The inverse sixth power distance dependence of Förster resonance energy transfer was experimentally confirmed by Stryer and Haugland using a donor and an acceptor separated on an oligoproline helix.

Haugland, Yguerabide and Stryer also experimentally demonstrated the theoretical dependence of Förster resonance energy transfer on the overlap integral by using a fused indolosteroid as a donor and a ketone as an acceptor.

Full text of Berg, Tymoczko, and Stryer, courtesy of NCBI.

* Jeremy M Berg, John L Tymoczko, and Lubert Stryer, Biochemistry 5th edition, 2002, W H Freeman.

* Jeremy M Berg, John L Tymoczko, and Lubert Stryer, Biochemistry 5th edition, 2002, W H Freeman.

* Stryer, Lubert ( 1995 ) Biochemistry 4th ed.

* S. P. Fodor, J. L. Read, M. C. Pirrung, L. Stryer, A. T. Lu, and D. Solas, “ Light-directed, spatially addressable parallel chemical analysis ,” Science 251, pp. 767 – 773, 1991.

* The Calvin Cycle and the Pentose Phosphate Pathway from Biochemistry, Fifth Edition by Jeremy M. Berg, John L. Tymoczko and Lubert Stryer.

Senomyx was founded by prominent biochemist Lubert Stryer in 1999.

In May 2001, Stryer returned to his professorship at Stanford University and resigned from Senomyx, but continues to be the Chairman of the Scientific Advisory Board.

The Arrhenius definition states that acids are substances which increase the concentration of hydronium ions ( H < sub > 3 </ sub > O < sup >+</ sup >) in solution.

This force is used in the formal definition of the ampere, which states that it is " the constant current that will produce an attractive force of 2 × 10 < sup >– 7 </ sup > newton per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum ".

A still weaker example is the axiom of countable choice ( AC < sub > ω </ sub > or CC ), which states that a choice function exists for any countable set of nonempty sets.

These states are labeled by a set of quantum numbers summarized in the term symbol and usually associated with particular electron configurations, i. e., by occupation schemes of atomic orbitals ( e. g., 1s < sup > 2 </ sup > 2s < sup > 2 </ sup > 2p < sup > 6 </ sup > for the ground state of neon -- term symbol: < sup > 1 </ sup > S < sub > 0 </ sub >).

For some elements, allotropes have different molecular formulae which can persist in different phases – for example, two allotropes of oxygen ( dioxygen, O < sub > 2 </ sub > and ozone, O < sub > 3 </ sub >), can both exist in the solid, liquid and gaseous states.

The fundamental theorem of arithmetic states that any positive integer n can be represented uniquely as a product of powers of primes: where p < sub > 1 </ sub > < p < sub > 2 </ sub > < ... < p < sub > k </ sub > are primes and the a < sub > j </ sub > are positive integers.

When fully implemented, CAIR will reduce SO < sub > 2 </ sub > emissions in 28 eastern states and the District of Columbia by over 70 percent and NOx emissions by over 60 percent from 2003 levels.

The Boltzmann distribution for the fractional number of particles N < sub > i </ sub > / N occupying a set of states i possessing energy E < sub > i </ sub > is:

Specifically it states that for any integers n ≥ 0 and m ≥ 1, the functions J < sub > n </ sub >( x ) and J < sub > n + m </ sub >( x ) have no common zeros other than the one at x = 0.

Cadmium has 8 known meta states, with the most stable being < sup > 113m </ sup > Cd ( t < sub > ½ </ sub >

For positive values of a and b, the binomial theorem with n = 2 is the geometrically evident fact that a square of side can be cut into a square of side a, a square of side b, and two rectangles with sides a and b. With n = 3, the theorem states that a cube of side can be cut into a cube of side a, a cube of side b, three a × a × b rectangular boxes, and three a × b × b rectangular boxes.

