3 1. निम्न द्विघात बहुपदों के शून्यक ज्ञात कीजिए और शून्यकों तथा गुणांकों के बीच के संबंध सत्यता की जाँच कीजिए :
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Complement (set theory)
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In set theory, the complement of a set A, often denoted by Ac (or A′),[1][2] are the elements not in A.[3]
A circle filled with red inside a square. The area outside the circle is unfilled. The borders of both the circle and the square are black.
If A is the area colored red in this image…
An unfilled circle inside a square. The area inside the square not covered by the circle is filled with red. The borders of both the circle and the square are black.
… then the complement of A is everything else.
When all sets under consideration are considered to be subsets of a given set U, the absolute complement of A is the set of elements in U that are not in A.
The relative complement of A with respect to a set B, also termed the set difference of B and A, written B \ A, is the set of elements in B that are not in A.[1]
Absolute complement
Relative complement
Complementary relation
LaTeX notation
In programming languages
See also
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References
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Last edited 29 days ago by Serols
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Friction
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For other uses, see Friction (disambiguation).
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.[2] There are several types of friction:
Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into static friction ("stiction") between non-moving surfaces, and kinetic friction between moving surfaces. With the exception of atomic or molecular friction, dry friction generally arises from the interaction of surface features, known as asperities (see Figure 1).
Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other.[3][4]
Figure 1: Simulated blocks with fractal rough surfaces, exhibiting static frictional interactions[1]
Lubricated friction is a case of fluid friction where a lubricant fluid separates two solid surfaces.[5][6][7]
Skin friction is a component of drag, the force resisting the motion of a fluid across the surface of a body.
Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation.[4]
When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into thermal energy (that is, it converts work to heat). This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to thermal energy whenever motion with friction occurs, for example when a viscous fluid is stirred. Another important consequence of many types of friction can be wear, which may lead to performance degradation or damage to components. Friction is a component of the science of tribology.
Friction is desirable and important in supplying traction to facilitate motion on land. Most land vehicles rely on friction for acceleration, deceleration and changing direction. Sudden reductions in traction can cause loss of control and accidents.
Friction is not itself a fundamental force. Dry friction arises from a combination of inter-surface adhesion, surface roughness, surface deformation, and surface contamination. The complexity of these interactions makes the calculation of friction from first principles impractical and necessitates the use of empirical methods for analysis and the development of theory.
Friction is a non-conservative force – work done against friction is path dependent. In the presence of friction, some kinetic energy is always transformed to thermal energy, so mechanical energy is not conserved.
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Laws of dry friction
Dry friction
Fluid friction
Lubricated friction
Skin friction
Internal friction
Radiation friction
Other types of friction
Reducing friction
Energy of friction
Applications
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References
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Last edited 25 days ago by Tensorit
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