If we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.

If I now risk some comparisons with Sons And Lovers let it be clear that I am not comparing the two works or judging their merits ; ;

If nothing else, at least two good songs came out of the project, `` Out Of This World '' and `` June Comes Around Every Year ''.

If he were to go with White, he would be out there two days, not just listening in the dark at some point between here and Papa-san, but moving ever deeper into enemy land -- behind Papa-san -- itself.

Somebody, got to be somebody If I don't put my two cents in soon, somebody else will I know they're waitin only for one thing: for the bastards what done it to be nailed.

If we cluster together, the redcoats can make an advantage out of it, but there's not a blessed thing they can do with two or three of us except chase us, and we can outrun them ''.

If you've travelled in Europe a time or two, it is quite certain that you've had that wanting-to-be-alone feeling or that you will get it on your next visit across the Atlantic.

If A is the major axis of an ellipsoid and B and C are the other two axes, the radius of curvature in the ab plane at the end of the axis Af, and the difference in pressure along the A and B axes is Af.

If we try to study T using characteristic values, we are confronted with two problems.

If the distribution of the 71 items were wholly concordant in the two families, the distance would of course be 0.

If the patient can perceive figure kinesthetically when he cannot perceive it visually, then, it would seem, the sense of touch has immediate contact with the spatial aspects of things in independence of visual representations, at least in regard to two dimensions, and, as we shall see, even this much spatial awareness on the part of unaided touch is denied by the authors.

If a child loses a molar at the age of two, the adjoining teeth may shift toward the empty space, thus narrowing the place intended for the permanent ones and producing a jumble.

If you are not well acquainted with the area in which you wish to locate, or if you are not sure that you and your family will like and make a success of farming, usually you would do better to rent a place for a year or two before you buy.

If the change, at first sight, seems minor, we may recall that it took the Italian painters about two hundred years to make an analogous change, and the Italian painters, by universal consent, were the most brilliant group of geniuses any art has seen.

If we add to these contacts with friendly members the `` contacts with an organization of the church '' ( 11.2 per cent of the cases ), then a substantial two thirds of all recruitment is through friendly contact.

If the Orioles are to break their losing streak within the next two days, it will have to be at the expense of the American League champion New York Yankees, who come in here tomorrow for a night game and a single test Sunday afternoon.

If one takes the middle number, 5, and multiplies it by 3 ( the base number of the magic square of three ), the result is 15, which is also the constant sum of all the rows, columns, and two main diagonals.

If we look about the world today, we can see clearly that there are two especially significant factors shaping the future of our civilization: science and religion.

** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.

* If two small categories are weakly equivalent, then they are equivalent.

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 there is a mixture of only two types of atoms, not counting impurities, such as a copper-nickel alloy, then it is called a binary alloy.

* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )

If a tile is placed between two hotel chains of the same size, the individual player who places the tile decides which hotel chain remains on the board and which is acquired.

If two players tie for majority, they will share both shareholder bonuses.

If two groups differ only in isotopes, atomic masses are used at each step to break ties in atomic number.

If there exists an isomorphism between two groups, then the groups are called isomorphic.

If the 3 generations are then put in a 3x3 hermitian matrix with certain additions for the diagonal elements then these matrices form an exceptional ( grassman -) Jordan algebra, which has the symmetry group of one of the exceptional Lie groups ( F < sub > 4 </ sub >, E < sub > 6 </ sub >, E < sub > 7 </ sub > or E < sub > 8 </ sub >) depending on the details.

If and are groups, a homomorphism from to is a function ƒ: → such that

If I is ordered ( not simply partially ordered ) and countable, and C is the category Ab of abelian groups, the Mittag-Leffler condition is a condition on the transition morphisms f < sub > ij </ sub > that ensures the exactness of.

If the ranges of the morphisms of the inverse system of abelian groups ( A < sub > i </ sub >, f < sub > ij </ sub >) are stationary, that is, for every k there exists j ≥ k such that for all i ≥ j: one says that the system satisfies the Mittag-Leffler condition.

If G and H are Lie groups, then a Lie-group homomorphism f: G → H is a smooth group homomorphism.

If G is any subgroup of GL < sub > n </ sub >( R ), then the exponential map takes the Lie algebra of G into G, so we have an exponential map for all matrix groups.

If the manifold is a circle these are called loop groups, and have central extensions whose Lie algebras are ( more or less ) Kac – Moody algebras.

If the molecule can be rotated in space so that the directions of those four groups match those of the analog groups in-glyceraldehyde's C2, then the isomer receives the '-' prefix.

If true, her worship may have resembled that of Perchta groups in Germanic areas.

If so, these ostraka provide an example of organized groups attempting to influence the outcome of ostracisms.

If the respondents needed to reflect the diversity of the population, the researcher would specifically seek to include participants of various minority groups such as race or religion, based on their proportionality to the total population as mentioned above.

If not stated otherwise, this article considers symmetry groups in Euclidean geometry, but the concept may also be studied in wider contexts ; see below.

⟨ H ⟩, be the group generated by H. Then the word problem in H < sup >*</ sup > is solvable: given two words h, k in the generators H of H < sup >*</ sup >, write them as words in X and compare them using the solution to the word problem in G. It is easy to think that this demonstrates a uniform solution the word problem for the class K ( say ) of finitely generated groups that can be embedded in G. If this were the case the non-existence of a universal solvable word problem group would follow easily from Boone-Rogers.

If so one would expect it to be difficult to prove as the mapping from presentations to simple groups would have to be non-recursive.

If the resolution of the data is better than 1. 4 Å ( 140 pm ), direct methods can be used to obtain phase information, by exploiting known phase relationships between certain groups of reflections.

* If X is a topological space, then the category of all sheaves of abelian groups on X is an abelian category.

If the group is finite, then eventually one arrives at uniquely determined simple groups by the Jordan – Hölder theorem.

If ƒ: A → B is a homomorphism between two algebraic structures ( such as homomorphism of groups, or a linear map between vector spaces ), then the relation ≡ defined by

If the cipher operates on single letters, it is termed a simple substitution cipher ; a cipher that operates on larger groups of letters is termed polygraphic.

If a di-isocyanate is treated with a compound containing two or more hydroxyl groups, such as a diol or a polyol, polymer chains are formed, which are known as polyurethanes.

* If we fix a homomorphism of abelian groups, we can consider the category consisting of all pairs where is an abelian group and is a group homomorphism with.