Consequently, we can assert that a complex function f, whose real and imaginary parts u and v are real-differentiable functions, is holomorphic if and only if, equations ( 1a ) and ( 1b ) are satisfied throughout the domain we are dealing with.

Consequently, although the filing of cybersquatting lawsuits began as a defensive strategy to combat cybersquatting, such lawsuits also can be used as a way of strongarming innocent domain name registrants into giving up domain names that the trademark owner is not, in fact, entitled to.

Consequently, rum-based drinks ( once frowned upon as being the domain of sailors and down-and-outs ), also became fashionable, and the Daiquirí saw a tremendous rise in popularity in the US.

Consequently, the jet bundle is now recognized as the correct domain for a geometrical covariant field theory and much work is done in general relativistic formulations of fields using this approach.

Consequently, the symbolic quest for the philosopher ’ s stone was not superseded by scientific advances, and was still the domain of respected scientists and doctors until the early eighteenth century.

By definition, the domain of T < sup >∗</ sup > consists of elements such that is continuous on the domain of T. Consequently, the domain of T < sup >∗</ sup > could be anything ; it could be trivial ( i. e., contains only zero ) It may happen that the domain of T < sup >∗</ sup > is a closed hyperplane and T < sup >∗</ sup > vanishes everywhere on the domain.

Consequently the Gaussian theory only supplies a convenient method of approximating to reality ; and no constructor would attempt to realize this unattainable ideal.

Consequently, Frege and Husserl independently elaborated a theory of sense and reference before 1891.

Consequently, modern special relativity is now sometimes described as only a " local theory ".

Consequently, the quantum theory describing the low energy limit is a theory that describes the dynamics of these points moving in spacetime, rather than strings.

Consequently, Nazi theory held that Slavs in the Soviet Union were being ruled by " Jewish Bolshevik " masters.

Consequently, it was thought a small number of people in the world, at that time, could fully understand the theory in detail, but this was discredited by Richard Feynman on video recording available on YouTube.

Consequently, if quantum mechanics is to be a complete theory, relational quantum mechanics argues that the notion of " state " describes not the observed system itself, but the relationship, or correlation, between the system and its observer ( s ).

Consequently, statistical mechanics should be seen just as a particular application of a general tool of logical inference and information theory.

The dependence of physical quantities, such as the electric charge or electron mass, on the scale Λ is hidden, effectively swapped for the longer-distance scales at which the physical quantities are measured, and, as a result, all observable quantities end up being finite, instead, even for an infinite Λ. Gell-Mann and Low thus realized in these results that, while, infinitesimally, a tiny change in g is provided by the above RG equation given ψ ( g ), the self-similarity is expressed by the fact that ψ ( g ) depends explicitly only upon the parameter ( s ) of the theory, and not upon the scale μ. Consequently, the above renormalization group equation may be solved for ( G and thus ) g ( μ ).

Consequently, it is suggested that the management of the CFP could be improved through the application of the theory of subsidiarity-the principle that political decisions should be handled at the lowest, least centralised competent level .< ref > The subsidiarity principle was introduced into EU policies as part of the 1992 Maastricht Treaty ; however, it does not apply to areas such as the CFP over which the Community retains exclusive competence.

Consequently, his mature poems are often based on the conflict between the Platonic theory of ideal beauty and the disappointing reality of foul industrialism ( Neznakomka, 1906 ).

Consequently, when the potential function has continuous families of global minima, the space of vacua for the quantum field theory is a manifold ( or orbifold ), usually called the vacuum manifold.

Consequently, this theory has no extensions.

In a quantum field theory having this property, the vacuum expectation value of a product of many operators-each of them being either in region A or in region B where A and B are very separated-asymptotically equals the product of the expectation value of the product of the operators in A, times a similar factor from the region B. Consequently, sufficiently separated regions behave independently.

Consequently, the maps of western science fail to show large ' unorthodox ' parts of both theory and practise of science and social science, and reveal a complete disregard for art and many other high level humanistic qualities.

Consequently, performance studies is interdisciplinary, drawing from theories of the performing arts, anthropology and sociology, literary theory, and legal studies.

Consequently, labeling theory postulates that it is possible to prevent social deviance via a limited social shaming reaction in " labelers " and replacing moral indignation with tolerance.

) Consequently a complete mathematical solution can be obtained merely using techniques of linear algebra without involving the subject of group theory which is often required in sequential move puzzles.

Consequently, theorems or techniques ( such as homology, cohomology or homotopy theory ) which are only dependent on the homotopy class of spaces and maps involved may be applied to with the assumption that and that is actually the inclusion of a subspace.

Consequently, in this theory technology is not rendered as an artifact, but instead examines how people, as they interact with a technology in their ongoing practices, enact structures which shape their emergent and situated use of that technology.

Consequently, many virtues of extra-dimensional theories may be reproduced even though the little Higgs theory is 3 + 1-dimensional.

Consequently no adiabatic process initiated at nonzero temperature can lead to zero temperature.

Consequently, as can be seen from the following examples, in a device which consumes power the anode is positive, and in a device which provides power the anode is negative:

Consequently, there is bleeding into the skin and other organs, which can cause red and / or black patchy rash and hemoptysis / hematemesis ( coughing up / vomiting of blood ).

Consequently, the borderline between idealist epistemologies and others can be vague.

Consequently, in intentional activities, even non-existent objects can be constituted, and form part of the whole noema.

Consequently, ISO 4217 can use " X " codes for non-country-specific currencies without risk of clashing with future country codes.

Consequently, only a small number of matzos can be baked at one time, and the chabura members are enjoined to work the dough constantly so that it is not allowed to ferment and rise.

) Consequently, since rotations can be undone by rotating backward, quantum computations are reversible.

Consequently, no one view can claim to represent the absolute truth.

Consequently, an opportunity for negotiation between combatants is not uncommon, as proximity and fluctuating advantage can encourage diplomacy.

Consequently, adding more management components or increasing the level of each component can increase the level of integration of the business process link.

Consequently, he can be regarded as a forefather of the Industrial Revolution.

Consequently, “ the decay of population is the greatest evil that a state can suffer ; and the improvement of it the object which ought, in all countries, to be aimed at in preference to every other political purpose whatsoever .” More recently a similar view has been expressed by Smart who argued that all other things being equal a universe with two million happy people is better than a universe with only one million happy people.

Consequently an op-amp makes a sloppy comparator with propagation delays that can be as slow as tens of microseconds.

Consequently, a phase-locked loop can track an input frequency, or it can generate a frequency that is a multiple of the input frequency.

Consequently, the amount of power transferred from the transmitter to the receiver can be expressed as the product of two independent factors ; one depending on the directional properties of the transmitting antenna, and the other depending on the directional properties of the receiving antenna.

Consequently, laudanum became mostly obsolete as an analgesic, since its principal ingredient is morphine, which can be prescribed by itself to treat pain.

Consequently, black jaguars may produce either black or spotted cubs, but a pair of spotted jaguars can only produce spotted cubs.

Consequently, Ricky realizes that he can only hurt his father by falsely telling him he is homosexual.

Consequently they are sometimes classified as low clouds despite the fact their bases can be in the middle height range when the moisture content of the air is very low.

Consequently, even a very small error in knowledge of initial conditions can result in arbitrarily large deviations from predicted behavior.

Consequently, sumo wrestlers can be identified immediately when in public.

Consequently, no one view can claim to represent the absolute truth.