Since TPF can run as a second level guest under IBM's z / VM, a user can employ the VM trace facility to closely follow the execution of code.

However, C language programming is much easier to obtain skilled people in, so most if not all new development is done in C. Since z / TPF allows assembler programs to be repackaged into 1 logical file, critical legacy applications can be maintained and actually improve efficiency-the cost of entering one of these programs will now come at the initial enter when the entire program is fetched into core and logical flow through the program is accomplished via simple branch instructions, instead of a dozen or so IBM instructions previously needed to perform what is known as ' core resident enter / back '.

Since z / VSE 3. 1, Fibre Channel access to storage devices is supported, although only on IBM's Enterprise Storage Server ( ESS ) and its successors.

Since it is nonnegative it has at most one real root in z, whence its discriminant is less than or equal to zero, that is,

Since this force varies with the position of the charge and by Coloumb's Law it is defined at all points in space, is a continuous function of the charge's position ( x, y, z ).

Since this * z changed to * r in the Scandinavian languages and in West Germanic ( German, Dutch, English, Frisian ), Verner's Law resulted in alternation of * s and * r in some inflectional paradigms, known as grammatischer Wechsel.

Since an nth degree polynomial equation can only have n distinct roots, this implies that the powers of a primitive root z, z < sup > 2 </ sup >, ... z < sup > n − 1 </ sup >, z < sup > n </ sup >

Since all z / OS installations usually have both TSO and TSO / E functions installed, it is normal to refer to both TSO and TSO / E as " TSO ".

Since all its poles lie on the negative real axis, from z

Since, for a free-electron model, the contribution to the current density is directly proportional to the area in energy space ( with the Sommerfeld supply density z < sub > S </ sub > as the constant of proportionality ), it is useful to think of the ECD as drawn from electron states in an area of size d < sub > F </ sub >< sup > 2 </ sup > ( measured in eV < sup > 2 </ sup >) in the energy-space diagram.

Since root locus is a graphical angle technique, root locus rules work the same in the z and s planes.

Since the factor ( z − a )< sup > n </ sup > does not depend on the variable of integration w, it can be pulled out:

Since z < sup > 1 / 2 </ sup > = e < sup > 1 / 2 Log ( z )</ sup >, on the contour outside the branch cut, we have gained 2π in argument along γ ( by Euler's Identity, represents the unit vector, which therefore has as its log.

Since the motion is planar, and p and L are perpendicular, p < sub > z </ sub >

Since rays in space can be parameterized by three coordinates, x, y, and z and two angles and, as shown at left, it is a five-dimensional function.

Since λ has modulus 1, multiplying any split-complex number z by λ preserves the modulus of z and represents a hyperbolic rotation ( also called a Lorentz boost or a squeeze mapping ).

Since g ( z < sub > N </ sub >) ≠ 0, it follows that g ' ( z )/ g ( z ) has no singularities at z < sub > N </ sub >, and thus is analytic at z < sub > N </ sub >, which implies that the residue of f ′( z )/ f ( z ) at z < sub > N </ sub > is k.

Since n grows faster than log < sub > 2 </ sub >( n ), there must exist a value n < sub > 0 </ sub > such that

This subextension is called a separable closure of K. Since a separable extension of a separable extension is again separable, there are no finite separable extensions of K < sup > sep </ sup >, of degree > 1.

Since the 1990s, SO < sub > 2 </ sub > emissions have dropped 40 %, and according to the Pacific Research Institute, acid rain levels have dropped 65 % since 1976.

Since B < sub > n </ sub >= 0 for all odd n > 1, and many formulas only involve even-index Bernoulli numbers, some authors write B < sub > n </ sub > instead of B < sub > 2n </ sub >.

Since the mass numbers of these are 12, 13 and 14 respectively, the three isotopes of carbon are known as carbon-12, carbon-13, and carbon-14, often abbreviated to < sup > 12 </ sup > C, < sup > 13 </ sup > C, and < sup > 14 </ sup > C.

Since the map d restricts to 0 on I < sub > x </ sub >< sup > 2 </ sup > ( the reader should verify this ), d descends to a map from I < sub > x </ sub > / I < sub > x </ sub >< sup > 2 </ sup > to the dual of the tangent space, ( T < sub > x </ sub > M )< sup >*</ sup >.

