For it includes the emotional ties that bind men to their homeland and the complex motivations that hold a large group of people together as a unit.

For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.

For example, the Banach – Tarski paradox is neither provable nor disprovable from ZF alone: it is impossible to construct the required decomposition of the unit ball in ZF, but also impossible to prove there is no such decomposition.

For example, if the sorted list to which we apply binary search has n elements, and we can guarantee that each lookup of an element in the list can be done in unit time, then at most log < sub > 2 </ sub > n + 1 time units are needed to return an answer.

For example, Calgary, Canada-based SemBioSys Genetics, Inc. reports that its safflower-produced insulin will reduce unit costs by over 25 % or more and approximates a reduction in the capital costs associated with building a commercial-scale insulin manufacturing facility of over $ 100 million, compared to traditional biomanufacturing facilities.

For example, after 10 rounds at 1 unit per round, the standard deviation will be 2 x 1 x sqrt ( 10 x 18 / 38 x 20 / 38 ) =

For each physical quantity, a number of different units ( some only of historical interest ) are shown and expressed in terms of the corresponding SI unit.

For instance, it defined chemical engineering to be a " science of itself, the basis of which is ... unit operations " in a 1922 report ; and with which principle, it had published a list of academic institutions which offered " satisfactory " chemical engineering courses.

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, a physics lab course might ask students to record lengths in centimetres, and masses in grams, but force ( a derived unit ) in newtons, a usage consistent with the SI system.

For example, if we suppose at t = 0 the extension is a unit distance ( x = 1 ), and the particle is not moving ( dx / dt = 0 ).

For example, a point on the unit circle in the plane can be specified by two Cartesian coordinates, but one can make do with a single coordinate ( the polar coordinate angle ), so the circle is 1-dimensional even though it exists in the 2-dimensional plane.

For a map, the bifurcation will occur when there are eigenvalues of DF < sub > μ </ sub > on the unit circle.

For this reason the unit became a popular choice among those looking to pirate games.

For a given market of a commodity, demand is the relation of the quantity that all buyers would be prepared to purchase at each unit price of the good.

For a given quantity of a consumer good, the point on the demand curve indicates the value, or marginal utility, to consumers for that unit.

For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles per unit time.

For instance, the Institute of Electrical and Electronics Engineers ( IEEE ) defined the unit accordingly for the use in power switchgear.

* For Whom the Bell Tolls, an Ernest Hemingway novel which tells the story of Robert Jordan, an American volunteer attached to a guerrilla unit during the Spanish Civil War.

For the 2007 Snakes and Arrows tour, Lee swapped the SansAmp RBI for a new unit by Sansamp, the RPM.

For instance, while words for transporter ionizer unit ( jolvoy ) or bridge ( of a ship ) ( meH ) have been known since close to the language's inception, the word for bridge in the sense of a crossing over water ( QI ) was unknown until August 2012.

For example, in many European countries, the hectolitre is the typical unit for production and export volumes of beverages ( milk, beer, soft drinks, wine, etc.

For larger volumes of fluids, such as annual consumption of tap water, lorry ( truck ) tanks, or swimming pools, the cubic metre is the general unit.

For example, sell in unit blocks rather than individual units.

For this reason, tangent covectors are frequently called one-forms.

For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point.

For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is defined to be the smallest such distance.

For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance.

#: For a given normal section there is a circle whose curvature is the same as the sectional curvature, is tangent to the surface and whose center lines along on the normal line.

For example, if the given manifold is a 2-sphere, one can picture the tangent space at a point as the plane which touches the sphere at that point and is perpendicular to the sphere's radius through the point.

For example, a curve that crosses itself doesn't have a unique tangent line at that point.

For example, a vector in three dimensional space can be decomposed with respect to two axes, respectively normal, and tangent to a surface ( see figure ).

For yields of less than a few hundred kilotons, this would not necessarily be true because the field strength at the Earth's tangent could be substantially less than 0. 5E < sub > max </ sub >.

For the case of two colliding bodies in two-dimensions, the overall velocity of each body must be split into two perpendicular velocities: one tangent to the common normal surfaces of the colliding bodies at the point of contact, the other along the line of collision.

For two-and three-dimensional collisions the velocities in these formulas are the components perpendicular to the tangent line / plane at the point of contact.

: For any point p in M and for any vector V in T < sub > p </ sub > M ( the tangent space to M at p ) there exists a unique geodesic: I → M such that

For the resulting vector field to be a spray ( on the deleted tangent bundle TM

For example, the three-dimensional object physics calls angular velocity is a differential rotation, thus a vector in the Lie algebra tangent to SO ( 3 ).

For each pair of tangent vectors u, v, R ( u, v ) is a linear transformation of the tangent space of the manifold.

For example, a smooth curve α ( t ): 1 → M has tangent vector α ′( t < sub > 0 </ sub >) in the tangent space TM ( α ( t < sub > 0 </ sub >)) at any point t < sub > 0 </ sub > ∈ ( 0, 1 ), and each such vector has length ‖ α ′( t < sub > 0 </ sub >)‖, where ‖·‖ denotes the norm induced by the inner product on TM ( α ( t < sub > 0 </ sub >)).

Therefore all tangent vectors in a point p span a linear space, called the tangent space at point p. For example, taking a 2-dimensional space, like the ( curved ) surface of the Earth, its tangent space at a specific point would be the flat approximation of the curved space.

For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.

: For a more general, but much more technical, treatment of tangent vectors, see tangent space.