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Optimality conditions for fractional variational problems with Caputo-Fabrizio fractional derivatives
In this paper, we study the necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrange...
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On the relation between measurement outcomes and physical properties
One of the most difficult problems in quantum mechanics is the analysis of the measurement processes. In this paper, we point out that many of these...
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A Brief Review of Non-convex Single-Objective Optimization
Single-objective optimization methods are among the mathematical methods most widely used in various applications. The classical methods starting...
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Well-Posedness and Coderivative Calculus
This chapter concerns the study of two important topics in variational analysis that don’t seem to be related to each other at the first glance.
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Random Closed Sets and Capacity Functionals
As the name suggests, a random set is an object with values being sets, so that the corresponding record space is the space of subsets of a given...
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Hierarchies and Performance Scores
As a synthesis of the structural parts described in Chapter 32 through Chapter 34 we establish the overall structure of performance. The objects of...
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Properties of the Linear Unconditional Problem of Combinatorial Optimization on Arrangements Under Probabilistic Uncertainty
The paper establishes the necessary condition for the solution of a linear unconditional problem of combinatorial optimization on arrangements where...
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Modulation
This chapter deals with the central issue of modulation between two given tonalities. It involves explicit models of tonalities, of cadences and—even...
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Global Compositions
The categories ObLoc and Loc are representations of local objects, i.e., of objects that are not composed of proper “parts”. However, music mainly...
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Coordinate-to-Operator feedback: Properties, features, outlooks
Consideration was given to the problem of control of the dynamic plants operating under uncertainty and, in particular, under unmeasurable external...
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Modeling of Extremal and Controllable Extremal Fuzzy Processes
New approaches to modeling so-called extremal fuzzy dynamic systems (EFDS) are developed. By applying the results of Chapters 3 and 4, fuzzy...
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Hysteresis model of unconscious-conscious interconnection: Exploring dynamics on m-adic trees
In this brief note, we focus attention on a possible implementation of a basic hysteretic pattern (the Preisach one), suitably generalized, into a...
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Subdifferentiation of Regularized Functions
We study the Moreau regularization process for functions satisfying a general growth condition on general Banach spaces. We give differentiability...
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Problems of States Estimation (Filtration) of Extremal Fuzzy Processes
A fuzzy-integral model of an extremal fuzzy process is considered. The model describes the evolution of one class of weakly structurable fuzzy...
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Identification of Fuzzy-Integral Models of Extremal Fuzzy Processes
Based on the fuzzy-integral model constructed in Chap. 5 , methods and algorithms are developed for...
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Extremal Fuzzy Dynamic Systems Theory and Applications
In this book the author presents a new approach to the study of weakly structurable dynamic systems. It differs from other approaches by considering...
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Optimization of Continuous Controllable Extremal Fuzzy Processes and the Choice of Decisions
This chapter deals with the problems of optimization of continuous controllable extremal fuzzy processes that were presented in Chaps. 3–5. Separate...
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Fractal theory of Saturn’s ring
The true reason, in our opinion, for the partition of Saturn’s ring as well as the rings of other planets into a large number of small subrings is...
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Orbits
This chapter deals with groups of symmetries, their action and orbits as musicological and mathematical concepts. Elementary local...