Therefore a naive algorithm to calculate the estimated variance is given by the following:

Therefore, the Gaussian Elimination algorithm applied to the augmented matrix begins with:

Therefore the start address of the data should be shifted such that this logic can be implemented avoiding unnecessary +/- 1 offsets in the coded algorithm.

Therefore it is not possible to produce an algorithm that reduces the size of every possible input sequence.

Therefore it is also sometimes called the DJP algorithm, the Jarník algorithm, or the Prim – Jarník algorithm.

Therefore, in any geometric problem we have an initial set of symbols ( points and lines ), an algorithm, and some results.

Therefore, the actual search tree that is traversed by the algorithm is only a part of the potential tree.

Therefore, for N even the convolution is cyclic, but in this case N is composite and one would normally use a more efficient FFT algorithm such as Cooley – Tukey.

Therefore, globally the algorithm runs in time O ( n log n ).

Therefore the complexity of the table algorithm is.

Therefore, the BLAST algorithm uses a heuristic approach that is less accurate than the Smith-Waterman algorithm but over 50 times faster.

Step 5 will also never return composite, because ( 2 ) is true for all prime numbers n. Therefore, the algorithm will return prime either in step 4 or in step 6.

Therefore, the algorithm either correctly finds a satisfying assignment or it correctly determines that the input is unsatisfiable.

Therefore an algorithm that finds a minimum spanning tree is a polynomial-time factor-2 approximation algorithm for the metric Steiner tree problem.

Therefore, the term " cryptosystem " is most often used when the key generation algorithm is important.

Therefore a general algorithm for finding eigenvalues could also be used to find the roots of polynomials.

Therefore, firefly algorithm is specially suitable for multimodal optimization problems.

Therefore the time efficiency of Marzullo's algorithm is O ( n log n ).

Therefore, the total expected time for this algorithm is O ( n log log n ).

Therefore, the Euclidean shortest path problem may be decomposed into two simpler subproblems: constructing the visibility graph, and applying a shortest path algorithm such as Dijkstra's algorithm to the graph.

According to historian Kurakichi Shiratori, one of emperor Shōwa's teachers: ' Therefore nothing in the world compares to the divine nature ( shinsei ) of the imperial house and likewise the majesty of our national polity ( kokutai ).

One of emperor Shōwa's teachers, historian Kurakichi Shiratori, remarked, " Therefore nothing in the world compares to the divine nature ( shinsei ) of the imperial house and likewise the majesty of our national polity ( kokutai ).

Therefore Christ compares truth to food and appropriating it to eating, just as, physically, food by being appropriated ( assimilated ) becomes the life sustenance, so also, spiritually, truth is both the giver of life and the sustenance of life, is life.

Therefore, the eigenvalues of are the fourth roots of unity: is + 1, − 1, + i, or − i.

Therefore, if Alice measures + x, the system ' collapses ' into state Ia, and Bob will get − x.

Therefore, the molecular structure of a simple monosaccharide can be written as H ( CHOH )< sub > n </ sub >( C = O )( CHOH )< sub > m </ sub > H, where n + 1 + m

Therefore, a < sup > 2 </ sup > + b < sup > 2 </ sup > < a < sup > 2 </ sup > + 2ab + b < sup > 2 </ sup > ≤ c < sup > 2 </ sup >.

With a declination of + 38. 78 °, Vega can only be viewed at latitudes north of 51 ° S. Therefore, it does not rise at all anywhere in Antarctica or in the southernmost part of South America, including Punta Arenas, Chile ( 53 ° S ).

Therefore ,-50 newtons + 500 newtons yields a net force forward of 450 newtons.

Therefore, the convex hull of a set X of three or more points in the plane is the union of all the triangles determined by triples of points from X, and more generally in N-dimensional space the convex hull is the union of the simplices determined by at most N + 1 vertices from X.

Therefore, a B-Double would weigh ( + + + ).

Therefore, 3 + 2 = 5.

