Then in 2 we show that any line involution with the properties that ( A ) It has no complex of invariant lines, and ( B ) Its singular lines form a complex consisting exclusively of the lines which meet a twisted curve, is necessarily of the type discussed in 1.

Nearest and next-nearest neighbors form a distorted octahedral complex, with the three atoms in the same double-layer being slightly closer than the three atoms in the next.

The nearest and next-nearest neighbors form a distorted octahedral complex, with the three atoms in the same double-layer being slightly closer than the three atoms in the next.

The axon initial segment ( AIS ) consists of a specialised complex of proteins which form part of the proximal axon of a neuron.

Twenty-five million years ago, a geological upheaval pushed up the Earth's crust to form the Armenian Plateau, creating the complex topography of modern Armenia.

) Like the central processing unit ( CPU ) in a modern computer, the mill would rely upon its own internal procedures, to be stored in the form of pegs inserted into rotating drums called " barrels ", to carry out some of the more complex instructions the user's program might specify.

Alkyne trimerization describes the cyclization of three alkynes, in the Dötz reaction an alkyne, carbon monoxide and a chromium carbene complex are the reactants. Diels-Alder reactions of alkynes with pyrone or cyclopentadienone with expulsion of carbon dioxide or carbon monoxide also form arene compounds.

* The complex numbers form a 2-dimensional unitary associative algebra over the real numbers.

* The quaternions form a 4-dimensional unitary associative algebra over the reals ( but not an algebra over the complex numbers, since if complex numbers are treated as a subset of the quaternions, complex numbers and quaternions do not commute ).

* Given any topological space X, the continuous real-or complex-valued functions on X form a real or complex unitary associative algebra ; here the functions are added and multiplied pointwise.

In the complex case, one can also check that the bilinear form is linear over i in one argument, and conjugate linear in the other.

The book has a long and complex history, but its final form is probably due to a Priestly redaction ( i. e., editing ) of a Yahwistic original text some time in the early Persian period ( 5th century BCE ).

In a slightly more complex form a sender and a receiver are linked reciprocally.

Linguists have found that, while humans form sentences in ways apparently governed by very complex systems, they are remarkably unaware of the rules that govern their own speech.

The cerebral cortex is a group of tight, dense, " gray matter " composed of the nucleus of the neurons whose axons then form the " white matter ", and is responsible for perception, relay of the sensory input ( sensation ) via the thalamic pathway, and most importantly directly or indirectly in charge of all the neurological functions, from simple reflexes to complex thinking.

This approach considers the complex realities surrounding the concept of crime and seeks to understand how changing social, political, psychological, and economic conditions may affect changing definitions of crime and the form of the legal, law-enforcement, and penal responses made by society.

It contains most of the cell's genetic material, organized as multiple long linear DNA molecules in complex with a large variety of proteins, such as histones, to form chromosomes.

In a synthesis reaction, two or more simple substances combine to form a more complex substance.

In complexation reactions, several ligands react with a metal atom to form a coordination complex.

Cnidarians form an animal phylum that is more complex than sponges, about as complex as ctenophores ( comb jellies ), and less complex than bilaterians, which include almost all other animals.

Freestyle features a dance tempo with stress on beats two and four ; syncopation with a bass line, lead synth, or percussion, and optional stabs of synthesized brass or orchestral samples ; sixteenth-note hi-hats ; a chord progression that lasts eight, 16, or 32 beats and is usually in a minor key ; relatively complex, upbeat melodies with singing, verses, and a chorus ; and themes about love or dancing.

A band like Hunters & Collectors, for example, saw their sound harden from their arty origins ( which included a brass-section, experimental percussion and complex arrangements ) to a more straightforward rock sound with emphasis on drums, bass and simple guitar riffs ; a sound that more suited the beer barns they were to play in over their extensive touring career.

The percussion artists perform complex patterns of rhythm and display their skill.

A year later they evolved into The Octet which added Ray Paczkowski on keyboards and Russell Remington on tenor sax and flute ; and The Dectet in 2002 through 2004 explored complex arrangements and changes of some songs included on Trey Anastasio, and was an evolved version of the octet, now a ten-piece band with the addition of Peter Apfelbaum on barritone sax and percussion, and Cyro Baptista on percussion.

Every Salsa composition involves complex African percussion based around the Clave Rhythm ( which has four types ), though there can be moments when the clave is hidden for a while, often when quoting Charanga, Changüí and Bomba.

The album Miditerranean Pads marked the beginning of very complex percussion arrangements that continued into the next two decades.

They played a form of bluesy, guitar-based and highlife-influenced jùjú that included complex talking drum-dominated percussion elements.

Symphonia: Sum Fluxae Pretium Spei ( 1993 – 1996 ) is his largest orchestral work, complex in structure and featuring contrasting layers of instrumental textures, from delicate wind solos to crashing brass and percussion outbursts.

In keeping with Brant ’ s belief that music can be as complex and contradictory as everyday life, his larger works often employ multiple, contrasting performing forces, as in Meteor Farm ( 1982 ) for symphony orchestra, large jazz band, two choruses, West African drum ensemble and chorus, South Indian soloists, large Javanese Gamelan ensemble, percussion orchestra and two Western solo sopranos.

Many percussion instruments, such as cymbals, tam-tams, and chimes, create complex and inharmonic sounds.

With this group he explored more complex and highly structured forms of composition, augmenting the group with everything from latin percussion to French horn to violin to accordion and an array of exotic instruments and vocalists.

However, the music remained complex, if narrower in focus, and Smith recorded additional keyboard and percussion parts onto backing tapes for the band to play over.

Colt found the mechanism so complex it included a spare percussion cylinder with each revolver.

Since reference pitches are not required, music may be broken up by complex and difficult to analyze pitch clusters, for example, a percussion sequence, and pitch analysis may resume immediately once an easier to identify pitch is played, for example, by a trumpet — no need to keep track of the last note of the previous line or solo nor any need to keep track of a series of intervals going back all the way to the start of a piece.

The Fulbe ( Fula ) of the north use complex vocal techniques with clapping percussion.

One or two of the more complex bifaces may have edges made straighter by a large percussion or two, but there is no sign of pressure flaking as depicted.

In percussion pieces such as Estudios de Fronteras ( 2004 ), Viñao used complex polyrhythms to realise with percussion instruments played by human performers ideas derived from Nancarrow ’ s etudes for pianola.

One of the highlights of a modern Carnatic music concert is the percussion solo ( thani avarthanam ), where the mridangam artist and other percussionists such as kanjira, morsing, and ghatam vidwans exchange various complex rhythmic patterns, culminating in a grand finale where the main artists resumes where he or she left off.

It is rhythmically complex, with percussion instruments including skratji ( a very large bass drum ) and snare drums, as well as saxophone, trumpet and occasionally trombone.

Folk music is dominated by vocal church music, as well as dances characterized by rich harmony and complex percussion made from slit drums or natural materials.

The African pedigree of African-American music is evident in some common elements: call and response, syncopation, percussion, improvisation, swung notes, blue notes, the use of falsetto, melisma, and complex multi-part harmony.

The Joujouka brotherhood play a form of reed, pipe, and percussion music that relies on drones, improvisation, and complex rhythms, much of which is unique to Joujouka.