scholarly journals Diagrammatic logic applied to a parameterisation process

2010 ◽  
Vol 20 (4) ◽  
pp. 639-654 ◽  
Author(s):  
CÉSAR DOMÍNGUEZ ◽  
DOMINIQUE DUVAL
Keyword(s):  
Category Theory ◽  
Formal Parameter ◽  
Actual Parameter ◽  
Definition Of ◽  
The Given ◽  
Parameter Passing

This paper provides an abstract definition of a class of logics, called diagrammatic logics, together with a definition of morphisms and 2-morphisms between them. The definition of the 2-category of diagrammatic logics relies on category theory, mainly on adjunction, categories of fractions and limit sketches. This framework is applied to the formalisation of a parameterisation process. This process, which consists of adding a formal parameter to some operations in a given specification, is presented as a morphism of logics. Then the parameter passing process for recovering a model of the given specification from a model of the parameterised specification and an actual parameter is shown to be a 2-morphism of logics.

scholarly journals Data Types as Functions

1978 ◽  
Vol 7 (89) ◽  
Author(s):  
Brian H. Mayoh
Keyword(s):  
Data Type ◽  
Extended Version ◽  
Data Types ◽  
Formal Parameter ◽  
Actual Parameter ◽  
Definition Of ◽  
Simple Definition

This paper introduces a new, simple definition of what a data type is. This definition gives one possible solution of the theoretical problems: when can an actual parameter of type T be substituted for a formal parameter of type T'? When can a type T' be implemented as another type T''? The preprint is an extended version of a paper presented at MFCS 78, Zakopane.

scholarly journals Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
Definition Of ◽  
The Given ◽  
Class Of Functions ◽  
Interval Valued ◽  
New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

scholarly journals A Generalization of the Hausdorff Dimension Theorem for Deterministic Fractals

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1546
Author(s):  
Mohsen Soltanifar
Keyword(s):  
Hausdorff Dimension ◽  
Lebesgue Measure ◽  
Virtual World ◽  
Fractal Dimensions ◽  
Definition Of ◽  
The Given

How many fractals exist in nature or the virtual world? In this paper, we partially answer the second question using Mandelbrot’s fundamental definition of fractals and their quantities of the Hausdorff dimension and Lebesgue measure. We prove the existence of aleph-two of virtual fractals with a Hausdorff dimension of a bi-variate function of them and the given Lebesgue measure. The question remains unanswered for other fractal dimensions.

Underground Built Heritage (UBH) as Valuable Resource in China, Japan and Italy

Heritage ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 3208-3237
Author(s):  
Roberta Varriale ◽  
Laura Genovese
Keyword(s):  
Research Council ◽  
Methodological Approach ◽  
National Research Council ◽  
Functional Classification ◽  
Static And Dynamic Analysis ◽  
Built Heritage ◽  
Living Space ◽  
Definition Of ◽  
The Given ◽  
National Systems

Recent research about the theoretical approach to elements of cultural heritage that can be included in the newly born class Underground Built Heritage (UBH), has provided several instruments for the functional classification and the static and dynamic analysis of all artefacts coherent with the given definition, while introducing several criteria for their reuse and the evaluation of connected enhancement processes as well. These guidelines can be adopted to analyze single artefacts, groups of homogenous or heterogeneous elements, and also selected territorial assets or national systems, even at a comparative level. With reference to this potential, research results from the application of this new methodological approach to the outputs of three ongoing projects by the National Research Council of Italy, all focusing on UBH, in three countries: China, Japan and Italy, are presented. With reference to the above-mentioned geographical contests, the research introduces a comparative study focusing on selected examples of artefacts that have been historically built underground to manage three functions: living space, religion and economy. This study, carried out based on data collected during onsite visits by the authors, consists in three steps: selection and analysis of case studies, definition of level of reuses on the basis of a given scale, and analysis of the different tools adopted for their conservation and enhancement. In the conclusions, possible future implementations of reuses of the analyzed elements are pointed out.

