What are the isometries of the Hilbert Cube I^\infty = the set of all sequences (x_i) such that x_i \in [0, 1] endowed with the metric
d((x_i), (y_i)) = \sum_{i=0}^\infty 2^{-i} |x_i - y_i| ?
My conjecture is that the only possible isometries of the Hilbert Cube (in this metric) are
f(x_i) = (y_i) such that y_i = x_i or y_i = 1 - x_i
where (x_i) and (y_i) denote sequences in I^\infty and x_i, y_i denote their i-th terms, respectively.
Is it still an open question?
Hi Waldemar! Yes, it's still open.
Hi, I am designing stacked patch antenna in CST Studio Suite using Multilayer Solver. At first I was performing simulation with microstrip line feeding, however now I would like to design an...
17 January 2024 969 0 View
Below you can find equetion which express flow curve which describes the plastic deformation behavior of a material in a uniaxial tensile (or compression) test. I looking for books, articles which...
06 August 2023 5,701 3 View
The intra-genomic diversity of ITS copies of the organisms i am studing is often very high. I am especially intrested in phylogenetic implications and evolutionary reasons. Example for high...
16 February 2022 1,784 0 View
Hi, What would be relatively simple but reliable software for the analysis of enzyme kinetics. I am especially interested in software capable of fitting bell-like curve to pH-dependence enzyme...
03 August 2021 4,842 8 View
Dear fellow researchers, during the course of my studies I am planing to conduct histological examinations of tadpoles (a) several stages and (b) several different species. In the short term I...
28 July 2020 3,794 0 View
I try to model fatigue crack growth in aluminium 2024-T3 alloy. I have plate specimens with finite width 'W' and a circular cut-out with an additional notch, as shown in Figure. 1. The number of...
23 February 2020 9,309 6 View
I am looking at understanding if a correlation exists between survey data on broader attitudes based on Likert scales and positive or negative perceptions. Perceptions are actually also on a scale...
11 October 2018 9,773 5 View
Recently, I tried to measure protease activity of different, crude venoms and also their fractions obtained after SEC. For this purpose I used Pierce™ Colorimetric Protease Assay Kit, which...
13 September 2018 7,236 4 View
Hello, I am using SPSS AMOS 24 to test mediation model with two mediators, in this model variable A predicts variable B via two mediators (see attached file). AMOS gives me estimate of one...
14 September 2017 1,580 21 View
Hi, is it possible to obtain inverse results by immunocytochemistry and Western blotting. Experimental series with low fluorescence in nuclei show strong band in Western blot and oppositely...
26 May 2016 8,813 4 View
We assume that the difference is huge and that it is not possible to compare the two spaces. The R^4 mathematical space considers time as an external controller and the space itself is immobile in...
10 August 2024 6,678 14 View
all math can be traversed by code? all math can be translate to code?
26 July 2024 9,530 0 View
The aim of the research here is to prevent the propagation of the crack in the fabricated elastic medium with useful applications.
25 July 2024 9,976 3 View
There exists a neural network model designed to predict a specific output, detailed in a published article. The model comprises 14 inputs, each normalized with minimum and maximum parameters...
14 July 2024 2,714 3 View
Please suggest me, I want to present my research work.
13 July 2024 1,461 1 View
how i can calculate mathematically COD concentration if i add 1gr from glucose to 1 L distilled water
08 July 2024 9,104 2 View
Computational topology of solitons The well-established research area of algebraic topology currently goes interdisciplinary with computer science in many directions. The Topological Data Analysis...
08 July 2024 2,816 0 View
btw have u ever know about math bounded and reality bounded? for example it happen when student interpret the solution of problem toward mathematics. if you have experience or research about that,...
03 July 2024 6,631 2 View
Greetings mathematicians and physicists, As we know, the idea of assuming a higher space dimension than the natural 3 dimension is effective in solving many physical and mathematical...
29 June 2024 9,220 6 View
In the isosceles triangle ABC (AC=AB), the angle at the vertex is 20°. Point D is chosen on the side AB such that AD=BC. Find the measure of angle CDB.
23 June 2024 7,541 8 View