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If the given system is closed, then one can think of a mixed state as representing a single system with an uncertain preparation history, as explicitly detailed above ; or we can regard the mixed state as representing an ensemble of systems, i. e. a large number of copies of the system in question, where p < sub > j </ sub > is the proportion of the ensemble being in the state.
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If and given
If, in the trustee's judgment, `` reasonable market conditions '' did not prevail during any given year, he was to be allowed to petition the court for an extension of time within the ten-year period.
If it is assumed that the formula given by Lodge of cosec Af applies, the pressure difference along the major axes can be calculated from the angle of inclination of the major axis, and from this the interfacial tension can be calculated.
If one assumes that the average flux did not change between measurements, a mass-distribution curve is obtained which relates the flux of particles larger than a given radius to the inverse 7/2 power of the radius.
If, however, we are seeking the optimal R-stage policy for a given feed state, only one search for a maximum is required at the final step.
If the latter knows nothing about the absent sitter except his name ( given by the experimenter ), he cannot possibly give any clues, conscious or unconscious, far less ask leading questions.
`` If you substitute ' atom ' for ' angel ', the problem is not insoluble, given the metallic content of the pin in question ''.
If a defendant has been convicted and can prove that his lawyer did not adequately handle his case and that there is a reasonable probability that the result of the trial would have been different had the lawyer given competent representation, he is entitled to a new trial.
** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.
** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.
( If the condition is thought to be cellulitis rather than abscess, consideration should be given to possibility of strep species as cause that are still sensitive to traditional anti-staphylococcus agents such as dicloxacillin or cephalexin in patients able to tolerate penicillin ).
If we use a cylindrical coordinate system with basis vectors, then the gradient of and the divergence of are given by
If the resulting four kilobyte table size is too large for a given target platform, the table lookup operation can be performed with a single 256-entry 32-bit ( i. e. 1 kilobyte ) table by the use of circular rotates.
* If the balance factor of P is-2 then the right subtree outweighs the left subtree of the given node, and the balance factor of the right child ( R ) must be checked.
* If the balance factor of P is 2, then the left subtree outweighs the right subtree of the given node, and the balance factor of the left child ( L ) must be checked.
If the path of the particle or centre of mass of the rigid body passes through the given origin, its angular momentum is zero.
If two equivalent amplifiers are being compared, the amplifier with higher gain settings would be more sensitive as it would take less input signal to produce a given amount of power.
If the norm of a Banach space satisfies this identity, the associated inner product which makes it into a Hilbert space is given by the polarization identity.
If BCG is accidentally given subcutaneously, then a local abscess may form ( a BCG-oma ) that can sometimes ulcerate, and may require treatment with antibiotics.
If given subcutaneously, it may induce local infection and spread to the regional lymph nodes, causing either suppurative and nonsuppurative lymphadenitis.
If BCG is accidentally given to an immunocompromised patient ( e. g., an infant with SCID ), it can cause disseminated or life-threatening infection.
If players cannot move either die in a roll, given the position of their checkers then that turn is over and the turn passes to the opponent.
If a source emits a known luminous intensity I < sub > v </ sub > ( in candelas ) in a well-defined cone, the total luminous flux Φ < sub > v </ sub > in lumens is given by
He explained that this is one of the most important analects: " If the people be led by laws, and uniformity sought to be given them by punishments, they will try to avoid the punishment, but have no sense of shame.
If they be led by virtue, and uniformity sought to be given them by the rules of propriety, they will have the sense of the shame, and moreover will become good.
* If the metric space X is compact and an open cover of X is given, then there exists a number such that every subset of X of diameter < δ is contained in some member of the cover.
If and system
If we cannot stop warfare in our own economic system, how can we expect to abolish it internationally??
If your house is to have a forced warm air system, cooling can be a part of it.
If you plan to add cooling later to your heating system, there are things to watch for.
If the problems of combining cooling with your heating are knotty, it may be cheaper to plan on a completely separate cooling system.
If you use one of the new year-round cooling system fluids such as `` Dowguard '' be sure to check it.
If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.
If tyrosine and a system generating hydrogen peroxide are added to a cell-free homogenate of the thyroid, large quantities of free mono-iodotyrosine can be formed ( Alexander, 1959 ).
If the house is not wired adequately for electricity or if plumbing or a central heating system must be installed, check into the cost of making these improvements.
If laborers are merely commodities competing against each other in a market place like so many bags of wheat and corn ( unsupported, by the way, by any agricultural subsidy ), then they may be pardoned for reacting with complete antagonism to a system that imposes such status upon them.
If the demands of these two sovereigns upon his duty of allegiance come into conflict, those of the United States have the paramount authority in American law ; likewise, those of the foreign land have paramount authority in their legal system.
If under the existing system he could not assemble forces quickly enough to intercept mobile Viking raiders, the obvious answer was to have a standing field force.
If administrative appeal is available, no appeal to the judicial system may be made.
If the system be entirely behind the aperture stop, then this is itself the entrance pupil ( front stop ); if entirely in front, it is the exit pupil ( back stop ).
If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their perpendicular height of incidence, i. e. their distance from the axis.
If a system consists of several particles, the total angular momentum about a point can be obtained by adding ( or integrating ) all the angular momenta of the constituent particles.
If not, the system may either be rejected or accepted on conditions previously agreed between the sponsor and the manufacturer.
If the pressure in a system remains constant ( isobaric ), a vapor at saturation temperature will begin to condense into its liquid phase as thermal energy ( heat ) is removed.
If a newer system is attempting to achieve integration with an older system which has known flaws ( or " bugs "), then the new system may be referred to as " bugwards-compatible ".
If a system is composed of two subsystems described in V and W respectively, then the Hilbert space of the entire system is the tensor product of the two spaces.
" That rich island ," he wrote on 1 December 1881, " the key to the Gulf of Mexico, is, though in the hands of Spain, a part of the American commercial system … If ever ceasing to be Spanish, Cuba must necessarily become American and not fall under any other European domination.
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