Given a small ball or marbles, he would invent games and play by himself for hours.

Given the small population of the region ( compared with the Central Canadian provinces or the New England states ), the regional economy is a net exporter of natural resources, manufactured goods, and services.

Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions.

Given the overall size of trade between Mexico and the United States, there are remarkably few trade disputes, involving relatively small dollar amounts.

Given its small domestic market but favourable location and a superb transport and communications base, Namibia is a leading advocate of regional economic integration.

Given typical workloads, Cray felt that the small cost incurred by being required to break large sequential memory accesses into segments was a cost well worth paying.

Given the small temperature range kinetic studies occur in, it is reasonable to approximate the activation energy as being independent of the temperature.

Given the type of warfare that had been carried out in the conflict — wherein highly mobile groups of soldiers and rebels continued to move to and from on the desert terrain, retreating at a time and then suddenly attacking to regain control of small towns and villages in the Eastern rebel held parts of Libya — had led to the technical becoming a vehicle of choice for both sides.

Given the slow speed and the coarse resolution this was not a feasible technique for printing large images, but could usefully print a small logo onto a letterhead and then the following letter, all in a single unattended print run without changing the print element.

* Given a small, privileged set of inputs ( e. g., reserved words for a compiler ), the permutation table can be adjusted so that those inputs yield distinct hash values, producing what is called a perfect hash function.

Given that the businesses in Miami Springs had always relied upon the large disposable incomes of the employees of the large airline carriers, the bankruptcy of both corporations in the same year created a chain reaction, eventually causing many small businesses to close their doors.

Given the borough's small size, as well as the county's small population, the presence of business and government remain limited.

Given the price of 1 / 32 Mark for six small fruit pies ( as seen in Dragonsinger ), it places the value at around $ 20 to the Mark.

: Little Hope Given Brain-Damaged Man ( A brain-damaged man is unlikely to recover, or a brain-damaged man is causing another situation to have little hope of resolution, or someone gave a brain-damaged man to a small girl named Hope.

Given any neighborhood of, we can choose a small positive and a small of either sign to get values both greater and less than.

Given Canada's small market and its position next to the dominant producer of feature films, the Canadian film industry receives substantial assistance from the government.

Given the prevalence of childhood sexual abuse, even if only a small proportion are repressed and only some of them are subsequently recovered, there should be a significant number of corroborated cases.

Given the small likelihood of his older brothers producing heirs, and William's relative youth and good health, it had long been considered extremely likely that he would become King in due course.

" Given that the parched region of the Gran Chaco ( largely uninhabited ) had been under dispute between Bolivia and Paraguay ever since the creation of both republics, each proceeded to establish a line of small garrisons ( fortines ), simply to establish a national presence and press their claims.

Given small differences in policies, the same type of software can produce radically different social outcomes.

Given the small size of the Netherlands, the latter co-operation is not likely to be symmetrical.

She also had a small role as a call girl hired by Al Pacino's character in Oliver Stone's sports drama Any Given Sunday, as well as a key supporting role in Woody Allen's The Curse of the Jade Scorpion.

Given a small angular displacement, the vessel may return to its original position ( stable ), move away from its original position ( unstable ), or remain where it is ( neutral ).

If V is finite-dimensional, then V * has the same dimension as V. Given a basis

Given a partial isometry V, the deficiency indices of V are defined as the dimension of the orthogonal complements of the domain and range:

Given an orientable Haken manifold M, by definition it contains an orientable, incompressible surface S. Take the regular neighborhood of S and delete its interior from M. In effect, we've cut M along the surface S. ( This is analogous, in one less dimension, to cutting a surface along a circle or arc.

; Degree of an extension: Given an extension E / F, the field E can be considered as a vector space over the field F, and the dimension of this vector space is the degree of the extension, denoted by: F.

Given the affine group of an affine space A, the stabilizer of a point p is isomorphic to the general linear group of the same dimension ( so the stabilizer of a point in Aff ( 2, R ) is isomorphic to GL ( 2, R )); formally, it is the general linear group of the vector space: recall that if one fixes a point, an affine space becomes a vector space.

* Given an eigenvalue λ < sub > i </ sub >, its geometric multiplicity is the dimension of Ker ( A − λ < sub > i </ sub > I ), and it is the number of Jordan blocks corresponding to λ < sub > i </ sub >.

Given an oriented manifold M of dimension n with fundamental class, and a G-bundle with characteristic classes, one can pair a product of characteristic classes of total degree n with the fundamental class.

Given two oriented submanifolds of complementary dimensions in a simply connected manifold of dimension, one can apply an isotopy to one of the submanifolds so that all the points of intersection have the same sign.

Given a field extension K / F, the field K can be considered as a vector space over the field F. The dimension of this vector space is the degree of the extension and is denoted by: F.

Given two maps f and g from an orientable manifold X to an orientable manifold Y of the same dimension, the Lefschetz coincidence number of f and g is defined as

Given this scaling dimension for, there are certain nonlinear modifications of massless scalar field theory which are also scale-invariant.

Given that the ZWZ focused on military aspects of the struggle, its civilian dimension was less clearly defined and developed more slowly — a situation exacerbated by the complex political discussions that were then unfolding between politicians in occupied Poland and the government in exile ( first located in Paris, and after the fall of France, in London ).

Given a connected and orientable manifold M of dimension 4k, the cup product gives rise to a quadratic form Q on the ' middle ' real cohomology group

Given below is the five point method for the first derivative ( five-point stencil in one dimension ).

Given Boston's natural and manmade geography, individuals from other neighborhoods in Boston must access the city's social center via one of the various bridges or tunnels that lead into central Boston.

Given the level of surveillance, and consistent with the conspiratorial traditions of Irish political movements, the union proceeded clandestinely, forming small groups of trusted friends in order to keep informers at bay, meeting in isolated locations and in subway tunnels.

Given the ( then highly unusual ) driver-only operation, the branch line was equipped with a two wire emergency telephone system at window level, a feature normally found only in tunnels on the London Underground.

Given this, one day met the strongest men of the population determined from the mountains to fill the huge birds ' nests, but the initiative was not bad, neighbors were able to seal the tunnels, the birds could not leave nests there were dead and never again do more harm to the community.