To distinguish it from generalized momentum, the product of mass and volume is also referred to as mechanical, kinetic or kinematic momentum.

Its success depended less on generalized mass appeal than on the so-called sanban ( three " ban "): jiban ( a strong, well-organized constituency ), kaban ( a briefcase full of money ), and kanban ( prestigious appointment, particularly on the cabinet level ).

In general relativity, negative mass is generalized to refer to any region of space in which for some observers the mass density is measured to be negative.

This generalized mass formula was named as " Samanta Formula " by Botvina and Pochodzalla and used to predict relative yields of hypernuclei in multifragmentation of nuclear spectator matter.

The probability mass function of the generalized Yule – Simon ( ρ, α ) distribution is defined as

The Boltzmann formula ( 1872 ) for the entropy production in the rarefied gas kinetics with detailed balance served as a prototype of many similar formulas for dissipation in mass action kinetics and generalized mass action kinetics with detailed balance.

According to the generalized mass action law, the reaction rate for an elementary reaction is

The principle of detailed balance for the generalized mass action law is: For given values there exists a positive equilibrium with detailed balance,.

For the Wegscheider conditions this kinetic law is the law of mass action ( or the generalized law of mass action ).

To describe dynamics of the systems that obey the generalized mass action law, one has to represent the activities as functions of the concentrations c < sub > j </ sub > and temperature.

For the ideal systems, and: the activity is the concentration and the generalized mass action law is the usual law of mass action.

Then, in the linear approximation near equilibrium the reaction rates for the generalized mass action law are

For systems that obey the generalized mass action law the semi-detailed balance condition is sufficient for the dissipation inequality ( for the Helmholtz free energy under isothermal isochoric conditions and for the dissipation inequalities under other classical conditions for the corresponding thermodynamic potentials ).

Let us represent the generalized mass action law in the equivalent form: the rate of the elementary process

This is the general dissipation formula for the generalized mass action law.

* Tandem mass spectrometry: non-invasive, rapid method ; a significant peak at C16 is indicative of generalized CPT II deficiency

The simplest type of carbohydrate is a monosaccharide, which among other properties contains carbon, hydrogen, and oxygen, mostly in a ratio of 1: 2: 1 ( generalized formula C < sub > n </ sub > H < sub > 2n </ sub > O < sub > n </ sub >, where n is at least 3 ).

Faulhaber's formula was generalized by V. Guo and J. Zeng to a q-analog.

Church subsequently modified his methods to include use of Herbrand – Gödel recursion and then proved ( 1936 ) that the Entscheidungsproblem is unsolvable: There is no generalized " effective calculation " ( method, algorithm ) that can determine whether or not a formula in either the recursive-or λ-calculus is " valid " ( more precisely: no method to show that a well formed formula has a " normal form ").

The formula was discovered independently by Leonhard Euler and Colin Maclaurin around 1735 ( and later generalized as Darboux's formula ).

This formula, too, is readily generalized to curved spacetime by replacing partial derivatives with their curved-manifold counterparts, covariant derivatives studied in differential geometry.

Euler's formula relating the number of edges, vertices, and faces of a convex polyhedron was studied and generalized by Cauchy and L ' Huillier, and is at the origin of topology.

Although originally expressed in Newton's third law, the conservation of linear momentum also holds in special relativity ( with a modified formula ) and, with appropriate definitions, a ( generalized ) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity.

The formula is also valid for formal power series and can be generalized in various ways.

It can be formulated for functions of several variables, it can be extended to provide a ready formula for F ( g ( z )) for any analytic function F, and it can be generalized to the case f '( a ) = 0, where the inverse g is a multivalued function.

These formulas are generalized by the Faà di Bruno's formula.

Buck has reported that the maximum relative error is less than 0. 20 % between-20 ° C and + 50 ° C when this particular form of the generalized formula is used to estimate the saturated vapor pressure of water.

The above formula comes from using the generalized chain rule to obtain the total derivative — with respect to x — of both sides of F ( x, y ) = 0:

* ( generalized Rodrigues ' formula ) P is proportional to.

The exponents 1, 2, 5, 7, 12, ... on the right hand side are given by the formula for k = 1, − 1, 2, − 2, 3, ...) and are called ( generalized ) pentagonal numbers.

With the series expansion of higher rank polygamma function a generalized formula can be given as

This formula can easily be generalized to RGB color or CMYK color by applying the formula to each channel separately.

A generalized heptagonal number is obtained by the formula

The Lefschetz trace formula can also be generalized to algebraic stacks over finite fields.

