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In mechanics, a diaphragm is a sheet of a semi-flexible material anchored at its periphery and most often round in shape. It serves either as a barrier between two chambers, moving slightly up into one chamber or down into the other depending on differences in pressure, or as a device that vibrates when certain frequencies are applied to it.A diaphragm pump uses a diaphragm to pump a fluid. A typical design is to have air on one side constantly vary in pressure, with fluid on the other side. The increase and decrease in volume caused by the action of the diaphragm alternately forces fluid out the chamber and draws more fluid in from its source. | https://en.wikipedia.org/wiki/Diaphragm_(mechanical_device) |
The action of the diaphragm is very similar to the action of a plunger with the exception that a diaphragm responds to changes in pressure rather than the mechanical force of the shaft. A diaphragm pressure tank is a tank which has pressurant sealed inside on one side of the diaphragm. It is favored in certain applications due to its high durability and reliability. | https://en.wikipedia.org/wiki/Diaphragm_(mechanical_device) |
This comes with a downside, as the vessel needs to be replaced in the case of a rupture of the diaphragm. Diaphragm tanks are used to store hypergolic propellant aboard space probes and various other spacecraft. Pressure regulators use diaphragms as part of their design. Most uses of compressed gasses, for example, in gas welding and scuba diving rely on regulators to deliver their gas output at appropriate pressures. Automotive fuel systems frequently require fuel-pressure regulators; this is true of many fuel injection systems as well as in vehicles fueled with liquefied petroleum gas (autogas) and compressed natural gas. | https://en.wikipedia.org/wiki/Diaphragm_(mechanical_device) |
In mechanics, a displacement field is an assignment of displacement vectors for all points in a region or body that are displaced from one state to another. A displacement vector specifies the position of a point or a particle in reference to an origin or to a previous position. For example, a displacement field may be used to describe the effects of deformation on a solid body. | https://en.wikipedia.org/wiki/Material_displacement_gradient_tensor |
In mechanics, a micromixer is a device based on mechanical microparts used to mix fluids. This device represents a key technology to fields such as chemical industry, pharmaceutical industry, analytical chemistry, biochemical analysis, and high-throughput synthesis, since it makes use of the miniaturization of the fluids associated in the mixing to reduce quantities involved in the chemical and/or biochemical processes. | https://en.wikipedia.org/wiki/Micromixer |
In mechanics, a moment is a measure of the turning effect of a force about some point in space. In most practical examples, moments are the results of forces acting at a distance from the point of interest. The stress on the body on which the force acts is then symmetric. If the moment results from a strong body force, such as that produced in a magnetic material in a strong magnetic field, the stress tensor is non-symmetric. | https://en.wikipedia.org/wiki/Body_moment |
In mechanics, a six-bar linkage is a mechanism with one degree of freedom that is constructed from six links and seven joints. An example is the Klann linkage used to drive the legs of a walking machine. In general, each joint of a linkage connects two links, and a binary link supports two joints. | https://en.wikipedia.org/wiki/Six-bar_linkage |
If we consider a hexagon constructed from six binary links with six of the seven joints forming its vertices, then the seventh joint can be added to connect two sides of the hexagon to form a six-bar linkage with two ternary links connected by one joint. This type of six-bar linkage is said to have the Watt topology.A six-bar linkage can also be constructed by first assembling five binary links into a pentagon, which uses five of the seven joints, and then completing the linkage by adding a binary link that connects two sides of the pentagon. This again creates two ternary links that are now separated by one or more binary links. This type of six-bar linkage is said to have the Stephenson topology. The Klann linkage has the Stephenson topology. | https://en.wikipedia.org/wiki/Six-bar_linkage |
In mechanics, a stress-induced transformation is called a deformation and may be described by a diffeomorphism. A diffeomorphism f: U → V {\displaystyle f:U\to V} between two surfaces U {\displaystyle U} and V {\displaystyle V} has a Jacobian matrix D f {\displaystyle Df} that is an invertible matrix. In fact, it is required that for p {\displaystyle p} in U {\displaystyle U} , there is a neighborhood of p {\displaystyle p} in which the Jacobian D f {\displaystyle Df} stays non-singular. Suppose that in a chart of the surface, f ( x , y ) = ( u , v ) . | https://en.wikipedia.org/wiki/Diffeomorphism |
{\displaystyle f(x,y)=(u,v).} The total differential of u is d u = ∂ u ∂ x d x + ∂ u ∂ y d y {\displaystyle du={\frac {\partial u}{\partial x}}dx+{\frac {\partial u}{\partial y}}dy} , and similarly for v.Then the image ( d u , d v ) = ( d x , d y ) D f {\displaystyle (du,dv)=(dx,dy)Df} is a linear transformation, fixing the origin, and expressible as the action of a complex number of a particular type. When (dx, dy) is also interpreted as that type of complex number, the action is of complex multiplication in the appropriate complex number plane. | https://en.wikipedia.org/wiki/Diffeomorphism |
As such, there is a type of angle (Euclidean, hyperbolic, or slope) that is preserved in such a multiplication. Due to Df being invertible, the type of complex number is uniform over the surface. Consequently, a surface deformation or diffeomorphism of surfaces has the conformal property of preserving (the appropriate type of) angles. | https://en.wikipedia.org/wiki/Diffeomorphism |
In mechanics, a variable-mass system is a collection of matter whose mass varies with time. It can be confusing to try to apply Newton's second law of motion directly to such a system. Instead, the time dependence of the mass m can be calculated by rearranging Newton's second law and adding a term to account for the momentum carried by mass entering or leaving the system. The general equation of variable-mass motion is written as F e x t + v r e l d m d t = m d v d t {\displaystyle \mathbf {F} _{\mathrm {ext} }+\mathbf {v} _{\mathrm {rel} }{\frac {\mathrm {d} m}{\mathrm {d} t}}=m{\mathrm {d} \mathbf {v} \over \mathrm {d} t}} where Fext is the net external force on the body, vrel is the relative velocity of the escaping or incoming mass with respect to the center of mass of the body, and v is the velocity of the body. In astrodynamics, which deals with the mechanics of rockets, the term vrel is often called the effective exhaust velocity and denoted ve. | https://en.wikipedia.org/wiki/Variable-mass_system |
