scholarly journals On Algebras of Algorithms and Specifications over Uninterpreted Data

2018 ◽  
Vol 26 (2) ◽  
pp. 141-147
Author(s):  
Ievgen Ivanov ◽  
Artur Korniłowicz ◽  
Mykola Nikitchenko
Keyword(s):  
Mathematical Models ◽  
Systems Theory ◽  
Data Structures ◽  
Computer Programs ◽  
Partial Function ◽  
Levels Of Abstraction ◽  
Multidimensional Arrays ◽  
Program Semantics ◽  
Algorithmic Algebra ◽  
Definition Of

Summary This paper continues formalization in Mizar [2, 1] of basic notions of the composition-nominative approach to program semantics [13] which was started in [8, 11]. The composition-nominative approach studies mathematical models of computer programs and data on various levels of abstraction and generality and provides tools for reasoning about their properties. Besides formalization of semantics of programs, certain elements of the composition-nominative approach were applied to abstract systems in a mathematical systems theory [4, 6, 7, 5, 3]. In the paper we introduce a definition of the notion of a binominative function over a set D understood as a partial function which maps elements of D to D. The sets of binominative functions and nominative predicates [11] over given sets form the carrier of the generalized Glushkov algorithmic algebra [14]. This algebra can be used to formalize algorithms which operate on various data structures (such as multidimensional arrays, lists, etc.) and reason about their properties. We formalize the operations of this algebra (also called compositions) which are valid over uninterpretated data and which include among others the sequential composition, the prediction composition, the branching composition, the monotone Floyd-Hoare composition, and the cycle composition. The details on formalization of nominative data and the operations of the algorithmic algebra over them are described in [10, 12, 9].

scholarly journals On an Algorithmic Algebra over Simple-Named Complex-Valued Nominative Data

2018 ◽  
Vol 26 (2) ◽  
pp. 149-158
Author(s):  
Ievgen Ivanov ◽  
Artur Korniłowicz ◽  
Mykola Nikitchenko
Keyword(s):  
Data Structures ◽  
Formal Definition ◽  
Existential Quantifier ◽  
Levels Of Abstraction ◽  
Multidimensional Arrays ◽  
Algorithmic Algebra ◽  
System 2 ◽  
Partial Predicate ◽  
Definition Of ◽  
Complex Valued

Summary This paper continues formalization in the Mizar system [2, 1] of basic notions of the composition-nominative approach to program semantics [14] which was started in [8, 12, 10]. The composition-nominative approach studies mathematical models of computer programs and data on various levels of abstraction and generality and provides tools for reasoning about their properties. In particular, data in computer systems are modeled as nominative data [15]. Besides formalization of semantics of programs, certain elements of the composition-nominative approach were applied to abstract systems in a mathematical systems theory [4, 6, 7, 5, 3]. In the paper we give a formal definition of the notions of a binominative function over given sets of names and values (i.e. a partial function which maps simple-named complex-valued nominative data to such data) and a nominative predicate (a partial predicate on simple-named complex-valued nominative data). The sets of such binominative functions and nominative predicates form the carrier of the generalized Glushkov algorithmic algebra for simple-named complex-valued nominative data [15]. This algebra can be used to formalize algorithms which operate on various data structures (such as multidimensional arrays, lists, etc.) and reason about their properties. In particular, we formalize the operations of this algebra which require a specification of a data domain and which include the existential quantifier, the assignment composition, the composition of superposition into a predicate, the composition of superposition into a binominative function, the name checking predicate. The details on formalization of nominative data and the operations of the algorithmic algebra over them are described in [11, 13, 9].

scholarly journals MODIFYING MATHEMATICAL MODELS FOR CALCULATING OPERATIONAL CHARACTERISTICS OF DIESEL ENGINES BURNING RME BIOFUELS / MATEMATINIŲ MODELIŲ PRITAIKYMAS DYZELIŲ, DIRBANČIŲ RME BIODEGALAIS, DARBO PROCESUI IR EKSPLOATACINIAMS RODIKLIAMS SKAIČIUOTI / ДОРАБОТКА МАТЕМАТИЧЕСКИХ МОДЕЛЕЙ РАСЧЕТА ПОКАЗАТЕЛЕЙ РАБОТЫ ДИЗЕЛЯ НА БИОДИЗЕЛИНАХ РРМЭ