In a development that has given substantive force to this approach to the Riemann hypothesis through functional analysis, Alain Connes has formulated a trace formula that is actually equivalent to a generalized Riemann hypothesis.

This formula is generalized to three dimensions by:

Torricelli extended this work to other curves such as the cycloid, and then the formula was generalized to fractional and negative powers by Wallis in 1656.

The 3kth pentatope number is the generalized pentagonal number obtained by taking the negative index −( 3k < sup > 2 </ sup > + k )/ 2 in the formula for pentagonal numbers.

In September, 1958, the patient developed generalized weakness and fatigue which was concurrent with exacerbation of his anemia ; ;

Since the early 1990s it was generalized in systemics for the investigation of functional human-like intelligence models, such as personoids, and, in parallel, developed as the SOAR environment.

In 1991, when liquid crystal displays were already well established, Pierre-Gilles de Gennes received the Nobel Prize in physics " for discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers ".

Refined mathematical methods have been developed for solving mechanics problems in generalized coordinates.

Pioneering applications of this in chemistry were performed by Rice and Ramsperger in 1927 and Kassel in 1928, and generalized into the RRKM theory in 1952 by Marcus who took the transition state theory developed by Eyring in 1935 into account.

The theorem was later utilized, popularized, generalized and further developed by James Clerk Maxwell, Lord Rayleigh, Henri Poincaré, Subrahmanyan Chandrasekhar, Enrico Fermi, Paul Ledoux and Eugene Parker.

In the first decade of the development of the theory, G. N. Clements developed a number of influential aspects of the theory involving harmonic processes, especially vowel harmony and nasal harmony, and John McCarthy generalized the theory to deal with the conjugational system of classical Arabic, on the basis of an autosegmental account of vowel and consonant slots on a central timing tier ( see also nonconcatenative morphology ).

He has developed a generalized relativistic-invariant probabilistic interpretation of quantum theory, in which is no longer a probability density in space, but a probability density in space-time.

The various branches of the DEM family are the distinct element method proposed by Cundall in 1971, the generalized discrete element method proposed by Hocking, Williams and Mustoe in 1985, the discontinuous deformation analysis ( DDA ) proposed by Shi in 1988 and the finite-discrete element method concurrently developed by several groups ( e. g., Munjiza and Owen ).

He introduced a class of closed orthogonal sets, developed asymptotic Liouville – Steklov method for orthogonal polynomials, proved theorems on generalized Fourier series, and developed an approximation technique later named Steklov function.

A generalized semiotic view is developed in biosemiotics, which states that intentionality is a criterial feature of life, thus interpreting the organic needs to be the primary form of intentions.

A generalized algorithm to correct for the pressure level difference between the finger and brachial sites within an individual patient was developed and this correction worked under all circumstances that it was tested, even when it was not designed for it, since it applied general physiological principles.

This derives from another generalized meaning that has developed, the cameo as an image of a head in an oval frame in any medium, such as a photograph.

In 1855 and 1856 he conducted column experiments that established what has become known as Darcy's law ; initially developed to describe flow through sands, it has since been generalized to a variety of situations and is in widespread use today.

This was supplied by the apparatus of Schwartz distributions, and a generalized eigenfunction theory was developed in the years after 1950.

A far reaching extension of the Gold ’ s approach is developed by Schmidhuber's theory of generalized Kolmogorov complexities, which are kinds of super-recursive algorithms.

Čížek first developed the Linear-CPMET and then generalized it to full CPMET in the same paper in 1966.

Analytical mechanics was primarily developed to extend the scope of classical mechanics in a systematic, generalized and efficient way to solve problems using the concept of constraints on systems and paths integrals.

Beck developed cognitive therapy — a form of psychotherapy — which transformed the understanding and treatment of many psychiatric conditions, including depression, suicidal behavior, generalized anxiety, panic attacks and eating disorders.

Many of the characteristic ANT tools ( including the notions of translation, generalized symmetry and the “ heterogeneous network ”), together with a scientometric tool for mapping innovations in science and technology (“ co-word analysis ”) were initially developed during the 1980s, predominantly in and around the CSI.

He was awarded a Nobel Prize for discovering that " methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers ".

These ideas were further developed and extensively generalized by Chandrasekhar in a series of fundamental papers and in 1950 in his book ...

Women are two to three times more likely to suffer from generalized anxiety disorder than men, although this finding appears to be restricted to only developed countries ; the spread of GAD is somewhat equal in developing nations.

Several notions of generalized solutions have been developed to cover such situations, including viscosity solution ( Pierre-Louis Lions and Michael Crandall ), minimax solution ( Andrei Izmailovich Subbotin ), and others.