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Page "Graded algebra" ¶ 41
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Here and homogeneous
Here, we present a common simple proof limited to the approximation of two antennas separated by a large distance compared to the size of the antenna, in a homogeneous medium.
Given a homogeneous prime ideal P of, let X be a subset of P < sup > n </ sup >( k ) consisting of all roots of polynomials in P .< ref > The definition makes sense since if and only if for any nonzero λ in k .</ ref > Here we show X admits a structure of variety by showing locally it is an affine variety.
Here it is stated that a function F of n variables x < sub > 1 </ sub >, ..., x < sub > n </ sub > that is homogeneous of degree r, satisfies
Here, and are unknown and and are the solutions to the homogeneous equation.

Here and elements
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 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 the vectors are elements of a given vector space V over a field K, and the coefficients are scalars in K.
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:

Here and are
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 ).

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