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    Tytuł:
    The monogenic functional calculus
    Autorzy:
    Jefferies, Brian
    McIntosh, Alan
    Picton-Warlow, James
    Powiązania:
    https://bibliotekanauki.pl/articles/1216280.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    functional calculus
    Clifford algebra
    monogenic function
    Opis:
    A study is made of a symmetric functional calculus for a system of bounded linear operators acting on a Banach space. Finite real linear combinations of the operators have real spectra, but the operators do not necessarily commute with each other. Analytic functions of the operators are formed by using functions taking their values in a Clifford algebra.
    Źródło:
    Studia Mathematica; 1999, 136, 2; 99-119
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Frechet differential of a power series in Banach algebras
    Autorzy:
    Silvestri, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/254781.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Frechet differentiation in Banach algebras
    functional calculus
    Opis:
    We present two new forms in which the Fréchet differential of a power series in a unitary Banach algebra can be expressed in terms of absolutely convergent series involving the commutant C(T) : A → [A, T]. Then we apply the results to study series of vector-valued functions on domains in Banach spaces and to the analytic functional calculus in a complex Banach space.
    Źródło:
    Opuscula Mathematica; 2010, 30, 2; 155-177
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A constructive proof of the composition rule for Taylors functional calculus
    Autorzy:
    Andersson, Mats
    Sandberg, Sebastian
    Powiązania:
    https://bibliotekanauki.pl/articles/1206005.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Taylor spectrum
    functional calculus
    Cauchy-Fantappiè-Leray formula
    Opis:
    We give a new constructive proof of the composition rule for Taylor's functional calculus for commuting operators on a Banach space.
    Źródło:
    Studia Mathematica; 2000, 142, 1; 65-69
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Holomorphic functional calculus in A-pseudoconvex algebras
    Autorzy:
    Łuczak, Maciej
    Powiązania:
    https://bibliotekanauki.pl/articles/962667.pdf
    Data publikacji:
    2005
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Holomorphic functional calculus
    spectral mapping theorem
    A-pseudoconvex algebra
    real algebra
    Opis:
    We define and study a holomorphic functional calculus for a single element in complex and real complete A-pseudoconvex algebras with unit. As a consequence of the main result we obtain the spectral mapping theorem and existence of the logarithm and the nth root of an algebra element.
    Źródło:
    Commentationes Mathematicae; 2005, 45, 2; 161-169
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Logicy i logika a poznanie przyrody
    Logicians and Logic on Study of Nature
    Autorzy:
    Kiczuk, Stanisław
    Powiązania:
    https://bibliotekanauki.pl/articles/2013931.pdf
    Data publikacji:
    2005
    Wydawca:
    Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
    Tematy:
    logika
    funktor prawdziwościowy
    funktor nieprawdziwościowy
    dwuwartościowy rachunek zdań
    wielowartościowy rachunek zdań
    logic
    truth-functional operator
    not truth-functional operator
    two valued propositional calculus
    many-valued propositional calculus
    Opis:
    Starting from the 1930s logicians tackled problems connected with applicability of logic in natural sciences and in many cases they tried to practically apply logic in these sciences. In the article entitled ‘Logicians and logic on study of nature’ it is stressed that the broadly understood formal logic supplies natural sciences, and especially physics, with a paradigm for a method of ordering theses. It is also shown what application of logic laws to natural sciences consists in, and theses are formulated concerning what the laws of classical propositional calculus state. A lot of attention is devoted to the language of modern and contemporary physics. Modern and contemporary physics uses two languages, i.e. the mathematical language and the so-called notional language. The logic of the former language is classical logical calculus. In connection with the notional language logicians construed a lot of systems of non-classical logics in which laws are given that govern the correct use of non-extensional operators connected with such terms occurring in natural sciences as “time”, “cause”, “change” etc. The language of well construed systems of non-classical logics may serve saving, storing and precise communicating the results obtained on the ground of natural sciences.
    Źródło:
    Roczniki Filozoficzne; 2005, 53, 1; 129-142
    0035-7685
    Pojawia się w:
    Roczniki Filozoficzne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Functional Completeness in CPL via Correspondence Analysis
    Autorzy:
    Leszczyńska-Jasion, Dorota
    Petrukhin, Yaroslav
    Shangin, Vasilyi
    Jukiewicz, Marcin
    Powiązania:
    https://bibliotekanauki.pl/articles/749866.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    correspondence analysis
    invertible rules
    classical propositional logic
    functional completeness
    sequent calculus
    automated deduction
    automated rules generation
    Opis:
    Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only branching rule is the rule of cut. The calculi pertain to classical propositional logic and any of its fragments that may be obtained from adding a set (sets) of rules characterizing a two-argument Boolean function(s) to the negation fragment of classical propositional logic. The properties of soundness and completeness of the calculi are demonstrated. The proof of completeness is conducted by Kalmár's method. Most of the presented sequent-calculus rules have been obtained automatically, by a rule-generating algorithm implemented in Python. Correctness of the algorithm is demonstrated. This automated approach allowed us to analyse thousands of possible rules' schemes, hundreds of rules corresponding to Boolean functions, and to nd dozens of those invertible. Interestingly, the analysis revealed that the presented proof-theoretic framework provides a syntactic characteristics of such an important semantic property as functional completeness.
    Źródło:
    Bulletin of the Section of Logic; 2019, 48, 1
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a mixed-type integral equation and fractional-order functional differential equations
    Autorzy:
    El-Sayed, A. M. A.
