Instead of also using E < sub > a </ sub >, however, the Eyring equation uses the concept of Gibbs free energy and the symbol * to denote the energy of the transition state.

Instead of describing a process which can only evolve in one way ( as in the case, for example, of solutions of an ordinary differential equation ), in a stochastic or random process there is some indeterminacy: even if the initial condition ( or starting point ) is known, there are several ( often infinitely many ) directions in which the process may evolve.

Instead, the rate equation may be more accurately described using steady-state kinetics.

In general, a pricing model function, f, does not have a closed-form solution for its inverse, g. Instead, a root finding technique is used to solve the equation:

Instead of dealing with only one possible reality of how the process might evolve under time ( as is the case, for example, for solutions of an ordinary differential equation ), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions.

Instead, p can be computed in the log domain by rewriting the original equation as follows:

Instead of the Boltzmann equation, the following system of equations was proposed for description of charged components of plasma ( electrons and positive ions ):

Instead of fixing the gauge by constraining the gauge field a priori via an auxiliary equation, one adds to the " physical " ( gauge invariant ) Lagrangian a gauge breaking term

Instead, this equation, in context, means only that when any energy is added to, or escapes from, a system in the center-of-momentum frame, the system will be measured as having gained or lost mass, in proportion to energy added or removed.

Instead, the entirety of the charge of the conductor resides on the surface, and can be expressed by the equation:

Instead of giving themselves spontaneously to the orgiastic release that jazz can give them, they undergo psychoanalysis or flirt with mysticism or turn to prostitutes for satisfaction.

Instead of closing the house in first ( as most builders do ) you can now cut your costs by not closing it in until you have to ( see p 121 ).

Instead, the audience can sit back at ease and, from the perspective of an enlightened time which no longer believes in such things, enjoy the dead seriousness with which the characters in the play take the witches and devils which are under discussion.

Instead of her old confidence in the simplest, purest, most moving musical expression, Miss Schwarzkopf is letting herself be tempted by the classic sin of artistic pride -- that subtle vanity that sometimes misleads a great artist into thinking that he or she can somehow better the music by bringing to it something extra, some personal dramatic touch imposed from the outside.

Instead, they can agree that certain paradigms should be treated in certain ways, and then agree on the similarities, the so-called warrants between a paradigm and the case at hand.

Instead of listing every single element, sometimes an ellipsis ("...") is used, if the writer believes that the reader can easily guess what is missing ; for example, presumably denotes the set of integers from 1 to 100.

Instead of conductivity, a reciprocal quantity called resistivity ρ, can be used:

Instead, a very vivid feeling can form.

Instead, with the topology of compact convergence, C ( a, b ) can be given the structure of a Fréchet space: a locally convex topological vector space whose topology can be induced by a complete translation-invariant metric.

Instead the broadcast can use the channel to include PSIP and can also subdivide across several video subchannels ( aka feeds ) of varying quality and compression rates, including non-video datacasting services that allow one-way high-bandwidth streaming of data to computers like National Datacast.

Instead of enabling the guest operating system to dialog with hardware, virtual device drivers take the opposite role and emulate a piece of hardware, so that the guest operating system and its drivers running inside a virtual machine can have the illusion of accessing real hardware.

Instead, India launched EDUSAT, an education satellite that can reach more of the country at a greatly reduced cost.

Instead, education officials across the world believe that by setting clear, achievable, higher standards, aligning the curriculum, and assessing outcomes, learning can be increased for all students, and more students can succeed than the 50 percent who are defined to be above or below grade level by norm referenced standards.

Instead the differentiation process is studied using E. invadens, a reptilian parasite that causes a very simiilar disease to E. histolytica and which can be induced to encyst in vitro.

Instead of directly modifying an FFT algorithm for these cases, DCTs / DSTs can also be computed via FFTs of real data combined with O ( N ) pre / post processing.

Instead of stacking the PC and CC registers ( normal 6809 behavior ) the FIRQ interrupt can be set to stack the entire register set, as the IRQ interrupt does.

Instead of importing a factor of production, a country can import goods that make intensive use of that factor of production and thus embody it.

Instead of considering the inverses for individual inputs and outputs, one can think of the function as sending the whole set of inputs, the domain, to a set of outputs, the range.

