If the direct-sum decomposition ( A ) is valid, how can we get hold of the projections Af associated with the decomposition??

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

If the valid element indices begin at 0, the constant B is simply the address of the first element of the array.

If the exponent r is even, then the inequality is valid for all real numbers x.

If the client remains connected to a network for which this IP is valid, the server may grant the request.

If time, space, and energy are secondary features derived from a substrate below the Planck scale, then Einstein's hypothetical algebraic system might resolve the EPR paradox ( although Bell's theorem would still be valid ).

If this understanding were valid, then it would it would follow:

If this understanding were valid, then it would it would follow:

If this understanding were valid, then it would it would follow:

If this triangulated graph is colorable using four colors or less, so is the original graph since the same coloring is valid if edges are removed.

If on the other hand Theorem 2 holds and φ is valid in all structures, then ¬ φ is not satisfiable in any structure and therefore refutable ; then ¬¬ φ is provable and then so is φ, thus Theorem 1 holds.

If the wavepacket has a relatively large frequency spread, or if the dispersion has sharp variations ( such as due to a resonance ), or if the packet travels over very long distances, this assumption is not valid.

If the works were renewed, the copyrights would still be valid in the United States.

If we neglect the possibility of overlapping states, which is valid if the temperature is high, then the number of times we count each state is approximately N < nowiki >!</ nowiki >.

If a player cannot make a valid move after first move of 6 they must pass the die to the next player.

If the defendant asserts his right to remain silent all interrogation must immediately stop and the police may not resume the interrogation unless the police have " scrupulously honored " the defendant ’ s assertion and obtain a valid waiver before resuming the interrogation.

If the defendant does reinitiate contact, a valid waiver must be obtained before interrogation may resume.

If his reasoning is valid, he goes on to argue, either it is not very immoral to value small luxuries over saving many lives, or such affluent people are very immoral.

If one player cannot make a valid move, play passes back to the other player.

If the substitution of an expression with its value is valid only at a certain point in the execution of the program, then the expression is not referentially transparent.

If an argument form is valid, the conjunction of the premises will be logically equivalent to the conclusion and this can be clearly seen in a truth table ; it is displayed.

# If they do have a demonstrable genetic relationship, do they form a valid linguistic taxon?

If the server is case sensitive and < tt >< nowiki > http :// en. example. org / wiki / URL </ nowiki ></ tt > is correct, < tt >< nowiki > http :// en. example. org / WIKI / URL </ nowiki ></ tt > or < tt >< nowiki > http :// en. example. org / wiki / url </ nowiki ></ tt > will display an HTTP 404 error page, unless these URLs point to valid resources themselves.

If the deviations from ideality are not too strong, Raoult's law will still be valid in a narrow concentration range when approaching x = 1 for the majority phase ( the solvent ).

If the number of bits changed is even, the check bit will be valid and the error will not be detected.

If we grasp this opportunity to build an age of productive partnership between the less fortunate nations and those that have already achieved a high state of economic advancement, we will make brighter the outlook for a world order based upon security and freedom.

If community exists, both freedom and security may exist as well.

If a suitably sized quantum computer capable of running Grover's algorithm reliably becomes available, it would reduce a 128-bit key down to 64-bit security, roughly a DES equivalent.

If a vulnerability is disclosed before the security patch released by the vendor, a zero-day attack is possible.

If security breach is discovered then all possible corrective actions are taken.

If one needs a weapon for self-defense one must " prove that his personal safety at risk to such an extent that in order to ensure the needed a weapon for security ".

If the collection holds guns of criminal interest, such as pistols or sub machine-guns the police may demand a very high safety level on the keeping of the guns ( such as security windows and vault doors ).

If the number of participants is large, and some of their physical or network distancee are great, then the probability of complete success ( which is, in ideal circumstances, required for system security ) will be rather low.

If a new password is passed to the system in unencrypted form, security can be lost ( e. g., via wiretapping ) before the new password can even be installed in the password database.

If the Security Council fails to act to maintain international peace and security due to a disagreement between its permanent members, the General Assembly has the power to convene an emergency special session and act to ensure peace and security under United Nations General Assembly Resolution 377.

If there is a problem with Release 11, the customer can return to Release 9 without experiencing dataset, configuration, or security profile compatibility problems ( fallback ) until ready to try moving forward again.

If patient's status is found to be illegal, hospitals may not discharge a patient prior to completion of care, though law enforcement and hospital security may take necessary action to prevent a patient from escaping or harming others.

If security depends on keeping that secret, then disclosure leads to major logistic difficulties in developing, testing, and distributing implementations of a new algorithm: it is " brittle.

A further 15 percent were in favor with qualifications such as: " If it doesn't get us into war ," or " If the British can give us some security for what we give them.

If they successfully breach security, they are often able to delete logs to cover their tracks.

If any of these security vulnerabilities are exploitable in the product's evaluated configuration, the product's Common Criteria certification should be voluntarily withdrawn by the vendor.

If not implemented correctly, it presents a security risk to overall platform integrity and protected data.

If there was a threat to " public order and security " he could legislate by decree and suspend civil rights.

If all components of the system are functional, then the resultant security assurance is at NIST 800-63 Level 3.

If a security's price does not reflect all the information about it, then there exist " unexploited profit opportunities ": someone can buy ( or sell ) the security to make a profit, thus driving the price toward equilibrium.

If used in this way, security measures should be considered to protect the rest of your infrastructure in case this server is compromised, as its web application is exposed to attack from the Internet.

If a mutual fund sells a security for a gain, the capital gain is taxable for that year ; similarly a realized capital loss can offset any other realized capital gains.

If parking services tow away or disable the car, then the bodyguard cannot use the car to escape with the client in case there is a security threat while the client is at his or her meeting.