Therefore the hole is taken to have positive charge of + e, precisely the opposite of the electron charge.

1122, which is greater than c. Therefore c is not greater than d < sup >( 1 + ε )</ sup > for any ε and a, b, c is not such a triple.

Therefore r ( x ) has n + 1 roots.

Therefore, these T cells are called CD8 + T cells.

Therefore is the number of solutions to x < sup > 3 </ sup > + 1 = y < sup > 3 </ sup > in the finite field Z / pZ.

Therefore the difference in the potential function from before this phase to after it is: O ( log n ) − m, and the amortized running time is then at most O ( log n + m ) + O ( log n ) − m = O ( log n ).

Therefore, if the theorem is true for polygons constructed from n triangles, the theorem is also true for polygons constructed from n + 1 triangles.

Therefore, the vast majority of length values is ' M ', ( 32 + 45

Therefore, the set of all equivalence classes of forms a partition of: every element of belongs to one and only one equivalence class.

Therefore, mens rea refers to the mental element of the offence that accompanies the actus reus.

Therefore, the assertion that an object R → R * is initial in E, that is, that there is a morphism from it to any other element of E, means that the ring R * is a most efficient solution to our problem.

These assumptions, required for the development of a general theory of brand selection and brand purchase, are problematic, because the resultant theories tend either to misunderstand or to ignore the “ irrational ” element in the behaviour of the person-as-consumer ; and because conspicuous consumption is a behaviour predominantly “ psychological ” in motivation and expression, Therefore, a comprehensive general theory would require a separate construct for the psychological elements of the socio-economic phenomenon that is conspicuous consumption.

Therefore the problem of computing derivatives, antiderivatives, integrals, power series expansions, Fourier series, residues, and linear functional transformations of rational functions can be reduced, via partial fraction decomposition, to making the computation on each single element used in the decomposition.

Therefore, it is hard to calculate which element should be the next group 3 element.

Therefore the conclusion when following an MDL approach is inevitably that there is not enough evidence to support the hypothesis of the biased coin, even though the best element of the second model class provides better fit to the data.

Therefore, current designs still incorporate an element of human control ( a " man in the loop ") – meaning that a ground controller must authorize weapons release.

Therefore, if u and v are non-zero elements of U, there is an element of R that induces an endomorphism of U transforming u to v. The natural question now is whether this can be generalized to arbitrary ( finite ) tuples of elements.

Therefore, the face of the element is not acted by loads and the structural element can be analyzed as two-dimensional, e. g. thin-walled structures such as plates subject to in-plane loading or thin cylinders subject to pressure loading.

Therefore, depending on where an observer is located, the light scattered from a small volume element may appear to be more or less polarized.

Therefore, for each conjugacy class C < sub > i </ sub > of size m < sub > i </ sub >, the characters are the same for each element of the conjugacy class and so we can just call χ < sub > ρ </ sub >( C < sub > i </ sub >) by an abuse of notation ).

Therefore, Jamiat ’ s endeavor is widely acclaimed in every element of life including religious scholars, teachers, students, intellectuals, politicians and those who belong to Pakistan ’ s defense ” The youth of Jamiat are committed and keep an aim that their Lord be pleased with them, that they be able to obtain His gracious approbation, and that when they ultimately stand before Him for the final judgment, they might be reckoned as worthy of success and salvation.

Therefore it is important to be able to create an element that is assigned with labels for different languages.

Therefore, understanding the third element leads to understanding the surgical-technical approach to correcting the isolated lower-pole and lobule prominence.

Therefore, one should take the time to review each element and ask oneself, " what went well?

Therefore, one could classify this tool as an element of strategic subversion.

Therefore, the length of each element corresponds to a certain frequency.

Therefore, the drowning of her character may represent the element water, which represents rebirth.

Therefore the mens rea element is that the man either believes the woman is not consenting or is " reckless or indifferent to the matter of consent ".

Therefore there is a defensive element in deciding whether to kick a bomb.