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These and simplifications
These grammatical simplifications resemble those observed in pidgins, creoles and other contact languages, which arise when speakers of two different languages need to communicate with one another.
These simplifications make it much easier to understand what is happening in the model.
These mathematical simplifications and calculations are the realm of Fourier analysis and synthesis – together, they can describe what happens when light passes through various slits, lenses or mirrors curved one way or the other, or is fully or partially reflected.
These newer models include more physical processes in the simplifications of the equations of motion in numerical simulations of the atmosphere.
These theorems may be considered as simplifications of the Boltzmann result.

These and complex
These quantum numbers only occur in certain combinations of values, and their physical interpretation changes depending on whether real or complex versions of the atomic orbitals are employed.
These were larger than the great majority of German woodcuts hitherto, and far more complex and balanced in composition.
These programs now easily run on most personal computers, and are often capable of more complex functions than those which would have necessitated the most powerful mainframe computers several decades ago.
These castes had a complex structure in the fragmented city states of Italy such as Genoa, Venice, Naples, Roma, Florence and Lombardy ; in some, the merchants were the nobili, in others the nobili despised the merchant caste and were agriculturalists, in yet others the nobili caste despised all work.
These cover Clement's celestial hierarchy, a complex schema in which the universe is headed by the Face of God, below which lie seven protoctists, followed by archangels, angels and humans.
These two groups of viruses share a distinctive 12-fold arrangement of subunits in the portal complex.
These range from specific market access issues and difficulties for businesses facing a highly regulated and complex system through to restrictions in the export of agricultural goods ( potatoes ) and fishery products because they do not conform with EU quality norms.
These hypothetical forms of life range from simple bacteria-like organisms to beings far more complex than humans.
These formulas can even serve as the definition of the trigonometric functions for complex arguments x.
These seizures arise from the frontal lobes and consist of complex motor movements, such as hand clenching, arm raising / lowering, and knee bending.
These G proteins are made from three subunits, with the G domain located on the largest one ( the α unit ); together with the two smaller subunits ( β and γ units ), they form a tightly associated protein complex.
These proteins help to modulate IGF action in complex ways that involve both inhibiting IGF action by preventing binding to the IGF-1 receptor as well as promoting IGF action possibly through aiding in delivery to the receptor and increasing IGF half-life.
These were originally considered primitive, but it now appears they developed from more complex ancestors.
These complex architectures allow some group I and group II introns to be self-splicing, that is, the intron-containing RNA molecule can rearrange its own covalent structure so as to precisely remove the intron and link the exons together in the correct order.
These resulted in increasingly complex structures of highly sophisticated and controlled color and surface integrity.
These functions were more complex than simple AND and OR gates.
These " aether-wind " experiments led to a flurry of efforts to " save " aether by assigning to it ever more complex properties, while only few scientists like Emil Cohn or Alfred Bucherer considered the possibility of the abandonment of the aether concept.
These oppositions are inherent to modernism: it is in its broadest cultural sense the assessment of the past as different to the modern age, the recognition that the world was becoming more complex, and that the old " final authorities " ( God, government, science, and reason ) were subject to intense critical scrutiny.
These are usually electrically fired and have complex sighting systems.
These programs provide support for dynamics and expression markings, chord and lyric display, and complex score styles.
These became essential with the appearance of complex synthesizers such as the Yamaha FS1R, which contained several thousand programmable parameters, but had an interface that consisted of fifteen tiny buttons, four knobs and a small LCD.
These polypeptides usually have a related function ( they often are the subunits composing a final complex protein ) and their coding sequence is grouped and regulated together in a regulatory region, containing a promoter and an operon.
These regions are all interconnected by means of complex neural pathways.
These works include complex polyphonic ensembles and reflect musical developments of their times.
These principles inevitably resulted in a large language which would need compilers substantially more complex than those for COBOL or Fortran.

These and field
These services include procurement and technical assistance and notice of surplus sales and invitations to bid on Government contracts for products and services within the registrants' field of operations.
These are as follows: ( 1 ) field work procedures.
These processes are important in the vacuum state and renormalization of a quantum field theory.
These ions, under the influence of the electric field, are accelerated into the cathode surface containing the sample, bombarding the sample and causing neutral sample atom ejection through the process known as sputtering.
These positions are further differentiated by which side of the field the player spends most time in.
These developments have indeed made our lives better, but the best contribution that bionics has made is in the field of biomedical engineering.
These connections shed the boundaries between combinatorics and parts of mathematics and theoretical computer science, but at the same time led to a partial fragmentation of the field.
These ideas were unified by Kenneth Wilson in 1972, under the formalism of the renormalization group in the context of quantum field theory.
These forces arise from the presence of the body in force fields, e. g. gravitational field ( gravitational forces ) or electromagnetic field ( electromagnetic forces ), or from inertial forces when bodies are in motion.
These regions may be initiated by field electron emission, but are then sustained by localized thermionic emission once a vacuum arc forms.
These small electron-emitting regions can form quite rapidly, even explosively, on a metal surface subjected to a high electrical field.
These field markings remained unchanged until the 1996 season.
These regiments, which rarely took the field as complete organizations, served throughout the American Indian Wars through the close of the frontier in the 1890s.
These generalizations of the convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing.
These are wide zones of the Sun where the magnetic field is unipolar and opens towards the interplanetary space.
These theories were given credence by the fact that when Germany surrendered in November 1918, its armies were still in French and Belgian territory, Berlin remained 450 miles from the nearest front, and the German armies retired from the field of battle in good order.
These ships carry equipment and supplies to support a major armed force with tanks, armoured personnel carriers, munitions, fuel, spare parts and even a mobile field hospital.
These two types or behaviors of EM field are sometimes referred to as the near and far field.
These organizations each host 1-2 conferences each year and provide peer-reviewed journals of current research in the field.
These methods are analogous to methods used in other areas of science, such as the field of system identification in systems analysis and control theory.
These unpaired dipoles ( often called simply " spins " even though they also generally include angular momentum ) tend to align in parallel to an external magnetic field, an effect called paramagnetism.
These theories predict that for each electroweak Higgs doublet, there is a corresponding colored Higgs triplet field with a very small mass ( many orders of magnitude smaller than the GUT scale here ).
These recent clinical successes have led to a renewed interest in gene therapy, with several articles in scientific and popular publications calling for continued investment in the field.

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