Then, dividing the units of energy ( such as eV ) by a fundamental constant that has units of velocity ( M < sup > 0 </ sup > L < sup > 1 </ sup > T < sup >-1 </ sup >), facilitates the required conversion of using energy units to describe momentum.

Then the preparer grinds the coffee using a traditional tool called a mokecha.

Then, using an electronic design automation tool, a technology-mapped netlist is generated.

Then, using back-substitution, each unknown can be solved for.

Then it would be that by recursion ( using the axiom of countable choice ) that a sequence of polynomials could be found so that, letting of minimal degree.

Then, in 1915, William Henry Bragg and William Lawrence Bragg, a British father-son pair, shared this Nobel Prize for their discoveries in the reverse problem-determining the structure of crystals using X-rays.

Then, on paper, they bought $ 200 worth of each, for a total bet of $ 1, 000, using the prices on September 29, 1980, as an index.

Then Socrates goes on to demonstrate the contrary of the commonly accepted part using the law of noncontradiction.

" Then the novel tells a story of boys trying to grow mandrake using hanged archbishop's semen.

Then, using information in its routing table or routing policy, it directs the packet to the next network on its journey.

Then Merlin, using " gear " and skill, easily dismantled the stones and sent them over to Britain, where Stonehenge was dedicated.

Then execute using or.

⟨ 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 trace of the identity matrix is the dimension of the space ; this leads to generalizations of dimension using trace.

Then burr holes are created into the patient ’ s skull using a drill.

Then, thus by T, which means w R w using the definition of.

Then, in August 1497, James laid siege to Norham Castle, using his father's bombard Mons Meg.

Then write a review without using any of the following words: " Progressive rock ", " Genesis ", " Fish ", " heavy metal ", " dinosaurs ", " predictable ", " concept album ".

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, using a simple greedy algorithm, the easy knapsack can be solved using O ( n ) arithmetic operations, which decrypts the message.

Examples: William Faulkner in A Rose for Emily ( Faulkner was an avid experimenter in using unusual points of view-see his Spotted Horses, told in third person plural ); Frank B. Gilbreth and Ernestine Gilbreth Carey in Cheaper By the Dozen ; Frederik Pohl in Man Plus ; and more recently, Jeffrey Eugenides in his novel The Virgin Suicides and Joshua Ferris in Then We Came to the End.

Then, using his fingers, he takes some of the blessed oil floating on the surface of the baptismal water and anoints the catechumen on the forehead, breast, shoulders, ears, hands and feet.

Then, detailed study was undertaken to determine the painting's original form, using scientific tests ( especially infrared reflectoscopy and microscopic core-samples ), and original cartoons preserved in the Royal Library at Windsor Castle.

Then the periodic Bernoulli functions P < sub > n </ sub > are defined as

Then, a periodic test will assure that the device has not become unsafe since the power-on self test.

Then our choice function can choose the least element of every set under our unusual ordering.

Then an arithmetic function a is

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 is a group whose identity element is The group inverse of an arbitrary group element is the function inverse

Then a mathematical procedure is used to find a filter transfer function which can be realized ( within some constraints ) and which approximates the desired response to within some criterion.

Then an " estimator " is a function that maps the sample space to a set of sample estimates.

Let R be a domain and f a Euclidean function on R. Then:

For instance, suppose that each input is an integer z in the range 0 to N − 1, and the output must be an integer h in the range 0 to n − 1, where N is much larger than n. Then the hash function could be h

Then the probability density function f *( x ) of the size biased population is

Then ƒ is invertible if there exists a function g with domain Y and range X, with the property:

Then for a specific value x of X, the function L ( θ | x )

Then,, and the constant function turns into the identity by substitution.

Then, in 1905, to explain the photoelectric effect ( 1839 ), i. e., that shining light on certain materials can function to eject electrons from the material, Albert Einstein postulated, based on Planck ’ s quantum hypothesis, that light itself consists of individual quantum particles, which later came to be called photons ( 1926 ).

The algorithm for deciding this is conceptually simple: it constructs ( the description of ) a new program t taking an argument n which ( 1 ) first executes program a on input i ( both a and i being hard-coded into the definition of t ), and ( 2 ) then returns the square of n. If a ( i ) runs forever, then t will never get to step ( 2 ), regardless of n. Then clearly, t is a function for computing squares if and only if step ( 1 ) terminates.

Then the output is related to the input by the transfer function as

Then because the construction of f was uniform, this is a recursive function of two variables.

Then, its electrical field traces out a helical pattern as a function of time.

Then the function

Then the function

Then, recalling that the likelihood function is defined up to a multiplicative constant, it is just as valid to say that the likelihood function is approximately

Then, on considering the lengths of the intervals to decrease to zero, the likelihood function for an observation from the discrete component is

Then has probability density function.