 | This article relies largely or entirely on a single source .(March 2024) |
| Tyrannosauripodidae | |
|---|---|
 | |
| Tyrannosauripus pillmorei | |
Trace fossil classification  | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Chordata |
| Clade: | Dinosauria |
| Clade: | Saurischia |
| Clade: | Theropoda |
| Family: | † Tyrannosauridae |
| Ichnofamily: | † Tyrannosauripodidae McCrea et al., 2014 |
| Ichnogenera | |
Tyrannosauripodidae is an ichnofamily of dinosaur footprints. [1]
The blue whale is a marine mammal and a baleen whale. Reaching a maximum confirmed length of 29.9 meters (98 ft) and weighing up to 199 tonnes, it is the largest animal known ever to have existed. The blue whale's long and slender body can be of various shades of greyish-blue dorsally and somewhat lighter underneath. Four subspecies are recognized: B. m. musculus in the North Atlantic and North Pacific, B. m. intermedia in the Southern Ocean, B. m. brevicauda in the Indian Ocean and South Pacific Ocean, and B. m. indica in the Northern Indian Ocean. There is also a population in the waters off Chile that may constitute a fifth subspecies.
In a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. This state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but they are equal. Thus, there are no net changes in the concentrations of the reactants and products. Such a state is known as dynamic equilibrium.
In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. More precisely, if is the function such that for every x, then the chain rule is, in Lagrange's notation,
Felidae is the family of mammals in the order Carnivora colloquially referred to as cats. A member of this family is also called a felid. The term "cat" refers both to felids in general and specifically to the domestic cat.
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field whose value at a point gives the direction and the rate of fastest increase. The gradient transforms like a vector under change of basis of the space of variables of . If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to minimize a function by gradient descent. In coordinate-free terms, the gradient of a function may be defined by:
Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, diamagnetic materials are repelled by magnetic fields and form induced magnetic fields in the direction opposite to that of the applied magnetic field. Paramagnetic materials include most chemical elements and some compounds; they have a relative magnetic permeability slightly greater than 1 and hence are attracted to magnetic fields. The magnetic moment induced by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect and modern measurements on paramagnetic materials are often conducted with a SQUID magnetometer.
A supernova is a powerful and luminous explosion of a star. A supernova occurs during the last evolutionary stages of a massive star, or when a white dwarf is triggered into runaway nuclear fusion. The original object, called the progenitor, either collapses to a neutron star or black hole, or is completely destroyed to form a diffuse nebula. The peak optical luminosity of a supernova can be comparable to that of an entire galaxy before fading over several weeks or months.
The tiger is the largest living cat species and a member of the genus Panthera native to Asia. It has a powerful, muscular body with a large head and paws, a long tail, and orange fur with black, mostly vertical stripes. It is traditionally classified into nine recent subspecies, though some recognise only two subspecies, namely mainland Asian tigers and island tigers of the Sunda Islands.
The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. In other words, the more accurately one property is measured, the less accurately the other property can be known.
The lion is a large cat of the genus Panthera, native to Africa and India. It has a muscular, broad-chested body; a short, rounded head; round ears; and a hairy tuft at the end of its tail. It is sexually dimorphic; adult male lions are larger than females and have a prominent mane. It is a social species, forming groups called prides. A lion's pride consists of a few adult males, related females, and cubs. Groups of female lions usually hunt together, preying mostly on large ungulates. The lion is an apex and keystone predator; although some lions scavenge when opportunities occur and have been known to hunt humans, lions typically do not actively seek out and prey on humans.
The leopard is one of the five extant species in the genus Panthera. It has a pale yellowish to dark golden fur with dark spots grouped in rosettes. Its body is slender and muscular reaching a length of 92–183 cm (36–72 in) with a 66–102 cm (26–40 in) long tail and a shoulder height of 60–70 cm (24–28 in). Males typically weigh 30.9–72 kg (68–159 lb), and females 20.5–43 kg (45–95 lb).
In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function, the Taylor polynomial is the truncation at the order of the Taylor series of the function. The first-order Taylor polynomial is the linear approximation of the function, and the second-order Taylor polynomial is often referred to as the quadratic approximation. There are several versions of Taylor's theorem, some giving explicit estimates of the approximation error of the function by its Taylor polynomial.
In differential geometry, a Riemannian manifold or Riemannian space(M, g), so called after the German mathematician Bernhard Riemann, is a real, smooth manifold M equipped with a positive-definite inner product gp on the tangent space TpM at each point p.
Some Buddhist terms and concepts lack direct translations into English that cover the breadth of the original term. Below are given a number of important Buddhist terms, short definitions, and the languages in which they appear. In this list, an attempt has been made to organize terms by their original form and give translations and synonyms in other languages along with the definition.
In the mathematical field of differential geometry, a metric tensor is an additional structure on a manifold M that allows defining distances and angles, just as the inner product on a Euclidean space allows defining distances and angles there. More precisely, a metric tensor at a point p of M is a bilinear form defined on the tangent space at p, and a metric field on M consists of a metric tensor at each point p of M that varies smoothly with p.
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular, of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per liter, having the unit symbol mol/L or mol/dm3 in SI units. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M or 1 M. Molarity is often depicted with square brackets around the substance of interest; for example, the molarity of the hydrogen ion is depicted as [H+].
In thermodynamics, the enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a solid to a liquid, at constant pressure.
Bats are flying mammals of the order Chiroptera. With their forelimbs adapted as wings, they are the only mammals capable of true and sustained flight. Bats are more agile in flight than most birds, flying with their very long spread-out digits covered with a thin membrane or patagium. The smallest bat, and arguably the smallest extant mammal, is Kitti's hog-nosed bat, which is 29–34 millimetres in length, 150 mm (6 in) across the wings and 2–2.6 g in mass. The largest bats are the flying foxes, with the giant golden-crowned flying fox reaching a weight of 1.6 kg and having a wingspan of 1.7 m.
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