    Sherif, Nagwa
    Ibrahim, I. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/745693.pdf
    Data publikacji:
    2005
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Nonlinear functional integral equation
    fractional calculus
    Volterra operator
    mixed type integral equation
    Schauder fixed point theorem
    Opis:
    In this paper we study the existence of solution of a nonlinear integral equation of (mixed type) Volterra-Fredholm type. As an application we prove the existence of solution of an initial value problem of fractional order in the space of Lebesgue integrable functions on the interval \([0, 1]\).
    Źródło:
    Commentationes Mathematicae; 2005, 45, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Uwagi o systemie logiki formalnej skonstruowanym dla logików nieformalnych
    Remarks on the System of Formal Logic Construed for Informal Logicians
    Autorzy:
    Kiczuk, Stanisław
    Powiązania:
    https://bibliotekanauki.pl/articles/2012940.pdf
    Data publikacji:
    2010
    Wydawca:
    Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
    Tematy:
    funktor prawdziwościowy
    logika nieformalna
    logika nieklasyczna
    klasyczny rachunek zdań
    truth-functional operator
    informal logic
    non-classical logic
    classical propositional calculus
    Opis:
    D. Sherry’s main theses included in his essay entitled “Formal Logic for Informal Logicians” are presented in the article. In a discussion with his theses it is shown that he prefers this kind of logic that has a lot of elements that are the same as in Aristotle’s logic understood as the art of thinking and the technique of discussion taken from Topics, and not the logic that was started in his Prior Analytics. It is also shown that not only patterns of inferring, but also the theses of logic, as well as theses to which no patterns correspond, that are guarantee reliability of inference patterns, may be intuitively obvious. In the article also attention is drawn to the fact that the PL- system of logic presented by Sherry was characterized by him by means of a rather poor logical terminology. In the American author’s argument there are no clear distinctions between the thesis of logic, the logical inference pattern and the rule of the procedure of proving. However, it can be established that the PL- system is constituted by argumentation patterns that are reliable owing to such theses of propositional logic as modus potens, modus tollens, disjunctive syllogism, conjunctive syllogism, complex destructive dilemma, and the two rules concerning creating proofs, i.e. the rule of conditional proof and the rule of reduction to the absurd. In the PL- system there are fewer theses than in the classical propositional calculus, but this has nothing in common with the so-called multivalent logics to which some theses of classical logic supposedly do not apply. Everything suggests that some systems of non-classical logic systems may be built on the PL- system; namely, the ones in which theses are given that govern the correct use of non-extensional operators connected with key terms appearing in many sciences, like e.g. “time”, “change”, “causality”. Sherry’s essay reveals that he is a supporter of the thesis that knowledge of formal logic is necessary for using informal logic efficiently, which is necessary for teaching logic properly.
    Źródło:
    Roczniki Filozoficzne; 2010, 58, 1; 95-108
    0035-7685
    Pojawia się w:
    Roczniki Filozoficzne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    O NIEKTÓRYCH PRAWACH LOGIKI I ZASADACH OGÓLNEJ TEORII BYTU
    Autorzy:
    Kiczuk, Stanisław
    Powiązania:
    https://bibliotekanauki.pl/articles/488533.pdf
    Data publikacji:
    2012
    Wydawca:
    Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
    Tematy:
    logika współczesna
    funktor prawdziwościowy
    klasyczny rachunek zdań
    zasada racji dostatecznej
    modern logic
    truth-functional operator
    classical propositional calculus
    principle of sufficient reason
    Opis:
    Some principles of general theory of being have their equivalents in laws of classical logic. For a long time this was not distinctly noticed, as logic was treated rather as technology of discussion, and not as a system of propositions stated in the objective language and concerning connections between facts. It may be generally said that some primary principles of being and some laws of logic state the same most fundamental connections between facts, between states of things. There are also principles of philosophy that do not have such equivalents in laws of logic. These include the principle of sufficient reason. The concept of intuitive truth of propositions that reappeared in modern logic first of all in connection with K. Gödel’s theorem of 1931 formed an intellectual climate that made it possible for classical logicians to accept also those principles of general theory of being that do not have equivalents in laws of standard logic. It may be said that these philosophical principles may be included in the outward basis of modern logic.
    Źródło:
    Roczniki Filozoficzne; 2012, 60, 2; 171-179
    0035-7685
    Pojawia się w:
    Roczniki Filozoficzne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Logika formalna czy logiki formalne?
    Formal Logic or Formal Logics?
    Autorzy:
    Kiczuk, Stanisław
    Powiązania:
    https://bibliotekanauki.pl/articles/2013349.pdf
    Data publikacji:
    2007
    Wydawca:
    Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
    Tematy:
    logika
    funktor prawdziwościowy
    logika standardowa
    logika nieklasyczna
    wielowartościowy rachunek zdań
    logika klasyczna
    logic
    truth-functional operator
    standard logic
    non-classical logic
    many-valued propositional calculus
    classical logic
    Opis:
    Apart from putting the theses contained in E. Agazzi’s work Why Is It Logical to Admit Several Logics? in an order and making them more distinct, an attempt is made to draw conclusions from the explicit wordings used by that author. Some theses presented in the text are shown against the views of other authors who discussed analogous problems. In this way, as it seems, modification, completing and elaborating has been possible of wordings that approve of the thesis about the existence of many logics that are contained in the analyzed text. Among others, the article emphasizes that Agazzi’s pronouncements about relations existing between standard logic and intuitionist logic cannot be accepted. Also, several remarks are made about the so-called many-valued logics. Agazzi’s theses that well constructed non-classical logics representing proper contents are necessary for representatives of various branches of knowledge is acceptable.
    Źródło:
    Roczniki Filozoficzne; 2007, 55, 1; 129-157
    0035-7685
    Pojawia się w:
    Roczniki Filozoficzne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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