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Page "Topological manifold" ¶ 24
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particular and they
Although they were forced to maintain a sharper watch, this activity enabled them to ride in and rack their broncs without any particular attention being paid them.
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 20-to-1 ratio for cochannel interference embodies one of the fundamental limiting principles which we must always take into account in AM assignments and allocations -- that signals from a particular station are potential sources of objectionable interference over an area much greater than that within which they provide useful service.
His pictures generalize, though they are inspired by a particular locale ; ;
Even though the registers may have an incomplete record of persons present in a particular area or include persons no longer living there, they contain precise information on ages, by date of birth, for some of the persons present ( especially children in relatively stable communities ) and supplementary information ( such as records of marital status ) for many others.
Eighteen errors were located, and then the director asked each individual to vote whether or not they felt that this manager had made the particular errors.
While the particular limits of these groupings may seem artificially arbitrary, they do fairly express a corresponding grouping of more variable material, and they eventuate also in five classes, along a similar scale, containing approximately equal numbers of cases, namely 19, 14, 15, 11, 12 in Athabascan.
Nevertheless, their conclusions and recommendations cannot please everybody, and they often represent a particular economic or political point of view.
Emerson, in his lecture, refers to the `` startling experience which almost every person confesses in daylight, that particular passages of conversation and action have occurred to him in the same order before, whether dreaming or waking, a suspicion that they have been with precisely these persons in precisely this room, and heard precisely this dialogue, at some former hour, they know not when ''.
In fact, there is much evidence to indicate they don't care a bit about anything beyond their particular regional, ethnic and occupational limits.
It seems to us that choices exercised by realtors in moral situations center in at least three areas: ( 1 ) the various ways in which they interpret a particular social issue ; ;
In particular, social sciences often develop statistical descriptions rather than the general laws derived in physics or chemistry, or they may explain individual cases through more general principles, as in many fields of psychology.
Some appellate courts, particularly supreme courts, have the power of discretionary review, meaning that they can decide whether they will hear an appeal brought in a particular case.
The monarchies of France and Spain in particular could not be expected to aid those they considered rebels against another legitimate monarch.
In particular, they refuted the assumption of Confucius as a godlike figure and considered him as the greatest sage, but simply a human and mortal
When looking at variations it needs to be kept in mind that different groups of people do not always sign one way and not the other, rather they prefer and use a particular form of a sign more often.
With some simplifications, in particular constant density, they can be given as follows:
After much discussion, James the Just, leader of the Jerusalem church, decrees that Gentile Christian converts need not follow all of the Mosaic Law, and in particular, they do not need to be circumcised.
However, there is no universal standard for the Goðar amongst organizations, and the title is usually only significant to the particular group with whom they work.
Exact ( not asymptotic ) measures of efficiency can sometimes be computed but they usually require certain assumptions concerning the particular implementation of the algorithm, called model of computation.
The absence of a turret also meant that tank destroyers could be manufactured significantly cheaper, faster and more easily than the tanks on which they were based and fou8nd particular favor when production resoureces were lacking.
General support units tend to be moved to where they are most required at any particular time.

particular and are
Among the many problems in the taxing of personal property, and of movable tangible property in particular, two are significant: ( 1 ) situs, ( 2 ) fair and equitable assessment of value.
It would seem, then, that movable property and equipment is not taxed as a whole but that certain types are taxed in towns where this is bound to be expedient for that particular kind of personal property.
The District Courts, in the framing of equitable decrees, are clothed ' with large discretion to model their judgements to fit the exigencies of the particular case.
Our instructions assume you are building this particular frame, which is for a junction.
A group of native trees or plants which are outstanding in a particular county can be featured at the site.
Many industry trade associations are developing campaigns to protect or enhance the share of the consumer's dollar being spent on their particular products.
`` We do not have people in our organization termed ' consultants ' or ' fellows ', who are specialists in one particular technical subject.
One species is restricted to statements which are neither explicit nor precise regarding a particular person, place, time or thing.
In particular, tangents to C are transformed into tangents to C'.
Institutionalization Though undoubtedly all six processes are operative within the whole social system and its subsystems, two processes that are of crucial importance to this study will be singled out for particular emphasis.
It supplies local data which are useful in administration and which can be used as a basis for intensive studies in particular situations.
The reasons for extracting this particular roleplaying application from the previous discussion of training are twofold.
There are certain tax attributes of a corporation whose nature and effect might depend on the facts of the particular reorganization involved.
The rows of animals and birds, in particular, suggest awareness of Oriental animal friezes, transmitted perhaps via Syrian silver bowls and textiles, but the specific forms of these rows on local vases and metal products are nonetheless Greek.
But these are dreamed in original action, in some particular continuity which we don't remember having seen in real life.
Of course, the perspective of those who are dealing directly with the world-wide problems of the People of God will always be different from the perspective of those who are dealing with the nearby problems of particular persons in a particular place.
In the adult world, there are a number of rather general and diffuse sources of ideological diffusion that further compound the adolescent's search for meaning during this particular identity crisis.
To pick out particular numbers is something of a problem, but one or two identifiable items are too conspicuously excellent to be missed.

