Then, by applying and maintaining sufficient pressure to prevent it from inhaling, the prey eventually succumbs due to asphyxiation.

Then, from the late 1960s onward, Stanford's goal became applying research and findings toward humanistic ends.

Then, applying transformation T to all the points on this sphere yields

Then, by applying and maintaining sufficient pressure to prevent it from inhaling, the prey eventually succumbs due to asphyxiation.

Then, applying the triangle inequality to both sides, using ( 5 ) and the fact that as well as are non-negative we obtain

Then ( the same result can be obtained by applying the current conservation principle ).

Then in early 1963, California guitar manufacturer Mosrite re-branded their uniquely styled, futuristic-looking Mark 1 electric guitar model for the Ventures by applying decals that stated " The Ventures Model " on the headstock.

Then one computes the next iteration of P by applying F < sub > j </ sub > on ( P. x, P. y ).

To see why this is true, suppose x ∈ X is the state at time s. Then by the definition of F, F < sub > t, s </ sub >( x ) is the state of the system at time t and consequently applying the definition once more, F < sub > u, t </ sub >( F < sub > t, s </ sub >( x )) is the state at time u.

Then, by applying the Phragmén – Lindelöf principle ( a kind of maximum principle for infinite domains ) one gets that

Then the basic EPS number is diluted one by one by applying each one, skipping any instruments that have an antidilutive effect.

Then, applying the differential pointwise to X yields the pushforward φ < sub >*</ sub > X, which is a vector field along φ, i. e., a section of φ < sup >*</ sup > TN over M.

Then applying different sampling methods will lead to different sets of individuals being observed for the same area of interest, and the species richness of each set may be different.

Then applying this to yields the probabilities:

Then applying ν < sub > 2 </ sub > to the equation yields

Then, for the class of scores which are discrete convolutions, configurations related to each other by translation of one protein by an exact lattice vector can all be scored almost simultaneously by applying the convolution theorem.

Then, we can calculate by means of Gram – Schmidt as follows:

Then England won in 1911 – 12 by four matches to one.

Then Chris Broad scored three hundreds in successive Tests and bowling successes from Graham Dilley and Gladstone Small meant England won the series 2 – 1.

Then by Arzelà – Ascoli theorem the space K is compact.

Then followed Woolwich Common ( 1907 – 1908 ), Pound Park ( 1908 – 1913 ), and Angerstein Lane ( 1913 – 1915 ).

Then he returned to Germany – crowned emperor and apparent victor over the papacy.

Then f = u + iv is complex-differentiable at that point if and only if the partial derivatives of u and v satisfy the Cauchy – Riemann equations ( 1a ) and ( 1b ) at that point.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

Then the second Cauchy – Riemann equation ( 1b ) asserts that is irrotational:

Then Goursat's theorem asserts that ƒ is analytic in an open complex domain Ω if and only if it satisfies the Cauchy – Riemann equation in the domain.

Then deforestation rates accelerate ( HFHD, high forest cover – high deforestation rate ), and forest cover is reduced ( LFHD.

Then in 1743 he further alienated his father by marrying Antoinette Champion ( 1710 – 1796 ), a devout Roman Catholic.

* 2002 – 2003 California recall: Then Governor of California Gray Davis announces that the state would face a record budget deficit of $ 35 billion, roughly double the figure reported during his reelection campaign one month earlier.

Then, in the time of Pope Gregory VII ( 1073 – 1085 ), canonists who in the Investiture Controversy quoted the prohibition in canon 22 of the Council of Constantinople of 869 – 870 against laymen influencing the appointment of prelates elevated this council to the rank of ecumenical council.

Then, not long before the finish, the Automobile Club de l ' Ouest ( ACO ), organizers of the Le Mans event, informed Ford that the geographical difference in starting positions would be taken into account at a close finish – meaning that the McLaren / Amon vehicle, which had started perhaps behind the Hulme-Miles car, would have covered slightly more ground over the 24 hours and would therefore be the winner.

Then, a major opportunity arose when Fox – buoyed by the returns from The Sound of Music ( 1965 ) – commissioned Kelly to direct Hello, Dolly!

Then, by allying with the rulers of Austria and Prussia, she incorporated the territories of the Polish – Lithuanian Commonwealth, where after a century of Russian rule non-Catholic mainly Orthodox population prevailed during the Partitions of Poland, pushing the Russian frontier westward into Central Europe.

Then in 1968 he became Professor of Informatics at ETH Zürich, taking two one-year sabbaticals at Xerox PARC in California ( 1976 – 1977 and 1984 – 1985 ).

Then – in the only paid employment he ever had – he took a job as a telegraph operator with the Great Northern Telegraph Company working first in Denmark and then in Newcastle-upon-Tyne, and was soon made a chief operator.

Then came this decision, which sped the process of gaining equality ( or perhaps hindered it ; ;

Then the whole process would be repeated to eliminate another variable.

) 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 copper is passed through an electro-winning process to increase its purity: An electric current is passed through the resulting solution of copper ions.

Then, removing the catalyst would also result in reaction, producing energy ; i. e. the addition and its reverse process, removal, would both produce energy.

Then we analyze its notes or frequencies by subjecting it to a process akin to Fourier transform ; this is the Mellin transform.

Then, the process repeats with the next neighboring digit until there are no more digits to process.

Then the binary collision approximation is no longer valid, but rather the collisional process should be understood as a many-body process.

Then repeat the process about six inches from the other end of the spar.

Then the following regression equation is postulated as a description of the process that generated the data:

Then he realised this is the difference between natural-form fruit trees and the process of change of tree form resulting from abandoning previously-pruned unnatural fruit trees.

Let denote the number of kernels which have popped up to time t. Then this is a continuous time, non-homogenous Markov process.

Then define a process Y, such that each state of Y represents a time-interval of states of X.

Then Walker resigned, in the process allegedly calling Hay a " cancer on the gay movement " ( a remark Walker later denied making ).

Then the gap is divided by the shrink factor again, the list is sorted with this new gap, and the process repeats until the gap is 1.

Then there is Barbara Dixon, a transsexual taxi driver who goes into great detail about her process of sexual conversion.

Then they undergo a process of exchange of matter and energy when they are put in contact by their separating wall becoming permeable to matter.

* Then, the BPI process owners should determine what outcomes would add value to the organization's objectives and how best to align its processes to achieve those outcomes ( TO-BE ).

The recording process took place in London, New York City, and Los Angeles, and featured a host of special guests, such as Barbra Streisand on " Tell Him "; the Bee Gees on " Immortality "; and world-renowned tenor Luciano Pavarotti on " I Hate You Then I Love You ".

Then the paper is chemically developed in a process that replaces the iron salts with platinum.