The strong feeling is certainly there ; ;

In the meantime, while the South has been undergoing this phenomenal modernization that is so disappointing to the curious Yankee, Southern writers have certainly done little to reflect and promote their region's progress.

And it is certainly no slight to either of them to compare both their achievements and their impact.

Piepsam is not, certainly, religious in any conventional sense.

How literature does this, or for whom, is certainly not clear, but the content, form, and language of the `` message '', as well as the source, would all play differentiated parts in giving and molding a sense of purpose.

In the field of political values, it is certainly true that students are not radical, not rebels against their parents or their peers.

This is certainly an irrational dogmatism, in which the modern mind attempts to understand the spirit of the sixteenth century on twentieth-century terms.

The human is deeper than a mass ideology, certainly deeper than the isolated individual ; ;

His may typify a certain kind of postwar New York experience, but his experience is certainly not typical of his `` generation's ''.

Prosperity for the whole nation is certainly preferred to a tax cut.

Some of the poetic cadence of the older version certainly is lost in the newer one, but almost anyone, with a fair knowledge of the English language, can understand the meaning, without the necessity of interpretation by a Biblical scholar.

Sir -- Your editorial, `` Housing Speedup '', is certainly not the answer to our slum problems.

This is one of the most constructive suggestions made in this critical field in years, and I certainly hope it sparks some action.

The outlook for entertainment electronics in 1961 is certainly far from clear at present, but recent surveys have shown a desire on the part of consumers to step up their buying plans for durable goods.

Torrid Adios ( Torrid-Adios Molly ) is not so masculine as most of the colts, but I like his type and he certainly is one of the best-gaited pacers on the grounds.

Again Reverend Corder saved the bridge when Union soldiers planned to destroy it, after filling its two lanes with hay and straw -- but for what reason is not recorded nor remembered, certainly not because of pressure from an opposing Confederate force.

But if space and money are no problem and small children are not on hand every day, it is certainly more restful to have your pool and entertainment area removed from the immediate environs of the house.

If your pool is located on or near sloping ground, it may have natural drainage which is certainly more desirable than to be faced with the annual expense and labor of first pumping out the water and then scooping out all the debris.

The effect, needless to say, is almost terrifying, and though at times a bit obscure, the film is certainly a much-needed catharsis for the `` repressed '' movie-goer.

After all, social life in the group of the bees is by no means general, although it certainly is a striking feature.

This is puzzling to an outsider conscious of the classic tradition of liberalism, because it is clear that these Democrats who are left-of-center are at opposite poles from the liberal Jefferson, who held that the best government was the least government.

It is clear that, while most writers enjoy picturing the Negro as a woolly-headed, humble old agrarian who mutters `` yassuhs '' and `` sho' nufs '' with blissful deference to his white employer ( or, in Old South terms, `` massuh '' ), this stereotype is doomed to become in reality as obsolete as Caldwell's Lester.

This is clear.

This confession serves to make clear in part what is behind this sexual revolution: the craving for sensation for its own sake, the need for change, for new experiences.

Experience is not seen, as it is in classical rationalism, as presenting us initially with clear and distinct objects simply located in space and registering their character, movements, and changes on the tabula rasa of an uninvolved intellect.

In this respect experience is broader and full of a richer variety of potential meanings than the mind of man or any of his arts or culture are capable of making clear and distinct.

and it is surely clear that the first of these is the result of the way in which the individual's command of language interacts with the other two.

This is clear when one distinguishes the types of motion appropriate to both regions.

The formal position of Americans who identify themselves with one or more of the several identities of the Jewish symbol is already clear ; ;

There is a clear relationship between their educational evaluations and their basic pattern of general values.

Therefore, it is plain that the clear distinctions of the nineteenth century are no longer with us.

While it is hazardous to project the trend of history, it seems clear that a genuine community is painfully emerging in the Western world, particularly among the countries of Western Europe.

Even in these cases we should promote self-help by making it clear that our supporting assistance is subject to reduction and ultimately to termination.

It is not clear, however, whether they are thinking of all movable property or only of boats, trailers, aircraft or certain other types of personal property whose assessment would be advantageous to their particular towns.

The haphazard fiscal year calendar is an obstacle to the planning of clear and efficient state-local revenue and expenditure relationships.

As mentioned, the primary allocation objective to be followed in the allocation of stations on clear channels is the provision of widespread service, free from destructive interference.

And the reason this could happen is clear: men of government, business men, lawyers and all who concerned themselves with the welfare of their fellow men did not let their concern to run their businesses at a profit restrict the development of freedom and opportunity.

If the lever is pulled to clear a signal or move a switch, the tappet moves a short distance lengthwise at the same time.

* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then

The three-dimensional Euclidean space R < sup > 3 </ sup > is a vector space, and lines and planes passing through the origin ( mathematics ) | origin are vector subspaces in R < sup > 3 </ sup >.

By transferring upper triangularisation of operators of finite-dimensional complex vector space, there is an internal orthonormal Hilbert space basis for where runs from to, such that each of the corresponding-dimensional subspaces is-invariant.

* An arbitrary subspace of a second countable space is second countable ; subspaces of separable spaces need not be separable ( see below ).

* Any topological space which is the union of a countable number of separable subspaces is separable.

In continuous wavelet transforms, a given signal of finite energy is projected on a continuous family of frequency bands ( or similar subspaces of the L < sup > p </ sup > function space L < sup > 2 </ sup >( R ).

It is now part of the theory of Grassmannians, to which these co-ordinates apply in generality ( k-dimensional subspaces of n-dimensional space ).

In the mathematical subfield of linear algebra or more generally functional analysis, the linear span ( also called the linear hull ) of a set of vectors in a vector space is the intersection of all subspaces containing that set.

Given a vector space V over a field K, the span of a set S ( not necessarily finite ) is defined to be the intersection W of all subspaces of V which contain S. W is referred to as the subspace spanned by S, or by the vectors in S. Conversely, S is called a spanning set of W.

A linear subspace is usually called simply a subspace when the context serves to distinguish it from other kinds of subspaces.

A way to characterize subspaces is that they are closed under linear combinations.

If V is a vector space, one distinguishes " vector hyperplanes " ( which are subspaces, and therefore must pass through the origin ) and " affine hyperplanes " ( which need not pass through the origin ; they can be obtained by translation of a vector hyperplane ).

* Two vector subspaces, A and B, of an inner product space, V, are called orthogonal subspaces if each vector in A is orthogonal to each vector in B.

In terms of Euclidean subspaces, the " orthogonal complement " of a line is the plane perpendicular to it, and vice-versa.

Note however that there is no correspondence with regards to perpendicular planes, because vectors in subspaces start from the origin ( definition of vector subspace ).

It is the technique that enables the division of such multi-dimensional spaces into subspaces.

Instead the combined state vector time-evolves a path through the " larger volume ", whose dimensionality is the sum of the dimensions of the two subspaces.

The invariant subspaces of the bilateral shift is characterized by Beurling's theorem.

This device is known as a decoherence-free subspaces.