Results in Mathematics
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Geometric Inequalities for Purely Real Submanifolds in Complex Space Forms
Results in Mathematics - Tập 55 - Trang 457-468 - 2009
As a generalisation of Kaehlerian slant submanifolds in Kaehler manifolds (i.e.,
proper slant submanifolds with the canonical endomorphism P parallel, ∇P = 0)
one considers purely real submanifolds with ∇P = 0. The class of purely real
submanifolds with ∇P = 0 also contains totally real submanifolds, in particular
Lagrangian submanifolds. We obtain Chen-like inequalities for purely real
submanifol...
Conjugacy Problem of Strictly Monotone Maps with Only One Jump Discontinuity
Results in Mathematics - Tập 75 - Trang 1-15 - 2020
The conjugacy problem is one of the important questions in iteration theory. As
far as we know, for discontinuous strictly monotone maps there is no complete
result. In this paper, we investigate the conjugacy problem of strictly monotone
maps with only one jump discontinuity. We give some sufficient and necessary
conditions for the conjugacy relationship. And we present some methods to
construct ...
On the Stability Problem of Differential Equations in the Sense of Ulam
Results in Mathematics - Tập 75 Số 1 - 2020
The $${{\,\mathrm{\mathcal {X}}\,}}$$ -series of a p-group and Complements of Abelian Subgroups
Results in Mathematics - Tập 78 - Trang 1-16 - 2023
Let G be a finite p-group. We denote by $${{\,\mathrm{\mathcal {X}}\,}}_i(G)$$
the intersection of all subgroups of G having index $$p^i$$ in G. In this paper,
the newly introduced series $$\{{{\,\mathrm{\mathcal {X}}\,}}_i(G)\}_i$$ is
investigated and a number of results concerning its behaviour are proved. As an
application of these results, we show that if an abelian subgroup A of G
intersects ...
On the Fundamental Theorem of $$\varvec{(p,q)}$$ -Calculus and Some $$\varvec{(p,q)}$$ -Taylor Formulas
Results in Mathematics - Tập 73 - Trang 1-21 - 2018
In this paper, the (p, q)-derivative and the (p, q)-integration are
investigated. Two suitable polynomial bases for the (p, q)-derivative are
provided and various properties of these bases are given. As application, two
(p, q)-Taylor formulas for polynomials are given, the fundamental theorem of
(p, q)-calculus is included and the formula of (p, q)-integration by part is
proved.
Monge–Kantorovich Norms on Spaces of Vector Measures
Results in Mathematics - Tập 70 - Trang 349-371 - 2016
One considers Hilbert space valued measures on the Borel sets of a compact
metric space. A natural numerical valued integral of vector valued continuous
functions with respect to vector valued measures is defined. Using this
integral, different norms (we called them Monge–Kantorovich norm, modified
Monge–Kantorovich norm and Hanin norm) on the space of measures are introduced,
generalizing the the...
A Construction of Refinable Sets for Interpolating Wavelets
Results in Mathematics - Tập 34 - Trang 359-372 - 2013
This paper describes a general construction of sets of vectors which are useful
for the construction of multivariate interpolating wavelets. The specific
example of bivariate interpolating wavelets on a triangle is presented to
illustrate the general construction.
Reflection Principles for Zero Mean Curvature Surfaces in the Simply Isotropic 3-space
Results in Mathematics - Tập 77 - Trang 1-13 - 2022
Zero mean curvature surfaces in the simply isotropic 3-space $${\mathbb {I}}^3$$
naturally appear as intermediate geometry between geometry of minimal surfaces
in $${\mathbb {E}}^3$$ and that of maximal surfaces in $${\mathbb {L}}^3$$ . In
this paper, we investigate reflection principles for zero mean curvature
surfaces in $${\mathbb {I}}^3$$ as with the above surfaces in $${\mathbb
{E}}^3$$ and $...
On Perturbed Isometries Between the Positive Cones of Certain Continuous Function Spaces
Results in Mathematics - Tập 78 - Trang 1-15 - 2023
Let X, Y be two compact Hausdorff perfectly normal spaces (in particular,
compact metrizable spaces), C(X) be the real Banach space of all continuous
functions on X, and $$C_+(X)$$ be the positive cone of C(X). In this paper, we
show that if there exists a $$\delta $$ -surjective $$\varepsilon $$ -isometry
$$F: C_+(X)\rightarrow C_+(Y)$$ , then X and Y are homeomorphic. Moreover, we
show that ther...
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