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EN
Carnot’s four-part ideal-gas cycle includes both isothermal and adiabatic expansions and compressions. Analyzing this cycle provides the fundamental basis for statistical thermodynamics. We explore the cycle here from a pedagogical view in order to promote understanding of the macroscopic thermodynamic entropy, the state function associated with thermal energy changes. From the alternative microscopic viewpoint the Hamiltonian H(q, p) is the energy and entropy is the (logarithm of the) phase-space volume Ω associated with a macroscopic state. We apply two novel forms of Hamiltonian mechanics to Carnot’s Cycle: (1) Gauss’ isokinetic mechanics for the isothermal segments and (2) Doll’s Tensor mechanics for the isentropic adiabatic segments. We explore the equivalence of the microscopic and macroscopic views of Carnot’s cycle for simple fluids here, beginning with the ideal Knudsen gas and extending the analysis to a prototypical simple fluid.
EN
The aim of the article is linguistic and semantic analysis of concepts such as armed conflict, war, civil war and coup d’etat. In the author’s opinion, these concepts do not coincide, and their correct classification will lead to a better understanding of the nature of international conflicts. Authors also draws attention to the need for cooperation between scientists and politicians in the aspect of greater effectiveness of international humanitarian law.
PL
Celem artykułu jest analiza językowa oraz znaczeniowa takich pojęć jak: konflikt zbrojny, wojna, wojna domowa i zamach stanu. W opinii autorów pojęcia te nie są ze sobą zbieżne, a dokonanie ich prawidłowej klasyfikacji doprowadzi do lepszego zrozumienia istoty konfliktów międzynarodowych. Autorzy zwracają ponadto uwagę, na konieczność współpracy naukowców z politykami w aspekcie większej skuteczności międzynarodowego prawa humanitarnego.
3
Content available remote Multiplicative Transition Systems
EN
The paper is concerned with algebras whose elements can be used to represent runs of a system from a state to a state. These algebras, called multiplicative transition systems, are categories with respect to a partial binary operation called composition. They can be characterized by axioms such that their elements and operations can be represented by partially ordered multisets of a certain type and operations on such multisets. The representation can be obtained without assuming a discrete nature of represented elements. In particular, it remains valid for systems with infinitely divisible elements, and thus also for systems with elements which can represent continuous and partially continuous runs.
4
Content available remote Multiplicative Transition Systems
EN
The paper is concerned with algebras whose elements can be used to represent runs of a system from a state to a state. These algebras, called multiplicative transition systems, are categories with respect to a partial binary operation called composition. They can be characterized by axioms such that their elements and operations can be represented by partially ordered multisets of a certain type and operations on such multisets. The representation can be obtained without assuming a discrete nature of represented elements. In particular, it remains valid for systems with innitely divisible elements, and thus also for systems with elements which can represent continuous and partially continuous runs.
PL
Praca dotyczy algebr, których elementy mogą być użyte do reprezentowania przebiegów dowolnego systemu od stanu do stanu. Te algebry, zwane multyplikatywnymi systemami tranzycyjnymi, są kategoriami ze względu na częściową operację binarną zwaną składaniem. Można je scharakteryzować aksjomatami tak, że ich elementy i operację składania można reprezentować częściowo uporządkowanymi wielozbiorami pewnego typu i operacją składania takich wielozbiorów. Taką reprezentację można otrzymać bez zakładania dyskretności reprezentowanych elementów. W szczególności jest ona możliwa dla systemów o nieskończenie podzielnych elementach, a więc i dla systemów których elementy mogą reprezentować przebiegi ciągłe i częściowo ciągłe.
5
Content available remote Towards a Framework for Modelling Behaviours of Hybrid Systems
EN
The paper is devoted to characterizing hybrid systems by specifying their possible runs, called processes, where each process is represented by a pomset in an intrinsic, global time independent way and can possibly be obtained by composing seąuentially and in parallel other processes.
