Related papers: A mu-differentiable Lagrange multiplier rule
We introduce $p$-derivations and give a few basic ways in which they act like derivatives by numbers.
Reinforcement learning methods for robotics are increasingly successful due to the constant development of better policy gradient techniques. A precise (low variance) and accurate (low bias) gradient estimator is crucial to face…
Fractional variation is defined as the limit of the difference quotient of the increments of a function and its argument raised to a fractional power. Fractional velocity can be suitable for characterizing singular behavior of derivatives…
In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$ where $A$ and $B$ are matrix polynomials.…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
The paper presents several combinatorial properties of the boolean cumulants. A corollary is a new proof of the multiplicative property of the boolean cumulant series that can be easily adapted for the case of boolean independence with…
This object of this paper to give several properties and applications of multiple p-adic q-L-function of two variables.
Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences.
We find general non-linear lagrangians of a U(1) field invariant under electric-magnetic duality. They are characterized by an arbitrary function and go to the Maxwell theory in the weak field limit. We give some explicit examples which are…
A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…
In a previous paper of the second author with K. Ono, surprising multiplicative properties of the partition function were presented. Here, we deal with $k$-regular partitions. Extending the generating function for $k$-regular partitions…
Reinforcement learning methods for robotics are increasingly successful due to the constant development of better policy gradient techniques. A precise (low variance) and accurate (low bias) gradient estimator is crucial to face…
We make an estimation of the support of a multivariable scaling function for an arbitrary dilation matrix. We give a method of calculating the values of the scaling function on a tight set using the knowledge of the size of the support.
The notion of a local fractional derivative (LFD) was introduced recently for functions of a single variable. LFD was shown to be useful in studying fractional differentiability properties of fractal and multifractal functions. It was…
In this paper we develop with considerable details a theory of multivector functions of a $p$-vector variable. The concepts of limit, continuity and differentiability are rigorously studied. Several important types of derivatives for these…
The convergence of multiple Fourier series of functions of bounded partial $% \Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of multiple…
We introduce a Lagrangian which can be varied to give both the equation of motion and world-line deviations of spinning particles simultaneously.
We define and characterize ultradifferentiable functions and their corresponding ultradistributions on $\RR^d_+$ using iterates of the Laguerre operator. The characterization is based on decay or growth conditions of the coefficients in…
We characterize the regularity of an FI-module using the derivative functors.
In a series of recent works, we have provided a number of explicit expressions for the derivative of the associated Legendre function of the first kind with respect to its degree, $[\partial P_{\nu}^{m}(z)/\partial\nu]_{\nu=n}$, with…