For example, exponents are usually formatted using superscripts, e. g..

For anarchist historian Paul Avrich " The two leading exponents of individualist anarchism, both based in Moscow, were Aleksei Alekseevich Borovoi and Lev Chernyi ( Pavel Dmitrievich Turchaninov ).

For instance, the behavior of water and CO < sub > 2 </ sub > at their boiling points fall in the same universality class because they have identical critical exponents.

For a dynamical system with evolution equation in an n – dimensional phase space, the spectrum of Lyapunov exponents

For the calculation of Lyapunov exponents from limited experimental data, various methods have been proposed.

The theorem also guarantees that there are problems in P requiring arbitrary large exponents to solve ; in other words, P does not collapse to DTIME ( n < sup > k </ sup >) for any fixed k. For example, there are problems solvable in n < sup > 5000 </ sup > time but not n < sup > 4999 </ sup > time.

For example, an exponential number will provide, as well as the base and exponents, the final value.

For example, if the symbols represent numbers, the expressions are evaluated according to a conventional order of operations which provides for calculation, if possible, of any expressions within parentheses, followed by any exponents and roots, then multiplications and divisions and finally any additions or subtractions, all done from left to right.

For exponents up to 300, 3a continues to be a good estimate of the number of digits.

For example, the category number has the exponents and in English and many other languages.

For more than ten years now, K-Tino ( on earlier albums Catino ) has been one of the main exponents of bikutsi.

For the albumin method, equal volumes of 30% bovine albumin, sample and 2% cells suspended in saline were allowed to stand at room temperature for 1 hr and then were centrifuged at 1000 rpm for 1 Aj.

For example, the level of improvement noted in a recent experiment with a short course of immediate treatment for parent-child relationship problems compared favorably with the results reported by typical child guidance clinics where the hours spent in purely diagnostic study may equal or exceed the number of hours devoted to actual treatment interviews in the experimental project.

For the illusion of depth created by the contrast between the affixed material and everything else gives way immediately to an illusion of forms in bas-relief, which gives way in turn, and with equal immediacy, to an illusion that seems to contain both -- or neither.

* For a normal distribution, the arithmetic mean is equal to both the median and the mode, other measures of central tendency.

For Euclid ’ s method to succeed, the starting lengths must satisfy two requirements: ( i ) the lengths must not be 0, AND ( ii ) the subtraction must be “ proper ”, a test must guarantee that the smaller of the two numbers is subtracted from the larger ( alternately, the two can be equal so their subtraction yields 0 ).

For example, the prime number theorem states that the number of prime numbers less than or equal to N is asymptotically equal to N / ln N. Therefore the proportion of prime integers is roughly 1 / ln N, which tends to 0.

For who is your equal in greatness, O dwelling place of God the Word?

For example, the equation y = x corresponds to the set of all the points on the plane whose x-coordinate and y-coordinate are equal.

For the simple case where the direction of the light beam along the line SE is perpendicular to the motion of the observer then only light emitted at an angle equal to the arc cosine of the ratio of the observer's speed to the speed of light will reach the telescope.

For instance, a change in the declination of γ Draconis would be mirrored by an equal and opposite change to the declination of a star 180 degrees opposite in right ascension.

For a steady state process, the rate at which mass enters the volume is equal to the rate at which it leaves the volume.

* The Ham sandwich theorem: For any compact sets A < sub > 1 </ sub >,..., A < sub > n </ sub > in ℝ < sup > n </ sup > we can always find a hyperplane dividing each of them into two subsets of equal measure.

For some schools of Hinduism and Buddhism the received textual tradition is an epistemological category equal to perception and inference ( although this is not necessarily true for some other schools ).

For example, the set with elements 2, 3, and 5 is equal to the set of all prime numbers less than 6.

For any reaction mixture to exist at equilibrium, the rates of the forward and backward ( reverse ) reactions are equal.

For example, the security available with a 1024-bit key using asymmetric RSA is considered approximately equal in security to an 80-bit key in a symmetric algorithm ( Source: RSA Security ).

For some squads the level of competition on the weekends can equal that of an all-star squad.

For example, a 133 MHz 6x86 will outperform a P5 Pentium at 166 MHz, and as a result Cyrix could market the 133 MHz chip as being a P5 Pentium 166's equal.

For example, the CGS derived unit of force is the dyne, equal to, while the SI derived unit of force is the newton,.

