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0 {\displaystyle \lambda =0} corresponds to the trivial case of no collision. Substituting the non trivial value of λ {\displaystyle \lambda } in (3) we get the desired result (1). Since all equations are in vectorial form, this derivation is valid also for three dimensions with spheres. == See also == Collision Inelas... | {
"page_id": 65907,
"source": null,
"title": "Elastic collision"
} |
An inelastic collision, in contrast to an elastic collision, is a collision in which kinetic energy is not conserved due to the action of internal friction. In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect, and the bodies are deformed. The... | {
"page_id": 65908,
"source": null,
"title": "Inelastic collision"
} |
nucleus. However, in the case of the proton, the evidence suggested three distinct concentrations of charge (quarks) and not one. == Formula == The formula for the velocities after a one-dimensional collision is: v a = C R m b ( u b − u a ) + m a u a + m b u b m a + m b v b = C R m a ( u a − u b ) + m a u a + m b u b m... | {
"page_id": 65908,
"source": null,
"title": "Inelastic collision"
} |
this gives the velocity updates: Δ v a → = J n m a n → Δ v b → = − J n m b n → {\displaystyle {\begin{aligned}\Delta {\vec {v_{a}}}&={\frac {J_{n}}{m_{a}}}{\vec {n}}\\\Delta {\vec {v_{b}}}&=-{\frac {J_{n}}{m_{b}}}{\vec {n}}\end{aligned}}} == Perfectly inelastic collision == A perfectly inelastic collision occurs when t... | {
"page_id": 65908,
"source": null,
"title": "Inelastic collision"
} |
is zero. In this frame most of the kinetic energy before the collision is that of the particle with the smaller mass. In another frame, in addition to the reduction of kinetic energy there may be a transfer of kinetic energy from one particle to the other; the fact that this depends on the frame shows how relative this... | {
"page_id": 65908,
"source": null,
"title": "Inelastic collision"
} |
In physics and in particular in the theory of magnetism, an antidynamo theorem is one of several results that restrict the type of magnetic fields that may be produced by dynamo action. One notable example is Thomas Cowling's antidynamo theorem which states that no axisymmetric magnetic field can be maintained through ... | {
"page_id": 32244084,
"source": null,
"title": "Antidynamo theorem"
} |
Maleic hydrazide, often known by the brand name Fazor, is a plant growth regulator that reduces growth through preventing cell division but not cell enlargement. It is applied to the foliage of potato, onion, garlic and carrot crops to prevent sprouting during storage. It can also be used to control volunteer potatoes ... | {
"page_id": 67895670,
"source": null,
"title": "Maleic hydrazide"
} |
Swallowing, also called deglutition or inglutition in scientific and medical contexts, is a physical process of an animal's digestive tract (e.g. that of a human body) that allows for an ingested substance (typically food) to pass from the mouth to the pharynx and then into the esophagus. In colloquial English, the ter... | {
"page_id": 196983,
"source": null,
"title": "Swallowing"
} |
of health care for people with difficulty in swallowing (dysphagia), it is an interesting topic with extensive scientific literature. === Coordination and control === Eating and swallowing are complex neuromuscular activities consisting essentially of three phases, an oral, pharyngeal and esophageal phase. Each phase i... | {
"page_id": 196983,
"source": null,
"title": "Swallowing"
} |
is moved from one side of the oral cavity to the other by the tongue. Buccinator (VII) helps to contain the food against the occlusal surfaces of the teeth. The bolus is ready for swallowing when it is held together by saliva (largely mucus), sensed by the lingual nerve of the tongue (VII—chorda tympani and IX—lesser p... | {
"page_id": 196983,
"source": null,
"title": "Swallowing"
} |
is IX and efferent limb is the pharyngeal plexus- IX and X). They are scattered over the base of the tongue, the palatoglossal and palatopharyngeal arches, the tonsillar fossa, uvula and posterior pharyngeal wall. Stimuli from the receptors of this phase then provoke the pharyngeal phase. In fact, it has been shown tha... | {
"page_id": 196983,
"source": null,
"title": "Swallowing"
} |
auditory tube, which equalises the pressure between the nasopharynx and the middle ear. This does not contribute to swallowing, but happens as a consequence of it. 8) Closure of the oropharynx The oropharynx is kept closed by palatoglossus (pharyngeal plexus—IX, X), the intrinsic muscles of tongue (XII) and styloglossu... | {
"page_id": 196983,
"source": null,
"title": "Swallowing"
} |
X) and inferior constrictor (pharyngeal plexus—IX, X). This phase is passively controlled reflexively and involves cranial nerves V, X (vagus), XI (accessory) and XII (hypoglossal). The respiratory center of the medulla is directly inhibited by the swallowing center for the very brief time that it takes to swallow. Thi... | {
"page_id": 196983,
"source": null,
"title": "Swallowing"
} |
the bolus of food through the esophagus into the stomach. 13) Relaxation phase Finally the larynx and pharynx move down with the hyoid mostly by elastic recoil. Then the larynx and pharynx move down from the hyoid to their relaxed positions by elastic recoil. Swallowing therefore depends on coordinated interplay betwee... | {
"page_id": 196983,
"source": null,
"title": "Swallowing"
} |
down the esophagus. With a continuous motion, an individual forges breathing and priorities the swallowed matter. This intermediate level of muscle manipulation is similar to the techniques used by sword swallowers. == In non-mammal animals == In many birds, the esophagus is largely a mere gravity chute, and in such ev... | {
"page_id": 196983,
"source": null,
"title": "Swallowing"
} |
Nuclear Science and Techniques is a monthly peer-reviewed, scientific journal that is published by Science Press and Springer. This journal was established in 1990. The editor-in-chief is Yu-Gang Ma. The journal covers all theoretical and experimental aspects of nuclear physics and technology, including synchrotron rad... | {
"page_id": 40173942,
"source": null,
"title": "Nuclear Science and Techniques"
} |
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually ... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
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initial values, which fixes the values of the constants. Stated formally, in general, an equation of motion M is a function of the position r of the object, its velocity (the first time derivative of r, v = dr/dt), and its acceleration (the second derivative of r, a = d2r/dt2), and time t. Euclidean vectors in 3D a... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
the universe developed incrementally over three millennia, thanks to many thinkers, only some of whose names we know. In antiquity, priests, astrologers and astronomers predicted solar and lunar eclipses, the solstices and the equinoxes of the Sun and the period of the Moon. But they had nothing other than a set of alg... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
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and projectiles, without his proving these propositions or suggesting a formula relating time, velocity and distance. De Soto's comments are remarkably correct regarding the definitions of acceleration (acceleration was a rate of change of motion (velocity) in time) and the observation that acceleration would be negati... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
He formulated the principle of the parallelogram of forces, but he did not fully recognize its scope. Galileo also was interested by the laws of the pendulum, his first observations of which were as a young man. In 1583, while he was praying in the cathedral at Pisa, his attention was arrested by the motion of the grea... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
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particles. There are analogs of equations of motion in other areas of physics, for collections of physical phenomena that can be considered waves, fluids, or fields. == Kinematic equations for one particle == === Kinematic quantities === From the instantaneous position r = r(t), instantaneous meaning at an instant valu... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
rotation axis) and v the tangential velocity of the particle. For a rotating continuum rigid body, these relations hold for each point in the rigid body. === Uniform acceleration === The differential equation of motion for a particle of constant or uniform acceleration in a straight line is simple: the acceleration is ... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
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is sufficient to know three out of the five variables to calculate the remaining two. In some programs, such as the IGCSE Physics and IB DP Physics programs (international programs but especially popular in the UK and Europe), the same formulae would be written with a different set of preferred variables. There u repla... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
t 2 [ 5 ] {\displaystyle {\begin{aligned}\mathbf {v} &=\mathbf {a} t+\mathbf {v} _{0}&[1]\\\mathbf {r} &=\mathbf {r} _{0}+\mathbf {v} _{0}t+{\tfrac {1}{2}}\mathbf {a} t^{2}&[2]\\\mathbf {r} &=\mathbf {r} _{0}+{\tfrac {1}{2}}\left(\mathbf {v} +\mathbf {v} _{0}\right)t&[3]\\\mathbf {v} ^{2}&=\mathbf {v} _{0}^{2}+2\mathbf... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
