Here the structure group has been reduced completely to the trivial group.The problem can now be handled by methods such as the Frobenius theorem.…

The most common definition is that a Lie group is simple if it is connected, non-abelian, and every closed connected normal subgroup is either the identity or the whole group.In particular, simple groups are allowed to have a non-trivial center.In this article the connected simple Lie groups with trivial center are listed.…

The case of five given elements is trivial, requiring only a single application of the sine rule.For four given elements there is one non-trivial case which is discussed below.…

In this article the connected simple Lie groups with trivial center are listed.Once these are known, the ones with non-trivial center are easy to list as follows.Any simple Lie group with trivial center has a universal cover, whose center is the fundamental group of the simple Lie group.…

Now, the name Mycoplasma should exclusively be used for members of the genus Mycoplasma, rather than the use as a trivial name for any mollicute.As the trivial name has been used in literature for a long time, this is yet not always the case.Traditionally the taxonomy of bacteria was based on similarities and differences in morphology (Linnaean taxonomy).…

Consider a finite p-group G (that is, a group with order p n, where p is a prime number and n > 0).We are going to prove that every finite p-group has a non-trivial center.…

Prior to World War II, Japanese rarely if ever saw science fiction as worthwhile literature.Instead, it was considered a form of trivial literature for children.…

In particular, simple groups are allowed to have a non-trivial center.In this article the connected simple Lie groups with trivial center are listed.Once these are known, the ones with non-trivial center are easy to list as follows.…

Factories and other organizations were often named after Partisans who were declared national heroes.This practice also spread to street names, names of parks and buildings, and some more trivial features.Before World War II, Croatia's industry was not significant, with the vast majority of the people employed in agriculture.…

They woke themselves by the use of alarm clocks at different hours of the night and recorded their dreams at the instant of waking They slept with a note pad right by their bed so as to be able to take note of any dreams as quickly as possible.Each morning, they studied all the records regardless of whether they seemed slight and trivial or significant.They also took account of the different types of dreams and they discovered elements of all various emotions As part of the project, they also considered the relation of the dream to the conscious, waking life, distinguishing the individuals and places in their dream experiences.…

Unlike stocks and shares, the majority of transactions in the philatelic or stamp market take place informally, by mail order, or in retail environments, and therefore the size of the market is hard to determine.The market is certainly much smaller than the financial markets but it is not trivial.…

Still, De Morgan is given credit for stating the laws in the terms of modern formal logic, and incorporating them into the language of logic.De Morgan's laws can be proved easily, and may even seem trivial.Nonetheless, these laws are helpful in making valid inferences in proofs and deductive arguments.…

If this condition holds for one x in X, it holds for all the elements of X.It follows that a non-trivial regular two-graph has an even number of points.…

Yet in a very strong sense the explanation of common descent is also trivial.Common descent tries to account only for the similarities between creatures.…

The smallest non-cyclic group has four elements; it is the Klein four-group.Four is also the order of the smallest non-trivial groups that are not simple.Four is the maximum number of dimensions of a real division algebra (the quaternions), by a theorem of Ferdinand Georg Frobenius.…

She is a capable enough sword fighter to fend off a trained samurai.Her extensive book-learning makes her a fountain of knowledge from the grand to the trivial.She can also read extremely fast; the novels note she is able to memorize every word in a book with only ten minutes' reading.…

In Euclidean space R n, or any convex subset of R n, there is only one homotopy class of loops, and the fundamental group is therefore the trivial group with one element.A path-connected space with a trivial fundamental group is said to be simply connected.…

Deepak Chopra and other proponents of ancient Vedic spiritual and other mystical teachings insist on the view that there is absolutely no coincidence in the world.Everything that occurs can be related to a prior cause or association, no matter how vast or how minute and trivial.All is affected by something related to it that is seen or unseen, cognized or unknowable.…

Rather than being a limitation of Recovery's program, this is intended to be a novel treatment approach.A day-today trivial event may generalize to other problems experienced by the member.Discussion of trivialities is less threatening than complex problems, making a discussion of coping mechanisms possible.…

From the fact that L = SL, it follows that many more problems are SL-complete with respect to log-space reductions: every problem in L or in SL is SL-complete; moreover, even if the reductions are in some smaller class than L, L-completeness is equivalent to SL-completeness.In this sense this class has become somewhat trivial.There are well-known classical algorithms such as depth-first search and breadth-first search which solve USTCON in linear time and space.…