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The study of infinitary operations actually started in the late 1950s [[#References|[a1]]]. A nullary operation is also called

Often, the natural number sequence is started at $ 0 $,

The forms of bar induction which one started to utilize in the foundations of mathematics in the 1960's do not deal with

...doxes describe counter-intuitive election outcomes. The mathematical study started in 1770 when J.C. Borda [[#References|[a1]]] constructed an example to argu ...ite number of ways to tally ballots, P.S. Laplace and other mathematicians started a two-century controversy by questioning which $\mathbf w^n$ would be "opt

occurs. The NOT BEFORE relations denote that a certain operation can be started (and/or can be finished) not before than in $ a ( i , j ) $, the given amount of time units, after some other operation has started (and/or finished): $ t _ {j} - t _ {i} \geq a( i, j) $,

...ts. For $A$ linear and unbounded, it is due to E. Hille and K. Yosida (who started these investigations in 1948). The one-parameter family of operators $S ( t ...of accretive-type operators is also known as Minty–Browder theory. It has started with some pioneering work of M.M. Vainberg, E.M. Zarantonello and R.I. Kach

...d structure and the condition that any operation $v_j=(x_r,x_s)$ cannot be started until the operations that end at $x_r$ are finished. The second have a vari

if the process has started from state $ 0 $)

...dre (1800), in the first edition of the textbook Eléments de la géométrie, started from the sum $S$ of the angles of a triangle. Having rejected the hypothesi

...cating grammar systems with communication by command, the communication is started by the senders, as in the WAVE paradigm of communication in parallel comput

an advertisement in which a newly started life insurance company sought 1936-1948. Eir was mostly Lundberg's own creation. It started its

...heorem [[#References|[a5]]] and in the mid 1950s research in Ramsey theory started to take hold. By the 1970s, Ramsey theory was firmly established [[#Referen

...functions. In the original definition, J.F. Colombeau [[#References|[a2]]] started from the space $\mathcal{C} ^ { \infty } ( \mathcal{D} ( \Omega ) )$ of inf

The replacement of differential problems by their difference analogues started in the works [[#References|[1]]], [[#References|[2]]] and [[#References|[4]

Considerable research on adaptive control started in the early 1950s. The primary motivation was control of high-performance

In 1929, K. Mahler [[#References|[a1]]] started the study of transcendence properties of the values of analytic functions $

...h systems of linearly independent vector fields on smooth manifolds. First started in [[#References|[1]]], studies on the topology of Stiefel manifolds led la

...types, both linear and non-linear. The development of variational methods started from the work of B. Riemann, K. Weierstrass and D. Hilbert. [[Imbedding the

[[#References|[1]]] started research on such forms on Riemann

...nd motion planning, cartography, etc. The discipline was named and largely started in the middle of the 1970s.

Machine translation started in the USA around 1955.

...er introduced [[Homogeneous coordinates|homogeneous coordinates]] and thus started the analytic direction in projective geometry.

of general relativity, he started a scientific activity which was university career of a great variety. In 1924 he started teaching

...ng that some jobs may be started (finished) only after some other jobs are started (finished). cities and finally returns to the city from which it started. A reformulation of this problem in terms of machine-scheduling ( "cities"

over this line; this started the theory of almost-periodic functions (cf. [[Almost-periodic function|Alm

...her words, [[Brownian motion|Brownian motion]]) living on $\mathbf{R}$ and started at $0$. The random set $\mathcal{Z} _ { 0 } : = \{ t : W _ { t } = 0 \}$, t

descended into poverty. This started off with the destruction

A.J. Sommese [[#References|[a6]]] started the modern study of the mapping (which he called the adjunction mapping) as

...spaces, and work on Bergman spaces on domains in $\mathbf{C} ^ { n }$ has started (see e.g. [[#References|[a22]]], [[#References|[a9]]], [[#References|[a18]]

variance and the theory of interval estimation. In 1931 he started

Beyond these two examples, an approach to a general theory was started in [[#References|[a3]]], where the concept of a coherent pair of measures i

..., a systematic construction of rigorous (non-perturbative) models has been started in space-time dimensions $d = 2,3$, see [[#References|[a9]]], [[#References

...#References|[a29]]], from which the history of Buchsbaum rings and modules started. In [[#References|[a29]]] they gave a characterization of Buchsbaum rings i Researches of the Buchsbaumness in Rees algebras recently (1999) started again, although the progress remains tardy (possibly because of the lack of

