No previous antitrust case, he said, had involved interests of such magnitude or presented such complex problems of relief.

We now observe that the case in which **zg is a Af curve on a quadric is impossible if the complex of singular lines consists exclusively of the lines which meet Aj.

C & O president Walter J. Tuohy was summoned back for cross-examination by New York Central attorneys before examiner John Bradford who is hearing the complex case.

A more complex case

In the case of the complex numbers, C, there is a unique nontrivial automorphism that sends R into R: complex conjugation, but there are infinitely ( uncountably ) many " wild " automorphisms ( assuming the axiom of choice ).

a − λ1 is not invertible ( because the spectrum of a is not empty ) hence a = λ1: this algebra A is naturally isomorphic to C ( the complex case of the Gelfand-Mazur theorem ).

The case was extremely complex, requiring the court to review diplomatic exchanges dating back over 100 years.

In the case of infinite sets, the behavior is more complex.

In this case signals will naturally flow through the bus in physical or logical order, eliminating the need for complex scheduling.

If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable: in this case the system transfer function has non-repeated poles at complex plane origin ( i. e. their real and complex component is zero in the continuous time case ).

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

In contrast, patient testimonials, case reports, and even expert opinion ( however some critics have argued that expert opinion " does not belong in the rankings of the quality of empirical evidence because it does not represent a form of empirical evidence " and continue that " expert opinion would seem to be a separate, complex type of knowledge that would not fit into hierarchies otherwise limited to empirical evidence alone.

Expert systems are designed to solve complex problems by reasoning about knowledge, like an expert, and not by following the procedure of a developer as is the case in conventional programming.

However, there could still be an even more complex flash-back construction in American films in the case of W. S. Van Dyke ' sThe Lady of the Dugout ( 1918 ).

In general, the surrounding graph must be systematically recolored to turn the ring's coloring into a good one, as was done in the case above where there were 4 neighbors ; for a general configuration with a larger ring, this requires more complex techniques.

Successful vaults depend on the speed of the run, the length of the hurdle, the power the gymnast generates from the legs and shoulder girdle, the kinesthetic awareness in the air, and the speed of rotation in the case of more difficult and complex vaults.

The most important case is the field of complex numbers.

The state variable S may be a 32-or 64-bit unsigned integer ; in that case, S0 can be 0, and G ( S, n ) can be just S mod n. The best choice of F is a complex issue and depends on the nature of the data.

In the complex case of this theorem, the C-linearity assumptions demand, in addition to the assumptions for the real case, that for every vector x ∈ U, the vector be also in U and.

Accidental war is so sensitive a subject that most of the people who could become directly involved in one are told just enough so they can perform their portions of incredibly complex tasks.

Perhaps the best way to indicate the versatility of design that characterizes the use of plastics in signs and displays would be to look at what is happening in only one of the areas in this complex field -- changeable signs.

Since emotional reactions in the higher vertebrates depend on individual experience and are aroused in man, in addition, by complex symbols, one would expect that the hypothalamus could be excited from the cortex.

Tylor formulated one of the early and influential anthropological conceptions of culture as " that complex whole, which includes knowledge, belief, art, morals, law, custom, and any other capabilities and habits acquired by as of society.

Apollo ( Attic, Ionic, and Homeric Greek:, Apollōn ( gen .: ); Doric:, Apellōn ; Arcadocypriot:, Apeilōn ; Aeolic:, Aploun ; ) is one of the most important and complex of the Olympian deities in ancient Greek and Roman religion, Greek and Roman mythology, and Greco – Roman Neopaganism.

* A. E. van Vogt, regarded as one of the most popular and complex science fiction writers during its " Golden Age "

Alfred Elton van Vogt ( April 26, 1912 – January 26, 2000 ) was a Canadian-born science fiction author regarded as one of the most popular and complex science fiction writers of the mid-twentieth century: the " Golden Age " of the genre.

There is one fundamental equation that describes sound wave propagation, but the phenomena that emerge from it are varied and often complex.

The Falcons 78, 000 square foot headquarters and training facilities or located on a 50-acre site in Flowery Branch, Ga., the complex which was one of the first of its kind was completed in 1999.

Thus aesthetic judgments might be seen to be based on the senses, emotions, intellectual opinions, will, desires, culture, preferences, values, subconscious behavior, conscious decision, training, instinct, sociological institutions, or some complex combination of these, depending on exactly which theory one employs.

The apical complex consists of a set of spirally arranged microtubules ( the conoid ), a secretory body ( the rhoptry ) and one or more polar rings.

In animals at least as complex as an earthworm, the embryo forms a dent on one side, the blastopore, which deepens to become the archenteron, the first phase in the growth of the gut.

The C version was, at the time, one of the most complex programs in that language.

The relative importance and interactions between these different antioxidants is a very complex question, with the various metabolites and enzyme systems having synergistic and interdependent effects on one another.

Using these tools, one can write a more complex text editor, and a simple compiler for a higher-level language and so on, until one can have a graphical IDE and an extremely high-level programming language.

Regulation is the complex orchestration of events starting with an extracellular signal such as a hormone and leading to an increase or decrease in the activity of one or more proteins.

Conversely, in more recent times, Russian existentialist philosopher Lev Shestov viewed Job as the embodiment of the battle between reason ( which offers general and seemingly comforting explanations for complex events ) and faith in a personal god, and one man's desperate cry for him.

After initially building his career on " tough guy " roles Lancaster abandoned his " all-American " image in the late 1950s in favor of more complex and challenging roles, and came to be regarded as one of the best actors of his generation as a result.

then performs a complex conjugation, and then a matrix transpose, one ends up with the ket

When the Banach algebra A is the algebra L ( X ) of bounded linear operators on a complex Banach space X ( e. g., the algebra of square matrices ), the notion of the spectrum in A coincides with the usual one in the operator theory.

The topic of race in Brazil is a complex and diverse one.

The chordates and three sister phyla, the Hemichordata, the Echinodermata and the Xenoturbellida, make up the deuterostomes, one of the two superphyla that encompass all fairly complex animals.