`` If there was collusion between an outside murderer and a member of the household it would be an elementary precaution to check on the door later.

If the arguments are both greater than zero then the algorithm can be written in more elementary terms as follows:

If one contemplates actual reaction mechanisms, stoichiometric coefficients will always be integers, since elementary reactions always involve whole molecules.

If the subsets of X in Σ correspond to numbers in elementary algebra, then the two set operations union ( symbol ∪) and intersection (∩) correspond to addition and multiplication.

If the outcome is the element of the elementary event of two pips on the first die and five on the second, then both of the events of " 7 pips " and " odd number of pips " have also happened.

If the Avogadro constant N < sub > A </ sub > and the Faraday constant F are independently known, the value of the elementary charge can be deduced, using the formula

If the former horn of the dilemma is chosen, arithmetical algebra becomes a mere shadow ; if the latter horn is chosen, the operations of algebra cannot be defined on the supposition that the elementary symbol is an integer number.

If both reactions are elementary reactions, then the rate of reaction is given by

If a Petri net is equivalent to an elementary net, then Z can be the countable set

If λ is any ordinal, κ is λ-strong means that κ is a cardinal number and there exists an elementary embedding j from the universe V into a transitive inner model M with critical point κ and

If λ is any ordinal, κ is λ-supercompact means that there exists an elementary embedding j from the universe V into a transitive inner model M with critical point κ, j ( κ )> λ and

If it is then assumed that the elementary opaque elements of all matter are identical ( i. e., having the same ratio of density to area ), it will follow that the shadow effect is, at least approximately, proportional to the mass ( P5 ).

If j is the elementary embedding mentioned in one of these axioms and κ is its critical point, then λ is the limit of as n goes to ω.

If this elementary product solution is substituted into the wave equation ( 2. 0 ), using the scalar Laplacian in rectangular coordinates:

If children were to begin training in Tang Te while in elementary school, then they will be well suited for military service.

If karate should be introduced beginning in the elementary schools, then we will produce many men each capable of defeating ten assailants.

If elementary events are assigned equal probabilities, then the probability of a disjunction of elementary events is just the number of events in the disjunction divided by the total number of elementary events.

If N is an elementary substructure of M, M is called an elementary extension of N. An embedding h: N → M is called an elementary embedding of N into M if h ( N ) is an elementary substructure of M.

If N is a substructure of M, then both N and M can be interpreted as structures in the signature σ < sub > N </ sub > consisting of σ together with a new constant symbol for every element of N. N is an elementary substructure of M if and only if N is a substructure of M and N and M are elementarily equivalent as σ < sub > N </ sub >- structures.

If a particle and antiparticle are in the appropriate quantum states, then they can annihilate each other and produce other particles.

If denotes the quantum state of a particle ( n ) with momentum p, spin J whose component in the z-direction is σ, then one has

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 we define r < sub > i </ sub > as the displacement of particle i from the center of mass, and v < sub > i </ sub > as the velocity of particle i with respect to the center of mass, then we have

If a particle of the beam crosses this surface, there will be some kind of interaction.

If we think of the atoms as impenetrable steel discs and the impinging particle as a bullet of negligible diameter, this ratio is the probability that the bullet will strike a steel disc, i. e., that the atomic projectile will be stopped by the foil.

If this acceleration is multiplied by the particle mass, the leading term is the centripetal force and the negative of the second term related to angular acceleration is sometimes called the Euler force.

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 entire volume of the observable universe ( taken to be 3 × 10 < sup > 80 </ sup > m < sup > 3 </ sup >) were packed solid with fine dust particles about 1. 5 micrometres in size, then the number of different ways of ordering these particles ( that is, assigning the number 1 to one particle, then the number 2 to another particle, and so on until all particles are numbered ) would be approximately one googolplex.

If the particles are indistinguishable, this is impossible by definition ; either particle can be in either state.

If the particles are bosons, they occupy a totally symmetric state, which is symmetric under the exchange of any two particle labels:

If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force

If a force is applied to a particle for a time interval, the momentum of the particle changes by an amount

If the particle is moving at speed in the first frame of reference, in the second it is moving at speed

If a charged particle moves in an electromagnetic field, its kinematic momentum is not conserved.

If, e. g., u is the speed of a particle, then the straightforward notation for its velocity is u, < u > u </ u >, or.

If the photon energy is absorbed, some of the energy liberates the electron from the atom, and the rest contributes to the electron's kinetic energy as a free particle.