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the net force acting on that object. | https://en.wikipedia.org/wiki/Centripetal_acceleration |
The magnitude of an object's acceleration, as described by Newton's Second Law, is the combined effect of two causes: the net balance of all external forces acting onto that object — magnitude is directly proportional to this net resulting force; that object's mass, depending on the materials out of which it is made — magnitude is inversely proportional to the object's mass.The SI unit for acceleration is metre per second squared (m⋅s−2, m s 2 {\displaystyle \mathrm {\tfrac {m}{s^{2}}} } ). For example, when a vehicle starts from a standstill (zero velocity, in an inertial frame of reference) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the vehicle turns, an acceleration occurs toward the new direction and changes its motion vector. | https://en.wikipedia.org/wiki/Centripetal_acceleration |
The acceleration of the vehicle in its current direction of motion is called a linear (or tangential during circular motions) acceleration, the reaction to which the passengers on board experience as a force pushing them back into their seats. When changing direction, the effecting acceleration is called radial (or centripetal during circular motions) acceleration, the reaction to which the passengers experience as a centrifugal force. If the speed of the vehicle decreases, this is an acceleration in the opposite direction of the velocity vector (mathematically a negative, if the movement is unidimensional and the velocity is positive), sometimes called deceleration or retardation, and passengers experience the reaction to deceleration as an inertial force pushing them forward. | https://en.wikipedia.org/wiki/Centripetal_acceleration |
Such negative accelerations are often achieved by retrorocket burning in spacecraft. Both acceleration and deceleration are treated the same, as they are both changes in velocity. Each of these accelerations (tangential, radial, deceleration) is felt by passengers until their relative (differential) velocity are neutralized in reference to the acceleration due to change in speed. | https://en.wikipedia.org/wiki/Centripetal_acceleration |
In mechanics, an equilibrant force is a force which brings a body into mechanical equilibrium. According to Newton's second law, a body has zero acceleration when the vector sum of all the forces acting upon it is zero: ∑ F = m a ; ∑ F = 0 ⇒ a = 0 {\displaystyle \sum \mathbf {F} =m\mathbf {a} ;\quad \sum \mathbf {F} =0\ \ \Rightarrow \ \ \mathbf {a} =0} Therefore, an equilibrant force is equal in magnitude and opposite in direction to the resultant of all the other forces acting on a body. The term has been attested since the late 19th century. | https://en.wikipedia.org/wiki/Equilibrant_force |
In mechanics, an impact is when two bodies collide. During this collision, both bodies decelerate. The deceleration causes a high force or shock, applied over a short time period. A high force, over a short duration, usually causes more damage to both bodies than a lower force applied over a proportionally longer duration. | https://en.wikipedia.org/wiki/Mechanical_impact |
At normal speeds, during a perfectly inelastic collision, an object struck by a projectile will deform, and this deformation will absorb most or all of the force of the collision. Viewed from a conservation of energy perspective, the kinetic energy of the projectile is changed into heat and sound energy, as a result of the deformations and vibrations induced in the struck object. However, these deformations and vibrations cannot occur instantaneously. | https://en.wikipedia.org/wiki/Mechanical_impact |
A high-velocity collision (an impact) does not provide sufficient time for these deformations and vibrations to occur. Thus, the struck material behaves as if it were more brittle than it would otherwise be, and the majority of the applied force goes into fracturing the material. Or, another way to look at it is that materials actually are more brittle on short time scales than on long time scales: this is related to time-temperature superposition. | https://en.wikipedia.org/wiki/Mechanical_impact |
Impact resistance decreases with an increase in the modulus of elasticity, which means that stiffer materials will have less impact resistance. Resilient materials will have better impact resistance. Different materials can behave in quite different ways in impact when compared with static loading conditions. | https://en.wikipedia.org/wiki/Mechanical_impact |
Ductile materials like steel tend to become more brittle at high loading rates, and spalling may occur on the reverse side to the impact if penetration doesn't occur. The way in which the kinetic energy is distributed through the section is also important in determining its response. Projectiles apply a Hertzian contact stress at the point of impact to a solid body, with compression stresses under the point, but with bending loads a short distance away. Since most materials are weaker in tension than compression, this is the zone where cracks tend to form and grow. | https://en.wikipedia.org/wiki/Mechanical_impact |
In mechanics, compression is the application of balanced inward ("pushing") forces to different points on a material or structure, that is, forces with no net sum or torque directed so as to reduce its size in one or more directions. It is contrasted with tension or traction, the application of balanced outward ("pulling") forces; and with shearing forces, directed so as to displace layers of the material parallel to each other. The compressive strength of materials and structures is an important engineering consideration. | https://en.wikipedia.org/wiki/Physical_compression |
In uniaxial compression, the forces are directed along one direction only, so that they act towards decreasing the object's length along that direction. The compressive forces may also be applied in multiple directions; for example inwards along the edges of a plate or all over the side surface of a cylinder, so as to reduce its area (biaxial compression), or inwards over the entire surface of a body, so as to reduce its volume. Technically, a material is under a state of compression, at some specific point and along a specific direction x {\displaystyle x} , if the normal component of the stress vector across a surface with normal direction x {\displaystyle x} is directed opposite to x {\displaystyle x} . | https://en.wikipedia.org/wiki/Physical_compression |
