If the rake angle **yc of the knife is high enough and the friction angle **yt between the front of the knife and the back of the chip is low enough to give a positive value for Af, the resultant vector R will lie above the plane of the substrate.

If there is refraction at a collective spherical surface, or through a thin positive lens, O ' 2 will lie in front of O ' 1 so long as the angle u2 is greater than u1 ( under correction ); and conversely with a dispersive surface or lenses ( over correction ).

If the eigenvalues are all positive, then the frequencies are all real and the stationary point is a local minimum.

If a " positive list " approach were taken, only species evaluated and approved for the positive list would be permitted in trade, thus lightening the review burden for member states and the Secretariat, and also preventing inadvertent legal trade threats to poorly known species.

To make a figure larger or smaller is equivalent to multiplying the Cartesian coordinates of every point by the same positive number m. If ( x, y ) are the coordinates of a point on the original figure, the corresponding point on the scaled figure has coordinates

If h is positive, then a + h is on the high part of the step, so the secant line from a to a + h has slope zero.

If the electrode has a positive potential with respect to the SHE, then that means it is a strongly reducing electrode which forces the SHE to be the anode ( an example is Cu in aqueous CuSO < sub > 4 </ sub > with a standard electrode potential of 0. 337 V ).

If ΔH is positive, the reaction is endothermic, that is heat is absorbed by the system due to the products of the reaction having a greater enthalpy than the reactants.

Axiom 1: If a property is positive, then its negation is not positive.

Axiom 4: If a property is positive, then it is necessarily positive

Theorem 1: If a property is positive, then it is consistent, i. e., possibly exemplified.

: If a property A entails a property B ( ie in every possible world if an object has property A it must also have property B ), and if A is positive, B must also be positive.

: Axiom 4: If a property A is positive, then it is so in every possible world.

If p is a non-zero real number, we can define the generalized mean with exponent p ( or power mean with exponent p ) of the positive real numbers as:

If X is a positive random variable and q > 0 then for all ε > 0

If the pH of the buffer is above the pI of the protein being run, the protein will migrate to the positive pole ( negative charge is attracted to a positive pole ).

If the pH of the buffer is below the pI of the protein being run, the protein will migrate to the negative pole of the gel ( positive charge is attracted to the negative pole ).

If it is 0, then the number is positive.

If a large, b-bit number is the product of two primes that are roughly the same size, then no algorithm has been published that can factor in polynomial time, i. e., that can factor it in time O ( b < sup > k </ sup >) for some constant k. There are published algorithms that are faster than O (( 1 + ε )< sup > b </ sup >) for all positive ε, i. e., sub-exponential.

If μ is positive, the origin will be shifted to the right, and if μ is negative, it will be shifted to the left.

If it comes down too hard on the potential dangers of fallout, it will box the President on resuming atmospheric tests.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

If such is the case, the particles within a distance of about Af of the Earth will have, relative to the Earth, a kinetic energy less than their potential energy and they will be captured into orbits about the Earth.

If this precaution was not taken, the potential customers would be at the mercy of " 2 sets of carob seeds ".

If there is a change in the potential energy of a system ; for example μ < sub > 1 </ sub >> μ < sub > 2 </ sub > ( μ is Chemical potential ) an energy flow will occur from S < sub > 1 </ sub > to S < sub > 2 </ sub >, because nature always prefers low energy and maximum entropy.

To avoid debates about the possibility of in-vitro fertilization, artificial insemination, or cloning, the original Darwin Awards book applied the following " deserted island " test to potential winners: If the person were unable to reproduce when stranded on a deserted island with a fertile member of the opposite sex, he or she would be considered sterile.

If the second electrode is also at standard conditions, then the measured cell potential is called the standard electrode potential for the electrode.

If the current is driven in the opposite direction by imposing an external potential, then work is done on the cell to drive electrolysis.

If the observer is at a lower gravitational potential than the source, a gravitational blueshift can be observed instead.

If drain-to-source voltage is increased, this creates a significant asymmetrical change in the shape of the channel due to a gradient of voltage potential from source to drain.

If we live on a brane ( as hypothesized by some theorists ) this " leakage " of gravitons from the brane into higher-dimensional space could explain why gravitation is such a weak force, and gravitons from other branes adjacent to our own could provide a potential explanation for dark matter.

If the political situation stabilizes, high crime levels wane, and new investment increases, tourism could take its place next to export-oriented manufacturing ( the assembly sector ) as a potential source of foreign exchange.

If a philosophy of Becoming is not possible without change, then ( the potential of ) what is to become must already exist in the present object.

If, however ,... potential suicide murderers ... will refrain from killing out of fear that their mothers will become homeless, it would be immoral to leave the Palestinian mothers untouched in their homes while Israeli children die on their school buses.

If the voltage changes by a large enough amount, an all-or-none electrochemical pulse called an action potential is generated, which travels rapidly along the cell's axon, and activates synaptic connections with other cells when it arrives.

If the net excitation received by a neuron over a short period of time is large enough, the neuron generates a brief pulse called an action potential, which originates at the soma and propagates rapidly along the axon, activating synapses onto other neurons as it goes.

If the change in electrical potential is large enough, it evokes an action potential, which is transmitted along the axon of the receptor cell, into the spinal cord.

If the top has mass and its center of mass is at a distance from the pivot point, its gravitational potential is

If the work done moving along a path which starts and ends in the same location is zero, then the force is said to be conservative and it is possible to define a numerical value of potential associated with every point in space.

If the potential is redefined at A to be and the potential at B to be, where is a constant ( i. e. can be any number, positive or negative, but it must be the same at A as it is at B ) then the work done going from A to B is

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 Af denotes the space of N times continuously differentiable functions, then the space V of solutions of this differential equation is a subspace 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 we are discussing differentiable complex-valued functions, then Af and V are complex vector spaces, and Af may be any complex numbers.

If and we have for all v, w in V, then we say that B is symmetric.

If a system is composed of two subsystems described in V and W respectively, then the Hilbert space of the entire system is the tensor product of the two spaces.

If is a ket in V and is a ket in W, the direct product of the two kets is a ket in.

If an epidemic of cholera is suspected, the most common causative agent is V. cholerae O1.

If V. cholerae serogroup O1 is not isolated, the laboratory should test for V. cholerae O139.

If V is finite-dimensional, then V * has the same dimension as V. Given a basis

* If G is a topological group and V is a topological vector space, a continuous representation of G on V is a representation ρ such that the application defined by is continuous.

* If V is a normed vector space with linear subspace U ( not necessarily closed ) and if is continuous and linear, then there exists an extension of φ which is also continuous and linear and which has the same norm as φ ( see Banach space for a discussion of the norm of a linear map ).

* If V is a normed vector space with linear subspace U ( not necessarily closed ) and if z is an element of V not in the closure of U, then there exists a continuous linear map with ψ ( x ) = 0 for all x in U, ψ ( z ) = 1, and || ψ || = 1 / dist ( z, U ).

# If V is a set of strings then V * is defined as the smallest superset of V that contains λ ( the empty string ) and is closed under the string concatenation operation.

# If V is a set of symbols or characters then V * is the set of all strings over symbols in V, including the empty string.