The seminal paper that started the whole theory of matroids is [[#References|[1]]] (also included in [[#Re

Recently one has started to study capacities in $ \mathbf C ^ {n} $

...problem is treated directly as a minimization problem, i.e. the method is started with an initial approximation of the solution, which is iteratively improve

...brating string, underwent deep changes even in the energetic polemics that started then. From then on there has been a constant deepening and evolution of thi

In his construction of the theory of analytic functions, Cauchy started from the concept of monogeneity. He called a function $ w = f ( z) $,

He then started as a pupil teacher at a

started", she later wrote. "I had to choose from other fields and

...mathbf{t} ^ { \text{em} }$ is a recurrent theme of vivid discussions which started with a priori proposals of an electromagnetic energy-momentum tensor by M.

...ipline is said to be non-pre-emptive if, once the service to a customer is started, it is not disrupted until the whole service requirement is completed. Thus

...eriodic orbits and compute the Floquet multipliers. Periodic orbits can be started from Hopf bifurcation points. Along branches of periodic orbits branch poin

...the input alphabet. The Turing machine $T$ starts with an empty tape. When started, $T$ writes all elements $w\in L$ on the tape separated from each other wit

molecules. Einstein started from general relations of statistical physics,

logic programming started with the observation that many operations over a Herbrand universe can be d

...al equations forms the main contribution of mathematics to meteorology. It started with a numerical integration procedure by L.F. Richardson [[#References|[a9

...cf. also [[Spectrum of an operator|Spectrum of an operator]]). Everything started with the classical Weyl asymptotic formula, and was later translated into t

periods. Having started out with partial differential equations, he

started

for imperative and functional programs, although work has started on similar developments based on (so-called small-step) structural operatio

The study of Hankel operators on the Hardy class $H ^ { 2 }$ was started by Z. Nehari [[#References|[a14]]] and P. Hartman [[#References|[a9]]] (cf.

...idehat { y }$ modulo $m ^ { c }\hat{ A}$. The study of Artin approximation started with the famous papers of M. Artin [[#References|[a3]]], [[#References|[a4]

is a complex parameter. Serious studies of this problem were started by J.Ch. Sturm and J. Liouville. The methods and notions that originated du

...he appearance of the works of Leibniz and Bernoulli, combinatorial methods started to be an independent branch of mathematics.

A profound study of inverse problems started in the 1940's (see [[#References|[11]]], [[#References|[12]]]). Let $ \la

treatise by [[Fisher, Irving|Irving Fisher]] on "Price Index Numbers" again started yet another controversy.

his most significant and lasting gifts to statistics. He started

In 1646 he started work on hydrostatics,

A systematic study of Kac–Moody algebras was started independently by V.G. Kac

While Bowley may have started his working life as a teacher of

A. Einstein started the construction of a new theory of gravitation with the introduction of th

...algebraic integers in algebraic number fields was solved by E. Kummer, who started from a special case; he tried to solve Fermat's last theorem on the impossi

...f collecting sets together to form new sets. The generative process can be started with A2), an outright existence axiom. The next axiom is another outright e

...ipative operators in a Hilbert space to maximal dissipative ones. Phillips started these investigations in connection with the Cauchy problem for dissipative

...+ \sigma^2/m$. Hence if we inspect such a process a long time after it has started

...constructions, which were made before the detailed study of Weyl algebras started.

...en it is of universal type and, indeed, $G _ { K } ( V ) = G$ is the group started with. Any other Chevalley group over $K$ associated with $\frak g$ is an ep

The development of cobordism theory started from the geometric definition and calculation of the groups $ \Omega _ {E

In 1921 S. Lefschetz started to use a new science — topology — in the study of algebraic varieties o

...e problem of the automation of deductive constructions by practical means, started to develop the language of practical mathematical logic. The language relat

Functional analysis as an independent mathematical discipline started at the turn of the 19th century and was finally established in the 1920's a

A remarkable breakthrough in knot theory has taken place recently. It started in 1984 with the discovery of a new polynomial invariant (in two variables)

...ped played a role in its shaping. The broad motives behind its development started a two-phased movement:<ref>Ferreirós (2001) p. 442</ref> ...atization of number theory. Further, in defining natural numbers, Dedekind started from infinite sets rather than finite sets, and was explicitly and specific