If the stress vector itself is opposite to x {\displaystyle x} , the material is said to be under normal compression or pure compressive stress along x {\displaystyle x} . In a solid, the amount of compression generally depends on the direction x {\displaystyle x} , and the material may be under compression along some directions but under traction along others. If the stress vector is purely compressive and has the same magnitude for all directions, the material is said to be under isotropic compression, hydrostatic compression, or bulk compression. | https://en.wikipedia.org/wiki/Physical_compression |
This is the only type of static compression that liquids and gases can bear. It affects the volume of the material, as quantified by the bulk modulus and the volumetric strain. The inverse process of compression is called decompression or dilation, in which the object enlarges or increases in volume. In a mechanical wave which is longitudinal, the medium is displaced in the wave's direction, resulting in areas of compression and rarefaction. | https://en.wikipedia.org/wiki/Physical_compression |
In mechanics, compressive strength (or compression strength) is the capacity of a material or structure to withstand loads tending to reduce size (as opposed to tensile strength which withstands loads tending to elongate). In other words, compressive strength resists compression (being pushed together), whereas tensile strength resists tension (being pulled apart). In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently. Some materials fracture at their compressive strength limit; others deform irreversibly, so a given amount of deformation may be considered as the limit for compressive load. | https://en.wikipedia.org/wiki/Compressive_strength |
Compressive strength is a key value for design of structures. Compressive strength is often measured on a universal testing machine. Measurements of compressive strength are affected by the specific test method and conditions of measurement. Compressive strengths are usually reported in relationship to a specific technical standard. | https://en.wikipedia.org/wiki/Compressive_strength |
In mechanics, friction torque is the torque caused by the frictional force that occurs when two objects in contact move. Like all torques, it is a rotational force that may be measured in newton meters or pounds-feet. | https://en.wikipedia.org/wiki/Friction_torque |
In mechanics, he proposed an alternative formulation of analytical mechanics known as Appell's equation of motion. He discovered a physical interpretation of the imaginary period of the doubly periodic function whose restriction to real arguments describes the motion of an ideal pendulum. | https://en.wikipedia.org/wiki/Paul_Émile_Appell |
In mechanics, strain is defined as relative deformation, compared to a reference position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered. Strain has dimension of a length ratio, with SI base units of meter per meter (m/m). Hence strains are dimensionless and are usually expressed as a decimal fraction, a percentage or in parts-per notation (e.g., parts per million, sometimes called "microstrains"). | https://en.wikipedia.org/wiki/Logarithmic_strain |
Strain can be formulated as the spatial derivative of displacement: where I is the identity tensor. The displacement of a body may be expressed in the form x = F(X), where X is the reference position of material points of the body; displacement has units of length and does not distinguish between rigid body motions (translations and rotations) and deformations (changes in shape and size) of the body. The spatial derivative of a uniform translation is zero, thus strains measure how much a given displacement differs locally from a rigid-body motion.A strain is in general a tensor quantity. | https://en.wikipedia.org/wiki/Logarithmic_strain |
Physical insight into strains can be gained by observing that a given strain can be decomposed into normal and shear components. The amount of stretch or compression along material line elements or fibers is the normal strain, and the amount of distortion associated with the sliding of plane layers over each other is the shear strain, within a deforming body. This could be applied by elongation, shortening, or volume changes, or angular distortion.The state of strain at a material point of a continuum body is defined as the totality of all the changes in length of material lines or fibers, the normal strain, which pass through that point and also the totality of all the changes in the angle between pairs of lines initially perpendicular to each other, the shear strain, radiating from this point. However, it is sufficient to know the normal and shear components of strain on a set of three mutually perpendicular directions. If there is an increase in length of the material line, the normal strain is called tensile strain; otherwise, if there is reduction or compression in the length of the material line, it is called compressive strain. | https://en.wikipedia.org/wiki/Logarithmic_strain |
In mechanics, suspension is a system of components allowing a machine (normally a vehicle) to move smoothly with reduced shock. Types may include: car suspension, four-wheeled motor vehicle suspension motorcycle suspension, two-wheeled motor vehicle suspension Motorcycle fork, a component of motorcycle suspension system bicycle suspensionRelated concepts include: Shock absorber Shock mount Vibration isolation Magnetic suspension Electrodynamic suspension Electromagnetic suspension | https://en.wikipedia.org/wiki/Suspension_(mechanics) |
In mechanics, the concept of force (in some direction) has a close analogue in the concept of torque (about some angle): A result of this similarity is that the SI unit for torque is the newton-metre, which works out algebraically to have the same dimensions as the joule, but they are not interchangeable. The General Conference on Weights and Measures has given the unit of energy the name joule, but has not given the unit of torque any special name, hence it is simply the newton-metre (N⋅m) – a compound name derived from its constituent parts. The use of newton-metres for torque but joules for energy is helpful to avoid misunderstandings and miscommunication.The distinction may be seen also in the fact that energy is a scalar quantity – the dot product of a force vector and a displacement vector. | https://en.wikipedia.org/wiki/Joule_(unit) |
By contrast, torque is a vector – the cross product of a force vector and a distance vector. Torque and energy are related to one another by the equation where E is energy, τ is (the vector magnitude of) torque, and θ is the angle swept (in radians). Since plane angles are dimensionless, it follows that torque and energy have the same dimensions. | https://en.wikipedia.org/wiki/Joule_(unit) |
In mechanics, the derivative of the position vs. time graph of an object is equal to the velocity of the object. In the International System of Units, the position of the moving object is measured in meters relative to the origin, while the time is measured in seconds. Placing position on the y-axis and time on the x-axis, the slope of the curve is given by: v = Δ y Δ x = Δ s Δ t . {\displaystyle v={\frac {\Delta y}{\Delta x}}={\frac {\Delta s}{\Delta t}}.} | https://en.wikipedia.org/wiki/Velocity_vs._time_graph |
Here s {\displaystyle s} is the position of the object, and t {\displaystyle t} is the time. Therefore, the slope of the curve gives the change in position divided by the change in time, which is the definition of the average velocity for that interval of time on the graph. If this interval is made to be infinitesimally small, such that Δ s {\displaystyle {\Delta s}} becomes d s {\displaystyle {ds}} and Δ t {\displaystyle {\Delta t}} becomes d t {\displaystyle {dt}} , the result is the instantaneous velocity at time t {\displaystyle t} , or the derivative of the position with respect to time. | https://en.wikipedia.org/wiki/Velocity_vs._time_graph |
A similar fact also holds true for the velocity vs. time graph. The slope of a velocity vs. time graph is acceleration, this time, placing velocity on the y-axis and time on the x-axis. Again the slope of a line is change in y {\displaystyle y} over change in x {\displaystyle x}: a = Δ y Δ x = Δ v Δ t {\displaystyle a={\frac {\Delta y}{\Delta x}}={\frac {\Delta v}{\Delta t}}} where v {\displaystyle v} is the velocity, and t {\displaystyle t} is the time. | https://en.wikipedia.org/wiki/Velocity_vs._time_graph |
This slope therefore defines the average acceleration over the interval, and reducing the interval infinitesimally gives d v d t {\displaystyle {\begin{matrix}{\frac {dv}{dt}}\end{matrix}}} , the instantaneous acceleration at time t {\displaystyle t} , or the derivative of the velocity with respect to time (or the second derivative of the position with respect to time). In SI, this slope or derivative is expressed in the units of meters per second per second ( m / s 2 {\displaystyle \mathrm {m/s^{2}} } , usually termed "meters per second-squared"). Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. | https://en.wikipedia.org/wiki/Velocity_vs._time_graph |
(Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.) The same multiplication rule holds true for acceleration vs. time graphs. When acceleration is multiplied | https://en.wikipedia.org/wiki/Velocity_vs._time_graph |
In mechanics, the eigenvectors of the moment of inertia tensor define the principal axes of a rigid body. The tensor of moment of inertia is a key quantity required to determine the rotation of a rigid body around its center of mass. | https://en.wikipedia.org/wiki/Left_eigenvector |
In mechanics, the flexural modulus or bending modulus is an intensive property that is computed as the ratio of stress to strain in flexural deformation, or the tendency for a material to resist bending. It is determined from the slope of a stress-strain curve produced by a flexural test (such as the ASTM D790), and uses units of force per area. The flexural modulus defined using the 2-point (cantilever) and 3-point bend tests assumes a linear stress strain response. | https://en.wikipedia.org/wiki/Flexural_modulus |
For a 3-point test of a rectangular beam behaving as an isotropic linear material, where w and h are the width and height of the beam, I is the second moment of area of the beam's cross-section, L is the distance between the two outer supports, and d is the deflection due to the load F applied at the middle of the beam, the flexural modulus: E f l e x = L 3 F 4 w h 3 d {\displaystyle E_{\mathrm {flex} }={\frac {L^{3}F}{4wh^{3}d}}} From elastic beam theory d = L 3 F 48 I E {\displaystyle d={\frac {L^{3}F}{48IE}}} and for rectangular beam I = 1 12 w h 3 {\displaystyle I={\frac {1}{12}}wh^{3}} thus E f l e x = E {\displaystyle E_{\mathrm {flex} }=E} (Elastic modulus) For very small strains in isotropic materials like glass, metal or polymer, flexural or bending modulus of elasticity is equivalent to the tensile modulus (Young's modulus) or compressive modulus of elasticity. However, in anisotropic materials, for example wood, these values may not be equivalent. Moreover, composite materials like fiber-reinforced polymers or biological tissues are inhomogeneous combinations of two or more materials, each with different material properties, therefore their tensile, compressive, and flexural moduli usually are not equivalent. | https://en.wikipedia.org/wiki/Flexural_modulus |
In mechanics, the net force is the sum of all the forces acting on an object. For example, if two forces are acting upon an object in opposite directions, and one force is greater than the other, the forces can be replaced with a single force that is the difference of the greater and smaller force. That force is the net force.When forces act upon an object, they change its acceleration. The net force is the combined effect of all the forces on the object's acceleration, as described by Newton's second law of motion. | https://en.wikipedia.org/wiki/Net_force |
When the net force is applied at a specific point on an object, the associated torque can be calculated. The sum of the net force and torque is called the resultant force, which causes the object to rotate in the same way as all the forces acting upon it would if they were applied individually.It is possible for all the forces acting upon an object to produce no torque at all. This happens when the net force is applied along the line of action. | https://en.wikipedia.org/wiki/Net_force |
In some texts, the terms resultant force and net force are used as if they mean the same thing. This is not always true, especially when in complex topics like the motion of spinning objects or situations where everything is perfectly balanced, known as static equilibrium. In these cases, it's important to understand that "net force" and "resultant force" can have distinct meanings. | https://en.wikipedia.org/wiki/Net_force |
In mechanics, the neutral plane or neutral surface is a conceptual plane within a beam or cantilever. When loaded by a bending force, the beam bends so that the inner surface is in compression and the outer surface is in tension. The neutral plane is the surface within the beam between these zones, where the material of the beam is not under stress, either compression or tension.As there is no lengthwise stress force on the neutral plane, there is no strain or extension either: when the beam bends, the length of the neutral plane remains constant. Any line within the neutral plane parallel to the axis of the beam is called the deflection curve of the beam. | https://en.wikipedia.org/wiki/Neutral_plane |
