When the angular velocity of this co-rotating frame is not constant, that is, for non-circular orbits, other fictitious forces — the Coriolis force and the Euler force — will arise, but can be ignored since they will cancel each other, yielding a net zero acceleration transverse to the moving radial vector, as required by the starting assumption that the vector co-rotates with the planet.

When k is even the coefficients of all its Euler factors are non-negative, so that each of the Euler factors has coefficients bounded by a constant times the coefficients of Z ( E < sup > k </ sup >, T ) and therefore converges on the same region and has no poles in this region.

* the constant coefficient a < sub > 0 </ sub > is the Euler characteristic of P. When P is a closed convex polytope, a < sub > 0 </ sub > = 1.

When this is done, it is necessary to specify when classic Euler angles are referred, using an adjective like " proper " or similar.

When the intrinsic rotations equivalence is used to name the possible conventions of Euler Angles the names are like Z-X ’- Z ’’.

When at home, Stone relied upon the research facilities and expertise made available to him by Esther Euler, head research librarian of the University of California at Los Angeles, to whom he dedicated and thanked, in addition to many others, in several of his works.

When n is odd and composite, at least half of all a with gcd ( a, n ) = 1 are Euler witnesses.

When the number of oscillators ( particles ) is increased to three, the orthogonal matrix can no longer be described by a single angle ; instead, three are required ( Euler angles ).

When told they were called " Anglii " ( Angles ), he replied with a Latin pun that translates well into English: “ Bene, nam et angelicam habent faciem, et tales angelorum in caelis decet esse coheredes ” (" It is well, for they have an angelic face, and such people ought to be co-heirs of the angels in heaven ").

When I show up he will know you are a good wife to have told him about it ''.

When the Know-nothings get control, it will read, All men are created equal except Negroes and foreigners and Catholics.

When the reactionary response is thus bolstered by an intellectual defense, the characteristics of that defense are explicable only in terms of the basic attitudes of unanalyzed reaction.

When combined with the metaphysical notion that pure forms of this universe are best appreciated when least embodied in a material substratum, it becomes clear that while earth will be dross on a scale of material-formal ratios, celestial bodies will be of a subtle, quickened, ethereal existence, in whose embodiment pure form will be the dominant component and matter will be absent or remain subsidiary.

She used to tell me, `` When I stand there and look at the flag blowing this way and that way, I have the wonderful, safe feeling that Americans are protected no matter which way the wind blows ''.

When we consider the disorganized state of the world community, and the legacy of predispositions adversely directed against all who are identified as Jews, it is obvious that the struggle for the minds and muscles of men needs to be prosecuted with increasing vigor and skill.

When these fields are surveyed together, important patterns of relationship emerge indicating a vast community of reciprocal influence, a continuity of thought and expression including many traditions, primarily literary, religious, and philosophical, but frequently including contact with the fine arts and even, to some extent, with science.

When different colors are used, she is just as likely to color trees purple, hair green, etc..

When finally the two bedraggled men reach their friend's home, Voltaire's fears are once again aroused.

`` When are you to leave ''??

When the roof blocks are all in place, the final rows of wall blocks are mortared into position.

When the aid operations are reorganized the Peace Corps should remain a semi-autonomous, functional unit.

When the budget goes to trustees for approval it is the president's budget, to which his faith and credit are committed ; ;

When they have 4 to 6 leaves and are thrifty little plants, it's time to set them out where they are to remain.

When aircraft are no longer helpless on airfields, they are no longer vulnerable to Aj.

When more than two figures are separated by subtraction symbols the subtraction must be carried out from the left to right if the result is to be correct.

When they're on, the top edges are planed even with the sheer batten.

When painting, Mason's physical eyes are half-closed, while his mind's eye is wide open, and this circumstance accounts in part for the impression he wishes to convey.

When improvements are recommended in working conditions -- such as lighting, rest rooms, eating facilities, air-conditioning -- do you try to set a measure of their effectiveness on productivity??

