Related papers: Multivector Functions of a Real Variable
The problem of inferring the distribution of a random vector given that its norm is large requires modeling a homogeneous limiting density. We suggest an approach based on graphical models which is suitable for high-dimensional vectors. We…
In this paper various notions of convexity of real functions with respect to Chebyshev systems defined over arbitrary subsets of the real line are introduced. As an auxiliary notion, a concept of a relevant divided difference and also a…
We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula, and study their limit in the continuum.
Notions of a "holomorphic" function theory for functions of a split-quaternionic variable have been of recent interest. We describe two found in the literature and show that one notion encompasses a small class of functions, while the other…
We develop the theory of (op)fibrations of 2-multicategories and use it to define abstract six-functor-formalisms. We also give axioms for Wirthm\"uller and Grothendieck formalisms (where either $f^!=f^*$ or $f_!=f_*$) or intermediate…
From physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth. The linear growth condition has special properties, which make it preferred. The manuscript investigates the general properties of the…
In the present paper, a notion of M-basis and multi dimension of a multi vector space is introduced and some of its properties are studied.
Pippenger's Galois theory of finite functions and relational constraints is extended to the infinite case. The functions involved are functions of several variables on a set $A$ and taking values in a possibly different set $B$, where any…
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.
Some differential implications of classical Marx-Strohh\"acker theorem are extended for multivalent functions. These results are also generalized for functions with fixed second coefficient by using the theory of first order differential…
We consider a functional being a difference of two differentiable convex functionals on a closed ball. Existence and multiplicity of critical points is investigated. Some applications are given.
In this work, approximations for real two variables function $f$ which has continuous partial $(n-1)$-derivatives $(n \ge 1)$ and has the $n$--th partial derivative of bounded bivariation or absolutely continuous are established. Explicit…
Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in…
In the present paper, several properties concerning generalized derivatives of multifunctions implicitly defined by set-valued inclusions are studied by techniques of variational analysis. Set-valued inclusions are problems formalizing the…
In this article, we determine the multivariate multifractal Legendre spectra of shifted L{\'e}vy functions. This allows us to explore how the validity of the multivariate multifractal formalism depends on the shift parameter. This article…
In this paper, we introduce a new generalized derivative, which we term the specular derivative. We establish the Quasi-Rolles' Theorem, the Quasi-Mean Value Theorem, and the Fundamental Theorem of Calculus in light of the specular…
The objective of the present paper (the second in a series of four) is to give a theory of multivector and extensor fields on a smooth manifold M of arbitrary topology based on the powerful geometric algebra of multivectors and extensors.…
In this paper, some sufficient conditions for the differentiability of the $n$-variable real-valued function are obtained, which are given based on the differentiability of the $n-1$-variable real-valued function and are weaker than…
The purpose of this paper is to show that functions that derivate the two-variable product function and one of the exponential, trigonometric or hyperbolic functions are also standard derivations. The more general problem considered is to…
We prove multidimensional integration by parts formulas for generalized fractional derivatives and integrals. The new results allow us to obtain optimality conditions for multidimensional fractional variational problems with Lagrangians…