To show that every beam must have a neutral plane, the material of the beam can be imagined to be divided into narrow fibers parallel to its length. When the beam is bent, at any given cross-section the region of fibers near the concave side will be under compression, while the region near the convex side will be under tension. Because the stress in the material must be continuous across any cross section, there must be a boundary between the regions of compression and tension at which the fibers have no stress. This is the neutral plane. | https://en.wikipedia.org/wiki/Neutral_plane |
In mechanics, the normal force F n {\displaystyle F_{n}} is the component of a contact force that is perpendicular to the surface that an object contacts, as in Figure 1. In this instance normal is used in the geometric sense and means perpendicular, as opposed to the common language use of normal meaning "ordinary" or "expected". A person standing still on a platform is acted upon by gravity, which would pull them down towards the Earth's core unless there were a countervailing force from the resistance of the platform's molecules, a force which is named the "normal force". | https://en.wikipedia.org/wiki/Normal_force |
The normal force is one type of ground reaction force. If the person stands on a slope and does not sink into the ground or slide downhill, the total ground reaction force can be divided into two components: a normal force perpendicular to the ground and a frictional force parallel to the ground. In another common situation, if an object hits a surface with some speed, and the surface can withstand the impact, the normal force provides for a rapid deceleration, which will depend on the flexibility of the surface and the object. | https://en.wikipedia.org/wiki/Normal_force |
In mechanics, the quantities in the CGS and SI systems are defined identically. The two systems differ only in the scale of the three base units (centimetre versus metre and gram versus kilogram, respectively), with the third unit (second) being the same in both systems. There is a direct correspondence between the base units of mechanics in CGS and SI. Since the formulae expressing the laws of mechanics are the same in both systems and since both systems are coherent, the definitions of all coherent derived units in terms of the base units are the same in both systems, and there is an unambiguous correspondence of derived units: v = d x d t {\displaystyle v={\frac {dx}{dt}}} (definition of velocity) F = m d 2 x d t 2 {\displaystyle F=m{\frac {d^{2}x}{dt^{2}}}} (Newton's second law of motion) E = ∫ F → ⋅ d x → {\displaystyle E=\int {\vec {F}}\cdot d{\vec {x}}} (energy defined in terms of work) p = F L 2 {\displaystyle p={\frac {F}{L^{2}}}} (pressure defined as force per unit area) η = τ / d v d x {\displaystyle \eta =\tau /{\frac {dv}{dx}}} (dynamic viscosity defined as shear stress per unit velocity gradient).Thus, for example, the CGS unit of pressure, barye, is related to the CGS base units of length, mass, and time in the same way as the SI unit of pressure, pascal, is related to the SI base units of length, mass, and time: 1 unit of pressure = 1 unit of force/(1 unit of length)2 = 1 unit of mass/(1 unit of length⋅(1 unit of time)2) 1 Ba = 1 g/(cm⋅s2) 1 Pa = 1 kg/(m⋅s2).Expressing a CGS derived unit in terms of the SI base units, or vice versa, requires combining the scale factors that relate the two systems: 1 Ba = 1 g/(cm⋅s2) = 10−3 kg / (10−2 m⋅s2) = 10−1 kg/(m⋅s2) = 10−1 Pa. | https://en.wikipedia.org/wiki/Centimeter_gram_second_system_of_units |
In mechanics, two or more springs are said to be in series when they are connected end-to-end or point to point, and it is said to be in parallel when they are connected side-by-side; in both cases, so as to act as a single spring: More generally, two or more springs are in series when any external stress applied to the ensemble gets applied to each spring without change of magnitude, and the amount strain (deformation) of the ensemble is the sum of the strains of the individual springs. Conversely, they are said to be in parallel if the strain of the ensemble is their common strain, and the stress of the ensemble is the sum of their stresses. Any combination of Hookean (linear-response) springs in series or parallel behaves like a single Hookean spring. The formulas for combining their physical attributes are analogous to those that apply to capacitors connected in series or parallel in an electrical circuit. | https://en.wikipedia.org/wiki/Series_and_parallel_springs |
In mechanics, virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement is different for different displacements. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action. | https://en.wikipedia.org/wiki/Virtual_work |
This displacement is therefore the displacement followed by the particle according to the principle of least action. The work of a force on a particle along a virtual displacement is known as the virtual work. Historically, virtual work and the associated calculus of variations were formulated to analyze systems of rigid bodies, but they have also been developed for the study of the mechanics of deformable bodies. | https://en.wikipedia.org/wiki/Virtual_work |
In mechanism design and auction theory, a profit extraction mechanism (also called profit extractor or revenue extractor) is a truthful mechanism whose goal is to win a pre-specified amount of profit, if it is possible. : 347 | https://en.wikipedia.org/wiki/Profit_extraction_mechanism |
In mechanism design, a Vickrey–Clarke–Groves (VCG) mechanism is a generic truthful mechanism for achieving a socially-optimal solution. It is a generalization of a Vickrey–Clarke–Groves auction. A VCG auction performs a specific task: dividing items among people. A VCG mechanism is more general: it can be used to select any outcome out of a set of possible outcomes. : 216–233 | https://en.wikipedia.org/wiki/Vickrey–Clarke–Groves_mechanism |
In mechanism design, a branch of economics, a budget-feasible mechanism is a mechanism in which the total payment made by the auctioneer is upper-bounded by a fixed pre-specified budget. They were first presented by Yaron Singer, and studied by several others. == References == | https://en.wikipedia.org/wiki/Budget-feasible_mechanism |
In mechanism design, a branch of economics, a weakly-budget-balanced (WBB) mechanism is a mechanism in which the total payment made by the participants is at least 0. This means that the mechanism operator does not incur a deficit, i.e., does not have to subsidize the market. Weak budget balance is considered a necessary requirement for the economic feasibility of a mechanism. | https://en.wikipedia.org/wiki/Budget-balanced_mechanism |
