{'fraction_non_alphanumeric': 0.01104417670682731, 'fraction_numerical': 0.0, 'mean_word_length': 5.516339869281046, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Fundamental Limits of Wave Control in Smart Environment

We focus on the wireless communication with several independent nodes in the bounded space. In particular, we discuss the existence and uniqueness of solutions for artificially constructing reachable intervals of wireless channel by adjusting the distribution of singular value of the multiple observation points simultaneously, under the point excitation sources in two-dimensional space. In this paper, it is theoretically proved that there is no physical exact solution for more than five observation points under part of the fixed wireless channel. In practical engineering, no amount of RIS arrays or elements can be deployed to construct a physical solution that accommodates more than five receivers simultaneously, when part of the wireless channel is given in advanced and unchangeable. Fundamental limits of wave control in smart environment is given by the number and range of independent variables of underdetermined functions.