For example, in a representative democracy, every vote has equal weight, no unreasonable restrictions can apply to anyone seeking to become a representative, and the freedom of its citizens is secured by legitimized rights and liberties which are generally protected by a constitution.

For the simple electric dipole given above, the electric dipole moment points from the negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges.

For the current loop, the magnetic dipole moment points through the loop ( according to the right hand grip rule ), with a magnitude equal to the current in the loop times the area of the loop.

For Bachelard, rationalism makes equal reference to all three systems of thinking.

For example, proposition I. 4, side-angle-side congruence of triangles, is proved by moving one of the two triangles so that one of its sides coincides with the other triangle's equal side, and then proving that the other sides coincide as well.

For this change is not a change from one positive position to another, but a change from order and truth to disorder and negation.

For example, one study on volunteerism found that feeling overwhelmed by others ' demands had an even stronger negative effect on mental health than helping had a positive one ( although positive effects were still significant ).

Also, supporters of this view would characterize Luke ’ s portrayal of the Roman Empire as positive because they believe Luke “ glosses over negative aspects of the empire and presents imperial power positively .” For example, when Paul is before the council defending himself, Paul says that he is “ on trial concerning the hope of the resurrection of the dead ” ( Acts 23: 6 ).

For many applications where one is only concerned about rotation around one axis, it is sufficient to discard the pseudovector nature of angular momentum, and treat it like a scalar where it is positive when it corresponds to a counter-clockwise rotation, and negative clockwise.

* For a finite field of prime order p, the algebraic closure is a countably infinite field which contains a copy of the field of order p < sup > n </ sup > for each positive integer n ( and is in fact the union of these copies ).

For positive values of a and b, the binomial theorem with n = 2 is the geometrically evident fact that a square of side can be cut into a square of side a, a square of side b, and two rectangles with sides a and b. With n = 3, the theorem states that a cube of side can be cut into a cube of side a, a cube of side b, three a × a × b rectangular boxes, and three a × b × b rectangular boxes.

For example, is a positive literal and is a negative literal.

For example, if an electric field is placed across a solution of Na < sup >+</ sup > and Cl < sup >−</ sup > ( and conditions are right ) the sodium ions move towards the negative electrode ( cathode ), while the chloride ions move towards the positive electrode ( anode ).

For example, the Daniell galvanic cell's copper electrode is the positive terminal and the cathode.

For example, reversing the current direction in a Daniell galvanic cell would produce an electrolytic cell, where the copper electrode is the positive terminal and the anode.

For a given material, it can have a positive or negative sign or exceptionally it can be zero, and this can depend on the temperature, as it does for water about 4 C. The concept of latent heat with respect to volume was perhaps first recognized by Joseph Black in 1762.

For larger values of n, Fermat's Last Theorem states there are no positive integer solutions ( x, y, z ).</ td >

For example, air pollution may generate a negative externality, and education may generate a positive externality ( less crime, etc .).

For any positive integer n, the set of all n-tuples of real numbers forms an n-dimensional vector space over R, which is denoted R < sup > n </ sup > and sometimes called real coordinate space.

For a reason that was not recorded, he identified the term " positive " with vitreous electricity and " negative " with resinous electricity.

For example, one of the most recent results is that, even after subtracting the positive influence of decadal variation, shown to be possibly present in the ENSO trend, the amplitude of the ENSO variability in the observed data still increases, by as much as 60 % in the last 50 years.

For closed ( orientable or non-orientable ) surfaces with positive genus, the maximum number p of colors needed depends on the surface's Euler characteristic χ according to the formula

For s-polarization, a positive r or t means that the electric fields of the incoming and reflected or transmitted wave are parallel, while negative means anti-parallel.

For p-polarization, a positive r or t means that the magnetic fields of the waves are parallel, while negative means anti-parallel.

* For every prime number p and positive integer n, there exists a finite field with p < sup > n </ sup > elements.

For example, the set of all positive integers is infinite:

For any positive integers and, there exists a graph with girth at least and chromatic number at least ; for instance, the Grötzsch graph is triangle-free and has chromatic number 4, and repeating the Mycielskian construction used to form the Grötzsch graph produces triangle-free graphs of arbitrarily large chromatic number.

For complex numbers with a positive real part, it is defined via an improper integral that converges: