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, No. 56 printed the patent giving the Electoral Prince the title of Duke of Cambridge.

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: 1.

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 example, a 12-to-one engine would power a supersonic VTOL fighter.

For example: Af.

For example: Af.

For example, for the problem Af, 10 from 25 equals 15, then 6 from 15 equals 9.

For example: Af.

For example, let's consider a standard 283 cubic inch Chevy Aj.

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 Friday after Thanksgiving can be substituted for Washington's birthday.

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 example, the automorphisms of the Riemann sphere are Möbius transformations.

For s an even positive integer, the product sin ( πs / 2 ) Γ ( 1 − s ) is regular and the functional equation relates the values of the Riemann zeta function at odd negative integers and even positive integers.

For a great many functions and practical applications, the Riemann integral can also be readily evaluated by using the fundamental theorem of calculus or ( approximately ) by numerical integration.

For functions on the real line, the Henstock integral is an even more general notion of integral ( based on Riemann's theory rather than Lebesgue's ) that subsumes both Lebesgue integration and improper Riemann integration.

For every Riemann surface, a meromorphic function is the same as a holomorphic function that maps to the Riemann sphere and which is not constant ∞.

For a two-dimensional surface, the Bianchi identities imply that the Riemann tensor can be expressed as

For example, in general relativity gravitation is associated with a tensor field ( in particular, with the Riemann curvature tensor ).

For example, the corresponding complex variety is the Riemann sphere and its initial Betti numbers are 1, 0, 1.

For the purposes of the Riemann – Roch theorem, the surface X is always assumed to be compact.

For discrete-time dynamical systems the orbits are sequences, for real dynamical systems the orbits are curves and for holomorphic dynamical systems the orbits are Riemann surfaces.

For Riemann surfaces, Rado's theorem implies that the surface is automatically second countable.

For instance, Möbius transformations ( transformations of the complex projective line, or Riemann sphere ) are affine ( transformations of the complex plane ) if and only if they fix the point at infinity.

* For the Riemann integral ( or the Darboux integral, which is equivalent to it ), improper integration is necessary both for unbounded intervals ( since one cannot divide the interval into finitely many subintervals of finite length ) and for unbounded functions with finite integral ( since, supposing it is unbounded above, then the upper integral will be infinite, but the lower integral will be finite ).

* For the Henstock – Kurzweil integral, improper integration is not necessary, and this is seen as a strength of the theory: it encompasses all Lebesgue integrable and improper Riemann integrable functions.

For example, in Riemann surface theory, the deformation theory of complex structures is studied classically by means of quadratic differentials ( namely sections of L ( K < sup > 2 </ sup >)).

For example, consider a CFT on the Riemann sphere.

For x -> ∞, the functions diverge ; the integral without prefactor is given by the Riemann zeta function:

For a compact Riemann surface S of genus greater than 1, its universal covering space is the unit disc D on which its fundamental group Γ acts by Möbius transformations.

For example, the Riemann zeta function has a functional equation relating its value at the complex number s with its value at 1 − s. In every case this relates to some value ζ ( s ) that is only defined by analytic continuation from the infinite series definition.

For example, it is easy to prove that the analytic functions from the Riemann sphere to itself are either

For if such a function f is nonconstant, then since the set of z where f ( z ) is infinity is isolated and the Riemann sphere is compact, there are finitely many z with f ( z ) equal to infinity.

For example, consider G = SL < sub > 2 </ sub >( C ), for which G / B is the Riemann sphere, an integral weight is specified simply by an integer n, and ρ = 1.

For number theorists his main fame is the series for the Riemann zeta function ( the leading function in Riemann's exact prime-counting function ).