Related papers: A mu-differentiable Lagrange multiplier rule
We propose a method for quantization of Lagrangians for which the Hamiltonian, as a function of momentum, is a branched function with cusps. Appropriate boundary conditions, which we identify, insure unitary time evolution. In special cases…
We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set,…
We prove new results on the derivative of the Minkowski question mark function. Some of our theorems are non-improvable.
The fractional Leibniz rule is generalized by the Coifman-Meyer estimate. It is shown that the arbitrary redistribution of fractional derivatives for higher order with the corresponding correction terms.
We prove an explicit degree formula for certain unitary Deligne-Lusztig varieties. Combining with an alternative degree formula in terms of Schubert calculus, we deduce several algebraic combinatorial identities which may be of independent…
A fractional power interpretation of the Laguerre derivative $(DxD)^\alpha,\ D\equiv {d\over dx} $ is discussed. The corresponding fractional integrals are introduced. Mapping and semigroup properties, integral representations and Mellin…
In this article we discuss an important students' misconception about derivatives, that the expression of the derivative of the function contains the information as to whether the function is differentiable or not where the expression is…
We introduce a gradient flow formulation of linear Boltzmann equations. Under a diffusive scaling we derive a diffusion equation by using the machinery of gradient flows.
In this paper, we introduce and share the new concept of $\mathcal{MT}(\lambda )$-functions and its some characterizations.
We introduce the notion of the difference quotient set of a real valued function $f$ on a set $E\subset[0,1]$, and compare this set to the range of $f$ on $E$. We discuss the measure theoretic properties of both the range and the difference…
We give a method of representing the modular invariant function by generators of a modular function field.
A technique is presented for finding the classical Lagrange function corresponding to a given dispersion relation. This allows us to study the classical analogue of the Standard-Model Extension. Developments are discussed.
We study differentiability properties of Zygmund functions and series of Weierstrass type in higher dimensions. While such functions may be nowhere differentiable, we show that, under appropriate assumptions, the set of points where the…
We solve a Lehmer-type question about the Mahler measure of integer-valued polynomials.
Some properties of $m$-density points and density-degree functions are studied. Moreover the following main results are provided: \vskip2mm \begin{itemize} \item {\it Let $\lambda$ be a continuous differential form of degree $h$ in…
In this paper we study the regularity properties of fractional maximal operators acting on $BV$-functions. We establish new bounds for the derivative of the fractional maximal function, both in the continuous and in the discrete settings.
In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional…
Given a probability distribution $\mu$ a set $\Lambda (\mu)$ of positive real numbers is introduced, so that $\Lambda (\mu)$ measures the "divisibility" of $\mu$. The basic properties of $\Lambda (\mu)$ are described and examples of…
In this expository paper, we illustrate two explicit methods which lead to special $L$-values of certain modular forms admitting complex multiplication (CM), motivated in part by properties of $L$-functions obtained from Calabi-Yau…
Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used to estimate gradients of expectations throughout machine learning and reinforcement learning; however, they are usually explained as simple mathematical tricks,…