For inhomogeneous systems the enthalpy is the sum of the enthalpies of the composing subsystems

For linear, homogeneous, isotropic materials E and D are proportional and constant throughout the region, there is no position dependence: For inhomogeneous materials, there is a position dependence throughout the material:

For an instrument whose payment stream is described by f ( t ), the value V ( t ) satisfies the inhomogeneous first-order ODE (" inhomogeneous " is because one has f rather than 0, and " first-order " is because one has first derivatives but no higher derivatives ) – this encodes the fact that when any cash flow occurs, the value of the instrument changes by the value of the cash flow ( if you receive a $ 10 coupon, the remaining value decreases by exactly $ 10 ).

For example in mathematical physics, the homogeneous equation may correspond to a physical theory formulated in empty space, while the inhomogeneous equation asks for more ' realistic ' solutions with some matter, or charged particles.

For this reason, the Lorentz group is sometimes called the homogeneous Lorentz group while the Poincaré group is sometimes called the inhomogeneous Lorentz group.

For n ≥ 0, let C < sup > n </ sup >( G, M ) be the group of all functions from G < sup > n </ sup > to M. This is an abelian group ; its elements are called the ( inhomogeneous ) n-cochains.

For the inhomogeneous case, we can use integrating factors ( a method akin to variation of parameters ).

For first-order inhomogeneous linear differential equations it is usually possible to find solutions via integrating factors or undetermined coefficients with considerably less effort, although those methods leverage heuristics that involve guessing and don't work for all inhomogenous linear differential equations.

For technical reasons, it is often preferable to introduce some sort of inhomogeneous term and to study maps satisfying the perturbed Cauchy – Riemann equation

For anisotropic multicomponent diffusion coefficients one needs 4-index quantities, for example,, where i, j are related to the components and α, β = 1, 2, 3 correspond to the space coordinates.

For anisotropic materials the E and D fields are not parallel, and so E and D are related by the permittivity tensor ( a 2nd order tensor field ), in component form:

For the anisotropic material, it requires the mathematics of a second order tensor and up to 21 material property constants.

For an anisotropic material, the individual resistivity components, e. g. ρ < sub > x </ sub > or ρ < sub > y </ sub >, can be calculated using the Montgomery method.

For non-isotropic ( anisotropic ) coatings, the optimal coating depends on the shape of the target and the radar direction, but duality, the symmetry of Maxwell's equations between the electric and magnetic fields, tells one that optimal coatings have η < sub > 0 </ sub > × η < sub > 1 </ sub > = 377 < sup > 2 </ sup > Ω < sup > 2 </ sup >, where η < sub > 0 </ sub > and η < sub > 1 </ sub > are perpendicular components of the anisotropic surface impedance, aligned with edges and / or the radar direction.

For an anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law.

For anisotropic filtering, Radeon 8500 uses a technique similar to that used in R100, but improved with trilinear filtering and some other refinements.

For a time-independent interaction, i. e. heteronuclear dipolar couplings, CSA and first-order quadrupolar couplings, the anisotropic component is greatly reduced and almost suppressed in the limit of fast spinning, i. e. when the spinning frequency is greater than the breadth of the interaction.

For instance, Forbes ranked media mogul and talk show host, Oprah Winfrey as the top earner " Forbes magazine ’ s annual ranking of the most powerful celebrities ", with earnings of $ 290 million in the past year.

For penetration on a significant scale the media themselves must be captured by the dominating / penetrating power.

For security, the AMS used a media block type system that placed a sealed electronics package within the projector console.

For example, in the 1990s and 2000s, the United States media contained stories of adolescents and young adults dying or becoming seriously ill from intentionally ingesting Datura.

For example, Graffiti Research Lab has encouraged the use of projected images and magnetic light-emitting diodes as new media for graffiti writers.

For instance, Fidesz loyalists occupy councils in charge of the media, judiciary, and budget for nine-year terms.

For example, DUKTIG ( meaning: good, well-behaved ) is a line of children's toys, OSLO is a name of a bed, BILLY ( a Swedish masculine name ) is a popular bookcase, DINERA ( meaning: ( to ) dine ) for tableware, KASSETT ( meaning: cassette ) for media storage.

For example, the free software such as InfraRecorder and mkisofs as well as Roxio Toast are able to create ISO 9660 filesystems that use multi-extent files to store files larger than 4 GB on appropriate media such as recordable DVDs.

For example, when five American soldiers accidentally burned several copies of Quran at nearby Bagram Airfield in February 2012, politicians in Kabul showed their personal anger in the media.

For example, the deaths of millions of people in an ethnic conflict in Africa might be afforded scant mention in American media, while the shooting of five people in a high school is analyzed in depth.

For this reason, many mass media outlets have a presence on the web, by such things as having TV ads that link to a website, or having games in their sites to entice gamers to visit their website.

