For a moment she held her face to the empty doorway ; ;

: For any set A, the power set of A ( with the empty set removed ) has a choice function.

For example, the spectrum of an element of a complex Banach algebra can never be empty, whereas in a real Banach algebra it could be empty for some elements.

For example, if a player's " home " or destination corner is empty ( not an opponent's starting corner ), the player can freely arrange his / her pieces to serve as a ' ladder ' or ' bridge ' between the two opposite ends.

( For example, if there are two empty positions between the jumping piece and the piece being jumped, the jumping piece lands leaving exactly two empty positions immediately beyond the jumped piece.

For example, as New England became increasingly settled and the resident wolves were eliminated, the coyote population increased, filling the empty ecological niche.

For four or more points on the same circle ( e. g., the vertices of a rectangle ) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the " Delaunay condition ", i. e., the requirement that the circumcircles of all triangles have empty interiors.

For instance, if in one shot a beer glass is empty, it should not be full in the next shot.

For any alphabet there is only one word of length 0, the empty word, which is often denoted by e, ε or λ.

* For each pair of objects x and y in G < sub > 0 </ sub >, there exists a ( possibly empty ) set G ( x, y ) of morphisms ( or arrows ) from x to y.

For some time many Russian liberals had been dissatisfied by what they regarded as the empty discussions of the intelligentsia.

# For iconoclasts, the only real religious image must be an exact likeness of the prototype – of the same substance – which they considered impossible, seeing wood and paint as empty of spirit and life.

For example, if the objects are long and thin then a sphere will enclose mainly empty space and a box is much better.

For example, the sum of the empty set is NULL, meaning zero, the average of the empty set is NULL, meaning undefined, and NULL appearing in the result of a LEFT JOIN can mean " no value because there is no matching row in the right-hand operand ".

For example, empty shoes placed outside of a Greek home would tell others that the family's son has died in battle.

For example, the set of rational numbers, as a subset of R has the property that the interior has an empty closure, but it is not nowhere dense ; in fact it is dense in R.

For example, Epson embeds a chip which prevents printing when the chip claims the cartridge is empty, although a researcher who over-rode the system found that in one case he could print up to 38 % more good quality pages, even though the chip stated that the cartridge was empty.

For an insulator, the Fermi level lies within the band gap, indicating an empty conduction band ; in this case, the minimum energy to remove an electron is about the sum of half the band gap and the electron affinity.

For example, the collection of all open intervals in the real line forms a base for a topology on the real line because the intersection of any two open intervals is itself an open interval or empty.

For example, the intersection of the two sets is not empty, because there are points that represent creatures that are in both the orange and blue circles.

For an instant John longed for the sound of the bells of Noyon-la-Sainte, the touch of his mother's hand, the lilt of Charles's voice in the square raftered rooms, his father's bass tones rumbling to the canons, and the sight of the beloved bishop.

For any such square the middle corner of these will be called the vertex of the square and the corner not on the curve will be called the diagonal point of the square.

For the Lo Shu square was a remarkably complete compendium of most of the chief religious and philosophical ideas of its time.

For example, a certain landowner might have been said to own 32, 000 acres of land, not 50 square miles of land.

For example, a vertex configuration of ( 4, 6, 8 ) means that a square, hexagon, and octagon meet at a vertex ( with the order taken to be clockwise around the vertex ).

For example, adjacent to square 5F are squares 4F, 6F, 5E, and 5G, but not 6E or 4G.

For positive values of a and b, the binomial theorem with n = 2 is the geometrically evident fact that a square of side can be cut into a square of side a, a square of side b, and two rectangles with sides a and b. With n = 3, the theorem states that a cube of side can be cut into a cube of side a, a cube of side b, three a × a × b rectangular boxes, and three a × b × b rectangular boxes.

For square matrices with entries in a non-commutative ring, for instance the quaternions, there is no unique definition for the determinant, and no definition that has all the usual properties of determinants over commutative rings.

** For example, consider the map ( which is the " realification " of the complex square function ) where U

For example, suppose the word square is defined by " A figure is square if and only if it has four perpendicular sides of equal length.

