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Let and Af
Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.
Let Af be the null space of Af.
Let us put Af.
Let us look at the operator Af.
Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.
Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.
Let Af denote the form of Af.
Let us assume that Af is identical to the form of an occurrence Af which preceded Af in the text.
Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.
Let this be denoted by Af.
Let Af where the maximization is over all admissible policies Af.

Let and .
`` Let the savages kill each other.
Let it burn down.
Let Senora Brannon live in her father's house for a time.
Let me pass over the trip to Sante Fe with something of the same speed which made Mrs. Roebuck `` wonduh if the wahtahm speed limit '' ( 35 m.p.h. ) `` is still in ee-faket ''.
Let me set the record this time, and let me get back OK, so the German will give me the exclusive.
Let us look in on one of these nerve centers -- SAC at Omaha -- and see what must still happen before a wing of B-52 bombers could drop their Aj.
Let me quote him even more fully, for his analysis is important to my theme.
Let us re-examine the publicized contrasts between Ptolemaic and Copernican astronomy.
Let us not confuse the issue by labeling the objective or the method `` psychoanalytic '', for this is a well established term of art for the specific ideas and procedures initiated by Sigmund Freud and his followers for the study and treatment of disordered personalities.
Let us differentiate a few of these ideas.
Let us survey for a moment the development of modern thought -- turning our attention from the Reformation toward the revolutionary and romantic movements that follow and dwelling finally on more recent decades.
`` Let him become honest, and they discard him.
Let me give Papa blood ''.
Let us now give some thought to the soul.
Let me then ( and in public ) glance into the mirror.
Let us see just how typical Krim is.
Let him bounce back, and he could really set up the staff.
Let us prepare for peace, instead of for a war which would mean the end of civilization.
Let us have more benches and fewer forbidden areas around fountains and gardens.
Let us, like the French, have outdoor cafes where we may relax, converse at leisure and enjoy the passing crowd.
Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.
One means to help the birds occurs to me: Let the chimes that ring over Washington Square twice daily, discontinue any piece of music but one.
Let them offer on behalf of those creatures whose melody has been the joy of mankind since time began, the hymn `` Abide With Me ''.
Let me tell you what happened to me today.
`` Let me do the submitting to the Royal Academy '', he suggested.

Af and .
The completeness of the connections provide that, for N people, there are Af lines of communication between the pairs, which can become a large number ( 1,225 ) for a party of fifty guests.
Looking at the diagram, we see that Af connection lines come in to each member.
In spite of the dreams of the host for oneness in the group, the Af incoming messages for each guest overload his receiving system beyond comprehension if N exceeds about six.
As our radius of penetration, R, increases, the area of new knowledge increases by Af, and the total of human knowledge becomes measured in terms of Af.
In one of these, an exploding-wire device to study systems thermodynamically up to 6,000 Af and 100 atmospheres pressure, a major goal was achieved.
The fast-opening of the shutter consists of a piece of aluminum foil ( approximately Af ) placed directly in front of the camera lens so that no light may pass into the camera.
in interstellar gas, concentrations as low as Af molecules per Af may be sufficient, as compared to the Af hydrogen atom's Af required for detection of the 21-cm line.
the frequencies are 1665.32 and 1667.36 Af, with an uncertainty of 0.10 Af.
The Bureau is pursuing an active program to provide a temperature scale and thermometer calibration services in the range 1.5 to 20 Af.
An acoustical interferometer has been constructed and used, with helium gas as the thermometric fluid, to measure temperatures near 4.2 and 2.1 Af.
Several germanium resistors have been thermally cycled from 300 to 4.2 Af and their resistances have been found to be reproducible within 1/3 millidegree when temperatures were derived from a vapor pressure thermometer whose tubing is jacketed through most of the liquid helium.
Preliminary calibrations of the resistors have been made from 4.21 to 2.16 Af at every 0.1 Af.
The reproducibilities of helium vapor-pressure thermometers have been investigated in conjunction with a `` constant temperature '' liquid helium bath from 4.2 to 1.8 Af.
The gradient was about one half of a millidegree at 4.2 Af but increased to several millidegrees for bath temperatures slightly greater than the **yl point.
A small pressure unbalance displaces the diaphragm and changes the capacitance between the diaphragm and an electrically insulated plate spaced 0.001 in. apart ( for Af ).
Over a temperature range from 25 to 200 Af and at pressures up to 250 atm, an overload of 300 psi, applied for a period of one day, results in an uncertainty in the pressure of, at most, one millimeter of mercury.
The results of the study, based on collision integrals computed from the latest critically evaluated data on intermolecular forces in air, will be reported in the form of a table of viscosity, thermal conductivity, thermal diffusion, and diffusion coefficients at temperatures of 1,000 to 10,000 Af and of logarithm of pressure in atmospheres from Af to Af times normal density.

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