ASSESSMENT AND FORECASTING OF FREIGHT CAR TECHNICAL STATE

2021 ◽  
Vol 2021 (5) ◽  
pp. 40-47
Author(s):  
Elena Rozhkova
Keyword(s):  
Graphical Model ◽  
Technical State ◽  
Distribution Law ◽  
Repair Service ◽  
Statistic Modeling ◽  
Average Operating ◽  
Freight Car ◽  
Run Up ◽  
Definition Of ◽  
The Given

The purpose of this work is the assessment and forecasting of freight car technical state at life stages. The scientific novelty consists in the definition of car operating run-up to the first failure and between failures, and also in the definition of car life to considerable repair fulfillment from the operating run between failures and development of a graphical model of freight car reliability. As a result of the statistic modeling of gondola car operating runs up to the first failure it is defined that the given random value conforms to a normal distribution law, the first car setoff in TOR due to wear failure takes place at the operating run of 85,000 km. Besides the operating run-up to the first failure there was defined an operating run-up between failures. It is proved that the operating run-up between failures conforms to the exponential law of distribution, the mathematical expectation of which is 13,000 km. The results of investigations mentioned above formed the basis of the graphical model of car reliability. An inter-repair service life of a car can be represented as a sum of the following operating run-ups: operating run-ups to the first failure, the product of operating run-ups between failures and the number of failures and a residual operating run-up (from the utmost current repair to the nearest scheduled repair). On the basis of the mentioned it is expedient to consider a technology for the realization of an enlarged repair with the purpose of the repetition exclusion in car setoffs during the inter-repair term. On the basis of the simulator there is obtained the dependence of the frequency of car enlarged current repair fulfillment depending on average operating run-up between failures. At present an enlarged current repair must be carried out only for gondola cars in the planned order after having reached 80,000 km. The repair mentioned can be carried out both under depot conditions, and under conditions of repair workshops. The advantage of such a system of repair consists in the increase car work reliability during the inter-repair term.

scholarly journals Object-Free Definition of Categories

2013 ◽  
Vol 21 (3) ◽  
pp. 193-205
Author(s):  
Marco Riccardi
Keyword(s):  
Binary Relation ◽  
Category Theory ◽  
Final Part ◽  
One To One ◽  
Definition Of

Summary Category theory was formalized in Mizar with two different approaches [7], [18] that correspond to those most commonly used [16], [5]. Since there is a one-to-one correspondence between objects and identity morphisms, some authors have used an approach that does not refer to objects as elements of the theory, and are usually indicated as object-free category [1] or as arrowsonly category [16]. In this article is proposed a new definition of an object-free category, introducing the two properties: left composable and right composable, and a simplification of the notation through a symbol, a binary relation between morphisms, that indicates whether the composition is defined. In the final part we define two functions that allow to switch from the two definitions, with and without objects, and it is shown that their composition produces isomorphic categories.

scholarly journals The Evaluation of Agricultural Land Use Sustainability in the Post-Socialist Camp Countries: Methodological and Practical Aspects

2021 ◽  
Vol 13 (2) ◽  
pp. 59-78
Author(s):  
Olena Kotykova ◽  
Mykola Babych
Keyword(s):  
Land Use ◽  
Agricultural Land ◽  
Sustainable Use ◽  
Correct Selection ◽  
Agricultural Land Use ◽  
Current State ◽  
Definition Of ◽  
The Given ◽  
Selection Of ◽  
Integral Indicator

An effective implementation of the sustainable use of agricultural land program is impossible without reliable results of the current state of the problem. In this sense, the correct selection of indicators and methods for determining the level of stability is important. The authors proposes the definition of the agricultural land use sustainability integral indicator based on three methodological approaches: the construction of the indicators system, each of them reflects some aspects of the land use sustainability at the macro level (according to the specific issues); the construction of the integral indicator for comparing the countries’ land use sustainability. According to the given methods it has been proved that agricultural land use in the countries of the post-socialist camp has a positive dynamics, but the sustainability indicators for all indicators have not achieved yet. This study was supported in part by the Erasmus SUPPA program – Jean Monnet Associations Application No 611556-EPP-1-2019-1-UA-EPPJMO-SUPPA.

