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For example, decidability is known for rational sequences of order up to 5 subject to the Skolem conjecture (also known as the exponential local-global principle). Decidability is also known for all simple rational sequences (those with simple characteristic polynomial) subject to the Skolem conjecture and the weak p-adic Schanuel conjecture .
The C POSIX library is a specification of a C standard library for POSIX systems. It was developed at the same time as the ANSI C standard. Some effort was made to make POSIX compatible with standard C; POSIX includes additional functions to those introduced in standard C. On the other hand, the 5 headers that were added to the C standard ...
List or describe a set of sentences in the language L σ, called the axioms of the theory. Give a set of σ-structures, and define a theory to be the set of sentences in L σ holding in all these models. For example, the "theory of finite fields" consists of all sentences in the language of fields that are true in all finite fields. An L σ ...
In statistics, the order of integration, denoted I(d), of a time series is a summary statistic, which reports the minimum number of differences required to obtain a covariance-stationary series. Integration of order d
In mathematics, and in particular in the field of algebra, a Hilbert–Poincaré series (also known under the name Hilbert series), named after David Hilbert and Henri Poincaré, is an adaptation of the notion of dimension to the context of graded algebraic structures (where the dimension of the entire structure is often infinite).
The List of T-Series films [note 1] is the list of films produced by T-Series. It was founded by Gulshan Kumar as music label in 1983. While best known as a music label, T-Series is also a film production company in Hindi cinema. It produces the films under the banner of T-Series Films. Bhushan Kumar, incumbent Chairman and Managing Director of ...
An example of a nonlinear delay differential equation; applications in number theory, distribution of primes, and control theory [5] [6] [7] Chrystal's equation: 1 + + + = Generalization of Clairaut's equation with a singular solution [8] Clairaut's equation: 1
The proof is the same as for complex-valued series: use the completeness to derive the Cauchy criterion for convergence—a series is convergent if and only if its tails can be made arbitrarily small in norm—and apply the triangle inequality. In particular, for series with values in any Banach space, absolute convergence implies convergence ...