Therefore, if the determinant equals zero then the parallelogram has no area, and that will happen when two vectors are on the same line.

Therefore, they may be represented as two radial vectors in a sphere in reciprocal space, which shows the values of q that are sampled in a given diffraction image.

Therefore, the three vectors

Therefore, through the use of second nature and third nature society is able to use and explore new vectors of possibility where information can be moulded to create new forms of interaction ( Wark, 1997, p. 28 ).

Therefore all tangent vectors in a point p span a linear space, called the tangent space at point p. For example, taking a 2-dimensional space, like the ( curved ) surface of the Earth, its tangent space at a specific point would be the flat approximation of the curved space.

Therefore these two vectors differ by a phase, which can depend on the two group elements ( a, L ) and ( b, M ).

Therefore, the column vectors of constitute a set of linearly independent solutions for.

Therefore, proportional positive vectors are equivalent when considered as compositions.

Therefore, one also talks about tangent vectors.

It turns out that S ( V ) is in effect the same as the polynomial ring, over K, in indeterminates that are basis vectors for V. Therefore this construction only brings something extra when the " naturality " of looking at polynomials this way has some advantage.

Therefore the multistatic ambiguity function is mostly usefully defined as a function of two-or three-dimensional position and velocity vectors for a given multistatic geometry and transmitted waveform.

Therefore, it is evident that many mistakes will occur if you try to store a large number of vectors.

Therefore, the g and h vectors are also subject to a related arbitrary rotation, despite the fact that the space spanned by the two vectors is invariant.

Therefore, strictly speaking, root vegetables ( such as potatoes, carrots or onion ) are not to be used as this will result in death of vegetables.

Therefore, a pair of words whose earlier forms are distinct, yet similar, as far back as they have been traced, could in theory have come from a common root in an even earlier language, making them real cognates.

Therefore the shortest possible path from the root of T to any leaf consists of B black nodes.

Therefore, the word " vaccination " — first used by Edward Jenner ( an English physician ) in 1796 — has the Latin root vaccinus meaning of or from cows.

Therefore, the root of the red / purple-branched variant can be consumed directly.

Therefore, in order for aspects of larger fictional universes to adhere to certain conditions of the overall continuity and even believability of the WNU ( whose root conceit has always been that characters the world knows as fictional actually lived, or are yet living, and that their adventures are based on true events embroidered by the genre authors who serve as their " biographers "), certain accounts of the characters ' lives that overly strain suspension of disbelief are often labeled as " distortion " of actual events, or dismissed as complete fabrication.

Therefore, bridge 3 is the root bridge.

Assuming that the cost of traversing any network segment is 1, the least cost path from bridge 4 to the root bridge goes through network segment c. Therefore, the root port for bridge 4 is the one on network segment c.

Therefore, z < sup > k </ sup > is a primitive ath root of unity where

Therefore the name of the island probably has the same root as the name of the Norse god Freyr, brother to Freyja.

Therefore it is safe to conclude that Fard was more focused on dealing with the root cause of evil that resided within the original people.

Therefore the square of a rational non-integer is always a non-integer ; by contrapositive, the square root of an integer is always either another integer, or irrational.

( To see this, note that there is some extension field in which f has a root ; necessarily, in E. Therefore, working over E, ( the final equality in the sequence follows from freshman's dream ), and f does not have distinct roots.

Therefore, he considers this pre-Greek root to be of Thracian origin, meaning " great ".

Therefore, the Five Pure Lights are the ' root ' ( Tibetan: gzhi ) of the Western scientific conceptions of matter and energy.

Therefore to extrapolate, the kīla is identified with consciousness and the root of sentience, the buddha-nature.

Therefore, posterior teeth ( i. e. molars and premolars ) should in almost all situations be crowned after undergoing root canal therapy to provide for proper protection against fracture ( mandibular premolars, being very similar in crown morphology to canines, may in some cases be protected with intracoronal restorations ).

