If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

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 Af is the null space of Af, then Theorem 12 says that Af.

If a node has fewer than two children, some of the child pointers may be set to a special null value, or to a special sentinel node.

If he has presumed to do this in the past or shall presume to do so in the future, his action shall be null and he shall be subject to the canonical penalties.

If F is continuous then under the null hypothesis converges to the Kolmogorov distribution, which does not depend on F. This result may also be known as the Kolmogorov theorem ; see Kolmogorov's theorem for disambiguation.

If the list is a simply linked list, then the item's location is its reference, and Λ is usually the null pointer.

# If A is a Lebesgue measurable set with λ ( A ) = 0 ( a null set ), then every subset of A is also a null set.

If the aether was dragged by mass then this experiment would have been able to detect the drag caused by the lead, but again the null result was found.

If μ is a positive measure, then N is null ( or zero measure ) if its measure μ ( N ) is zero.

If μ is not a positive measure, then N is μ-null if N is | μ |- null, where | μ | is the total variation of μ ; equivalently, if every measurable subset A of N satisfies μ ( A )

If values are stored by reference, e. g. objects, null references can be used and so the cluster can be represented by a vector containing 3 slots for value pointers plus 4 slots for child references in the tree.

If gg is null, then x obviously is now the root and must be updated as such.

If the null hypothesis that is rejected, then the alternative hypothesis that and equivalently that causes y cannot be rejected.

If an object is both initial and terminal, it is called a zero object or null object.

If V and W are vector spaces, the null space ( or kernel ) of a linear transformation T: V → W is the set of all vectors in V that map to zero:

If the linear map is represented by a matrix, then the kernel of the map is precisely the null space of the matrix.

If the string inserted is too short, then it is padded out, usually with spaces or null characters.

If the BOM character appears in the middle of a data stream, Unicode says it should be interpreted as a " zero-width non-breaking space " ( essentially a null character ).

If a test of significance gives a p-value lower than the significance level α, the null hypothesis is rejected.

If is continuously differentiable then the hypersurface is a differentiable manifold in the neighbourhood of the points where the gradient is not null.

If one corrects and adjusts for the confounding by smoking, via stratification or multivariable regression modelling to statistical control for smoking, then one finds that the association between birth weight and mortality may be attenuated towards the null.

If every ion is a " spectator ion ", then there was no reaction, and the net ionic equation is null.

If we consider the thesis and its converse as definition, then the hypothesis is an hypothesis about the application of the mathematical theory developed from the definition.

If empirical data reach significance under the appropriate statistical formula, the research hypothesis is supported.

The evidence was compiled by W de Sitter ( 1927 ) who wrote " If we accept this hypothesis, then the ' astronomical time ', given by the earth's rotation, and used in all practical astronomical computations, differs from the ' uniform ' or ' Newtonian ' time, which is defined as the independent variable of the equations of celestial mechanics ".

If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would ( by definition ) be outside the observable universe, it is difficult to imagine ( much less construct ) experiments to test this hypothesis.

If there were such a number then the theory would be inconsistent, contrary to the consistency hypothesis.

If Prout's hypothesis had proven accurate, then the abstract concept of mass, as we now know it, might never have evolved, since mass could always be defined in terms of amounts of the hydrogen atomic mass.

If this hypothesis is correct, it also is likely that male Pteranodon played little to no part in rearing the young ; such a behavior is not found in the males of modern polygynous animals who father many offspring at the same time.

Many of his stories, such as Gulf, If This Goes On —, and Stranger in a Strange Land, depend strongly on the premise, related to the well-known Sapir – Whorf hypothesis, that by using a correctly designed language, one can change or improve oneself mentally, or even realize untapped potential ( as in the case of Joe Green in Gulf ).

If such an Interstellar Internet exists, the hypothesis states, communications between servers are mostly through narrow-band, highly directional radio or laser links.

The theorem " If n is an even natural number then n / 2 is a natural number " is a typical example in which the hypothesis is that " n is an even natural number " and the conclusion is that " n / 2 is also a natural number ".

If the first person accepts the hypothesis that " All ravens are black " then, according to the argument, about 50 objects whose colors were previously in doubt ( the ravens ) are now thought to be black, while nothing different is thought about the remaining objects ( the non-ravens ).

If the evidence doesn't match up with a hypothesis, one should reject the hypothesis.

If this hypothesis were true however, age at menopause should be negatively correlated with reproductive effort and the available data does not support this.

If the giant impact hypothesis is correct, they must be due to some other cause.

* If the continuum hypothesis holds then is the unique Parovicenko space, up to isomorphism.

If the Noetherianity hypothesis is dropped, then R can have dimension anywhere between d + 1 and 2d + 1.

If there were such a number then the theory would be inconsistent, contrary to the consistency hypothesis.

If an experiment is carefully conducted, the results usually either support or disprove the hypothesis.

The book commences on a hypothesis of novelistic elements (" If ...") on a when, a someone ... would do what?