If the particle is in an eigenstate of position, then its momentum is completely unknown.

If the spin of a particle has a positive projection on its direction of motion then it is called left-handed ; otherwise, it is right-handed.

If Alice has a particle which is entangled with a particle owned by Bob, and Bob teleports it to Carol, then afterwards, Alice's particle is entangled with Carol's.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If we fail to develop the means to hunt down and destroy the enemy's military force with extreme care and precision, and if war comes in spite of our most ardent desires for peace, our choice of alternatives will be truly frightening.

If, in Larkin's eyes, they are nothing but Piccadilly farmers, he has as much to learn about them as they have to learn about the ways of truly rural living.

Naamani Tarkow has written: " If one is to make sweeping statements, one may say that, save Magna Carta ( more truly, its implications ), the Act of Settlement is probably the most significant statute in English history ".

If the descent were truly unbroken, father-to-son, since Confucius's lifetime, the males in the family would all have the same Y chromosome as their direct male ancestor, with slight mutations due to the passage of time.

:“ If an integer n is greater than 2, then has no solutions in non-zero integers a, b, and c. I have a truly marvelous proof of this proposition which this margin is too narrow to contain .”

If a criminal were truly aware of the mental and spiritual consequences of his actions, he would neither commit nor even consider committing those actions.

If we wish for nothing but what God wills, we shall be truly free, and all will come to pass with us according to our desire ; and we shall be as little subject to restraint as Zeus himself.

The Council of Trent decreed: " If anyone shall say that a man once justified can sin no more, nor lose grace, and that therefore he who falls and sins was never truly justified ; or, on the contrary, that throughout his whole life he can avoid all sins even venial sins, except by a special privilege of God, as the Church holds in regard to the Blessed Virgin: let him be anathema.

If truly irreducible systems are found, the argument goes, then intelligent design must be the correct explanation for their existence.

If the key is truly random, as large as or greater than the plaintext, never reused in whole or part, and kept secret, the ciphertext will be impossible to decrypt or break without knowing the key.

If they were elected it would pose the dilemma of which House was truly representative of the electorate.

If such a union of human and divine occurred, Nestorius believed that Christ could not truly be con-substantial with God and con-substantial with us because he would grow, mature, suffer and die ( which Nestorius argued God cannot do ) and also would possess the power of God that would separate him from being equal to humans.

Nimoy also played the Mermelstein role and believes: " If every project brought me the same sense of fulfillment that Never Forget did, I would truly be in paradise.

If the central office is not convinced that such a message is truly sent from an authorized source, acting on such a request could be a grave mistake.

If the arbitrary area for excavation is wisely chosen, the sequence should be revealed and excavation can return to a truly stratigraphic method.

If such a union of human and divine occurred, Nestorius believed that Christ could not truly be con-substantial with God and con-substantial with us because he would grow, mature, suffer and die ( which he said God cannot do ) and also would possess the power of God that would separate him from being equal to humans.

If there be an object truly ridiculous in nature, it is an American patriot, signing resolutions of independency with the one hand, and with the other brandishing a whip over his affrighted slaves.

If man and he were truly generic, the parallel phrase would have been he has difficulties in childbirth.

If you want to know which, pay attention to what it means to be truly human in a world that half the time we're in love with and half the time scares the hell out of us.

If the British people were ever to ask themselves what power they truly enjoyed under our political system they would be amazed to discover how little it is, and some new Chartist agitation might be born and might quickly gather momentum.

For example, given a graph G =( V, E ), the shortest path p from a vertex u to a vertex v exhibits optimal substructure: take any intermediate vertex w on this shortest path p. If p is truly the shortest path, then the path p < sub > 1 </ sub > from u to w and p < sub > 2 </ sub > from w to v are indeed the shortest paths between the corresponding vertices ( by the simple cut-and-paste argument described in CLRS ).

If he truly was the author of the five or six long works in Scots which different witnesses ascribe to him, then he would have been one of the most voluminous writers of Early Scots, if not the most voluminous of all Scots poets.

If Vedanta truly epitomises the state of learnedness, in achieving this spiritual progress " the first stage for a layman is the external / material worship ; struggling to rise high, mental prayer is the next stage, but the highest stage is when the divine has been realized " Unity in variety is the scheme of nature, and the Hindu has recognized it and practised eversince the yore through his equanimity to all and universal tolerance ".