Therefore, manufacturers properly bear the burden of finding, correcting, and warning consumers of those dangers.

Therefore, referential transparency allows us to reason about our code which will lead to more robust programs, the possibility of finding bugs that we couldn't hope to find by testing, and the possibility of seeing opportunities for optimization.

Therefore, Analysis is the process of finding the reasoned facts.

Therefore, recent work concentrates on finding alternative solutions, in which for example currents are summed instead of voltages, resulting in a lower theoretical limit for the operating voltage ( Banba, 1999 ).

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

Therefore, one can easily find the pK < sub > a </ sub > of the monoprotic acid by finding the pH of the point halfway between the beginning of the curve and the equivalence point, and solving the simplified equation.

Therefore, the anomalies in a system help point the developer in the right direction in finding defects.

Therefore, updating data for one source and finding the best interval can be done in O ( n ) time.

Therefore, if we consider the error correction as finding the codeword closest to the received word, as long as the number of errors is no more than, there is only one codeword in the hamming ball centered at with radius, therefore all errors could be corrected.

Therefore, the court taking judicial notice would simply allow the jury to make the finding that the court took notice of, but would not require this outcome, and would not prevent the defense from presenting evidence to rebut the noticed fact.

Therefore, an algorithmic approach was created to help in the evaluation of patients with complaints of lower leg pain, and assist in finding a diagnosis.

" Therefore, the assessment of most civil penalties requires a finding of " clear and convincing evidence " before a civil defendant will be held liable.

Therefore the problem of determining the domatic number of a given graph is NP-hard, and the problem of finding a maximum-size domatic partition is NP-hard as well.

Therefore, consequent to the quest in finding herbs and the fern flower may be the blooming of relationships between pairs of men and women within the forest.

Therefore the authenticity of this finding is questionable.

Therefore, given that we are only interested in finding the best value for θ we may drop the y < sub > i </ sub >!

Therefore, in general Euclidean spaces every similarity is an affine transformation, because the Euclidean group E ( n ) is a subgroup of the affine group.

Therefore, in Euclidean geometry, any two lines that are both perpendicular to a third line are parallel to each other, because of the parallel postulate.

Therefore the symmetry group of a Euclidean space is the Euclidean group and for a Minkowski space it is the Poincaré group.

" Therefore any result in Euclidean geometry that follows from these three postulates will hold in elliptic geometry, such as proposition 1 from book I of the Elements, which states that given any line segment, an equilateral triangle can be constructed with the segment as its base.

Therefore the vectors of the root system are in eight-dimensional Euclidean space: they are described explicitly later in this article.

Therefore a symmetry group of rotational symmetry is a subgroup of E < sup >+</ sup >( m ) ( see Euclidean group ).

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.

Therefore, the matrix being positive definite means that f has a unique minimum ( zero ) when z is zero, and is strictly positive for any other z.

Therefore, the legislation of a society is vital to maintaining a society with optimum pleasure and the minimum degree of pain for the greatest amount of people.

Therefore, the lowest-energy state ( the ground state ) of the system must have a distribution in position and momentum that satisfies the uncertainty principle, which implies its energy must be greater than the minimum of the potential well.

Therefore, the objective function attains the global maximum ( subject to the constraints ) at and the global minimum at The point is a local minimum and is a local maximum, as may be determined by consideration of the Hessian matrix of.

Therefore, the definition of statutory rape is limited to sex with a person under the minimum age of consent.

Therefore the minimum thermal gradient necessary to create a stable solid front is as expressed below.

Therefore graduates from the MBBS or MBChB degrees do not hold doctorates, however physicians holding these degrees are referred to as ' Doctor ' as they are fully licensed as physicians upon the completion of mandatory clinical internship minimum of one full year after graduating from the medical college.

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 separation between D-branes controls the minimum mass open strings may have.

Therefore, work rules requiring minimum crew sizes, the assignment of duties to craft workers, and other " make-work " agreements do not constitute featherbedding.

Therefore, a body may not proceed to the global minimum of potential energy, as it would naturally tend to due to entropy.

Therefore most characters should, at a minimum, be placed in one of those subcategories instead of this main catch-all category.

Therefore it was designed to make no assumptions about the underlying channel other than a minimum bandwidth of 2400 Hz.

Therefore, Ramesses VII himself would have been on the throne for a minimum reign of 7 years and 8 or 9 months.

Therefore the European Commission proposed that it should be empowered to impose a minimum quality of services requirements.

Therefore protein design is the search for sequences which have the chosen structure as a free energy minimum.

Example: At 1000 kHz the wavelength is 300 m. Therefore the minimum length of the cage antenna is a bit more than 150 m ; 75 m for the radiator, 75 m for the cage and some metres to make the lower end of the cage inaccessible from the ground as the lower end of the cage carries a very high RF voltage. This antenna type is know in America as " Folded unipole " and extensively studied by John H. Mullaney

An independent set in L ( G ) corresponds to a matching in G, and a dominating set in L ( G ) corresponds to an edge dominating set in G. Therefore a minimum maximal matching has the same size as a minimum edge dominating set.

Therefore is at least the minimum number of linearly dependent columns.

Therefore we have, which is the minimum number of linearly dependent columns in.

Therefore, it is believed that the minimum connected dominating set problem and the maximum leaf spanning tree problem cannot be solved in polynomial time.