From the definition of matrix multiplication, there exists an × matrix, such that.

( From this Cox eventually infers that conjunction of plausibilities is associative, and then that it may as well be ordinary multiplication of real numbers.

From 1929 until the rapid multiplication in the number of swing bands from 1935 on, the Casa Loma Orchestra was one of the top North American dance bands.

From this principle the error rules of summation, multiplication etc.

From complex multiplication, the magnitude of the bispectrum is equal to the product of the magnitudes of each of the frequency components, and the phase of the bispectrum is the sum of the phases of each of the frequency components.

From this follows a simple algorithm, which can be stated in a high-level description English prose, as:

From this it follows that correctness of drawing depends solely upon the principal rays ; and is independent of the sharpness or curvature of the image field.

From Okhla the canal follows the high land between the Khari-Nadi and the Yamuna and finally joins the Banganga river about below Agra.

From the commutativity of kets with ( complex ) scalars now follows that

From this it follows that the set of complements of the problems in NP is a subset of the set of complements of the problems in co-NP, i. e., co-NP is a subset of NP.

From Woodside to near Sandilands ( routes 1, 2 and 4 ) and from near Sandilands almost to Lloyd Park ( route 3 ) Tramlink follows the former Woodside and South Croydon Railway, including the Park Hill ( or Sandilands ) tunnels.

From the above rule of calculation of heat with respect to volume, there follows one with respect to pressure.

From the criterion it also follows that Carmichael numbers are cyclic .< ref > Proof sketch: If is square-free but not cyclic, for two prime factors and of.

From the east-coast of Sweden to Lake Vänern the locks are as follows:

From these two axioms, it follows that for every g in G, the function which maps x in X to g · x is a bijective map from X to X ( its inverse being the function which maps x to g < sup >− 1 </ sup >· x ).

And He is called Angel and Apostle ; for He declares whatever we ought to know, and is sent forth to declare whatever is revealed ; as our Lord Himself says, “ He that heareth Me, heareth Him that sent Me .” From the writings of Moses also this will be manifest ; for thus it is written in them, “ And the Angel of God spoke to Moses, in a flame of fire out of the bush, and said, I am that I am, the God of Abraham, the God of Isaac, the God of Jacob, the God of thy fathers ; go down into Egypt, and bring forth My people .” And if you wish to learn what follows, you can do so from the same writings ; for it is impossible to relate the whole here.

From the point of view of a passenger, latency can be described as follows.

From May to July 2006, several groups presented papers that filled in the details of Perelman's proof of the Poincaré conjecture, as follows:

From this it follows that there are three divisions of oratory-( 1 ) political, ( 2 ) forensic, and ( 3 ) the ceremonial oratory of display ".

From this, the disease activity of the patient can be classified as follows:

From the above stated equations it can be expressed as follows:

From Mars there follows a space of 4 + 24 = 28 such parts, but so far no planet was sighted there.

From outside to inside, the path to the uterus is as follows:

:: From the fact that if this match is scratched it will light, it follows that if it does not light it was not scratched.

:: From the fact that if this match is scratched it will light, it follows that if it were not to light it would not have been scratched.

From the gene-centred view follows that the more two individuals are genetically related, the more sense ( at the level of the genes ) it makes for them to behave selflessly with each other.

From here the canal follows the course of the River Bulbourne through Bourne End with the well-known swingbridge at Winkwell, and the " Port of Berkhamsted ".

From this general law, it follows that there is an inverse relationship between the wavelength of the peak of the emission of a black body and its temperature when expressed as a function of wavelength, and this less powerful consequence is often also called Wien's displacement law in many textbooks.

From these calculations follows an acceptable flood risk from the sea at 1 in 4, 000 – 10, 000 years, while it is 1 in 100 – 2, 500 years for a river flood.

From there U. S. Highway 30 which follows the Platte River is a better approximate path for those traveling the north side of the Platte.