Transport ◽  
2011 ◽  
Vol 26 (1) ◽  
pp. 50-60 ◽  
Author(s):  
Sergejus Lebedevas ◽  
Galina Lebedeva ◽  
Kristina Bereišienė
Keyword(s):  
Diesel Engine ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Diesel Engines ◽  
Fuel Injection ◽  
Internal Heat ◽  
Computer Programs ◽  
Toxic Substances ◽  
Load Range ◽  
Operational Characteristics

The article considers and solves the problems of adapting the mathematical models, used in calculating operational characteristics of diesel engines burning mineral diesel oil, to engines converted to RME biofuels. The analysis of mathematical models of calculating the main technical and economic characteristics of diesel engines as well as the parameters of the in-cylinder process and the concentration of toxic substances in the exhaust gases is performed. The need for adjusting the calculation algorithms is also demonstrated. The computer programs based on single-zone thermodynamic models are used in the research. The programs of mathematical modelling are modified, i.e. supplemented with the algorithm for calculating energy characteristics of the combustion products (e.g. specific heat capacity, internal heat, the lower calorific value, etc.). Based on the computer programs, modified for examining diesel engines burning biofuels, the computer-aided mathematical modelling experiment is carried out. The results of modelling are compared with the data obtained in testing the diesel engine 1A41. The mathematical modelling performed demonstrates the accuracy acceptable for solving practical problems: the difference between the obtained calculation results and diesel engine testing data for the load range of (1.0÷0.5) Pi nom does not exceed ± 5÷7%. Higher accuracy of modelling the characteristics of diesel engines, operating in the low- and medium-load modes, may be accounted for by the adjustment of the algorithm for calculating the induction period and the on-set phase of fuel injection. Santrauka Publikacijoje pateikti dyzelio darbo proceso ir eksploatacinių rodiklių skaičiavimo matematinių modelių tobulinimo rezultatai, siekiant matematinius modelius pritaikyti dyzeliui dirbant riebiųjų rūgščių metilesterių, taip pat RME, biodegalais. Atlikta skaičiavimo algoritmų analizė ir pagrįsti pagrindiniai jų tobulinimo aspektai. Sukurtas kompiuterinis programinis modelis, skirtas darbinio kūno dyzelio cilindre energiniams parametrams skaičiuoti (specifinei šilumai, vidinei energijai), dyzeliui dirbant plačiąja elementinės cheminės sudėties biodegalų gama. Atliktas 1A41 dyzelio techninių ir ekonominių bei ekologinių rodiklių modeliavimas kompiuteriu, naudojant patobulintus matematinius modelius. Parodytas gautų rezultatų, pakankamų praktiniams uždaviniams spręsti, tikslumas: dyzeliui dirbant artimos nominaliosios apkrovos režimais (1,0÷0,5) Pi nom skirtumas tarp skaičiavimo ir dyzelio motorinių tyrimų rezultatų neviršija ±5÷7%. Dyzeliui dirbant mažos apkrovos režimu, matematinio modeliavimo rezultatų adekvatumo didinimas susijęs su kuro įpurškimo fazės bei savaiminio užsiliepsnojimo indukcijos periodo skaičiavimo algoritmo tobulinimu. Резюме Рассмотрены и решены задачи адаптации математических моделей расчета показателей дизеля при переводе их работы с минерального дизелина на биодизелины метилового эфира рапсового масла (МЭРМ). Выполнен анализ и дано обоснование направлений доработки расчетных алгоритмов ряда однозонных термодинамических математических моделей, используемых в практике исследования эксплуатационных показателей, параметров индикаторного процесса и эмиссии токсичных компонентов в выхлопных газах дизелей. В форме программного модуля составлен алгоритм расчета энергетических параметров рабочего тела в цилиндре (удельной теплоемкости, теплоты сгорания, внутренней энергии) для топлив с широким элементарным химическим составом. С использованием доработанных компьютерных программ выполнен широкий расчетный эксперимент и сопоставлены его результаты с данными моторных стендовых испытаний одноцилиндрового отсека дизеля 1А41. Показана приемлемая для решения практических задач точность математического моделирования: для нагрузочных режимов (1÷0,5) Pmi расхождения расчетных и экспериментальных значений параметров работы дизеля не превышают ±5÷7%. Повышение качества моделирования показателей дизеля на режимах средних и малых нагрузок связано с уточнением алгоритма расчета периода индукции и фазы начала видимого горения топлива в цилиндре.

