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We successively reanalyzed modern Lie-algebraic approaches lying in the background of effective constructions of integrable super-Hamiltonian systems on functional N=1,2,3- supermanifolds, possessing rich supersymmetries and endowed with suitably related compatible Poisson structures. As an application, we describe countable hierarchies of new nonlinear Lax-type integrable N=2,3-semi-supersymmetric dynamical systems and constructed their central extended superconformal Lie superalgebra K(1|3) and its finite-dimensional coadjoint orbits, generated by the related Casimir functionals. Moreover, we generalized these results subject to the suitably factorized super-pseudo-differential Lax-type representations and present the related super-Poisson brackets and compatible suitably factorized Hamiltonian superflows. As an interesting point, we succeeded in the algorithmic construction of integrable super-Hamiltonian factorized systems generated by Casimir invariants of the centrally extended super-pseudo-differential operator Lie superalgebras on the N=1,2,3-supercircle.

The coefficient inverse problem for a degenerate parabolic equation is studied in a free boundary domain. The degeneration of the equation is caused by time dependent function at the higher order derivative of unknown function. It is assumed that the coefficient at the minor derivative of the equation is a polynomial of the first order for the space variable with two unknown time depended functions. The conditions of existence and uniqueness of the classical solution to such inverse problem are established for the weak degeneration case at the Dirichlet boundary conditions and the values of heat moments as overdetermination conditions. [ABSTRACT FROM AUTHOR]

We analyze smooth nonlinear mappings for Hilbert and Banach spaces that carry small balls to convex sets, provided that the radii of the balls are small enough. We focus on the study of new and mildly sufficient conditions for the nonlinear mapping of Hilbert and Banach spaces to be locally convex, and address a suitably reformulated local convexity problem analyzed within the Leray–Schauder homotopy method approach for Hilbert spaces, and within the Lipschitz smoothness condition for both Hilbert and Banach spaces. Some of the results presented in this work prove to be interesting and novel, even for finite-dimensional problems. Open problems related to the local convexity property for nonlinear mappings of Banach spaces are also formulated.

Background and Purpose: The ligands of the imidazoline and α-adrenergic receptors are mainly imidazoline and guanidine derivatives, known as centrally-acting antihypertensives and compounds with potential use in various neurological disorders. The extent of their ionisation has a major influence on their behaviour in the different analytical systems. The main objective of this work was to compare the mechanism of chromatographic retention and electrophoretic mobility under acidic, neutral and basic conditions., Experimental Approach: Multiple Linear Regression and Partial Least Squares Regression were applied for the QSRR (quantitative structure-retention relationship) and QSMR (quantitative structure-mobility relationship) modelling and to select the most important molecular parameters describing the chromatographic and electrophoretic behaviour of the investigated compounds., Key Results: The most important molecular descriptors, such as the chemical composition of the compounds, lipophilicity, polarizability and molecular branching, in the selected QSRR models showed that an important insight into the retention behaviour can be derived from the 0D-, 1D- and 2D-descriptors. The electrophoretic mobility could be explained by 2D- and 3D-descriptors, which provide information on the molecular mass, size and complexity, as well as on the influence of charge transfer and electronic properties on the migration behaviour., Conclusion: All created QSRR/QSMR models met the stringent validation criteria and showed high potential in describing the chromatographic and electrophoretic behaviour of investigated compounds., Competing Interests: Conflict of interest: The authors declare no conflict of interest., (Copyright © 2024 by the authors.)