vectors. Choosing s to measure up from the ground, the acceleration a must be in fact −g, since the force of gravity acts downwards and therefore also the acceleration on the ball due to it. At the highest point, the ball will be at rest: therefore v = 0. Using equation [4] in the set above, we have: s = v 2 − u 2 − 2 ... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
using the definitions of physical quantities above for angular velocity ω and angular acceleration α. These are instantaneous quantities which change with time. The position of the particle is r = r ( r ( t ) , θ ( t ) ) = r e ^ r {\displaystyle \mathbf {r} =\mathbf {r} \left(r(t),\theta (t)\right)=r\mathbf {\hat {e}} ... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
θ e ^ φ a = ( a − r ( d θ d t ) 2 − r ( d φ d t ) 2 sin 2 θ ) e ^ r + ( r d 2 θ d t 2 + 2 v d θ d t − r ( d φ d t ) 2 sin θ cos θ ) e ^ θ + ( r d 2 φ d t 2 sin θ + 2 v d φ d t sin θ + 2 r d θ d t d φ d t cos θ ) e ^ φ {\displaystyle {\begin{aligned}\mathbf {r} &=\mathbf {r} \left(t\right)=r\mathbf {\hat {e}... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
m is a constant in Newtonian mechanics. Newton's second law applies to point-like particles, and to all points in a rigid body. They also apply to each point in a mass continuum, like deformable solids or fluids, but the motion of the system must be accounted for; see material derivative. In the case the mass is not co... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
≠ j F i j {\displaystyle {\frac {d\mathbf {p} _{i}}{dt}}=\mathbf {F} _{E}+\sum _{i\neq j}\mathbf {F} _{ij}} where pi is the momentum of particle i, Fij is the force on particle i by particle j, and FE is the resultant external force due to any agent not part of system. Particle i does not exert a force on itself. Euler... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
a simple pendulum, − m g sin θ = m d 2 ( ℓ θ ) d t 2 ⇒ d 2 θ d t 2 = − g ℓ sin θ , {\displaystyle -mg\sin \theta =m{\frac {d^{2}(\ell \theta )}{dt^{2}}}\quad \Rightarrow \quad {\frac {d^{2}\theta }{dt^{2}}}=-{\frac {g}{\ell }}\sin \theta \,,} and a damped, sinusoidally driven harmonic oscillator, F 0 sin ( ω t ) ... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
( r j − r i ) {\displaystyle {\frac {d^{2}\mathbf {r} _{i}}{dt^{2}}}=G\sum _{i\neq j}{\frac {m_{j}}{|\mathbf {r} _{j}-\mathbf {r} _{i}|^{3}}}(\mathbf {r} _{j}-\mathbf {r} _{i})} where i = 1, 2, ..., N labels the quantities (mass, position, etc.) associated with each particle. == Analytical mechanics == Using all three ... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
\mathbf {q} }}\,,\quad \mathbf {\dot {q}} =+{\frac {\partial H}{\partial \mathbf {p} }}\,,} where the Hamiltonian H = H [ q ( t ) , p ( t ) , t ] , {\displaystyle H=H\left[\mathbf {q} (t),\mathbf {p} (t),t\right]\,,} is a function of the configuration q and conjugate "generalized" momenta p = ∂ L ∂ q ˙ , {\displaystyle... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
the action of a physical system has a corresponding conservation law, a theorem due to Emmy Noether. All classical equations of motion can be derived from the variational principle known as Hamilton's principle of least action δ S = 0 , {\displaystyle \delta S=0\,,} stating the path the system takes through the configu... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
of just mv, implying the motion of a charged particle is fundamentally determined by the mass and charge of the particle. The Lagrangian expression was first used to derive the force equation. Alternatively the Hamiltonian (and substituting into the equations): H = ( P − q A ) 2 2 m + q ϕ {\displaystyle H={\frac {\left... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
gravitational field - because gravity is a fictitious force. The relative acceleration of one geodesic to another in curved spacetime is given by the geodesic deviation equation: D 2 ξ α d s 2 = − R α β γ δ d x α d s ξ γ d x δ d s {\displaystyle {\frac {D^{2}\xi ^{\alpha }}{ds^{2}}}=-R^{\alpha }{}_{\beta \gamma \delta ... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
equations === Equations that describe the spatial dependence and time evolution of fields are called field equations. These include Maxwell's equations for the electromagnetic field, Poisson's equation for Newtonian gravitational or electrostatic field potentials, the Einstein field equation for gravitation (Newton's l... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
analogue of the classical equations of motion (Newton's law, Euler–Lagrange equation, Hamilton–Jacobi equation, etc.) is the Schrödinger equation in its most general form: i ℏ ∂ Ψ ∂ t = H ^ Ψ , {\displaystyle i\hbar {\frac {\partial \Psi }{\partial t}}={\hat {H}}\Psi \,,} where Ψ is the wavefunction of the system, Ĥ is... | {