scholarly journals Sensing the City: Legibility in the Context of Mediated Spatial Terrains

2018 ◽  
Vol 22 (1) ◽  
pp. 90-102 ◽  
Author(s):  
Sharon Wohl
Keyword(s):  
Systems Theory ◽  
Urban Space ◽  
Complex Adaptive Systems ◽  
Adaptive Systems ◽  
Complex Adaptive ◽  
Complex Adaptive Systems Theory ◽  
Definition Of ◽  
The City

Smartphones, with their “pervasive presence” in contact with our bodies, have come to act as sensory prosthetics that mediate our experience of the city. They activate new possibilities of navigating the urban, such that we can find exactly what we want, rather than what has been placed before us. This article argues that smartphone technologies produce a more fluid engagement with urban space: where space is not so much “given” as “enacted.” In this context, notions of “legibility” take on new algorithmic and virtual forms. Thus, according to Hamilton and colleagues, where “the legible city waited to be read, the transparent city of data waits to be accessed.” Here, stable features dissolve as urban space becomes increasingly fluid and contingent, no longer limited by static patterns of inhabitation. Instead, how we move and where we move shift in accordance with the kinds of urban resources being activated at any given location, at any given moment, and in conjunction with the shifting vicissitudes of the crowd. In this context, the virtual (in its technological definition of cyber-enabled or -enacted space) mediates and activates the virtual (in its philosophical definition pertaining to the capacities of an entity that may or may not be manifested depending on context). The article considers the implications of this novel spatial mediation using an ontological perspective informed by complex adaptive systems theory, which considers forms and objects not as absolutes but rather as contingent entities activated through interactions.

scholarly journals Computer Synthesis Approaches of Hyperboloid Gear Drives with Linear Contact

2014 ◽  
Vol 44 (3) ◽  
pp. 3-20 ◽  
Author(s):  
Valentin Abadjiev ◽  
Haruhisa Kawasaki
Keyword(s):  
Mathematical Models ◽  
Contact Point ◽  
Optimal Solution ◽  
Computer Programs ◽  
Strength Analysis ◽  
Computer Design ◽  
Scientific Support ◽  
High Reduction ◽  
The Creation ◽  
Gear Drives

Abstract The computer design has improved forming different type software for scientific researches in the field of gearing theory as well as performing an adequate scientific support of the gear drives manufacture. Here are attached computer programs that are based on mathematical models as a result of scientific researches. The modern gear transmissions require the construction of new mathematical approaches to their geometric, technological and strength analysis. The process of optimization, synthesis and design is based on adequate iteration procedures to find out an optimal solution by varying definite parameters. The study is dedicated to accepted methodology in the creation of soft- ware for the synthesis of a class high reduction hyperboloid gears - Spiroid and Helicon ones (Spiroid and Helicon are trademarks registered by the Illinois Tool Works, Chicago, Ill). The developed basic computer products belong to software, based on original mathematical models. They are based on the two mathematical models for the synthesis: “upon a pitch contact point” and “upon a mesh region”. Computer programs are worked out on the basis of the described mathematical models, and the relations between them are shown. The application of the shown approaches to the synthesis of commented gear drives is illustrated.

scholarly journals Categories as Mathematical Models

2018 ◽  
Author(s):  
David I. Spivak
Keyword(s):  
Dynamical Systems ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Category Theory ◽  
Vector Spaces ◽  
Mathematical Objects ◽  
Working Definition ◽  
Modelling Framework ◽  
Categorical Models ◽  
Definition Of

Category theory is presented as a mathematical modelling framework that highlights the relationships between objects, rather than the objects in themselves. A working definition of model is given, and several examples of mathematical objects, such as vector spaces, groups, and dynamical systems, are considered as categorical models.

scholarly journals FIPS: An R Package for Biomathematical Modelling of Human Fatigue Related Impairment

2020 ◽  
Author(s):  
Michael David Wilson ◽  
Luke Joseph Gough Strickland ◽  
Timothy Ballard
Keyword(s):  
Mathematical Models ◽  
Open Source ◽  
Data Structures ◽  
R Package ◽  
System Safety ◽  
Model Interpretation ◽  
Performance Impairment ◽  
Significant Barrier ◽  
Human Fatigue ◽  
Interpretation Model

