Here ΔG is change in Gibbs free energy, T is absolute temperature, R is the gas constant and Q is reaction quotient.

Donald Hall goes as far as to say that " the form of free verse is as binding and as liberating as the form of a rondeau ," and T. S. Eliot wrote, " No verse is free for the man who wants to do a good job.

Precisely, we can systematically define a model of any consistent effective first-order theory T in PA by interpreting each symbol of T by an arithmetical formula whose free variables are the arguments of the symbol.

As KornShell was initially only available through a proprietary license from AT & T, a number of free and open source alternatives were created.

With the addition of an additional radio frequency pulse and additional manipulation of the magnetic gradients, a T < sub > 2 </ sub >- weighted sequence can be converted to a FLAIR sequence, in which free water is now dark, but edematous tissues remain bright.

The five free tetrominos, top to bottom I, O, Z, T, L, marked with light and dark squares.

Dubbed OSF / 1, the aim was to compete with System V Release 4 from AT & T and Sun Microsystems, and it has been argued that a primary goal was for the operating system to be free of AT & T intellectual property.

For processes involving a system at constant pressure p and temperature T, the Gibbs free energy is the most useful because, in addition to subsuming any entropy change due merely to heat, it does the same for the pdV work needed to " make space for additional molecules " produced by various processes.

The historically earlier Helmholtz free energy is defined as F = U − TS, where U is the internal energy, T is the absolute temperature, and S is the entropy.

Kalamazoo is the hometown of New York Yankees all-star shortstop Derek Jeter, Green Bay Packers wide receiver Greg Jennings, and free agent running back T. J. Duckett.

At high temperatures ( T > Θ ) the mean free path and therefore λ < sub > L </ sub > has a temperature dependence T < sup >− 1 </ sup >, to which one arrives from formula by making the following approximation < math >

where G is the Gibb's free energy, S is the entropy, V is the system volume, P is its pressure and T is its absolute temperature.

I. H. O. T. F. M .- Man is an ardent defender of Adam Smith's invisible hand metaphor, and usually intervenes in situations where the purity of free market economics is in jeopardy.

A history of free trade in Great Britain, London: T. Fisher Unwin.

* Only a freeman ( not even a slave who will become free in the next month ) can be a Ba ' al T ' qiah.

So, a collection of functions with given signatures generate a free algebra, the term algebra T. Given a set of equational identities ( the axioms ), one may consider their symmetric, transitive closure E. The quotient algebra T / E is then the algebraic structure or variety.

, the city began experimenting with a free shuttle bus service named S. C. O. O. T to help with transportation difficulties for those living in the hills of the town, and especially to make up for a lack of school buses.

This colony – the National Colony – was to be a village of temperance with a capital “ T ”, a place where evangelical Methodists, Presbyterians, Congregationalists and Baptists could live free of the sins of alcohol.

Other variable stars are U Camelopardalis, VZ Camelopardalis, and Mira variables T Camelopardalis, X Camelopardalis, and R Camelopardalis.

In the catenary the value of T is variable, but ratio remains valid at a local level, so

T Leporis is also a Mira variable observed in detail by ESO's Very Large Telescope Interferometer.

The continuous signal varies over time ( or space in a digitized image, or another independent variable in some other application ) and the sampling process is performed by measuring the continuous signal's value every T units of time ( or space ), which is called the sampling interval.

T is valid in any reflexive frame: if, then since w R w. On the other hand, a frame which validates T has to be reflexive: fix w ∈ W, and define satisfaction of a propositional variable p as follows: if and only if w R u.

More formally, a multivariate random variable is a column vector X = ( X < sub > 1 </ sub >, ..., X < sub > n </ sub >)< sup > T </ sup > ( or its transpose, which is a row vector ) whose components are scalar-valued random variables on the same probability space ( Ω,, P ), where Ω is the sample space, is the sigma-algebra ( the collection of all events ), and P is the probability measure ( a function returning every event's probability ).

The rows correspond to the dimensions, and t, and the columns to the dimensional variables D, T, V. For instance, the 3rd column, ( 1, − 1 ), states that the V ( velocity ) variable has units of.

( The rows correspond to the dimensions t, m, and l, and the columns to the dimensional variables T, M, L and g. For instance, the 4th column, (− 2, 0, 1 ), states that the g variable has units of.

that we may and do choose the value of ε so that the potential V < sub > T </ sub > is equal to V < sub > S </ sub > plus a constant independent of the variable Δd.

where ε is a real variable indicating the amount of flow, and T is a real constant ( which could be zero ) indicating how much the flow shifts time.

The T variable in the I = PAT equation represents how resource intensive the production of affluence is ; how much environmental impact is involved in creating, transporting and disposing of the goods, services and amenities used.

The formal semantics of such atoms is defined given a database db over S and a tuple variable binding val: V -> T < sub > D </ sub > that maps tuple variables to tuples over the domain in S:

T Tauri stars ( TTS ) are a class of variable stars named after their prototype – T Tauri.

That ’ s because the change in the free energy function A ( T, V ) equals the work done during a reversible process the free energy function being a state variable should take on a unique value regardless of path.

LSI + 61 ° 303 is a variable radio source characterized by periodic, non-thermal radio outbursts with a period of 26. 496 d. The 26. 5 d period has been attributed to the eccentric orbital motion of a compact object, probably a neutron star, around a rapidly rotating B0 Ve star, with a T < sub > eff </ sub > ~ 26, 000 K and luminosity of 10 < sup > 31 </ sup > watts ( 10 < sup > 38 </ sup > erg s < sup >− 1 </ sup >).

T Indi is the only bright variable star in Indus.

The T cell receptor ( TCR ) consists of both constant and variable regions.

The variable region determines what antigen the T cell can respond to.

Let the coin tosses be represented by a sequence of independent random variables, each of which is equal to H with probability p, and T with probability Let N be time of appearance of the first H ; in other words,, and If the coin never shows H, we write N is itself a random variable because it depends on the random outcomes of the coin tosses.

Directly across from the Gardens I found a bus stop sign for T 4 and rode it down to the Bosphorus, with the sports center on my left just before I reached the water and the entrance to Dolmabahce Palace immediately after that.

He also bought a huge square of pegboard for hanging up his tools, and lumber for his workbench, sandpaper and glue and assorted nails, levels and T squares and plumb lines and several gadgets that he had no idea how to use or what they were for.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

The lines are asymmetric and over the range of field Af gauss and temperature Af the asymmetry increases with increasing Af and decreasing T.

We are trying to study a linear operator T on the finite-dimensional space V, by decomposing T into a direct sum of operators which are in some sense elementary.

We can do this through the characteristic values and vectors of T in certain special cases, i.e., when the minimal polynomial for T factors over the scalar field F into a product of distinct monic polynomials of degree 1.

If we try to study T using characteristic values, we are confronted with two problems.

Second, even if the characteristic polynomial factors completely over F into a product of polynomials of degree 1, there may not be enough characteristic vectors for T to span the space V.

This is clearly a deficiency in T.

The second situation is illustrated by the operator T on Af ( F any field ) represented in the standard basis by Af.

The characteristic polynomial for A is Af and this is plainly also the minimal polynomial for A ( or for T ).

Thus T is not diagonalizable.

If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

( C ) if Af is the operator induced on Af by T, then the minimal polynomial for Af is Af.

It is certainly clear that the subspaces Af are invariant under T.

If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.