Predictability problems of global change as seen through natural systems complexity description. 2. Approach

Developing the general statements of the proposed global change theory, outlined in Part 1 of the publication, Kolmogorov's probability space is used to study properties of information measures (unconditional, joint and conditional entropies, information divergence, mutual information, etc.). Sets of elementary events, the specified algebra of their sub-sets and probability measures for the algebra are composite parts of the space. The information measures are analyzed using the mathematical expectance operator and the adequacy between an additive function of sets and their equivalents in the form of the measures. As a result, explanations are given to multispectral satellite imagery visualization procedures using Markov's chains of random variables represented by pixels of the imagery. The proposed formalism of the information measures application enables to describe the natural targets complexity by syntactically governing probabilities. Asserted as that of signal/noise ratios finding for anomalies of natural processes, the predictability problem is solved by analyses of temporal data sets of related measurements for key regions and their background within contextually coherent structures of natural targets and between particular boundaries of the structures

Predictability problems of global change as seen through natural systems complexity description. 1. General Statements

The overall problem of global change is considered as the mathematical discrete dynamics discipline that deals with the sets, measures and metrics (SMM) categories in information sub-spaces. The SMM conception enables to unify techniques of data interpretation and analysis and to explain how effectively the giant amounts of information from multispectral satellite radiometers and ground-based instruments are to be processed. It is shown that Prigogine's chaos/order theory and Kolmogorov's probability space are two milestones in understanding the predictability problems of global change. The essence of the problems is maintained to be in filtering out a “useful signal” that would spread from key regions of the globe as compared to their background. Global analysis, interpretation and modelling issues are outlined in the framework of incorrect mathematical problems and of the SMM categories, which contribute to solving the comparability problem for different sets of observations

Piezo-Responsive Hydrogen-Bonded Frameworks Based on Vanillin-Barbiturate Conjugates

A concept of piezo-responsive hydrogen-bonded π-π-stacked organic frameworks made from Knoevenagel-condensed vanillin–barbiturate conjugates was proposed. Replacement of the substituent at the ether oxygen atom of the vanillin moiety from methyl (compound 3a) to ethyl (compound 3b) changed the appearance of the products from rigid rods to porous structures according to optical microscopy and scanning electron microscopy (SEM), and led to a decrease in the degree of crystallinity of corresponding powders according to X-ray diffractometry (XRD). Quantum chemical calculations of possible dimer models of vanillin–barbiturate conjugates using density functional theory (DFT) revealed that π-π stacking between aryl rings of the vanillin moiety stabilized the dimer to a greater extent than hydrogen bonding between carbonyl oxygen atoms and amide hydrogen atoms. According to piezoresponse force microscopy (PFM), there was a notable decrease in the vertical piezo-coefficient upon transition from rigid rods of compound 3a to irregular-shaped aggregates of compound 3b (average values of d33 coefficient corresponded to 2.74 ± 0.54 pm/V and 0.57 ± 0.11 pm/V), which is comparable to that of lithium niobate (d33 coefficient was 7 pm/V). © 2022 by the authors.2.1.06.03, 20211572; Russian Foundation for Basic Research, РФФИ: 20-53-00043-Bel_a; Ministry of Science and Technology, Taiwan, MOST: 19-52-06004 MNTI_a; Ural Federal University, UrFU: 2968; Ministry of Science and Higher Education of the Russian Federation: 075-15-2021-677The work was supported by the Russian Foundation for Basic Research (RFBR, project no. 20-53-00043-Bel_a) and the PFM measurements were done under RFBR and MOST project no. 19-52-06004 MNTI_a. The equipment of the Ural Center for Shared Use “Modern nanotechnology” Ural Federal University (Reg. No. 2968), which is supported by the Ministry of Science and Higher Education RF (project No. 075-15-2021-677), was used. T.V.S. acknowledges the support from the State Program of Scientific Researchers of Belarus (research issue 2.1.06.03, state registration number: 20211572)