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Page "Uniformization theorem" ¶ 17
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For and general
For many years a state tax on cities and towns was paid by the several municipalities to the state from the proceeds of the general property tax.
For the policy officer will know that action can almost never be secret and that in general the effectiveness of policy will be conditioned by the readiness of the country to sustain it.
For the near term, however, it must be realized that the industrial and commercial market is somewhat more sensitive to general business conditions than is the military market, and for this reason I would expect that any gain in 1961 may be somewhat smaller than those of recent years ; ;
For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.
For many of these unwed mothers, the data on their family life and early childhood experiences revealed several indications and sources of their basic mistrust of their parents in particular and of the world in general.
-- For a second month in a row, Multnomah County may be short of general assistance money in its budget to handle an unusually high summer month's need, the state public welfare commission was told Friday.
For general morale reasons and to encourage the efforts of his supply officers, when food was short for combat troops he cut the rations of his headquarters staff accordingly.
For this latest addition to the Great Letters Series, under the general editorship of Louis Kronenberger, Miss Hardwick has made a selection which admirably displays the variety of James's genius, not to mention the felicities of his style.
* For the general reader.
For general computer use access technology such as screen readers, screen magnifiers and refreshable Braille displays has been widely taken up along with standalone reading aids that integrate a scanner, optical character recognition ( OCR ) software, and speech software in a single machine.
For biologists, this includes human beings, although for the general public the term " animal " means only non-human animals.
For example, in some groups, the group operation is commutative, and this can be asserted with the introduction of an additional axiom, but without this axiom we can do quite well developing ( the more general ) group theory, and we can even take its negation as an axiom for the study of non-commutative groups.
For other uses, see Alexander and Alexander ( Aetolian general )
For Hume, philosophy can be split into two general parts: natural philosophy and the philosophy of human nature ( or, as he calls it, " moral philosophy ").
For the frequent case of propositional logic, the problem is decidable but Co-NP-complete, and hence only exponential-time algorithms are believed to exist for general proof tasks.
For example, if James's will states that he is leaving $ 500, 000 to his son Sam then the money would be a general devise.
For years, it was traded privately until a ROM was made available to the general public.
For example, abstracting a leather soccer ball to the more general idea of a ball retains only the information on general ball attributes and behavior, eliminating the other characteristics of that particular ball.
For this reason, players should choose badminton shoes rather than general trainers or running shoes, because proper badminton shoes will have a very thin sole, lower a person's centre of gravity, and therefore result in fewer injuries.
For many years, the U. S. has borrowed and bought while in general, the rest of the world has lent and sold.
For several decades from the 1970s to early 2000s, the focus in designing high performance general purpose CPUs was largely on achieving high ILP through technologies such as pipelining, caches, superscalar execution, out-of-order execution, etc.
For example, the Napoleonic code expressly forbade French judges from pronouncing general principles of law.
For example, the copyright to a Mickey Mouse cartoon restricts others from making copies of the cartoon or creating derivative works based on Disney's particular anthropomorphic mouse, but does not prohibit the creation of other works about anthropomorphic mice in general, so long as they are different enough to not be judged copies of Disney's.
For many decades, consciousness as a research topic was avoided by the majority of mainstream scientists, because of a general feeling that a phenomenon defined in subjective terms could not properly be studied using objective experimental methods.

For and surfaces
For phosphor to fiber and fiber to air surfaces, and assuming Af, we obtain Af percent.
For higher speeds, the flow will compress more significantly as it comes into contact with surfaces and slows.
For images of fractal patterns, this has been expressed by phrases such as " smoothly piling up surfaces " and " swirls upon swirls ".
For closed ( orientable or non-orientable ) surfaces with positive genus, the maximum number p of colors needed depends on the surface's Euler characteristic χ according to the formula
For example, air hoar is a deposit of hoar frost on objects above the surface, such as tree branches, plant stems, wires ; surface hoar is formed by fernlike ice crystals directly deposited on snow, ice or already frozen surfaces ; crevasse hoar consists of crystals that form in glacial crevasses where water vapour can accumulate under calm weather conditions ; depth hoar refers to cup shaped, faceted crystals formed within dry snow, beneath the surface.
For this reason spherical reference surfaces are frequently used in mapping programs.
For example once one gets to 3-dimensional surfaces, one has to deal with solid objects with knot-shaped holes, and then one needs the whole of knot theory just to classify them.
For mirrors with parabolic surfaces, parallel rays incident on the mirror produce reflected rays that converge at a common focus.
For compact space | compact 2-dimensional surfaces without boundary ( topology ) | boundary, if every loop can be continuously tightened to a point, then the surface is topologically Homeomorphism | homeomorphic to a 2-sphere ( usually just called a sphere ).
For instance, the naturally occurring citric and ascorbic acids in lemon or other citrus juice can inhibit the action of the enzyme phenolase which turns surfaces of cut apples and potatoes brown if a small amount of the juice is applied to the freshly cut produce.
For similar reasons, objects intended to avoid detection will not have inside corners or surfaces and edges perpendicular to likely detection directions, which leads to " odd " looking stealth aircraft.
For example if the light source emitted white light and the two diffuse surfaces were blue, then the resulting color of the pixel is blue.
For most points on most surfaces, different sections will have different curvatures ; the maximum and minimum values of these are called the principal curvatures.
#: For most surfaces the focal surface forms two sheets each of which is a surface and which come together at umbilical points.
For channel surfaces one sheet forms a curve and the other sheet is a surface ; For cones, cylinders, toruses and cyclides both sheets form curves.
For most uses, dilution with water is recommended for safety and to avoid damaging the surfaces being cleaned.
For this reason wormholes have been defined geometrically, as opposed to topologically, as regions of spacetime that constrain the incremental deformation of closed surfaces.
For still water, this is the difference in height between the inlet and outlet surfaces.
* For specular surfaces, such as glass or polished metal, reflectivity will be nearly zero at all angles except at the appropriate reflected angle-that is, reflected radiation will follow a different path from incident radiation for all cases other than radiation normal to the surface.
* For diffuse surfaces, such as matte white paint, reflectivity is uniform ; radiation is reflected in all angles equally or near-equally.
For surfaces with b boundary components, the equation reads χ = 2 − 2g − b.
For a long cylinder far from other surfaces, this reduces the effective area by a factor of π / 2
For example, PCC trolley brakes include a flat shoe which is clamped to the rail with an electromagnet ; the Murphy brake pinches a rotating drum, and the Ausco Lambert disc brake uses a hollow disc ( two parallel discs with a structural bridge ) with shoes that sit between the disc surfaces and expand laterally.
For the case of two colliding bodies in two-dimensions, the overall velocity of each body must be split into two perpendicular velocities: one tangent to the common normal surfaces of the colliding bodies at the point of contact, the other along the line of collision.

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