scholarly journals Model of the co-operative trade alliance for independent retail networks in Czech Republic

2011 ◽  
Vol 59 (2) ◽  
pp. 377-384
Author(s):  
Marek Záboj
Keyword(s):  
Czech Republic ◽  
Trade Negotiation ◽  
Factors Affecting ◽  
Regional Market ◽  
Fast Moving Consumer Goods ◽  
Definition Of ◽  
Common Trade ◽  
The Given ◽  
Retail Formats ◽  
Transnational Trade

The main objective of the contribution is proposal of the model of co-operative trade alliance for independent trade alliances with fast-moving consumer goods (FMCG) in Czech Republic. Reason of the choice of this topic is sustain of variety of retail formats in Czech market in connection with position small and medium sized trade firms in comparison with transnational trade chains. Independent trade firms face to much bigger competitors operating supermarkets and hypermarkets, namely not even in size of sales area, width and depth of the assortment but also in possibility of negotiation of more profitable trade conditions with their suppliers. Effort of these independent trade firms, which operate mostly just in local or maximally regional market, is then mutual co-operation in form of consumer co-operatives, associations, alliances and networks. These groupings then mainly through common trade negotiation and purchase get for much more advantageous delivery and payment conditions from their suppliers. Besides they can participate in mutual financing of using of promotion instruments. Partial aim of the paper is investigation of opinion and willingness of Czech trade alliances with FMCG to utilize the opportunity of mutual co-operation in common trade alliance. Next partial goal is identification of the factors affecting formation of joint co-operative grouping and its structure, eventually definition of entry conditions which should be fulfilled by individual members.The system approach will be used to realize the given objective. This approach appears as the most suitable in consideration of anticipated structure and character of supposed model. The result will be then proposal of model of mutual co-operation between individual trade alliances.

scholarly journals The Problem of Fundamentalism in Foreign Orthodoxy: the Review

2019 ◽  
pp. 23-35
Author(s):  
Anna M. Yakovleva ◽  
◽  
Alexey V. Volobuev ◽  
Keyword(s):  
Public Sphere ◽  
21St Century ◽  
The Public ◽  
Mass Consciousness ◽  
Conservative Beliefs ◽  
The Public Sphere ◽  
Definition Of ◽  
The Given ◽  
Modern Era ◽  
The Church

. The review deals with the problem of Orthodox fundamentalism in the discussion of Englishspeaking authors of different denominations, representatives of canonical and non-canonical Orthodox churches, which took place in theological discussions, in journalism and at scientific conferences mainly in recent years. The main materials are first introduced into the scientific circulation in Russian. The concepts of fundamentalism in Orthodoxy in the foreign press are presented; the definitions of Orthodox fundamentalism, the main theses of opponents and their argumentation are given. Frequently, the word “fundamentalism” in relation to Orthodoxy is used as a banal nickname for those opponents who have traditional or conservative beliefs, are prone to “ritualism”, shows intolerance and lack of readiness for dialogue, including ecumenical. However, since the beginning of the 21st century, theologians, priests and scholars have been trying to give a stricter definition of such fundamentalism as a phenomenon of the modern era, especially in its demise. It is primarily about the attitude to the works of the holy fathers of the Church. It is expressed, in particular, the opinion that the veneration of patristic writings, along with the resolutions of the Councils (which constitutes the Holy Tradition) should be revised. However, the concept of “Orthodox fundamentalism”, as follows from the given review, has not yet been formed. But one can speak of such signs of it, connected, in particular, with a wide exit to the public sphere of mass consciousness, as the striving to minimize theological provisions, absolutization of some provisions of dogma to the detriment of others, and the logos (modern) reading of the myth.

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.

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