Related papers: Sequential derivatives
The class of ordinary linear constant coefficient differential equations is naturally embedded into a wider class by associating differential equations to algebraic curves.
In this paper, we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.
Many modern numerical methods in computational science and engineering rely on derivatives of mathematical models for the phenomena under investigation. The computation of these derivatives often represents the bottleneck in terms of…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
Data of sequential nature arise in many application domains in forms of, e.g. textual data, DNA sequences, and software execution traces. Different research disciplines have developed methods to learn sequence models from such datasets: (i)…
In this paper directional derivative sets and differentials of a given set valued map are studied. Relations between the set valued map and compact subsets of the directional derivative sets of the given map are investigated. Upper and…
D-finite functions and P-recursive sequences are defined in terms of linear differential and recurrence equations with polynomial coefficients. In this paper, we introduce a class of numbers closely related to D-finite functions and…
In the context of infinity categories, we rethink the notion of derived functor in terms of correspondences. This is especially convenient for the description of a passage from an adjoint pair (F,G) of functors to a derived adjoint pair…
We develop a notion of (principal) differential rank for differential-valued fields, in analog of the exponential rank and of the difference rank. We give several characterizations of this rank. We then give a method to define a derivation…
Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…
We consider the primes which divide the denominator of the x-coordinate of a sequence of rational points on an elliptic curve. It is expected that for every sufficiently large value of the index, each term should be divisible by a primitive…
An economic interpretation of the Caputo derivatives of non-integer orders is proposed. The suggested economic interpretation of the fractional derivatives is based on a generalization of average and marginal values of economic indicators.…
The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…
In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential…
It is shown that a separated sequence of points in the unit disc of the complex plane is in fact uniformly separated, if there exists a certain intermediate sequence whose separated subsequences are uniformly separated. This property is…
In this paper, we introduce a new type of Darbo's fixed point theorem by using concept of function sequences with shifting distance property. Afterward, we investigate existence of fixed point under this the theorem. Also we are going to…
A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their…