In some areas, the progress is slower than in others.

Britain until recently went along in some areas with all of the enthusiasm of the groom at a shotgun wedding.

For some time the Communists honored the distinction between the Soviet zone of Germany and the Soviet sector of Berlin by promulgating separately the laws for the two areas.

In Southern Illinois, the new federal program of help to economically depressed areas ought to provide some stimulus to growth.

In the more primitive areas, where the capacity to absorb and utilize external assistance is limited, some activities may be of such obvious priority that we may decide to support them before a well worked out program is available.

While this may well be true in general, I believe it is also important to keep in mind that some recent developments suggest that over the next year or so military electronics may be one of the most strongly growing areas in an economy which is not expanding rapidly in other directions.

Marine dealers and even some manufacturers who sell direct in non-dealer areas cooperate in enabling you to launch now and pay later.

After all, we did pretty well in some other areas of the Olympics competition.

Here are some key areas to examine to make sure your pricing strategy will be on target:

They are laid a minimum of 24'' '' deep and in some areas four feet down, particularly under roads, to stay clear of all other piping such as water and sewers and to minimize shocks from heavy trucking.

The mucosa of the jejunum and ileum showed similar changes, and in some areas the submucosa was edematous and contained considerable numbers of neutrophils.

From here they proceeded to ( 3 ) These same areas in relation to their own future family life stages, developing these to the extent of examining various crises which could be expected to confront them at some time or other.

Apart from some areas of recurring trouble, like Bani Mellal, where inexperienced officials had been appointed, there is little evidence that local officials intervened in the electoral process.

These signs are the inventories of unsold houses in some areas of the country and the moderate rise in vacancy rates for apartments ( 7.6% in September ).

In some cases, it may be more advantageous to assign locations to RDWS associated with DA and DC areas in some other part of storage, i.e., not immediately preceding the DA or DC areas.

It is this spirit which explains some of the anomalies of American Catholic higher education, in particular the wasteful duplication apparent in some areas.

Studies of membership trends, even in some areas where population is expanding, show that numbers of churches have had little net increase, though many new members were received.

However, in some areas the aardwolf is hunted for its fur.

In ancient times, navigation through the sea was easier than travelling across the rough terrain of the Greek mainland ( and to some extent the coastal areas of Anatolia ).

Alpine festivals vary from country to country and often include the display of local costumes such as dirndl and trachten, the playing of Alpenhorns, wrestling matches, some pagan traditions such as Walpurgis Night, and in many areas Carnival is celebrated before Lent.

The government has undertaken regulatory reforms in some areas, including substantial opening of trade policy, but inefficient public administration in which commercial and regulatory interests are co-mingled limit the impact of these reforms.

From the town surveyor, Hans learned drawing and mathematics and, from a university student, some academic subjects.

Just as in the arts the Greeks sought some reality behind appearances, so in mathematics they sought permanent principles which could be applied wherever the conditions were the same.

In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, though it is used in almost every academic field to some extent.

The axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced.

In mathematics, the associative property is a property of some binary operations.

* Absorbing element, in mathematics, an element that does not change when it is combined in a binary operation with some other element

Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution ; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.

This is philosophically unsatisfying to some and has motivated additional work in set theory and other methods of formalizing the foundations of mathematics such as New Foundations by Willard Van Orman Quine.

In mathematics, the Borsuk – Ulam theorem, named after Stanisław Ulam and Karol Borsuk, states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point.

The term can also be applied to some degree to functions in mathematics, referring to the anatomy of curves.

Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows ( also called morphisms, although this term also has a specific, non category-theoretical meaning ), where these collections satisfy some basic conditions.

Categories now appear in most branches of mathematics, some areas of theoretical computer science where they correspond to types, and mathematical physics where they can be used to describe vector spaces.

In mathematics, a countable set is a set with the same cardinality ( number of elements ) as some subset of the set of natural numbers.

In mathematics, specifically general topology and metric topology, a compact space is a mathematical space in which any infinite collection of points sampled from the space must — as a set — be arbitrarily close to some point of the space.

The Langlands program is a far-reaching web of these ideas of ' unifying conjectures ' that link different subfields of mathematics, e. g. number theory and representation theory of Lie groups ; some of these conjectures have since been proved.

In mathematics, a contraction mapping, or contraction, on a metric space ( M, d ) is a function f from M to itself, with the property that there is some nonnegative real number < math > k < 1 </ math > such that for all x and y in M,

Decision problems typically appear in mathematical questions of decidability, that is, the question of the existence of an effective method to determine the existence of some object or its membership in a set ; many of the important problems in mathematics are undecidable.

Certain forms treat all knowledge as empirical, while some regard disciplines such as mathematics and logic as exceptions.

Note that congruences alter some properties, such as location and orientation, but leave others unchanged, like distance and angle s. The latter sort of properties are called invariant ( mathematics ) | invariant s and studying them is the essence of geometry.

# Variables describe some of the properties of mathematics.

Unsurprisingly, Galois ' collected works amount to only some 60 pages, but within them are many important ideas that have had far-reaching consequences for nearly all branches of mathematics.

* Function ( mathematics ), an abstract entity that associates an input to a corresponding output according to some rule

A number representation ( called a numeral system in mathematics ) specifies some way of storing a number that may be encoded as a string of digits.