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, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances.
Enthalpy, a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant pressure, which is conveniently provided by the large ambient atmosphere. The pressure–volume term expresses the work required to establish the system's physical dimensions, i.e. to make room for it by displacing its surroundings. The pressure-volume term is very small for solids and liquids at common conditions, and fairly small for gases. Therefore, enthalpy is a stand-in for energy in chemical systems; bond, lattice, solvation and other "energies" in chemistry are actually enthalpy differences. As a state function, enthalpy depends only on the final configuration of internal energy, pressure, and volume, not on the path taken to achieve it.
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 physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur.
In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force. It describes the rate of change of angular momentum that would be imparted to an isolated body. The concept originated with the studies by Archimedes of the usage of levers, which is reflected in his famous quote: "Give me a lever and a place to stand and I will move the Earth". Just as a linear force is a push or a pull applied to a body, a torque can be thought of as a twist applied to an object with respect to a chosen point. Torque is defined as the product of the magnitude of the perpendicular component of the force and the distance of the line of action of a force from the point around which it is being determined. The law of conservation of energy can also be used to understand torque. The symbol for torque is typically , the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.
In probability theory, a probability density function (PDF), or density of an absolutely continuous random variable, is a function whose value at any given sample in the sample space can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample. Probability density is the probability per unit length, in other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0, the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample.
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
- A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.
- When a body is acted upon by a force, the time rate of change of its momentum equals the force.
- If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.
The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the parabolic partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price given the risk of the security and its expected return. The equation and model are named after economists Fischer Black and Myron Scholes; Robert C. Merton, who first wrote an academic paper on the subject, is sometimes also credited.
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.
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum amount of non-volume expansion 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 where P is pressure, T is the temperature, U is the internal energy, V is volume, H is the enthalpy, and S is the entropy.
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 virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
An aurone is a heterocyclic chemical compound, which is a type of flavonoid. There are two isomers of the molecule, with (E)- and (Z)-configurations. The molecule contains a benzofuran element associated with a benzylidene linked in position 2. In aurone, a chalcone-like group is closed into a 5-membered ring instead of the 6-membered ring more typical of flavonoids.
A transformer is a deep learning model. It is distinguished by its adoption of self-attention, differentially weighting the significance of each part of the input data. It is used primarily in the fields of natural language processing (NLP) and computer vision (CV).
