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certain and areas
`` In addition to the usual tools, I make constant use of cleansing tissue, not only to wipe my brushes, but to mop up certain areas, to soften edges, and to open up lights in dark washes.
No antigen was detectable in certain dark spherical areas in most cells.
The choice of the single member district was dictated to a certain extent by problems of communication and understanding in the more remote areas of the country, but it also served to minimize the national political value of the elections.
Elaborate studies have been made in labor surplus areas in order to identify sufficient numbers of local job vacancies and future replacement needs for certain skills to justify training programs for those skills.
Moreover, it is likely that Federal policies aimed at stimulating a faster rate of economic growth of the country, to keep ahead of the Communist countries and to demonstrate that our free economic system is better than theirs, will lead to rising Federal spending in certain areas such as education, housing, medical aid, and the like.
In certain other pictures, however, Braque began to paint areas in exact simulation of wood graining or marbleizing.
Small areas that aren't right for a certain crop may lie next to areas that are well suited to that crop.
It is not often realized to what degree certain trades are in many communities closed areas of employment, except for a lucky few.
`` When they became members of the city police narcotics unit '', Sokol said, `` they were told they would have to get to know certain areas of Chicago in which narcotics were sold and they would have to get to know people in the narcotics racket.
and whether these would qualify them for `` congenial '', `` happy '' relations to other people in certain community areas.
Later, consequences for UNITA members in Luanda were harsh with FAPLA veterans persecuting their erstwhile opponents in certain areas and reports of vigilantism.
In recent years, persuasion has tipped over into debates over conformity in certain areas of doctrine, discipline, worship, and ethics.
Mixed fracture surfaces can be characterised by a certain percentage of adhesive and cohesive areas.
However, certain Zarubintsy elements remained, found scattered throughout neighbouring areas of eastern Europe.
Females prefer to use traditional calving grounds restricted to certain areas, while newborn calves lie in hiding for a week or more, receiving short visits by the mother to suckle.
In certain areas of the UK, such as Lancashire, the price was increased to 99p, while elsewhere it remained as 85p.
* Sea caves are made when certain rock beds are more susceptible to erosion than the surrounding rock beds because of different areas of weakness.
Another concern is that certain sectors of society are not sufficiently benefiting from the PRC's economic development ; one example of this is the wide gap between urban and rural areas.
The few other areas that operate the special legislative procedures are justice & home affairs, budget and taxation and certain aspects of other policy areas: such as the fiscal aspects of environmental policy.
The EU's budget ( which is around 116. 4 billion euro ) is subject to a form of the ordinary legislative procedure with a single reading giving Parliament power over the entire budget ( prior to 2009, its influence was limited to certain areas ) on an equal footing to the Council.
In certain areas of the law another head of damages has long been available, whereby the defendant is made to give up the profits made through the civil wrong in restitution.
" When Robert B. Anderson, Eisenhower's first Secretary of the Navy argued that the Navy must recognize the " customs and usages prevailing in certain geographic areas of our country which the Navy had no part in creating ", Eisenhower overruled him: " We have not taken and we shall not take a single backward step.
Men are often the victim in certain areas of employment as men begin to seek work in office and childcare settings traditionally perceived as " women's jobs ".

certain and mathematics
In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.
In chemistry, physics, and mathematics, the Boltzmann distribution ( also called the Gibbs Distribution ) is a certain distribution function or probability measure for the distribution of the states of a system.
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.
In mathematics, more specifically in abstract algebra and ring theory, a Euclidean domain ( also called a Euclidean ring ) is a ring that can be endowed with a certain structure – namely a Euclidean function, to be described in detail below – which allows a suitable generalization of the Euclidean division of the integers.
* In mathematics, a certain kind of subset of a partially ordered set.
Kronecker, now seen as one of the founders of the constructive viewpoint in mathematics, disliked much of Cantor's set theory because it asserted the existence of sets satisfying certain properties, without giving specific examples of sets whose members did indeed satisfy those properties.
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects from a certain collection.
In mathematics, graphs are useful in geometry and certain parts of topology, e. g. Knot Theory.
In mathematics, more specifically in the area of modern algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.
Idempotence ( ) is the property of certain operations in mathematics and computer science, that they can be applied multiple times without changing the result beyond the initial application.
It can refer to certain areas of literature, languages, philosophy, history, mathematics, psychology, and science.
Albert Einstein stated that " as far as the laws of mathematics refer to reality, they are not certain ; and as far as they are certain, they do not refer to reality.
An alternative view is that certain scientific fields ( such as theoretical physics ) are mathematics with axioms that are intended to correspond to reality.
In mathematics, modular arithmetic ( sometimes called clock arithmetic ) is a system of arithmetic for integers, where numbers " wrap around " upon reaching a certain value — the modulus.
Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the Scientific Revolution in the 17th century, the natural sciences emerged as unique research programs in their own right.
However this definition does not allow star polytopes with interior structures, and so is restricted to certain areas of mathematics.
In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups ; they share many properties with their finite quotients.
He or she will usually have a primary qualification in one of several fields: mathematics, the physical sciences ( e. g. chemistry, physics, biology ), engineering ( e. g. mechanical, chemical, Materials Science & Engineering or civil engineering ), medicine, or certain technologies, notably materials or food.
Everett did not draw the conclusion that it was the lack of numbers in their language that prevented them from grasping mathematics, but instead concluded that the Pirahã had a cultural ideology that made them extremely reluctant to adopt new cultural traits, and that this cultural ideology was also the reason that certain linguistic features that were otherwise believed to be universal did not exist in their language.
When theories are studied in mathematics, they are usually expressed in some formal language and their statements are closed under application of certain procedures called rules of inference.
In various branches of mathematics, a useful construction is often viewed as the “ most efficient solution ” to a certain problem.
His dissertation, entitled, " Solutions of the Mathieu equation of period 4 pi and certain related functions ", was beyond the comprehension of the chemistry and physics faculty, and only when some members of the mathematics department, including the chairman, insisted that the work was good enough that they would grant the doctorate if the chemistry department would not, was he granted a Ph. D. in chemistry in 1935.
In electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal.

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