In many workplace contexts, accurate predictions of a human’s fatigue state can drastically improve system safety. Biomathematical models of fatigue (BMMs) are a family of dynamic phenomenological models that predict the neurobehavioural outcomes of fatigue (e.g., sleepiness, performance impairment) based on sleep/wake history (Dawson, Darwent, & Roach, 2017). However, to-date there are no open source implementations of BMMs, and this presents a significant barrier to their broadscale adoption by researchers and industry practitioners. FIPS is an open source R package (R Core Team, 2020) to facilitate BMM research and simulation. FIPS has implementations of several published bio-mathematical models and includes functions for easily manipulating sleep history data into the required data structures. FIPS also includes default plot and summary methods to aid model interpretation. Model objects follow tidy data conventions (Wickham, 2014), enabling FIPS to be integrated into existing research workflows of R users.

scholarly journals One Approach to the Synthesis, Design and Manufacture of Hyperboloid Gear Sets With Face Mating Gears. Part 1: Basic Theoretical and Cad Experience

2016 ◽  
Vol 46 (2) ◽  
pp. 3-26 ◽  
Author(s):  
Valentin Abadjiev ◽  
Emilia Abadjieva
Keyword(s):  
Mathematical Modelling ◽  
Mathematical Models ◽  
Contact Point ◽  
Computer Programs ◽  
Tooth Contact ◽  
Synthesis Design ◽  
Gear Drives ◽  
Design And Manufacture ◽  
Special Case

Abstract Hyperboloid gear drives with face mating gears are used to transform rotations between shafts with non-parallel and non-intersecting axes. A special case of these transmissions are Spiroid and Helicon gear drives. The classical gear drives of this type are the Archimedean ones. The objective of this study are hyperboloid gear drives with face meshing, when the pinion possesses threads of conic convolute, Archimedean and involute types, or the pinion has threads of cylindrical convolute, Archimedean and involute types. For simplicity, all three types transmis- sions with face mating gears and a conic pinion are titled Spiroid and all three types transmissions with face mating gears and a cylindrical pinion are titled Helicon. Principles of the mathematical modelling of tooth contact synthesis are discussed in this study. The presented research shows that the synthesis is realized by application of two mathematical models: pitch contact point and mesh region models. Two approaches for synthesis of the gear drives in accordance with Olivier’s principles are illustrated. The algorithms and computer programs for optimization synthesis and design of the studied hyperboloid gear drives are presented.

The Holon/Parton Theory of the Unit of Culture (or the Meme, and Narreme)

2018 ◽  
pp. 1590-1627
Author(s):  
J. T. Velikovsky
Keyword(s):  
Cultural Studies ◽  
Systems Theory ◽  
Information Science ◽  
Theory Model ◽  
Communication Media ◽  
Evolutionary Systems ◽  
Arts And Sciences ◽  
The Arts ◽  
Definition Of

A universal problem in the disciplines of communication, creativity, philosophy, biology, psychology, sociology, anthropology, archaeology, history, linguistics, information science, cultural studies, literature, media and other domains of knowledge in both the arts and sciences has been the definition of ‘culture' (see Kroeber & Kluckhohn, 1952; Baldwin et al., 2006), including the specification of ‘the unit of culture', and, mechanisms of culture. This chapter proposes a theory of the unit of culture, or, the ‘meme' (Dawkins, 1976; Dennett, 1995; Blackmore, 1999), a unit which is also the narreme (Barthes, 1966), or ‘unit of story', or ‘unit of narrative'. The holon/parton theory of the unit of culture (Velikovsky, 2014) is a consilient (Wilson, 1998) synthesis of (Koestler, 1964, 1967, 1978) and Feynman (1975, 2005) and also the Evolutionary Systems Theory model of creativity (Csikszentmihalyi, 1988-2014; Simonton, 1984-2014). This theory of the unit of culture potentially has applications across all creative cultural domains and disciplines in the sciences, arts and communication media.

The Missing System in Social Work's Application of Systems Theory

1982 ◽  
Vol 63 (9) ◽  
pp. 547-553 ◽  
Author(s):  
Judith Marks Mishne
Keyword(s):  
Social Work ◽  
Knowledge Base ◽  
Systems Theory ◽  
Psychological Perspective ◽  
The Social ◽  
Definition Of

Amid ongoing struggles regarding definition of the knowledge base for the social work profession, a meaningful application of an ego psychological perspective offers a significant, although not exclusive link. The concept is capable of contributing to coherence in the educational and practice base of social work.

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