For example, the CIA World Factbook uses the word in its " Country name " field to refer to " a wide variety of dependencies, areas of special sovereignty, uninhabited islands, and other entities in addition to the traditional countries or independent states ".< sup id = Note_1 >

Note that for any fixed w the function f ( x ) = F ( w x ) is computable ; thus the universality property states that all computable functions of one variable can be obtained in this fashion.

Image: pons_asinorum. png | The bridge of asses theorem states that if A = B then C = D.

The film states that this occurred in 1992, while the book gives 1997 as HAL's birthyear .< ref name = Urbana 1992 / 7 >

The intermediate value theorem states the following: If f is a real-valued continuous function on the interval b, and u is a number between f ( a ) and f ( b ), then there is a c ∈ b such that f ( c ) = u.

While the group asserts that it " unequivocally condemns terrorism " and states that it has a " strict no-tolerance policy against terrorism and other felonious acts ," it was described as " a right-wing terrorist group " by the FBI in 2001 .< ref name = spl >

This element also has 5 meta states, with the longest-lived being < sup > 258m </ sup > Md ( t < sub > ½ </ sub > = 58 minutes ).

Informally speaking, the prime number theorem states that if a random integer is selected in the range of zero to some large integer N, the probability that the selected integer is prime is about 1 / ln ( N ), where ln ( N ) is the natural logarithm of N. For example, among the positive integers up to and including N = 10 < sup > 3 </ sup > about one in seven numbers is prime, whereas up to and including N = 10 < sup > 10 </ sup > about one in 23 numbers is prime ( where ln ( 10 < sup > 3 </ sup >)= 6. 90775528. and ln ( 10 < sup > 10 </ sup >)= 23. 0258509 ).

where N < sub > 2 </ sub >( 0 ) is the number of excited atoms at time t = 0, and τ < sub > 21 </ sub > is the lifetime of the transition between the two states.

Radiationless transition between levels, such as between the excited S = 0 and S = 1 states, may proceed quickly enough to siphon off a portion of the S = 0 population before it spontaneously returns to the ground state.

This element also has five meta states with the most stable being < sup > 44m </ sup > Sc ( t < sub > ½ </ sub > = 58. 6 h ).

Lagrange's four-square theorem of 1770 states that every natural number is the sum of at most four squares ; since three squares are not enough, this theorem establishes g ( 2 ) = 4.

Polignac's conjecture from 1849 states that for every positive even natural number k, there are infinitely many consecutive prime pairs p and p ′ such that p ′ − p = k ( i. e. there are infinitely many prime gaps of size k ).

alt = A child with one arm or leg in each of the four states

alt = A concrete pad with the state seals of the four states.

The theorem loosely states that if we have a physically meaningful equation involving a certain number, n, of physical variables, and these variables are expressible in terms of k independent fundamental physical quantities, then the original expression is equivalent to an equation involving a set of p = n − k dimensionless parameters constructed from the original variables: it is a scheme for nondimensionalization.

The transfer principle states that true first order statements about R are also valid in * R. For example, the commutative law of addition, x + y = y + x, holds for the hyperreals just as it does for the reals ; since R is a real closed field, so is * R. Since for all integers n, one also has for all hyperintegers H. The transfer principle for ultrapowers is a consequence of Łoś ' theorem of 1955.

For example, the axiom that states " for any number x, x + 0 = x " still applies.

Alaska has a longer coastline than all the other U. S. states combined .< ref >

124-126 .</ ref > While other philosophers also recognized such transitions in states of matter, Anaximenes was the first to associate the quality pairs hot / dry and cold / wet with the density of a single material and add a quantitative dimension to the Milesian monistic system .< ref > Kirk, G. S., J. E.

Church, Ministry and Sacraments in the New Testament Paternoster Press: 1993, p. 92f </ ref > Moving on to Ignatius of Antioch, Barrett states that here we find a sharp distinction between ' presbyter ' and ' bishop ': the latter now stands out as " an isolated figure " who is to be obeyed and without whom it is not lawful to baptise or hold a love-feast .< Barrett, C. K.