PL
Praca dotyczy opisywania systemów hybrydowych poprzez definiowanie przebiegów ich działania zwanych procesami, gdzie procesy są reprezentowane strukturami częściowo uporządkowanymi i mog^ być definiowane przez szeregowe i równoległe składanie wcześniej zdefiniowanych procesów.
6
Content available remote Towards a Framework for Modelling Behaviours of Hybrid Systems
EN
The paper is devoted to characterizing hybrid systems by specifying their possible runs, called processes, where each process is represented by a pomset in an intrinsic, global time independent way and can possibly be obtained by composing sequentially and in parallel other processes.
7
Content available remote Behaviour Algebras
EN
The paper is concerned with algebras whose elements can be used to represent runs of a system, called processes. These algebras, called behaviour algebras, are categories with respect to a partial binary operation called sequential composition, and they are partial monoids with respect to a partial binary operation called parallel composition. They are characterized by axioms such that their elements and operations can be represented by labelled posets and operations on such posets. The respective representation is obtained without assuming a discrete nature of represented elements. In particular, it remains true for behaviour algebras with infinitely divisible elements, and thus also with elements which can represent continuous and partially continuous processes. An important consequence of the representation of elements of behaviour algebras by labelled posets is that elements of some subalgebras of behaviour algebras can be endowed in a consistent way with structures such as a graph structure etc.
8
Content available remote Behaviour algebras
EN
The paper is concerned with algebras whose elements can be used to represent runs of a system, called processes. These algebras, called behaviour algebras, are categories with respect to a partial binary operation called seąuential composition, and they arę partial monoids with respect to a partial binary operation called parallel composition. They are characterized by axioms such that their elements and operations can be represented as specific pomsets and specific operations on such pomsets. The respective representation theorem is universal in the sense that it is obtained without assuming a discrete nature of represented elements. In particular, it remains true for behaviour algebras with infinitely divisible elements, and thus also with elements which can represent continuous processes. An important consequence of the representation theorem is that elements of some subalgebras of behaviour algebras can be endowed in a consistent way with structures such as a graph structure etc.
PL
Praca dotyczy algebr częściowych, których elementy mogą służyć do reprezentowania procesów, tzn. przebiegów zachowania się systemów. Algebry te, zwane algebrami zachowań, są kategoriami ze względu na częściową operację binarną składania szeregowego, oraz są monoidami częściowymi ze względu na częściową operację binarną składania równoległego. Zostały one scharakteryzowane aksjomatycznie tak, że ich elementy i operacje można reprezentować klasami izomorficznych poetykietowanych zbiorów częściowo uporządkowanych i operacjami na takich klasach. Orzekające o tym twierdzenie o reprezentacji jest uniwersalne w tym sensie, że zostało uzyskane bez zakładania dyskretnej natury reprezentowanych elementów. W szczególności pozostaje prawdziwe dla algebr zachowań z nieskończenie podzielnymi elementami, które mogą reprezentować procesy ciągłe. Ważną konsekwencją tego twierdzenia jest też to, że elementy pewnych podalgebr algebr zachowań można wyposażać sensownie w struktury takie jak struktury grafowe itp.
9
Content available remote An Axiomatic Characterization of Algebras of Processes of Petri Nets
EN
The paper is concerned with algebras which can be obtained by endowing sets of processes of Petri nets with a sequential and a parallel composition. The considered algebras are categories with additional structures and special properties. It is shown that all structures which enjoy such properties can be represented as algebras of processes of Petri nets.
EN
The paper is concerned with modelling distributed systems by specifying their states and processes. Processes are defined as activities in a universe of objects, each object with a set of possible internal states, each activity changing states of some objects and establishing or destroying relations among objects. Partial operations of composing processes sequenially and in parallel are defined. It is shown that certain sets of processes form together with these operations categories with additional structures and special properties, that processes of a system can be represented as morphisms of such categories, and that independence of processes can be characterized in a natural, purely algebraic way.
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