From a geometrical point of view, looking at the states of each variable of the system to be controlled, every " bad " state of these variables must be controllable and observable to ensure a good behaviour in the closed-loop system.

From the variables defined above, we find two other common expression for the value produced during a given period as:

From a geometric standpoint, if we consider f ( x, θ ) as a function of two variables then the family of probability distributions can be viewed as a family of curves parallel to the x-axis, while the family of likelihood functions are the orthogonal curves parallel to the θ-axis.

From the intervals H < sub > x </ sub > and H < sub > y </ sub > for variables x and y, one can easily obtain intervals for x + y ( H < sub > x </ sub >+ H < sub > y </ sub >) and for x − y ( H < sub > x </ sub >− L < sub > y </ sub >); note that these are exact abstractions, since the set of possible outcomes for, say, x + y, is precisely the interval ( H < sub > x </ sub >+ H < sub > y </ sub >).

From 2004 to 2006, Stephen B. Plank and colleagues from John Hopkins University conducted a correlational study to determine the degree to which the physical appearance of the school and classroom setting influence student behavior, particularly in respect to the variables concerned in their study: fear, social disorder, and collective efficacy.

From analyses of the survey data, the researchers determined that the variables concerning their study are statistically significant to the physical conditions of the school and classroom setting.

From now on, we will assume that the random variables under consideration are continuous and, where convenient, we will also assume that they have a probability density function ( that is, they are absolutely continuous ).

From any two of the circuit variables there are six constitutive relations that can be formed.

From the perspective of object memory layout, the member variables of the source instance can be thought of as having been " sliced off ", leaving the corresponding member variables in the destination instance unchanged.

From a very young age he was an outstanding figure in the school of Henri Cartan, working on algebraic topology, several complex variables and then commutative algebra and algebraic geometry, in the context of sheaf theory and homological algebra techniques.

From this point onwards there was a foundational theory, which could be applied to analytic geometry ( a name adopted, confusingly, for the geometry of zeroes of analytic functions — this is not the analytic geometry learned at school ), automorphic forms of several variables, and partial differential equations.

( From a procedural standpoint, this agglomeration step involves replacing two columns in the attribute-value table — representing the two agglomerating variables — with a single column that has a unique value for every unique combination of values in the replaced columns.

From the notion of the solutions contained in a totality comes forth that of the independence of their relative positions ( of the variables ) in the system of variables used, insofar as new variables could take their place by transformation.

From a practical and mathematical standpoint, a valid reason to use this non-informative prior instead of others, like the ones obtained through a limit in conjugate families of distributions, is that it is not dependent upon the set of parameter variables that is chosen to describe parameter space.

From an economic point of view it is considered that, if the joint dynamics of a set of variables can be represented by a VAR model, then the structural form is a depiction of the underlying, " structural ", economic relationships.

From what I was able to gauge in a swift, greedy glance, the figure inside the coral-colored boucle dress was stupefying.

From the Renaissance onward the chained nude figure of Andromeda typically was the centre of interest, and often she was shown alone, fearfully awaiting the monster.

From the unexpected realism of his first major figure — inspired by his 1875 trip to Italy — to the unconventional memorials whose commissions he later sought, Rodin's reputation grew, such that he became the preeminent French sculptor of his time.

A fundamental rhythmic figure heard in Gottschalk's compositions such as " Souvenirs From Havana " ( 1859 ), many different slave musics of the Caribbean, as well as the bamboula, and other Afro-Caribbean folk dances performed in New Orleans Congo Square, is the three-stroke pattern known in Cuban music as tresillo.

From the point of view of material modelling, masonry is a special material of extreme mechanical properties ( with a very high ratio between strength in compression and in tension ), so that the applied loads do not diffuse as they do in elastic bodies, but tend to percolate along lines of high stiffness, see the figure on the right and watch a video for more details.

From a previously unassailable position, Scott became a figure of controversy, with questions raised about his competence and character.

< imagemap > File: 1st millennium montage. png | From left, clockwise: Depiction of Jesus, the central figure in Christianity ; The Colosseum, a landmark of the once mighty Roman Empire ; Gunpowder is invented during the latter part of the millennium, in China ; Chess, a new board game, takes on popularity across the globe ; The Roman Empire falls, and then reappears ushering in the Early Middle Ages ; The skeletal remains of a young woman, known as the " ring lady ", killed by the eruption of Mount Vesuvius in AD 79 ; Attila the Hun, leader of the Hunnic Empire, which takes most of western Europe.

From the late 1980s onwards, Adams was an important figure in the Northern Ireland peace process, initially following contact by the then Social Democratic and Labour Party ( SDLP ) leader John Hume and subsequently with the Irish and British governments and then other parties.

From the geometry of the above figure we have:

From the inception of the gag resolutions, Adams was a central figure in the opposition to the gag rules.

From 1955 until 1997 Sichuan had been China's most populous province, hitting 100 million mark shortly after the 1982 census figure of 99, 730, 000.

From his family Gideon ( biblical figure ) sprang ( Josh.

