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Explicit Form of the Faulhaber Polynomials

The College Mathematics Journal, 2015
Hersh recently showed that the Faulhaber polynomials, related to sums of consecutive powers, can be expressed as even or odd polynomials in the variable offset by one-half.
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Focus on grammatical form: explicit or implicit?

System, 2002
Grammar teaching has been and continues to be an area of some controversy and debate have led to the emergence of a new classroom option for language teachers: that of Focus on Form (as opposed to Focus on Meaning or Focus on FormS). Against this background of ‘interesting times’ for grammar teaching, this paper reports research into teachers ...
John Burgess, Siân Etherington
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Generalized free field in explicit form

Reports on Mathematical Physics, 1971
Abstract The calculations showing that the generalized free field and its normal products may be taken at a point are performed. The Fourier transform of the field and its support is discussed. It is shown that the well-known expression, utilizing the Fourier transform of the field, gives the generators of the Poincare group. All this is done at the
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Realizations of chiral transformations: explicit forms

Canadian Journal of Physics, 1970
The parallel approaches to the general problem of giving nonlinear realizations of chiral SU(n) [Formula: see text]SU(n) appropriate to phenomenological field theories as derived by Callan, Coleman, Wess, and Zumino on the one hand, and by Barnes and Isham on the other, are reviewed and compared.
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The Exponential Habit Forming Utility: Explicit Forms and Graphical Illustrations

2014
This thesis focuses on characterizing the optimal consumption and investment strategy for an investor, in a simple financial market, when his consumption habit is considered in the utility formulation. We consider a continuous-time market model for which we maximize the overall utility within an infinite horizon.
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Explicit form for impedance of cauer networks

International Journal of Computer Mathematics, 2001
In this paper a new procedure is established to obtain in closed form the poles and zeros of the impedance function of a first Cauer Network. The technique involves the continued fraction representation of the corresponding Laplace transform as a rational function whose numerators and denominators can be represented by tridiagonal determinants.
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Sharp Bonferroni-Type Inequalities in Explicit Forms

1992
Let p m ( or gm) be the probability that exactly (or at least) m out of n events, A 1,…,A n, occur. Let The explicit forms of sharp Bonferroni-type inequalities on p{nm} and q m using or, l≤k, are obtained. These inequalities extend some of the known inequalities, including, for example, the classical Bonferroni inequalities of three terms.
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Apical–basal polarity and the control of epithelial form and function

Nature Reviews Molecular Cell Biology, 2022
Clare E Buckley, Daniel St Johnston
exaly  

Ruthenium-Catalyzed Cycloadditions to Form Five-, Six-, and Seven-Membered Rings

Chemical Reviews, 2021
Rosalie S Doerksen   +2 more
exaly  

On the explicit form of $n$-group operations

Publicationes Mathematicae Debrecen, 2022
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