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For example, it follows that any closed oriented Riemannian surface can be C < sup > 1 </ sup > isometrically embedded into an arbitrarily small ε-ball in Euclidean 3-space ( there is no such C < sup > 2 </ sup >- embedding since from the formula for the Gauss curvature an extremal point of such an embedding would have curvature ≥ ε < sup >- 2 </ sup >).
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For and example
For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.
For example, suppose a man wearing a $200 watch, driving a 1959 Rolls Royce, stops to ask a man on the sidewalk, `` What time is it ''??
For example, there are persons who are in physical science, in the field of mineralogy, trained in crystallography, who use only X-rays, applying only the powder technique of X-ray diffraction, to clay minerals only, and who have spent the last fifteen years concentrating on the montmorillonites ; ;
For example, he captured some persons from York County, who with teams were taking to Philadelphia the furniture of a man who had just been released from prison through the efforts of his wife, and who apparently was helpless to prevent the theft of his household goods.
For example, even the most successful executive lives in a two-room apartment while ordinary people rent space in the stairwells of office buildings in which to sleep at night ; ;
For example, in the third chapter of Matthew, verses 13-16, describing the baptism of Jesus, the 1611 version reads:
For example, it probably will be necessary for the Corps to have authority to pay medical expenses of volunteers.
For example, the importance of the Regulus 2, a very promising aerodynamic ship-to-surface missile designed to be launched by surfaced submarines, was greatly diminished by the successful acceleration of the much more advanced Polaris ballistic missile launched by submerged submarines.
For example, the interest of past members of the Foundation's Advisory Board remains such that they place their knowledge and judgments at our disposal much as they had done when they were, formally, members of that Board.
For example, out of the social evils of the English industrial revolution came the novels of Charles Dickens ; ;
For an example let's dream up an engine that has a final combustion chamber volume of 5 cubic inches and a cylinder volume of 45 cubic inches.
For example, a Browning trap version of the Superposed over/under, the Broadway ( from $350 up, depending on grade ), differs from standard models in that it is equipped with a full beavertail fore end, a cushion recoil pad and a barrel-wide ventilated rib for fast sighting.
For example, the Chamber of Commerce of Gatlinburg, Tennessee, sponsors special camera tours into the Great Smoky Mountains to get pictures of the profusion of wild flowers flourishing in these wooded regions.
For example, the officials of Poughkeepsie town ( township ) where the project is located think highly of it because it simplifies their snow clearing problem.
For example, don't pay in a truck policy for medical coverage that you may be paying for in a health and accident policy.
For example: If your bodily injury claims start payment after the first $250, a 25% premium saving is often made.
For and follows
This belief follows the theology of St. Paul: For it is by grace you have been saved, through faith — and this not from yourselves, it is the gift of God, not by works, so that no one can boast.
For Hume, every effect only follows its cause arbitrarily — they are entirely distinct from one another.
For mammals, the relationship between brain volume and body mass essentially follows a power law with an exponent of about 0. 75.
For example, the conservation of energy follows from the time-invariance of physical systems, and the fact that physical systems behave the same regardless of how they are oriented in space gives rise to the conservation of angular momentum.
For example, settlement of class actions follows a predictable path of negotiation with class counsel and representatives, court scrutiny, and notice.
For some subjects a numerical geographical subdivision follows the classification letters on the first line.
For example, if a flat-panel display is examined under a magnifying glass, the pixels may appear as follows:
For one of his biographers, Hepworth Dixon, Bacon's influence in modern world is so great that every man who rides in a train, sends a telegram, follows a steam plough, sits in an easy chair, crosses the channel or the Atlantic, eats a good dinner, enjoys a beautiful garden, or undergoes a painless surgical operation, owes him something.
For the QED interaction Lagrangian,, describing the interaction of a fermionic field with a bosonic gauge field, the Feynman rules can be formulated in coordinate space as follows:
For positive integer m the derivative of gamma function can be calculated as follows ( here γ is the Euler – Mascheroni constant ):
According to Nicholas de Lange, Judaism offers no clear teaching about the destiny which lies in wait for the individual after death and its attitude to life after death has been expressed as follows: " For the future is inscrutable, and the accepted sources of knowledge, whether experience, or reason, or revelation, offer no clear guidance about what is to come.
For a decade now, the evidence is growing that HSC maturation follows a myeloid-based model instead of the ' classical ' schoolbook dichotomy model.
For purposes of delineating the metre, the BIPM currently considers the HeNe laser wavelength to be as follows: with an estimated relative standard uncertainty ( U ) of.
For objects extended in space, such as a diver jumping from a diving board, the object itself follows a complex motion as it rotates, but the center of mass of the object nevertheless forms a parabola.
For example, the first four perfect numbers are generated by the formula 2 < sup > p − 1 </ sup >( 2 < sup > p </ sup >− 1 ), with p a prime number, as follows:
For instance, the number of cities having a certain population size is found to vary as a power of the size of the population, and hence follows a power law.
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