Related papers: Operations on Legendrian submanifolds
On locally conformally flat manifolds we describe a construction which maps generalised conformal Killing tensors to differential operators which may act on any conformally weighted tensor bundle; the operators in the range have the…
This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…
We consider two types of convolutions ($\ast$ and $\star$) of functions on spaces of finite configurations (finite subsets of a phase space), and some their properties are studied. A connection of the $\ast$-convolution with the convolution…
Fold functions are a general mechanism for computing over recursive data structures. First-order folds compute results bottom-up. With higher-order folds, computations that inherit attributes from above can also be expressed. In this paper,…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
We introduce and analyze a novel class of binary operations on finite-dimensional vector spaces over a field K, defined by second-order multilinear expressions with linear shifts. These operations generate polynomials whose degree increases…
In this paper we introduce and study a class of structured set-valued operators which we call union averaged nonexpansive. At each point in their domain, the value of such an operator can be expressed as a finite union of single-valued…
Let $Z \to Y^{2n+1}$ be the bundle of Legendrian $n$-planes over a contact manifold $Y$. We consider a foliation of $Z$ by canonical lifts of Legendrian submanifolds, called \emph{Legendrian submanifold path geometry}, whose flat model is…
In this paper we talk about the so-called SuperMathematics Functions (SMF), which often constiture the base for generating technical neo-geometrical objects.
Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…
In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal…
We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion of left invariant submodular function defined on power sets…
We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by semi-norms which are defined by a combination of classical norms and multiplication or…
We calculate the least upper bounds of pointwise and uniform approximations for classes of $2\pi$-periodic functions expressible as convolutions of an arbitrary square summable kernel with functions, which belong to the unit ball of the…
Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a…
Adams operations are the natural transformations of the representation ring functor on the category of finite groups, and they are one way to describe the usual lambda-ring structure on these rings. From the representation-theoretical point…
The notion of the H\"older convolution is introduced. The main result is that, under general conditions on functions L_1, ..., L_n, the function inverse to the Legendre--Fenchel transform of the H\"older convolution of L_1, ..., L_n…
We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function…
Given an L-space knot we show that its Upsilon function is the Legendre transform of a counting function equivalent to the d-invariants of its large surgeries. The unknotting obstruction obtained for the Upsilon function is, in the case of…
We study augmentations of a Legendrian surface $L$ in the $1$-jet space, $J^1M$, of a surface $M$. We introduce two types of algebraic/combinatorial structures related to the front projection of $L$ that we call chain homotopy diagrams…