`` For instance, regarding the fact that the Gross Committee issued two interim announcements to the press during its investigation.

For instance, college-educated people consistently show up in study after study as more often than others supporters of the Bill of Rights and other democratic rights and liberties.

For instance, so-called `` conservative '' organizations, some of them secret, are sprouting in the garden of joining where `` liberal '' organizations once took root.

For instance -- what about all those people Harold Rhodes went toward unhesitatingly, as if this were the one moment they would ever have together, their one chance of knowing each other??

For instance, a site adjoining other publicly owned lands, such as a national forest or a public road, may be desirable, whereas a site next to an industrial plant might not.

( For instance, see Example 2 of Section 5-5, on red cards in hands of 5.

For instance, the following statement was rated low in compulsivity, `` She's naturally quite neat about things, but it doesn't bother her at all if her room gets messy.

For instance, in giving school grades or in making recommendations for the award of a college scholarship, does he consciously or unconsciously favor students of one or another social class??

For instance, there have been two Presidential Commissions on higher education since World War 2.

For instance, the dreamer sees himself seated behind neighbor Smith and, with photographic realism, sees Smith driving the car ; ;

For instance:

`` For instance, Djakarta, Indonesia, has three groups of dancers interested in coming here.

For instance, the Edwin Pauleys Jr., formerly of Chantilly Rd., are now at home on North Arden Dr. in Beverly Hills.

For instance, we cannot know whether even for church members the degree of conformity to Christian standards of morality increased or declined as the proportion of church members in the population rose.

`` For instance, Hesperus agreed to help me find my property, and I agreed to take him to Earth.

For instance, a C-Leg knee alone is not a prosthesis, but only a prosthetic part.

For instance, the word " bank " has several distinct lexical definitions, including " financial institution " and " edge of a river ".

For instance, a local society in the middle of a large city may have regular meetings with speakers, focusing less on observing the night sky if the membership is less able to observe due to factors such as light pollution.

For instance, according to Classical Arabic and Modern Standard Arabic, the Arabic root ( to sacrifice ) can be derived the forms ( he sacrificed ), ( you ( masculine singular ) sacrificed ), ( he slaughtered ), ( he slaughters ), and ( slaughterhouse ).

For instance, we read of Whiting, the last abbot of Glastonbury, judicially murdered by Henry VIII, that his house was a kind of well-ordered court, where as many as 300 sons of noblemen and gentlemen, who had been sent to him for virtuous education, had been brought up, besides others of a lesser rank, whom he fitted for the universities.

For instance, the n

For instance, in 51, Agrippina ordered the execution of Britannicus ’ tutor Sosibius because he had confronted her and was outraged by Claudius ’ adoption of Nero and his choice of Nero as successor, instead of choosing his own son Britannicus.

For instance, antibacterial resistance genes can be exchanged between different bacterial strains or species via plasmids that carry these resistance genes.

For instance, iron changes from a body-centered cubic structure ( ferrite ) to a face-centered cubic structure ( austenite ) above 906 ° C, and tin undergoes a transformation known as tin pest from a metallic phase to a semiconductor phase below 13. 2 ° C.

For instance member nations of the Commonwealth where English is not spoken natively, such as India, often closely follow British English forms, while many American English usages are followed in other countries which have been historically influenced by the United States, such as the Philippines.

For example: the similarity of southern continent geological formations had led Roberto Mantovani to conjecture in 1889 and 1909 that all the continents had once been joined into a supercontinent ( now known as Pangaea ); Wegener noted the similarity of Mantovani's and his own maps of the former positions of the southern continents.

For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1. 2 × 10 < sup > 12 </ sup > ( over a trillion ).

For example, the Riemann hypothesis is a conjecture from number theory that ( amongst other things ) makes predictions about the distribution of prime numbers.

For dimensions greater than three, one can pose the Generalized Poincaré conjecture: is a homotopy n-sphere homeomorphic to the n-sphere?

For example, the Collatz conjecture has been verified for start values up to about 2. 88 × 10 < sup > 18 </ sup >.

For example, the Mertens conjecture is a statement about natural numbers that is now known to be false, but no explicit counterexample ( i. e., a natural number n for which the Mertens function M ( n ) equals or exceeds the square root of n ) is known: all numbers less than 10 < sup > 14 </ sup > have the Mertens property, and the smallest number which does not have this property is only known to be less than the exponential of 1. 59 × 10 < sup > 40 </ sup >, which is approximately 10 to the power 4. 3 × 10 < sup > 39 </ sup >.

For small values of n, the strong Goldbach conjecture ( and hence the weak Goldbach conjecture ) can be verified directly.

For instance, Nils Pipping in 1938 laboriously verified the conjecture up to n ≤ 10 < sup > 5 </ sup >.

For non-oriented manifolds the easiest way to state a geometrization conjecture is to first take the oriented double cover.

For the proof of the conjectures, see the references in the articles on geometrization conjecture or Poincaré conjecture.

For most abelian varieties, the algebra Hdg *( X ) is generated in degree one, so the Hodge conjecture holds.

He measures the quality of fit to Cramér's conjecture by measuring the ratio R of the logarithm of a prime to the square root of the gap ; he writes, “ For the largest known maximal gaps, R has remained near 1. 13 .” is still less than 1, and it does not provide support to Granville's refinement that c should be greater than 1.

For a compact manifold with positive bisectional curvature, the Frankel conjecture proved by Siu and Yau, and independently by Mori, shows that it is complex projective space.

For example, the Künneth standard conjecture, which states the existence of algebraic cycles π < sup > i </ sup > ⊂ X × X inducing the canonical projectors H < sup >∗</ sup >( X ) ↠ H < sup > i </ sup >( X ) ↣ H < sup >∗</ sup >( X ) ( for any Weil cohomology H ) implies that every pure motive M decomposes in graded pieces of weight n: M = ⊕ Gr < sub > n </ sub > M.

:: Kakeya maximal function conjecture: For all, there exists a constant such that for any function f and all,

For finitely generated linear groups, however, the von Neumann conjecture is true by the Tits alternative: every subgroup of GL ( n, k ) with k a field either has a normal solvable subgroup of finite index ( and therefore is amenable ) or contains the free group on two generators.

For n = 3, the h-cobordism theorem for smooth manifolds has not been proved and, due to the Poincaré conjecture, is equivalent to the hard open question of whether the 4-sphere has non-standard smooth structures.

For n = 2, the h-cobordism theorem is true – it is equivalent to the Poincaré conjecture, which has been proved by Grigori Perelman.

As Grünbaum writes, simplicial arrangements “ appear as examples or counterexamples in many contexts of combinatorial geometry and its applications .” For instance, use simplicial arrangements to construct counterexamples to a conjecture on the relation between the degree of a set of differential equations and the number of invariant lines the equations may have.

For example the difference between a counterexample to a lemma ( a so-called ' local counterexample ') and a counterexample to the specific conjecture under attack ( a ' global counterexample ' to the Euler characteristic, in this case ) are discussed.

For odd n, only two examples are known that match Dirac's lower bound conjecture, that is, with One example, by, consists of the vertices, edge midpoints, and centroid of an equilateral triangle ; these seven points determine only three ordinary lines.

For elliptic curves over the rational numbers, the Hasse – Weil conjecture follows from the modularity theorem.