A strongly-budget-balanced (SBB) mechanism is a mechanism in which the total payment made by the participants is exactly 0. This means that all payments are made among the participants - the mechanism has neither a deficit nor a surplus. The term budget-balanced mechanism is sometimes used as a shorthand for WBB, and sometimes as a shorthand for SBB. | https://en.wikipedia.org/wiki/Budget-balanced_mechanism |
In mechanism design, an agent is said to have single-parameter utility if his valuation of the possible outcomes can be represented by a single number. For example, in an auction for a single item, the utilities of all agents are single-parametric, since they can be represented by their monetary evaluation of the item. In contrast, in a combinatorial auction for two or more related items, the utilities are usually not single-parametric, since they are usually represented by their evaluations to all possible bundles of items. | https://en.wikipedia.org/wiki/Single-parametric_utility |
In mechanism design, implementability is a property of a social choice function. It means that there is an incentive-compatible mechanism that attains ("implements") this function. There are several degrees of implementability, corresponding to the different degrees of incentive-compatibility, e.g: A function is dominant-strategy implementable if it is attainable by a mechanism which is dominant-strategy-incentive-compatible (also called strategyproof). | https://en.wikipedia.org/wiki/Implementability_(mechanism_design) |
A function is Bayesian-Nash implementable if it is attainable by a mechanism which is Bayesian-Nash-incentive-compatible.See for a recent reference. In some textbooks, the entire field of mechanism design is called Implementation theory. == References == | https://en.wikipedia.org/wiki/Implementability_(mechanism_design) |
In mechanism design, monotonicity is a property of a social choice function. It is a necessary condition for being able to implement the function using a strategyproof mechanism. Its verbal description is: If changing one agent's type (while keeping the types of other agents fixed) changes the outcome under the social choice function, then the resulting difference in utilities of the new and original outcomes evaluated at the new type of this agent must be at least as much as this difference in utilities evaluated at the original type of this agent. In other words:: 227 If the social choice changes when a single player changes his valuation, then it must be because the player increased his value of the new choice relative to his value of the old choice. | https://en.wikipedia.org/wiki/Monotonicity_(mechanism_design) |
In mechanism design, the term single-crossing condition (often referred to as the Spence-Mirrlees property for Michael Spence and James Mirrlees, sometimes as the constant-sign assumption) refers to the requirement that the isoutility curve for agents of different types cross only once. This condition guarantees that the transfer in an incentive-compatible direct mechanism can be pinned down by the transfer of the lowest type. This condition is similar to another condition called strict increasing difference (SID). Formally, suppose the agent has a utility function V ( q , θ ) {\displaystyle V(q,\theta )} , the SID says ∀ q 2 > q 1 , θ 2 > θ 1 {\displaystyle \forall q_{2}>q_{1},\theta _{2}>\theta _{1}} we have V ( q 2 , θ 2 ) − V ( q 1 , θ 2 ) > V ( q 2 , θ 1 ) − V ( q 1 , θ 1 ) {\displaystyle V(q_{2},\theta _{2})-V(q_{1},\theta _{2})>V(q_{2},\theta _{1})-V(q_{1},\theta _{1})} . The Spence-Mirrlees Property is characterized by ∂ 2 V ∂ θ ∂ q ( q , θ ) > 0 {\displaystyle {\frac {\partial ^{2}V}{\partial \theta \partial q}}(q,\theta )>0} . | https://en.wikipedia.org/wiki/Single-crossing_condition |
In media and popular culture, lawn jockeys sometimes appear as a prop or conversation piece, in most cases merely trivial and non-notable in nature, although notable racial connotations are often associated with earlier examples of lawn jockeys versus more modern contemporary examples. Sometimes a reference to a lawn jockey is used to illustrate a racist or race-based point in popular culture. For example, in a Season 1 episode of The Golden Girls, Sophia makes a subtle hint at Blanche's Southern American roots being steeped in racism, suggesting to the woman that she "tar and feather the neighbour's lawn jockey" in order to make her father feel at home during his visit to the more liberal city of Miami, Florida. In All in the Family, the gift of a black lawn jockey is bestowed to main character Archie Bunker to annoy him, owing to his reputed racial bigotry, although in an unexpected twist, Archie actually finds the racist gift inappropriate and bothersome, refusing to put it out on his own property. | https://en.wikipedia.org/wiki/Lawn_jockey |
In Season 1, episode 13 of Maude, Arthur refers to a black man protesting slumlords on Maude's front lawn as "so much more animated than those little black jockeys". Lawn jockeys are often associated with wealthy white American families in popular culture, either for satire and sociopolitical symbolism, or for legitimate aesthetic appeal. Examples of this trend include, but are not limited to, the following: Raymond Chandler's 1942 Philip Marlowe novel The High Window features a lawn jockey decorating the Pasadena home of Marlowe's clients, the wealthy but dysfunctional Murdock family. | https://en.wikipedia.org/wiki/Lawn_jockey |
Marlowe sardonically speaks to the statue several times, regarding it as the family's stablest member. A black lawn jockey plays a symbolic role (as well as providing the story's title, in the protagonist's Southern vernacular) in Flannery O'Connor's 1955 short story "The Artificial Nigger". A lawn jockey comes to life Stephen King's 2008 novel Duma Key. | https://en.wikipedia.org/wiki/Lawn_jockey |
The Negro (Le nèg'), a 2002 film by Québécois director Robert Morin, about a black adolescent who resents lawn jockeys as racist and destroys one, resulting in his murder. A lawn jockey and images of lawn jockeys appear in several episodes of Dear White People. A lawn jockey was seen in Home Alone getting knocked over three times by cars. | https://en.wikipedia.org/wiki/Lawn_jockey |
A lawn jockey that comes alive is one of the enemies found in the video game Paperboy. Lawn jockeys are often referenced in relation to Blanche Devereaux's Southern family in The Golden Girls, often as a subtle implication that Blanche's family (who lived on a plantation and, historically, owned slaves) are racist. Despite this, Blanche is not racist herself, nor are her children or her father, "Big Daddy" Hollingsworth. It is said at one point that Big Daddy's father, Grandpappy Hollingsworth of Alabama, would get drunk and order a black lawn jockey on the property to "do a little dance".The central character in Frank Zappa's song "Uncle Remus" is a student protester who vows to visit Beverly Hills in the night and "knock the lawn jockeys off the rich people's lawn, And before they get up I'll be gone, I'll be gone". | https://en.wikipedia.org/wiki/Lawn_jockey |