Therefore the redistribution of auxin toward the lower flank of a root, that has been reoriented in the gravity field, can initiate differential growth resulting in root curvature.

Therefore the anomalous phase may only be equal to a square root of one, in other words, plus or minus one.

Therefore if then there is no lifting of r to a root of f ( x ) mod p < sup > k + 1 </ sup >, while if then every lifting of r to modulus p < sup > k + 1 </ sup > is a root of f ( x ) mod p < sup > k + 1 </ sup >.

" Therefore, in terms of liberalism, both Peking University and Taiwan University are born from the same root.

Therefore no complete system, i. e. including the electromagnetic modes, can have negative temperatures, since there is no highest energy state, so that the sum of the probabilities of the states would diverge for negative temperatures.

Therefore, in order to describe a given signal completely, it's necessary to quote the color system and the broadcast standard as capital letter.

Therefore a computer system usually contains several kinds of storage, each with an individual purpose.

Therefore, they were un-priced and hence the system would be necessarily inefficient since the central planners would not know how to allocate the available resources efficiently.

Therefore, the change in enthalpy can be devised or represented without the need for compressive or expansive mechanics ; for a simple system, with a constant number of particles, the difference in enthalpy is the maximum amount of thermal energy derivable from a thermodynamic process in which the pressure is held constant.

Therefore enthalpy can only accurately be used in a closed system.

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

Therefore, the behavior of a linear time-invariant system can be analyzed at each frequency independently.

Therefore, carbon-rich fuels like gases made from coal are compatible with the system.

Therefore any electron can interchange with another one with no observable physical change of the system at all.

Therefore, " e proposed a system to pay people with certificates indicating how many hours of work they did.

Therefore, to keep its economy afloat, Japan ran massive budget deficits ( added trillions in Yen to Japanese financial system ) to finance large public works programs.

" Therefore, although the thesis of the " Mysterium Cosmographicum " was in error, modern astronomy owes much to this work " since it represents the first step in cleansing the Copernican system of the remnants of the Ptolemaic theory still clinging to it.

Therefore, he was able to hold knowledge across a vast array of subjects: " the international world order, the political and economic organisation of contemporary society, especially France, the institutional and legal frameworks that regulate the lives of ordinary citizens, the educational system, the media networks that control and disseminate information.

Therefore, the Maltese court system safeguards both the positions of the judge and to a certain extent, the position of the courts, from political interference by government or by Parliament.

Therefore, the optimal mutation rate for a species is a trade-off between costs of a high mutation rate, such as deleterious mutations, and the metabolic costs of maintaining systems to reduce the mutation rate, such as DNA repair enzymes .< ref name = Sniegowski > Viruses that use RNA as their genetic material have rapid mutation rates, which can be an advantage since these viruses will evolve constantly and rapidly, and thus evade the defensive responses of e. g. the human immune system.

Therefore, a system which rewards effort in this way is not just, because effort and hard work is not something we can claim credit for.

Therefore, the abundance of < sup > 60 </ sup > Ni present in extraterrestrial material may provide insight into the origin of the solar system and its early history.

Therefore, the effects of a neurotransmitter system depend on the connections of the neurons that use the transmitter, and the chemical properties of the receptors that the transmitter binds to.

Therefore, the absence of life in Venus, with a somewhat similar composition to Earth's primitive conditions or the absence of life on Mars, given the proposed " resilience " of life in space, damages the panspermia theory, at least based on observations of our own Solar System-the theory suggests that life would be more abundant in the Solar system.

Therefore, the most important requirement of a real-time system is predictability and not performance.

Therefore, in that model of voting behavior, the two-round system passes all criteria that the contingent vote passes, and fails all criteria the contingent vote fails.

Therefore the task of a scheme selection for achieving the optimal values of the steganographic system is not trivial.

Therefore, to establish a mathematical statement as a theorem, the existence of a line of reasoning from axioms in the system ( and other, already established theorems ) to the given statement must be demonstrated.

Therefore, many things only become apparent once a certain amount of work has been done on a new system, allowing a user to experience it.