When sufficiently accurate and complete measurements are available, it will be possible to set limits on the thermal and electrical characteristics of the surface and subsurface materials of the moon.

When some thirteen records of newly and recently born individuals are collated, little or no correlation between length and distribution can be detected.

When three dice are tossed repeatedly, what is the probability that the number of aces is 0 ( or 1, or 2, or 3 )??

When having legal status recognized, or defined in law, as in ancient China, concubinage was akin, although inferior, to marriage.

When dealing with graded algebras, the commutator is usually replaced by the graded commutator, defined in homogeneous components as

When an order has been defined in this way, a sorting algorithm can be used to put a list of any number of items into that order.

When the plasma goes upward from the footpoints towards the loop top, as it always occurs during the initial phase of a compact flare, it is defined as chromospheric evaporation.

When defined for a topological vector space there is a subspace of this dual space, corresponding to continuous linear functionals, which constitutes a continuous dual space.

When the database is ready ( all its data structures and other needed components are defined ) it is typically populated with initial application's data ( database initialization, which is typically a distinct project ; in many cases using specialized DBMS interfaces that support bulk insertion ) before making it operational.

When the determinant is equal to one, the linear mapping defined by the matrix is equi-areal and orientation-preserving.

When setting up PBXs to run a DPNSS connection one end must be defined as the primary or ' A ' end.

When used in science, for example geology, eras denote clearly defined periods of time of arbitrary but well defined length, such as for example the Mesozoic Era from 252 Ma – 66 Ma, delimited by a start event and an end event.

When England switched to the shorter foot in the late 13th century, rods and furlongs remained unchanged, since property boundaries were already defined in rods and furlongs.

When an object changes its color smoothly, the animation can be defined by keyframes — the first showing its original color, and the second showing its final color.

When Edward Witten named M-theory, he did not specify what the M stood for — perhaps because the nascent theory was not fully defined.

When there has also been an osteoporotic fracture ( also termed " low trauma-fracture " or " fragility fracture "), defined as one that occurs as a result of a fall from a standing height, the term " severe or established " osteoporosis is used.

When the exact chromaticities of the red, green, and blue primaries are defined, the color model then becomes an absolute color space, such as sRGB or Adobe RGB ; see RGB color spaces for more details.

When a tabloid is defined as " roughly " and commonly " half the size of a broadsheet ," confusion can arise because " Many broadsheets measure roughly ", half of which is roughly not.

When it becomes necessary to distinguish these special vectors from vectors as defined in pure mathematics, they are sometimes referred to as geometric, spatial, or Euclidean vectors.

When the length of vectors is defined, it is possible to also define a dot product — a scalar-valued product of two vectors — which gives a convenient algebraic characterization of both length ( the square root of the dot product of a vector by itself ) and angle ( a function of the dot product between any two vectors ).

When using this convention, in contrast to the other convention, the defined handedness of the wave matches the handedness of the screw type nature of the field in space.

When practiced outside the laws of war, it is often defined as terrorism, though rarely by its practitioners or their supporters.

When reactive elements such as capacitors, inductors, or transmission lines are involved in a circuit to which AC or time-varying voltage or current is applied, the relationship between voltage and current becomes the solution to a differential equation, so Ohm's law ( as defined above ) does not directly apply since that form contains only resistances having value R, not complex impedances which may contain capacitance (" C ") or inductance (" L ").

When abstraction proceeds into the operations defined, enabling objects of different types to be substituted, it is called polymorphism.

:( a ) When people and organizations focus primarily on quality, defined by the following ratio,

When used in computer graphics to render scenes composed of planar polygons, the partitioning planes are frequently ( but not always ) chosen to coincide with the planes defined by polygons in the scene.

When both descendants are similar in a particular respect, evolution is defined as parallel if the ancestors considered were also similar, and convergent if they were not.