In media new methodology was named "Rotterdam plus". In this verbal construction “Rotterdam” means coal index price, and "plus" means logistic costs for delivering coal from port of Rotterdam to Ukraine's thermal power plants. | https://en.wikipedia.org/wiki/Rotterdam_plus |
In media planning, reach is one of the most important factors, as the whole media planning is all about reach. The Purpose of the reach is exposure of brand (Belch & Belch, 2012). The higher the reach; the higher the brand exposure (Belch & Belch, 2012). And of course, higher exposure means high chances of new customers. | https://en.wikipedia.org/wiki/Media_planning |
When it comes to media planning most of the businesses decide well in advanced what their target market would be (Belch & Belch, 2012). They Choose their target market on the assumption that they already know who their customers would be (Ossi, 2015). Even though, choosing a target market for reach in media planning could be a very successful way to get to the potential customers of the brand, but this method leaves out potential customers outside of the target market; Customers the brand thought were not important to reach to (Ossi, 2015). | https://en.wikipedia.org/wiki/Media_planning |
Smart businesses also reach outside of their targeted market in order to know other segments that could be targeted (Ossi, 2015). Therefore, starting with a broader reach and then choosing target markets would be a much-informed decision; derived from actual data rather than just assumption. A broader reach is also beneficial for general brand awareness, otherwise many people outside of the targeted market never even get to hear about the brand. | https://en.wikipedia.org/wiki/Media_planning |
In media planning, frequency is also a very important factor to consider. Most small businesses say "We just want to see what happens", which just wastes their money leading to disappointment on media planning ("The importance of frequency," n.d.). In Advertisement, once is just not enough ("The importance of frequency," n.d.). | https://en.wikipedia.org/wiki/Media_planning |
The biggest problem in media planning is; advertisers assume that someone would see their advertisement, would walk in their store and just buy something! !That is definitely not how it happens. | https://en.wikipedia.org/wiki/Media_planning |
There are five different steps for buying cycle a consumer goes through before actually purchasing something (Euan, 2013). These are awareness, interest, need, comparison and purchase ("The importance of frequency," n.d.). Frequency is important as it pushes a consumer towards the actual step of purchasing something. | https://en.wikipedia.org/wiki/Media_planning |
The understanding of how exactly a consumer goes through the buying cycle is very essential to grasp the importance of frequency in media planning. Initially, the idea of reach is there to increase the awareness and exposure, but people forget. 80% of people forget the advertisement they see within 24 hours or even sooner ("The importance of frequency when advertising," 2016). | https://en.wikipedia.org/wiki/Media_planning |
So, frequency is also important for awareness - decreasing the chances for forgetfulness. Secondly, frequency builds familiarity, familiarity builds trust ("The importance of frequency," n.d.) and trust builds interest. | https://en.wikipedia.org/wiki/Media_planning |
In need, it is absolute that the consumer is aware of the company and have somewhat trust/ interest. And again, frequency plays essential role is remembrance, trust and interest. Higher frequency also helps to beat the competition ("The importance of frequency when advertising," 2016). | https://en.wikipedia.org/wiki/Media_planning |
And finally, the consumer is on the final step of buying cycle the purchase, with the help of frequent advertisement. Without the good amount of frequency, a consumer would be very unlikely to get to the purchasing step. Thus, frequency is important because consistence advertisement reinforces top of mind brand awareness, brand favorability and brand loyalty among the current and potential consumers. Patience and effective frequency plays a great role in a business's long-term success. | https://en.wikipedia.org/wiki/Media_planning |
In media reports, people have attributed unexpected effects of increasing fear and anxiety, panic or "meltdowns" after practicing, which they suggest could expose bipolar vulnerability or repressed PTSD symptoms. However, according to published peer-reviewed academic articles, these negative effects of meditation are rare for mindfulness meditation, and appear to happen due to a poor understanding of what actually constitutes mindfulness/meditation practices. | https://en.wikipedia.org/wiki/Mindfulness_meditation |
In media server applications, it is often necessary for several call legs to interact with each other, for example in a multi-party conference. Some deficiencies were identified in VoiceXML for this application and so companies designed specific scripting languages to deal with this environment. The Media Server Markup Language (MSML) was Convedia's solution, and Media Server Control Markup Language (MSCML) was Snowshore's solution. Snowshore is now owned by Dialogic and Convedia is now owned by Radisys. | https://en.wikipedia.org/wiki/VoiceXML |
These languages also contain 'hooks' so that external scripts (like VoiceXML) can run on call legs where IVR functionality is required. There was an IETF working group called mediactrl ("media control") that was working on a successor for these scripting systems, which it is hoped will progress to an open and widely adopted standard. The mediactrl working group concluded in 2013. | https://en.wikipedia.org/wiki/VoiceXML |
In media studies, concision is a form of broadcast media censorship by limiting debate and discussion of important topics on the rationale of time allotment.Media critics such as Noam Chomsky contend that this practice, especially on commercial broadcasts with advertising, encourages broadcasters to exclude people and ideas that they judge cannot conform to the time limits of a particular program. This leads to a limited number of "the usual suspects" who will say expected ideas that will not require extensive explanation such as mainstream political ones. The beauty of concision, you know, saying a couple of sentences between two commercials, the beauty of that is you can only repeat conventional thoughts. Suppose I go on Nightline, whatever it is, two minutes, and I say Gaddafi is a terrorist, Khomeini is a murderer etcetera etcetera... I don't need any evidence, everyone just nods. | https://en.wikipedia.org/wiki/Concision_(media_studies) |
