Then, I remembered that the girls had had a banana for dessert every day for the last week.

Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.

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

After this, the senior priest ( or bishop ) pours pure olive oil and a small amount of wine into the shrine lamp, and says the " Prayer of the Oil ", which calls upon God to "... sanctify this Oil, that it may be effectual for those who shall be anointed therewith, unto healing, and unto relief from every passion, every malady of the flesh and of the spirit, and every ill ..." Then follow seven series of epistles, gospels, long prayers, Ektenias ( litanies ) and anointings.

Then, since every real is the limit of some Cauchy sequence of rationals, the completeness of the norm extends the linearity to the whole real line.

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 almost every point of A returns to A infinitely often.

Then I got the script and my name was on every page because it was about my car.

In every medium, spy thrillers introduce children and adolescents to deception and espionage at earlier ages, as in the Agent Cody Banks film, the Alex Rider adventure novels by Anthony Horowitz, chick lit novels such as I'd Tell You I Love You, But Then I'd Have to Kill You and the CHERUB series, by Robert Muchamore.

Then the equivalence class of the identity is the symmetry group of the figure, and every equivalence class corresponds to one isomorphic version of the figure.

Those who believe and those who are Jews and Christians, and Sabians, whoever believes in Allah and the Last Day and do righteous good deeds shall have their reward with their Lord, on them shall be no fear, nor shall they grieve ... let there be no compulsion in religion "-that all monotheistic religions or people of the book have a chance of salvation, to the most exclusive teaching common amongst Salafis and Wahhabis, and supported by several works of medieval Islamic theology and by traditions ( hadith ) which are considered correct ( sahih ) by Sunni Muslims, for the most part are summed up in Surah 9: 5, 29: " Then, when the sacred months have passed, slay the idolaters wherever ye find them, and take them, and besiege them, and lay in wait in every stratagem of war.

Then every subset of X is either considered " almost everything " ( has measure 1 ) or " almost nothing " ( has measure 0 ).

It looked to me as if the whole town would break out into a riot ... Then suddenly I heard a heavy thump, and as if by magic the whole crowd dispersed in every direction ... One of the regular patrons had felled one of the noisiest rioters .... And it was the effect of this which had scattered everybody so suddenly.

Then I shall crucify you every one.

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 a fuzzy subset s: S of a set S is recursively enumerable if a recursive map h: S × N Ü exists such that, for every x in S, the function h ( x, n ) is increasing with respect to n and s ( x ) = lim h ( x, n ).

Suppose a partially ordered set P has the property that every chain ( i. e. totally ordered subset ) has an upper bound in P. Then the set P contains at least one maximal element.

Suppose a non-empty partially ordered set P has the property that every non-empty chain has an upper bound in P. Then the set P contains at least one maximal element.

Then, when the clock reaches midnight, there will be firework at Taipei 101 and every year since, the firework has last longer than the year before.

Then, still black with smoke and with his uniform in shreds, Nelson went on board Victory where he was received on the quarter-deck by Admiral Jervis – " the Admiral embraced me, said he could not sufficiently thank me, and used every kind expression which could not fail to make me happy.

Then is an open cover of S, but any finite subcollection of has the form of C discussed previously, and thus cannot be an open subcover of S. This contradicts the compactness of S. Hence, every accumulation point of S is in S, so S is closed.

Then every hom-set has an addition, endowing it with the structure of an abelian monoid, and such that the composition of morphisms is bilinear.

Then, only time and the component in the direction of v ;

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

Then you type the first component, which is also ' Y ' for the 点 stroke, then a ' G ' for the 横 stroke ， and since you now already have three strokes, you type the last stroke, which also happens to be a 捺, arriving at the keycode ' YYGY ' for the complete character.

Then until the invention of transistor, the vacuum tube was essential component in electric instruments.

Then people could join the FMLN directly instead of having to join one of its component parties.

Then A meets each path component of X and the diagram P of morphisms induced by inclusion

Then, the second pass of the algorithm loops through the vertices in this order, and for each vertex that has not already been assigned to a component, it performs a depth-first search of the transpose graph starting from that vertex, backtracking when the search reaches a previously assigned vertices ; the unsassigned vertices reached by this search form a new component.

Then, the i < sup > th </ sup > component of the polarization is related to the j < sup > th </ sup > component of the electric field according to:

Then, for any function H (·) for which exists, and assuming that the component densities p < sub > i </ sub >( x ) exist,

Then in 1885, Carl Auer von Welsbach succeeded in separating salts of the last two component elements, which were soon named praseodymium and neodymium.

Then F can be decomposed into a curl-free component and a divergence-free component:

Then localised heat is applied to the component to remove, with less heating required than from cold.

Then the kth component of the covariant derivative of Y with respect to X is given by

Then the material or component can be re-designed to reduce the probability of failure.

Then the remaining component force is only the wetting force.

Then a stable map is a pseudoholomorphic map with at least one stable domain component, such that for each of the other domain components

Then the graph is regular if and only if is an eigenvector of A.

Then, the relationship between radiated power and photon energy is shown in the graph on the rightside.

Then the graph of A * is the orthogonal complement of JG ( A ):

Then, the overall graph is the complement of the disjoint union of the complements of these independent sets.

Then a graph is any function s for which π ( s ( x ))= x.

Then having found the weight of the shortest Hamilton path, determine which edges are in the path by asking for each edge whether there is a Hamiltonian path with weight for the graph modified so that edge has weight ( if there is no such path in the modified graph, then edge must be in the shortest path for the original graph ).

Then total coloring becomes a ( proper ) vertex coloring of the total graph.

# Let G be a connected graph and let H be the clutter on consisting of all edge sets of spanning trees of G. Then is the collection of all minimal edge cuts in G.

Let G be a connected finite graph embedded in Euclidean space of dimension n. Let V be a closed regular neighborhood of G. Then V is an n-dimensional handlebody.

Now let G be some graph, let v be a vertex of G, and let R be a random walk on G starting from v. Let T be some stopping time for R. Then the loop-erased random walk until time T is LE ( R ()).

Then, any topological sort of this graph is a valid instruction schedule.

Let G = ( V, E ) be a simple graph and let K consist of all 2-element subsets of V. Then H = ( V, K

where S ranges across subsets of of size n − 1, and F < sub > S </ sub > denotes the ( n − 1 )- by -( n − 1 ) matrix whose columns are those of F with index in S. Then every S specifies n − 1 edges of the original graph, and it can be shown that those edges induce a spanning tree iff the determinant of F < sub > S </ sub > is + 1 or − 1, and that they do not induce a spanning tree iff the determinant is 0.

Then the matrix A is irreducible if and only if its associated graph G < sub > A </ sub > is strongly connected.

Then, a graph. is plotted of the points that a particular value for the changed variable visits after transient factors have been neutralised.

Then this AND / OR graph will be the same as the product model or product compositions.

Then every graph on vertices and edges contains a ( triangular ).

Let φ: S → 2 < sup > S </ sup > be a set-valued function on S with a closed graph and the property that φ ( x ) is non-empty and convex for all x ∈ S. Then φ has a fixed point.