From above one could only occasionally catch a glimpse of life on the floor of this green sea: a neighbor's gingham skirt flashing into sight for an instant on the path beneath her grape-arbor, or the movement of hands above a clothesline and the flutter of garments hung there, half-way down the block.

From his first bout with the canny Woodruff, Pike had learned that it was better not to attack him directly, so, harping on the theme that the cost of printing was too high, he condemned the governor for permitting such a state of affairs to exist.

The CTCA distributed a khaki-bound songbook that provided the impetus for spirited renditions of the selections found therein, plus a number of others whose lyrics were more earthy -- from `` Johnny Get Your Gun '' to `` Keep The Home Fires Burning '' to `` Mademoiselle From Armentieres ''.

From necessity, they are also inspired by the `` hard-sell '' attitude of the sponsor, so, finally, it is the sponsor who must take the responsibility for the good or bad taste of his advertising.

From the moment that Hino had first walked into the mission to ask for a job, any job -- his qualifications neatly written on a piece of paper in a precise hand -- he had been ready to become a Christian.

From the wealth of material and the wide variety of different electronic techniques perfected in the past few years we have selected a few examples which appear to be headed for use in the immediate future and which offer completely new tools in medical research.

From Gottingen ( 1801 ) where he stayed for 10 days, he wrote, `` The first question asked everywhere is about galvanism.

From the brightness of the F component of the solar corona and the brightness of the zodiacal light, an estimate of the particle sizes, concentrations, and spatial distribution can be derived for regions of space near the ecliptic plane.

From an estimated mass of 25 g for a zero-magnitude meteorite, the other masses are derived with the assumption of a mass decrease by a factor of 2.512 for each unit increase in magnitude.

From the evidence `` it may be conjectured that core - core marriages are the preferred unions for core males and females ; ;

The details of the setting of `` Neutral Tones '' are not, strictly speaking, metaphorical, but they combine to create a mood which is appropriate both to a dismal winter day and to the end of love, and in this way love and weather, the emotions and the elements, symbolize each other in a way that is common to many of Hardy's best poems ( `` Weathers '', `` The Darkling Thrush '', and `` During Wind and Rain '', for example ) and to some moving passages in the novels as well ( Far From The Madding Crowd is full of scenes constructed in this way ).

From the collection centers, toys will be taken to a warehouse at 198 Second street, where they will be repaired and made ready for distribution.

From there he chipped back and sank his putt for a par 4.

From this taste of the 1920s, we leaped way out to Stan Getz's private brand of progressive jazz, which did lovely, subtle things for `` Baubles, Bangles And Beads '', and a couple of ballards.

From time to time it has been proposed as a replacement for The Star-Spangled Banner as the national anthem, including television sign-offs.

A Modest Proposal for Preventing the Children of Poor People From Being a Burden on Their Parents or Country, and for Making Them Beneficial to the Publick, commonly referred to as A Modest Proposal, is a Juvenalian satirical essay written and published anonymously by Jonathan Swift in 1729.

From the 2000s many Chinese have settled and started up small businesses, while at least as many have come as workforce for large ( construction or other ) enterprises.

From 1764 onwards, there was a gradual change from a slave-based society to one based on production for domestic consumption and export.

From the mid-1980s through at least 1992, the United States was the primary source of military and other support for the UNITA rebel movement, which was led from its creation through 2002 by Jonas Savimbi.

From January – September 2010, bilateral trade with the United States measured approximately $ 150 million, on track for about a 30 percent increase over 2009.

From here the Aar flows northeast for a long distance, past the ambassador town Solothurn ( below which the Grosse Emme flows in on the right ), Aarburg ( where it is joined by the Wigger ), Olten, Aarau, near which is the junction with the Suhre, and Wildegg, where the Hallwiler Aa falls in on the right.

From there she negotiated with the emperor for the safety of family members left in the capital, while protesting her sons ' innocence of hostile actions ; under the falsehood of making a vesperal visit to worship at the church, she deliberately excluded the grandson of Botaneiates and his loyal tutor, met with Alexios and Isaac and fled for the forum of Constantine.