Variational Principles for Maximization Problems with Lower-semicontinuous Goal Functions

Let X be a completely regular topological space and f a real-valued bounded from above lower semicontinuous function in it. Let C(X) be the space of all bounded continuous real-valued functions in X endowed with the usual sup-norm. We show that the following two properties are equivalent: X is α-favourable (in the sense of the Banach-Mazur game); The set of functions h in C(X) for which f + h attains its supremum in X contains a dense and Gδ-subset of the space C(X). In particular, property (b) has place if X is a compact space or, more generally, if X is homeomorphic to a dense Gδ subset of a compact space.We show also the equivalence of the following stronger properties: X contains some dense completely metrizable subset; the set of functions h in C(X) for which f + h has strong maximum in X contains a dense and Gδ-subset of the space C(X). If X is a complete metric space and f is bounded, then the set of functions h from C(X) for which f + h has both strong maximum and strong minimum in X contains a dense Gδ-subset of C(X).

Językowe wykładniki intencji prawodawcy w Kodeksie Działyńskich

Linguistic Exponents of the Legislator’s Intention in the Działyński Code The article presents syntactic methods of expressing the legislator’s intentions in the medieval legal document called Kodeks Działyńskich (the Działyński code). The intention is understood by the authors as ‘the goal towards which the action of the legislator is directed’. This type of element of a legislative text does not appear in modern legal texts, apart from the Code of Canon Law. However, in the oldest texts, the purpose of which was to change a functioning custom into binding law, the justification for introducing certain regulations was very important. We also pay attention to the information about the legislator, which is included in the text. The information is expressed by pluralis maiestaticus forms of performative verbs. Three types of syntactic structures serve to express the intention of the legislator: subordinate clauses introduced by the conjunction: aby, participial sentence equivalents based on the verb chcieć, and prepositional phrases with prepositions: na, ku and dla. These structures usually occur in preposition to the superior predicate. The fragments excerpted from the text are characterized by a considerable degree of cohesiveness, not only in terms of meaning but also in structure. A sentence or a participal construction in the semantic relation of the goal functions in a broader context, therefore it becomes necessary to introduce reference indicators and anaphorical elements such as repetitions, pronouns and pronominalization.

ONLINE FUZZY CLUSTERING OF INCOMPLETE DATA USING CREDIBILISTIC APPROACH AND SIMILARITY MEASURE OF SPECIAL TYPE

Context. In most clustering (classification without a teacher) tasks associated with real data processing, the initial information is usually distorted by abnormal outliers (noise) and gaps. It is clear that “classical” methods of artificial intelligence (both batch and online) are ineffective in this situation.The goal of the paper is to propose the procedure of fuzzy clustering of incomplete data using credibilistic approach and similarity measure of special type. Objective. The goal of the work is credibilistic fuzzy clustering of distorted data, using of credibility theory. Method. The procedure of fuzzy clustering of incomplete data using credibilistic approach and similarity measure of special type based on the use of both robust goal functions of a special type and similarity measures, insensitive to outliers and designed to work both in batch and its recurrent online version designed to solve Data Stream Mining problems when data are fed to processing sequentially in real time. Results. The introduced methods are simple in numerical implementation and are free from the drawbacks inherent in traditional methods of probabilistic and possibilistic fuzzy clustering data distorted by abnormal outliers (noise) and gaps. Conclusions. The conducted experiments have confirmed the effectiveness of proposed methods of credibilistic fuzzy clustering of distorted data operability and allow recommending it for use in practice for solving the problems of automatic clusterization of distorted data. The proposed method is intended for use in hybrid systems of computational intelligence and, above all, in the problems of learning artificial neural networks, neuro-fuzzy systems, as well as in the problems of clustering and classification.

Pitch as a business PR-text: Communicative and pragmatic aspect

The article discusses pitching as a communication technology and a pitch as a business PRtext. For a more complete and correct definition of the concepts of a pitch and pitching, the semantics of the multi-valued pitch lexeme underlying them are analyzed. The types of pitching are described by the field of activity, by the intended purpose and by the time of the presentation. The subject of the study was the textual features of the investment pitch as a PR communication tool. The main purpose of the work is to analyze the structural and content components of the investment pitch in the communicative and pragmatic aspect, including the characteristics of the addresser, addressee, object, goal, functions, etc. The material for the study was selected using the method of random sampling of 28 video recordings of pitch presentations presented on the foreign TV shows Shark Tank and Dragons’ Den, posted on the social network YouTube. The analysis of the material showed that the text of the pitch is based on the principle of combining standard and expression, noted by V. G. Kostomarov, in relation to the language of the newspaper. The tendency towards standardization is manifested in the typical structure of the pitch, the tendency towards expressiveness — in the use of certain verbal and paraverbal means, with the help of which the addresser seeks to express a subjective attitude not only to the content of speech, but also to the addressee, influencing his consciousness and stimulating him to make the necessary decisions. Based on the identified differential features, the definition of an investment pitch is proposed. It is concluded that the investment pitch can be included in a number of other proposals coming from the PR subject — proposals for cooperation, commercial proposals and proposals for sponsorship, calling it an offer for investors.

Sustainability Problematization and Modeling Opportunities

A sound theoretical ground is required for sustainability related concepts reconciliation and operationalization. The current study investigates the opportunities to conceive a homogenous sustainability model derived from theoretical ecology, using as a prototype the “organization” concept from the Chemical Organizations Theory (COT). A sustainability problematization and a literature examination try to capture and link some useful perspectives and sustainability connected concepts. Some of the most influential methods and tools are reviewed, in particular among those relating to the triple bottom line framework and to the ecological footprint family, together with concepts close to the core sustainability definition, like resilience and circularity. Theoretical ecology provides candidate goal functions based on self-organization gradients, such as fitness functions and thermodynamic orientors. The COT formalism provides a higher abstraction level and the algorithms for patterns identification in a reactions network. The sustainability problematization reveals the motifs of a possible model of “total ecosystem”, which subordinates the anthropic cultural (social–economic) system to the thermodynamic, chemical, biological, and cultural determinisms regulating biological and cultural species of an ecological network.

Optimization problems for ensuring ecological safety of main oil pipelines

This article is devoted to the search for optimal conditions for environmental and economic security of oil main pipelines using classical calculus of variations. The goal functions here are either stochastic reliability criteria for deterministic parametric criteria, or parametric criteria for specified reliability criteria. The functions of the optimization process are environmental and technological indicators of the system, taking into account the characteristics of oil pipelines or a set of measures to improve their reliability. The arguments are environmental and economic indicators that reflect the impact of control actions on the state of the environment and on the level of costs for the implementation of proposals. The formulation and study of the variational problem showed that only the introduction of environmental technologies and structures can minimize the cost of ensuring the safety of the impact of oil main pipelines on the host ecosystem.

A Framework for Optimal Placement of Strain Gauges on Elastic Elements of Force Sensors Using Genetic Algorithms

This paper presents a digital education tool for learning the specifics and behavior of a multi-objective genetic algorithm (MOGA) used to solve the problem of optimal placement of strain gauges on the elastic element of a force sensor. The paper formulates the problem statement and specifies how this problem can be solved using the MOGA. For the problem, the design variables are the locations of strain gauges and angles at which they are positioned. The goal functions are the output signal of the sensor and the measurement error from bending moments, which can be caused by the off-centric application of load. The solution algorithm is implemented within a framework that can be used to investigate and learn how parameters of MOGA influence its performance. The framework is used to run computational experiments for the given problem to find the optimal placement of strain gauges on the elastic element of a given force sensor. The performance of the MOGA in solving this problem is compared to that of the traditional approach.