Then, the solutions are mutated and selected for those with higher fitness, until a satisfying solution has been found.

Then the satisfying instances of the resulting 2SAT formula encode solutions to the vertex cover problem, and there is a satisfying assignment with true variables if and only if there is a vertex cover with vertices.

Then at one point in the 1960s, Kurokawa and a small group of architects began a new wave of contemporary Japanese architecture, believing that previous solutions and imitations were not satisfactory for the new era: life was not present in Modernism.

Then he recommends solutions such as systematic questioning, freewriting, and encouragement.

Then, among all possible solutions, we are ideally interested in those solutions that perform well in all considered criteria.

Then, one can prove that solutions exist at least locally, using ideas not terribly dissimilar from those encountered in studying other differential equations.

Then, Fredholm's theorem is that, for any fixed value of, these equations have either the trivial solution or have the same number of linearly independent solutions,.

Then in 2007 Richer created Total Intelligence Solutions with Cofer Black and Matthew G. Devost, Co-founder and President of Terrorism Research Center, which, according to Richer, " is about delivering evolved intelligence and security solutions to the world's most demanding customers.

Then the non-homogeneous recurrence can be rewritten in homogeneous form as

Then any solution of the inhomogeneous equation may have a solution of the homogeneous equation added to it, and still remain a solution.

Then, by placing an arbitrary metric g on a given smooth manifold M and evolving the metric by the Ricci flow, the metric should approach a particularly nice metric, which might constitute a canonical form for M. Suitable canonical forms had already been identified by Thurston ; the possibilities, called Thurston model geometries, include the three-sphere S < sup > 3 </ sup >, three-dimensional Euclidean space E < sup > 3 </ sup >, three-dimensional hyperbolic space H < sup > 3 </ sup >, which are homogeneous and isotropic, and five slightly more exotic Riemannian manifolds, which are homogeneous but not isotropic.

Then, M is identified as a homogeneous space

Then a symmetric space for G is a homogeneous space G / H where the stabilizer H of a typical point is an open subgroup of the fixed point set of an involution σ of G. Thus σ is an automorphism of G with σ < sup > 2 </ sup > = id < sub > G </ sub > and H is an open subgroup of the set

Then the coordinates of the d points of intersection are algebraic functions of the Plücker coordinates of U, and by taking a symmetric function of the algebraic functions, a homogeneous polynomial known as the Chow form ( or Cayley form ) of Z is obtained.

Then fill the system and add a rust inhibitor.

Then, for any given sequence of integers a < sub > 1 </ sub >, a < sub > 2 </ sub >, …, a < sub > k </ sub >, there exists an integer x solving the following system of simultaneous congruences.

Then, standard tools such as ls, cp, and rm can be used to manipulate files on the remote system.

Then the pair (( A < sub > i </ sub >)< sub > i ∈ I </ sub >, ( f < sub > ij </ sub >)< sub > i ≤ j ∈ I </ sub >) is called an inverse system of groups and morphisms over I, and the morphisms f < sub > ij </ sub > are called the transition morphisms of the system.

* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.

This melding of scientific and social speculation is clearly present in the novel Voyage from Yesteryear ( strongly influenced by Eric Frank Russell's famous story " And Then There Were None ") about a high-tech anarchist society in the Alpha Centauri system, a starship sent from Earth by a dictatorial government, and the events following their first contact.

Then on Oct 23, 1972, Balliett's student, Dr. Juno Jordan, changed Numerology further and helped it to become the system known today under the title " Pythagorean ", although Pythagoras himself had nothing to do with the system.

Then, as the number of users increases, the system becomes even more valuable and is able to attract a wider user base.

Then, on August 15, 1971, United States President Richard Nixon announced that the United States dollar would no longer be convertible to gold, effectively ending the system.

Then the following dynamical system describes PLL behavior

Then we can translate this system into fuzzy program in such a way that f is the interpretation of a vague predicate Good ( x, y ) in the least fuzzy Herbrand model of this program.

Then hypothiocyanite, OSCN, cannot be produced by immune defense system.

Then the system is in state

Then, using physical arguments, one derives a suitable " fundamental volume " for the particular system to reflect the fact that quantum mechanical microstates are discretely distributed on the phase space.

# Then at the operating system level ( to let system software access multiple address spaces and utilize larger address spaces )

Then the density matrix for this system is

Then the matrices would progress through the machine, where a special keying system on one end of the matrix, unique for each character, would allow the matrix to drop only into the correct storage slot, ready for future use.

Then we will study the coordinate transformations between this coordinate and the fixed " laboratory " system.

Then there is the type of activity that uses the network to waste time, as indicated in SurfControl's advice on writing AUPs, of technical staff to troubleshoot a problem for which the user is the cause, corrupting or destroying other user's data, violating the privacy of others online, using the network in such a way that it denies the service to others, continuing to use software or other system for which the user has already been warned about using, and any other misuse of the network such as introduction of viruses.

Then, oxygen is added to the system.

Then, as community sentiment favored forming a public school system, the college was closed, and the property deeded to the Pea Ridge Public School.

Then they were given 1/2 to 1-1/2 avocados per day as a substitute for part of their dietary fat consumption.

) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is

Then the pullback of the covector determined by g ( denoted dg ) is given by

Then, in the later account found in the Syriac Doctrine of Addai, a painted image of Jesus is mentioned in the story ; and even later, in the account given by Evagrius, the painted image is transformed into an image that miraculously appeared on a towel when Christ pressed the cloth to his wet face.

Then, he wore a Harlequin cap, given to successful cricketers at Oxford.

Then N < sub > x </ sub > is a directed set, where the direction is given by reverse inclusion, so that S ≥ T if and only if S is contained in T. For S in N < sub > x </ sub >, let x < sub > S </ sub > be a point in S. Then ( x < sub > S </ sub >) is a net.

Then to define multiplication, it suffices by the distributive law to describe the product of any two such terms, which is given by the rule

Then the total number of i-type organisms after the first round of reproduction, given as, is

Then by the law of moment of momentum, the torque on the fluid is given by:

⟨ H ⟩, be the group generated by H. Then the word problem in H < sup >*</ sup > is solvable: given two words h, k in the generators H of H < sup >*</ sup >, write them as words in X and compare them using the solution to the word problem in G. It is easy to think that this demonstrates a uniform solution the word problem for the class K ( say ) of finitely generated groups that can be embedded in G. If this were the case the non-existence of a universal solvable word problem group would follow easily from Boone-Rogers.

Then the solution of the Laplace equation inside the sphere is given by

Then, Pandulf's nephew Pandulf II was given Benevento when Otto II partitioned Landulf IV's territory, with Landulf IV keeping Capua.

Then he ordered 2 golden pieces to be given to every householder in Constantinople and 200 pounds of gold ( including 200 silver pieces annually ) to be given to the Byzantine Church.

Then we imagine the rays are parallel ( and given by two angles ), and we let the colour of a point on the surface be determined by the angle between this direction and the slope of the surface at the point.

Then the formula Cold ( r )→ High ( t ) is true for any t and therefore any t gives a correct control given r. A rigorous logical justification of fuzzy control is given in Hájek's book ( see Chapter 7 ) where fuzzy control is represented as a theory of Hájek's basic logic.

Then the n-th series coefficient c < sub > n </ sub > is given by:

Then, given any point x and neighbourhood G of x, there is a closed neighbourhood E of x that is a subset of G.

Then given the Hamiltonian operator, the equation to satisfy for all functions ( with associated multiplication operator ) is

* Then, to return a new sample given the most recent sample, we proceed as follows:

Then follow the characters of their family and given names.