Kinnock himself later claimed to have half-expected his defeat in the 1992 election and proceeded to turn himself into a media personality, even hosting a chat show on BBC Wales and twice appearing – with considerable success – on the topical panel show Have I Got News For You within a year of the defeat.

For decades, the majority of science fiction media fandom has been represented by males of all ages and for most of its modern existence, a fairly diverse racial demographic.

For example, in the 1930s, muzak was among the earliest popularly available streaming media ; nowadays Internet television is a common form of streamed media.

For example the Berlin Philharmonic Orchestra sells internet live streams of whole concerts, instead of several CDs or similar fixed media, by their so-called " Digital Concert Hall " using YouTube for " trailing " purposes only.

For more information about support in software media players look at comparison of media players.

For non-linear media, E and D are not proportional.

For those media in which the amplitudes are unchanged but a differential phase delay occurs, the Jones matrix is unitary, while those affecting amplitude without phase have Hermitian Jones matrices.

For example, the transmission medium for sound received by the ears is usually air, but solids and liquids may also act as transmission media for sound.

For telecommunications purposes in the United States, Federal Standard 1037C, transmission media are classified as one of the following:

For the season, Carey averaged 7 marks, 18 disposals and 2. 6 goals per game, led the league in marks and contested marks and took out a host of individual awards from the media and Players ' Association as the seasons best player.

* 2012: Staff of The Tuscaloosa News, " For its enterprising coverage of a deadly tornado, using social media as well as traditional reporting to provide real-time updates, help locate missing people and produce in-depth print accounts even after power disruption forced the paper to publish at another plant 50 miles away.

For these centers, too, are on the gold circuit.

For the present it is enough to note that in the grotesque figure of Jacoby, at the moment of his collapse, all these elements come together in prophetic parody.

William Wimsatt and Cleanth Brooks, it seems to me, have a penetrating insight into the way in which this control is effected: `` For if we say poetry is to talk of beauty and love ( and yet not aim at exciting erotic emotion or even an emotion of Platonic esteem ) and if it is to talk of anger and murder ( and yet not aim at arousing anger and indignation ) -- then it may be that the poetic way of dealing with these emotions will not be any kind of intensification, compounding, or magnification, or any direct assault upon the affections at all.

For years the United States had been trying to get these countries to exclude Castro's representative from secret military talks.

For, granting that there are great present-day problems to be solved, these problems make great demands ; ;

For example, the Chamber of Commerce of Gatlinburg, Tennessee, sponsors special camera tours into the Great Smoky Mountains to get pictures of the profusion of wild flowers flourishing in these wooded regions.

For some unusual photographic subjects, if your vacation takes you nearby, try these events: the 600-mile auto race in Charlotte, N.C.,, on May 27 ; ;

For me, these will belong more completely to their surroundings if they are conceived in this early stage, though I freely admit that I do not hesitate to add or eliminate figures on the full sheet when it serves my final purpose.

For many of these measurements the chest must be opened, but the blood vessels and the heart itself remain undisturbed.

For prevention of these diseases during periods of stress such as shipping, excessive handling, vaccination, extreme weather conditions: 350 milligrams per head per day for 30 days only.

For long hauls these shipments should be protected with water-proof paper.

( 3 ) For anionics, these micelles appear to be roughly spherical assemblages in which the hydrocarbon tails come together so that the polar groups ( the ionized ends ) face outward towards the aqueous continuous phase.

For the interpretation of these significant investigations, it should be remembered that reciprocal relations exist in the hypothalamus with respect to autonomic and somatic functions which are closely associated with the emotions.

For any such square the middle corner of these will be called the vertex of the square and the corner not on the curve will be called the diagonal point of the square.

For the vertex at Af, these values will be denoted by Af.

For each of these lines meets Q in three points, namely two points on **zg and one point on one of the multiple secants.

For Yokuts, I tabulated these 71 items in five columns, according as they were expressed by 1, 2, 3, 4, and more than 4 stems.

For the purposes of this discussion, the problem of relative prices is encompassed in these two variables, since GNP includes other prices.

For a statement of costs per kilowatt-hour would ignore the fact that many of these costs are not a function of kilowatt-hour output ( or consumption ) of energy.

For these crimes he was sentenced to be hanged in public on Friday, December 2, 1859.

For all these points he relies exclusively on Berle and Means's study of 1932, The Modern Corporation And Private Property.

For a chemical process the first of these might involve the concentrations of the different chemical species, and the temperature or pressure of the stream.

`` For these and other reasons '', says Dr. Brodie, `` orthodontics can prolong the life of teeth ''.

For many of these unwed mothers, the data on their family life and early childhood experiences revealed several indications and sources of their basic mistrust of their parents in particular and of the world in general.

For almost one-sixth of the national population discrimination in the free selection of residence casts a considerable shadow upon these values assumed as self-evident by most Americans.