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Page "Control theory" ¶ 68
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If and simply
If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.
If D denotes the differentiation operator and P is the polynomial Af then V is the null space of the operator p (, ), because Af simply says Af.
If William wished to continue operations for a year, why not simply leave the Negroes undisturbed and pay them `` as high wages to remain there as are ever paid the labor of persons of their sex & age.
If the valid element indices begin at 0, the constant B is simply the address of the first element of the array.
If A is commutative then the center of A is equal to A, so that a commutative R-algebra can be defined simply as a homomorphism of commutative rings.
If the concentration of element or compound in a sample is too high for the detection range of the technique, it can simply be diluted in a pure solvent.
If there is no number to its left, simply look at the column headed " 1 " in the previous row.
If the tree contains data, we can simply simultaneously store it in a consecutive array in preorder.
If F is clear from context then Ω < sub > F </ sub > may be denoted simply Ω, although different prefix-free universal computable functions lead to different values of Ω.
If requested data is contained in the cache ( cache hit ), this request can be served by simply reading the cache, which is comparatively faster.
If the frame contains areas where nothing has moved, the system simply issues a short command that copies that part of the previous frame, bit-for-bit, into the next one.
If the depletion layer is large enough to catch the whole shower or to stop a heavy particle, a fairly accurate measurement of the particle ’ s energy can be made, simply by measuring the charge conducted and without the complexity of a magnetic spectrometer, etc.
If the panegyric detailing the ceremony implied that the true center of the Empire was not Rome, but where the Emperor sat ("... the capital of the Empire appeared to be there, where the two emperors met "), it simply echoed what had already been stated by the historian Herodian in the early third century: " Rome is where the emperor is ".
If that class is not available, or unknown at compile time, the application simply won't compile.
If we view the DFT as just a coordinate transformation which simply specifies the components of a vector in a new coordinate system, then the above is just the statement that the dot product of two vectors is preserved under a unitary DFT transformation.
If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.
If this does not simply reflect Gregory ’ s ignorance of Kentish affairs, which seems unlikely given the close ties between Kent and the Franks, then some assert that Æthelberht ’ s reign cannot have begun before 589.
# If the remainder from dividing N by 6 is not 2 or 3 then the list is simply all even numbers followed by all odd numbers ≤ N
If a fatwā does not break new ground, then it is simply called a ruling.
If the rock is analyzed and found to be felsic but is metamorphic and has no definite volcanic protolith, it may be sufficient to simply call it a ' felsic schist '.
If some of the units in the fold are facing downward, the structure is called an overturned anticline or syncline, and if all of the rock units are overturned or the correct up-direction is unknown, they are simply called by the most general terms, antiforms and synforms.
The Church would not simply grant this favour, so Henry cited the passage in the Book of Leviticus where it said, " If a man taketh his brother's wife, he hath committed adultery ; they shall be childless.
This can be verified simply by investigating, e. g., a polycrystalline material under a polarizing microscope having the polarizers crossed: If the crystallites are larger than the resolution limit, they will be visible.
Then an element e of S is called a left identity if e * a = a for all a in S, and a right identity if a * e = a for all a in S. If e is both a left identity and a right identity, then it is called a two-sided identity, or simply an identity.

If and stable
If an element has isotopes that are not radioactive, they are termed " stable.
If a state is not controllable, but its dynamics are stable, then the state is termed Stabilizable.
If such an eigenvalue is not stable, the dynamics of this eigenvalue will be present in the closed-loop system which therefore will be unstable.
If the ambient temperature exceeds T < sub > m </ sub >, the homologous pairing of the sticky ends would not be stable because the high temperature disrupts hydrogen bonding.
If in the third identity we take H = G, we get that the set of commutators is stable under any endomorphism of G. This is in fact a generalization of the second identity, since we can take f to be the conjugation automorphism.
If the spacecraft started to reenter nose first ( another stable reentry attitude for the spacecraft ), airflow over the spoiler would flip the spacecraft around to the proper, heatshield-first reentry attitude, a technique called shuttlecocking.
If the feedback network is made of components with relatively constant, stable values, the variability of the op-amp's open loop response does not seriously affect the circuit's performance.
If the center of gravity exists within the foundations, the body is stable since no net torque acts on the body.
The band remained stable enough to record If I Should Fall from Grace with God in 1988 ( with its Christmas hit duet with Kirsty MacColl " Fairytale of New York ", which was voted " the best Christmas song ever " in VH1 UK polls in 2004 ) and 1989's Peace and Love.
If the constricted object ( such as a temporarily whipped rope ) ends very close to where a constrictor binds it, a boa knot may prove a more stable solution.
If the predicted half-life falls into an experimentally accessible range, such isotopes have a chance to move from the list of stable nuclides to the radioactive category, once their activity is observed.
If a situation calls for more mediated responses, the fixity of the situation is more prevalent, and therefore is attributed with a stable demand of expectations.
If the air is generally stable, nothing more than lenticular cap clouds will form.
If the instrument is in an environment where it gets infrequent use, then buying argon in the gas state will be most appropriate as it will be more than enough to suit smaller run times and gas in the cylinder will remain stable for longer periods of time, whereas liquid argon will suffer loss to the environment due to venting of the tank when stored over extended time frames.
understood, it is not known precisely how long it will take white dwarfs to cool to blackness .< sup >, § IIIE, IVA .</ sup > Barrow and Tipler estimate that it would take 10 < sup > 15 </ sup > years for a white dwarf to cool to 5 K ; however, if weakly interacting massive particles exist, it is possible that interactions with these particles will keep some white dwarfs much warmer than this for approximately 10 < sup > 25 </ sup > years .< sup >, § IIIE .</ sup > If protons are not stable, white dwarfs will also be kept warm by energy released from proton decay.
If the stone is correctly interpreted as depicting this myth, it demonstrates that the myth was in a stable form for a period of about 500 years to the recording of the myth in the Prose Edda around the year 1220.
If more than one stable equilibrium state is possible for a system, any equilibria whose potential energy is higher than the absolute minimum represent metastable states.
If a subject's history of reinforcement is consistent, such variations will remain stable because the same successful variations are more likely to be reinforced than less successful variations.
If, however, the existence of stable tetraneutrons were ever independently confirmed, considerable adjustments would have to be made to current nuclear models.
If the underlying problem is well-posed, there should be a stable algorithm for solving it.
If the patient is stable, adenosine may be administered first, as the medicine performs a sort of " chemical cardioversion " and may stabilize the heart and let it resume normal function on its own without using electricity.
If a simple yes or no on the stability issue is all that is needed, the amplifier is stable if f < sub > 0dB </ sub > < f < sub > 180 </ sub >.
If Britain is to have a stable, affordable pension system, people need to work longer, but we will reward their hard work with a decent state pension that will enable them to enjoy quality of life in their retirement.

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