Related papers: Derived functors of the divided power functors
We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version…
Fractional $q$-extensions of some classical $q$-orthogonal polynomials are introduced and some of the main properties of the new defined functions are given. Next, a fractional $q$-difference equation of Gauss type is introduced and solved…
This is a partial derivative of \cite{MR94g:17044}. We give a list of examples/problems that some will find amusing.
In this article, we propose new proportional fractional operators generated from local proportional derivatives of a function with respect to another function. We present some properties of these fractional operators which can be also…
In this paper, we strengthen the splitting theorem proved in [14, 15] and provide a different approach using ideas from the weak KAM theory.
This paper has been withdrawn by the authors because the paper is largely revised and improved, and to appear in Mechanics Research Communications.
I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
We describe simple criteria under which a given functor is naturally equivalent to an enriched one. We do this for several bases of enrichment, namely (pointed) simplicial sets, (pointed) topological spaces and orthogonal spectra. We also…
New results on comparison of distributions of Gaussian quadratic forms are presented
Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial…
We prove new results on the derivative of the Minkowski question mark function. Some of our theorems are non-improvable.
In this note we prove that the simplicial derived functors introduced by Tierney and Vogel [TV69] are naturally isomorphic to the cubical derived functors introduced by the author in [P09]. We also explain how this result generalizes the…
In this short note, we propose an unified method to derive formulas for derivations conjugated by exponential functions on an almost complex manifold. In v3, we corrected some mistakes in previous versions.
We relate non integer powers ${\mathcal L}^{s}$, $s>0$ of a given (unbounded) positive self-adjoint operator $\mathcal L$ in a real separable Hilbert space $\mathcal H$ with a certain differential operator of order $2\lceil{s}\rceil$,…
We develop the theory of Mackey profunctors, a version of Mackey functors for profinite groups.
Certain new inequalities for the sums of factorials are presented.
The $E_2$ term of the Adams spectral sequence may be identified with certain derived functors, and this also holds for a number of other spectral sequences. Our goal is to show how the higher terms of such spectral sequences are determined…
We present a generalization of a formula of higher order derivatives and give a short proof.
Instantaneous derivation of the Thomas precession with only basic vector calculus.