"page_id": 65913,
"source": null,
"title": "Equations of motion"
} |
In vitro compartmentalization (IVC) is an emulsion-based technology that generates cell-like compartments in vitro. These compartments are designed such that each contains no more than one gene. When the gene is transcribed and/or translated, its products (RNAs and/or proteins) become 'trapped' with the encoding gene i... | {
"page_id": 15991162,
"source": null,
"title": "In vitro compartmentalization"
} |
For stable emulsion formation, a mixture of HLB (hydrophile-lipophile balance) and low HLB surfactants are needed. Some combinations of surfactants used to generate oil-surfactant mixture are mineral oil / 0.5% Tween 80 / 4.5% Span 80 / sodium deoxycholate and a more heat stable version, light mineral oil / 0.4% Tween ... | {
"page_id": 15991162,
"source": null,
"title": "In vitro compartmentalization"
} |
overexpression of a desired protein would be toxic to a host cell minimizing the utility of the transcription and translation mechanisms. IVC has used bacterial cell, wheat germ and rabbit reticulocyte (RRL) extracts for transcription and translation. It is also possible to use bacterial reconstituted translation syste... | {
"page_id": 15991162,
"source": null,
"title": "In vitro compartmentalization"
} |
protein. Two strategies have been demonstrated. The first is to form M.HaeIII fusion proteins. Each expressed protein/polypeptide will be in fusion with Hae III DNA methyltransferase domain, which is able to bind covalently to DNA fragments containing the sequence 5′-GGC*-3′, where C* is 5-fluoro-2 deoxycytidine. The s... | {
"page_id": 15991162,
"source": null,
"title": "In vitro compartmentalization"
} |
Hydrophobic and hydrophilic components can be delivered to each droplet in a step-wise fashion without compromising the chemical integrity of the droplet, and thus by controlling what to be added and when to be added, the reaction in each droplet is controlled. In addition, depending on the nature of the reaction to be... | {
"page_id": 15991162,
"source": null,
"title": "In vitro compartmentalization"
} |
Integrative and conjugative elements (ICEs) are mobile genetic elements present in both Gram-positive and Gram-negative bacteria. In a donor cell, ICEs are located primarily on the chromosome, but have the ability to excise themselves from the genome and transfer to recipient cells via bacterial conjugation. Due to the... | {
"page_id": 66978170,
"source": null,
"title": "Integrative and conjugative element"
} |
as regulatory genes. All integrative and conjugative elements encode integrases that are essential for controlling the excision, transfer and integration of an ICE. The representative example of ICE integrases is the integrase encoded by lambda phage. The transfer of an integrated ICE element from the donor to recipien... | {
"page_id": 66978170,
"source": null,
"title": "Integrative and conjugative element"
} |
The Vg1 ribozyme is a manganese dependent RNA enzyme or ribozyme which is the smallest ribozyme to be identified. It was identified in the 3′ UTR of Xenopus Vg1 mRNA transcripts and mouse beta-actin mRNA. This ribozyme was identified from in vitro studies that showed that the Vg1 mRNA was cleaved within the 3′ UTR in t... | {
"page_id": 24117627,
"source": null,
"title": "Vg1 ribozyme"
} |
Since the first printing of Carl Linnaeus's Species Plantarum in 1753, plants have been assigned one epithet or name for their species and one name for their genus, a grouping of related species. Many of these plants are listed in Stearn's Dictionary of Plant Names for Gardeners. William Stearn (1911–2001) was one of t... | {
"page_id": 65667453,
"source": null,
"title": "List of plant genus names with etymologies (A–C)"
} |
Citations == == References == Bayton, Ross (2020). The Gardener's Botanical: An Encyclopedia of Latin Plant Names. Princeton, New Jersey: Princeton University Press. ISBN 978-0-691-20017-0. Burkhardt, Lotte (2018). Verzeichnis eponymischer Pflanzennamen – Erweiterte Edition [Index of Eponymic Plant Names – Extended Edi... | {
"page_id": 65667453,
"source": null,
"title": "List of plant genus names with etymologies (A–C)"
} |
The molecular formula C5H5NS (molar mass: 111.16 g/mol, exact mass: 111.0143 u) may refer to: 2-Mercaptopyridine Thiazepines 1,2-Thiazepine 1,3-Thiazepine 1,4-Thiazepine | {
"page_id": 23921022,
"source": null,
"title": "C5H5NS"
} |
In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics. Kinematics is concerned with systems of specification of objects' positions and velocities and mathematica... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
thus has no physical basis. Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engineering, robotics, and biomechanics, kinematics is used to describe the motion of systems composed of joined parts (multi-link systems) such as an engine, a robotic... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
he constructed from the Greek κίνημα kinema ("movement, motion"), itself derived from κινεῖν kinein ("to move"). Kinematic and cinématique are related to the French word cinéma, but neither are directly derived from it. However, they do share a root word in common, as cinéma came from the shortened form of cinématograp... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
vector r {\displaystyle {\bf {r}}} can be expressed as r = ( x , y , z ) = x x ^ + y y ^ + z z ^ , {\displaystyle \mathbf {r} =(x,y,z)=x{\hat {\mathbf {x} }}+y{\hat {\mathbf {y} }}+z{\hat {\mathbf {z} }},} where x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} are the Cartesian coordinates and x ^ {\... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
a particle is a vector quantity that describes the direction as well as the magnitude of motion of the particle. More mathematically, the rate of change of the position vector of a point with respect to time is the velocity of the point. Consider the ratio formed by dividing the difference of two positions of a particl... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
a non-rotating frame of reference, the derivatives of the coordinate directions are not considered as their directions and magnitudes are constants. The speed of an object is the magnitude of its velocity. It is a scalar quantity: v = | v | = d s d t , {\displaystyle v=|\mathbf {v} |={\frac {{\text{d}}s}{{\text{d}}t}},... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
the time interval. The acceleration of the particle is the limit of the average acceleration as the time interval approaches zero, which is the time derivative, a = lim Δ t → 0 Δ v Δ t = d v d t = a x x ^ + a y y ^ + a z z ^ . {\displaystyle \mathbf {a} =\lim _{\Delta t\to 0}{\frac {\Delta \mathbf {v} }{\Delta t}}={\fr... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
_{B}} which is the difference between the components of their position vectors. If point A has position components r A = ( x A , y A , z A ) {\displaystyle \mathbf {r} _{A}=\left(x_{A},y_{A},z_{A}\right)} and point B has position components r B = ( x B , y B , z B ) {\displaystyle \mathbf {r} _{B}=\left(x_{B},y_{B},z_{... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
to another point B is simply the difference between their accelerations. a C / B = a C − a B {\displaystyle \mathbf {a} _{C/B}=\mathbf {a} _{C}-\mathbf {a} _{B}} which is the difference between the components of their accelerations. If point C has acceleration components a C = ( a C x , a C y , a C z ) {\displaystyle \... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
{v} +\mathbf {v} _{0}}{2}}\right)t.} A relationship between velocity, position and acceleration without explicit time dependence can be obtained by solving the average acceleration for time and substituting and simplifying t = v − v 0 a {\displaystyle t={\frac {\mathbf {v} -\mathbf {v} _{0}}{\mathbf {a} }}} ( r − r 0 )... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
magnitudes of the vectors | a | = a , | v | = v , | r − r 0 | = Δ r {\displaystyle |\mathbf {a} |=a,|\mathbf {v} |=v,|\mathbf {r} -\mathbf {r} _{0}|=\Delta r} where Δ r {\displaystyle \Delta r} can be any curvaceous path taken as the constant tangential acceleration is applied along that path, so v 2 = v 0 2 + 2 a Δ r ... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
{at^{2}}{2}}} . Adding v 0 t {\displaystyle v_{0}t} and a t 2 2 {\textstyle {\frac {at^{2}}{2}}} results in the equation Δ r {\displaystyle \Delta r} results in the equation Δ r = v 0 t + a t 2 2 {\textstyle \Delta r=v_{0}t+{\frac {at^{2}}{2}}} . This equation is applicable when the final velocity v is unknown. == Part... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
{y} }}+z(t){\hat {\mathbf {z} }},} where the constant distance from the center is denoted as r, and θ(t) is a function of time. The cylindrical coordinates for r(t) can be simplified by introducing the radial and tangential unit vectors, r ^ = cos ( θ ( t ) ) x ^ + sin ( θ ( t ) ) y ^ , θ ^ = − sin ( θ ( t ) ) x ... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
is not constrained to lie on a circular cylinder, so the radius R varies with time and the trajectory of the particle in cylindrical-polar coordinates becomes: r ( t ) = r ( t ) r ^ + z ( t ) z ^ . {\displaystyle \mathbf {r} (t)=r(t){\hat {\mathbf {r} }}+z(t){\hat {\mathbf {z} }}.} Where r, θ, and z might be continuous... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
}}} is called the Coriolis acceleration. === Constant radius === If the trajectory of the particle is constrained to lie on a cylinder, then the radius r is constant and the velocity and acceleration vectors simplify. The velocity of vP is the time derivative of the trajectory r(t), v P = d d t ( r r ^ + z z ^ ) = r ω ... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
a , {\displaystyle a_{r}=-v\theta ,\quad a_{\theta }=a,} are called, respectively, the radial and tangential components of acceleration. The notation for angular velocity and angular acceleration is often defined as ω = θ ˙ , α = θ ¨ , {\displaystyle \omega ={\dot {\theta }},\quad \alpha ={\ddot {\theta }},} so the rad... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
is called the special Euclidean group on Rn, and denoted SE(n). === Displacements and motion === The position of one component of a mechanical system relative to another is defined by introducing a reference frame, say M, on one that moves relative to a fixed frame, F, on the other. The rigid transformation, or displac... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
M is displaced by the translation vector d relative to the origin of F and rotated by the angle φ relative to the x-axis of F, the new coordinates in F of points in M are given by: P = [ T ( ϕ , d ) ] r = [ cos ϕ − sin ϕ d x sin ϕ cos ϕ d y 0 0 1 ] [ x y 1 ] . {\displaystyle \mathbf {P} =[T(\phi ,\mathbf {d} )]... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
}}(t)={\ddot {\mathbf {d} }}(t)=\mathbf {a} _{O},} where the dot denotes the derivative with respect to time and vO and aO are the velocity and acceleration, respectively, of the origin of the moving frame M. Recall the coordinate vector p in M is constant, so its derivative is zero. == Rotation of a body around a fixe... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
( t ) − 1 ] P = [ Ω ] P , {\displaystyle \mathbf {v} _{P}=[{\dot {A}}(t)][A(t)^{-1}]\mathbf {P} =[\Omega ]\mathbf {P} ,} where the matrix [ Ω ] = [ 0 − ω ω 0 ] , {\displaystyle [\Omega ]={\begin{bmatrix}0&-\omega \\\omega &0\end{bmatrix}},} is known as the angular velocity matrix of M relative to F. The parameter ω is ... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
velocity ω is the rate at which the angular position θ changes with respect to time t: ω = d θ d t {\displaystyle \omega ={\frac {{\text{d}}\theta }{{\text{d}}t}}} The angular velocity is represented in Figure 1 by a vector Ω pointing along the axis of rotation with magnitude ω and sense determined by the direction of ... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
in kinematics define the velocity and acceleration of points in a moving body as they trace trajectories in three-dimensional space. This is particularly important for the center of mass of a body, which is used to derive equations of motion using either Newton's second law or Lagrange's equations. === Position === In ... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
=== Velocity === The velocity of the point P along its trajectory P(t) is obtained as the time derivative of this position vector, v P = [ T ˙ ( t ) ] p = [ v P 0 ] = ( d d t [ A ( t ) d ( t ) 0 1 ] ) [ p 1 ] = [ A ˙ ( t ) d ˙ ( t ) 0 0 ] [ p 1 ] . {\displaystyle \mathbf {v} _{P}=[{\dot {T}}(t)]\mathbf {p} ={\begin{bma... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
{A}}&{\dot {\mathbf {d} }}\\0&0\end{bmatrix}}{\begin{bmatrix}A&\mathbf {d} \\0&1\end{bmatrix}}^{-1}{\begin{bmatrix}\mathbf {P} (t)\\1\end{bmatrix}}\\[4pt]&={\begin{bmatrix}{\dot {A}}&{\dot {\mathbf {d} }}\\0&0\end{bmatrix}}A^{-1}{\begin{bmatrix}1&-\mathbf {d} \\0&A\end{bmatrix}}{\begin{bmatrix}\mathbf {P} (t)\\1\end{bm... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
}}=[{\dot {S}}]\mathbf {P} +[S][S]\mathbf {P} .} This equation can be expanded firstly by computing [ S ˙ ] = [ Ω ˙ − Ω ˙ d − Ω d ˙ + d ¨ 0 0 ] = [ Ω ˙ − Ω ˙ d − Ω v O + A O 0 0 ] {\displaystyle [{\dot {S}}]={\begin{bmatrix}{\dot {\Omega }}&-{\dot {\Omega }}\mathbf {d} -\Omega {\dot {\mathbf {d} }}+{\ddot {\mathbf {d} ... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
constraints are constraints on the movement of components of a mechanical system. Kinematic constraints can be considered to have two basic forms, (i) constraints that arise from hinges, sliders and cam joints that define the construction of the system, called holonomic constraints, and (ii) constraints imposed on the ... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
that form a machine kinematic pairs. He distinguished between higher pairs which were said to have line contact between the two links and lower pairs that have area contact between the links. J. Phillips shows that there are many ways to construct pairs that do not fit this simple classification. ==== Lower pair ==== A... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
rotation about and slide along the axis. A spherical joint, or ball joint, requires that a point in the moving body maintain contact with a point in the fixed body. This joint has three degrees of freedom. A planar joint requires that a plane in the moving body maintain contact with a plane in fixed body. This joint ha... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
have a common joint; in the Stephenson topology, the two ternary links do not have a common joint and are connected by binary links. N = 8, j = 10 : eight-bar linkage with 16 different topologies; N = 10, j = 13 : ten-bar linkage with 230 different topologies; N = 12, j = 16 : twelve-bar linkage with 6,856 topologies. ... | {
"page_id": 65914,
"source": null,
"title": "Kinematics"
} |
In nuclear physics, a Borromean nucleus is an atomic nucleus comprising three bound components in which any subsystem of two components is unbound. This has the consequence that if one component is removed, the remaining two comprise an unbound resonance, so that the original nucleus is split into three parts. The name... | {
"page_id": 41615741,
"source": null,
"title": "Borromean nucleus"
} |
12C and 16O) may be clusters of alpha particles, having a similar structure to Borromean nuclei. As of 2012, the heaviest known Borromean nucleus was 29F. Heavier species along the neutron drip line have since been observed; these and undiscovered heavier nuclei along the drip line are also likely to be Borromean nucle... | {
"page_id": 41615741,
"source": null,
"title": "Borromean nucleus"
} |
Megvii (Chinese: 旷视; pinyin: Kuàngshì) is a Chinese technology company that designs image recognition and deep-learning software. Based in Beijing, the company develops artificial intelligence (AI) technology for businesses and for the public sector. Megvii is the largest provider of third-party authentication software... | {
"page_id": 60883332,
"source": null,
"title": "Megvii"
} |
Xinjiang. Human Rights Watch released a correction to its report in June 2019 stating that Megvii did not appear to have collaborated on IJOP, and that the Face++ code in the app was inoperable. In March 2020, Megvii announced that it would make its deep learning framework MegEngine open-source. As of 2024, Megvii oper... | {
"page_id": 60883332,
"source": null,
"title": "Megvii"
} |
The Frink Medal for British Zoologists is awarded by the Zoological Society of London "for significant and original contributions by a professional zoologist to the development of zoology." It consists of a bronze plaque (76 by 83 millimetres), depicting a bison and carved by British sculptor Elisabeth Frink. The Frink... | {
"page_id": 8192389,
"source": null,
"title": "Frink Medal"
} |
Mark and recapture is a method commonly used in ecology to estimate an animal population's size where it is impractical to count every individual. A portion of the population is captured, marked, and released. Later, another portion will be captured and the number of marked individuals within the sample is counted. Sin... | {
"page_id": 1507717,
"source": null,
"title": "Mark and recapture"
} |
captures another sample of individuals. Some individuals in this second sample will have been marked during the initial visit and are now known as recaptures. Other organisms captured during the second visit, will not have been captured during the first visit to the study area. These unmarked animals are usually given ... | {
"page_id": 1507717,
"source": null,
"title": "Mark and recapture"
} |
to the study area. This method assumes that the study population is "closed". In other words, the two visits to the study area are close enough in time so that no individuals die, are born, or move into or out of the study area between visits. The model also assumes that no marks fall off animals between visits to the ... | {
"page_id": 1507717,
"source": null,
"title": "Mark and recapture"
} |
An alternative less biased estimator of population size is given by the Chapman estimator: N ^ C = ( n + 1 ) ( K + 1 ) k + 1 − 1 {\displaystyle {\hat {N}}_{C}={\frac {(n+1)(K+1)}{k+1}}-1} === Sample calculation === The example (n, K, k) = (10, 15, 5) gives N ^ C = ( n + 1 ) ( K + 1 ) k + 1 − 1 = 11 × 16 6 − 1 = 28.3 {\... | {
"page_id": 1507717,
"source": null,
"title": "Mark and recapture"
} |
k + 0.5 ( n − k + 0.5 ) ( K − k + 0.5 ) . {\displaystyle {\hat {\sigma }}_{0.5}={\sqrt {{\frac {1}{k+0.5}}+{\frac {1}{K-k+0.5}}+{\frac {1}{n-k+0.5}}+{\frac {k+0.5}{(n-k+0.5)(K-k+0.5)}}}}.} The example (n, K, k) = (10, 15, 5) gives the estimate N ≈ 30 with a 95% confidence interval of 22 to 65. It has been shown that th... | {
"page_id": 1507717,
"source": null,
"title": "Mark and recapture"
} |
− f ) ( 1 − q ) , {\displaystyle P={\frac {5}{10}}fq+{\frac {5}{90}}(1-f)(1-q),} where the first term refers to the probability of detection (capture probability) in a high risk zone, and the latter term refers to the probability of detection in a low risk zone. Importantly, the formula can be re-written as a linear eq... | {
"page_id": 1507717,
"source": null,
"title": "Mark and recapture"
} |
models available for the analysis of these experiments. A simple model which easily accommodates the three source, or the three visit study, is to fit a Poisson regression model. Sophisticated mark-recapture models can be fit with several packages for the Open Source R programming language. These include "Spatially Exp... | {
"page_id": 1507717,
"source": null,
"title": "Mark and recapture"
} |
estimation to pond breeding salamanders". Transactions of the Illinois Academy of Science. 94 (2): 111–118. Royle, J. A.; R. M. Dorazio (2008). Hierarchical Modeling and Inference in Ecology. Elsevier. ISBN 978-1-930665-55-2. Seber, G.A.F. (2002). The Estimation of Animal Abundance and Related Parameters. Caldwel, New ... | {
"page_id": 1507717,
"source": null,
"title": "Mark and recapture"
} |
The molecular formula C20H27N3O6 (molar mass: 405.44 g/mol, exact mass: 405.1900 u) may refer to: Imidapril Febarbamate, or phenobamate | {
"page_id": 40960388,
"source": null,
"title": "C20H27N3O6"
} |
In many-body theory, the term Green's function (or Green function) is sometimes used interchangeably with correlation function, but refers specifically to correlators of field operators or creation and annihilation operators. The name comes from the Green's functions used to solve inhomogeneous differential equations, ... | {
"page_id": 7864709,
"source": null,
"title": "Green's function (many-body theory)"
} |
the Hermitian conjugate of the annihilation operator ψ ( x , τ ) {\displaystyle \psi (\mathbf {x} ,\tau )} .] In real time, the 2 n {\displaystyle 2n} -point Green function is defined by G ( n ) ( 1 … n ∣ 1 ′ … n ′ ) = i n ⟨ T ψ ( 1 ) … ψ ( n ) ψ ¯ ( n ′ ) … ψ ¯ ( 1 ′ ) ⟩ , {\displaystyle G^{(n)}(1\ldots n\mid 1'\ldots... | {
"page_id": 7864709,
"source": null,
"title": "Green's function (many-body theory)"
} |
that Fourier transform of the two-point ( n = 1 {\displaystyle n=1} ) thermal Green function for a free particle is G ( k , ω n ) = 1 − i ω n + ξ k , {\displaystyle {\mathcal {G}}(\mathbf {k} ,\omega _{n})={\frac {1}{-i\omega _{n}+\xi _{\mathbf {k} }}},} and the retarded Green function is G R ( k , ω ) = 1 − ( ω + i η ... | {
"page_id": 7864709,
"source": null,
"title": "Green's function (many-body theory)"
} |
\cdot (\mathbf {x} -\mathbf {x} ')-i\omega _{n}(\tau -\tau ')},} where the sum is over the appropriate Matsubara frequencies (and the integral involves an implicit factor of ( L / 2 π ) d {\displaystyle (L/2\pi )^{d}} , as usual). In real time, we will explicitly indicate the time-ordered function with a superscript T:... | {
"page_id": 7864709,
"source": null,
"title": "Green's function (many-body theory)"
} |
by G T ( k , ω ) = [ 1 + ζ n ( ω ) ] G R ( k , ω ) − ζ n ( ω ) G A ( k , ω ) , {\displaystyle G^{\mathrm {T} }(\mathbf {k} ,\omega )=[1+\zeta n(\omega )]G^{\mathrm {R} }(\mathbf {k} ,\omega )-\zeta n(\omega )G^{\mathrm {A} }(\mathbf {k} ,\omega ),} where n ( ω ) = 1 e β ω − ζ {\displaystyle n(\omega )={\frac {1}{e^{\be... | {
"page_id": 7864709,
"source": null,
"title": "Green's function (many-body theory)"
} |
d τ G ( τ ) e i ω n τ . {\displaystyle {\mathcal {G}}(\omega _{n})=\int _{0}^{\beta }d\tau \,{\mathcal {G}}(\tau )\,e^{i\omega _{n}\tau }.} Finally, note that G ( τ ) {\displaystyle {\mathcal {G}}(\tau )} has a discontinuity at τ = 0 {\displaystyle \tau =0} ; this is consistent with a long-distance behaviour of G ( ω n... | {
"page_id": 7864709,
"source": null,
"title": "Green's function (many-body theory)"
} |
{R} }(\mathbf {k} ,\omega )=\int _{-\infty }^{\infty }{\frac {d\omega '}{2\pi }}{\frac {\rho (\mathbf {k} ,\omega ')}{-(\omega +i\eta )+\omega '}},} where the limit as η → 0 + {\displaystyle \eta \to 0^{+}} is implied. The advanced propagator is given by the same expression, but with − i η {\displaystyle -i\eta } in th... | {
"page_id": 7864709,
"source": null,
"title": "Green's function (many-body theory)"
} |
− ω ′ , {\displaystyle \operatorname {Re} G^{\mathrm {R} }(\mathbf {k} ,\omega )=-2P\int _{-\infty }^{\infty }{\frac {d\omega '}{2\pi }}{\frac {\operatorname {Im} G^{\mathrm {R} }(\mathbf {k} ,\omega ')}{\omega -\omega '}},} where P {\displaystyle P} denotes the principal value of the integral. The spectral density obe... | {
"page_id": 7864709,
"source": null,
"title": "Green's function (many-body theory)"
} |
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