From the late Post-Classic Paris Codex back in time to the Pre-Classic San Bartolo murals, god D ( Itzamna ) has the so-called Principal Bird Deity-perhaps the Yaxcocahmut mentioned above-for a transformative shape ( see figure ).

From the polemical contemporary works which describe his career have emerged the outlines of a complex figure, charting a dangerous course through the chaos of the late 5th century Athenian political scene ; although historians from ancient times to the present have offered far more specific portraits, of one form or another, it may be that nothing more than that outline will ever be known with certainty.

From 1840 onward, Millerism was transformed from an “ obscure, regional movement into a national campaign .” The key figure in this transformation was Joshua Vaughan Himes — the pastor of Chardon Street Chapel in Boston, and an able and experienced publisher.

From 1946 onwards, he made numerous trips back to Europe, becoming an important musical figure in the early years of the Edinburgh Festival and in Salzburg, Vienna and Munich.

From a pre-expansion strength of just five squadrons, four of which were flying boats, the figure of maritime squadrons rose to 18 by September 1939, with a strength of just 176 aircraft.

From photos, the gap appears to affect a single figure, but as Koeppel, Conlin, and Stern have proven, in-site examination reveals that one is a foreground and the other a background figure.

From 1948 onwards, Byas became a familiar figure not only around the Saint-Germain-des-Prés in Paris, but also on the Riviera, where he could be seen in Saint-Tropez sporting a mask, tuba, flippers and an underwater spear-gun.

From the 1930s onwards he became an increasingly controversial figure ; from 1932 until four years after his death no publisher other than his own published his work.

From his first appointment as prime minister under the British mandate in 1930, Nuri was a major political figure in Iraq under the monarchy.

From the figure of the artist, the viewer's eye leaps again diagonally into the pictorial space.

From William Allan ( afterwards Sir William Allan and president of the Royal Scottish Academy ) and John Burnet, the engraver of Wilkie's works, we have an interesting account of his early studies, of his indomitable perseverance and power of close application, of his habit of haunting fairs and marketplaces, and transferring to his sketchbook all that struck him as characteristic and telling in figure or incident, and of his admiration for the works of Carse and David Allan, two Scottish painters of scenes from humble life.

From the terraces -- eighteen in all -- broad flights of steps descend into the water or onto still more terraces barely above the level of the river.

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 above me and somewhere behind me, a rifle cracked.

From the early Middle Ages until after the Second Vatican Council the sacrament was administered, within the Latin Church, only when death was approaching and, in practice, bodily recovery was not ordinarily looked for, giving rise, as mentioned above to the name " Extreme Unction " ( i. e. final anointing ).

From the above, it is possible to reformulate the definition to either of the following:

From the above equation, it can be re-arranged to show that

From a geostructural perspective the Azores is located above an active triple junction between three of the world's large tectonic plates ( the North American Plate, the Eurasian Plate and the African Plate ), a condition that has translated into the existence of many faults and fractures in this region of the Atlantic.

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

From the Shockley ideal diode equation given above, it might appear that the voltage has a positive temperature coefficient ( at a constant current ), but usually the variation of the reverse saturation current term is more significant than the variation in the thermal voltage term.

From the above properties an important feature arises: Looking at two triangles ABD and BCD with the common edge BD ( see figures ), if the sum of the angles α and γ is less than or equal to 180 °, the triangles meet the Delaunay condition.

From another perspective, the farmer and the miller both reduce a risk and acquire a risk when they sign the futures contract: the farmer reduces the risk that the price of wheat will fall below the price specified in the contract and acquires the risk that the price of wheat will rise above the price specified in the contract ( thereby losing additional income that he could have earned ).

From the above equations, it can be shown that the spin singlet can also be written as

From Muhammad IV ( 1859 – 1873 ) and Hassan I ( 1873 – 1894 ) the Alaouites tried to foster trading links, above all with European countries and the United States.

From his remarks on the importance of public, observable behavior ( as opposed to private experiences ), it may seem that Wittgenstein is simply a behaviorist — one who thinks that mental states are nothing over and above certain behavior.

From Persia, in medieval times polo spread to the Byzantines ( who called it tzykanion ), and after the Muslim conquests to the Ayyubid and Mameluke dynasties of Egypt and the Levant, whose elites favoured it above all other sports.

From above we can deduce that the eigenvalues of each σ < sub > i </ sub > are ± 1.

From a knowledge of the probabilities of each of these subprocesses – E ( A to C ) and P ( B to D ) – then we would expect to calculate the probability of both happening by multiplying them, using rule b ) above.

From the information above and the average cost per employee over time, or cost accrual ratio, a project manager can estimate:

* From the above property, one can deduce the following: If X is a separable space having an uncountable closed discrete subspace, then X cannot be normal.

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

From a variety of sites which were offered, Shrum recommended to the provincial government that the summit of Burnaby Mountain, 365 meters above sea level, be chosen for the new university.

From the definitions above, it is evident that, and.

From the definitions above, use of the terms " network " or " station " in reference to nationwide cable / satellite channels is technically inaccurate.