If matrix support is polar ( e. g. paper, silica etc.

If the polar reciprocal of the canonical form in the sphere is congruent to the original, then the figure is self-dual.

Formulae connecting a tangential angle, the angle anchored at the ellipse's center ( called also the polar angle from the ellipse center ), and the parametric angle t < ref > If the ellipse is illustrated as a meridional one for the earth, the tangential angle is equal to geodetic latitude, the angle is the geocentric latitude, and parametric angle t is a parametric ( or reduced ) latitude of auxiliary circle </ ref > are:

If instead we use polar coordinates with the origin at one focus, with the angular coordinate still measured from the major axis, the ellipse's equation is

If Earth were smaller, a thinner atmosphere would allow temperature extremes, thus preventing the accumulation of water except in polar ice caps ( as on Mars ).

If B is a circle, then these eigenfunctions have an angular component that is a trigonometric function of the polar angle θ, multiplied by a Bessel function ( of integer order ) of the radial component.

If the polar vertex is " pulled down " 90 °, so that the vertex is on the equator, or transverse diameter, then it becomes the transverse graticule, upon which all spherical trigonometry is ultimately based ( if the longitudinal vertex is between the poles and equator, then it is considered an oblique graticule ).

If eaten in one meal, 30 to 90 grams of polar bear liver is enough to kill a human being, or to make even sled dogs very ill.

If z is a complex number, written in polar form as

If a curve is defined in polar coordinates as, then its curvature is

There exists a link between sudden stratospheric warmings and the quasi-biennial oscillation: If the QBO is in its easterly ( westward ) phase, the atmospheric waveguide is modified in such a way that upward-propagating Rossby waves are focused on the polar vortex, intensifying their interaction with the mean flow.

If the result is between 0. 4 and 1. 7 then, generally, the bond is polar covalent.

If a complex number is represented in polar form z = re < sup > iθ </ sup >, then the logarithm of z is

If a split-complex number z does not lie on one of the diagonals, then z has a polar decomposition.

If C < sub > 1 </ sub > and C < sub > 2 </ sub > are given in polar coordinates by and respectively, then the equation describes the cissoid of C < sub > 1 </ sub > and C < sub > 2 </ sub > relative to the origin.

If the domain is a circle of radius a, then it is appropriate to introduce polar coordinates r and θ.

If dinosaurs found a similar haven in which they outlived the rest of their kind, then we think polar Gondwana, including southeastern Australia, is a likely place to look for it.

If the metabolites of phase I reactions are sufficiently polar, they may be readily excreted at this point.

If the body lacks cylinder ( axial ) symmetry, a last rotation around its z-axis ( which has polar coordinates and ) is necessary to specify its orientation completely.

If a chemical is very nonpolar it will not dissolve at all in a very polar solvent.

If the filter paper has small pores, long chained non polar liquids such as oil may clog the filter paper.

If the introduced surface had an ionic or polar nature, there would be water molecules standing upright on 1 ( along the axis of an orbital for ionic bond ) or 2 ( along a resultant polarity axis ) of the 4 sp3 orbitals.

If the mobile phase is changed to a more polar solvent or mixture of solvents, it is more capable of dispelling solutes from the silica binding places and all compounds on the TLC plate will move higher up the plate.

If a circle with radius a is rotated about an axis at distance b from its center, then the equation of the resulting hippopede in polar coordinates

If the lever is pulled to clear a signal or move a switch, the tappet moves a short distance lengthwise at the same time.

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 the distribution of the 71 items were wholly concordant in the two families, the distance would of course be 0.

If this particular quasar and our galaxy could be seen side by side at the same distance, the quasar would be 5 magnitudes ( or 100 times ) brighter than our galaxy.

If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their perpendicular height of incidence, i. e. their distance from the axis.

If a detector was placed at a distance of 1 m, the ion flight times would be X and Y ns.

If women attended, they were often isolated to a section away from the men, supposedly to distance them from any vulgarities that the male spectators ( or players ) might speak.

If there is a tie, we must consider the atoms at distance 2 from the stereocenter — as a list is made for each group of the atoms bonded to the one directly attached to the stereocenter.

If there is still a tie, each atom in each of the two lists is replaced with a sub-list of the other atoms bonded to it ( at distance 3 from the stereocenter ), the sub-lists are arranged in decreasing order of atomic number, and the entire structure is again compared atom by atom.

* If is the norm ( usually noted as ) defined in the square-summable sequence space ℓ < sup > 2 </ sup > ( which also matches the usual distance in a continuous and isotropic cartesian space ), then

* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then

If the weight of the roadway per unit length is w and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the weight on the cable from c to r is wx where x is the horizontal distance between c to r. Proceeding as before gives the differential equation

If the axes are named x, y, and z, then the x coordinate is the distance from the plane defined by the y and z axes.

If S is an arbitrary set, then the set S < sup > N </ sup > of all sequences in S becomes a complete metric space if we define the distance between the sequences ( x < sub > n </ sub >) and ( y < sub > n </ sub >) to be, where N is the smallest index for which x < sub > N </ sub > is distinct from y < sub > N </ sub >, or 0 if there is no such index.

If, for the same focal length setting, the subject distance is adjusted to provide the same field of view at the subject, at the same f-number and final-image size, the smaller format has greater DOF, as with the “ same picture ” comparison above.

If pictures are taken from the same distance using the same f-number, same focal length, and the final images are the same size, the smaller format has less DOF.

If pictures taken from the same subject distance using the same focal length, are given the same enlargement, both final images will have the same DOF.

If extension is executed properly the discus will be at the right angle to ride on the air current and thus be taken a farther distance.

If the viewing distance is large compared with the separation of the slits ( the far field ), the phase difference can be found using the geometry shown in the figure below right.

If an ideal thermally conductive blackbody was the same distance from the Sun as the Earth is, it would have a temperature of about 5. 3 ° C.

If the target is a hard and heavy object, or if it is resting on some sort of anvil, the head can travel only a very short distance d before stopping.

If the bullets have to travel a varying distance from the case to the point where they engage the rifling, then this can result in variations in pressure and velocity.

If the competitor starts the leap with any part of the foot past the foul line, the jump is declared a foul and no distance is recorded.

If a first body of mass M < sub > A </ sub > is placed at a distance R from a second body of mass M < sub > B </ sub >, each body experiences an attractive force F < sub > g </ sub >

If the pressure from particles within the magnetosphere is neglected, it is possible to estimate the distance to the part of the magnetosphere that faces the Sun.