Instead of having to carry around hundreds of CD-Gs or laserdiscs, KJs can " rip " their entire libraries onto their hard drives and play the songs and lyrics from the computer.

Instead of a tuilik, most traditional kayakers today use a spraydeck made of waterproof synthetic material stretchy enough to fit tightly around the cockpit rim and body of the kayaker, and which can be released rapidly from the cockpit to permit easy exit.

Instead, for him, the idea of an " infectious idea " can be a useful conceit if used under certain conditions.

Instead of picking up a newspaper, or watching the 10 o ' clock news, people can log onto the internet to get the news they want, when they want it.

Instead of emotional recrimination, loaded phrases and sloganeering, we need a dispassionate study of the facts, a better understanding of the opposite viewpoint and a more serious effort to extend the areas of agreement until a solution is reached.

Instead of the expected `` annoyances '' due to the nature of his mission, he received many calling cards and invitations from `` gentlemen of mark, on whom I had no sort of claim, & have had many more invitations than I could accept ''.

Instead many Canadian companies have focused their exploration and expansion activities overseas where prices are lower and governments more accommodating.

Instead The Far Side used a wide variety of characters including humans, monsters, aliens, chickens, cows, worms, amoebas and more.

Instead of focusing merely on the individual objects ( e. g., groups ) possessing a given structure, category theory emphasizes the morphisms – the structure-preserving mappings – between these objects ; by studying these morphisms, we are able to learn more about the structure of the objects.

Instead of attempting to defend all of southern China, Li ordered what remained of the Nationalist armies to withdraw to Guangxi and Guangdong, hoping that he could concentrate all available defenses on this smaller, and more easily defensible, area.

Instead, the aim is to create room for critical thinking and more inclusive understanding of the past and conceptions of “ the other .”

One critic states of psychologists that " Instead of replacing ' metaphysical ' terms such as ' desire ' and ' purpose ', they used it to legitimize them by giving them operational definitions ... the initial, quite radical operationalist ideas eventually came to serve as little more than a ' reassurance fetish ' ( Koch 1992 ) for mainstream methodological practice.

Instead, the game spawns even more enemies if the player kills a woman.

Instead he believes his work, especially his earlier more autobiographical poems, are rooted in a changing country which echoes the Welshness of the past and the Anglicisation of the new industrial nation: " rural and urban, chapel-going and profane, Welsh and English, Unforgiving and deeply compassionate.

Instead, their goal was to emulate the moral life of Christ more completely.

Instead, it was found more effective when only trying to learn important information.

Instead they are dominated by generally older, more evolved stars that are orbiting the common center of gravity in random directions.

Instead, the Reichsgut was increasingly pawned to local dukes, sometimes to raise money for the Empire, but more frequently to reward faithful duty or as an attempt to establish control over the dukes.

Instead of using improved techniques to increase the productivity of the land, Honduran farmers have merely expanded the hectarage under cultivation to produce more crops — pushing their fields ever farther into the forests.

Instead of looking towards Persia, Babur was more focused on the Indian subcontinent, which included the region known as Kabulistan.

Instead, Jews interested in observing Halakha typically choose to follow specific rabbis or affiliate with a more tightly structured community.

Instead, he improvised: " He says more than he should, something different from what his advisers had recommended, and is more provocative than he had intended to be.

Instead they favor more evolutionary methods of bringing about anarchy through alternative experiences and experiments and education which could be brought about today.

Instead of prompting a backlash against the movement from which the attackers originated, however, Saudi Arabia, already very conservative, responded by shoring up its fundamentalist credentials with even more Islamic restrictions.

Instead, Godfrey himself seems to have used the more ambiguous term princeps, or simply retained his title of dux from Lower Lorraine.

The results were summarized by historian, playwright, and gay-rights activist Martin Duberman, " Instead of Kinsey's 37 % ( men who had at least one homosexual experience ), Gebhard and Johnson came up with 36. 4 %; the 10 % figure ( men who were " more or less exclusively homosexual for at least three years between the ages of 16 and 55 "), with prison inmates excluded, came to 9. 9 % for white, college-educated males and 12. 7 % for those with less education.