Related papers: The Specular Derivative
We summarize our work on constant roll inflationary models. It was understood recently that constant roll inflation, in a regime beyond the slow roll approximation, can give models that are in agreement with the observational constraints.…
In this paper, we study $q$-difference analogues of several central results in value distribution theory of several complex variables such as $q$-difference versions of the logarithmic derivative lemma, the second main theorem for…
The derivative expansion approach to the calculation of the interaction between two surfaces, is a generalization of the proximity force approximation, a technique of widespread use in different areas of physics. The derivative expansion…
We build a longitudinally smooth differentiable groupoid associated to any manifold with corners. The pseudodifferential calculus on this groupoid coincides with the pseudodifferential calculus of Melrose (also called b-calculus). We also…
We introduce a notion of generalized homogeneous derivations on graded rings as a natural extension of the homogeneous derivations defined by Kanunnikov. We then define gr-generalized derivations, which preserve the degrees of homogeneous…
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…
The "marginal" distributions for measurable coordinate and spin projection is introduced. Then, the analog of the Pauli equation for spin-1/2 particle is obtained for such probability distributions instead of the usual wave functions. That…
In this paper, we introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approach for generalized differentiation of nearly convex…
The paper develops a calculus for a class of real-valued functions having a quadratic variation. The main result is a solution of the representation problem for a class of evolutions having a quadratic variation. The result is applied to…
In this paper, we present a new explicit formula for the curvatures of a regular curve with an arbitrary parameter in the Euclidean space $\mathbb{R}^n$, $n\geq 2$, expressed only in terms of its derivatives. We introduce also the notion of…
In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new…
Given an algebra $A$ over a differential field $K$, we study derivations on $A$ that are compatible with the derivation on $K$. There is a universal object, which is a twisted version of the usual module of differentials, and we establish…
In this paper, we prove Smale's mean value conjecture by making use of quasiconformal deformations and holomorphic motions.
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
We describe some results of value distribution theory of holomorphic curves and quasiregular maps, which are obtained using potential theory. Among the results discussed are: extensions of Picard's theorems to quasiregular maps between…
In this paper, we propose a new concept of derivative with respect to an arbitrary kernel-function. Several properties related to this new operator, like inversion rules, integration by parts, etc. are studied. In particular, we introduce…
We introduce a simple extension of the $\lambda$-calculus with pairs---called the distributive $\lambda$-calculus---obtained by adding a computational interpretation of the valid distributivity isomorphism $A \Rightarrow (B\wedge C)\ \…
We generalize the concept of a number derivative, and examine one particular instance of a deformed number derivative for finite field elements. We find that the derivative is linear when the deformation is a Frobenius map and go on to…