Since at this stress the slope of the material's stress-strain curve, E < sub > t </ sub > ( called the tangent modulus ), is smaller than that below the proportional limit, the critical load at inelastic buckling is reduced.

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since < tt > ns1 </ tt > is contained in < tt > example. org </ tt >, this requires resolving < tt > example. org </ tt > first, which presents a circular dependency.

Since every equivalence relation over X corresponds to a partition of X, and vice versa, the number of possible equivalence relations on X equals the number of distinct partitions of X, which is the nth Bell number B < sub > n </ sub >:

Since all probabilities p < sub > i </ sub > add up to one: p < sub > 1 </ sub > + p < sub > 2 </ sub > + ... + p < sub > k </ sub > = 1, the expected value can be viewed as the weighted average, with p < sub > i </ sub >’ s being the weights:

Since 1983 ,< ref >

During a 1935 – 1942 colonization attempt, the island was most likely on Hawaii time, which was then 10. 5 hours behind UTC .< ref > Since it is uninhabited the island's time zone is unspecified, but it lies within a nautical time zone 12 hours behind UTC.

Since the 2002 civil war in Côte d ' Ivoire, relations between it and Burkina Faso have been filled with accusations of Burkinabé support for rebels on one side and claims of mistreatment of Burkinabé workers on the other .< ref > Blaise Campaoré :<< La crise ivoirienne inquiète le Burkina >>, Le Figaro, December 11, 2005 </ ref > Côte d ' Ivoire remains Burkina Faso's largest regional trading partner in spite of their disputes and tens of thousands of Burkinabés continue to work in the Ivory Coast.

Since the difference between the U. S. and International acre is only about a quarter of the size of an A4 sheet of paper ( 0. 016 square metres, 160 square centimetres or 24. 8 square inches ), it is usually not important which one is being discussed.

A set S is called countable if there exists an injective function f from S to the natural numbers Since there is an obvious bijection between and it makes no difference whether one considers 0 to be a natural number of not.

Since the separation of variables in this case involves dividing by y, we must check if the constant function y = 0 is a solution of the original equation.

Since 1993, the Eritrean People ’ s Liberation Front army has been involved in tree planting ; the annual average rate of deforestation during 1990 – 2000 was 0. 3 percent.

Since the release of EDIF 4 0 0, the entire EDIF standards organisation has essentially dissolved.

The event temporarily warmed air temperature by 1. 5 ° C, compared to the usual increase of 0. 25 ° C associated with El Niño events .< ref name =" Trenberth "> Since then, mass coral bleaching has become common worldwide, with all regions having suffered " severe bleaching ".

Since the Tigers " ran up a 61 to 0 score on the hapless Mountain Staters, the pass played no important part in the result.

Since Version 0. 7 ( 2008 ), it offers two modes of operation: a darknet mode in which it connects only to friends, and an opennet-mode in which it connects to any other Freenet user.

Since Version 0. 7, Freenet offers two different levels of security: Opennet and Darknet.

Since version 0. 6, gnutella is a composite network made of leaf nodes and ultra nodes ( also called ultrapeers ).

Since version 7. 0, support for " reversible debugging " — allowing a debugging session to step backward, much like rewinding a crashed program to see what happened — is available.

Since 1995, Hungary has pegged the forint against a basket of currencies ( in which the U. S. dollar is 30 %), and the central rate against the basket is devalued at a preannounced rate, originally set at 0. 8 % per month, the Forint is now an entirely free-floating currency.

Since 2004, the alcohol content of Kahlúa is 20. 0 % ( 21. 5 % alc.

Since metallic radii are always biggest for the highest coordination number, correction for less dense coordinations involves dividing by x, where 0 < x < 1.

( Since 1 > 0, then 1 + 1 > 0, and 1 + 1 + 1 > 0, etc.

Since a proportion must be between 0 and 1, inclusive, the index α must be positive, but in order for the total income of the whole population to be finite, α must also be greater than 1.

Since Lowell astronomers thought Pluto was massive enough to perturb planets, they assumed that it should have an albedo of 0. 07 ( meaning that it reflected only 7 % of the light that hit it ); about as dark as asphalt and similar to that of Mercury, the least reflective planet known.

Since J2SE5. 0, Java's library contains a interface that specifies queue operations ; implementing classes include and ( since J2SE 1. 6 ).

Since an event of probability 0 should not contribute to the entropy, and given that, the convention is adopted that.