Here the kets and columns are identified with the vectors of V and the bras and rows with the dual vectors or linear functionals of the dual space V < sup >*</ sup >, with conjugacy associated with duality.

Here the first three vectors are linearly independent ; but the fourth vector equals 9 times the first plus 5 times the second plus 4 times the third, so the four vectors together are linearly dependent.

Here, each vector Y < sub > j </ sub > of the f ' basis is a linear combination of the vectors X < sub > i </ sub > of the f basis, so that

Here are some examples of probability vectors:

Here the ( pc )< sup > 2 </ sup > term represents the square of the Euclidean norm ( total vector length ) of the various momentum vectors in the system, which reduces to the square of the simple momentum magnitude, if only a single particle is considered.

Here, and are vectors in the tangent space ; that is,.

Here the vectors N, B and the torsion are not well defined.

Here the underlying random variables may be random vectors, each having the same dimension, in which case the mixture distribution is a multivariate distribution.

Here, general means maximizing the number of input vectors that the

Here and are vectors in, is a complex number, and denotes the complex conjugate of.

Here a non-trivial coordinate subspace means a linear subspace spanned by any proper subset of basis vectors.

Here, r is attained for x taken to be the Perron-Frobenius eigenvector v. The proof requires that values f on the other vectors are less or equal.

Here, it is useful to know that any Killing vectors which may be present will ( in the case of a vacuum solution ) automatically satisfy the curved spacetime Maxwell equations.

Here, is the dyadic product of two vectors and.

Here in an evening Persians enjoy many of the things which are important to them: poetry, water, the moon, a beautiful face.

Here are the two Preambles: Federal Constitution, 1789

Here artistic realism involves the audience in an impassioned participation in events whose overtones and implications are transcendent.

Here, in two nations alone, are almost five hundred million people, all working, and working hard, to raise their standards, and in doing so, to make of themselves a strong bulwark against the spread of an ideology that would destroy liberty.

Here we may observe that at least one modern philosophy of history is built on the assumption that ideas are the primary objectives of the historian's research.

Here, as in all sectors of the economy, quality and justice are both dependent on the right of the individual to deal directly with his employer if he so chooses.

Here then is our problem: aircraft are vital to winning a war today because they can perform those missions which a missile is totally incapable of performing ; ;

Here they are, with my comments and judgments.

Here are the brands ( in alphabetical order ) and the new models.

Here are a couple of the latest, highly styled ways to fix skinless franks in your own back yard!!

Here are suggestions for the frankfurter trimmings: 1.

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

Here are some of the newer items currently available:

Here a variety of meanings and emotions are concentrated, or reduced, in their communicative expression, to some comparatively simple-seeming verbal or nonverbal statement.

Here again laboratory approaches are being evolved, for it is recognized how `` elastic '' these readings can be, how they can apply to many people, and are often stated in general terms all too easily applied to any individual's own case.

Here I do not speak of military power where our advantage is obvious and overwhelming but of political power -- of influence, if you will -- about which the relevant questions are: Is Soviet influence throughout the world greater or less than it was ten years ago??

Here, at the Ravine Lodge, President Dickey acts as host every year to about a hundred freshmen who are being introduced by the Dartmouth Outing Club to life on the trails.

Here are hatched plans for getting a share of the American bounty, the secret of the anti-missile missile, or an invitation to dinner.

`` Here are two old men, mad at each other and too proud to pick up the phone '', said a House Democratic leader.

Here are several:

Here are a few facts and figures I've assembled.

Here are some examples:

Here are some statements that require the axiom of choice in the sense that they are not provable from ZF but are provable from ZFC ( ZF plus AC ).

Here the reasonable mastery of the elements of administration can do much to free a president for his primary role.

Here we can store 6 elements they are stored linearly but starting from first row linear then continuing with second row.

In 3 dimensions, a differential 0-form is simply a function f ( x, y, z ); a differential 1-form is the following expression: a differential 2-form is the formal sum: and a differential 3-form is defined by a single term: ( Here the a-coefficients are real functions ; the " wedge products ", e. g. can be interpreted as some kind of oriented area elements,, etc.

Here, the apostle attempted to convey the underlying concepts about Christ to a Greek audience, and the sermon illustrates some key elements of future Christological discourses that were first brought forward by Paul.

Here, a " specification " can be manifested as either a plan or a finished product, and " primitives " are the elements from which the design object is composed.

Here are some simple but useful commutator identities, true for any elements s, g, h of a group G:

Here, the sum is taken over all different states under permutations p acting on N elements.

Here the boys picked up the elements of mathematics and drawing.

Here is an example of this sort algorithm sorting five elements:

Here he added elements of local architectural styles to his classicism, and based his urbanization scheme on Mughal water gardens.

Here the homogeneous elements are either of degree 0 ( even ) or 1 ( odd ).

Here alone are numerous opportunities for adding elements to the design concept.

" Here Goodrick-Clarke brings down the description of cryptohistory to two elements: " A complete ignorance of the primary sources " and the repetition of " inaccuracies and wild claims ".

Here also he wrote Lucinde ( 1799 ), an unfinished romance, which is interesting as an attempt to transfer to practical ethics the Romantic demand for complete individual freedom, and Alarcos, a tragedy ( 1802 ) in which, without much success, he combined romantic and classical elements.

Here are no colonies of Germans, as at Saint Petersburg ; no English factories, as at Lisbon: no multitudes of insolent Yankees lounging through the streets, as at the Havannah, with an air which seems to say, the land is our own whenever we choose to take it ; but a population which, however strange or wild, and composed of various elements, is Spanish, and will remain so as long as the city itself shall exist.

Here is a test class that specifies a number of elements of the implementation.

Here, < sup > α </ sup > M is the class of all sequences of length α whose elements are in M.

Here, every fiber has elements.

Here are some examples of widely used structuring elements ( denoted by B ):

Here he arranged the " orbes " in the new Copernican order, expanding one sphere to carry " the globe of mortalitye ", the Earth, the four elements, and the Moon ; and expanding the starry sphere infinitely upward to encompass all the stars, and also to serve as " the court of the Great God, the habitacle of the elect, and of the coelestiall angelles.

Here it is also possible to see the influence of older story-telling elements such as Grimm's Fairy Tales where children learn about the dangers of allowing strangers into the home.

Here he dropped all Asian language elements and many traditions in favor of American English.

Here, ∆ t < sub > 1 </ sub > and ∆ t < sub > 2 </ sub > represent the propagation delay s of the logic elements.

Here the rank of Q < sub > i </ sub > should be interpreted as meaning the rank of the matrix B < sup >( i )</ sup >, with elements B < sub > j, k </ sub >< sup >( i )</ sup >, in the representation of Q < sub > i </ sub > as a quadratic form: