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In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities. The orientation of an object's acceleration is given by the orientation of the net force acting on that object. The magnitude of an object's acceleration, as described by Newton's Second Law, is the combined effect of two causes:
In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity , a number ranging from to .
In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest. Formally, a kinetic energy is any term in a system's Lagrangian which includes a derivative with respect to time and the second term in a Taylor expansion of a particle's relativistic energy.
In Newtonian mechanics, momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity, then the object's momentum p is :
In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, power is sometimes called activity. Power is a scalar quantity.
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
- The laws of physics are invariant (identical) in all inertial frames of reference.
- The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer.
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors, dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system; those components form an array, which can be thought of as a high-dimensional matrix.
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit.
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. The equation is named after Erwin Schrödinger, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933.
In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force strength and the distance traveled. A force is said to do positive work if when applied it has a component in the direction of the displacement of the point of application. A force does negative work if it has a component opposite to the direction of the displacement at the point of application of the force.
In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as
In biochemistry, Michaelis–Menten kinetics, named after Leonor Michaelis and Maud Menten, is the simplest case of enzyme kinetics, applied to enzyme-catalysed reactions of one substrate and one product. It takes the form of an equation describing the rate reaction rate to , the concentration of the substrate A. Its formula is given by the Michaelis–Menten equation:
Time dilation is the difference in elapsed time as measured by two clocks, either due to a relative velocity between them or due to a difference in gravitational potential between their locations. When unspecified, "time dilation" usually refers to the effect due to velocity.
In fluid dynamics, drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers or between a fluid and a solid surface.
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by , is the factor by which the eigenvector is scaled.
A capacitor is a device that stores electrical energy in an electric field by accumulating electric charges on two closely spaced surfaces that are insulated from each other. It is a passive electronic component with two terminals.
Indium (111In) altumomab pentetate (INN) is a mouse monoclonal antibody linked to pentetate which acts as a chelating agent for the radioisotope indium-111. The drug is used for the diagnosis of colorectal cancer but has not been approved for use.
Technetium (99mTc) arcitumomab is a drug used for the diagnostic imaging of colorectal cancers, marketed by Immunomedics. It consists of the Fab' fragment of a monoclonal antibody and a radionuclide, technetium-99m.
3F8 is a murine IgG3 monoclonal antibody which binds to GD2.
A Transformer is a deep learning architecture that relies on the attention mechanism. It is notable for requiring less training time compared to previous recurrent neural architectures, such as long short-term memory (LSTM), and has been prevalently adopted for training large language models on large (language) datasets, such as the Wikipedia Corpus and Common Crawl, by virtue of the parallelized processing of input sequence. More specifically, the model takes in tokenized input tokens, and at each layer, contextualizes each token with other (unmasked) input tokens in parallel via attention mechanism. Though the Transformer model came out in 2017, the core attention mechanism was proposed earlier in 2014 by Bahdanau, Cho, and Bengio for machine translation. This architecture is now used not only in natural language processing, computer vision, but also in audio, and multi-modal processing. It has also led to the development of pre-trained systems, such as generative pre-trained transformers (GPTs) and BERT.
References
- ↑ Radioimmunodetection at the U.S. National Library of Medicine Medical Subject Headings (MeSH)
- ↑ DeNardo SJ (April 2005). "Radioimmunodetection and therapy of breast cancer". Semin Nucl Med. 35 (2): 143–51. doi:10.1053/j.semnuclmed.2004.12.001. PMID 15765377.
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