`` 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 subprogram in Euclid's algorithm to compute the remainder would execute much faster if the programmer had a " modulus " ( division ) instruction available rather than just subtraction ( or worse: just Minsky's " decrement ").

For any real number the absolute value or modulus of is denoted by ( a vertical bar on each side of the quantity ) and is defined as

For example, some references, and Wolfram's Mathematica software, define the complete elliptic integral of the first kind in terms of the parameter m, instead of the elliptic modulus k.

For example the real part, imaginary part and modulus of a point or ratio z ( taking one of the two viewpoints above ) are constructible as these may be expressed as

For ideal gases the bulk modulus P is simply the gas pressure multiplied by the adiabatic index.

For a gas, K ( the bulk modulus in equations above, equivalent to C, the coefficient of stiffness in solids ) is approximately given by

For instance the classical Bernoulli's method to find the root greater in modulus, if it exists, turns out to be the power method applied to the companion matrix.

For homogeneous turbulence ( i. e., statistically invariant under translations of the reference frame ) this is usually done by means of the energy spectrum function, where k is the modulus of the wavevector corresponding to some harmonics in a Fourier representation of the flow velocity field u ( x ):

For example, from the table for modulus 6

For example, from the table for modulus 15

For this reason some authors add to the definition that a quadratic residue q must not only be a square but must also be relatively prime to the modulus n.

For many materials, Young's modulus is essentially constant over a range of strains.

For example, carbon fiber has much higher Young's modulus ( is much stiffer ) when force is loaded parallel to the fibers ( along the grain ).

For homogeneous isotropic materials simple relations exist between elastic constants ( Young's modulus E, shear modulus G, bulk modulus K, and Poisson's ratio ν ) that allow calculating them all as long as two are known:

For example according to Errett Bishop's definitions, the continuity of a function ( such as sin x ) should be proved as a constructive bound on the modulus of continuity, meaning that the existential content of the assertion of continuity is a promise that can always be kept.

For multi-loop integrals that will depend on several variables we can make a change of variables to polar coordinates and then replace the integral over the angles by a sum so we have only a divergent integral, that will depend on the modulus and then we can apply the zeta regularization algorithm, the main idea for multi-loop integrals is to replace the factor after a change to hyperspherical coordinates so the UV overlapping divergences are encoded in variable r. In order to regularize these integrals one needs a regulator, for the case of multi-loop integrals, these regulator can be taken as so the multi-loop integral will converge for big enough's ' using the Zeta regularization we can analytic continue the variable's ' to the physical limit where s = 0 and then regularize any UV integral.

For the special case of unconstrained uniaxial tension or compression, Young's modulus can be thought of as a measure of the stiffness of a material.

For the case of real valued unitary matrixes we obtain orthogonal matrices, In this case all eigenvalues are real, and so the unit modulus eigenvalue constraint is replaced by the binary constraint that all eigenvalues lie in the set

For example, below the yield stress ( in the activated or " on " state ), the fluid behaves as a viscoelastic material, with a complex modulus that is also known to be dependent on the magnetic field intensity.

For instance, the modulus of − 3 + 4 < var > i </ var > is 5.

For example, when the modulus is 12, then any two numbers that leave the same remainder when divided by 12 are equivalent ( or " congruent ") to each other.

For instance the stress required for homogeneous nucleation in copper has been shown to be, where G is the shear modulus of copper ( 46 GPa ).