consider the subgroup generated by the set of commutators because in general the set of commutators is not closed under the group operation.

Note however that working with the current two form itself and the exterior derivative is usually easier than working with the vector field and divergence, because unlike the divergence, the exterior derivative commutes with a change of ( curvilinear ) coordinate system.

( 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 because of historical accident, students encounter a source of possible confusion between the terminology of physics and biology.

Note that because of historical accident, students encounter a possible source of confusion between the terminology of physics and biology.

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 that we have omitted the Π < sub > j </ sub > n < sub > j </ sub > term, because each single-particle state can appear only once in a fermionic state.

Note that the dipole – dipole interaction between two atoms is usually zero, because atoms rarely carry a permanent dipole.

Note that the terms < tt > x </ tt > and < tt > y </ tt > aren't alpha-equivalent, because they are not bound in a lambda abstraction.

Note: while the 741 was historically used in audio and other sensitive equipment, such use is now rare because of the improved noise performance of more modern op-amps.

Note that bluffs can be especially powerful in high-low split games, because a player making a successful bluff wins the whole pot rather than having to share it.

Note that pot odds do not matter in this situation, because the factor here is whether it is more profitable to raise or call, rather than to call or fold.

( Note that ( f-y ) and ( y-f ) produce the same result because it is squared.

( Note that in SQL the heading is not always a set of column definitions as described above, because it is possible for a column to have no name and also for two or more columns to have the same name.

Note that this concealment is often preferably outdoors, because firing an RPG within an enclosed area may create a dangerous backblast.