On the other hand, suppose you're saying something that isn't just regurgitating conventional pieties, suppose you say something that's the least bit unexpected or controversial, people will quite reasonably expect to know what you mean. If you said that you'd better have a reason, better have some evidence. You can't give evidence if you're stuck with concision. | https://en.wikipedia.org/wiki/Concision_(media_studies) |
That's the genius of this structural constraint. Furthermore, introducing controversial or unexpected statements that do not conform to those conventional ideas are discouraged as time inefficient because the person will be required to explain and support them in detail. Since this can often take considerable time in itself and digress from the primary discussion topic of the broadcast, this is discouraged. Alternatively, the explanation could be subject to extensive editing for time which could lead to an inadequate presentation of the subject's thoughts. | https://en.wikipedia.org/wiki/Concision_(media_studies) |
In media studies, mass communication, media psychology, communication theory, and sociology, media influence and media effects are topics relating to mass media and media culture's effects on individual or an audience's thoughts, attitudes, and behavior. Whether it is written, televised, or spoken, mass media reaches a large audience. Mass media's role and effect in shaping modern culture are central issues for study of culture. | https://en.wikipedia.org/wiki/Uses_and_gratifications_theory |
In media studies, mass communication, media psychology, communication theory, and sociology, media influence and the media effect are topics relating to mass media and media culture's effects on individuals' or audiences' thoughts, attitudes, and behaviors. Through written, televised, or spoken channels, mass media reach large audiences. Mass media's role in shaping modern culture is a central issue for the study of culture.Media influence is the actual force exerted by a media message, resulting in either a change or reinforcement in audience or individual beliefs. Whether a media message has an effect on any of its audience members is contingent on many factors, including audience demographics and psychological characteristics. | https://en.wikipedia.org/wiki/Media_influence |
These effects can be positive or negative, abrupt or gradual, short-term or long-lasting. Not all effects result in change; some media messages reinforce an existing belief. | https://en.wikipedia.org/wiki/Media_influence |
Researchers examine an audience after media exposure for changes in cognition, belief systems, and attitudes, as well as emotional, physiological and behavioral effects. The influences of mass media (or 'media effects') are observed in various aspects of human life, from voting behaviors to perceptions of violence, from evaluations of scientists to our understanding of others' opinions. The overall influence of mass media has changed drastically over the years, and will continue to do so as the media itself develops. | https://en.wikipedia.org/wiki/Media_influence |
In the new media environment, we have dual identities - consumers and creators. We not only obtain information through new media, but also disseminate information to wide audiences.Further, the influence of the media on the psychosocial development of children is profound. Thus, it is important for physicians to discuss with parents their child's exposure to media and to provide guidance on age-appropriate use of any media, including television, radio, music, video games and the Internet.There are several scholarly studies which addresses media and its effects. | https://en.wikipedia.org/wiki/Media_influence |
Bryant and Zillmann defined media effects as "the social, cultural, and psychological impact of communicating via the mass media". Perse stated that media effects researchers study "how to control, enhance, or mitigate the impact of the mass media on individuals and society". Lang stated media effects researchers study "what types of content, in what type of medium, affect which people, in what situations". McLuhan points out in his media ecology theory that "The medium is the message." | https://en.wikipedia.org/wiki/Media_influence |
In media terms, an interview disc is a recorded disc with spoken word recordings in an interview style format, with a specific person or group of people, as opposed to the usual music features. The source of the recording can vary. | https://en.wikipedia.org/wiki/Interview_disc |
In media the term "to silhouette" is used for the process of separating or masking a portion of an image (such as the background) so that it does not show. Traditionally silhouettes have often been used in advertising, particularly in poster design, because they can be cheaply and effectively printed. | https://en.wikipedia.org/wiki/Silhouette |
In media where italicization is not possible, alternatives are used as substitutes: In typewritten or handwritten text, underlining is typically used. In plain-text computer files, including e-mail communication, italicised words are often indicated by surrounding them with slashes or other matched delimiters. For example: I was /really/ annoyed. | https://en.wikipedia.org/wiki/Italic_type |
They >completely< forgot me! I had _nothing_ to do with it. (Commonly interpreted as underlining, which is an alternative to italics.) | https://en.wikipedia.org/wiki/Italic_type |
It was *absolutely* horrible. (Commonly interpreted as bold. This and the previous example signify italic in Markdown, where bolding uses **double asterisks**, and underlining uses __double underscores__.) | https://en.wikipedia.org/wiki/Italic_type |
Where the italics do not indicate emphasis, but are marking a title or where a word is being mentioned, quotation marks may be substituted: The word "the" is an article. The term "even number" refers to a number that is a multiple of 2. The novel "Fahrenheit 451" was written by Ray Bradbury. | https://en.wikipedia.org/wiki/Italic_type |
In media, to frame is "to select some aspects of a perceived reality and make them more salient in a communication context, in such a way as to promote a particular problem definition, casual interpretation, moral evaluation, and/or treatment recommendation for the item described". The role framing plays in the effects of media presentation has been widely discussed, with the central notion that associated perceptions of factual information can vary based upon the presentation of the information. Often times journalists do not necessarily develop and use these frames consciously, but they are used as a way to organize ideas and suggest what is an issue in the media. | https://en.wikipedia.org/wiki/Framing_effect |
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