scholarly journals A NOTE ON THE CANTOR-SCHROEDER-BERNSTEIN THEOREM AND ITS PROOF WITHOUT WORDS

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Z.R. Konigsberg
Keyword(s):  
Bernstein Theorem

A proof for Cantor-Schröder-Bernstein Theorem using the diagonal argument

2021 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Bernstein Theorem ◽  
Diagonal Argument

We prove Cantor-Schröder-Bernstein theorem using the diagonal argument.

scholarly journals A simple visual proof of the Schröder-Bernstein theorem

10.4171/em/65 ◽  
2007 ◽  
pp. 118-120
Author(s):  
Dongvu Tonien
Keyword(s):  
Bernstein Theorem

scholarly journals Input Pattern Classification Based on the Markov Property of the IMBT with Related Equations and Contingency Tables

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 245
Author(s):  
István Finta ◽  
Sándor Szénási ◽  
Lóránt Farkas
Keyword(s):  
Binary Tree ◽  
Contingency Tables ◽  
Markov Property ◽  
Input Pattern ◽  
Statistical Characteristics ◽  
Bernstein Theorem ◽  
Data Packets ◽  
Efficient Data ◽  
Search Operation ◽  
Fibonacci Sequences

In this contribution, we provide a detailed analysis of the search operation for the Interval Merging Binary Tree (IMBT), an efficient data structure proposed earlier to handle typical anomalies in the transmission of data packets. A framework is provided to decide under which conditions IMBT outperforms other data structures typically used in the field, as a function of the statistical characteristics of the commonly occurring anomalies in the arrival of data packets. We use in the modeling Bernstein theorem, Markov property, Fibonacci sequences, bipartite multi-graphs, and contingency tables.

scholarly journals Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Ruiwei Xu ◽  
Linfen Cao
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Indefinite Metric ◽  
Bernstein Theorem ◽  
Strictly Convex ◽  
Convex Solution

Letf(x)be a smooth strictly convex solution ofdet(∂2f/∂xi∂xj)=exp(1/2)∑i=1nxi(∂f/∂xi)-fdefined on a domainΩ⊂Rn; then the graphM∇fof∇fis a space-like self-shrinker of mean curvature flow in Pseudo-Euclidean spaceRn2nwith the indefinite metric∑dxidyi. In this paper, we prove a Bernstein theorem for complete self-shrinkers. As a corollary, we obtain if the Lagrangian graphM∇fis complete inRn2nand passes through the origin then it is flat.

ON THE GAUSSIAN CURVATURE OF MAXIMAL SURFACES AND THE CALABI–BERNSTEIN THEOREM

2001 ◽  
Vol 33 (4) ◽  
pp. 454-458 ◽  
Author(s):  
LUIS J. ALÍAS ◽  
BENNETT PALMER
Keyword(s):  
Minkowski Space ◽  
Upper Bound ◽  
Gaussian Curvature ◽  
Total Curvature ◽  
Local Geometry ◽  
Maximal Surface ◽  
Bernstein Theorem ◽  
New Approach ◽  
Maximal Surfaces

In this paper, a new approach to the Calabi–Bernstein theorem on maximal surfaces in the Lorentz– Minkowski space L3 is introduced. The approach is based on an upper bound for the total curvature of geodesic discs in a maximal surface in L3, involving the local geometry of the surface and its hyperbolic image. As an application of this, a new proof of the Calabi–Bernstein theorem is provided.

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