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
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......
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 m......
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
......
Form Class Groups and Class Fields of CM-Fields
Results in Mathematics - Tập 78 - Trang 1-33 - 2022
Let F be a totally real number field of class number one, and let K be a CM-field with F as its maximal real subfield. For each positive integer N, we construct a class group of certain binary quadratic forms over F which is isomorphic to the ray class group of K modulo N. Assuming further that the narrow class number of F is one, we construct a class field of the reflex field of K in terms of the......
Some Applications of the Hodge-de Rham Decomposition to Ricci Solitons
Results in Mathematics - Tập 60 - Trang 245-254 - 2011
The aim of this paper is to present a link between the Perelman potential for a compact Ricci soliton M
n
and the Hodge-de Rham decomposition theorem, we shall use this result to present an integral formula which enables us to establish conditions under which the Ricci soliton is trivial. Moreover, given a Ricci soliton such that its associated v......
On the Comparison Of The M-Th Eigenvalue for the Equation Ly+λq(x)y=0
Results in Mathematics - Tập 20 - Trang 481-498 - 2013
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