For example, JPEG compression uses a variant of the Fourier transformation ( discrete cosine transform ) of small square pieces of a digital image.

For example, both the Egyptians and the Babylonians were aware of versions of the Pythagorean theorem about 1500 years before Pythagoras ; the Egyptians had a correct formula for the volume of a frustum of a square pyramid ;

For example, a 4-cycle ( square ) has girth 4.

For houses in and around Geneva, the average price was 11, 595 Swiss francs ( CHF ) per square metre () ( June 2011 ), with a lowest price per square metre () of 4, 874 Swiss francs ( CHF ), and a maximum price of 21, 966 Swiss francs ( CHF ).

For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product ; that is.

# For a given orbit, the ratio of the cube of its semi-major axis to the square of its period is constant.

For a number written in scientific notation, this logarithmic rounding scale requires rounding up to the next power of ten when the multiplier is greater than the square root of ten ( about 3. 162 ).

For problems with all four properties, the time for a quantum computer to solve this will be proportional to the square root of the number of inputs.

For other examples, see proof that the square root of 2 is not rational and Cantor's diagonal argument.

`` For Christ's sake, don't waste your powder on one of 'em ''!!

For although I had crossed a corner of the hall on my way to the toilet I still could not tell for sure how far to the rear the darkness extended.

For less than a dozen miles from the unplowed land of the dead man lived another settler who had ignored the warnings that his existence might be foreclosed on -- a blatant and defiant rustler named Fred Powell.

For a brief period each year, the rays of the sun are warm enough to melt some of the snows piled a mile deep at the base of the headwalls, and then the pinnacles glisten in the daytime at high noon, and billions of gallons of water begin their slow seepage under the glaciers and across the rockstrewn hanging valleys on their long, meandering journey to the sea -- running east past the sky-carving massifs of Gurla Mandhata and Kemchenjunga, then turning south and curling down through the jungles of Assam, past the Khasi Hills, and into Bengal, past Sirinjani and Madaripur, until the hard water of the melting snows mingles with the soft drainage of fields and at length fans out to meld with the teeming salt depths of the Bay of Bengal.

For last-ditch emergencies SAC has alternate command posts on KC-135 jet tankers.

For these centers, too, are on the gold circuit.

For the beatnik, like the hipster, is in opposition to a society that is based on the repression of the sex instinct.

For over a hundred years Southerners have felt that the North was picking on them.

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 the occasion on which everyone already knows everyone else and the host wishes them to meet one or a few honored newcomers, then the `` open house '' system is advantageous because the honored guests are fixed connective points and the drifting guests make and break connections at the door.

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 ; ;

The second specific comment was the report of Eisenhower's Commission on National Goals, titled Goals For Americans.

For them only a little more needed to be learned, and then all physical knowledge could be neatly sorted, packaged and put in the inventory to be drawn on for the solution of any human problem.

For the figure of Vincent Berger Malraux has obviously drawn on his studies of T. E. Lawrence ( though Berger fights on the side of the Turks instead of against them ), and like both Lawrence and Malraux himself he is a fervent admirer of Nietzsche.

For every person on Taiwan, there are sixty in Mainland China.

Small Business Administration, What It Is, What It Does, SBA Services For Community Economic Development, and various other useful publications on currently important management, technical production, and marketing topics are available, on request, from Small Business Administration, Washington 25, D.C..

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.

and overhead projector transparency sets on the subjects of Military Sanitation: First Aid For Soldiers ; ;

In May 1960, the Armed Forces Institute of Pathology began a series of articles on the `` Medical Museum '', and in June, the Institute started contributing a regular monthly `` Case For Diagnosis ''.

For each State ( except Puerto Rico, Guam, the Virgin Islands, and, prior to 1962, Alaska and Hawaii ) determine average per capita income based on the last three years.

For readjustment to the U.S., volunteers should be given some separation allowance at the end of their overseas service, based on the length of time served.

For the making of selections on the basis of excellence requires that any foundation making the selections shall have available the judgments of a corps of advisors whose judgments are known to be good: such judgments can be known to be good only by the records of those selected, by records made subsequent to their selection over considerable periods of time.

For change is dependent on the possibilities that individual men glimpse for the future.