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F\'elix and Thomas extended the loop products and coproducts to simply-connected Gorenstein spaces. We explicitly describe these operations with rational coefficients in terms of Sullivan models. Moreover, by this description, we prove some…
Many scientifically well-motivated statistical models in natural, engineering and environmental sciences are specified through a generative process, but in some cases it may not be possible to write down a likelihood for these models…
A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.
The determinant of a lower Hessenberg matrix (Hessenbergian) is expressed as a sum of signed elementary products indexed by initial segments of nonnegative integers. A closed form alternative to the recurrence expression of Hessenbergians…
When various observers obtain information in an independent fashion about a classical system, there is a simple rule which allows them to pool their knowledge, and this requires only the states-of-knowledge of the respective observers. Here…
This work introduces a new functional series for expanding an analytic function in terms of an arbitrary analytic function. It is generally applicable and straightforward to use. It is also suitable for approximating the behavior of a…
We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without…
A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise from the generalization of the gamma function…
For a two parameter family of Bernoulli numbers $B_{n, p}$ the exponential generating function is derived by elementary methods.
We present a general simplification of quantified SMT formulas using variable elimination. The simplification is based on an analysis of the ground terms occurring as arguments in function applications. We use this information to generate a…
We present an elementary proof of the generalization of the $k$-bonacci Binet formula, a closed form calculation of the $k$-bonacci numbers using the roots of the characteristic polynomial of the $k$-bonacci recursion.
By using a general formalism, we expose a simplified proof of the convergence of the B\'ezier polynomials attached to a continuous function defined in arbitrary dimensional simplex. We obtain an error estimate that contains the error in…
In terms of the derivative operator, integral operator and Saalsch\"{u}tz's theorem, two families of summation formulae involving generalized harmonic numbers are established.
A different application of the familiar integral representation for the modifed Bessel function drives to a new Kontorovich-Lebedev-like integral transformation of a general complex index. Mapping and operational properties, a convolution…
By means of the derivative operator and Whipple-type $_3F_2$-series identities, two families of summation formulae involving generalized harmonic numbers are established.
We present here a construction for the derived term automaton (aka partial derivative, or Antimirov, automaton) of a rational (or regular) expression based on a sole induction on the depth of the expression and without making reference to…
In this note, we propose simple summations for primes, which involve two finite nested sums and Bernoulli numbers. The summations can also be expressed in terms of Bernoulli polynomials.
In this article, we compute the Buchsbaum-Rim function of two variables associated to a direct sum of cyclic modules and give a formula for the last positive associated Buchsbaum-Rim multiplicity in terms of the ordinary Hilbert-Samuel…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpi\'nski gasket that…