These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice.

These sets were expanded in 1963 to 7 bits of coding, called the American Standard Code for Information Interchange ( ASCII ) as the Federal Information Processing Standard which replaced the incompatible teleprinter codes in use by different branches of the U. S. government.

These cable sets have a transmitter board located in the computer, an expansion board in the remote backplane, and a cable between the two.

These sets are disjoint because P is a prefix-free set.

These sets have a more novel look, and the often heavier weight makes them feel more substantial, but such materials and the resulting products are usually much more expensive than polymer materials.

These sets are observer-independent.

These sets have ISO-8859-n as their preferred MIME name or, in cases where a preferred MIME name isn't specified, their canonical name.

These are also commonly found in most Filipino kitchens, with some sets displayed on the walls and other sets for more practical use.

These time-delayed fuses led from the cab of the truck, through plastic fish-tank tubing conduit, to two sets of non-electric blasting caps.

These linked sets of proteins are called electron transport chains.

These were avoided in PM by building an elaborate system of types: a set of elements is of a different type than is each of its elements ( a set is not an element ; one element is not the set ) and one cannot speak of the " set of all sets " and similar constructs, which would lead to paradoxes ( see Russell's paradox ).

These open sets with the operations of intersection and union form a lattice with certain properties.

These existed before the open-circuit sets and are still used, but less so than open-circuit sets.

These reprints collect the issues into different sets.

These subsets will be called the measurable sets.

These four come in two sets of two.

These deists, while maintaining individual positions, still shared several sets of assumptions and arguments that Paine articulated in The Age of Reason.

These coins were not included in the 2012 uncirculated sets or the three-coin ATB quarter sets ( which consisted of an uncirculated " P " and " D " and proof " S " specimen ) and no " S " mint-marked quarters are being released into circulation, so that mintages will be determined solely by direct demand for the " S " mint-marked coins.

These sets often included the 53 Dual Triode Audio Output.

These have three sets of paired chromosomes, three times as many as in diploid wheat.

These experts volunteer to serve on study committees that are convened to answer specific sets of questions.

These contain pages of " drill charts ", which often either give a picture or list coordinates that band members use to find ' pages ' or ' sets ' on the field.

These linear combinations are also known as Bessel functions of the third kind ; they are two linearly independent solutions of Bessel's differential equation.

These coordinates are a very special example of a more general concept of local coordinates from the theory of differential forms.

: These are similar to tunnel diodes in that they are made of materials such as GaAs or InP that exhibit a region of negative differential resistance.

These costs ( which can be a significant part of the entire plant costs ) involve the differential impact of the presence of drying equipment in a specific plant.

These same interpolation formulas nevertheless continue to be used as part of the software algorithms for solving differential equations.

These are extended objects that are charged sources for differential form generalizations of the vector potential electromagnetic field.

These differential equations have to be solved simultaneously, either analytically or numerically.

These conditions ensure that external noise affects each leg of the differential line equally and thus appears as a common mode signal that is removed by the receiver.

These two examples illustrate that general solutions of ordinary differential equations ( ODEs ) involve arbitrary constants, but solutions of PDEs involve arbitrary functions.

These are differential operators, except for potential energy V which is just a multiplicative factor.

These effects can be combined in a partial differential equation for the magnetic field called the magnetic induction equation:

These motorists are responsible for being duly careful around farm tractors and sharing the road with them, but many shirk this responsibility, so various ways to minimize the interaction or minimize the speed differential are employed where feasible.

These systems still have a differential, but it will not have attached axle housing tubes.

These included 3 additional oil coolers, revised ECU map, full Connelly leather interior, underbody diffusers, stiffer suspension, active rear limited slip differential, extra display feature on the in car display.

These classical equations are differential equations of motion for a test particle in the presence of a gravitational field, i. e. setting up and solving these equations allows the motion of a test mass to be determined and described.

These technologies include folding, inserted alloys, and differential hardening of the edge.

These equations are special cases of the Sturm – Liouville differential equation.

These may be manipulated to yield as second order linear differential equation in:

These are connected so that differential motion of the lines rotates the bellcrank, causing a pushrod to move either forward or aft.

These sense the air temperature using the differential expansion of two metals to actuate an on / off switch.

These results may also be derived by solving the differential equations describing the circuit:

These conditions can be local ( like demanding that the sections in the domain vanish at the boundary ) or more complicated global conditions ( like requiring that the sections in the domain solve some differential equation ).

These included number theory, algebras with involution, mathematical analysis, differential geometry and classical mechanics.

These are, however, important in connection with the study of semigroups that arise in partial differential equations, harmonic analysis, and probability theory.