particular and locally
Furthermore, each Riemannian metric is naturally associated with one particular kind of connection, the Levi-Civita connection, and this is, in fact, the connection that satisfies the equivalence principle and makes space locally Minkowskian ( that is, in suitable locally inertial coordinates, the metric is Minkowskian, and its first partial derivatives and the connection coefficients vanish ).
" Longhair's particular style was known locally as rumba-boogie.
This method treats the system locally as if it were uniform with the local properties ; in particular, the local wave velocity associated with a frequency is the only thing needed to estimate the corresponding local wavenumber or wavelength.
In particular, weak topologies are locally convex.
* The Euclidean spaces R < sup >< var > n </ var ></ sup > ( and in particular the real line R ) are locally compact as a consequence of the Heine – Borel theorem.
In particular, any continuously differentiable function is locally Lipschitz, as continuous functions are locally bounded so its gradient is locally bounded as well.
In particular the set of all real-valued Lipschitz functions on a compact metric space X having Lipschitz constant ≤ K is a locally compact convex subset of the Banach space C ( X ).
In particular, any locally integrable function has a distributional derivative.
In particular, it must be made from specified grapes ( see below ), of which Ugni Blanc, known locally as Saint-Emilion, is the one most widely used at the present time.
If the sample is oriented so that one particular plane is only slightly tilted away from the strongest diffracting angle ( known as the Bragg Angle ), any distortion of the crystal plane that locally tilts the plane to the Bragg angle will produce particularly strong contrast variations.
Genetic erosion in agricultural and livestock biodiversity is the loss of genetic diversity, including the loss of individual genes, and the loss of particular combinants of genes ( or gene complexes ) such as those manifested in locally adapted landraces of domesticated animals or plants adapted to the natural environment in which they originated.
Local food or the local food movement is a " collaborative effort to build more locally based, self-reliant food economies-one in which sustainable food production, processing, distribution, and consumption is integrated to enhance the economic, environmental and social health of a particular place.
In particular, covering maps are locally trivial.
In particular, many authors require both spaces to be path-connected and locally path-connected.
These were originally worked locally, but it later became normal practice to operate all the signals on a particular block with levers grouped together in a signal box.
The inverse function theorem ( and the implicit function theorem ) can be seen as a special case of the constant rank theorem, which states that a smooth map with locally constant rank near a point can be put in a particular normal form near that point.
With family names originating locally, many names display particular characteristics of the local dialects, such as the south German, Austrian and Swiss diminutive endings-l-el, '- erl ,-le or-li as in Kleibl, Schäuble or Nägeli ( from ' Nagel ', nail ).
It exists globally in all who identify themselves as Christians and locally in particular places where believers gather for the worship of God.
Japanese sables ( known locally as クロテン or kuroten ) in particular are marked with black on their legs and feet.
For the purposes of functional analysis, and in particular of harmonic analysis, one wishes to carry over the group ring construction to topological groups G. In case G is a locally compact Hausdorff group, G carries an essentially unique left-invariant countably additive Borel measure μ called Haar measure.
In particular, in 2 dimensions, if the vertices can take on values in a locally compact abelian group G and the action / energy only depends on the edges ( e. g. the Ising model for Z < sub > 2 </ sub >, the Potts model for Z < sub > n </ sub >, the XY model for U ( 1 ) ), then its dual via the Kramers – Wannier duality to a model where the vertices take on values in the dual group G ′.
* The Krein – Milman theorem states that if S is convex and compact in a locally convex space, then S is the closed convex hull of its extreme points: In particular, such a set has extreme points.

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