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It is shown that in order to increase the efficiency of using methods of abstract algebra in modern information technologies, it is important to establish an explicit connection between operations corresponding to various varieties of multivalued logics and algebraic operations. For multivalued logics, the number of variables in which is equal to a prime number, such a connection is naturally established through explicit algebraic expressions in Galois fields. It is possible to define an algebraic δ-function, which allows you to reduce any truth table to an algebraic expression, for the case when the number of values accepted by a multivalued logic variable is equal to an integer power of a prime number. In this paper, we show that the algebraic δ-function can also be defined for the case when the number of values taken by a multivalued logic variable is p − 1, where p is a prime number. This function also allows to reduce logical operations to algebraic expressions. Specific examples of the constructiveness of the proposed approach are presented, as well as electronic circuits that experimentally prove its adequacy. [ABSTRACT FROM AUTHOR]

An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1. For such numbers, it is possible to implement a multiplication algorithm modulo p, similar to the multiplication algorithm modulo the Mersenne number. It is shown that for such numbers a simple algorithm for digital logarithm calculations may be proposed. This algorithm allows, among other things, to reduce the multiplication operation modulo a prime number p = 2n+1 to an addition operation. [ABSTRACT FROM AUTHOR]

Multivalued logics are becoming one of the most important tools of information technology. They are in great demand for creation of artificial intelligence systems that are close to human intelligence, since the functioning of the latter cannot be reduced to the operations of binary logic. At the same time, the problem of improving the efficiency of using the results of research in multivalued logics, as well as the problem of interpreting variables of multivalued logic, is acute. These problems create certain interdisciplinary barriers and make it difficult to implement the results of research in the field of multivalued logics in other fields of knowledge. It is shown that the problem of interpreting multivalued logic variables can be removed by establishing correspondence with fuzzy logic variables. Improving the efficiency of using of operations of multivalued logics and their variables can be provided by using their close connection to Galois fields. This connection, among other things, makes it possible to reduce any operations of multivalued logics, the number of variables in which is equal to a prime number, to algebraic functions whose arguments take values in Galois fields. This allows, among other things, to eliminate the very cumbersome constructions used in works on multivalued logic and make its apparatus convenient for use in related scientific disciplines in information technology. Direct verification of the adequacy of algorithms based on the use of Galois fields can be carried out by means of radio-electronic circuits, examples of which are presented in the present paper. [ABSTRACT FROM AUTHOR]

Utilizing turbidimetry data, an examination is conducted on the behavior of solutions containing N-vinylpyrrolidone and vinyl propyl ether copolymer within a temperature range coinciding with the occurrence of a phase transition. The investigation reveals that within specific conditions prevailing in this domain, the emergence of entities denoted as hydrophobic–hydrophilic associates is conceivable. These entities are characterized by the presence of a relatively dense core, upheld by hydrophobic interplays, and they are proficient in effectively dispersing irradiation within the optical spectrum. Encircling this core is a hydrophilic periphery that impedes the formation of insoluble precipitates. The development of such associates transpires when hydrophobic interactions have attained a discernible prominence, although they remain inadequate to counteract the forces that drive the expansion of macromolecular coils. Under these circumstances, the energetically favored course of action entails the constitution of a core for the aforementioned associates, involving discrete segments from diverse macromolecules. Notably, the introduction of an additional constituent (ethanol) to the solution, which selectively mitigates hydrophobic interactions, serves to stabilize the hydrophobic–hydrophilic associations. [ABSTRACT FROM AUTHOR]

Generalized Rademacher functions, constructed as a sequence of elements of Galois fields are intended to find the spectral representation of signals with levels. These functions form a complete basis on the interval corresponding to -1 discrete time intervals and for passing into the classical Rademacher functions. The advantage of such spectra obtained using Galois Fields Fourier Transform is that the range of variation of the spectrum amplitudes remains the same as the range of variation of the original signal, which is modeled on discrete time functions taking values in the Galois field. [ABSTRACT FROM AUTHOR]

It has been shown that there exist conditions under which thermosensitive copolymers of N-vinylpyrrolidone with methyl acrylate form hydrophobic–hydrophilic associations, which are unstable dynamic meshes, the bonds in which are continuously broken and created again, and the nature of the formation of such meshes depends significantly on the proportion of the hydrophobic component in the copolymer. It is shown that the interaction of the above copolymers with polyacrylic acid results in the formation of not only classical interpolymer complexes, but also hydrophilic interpolymer associates, which also represent unstable networks existing in a dynamic mode. In such meshes, the molecules of the above copolymers serve as a kind of cross-agent connecting the polyacid molecules. There are also conditions under which such meshes acquire a complex structure, since unstable bonds between macromolecular tangles of both the same and different types take part in their formation. It is shown that the transition from the formation of interpolymer complexes to the formation of hydrophilic interpolymer associates can occur, among other things, due to changes in the acidity or concentration of low-molecular salt in solution. [ABSTRACT FROM AUTHOR]

Abstract: We designed new terpolymers responsive to pH, temperature, and metal ions. Binding of metal ions amplifies the magnitude of thermal response. Variations in the pH and concentration of metal ions enable tuning the lower critical solution temperature (LCST) and thermosensitivity in a broad range. Upon changes in pH and/or temperature, polymers form associates with narrow size distribution ranging from less than 5nm to more than 250nm in diameter. The multistimuli-responsive properties of newly synthesized polymers are the result of combining hydrophobic, ionogenic, and non-charged hydrophilic moieties within the terpolymer structure. Polymers are produced by a potentially scalable method from inexpensive starting materials, 2-hydroxyethylacrylate (HEA), butylmethacrylate (BMA), and acrylic acid (AA). Polymers and their aggregates are characterized by NMR, dynamic light scattering, and electron microscopy. The ability to control the size of polymer aggregates and the magnitude of response to external stimuli opens exciting opportunities for practical applications. [Copyright &y& Elsevier]