<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">In the paper I construct the configuration <italic>G</italic> which is a partial linear space. It consists of <italic>k</italic>-element subsets of some base set as points and (<italic>k</italic> + 1)-element subsets as lines. The incidence is given by inclusion. I also introduce automorphisms of partial linear spaces and show that automorphisms of <italic>G</italic> are generated by permutations of the base set.</abstract>

Combinatorial Grassmannians

<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">In this article we define the Riemann indefinite integral of functions of real variable and prove the linearity of that [1]. And we give some examples of the indefinite integral of some elementary functions. Furthermore, also the theorem about integral operation and uniform convergent sequence of functions is proved.</abstract>

Gifu National College of Technology, Japan

Riemann Indefinite Integral of Functions of Real Variable

<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">Summary. In this article, we define the partial differentiation of functions of real variable and prove the linearity of this operator [18].</abstract>

Partial Differentiation on Normed Linear Spaces <italic>Rn</italic>

<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">This article includes proofs of several facts that are supplemental to the theorems proved in [10]. Next, it builds upon that theory to extend the framework for proving facts about formal languages in general and regular expression operators in particular. In this article, two quantifiers are defined and their properties are shown: <italic>m</italic> to <italic>n</italic> occurrences (or the union of a range of powers) and optional occurrence. Although optional occurrence is a special case of the previous operator (0 to 1 occurrences), it is often defined in regex applications as a separate operator - hence its explicit definition and properties in the article. Notation and terminology were taken from [13].</abstract>

Regular Expression Quantifiers — <italic>m</italic> to <italic>n</italic> Occurrences

<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">The goal of this article is to formalize the Jordan-Hölder theorem in the context of group with operators as in the book [5]. Accordingly, the article introduces the structure of group with operators and reformulates some theorems on a group already present in the Mizar Mathematical Library. Next, the article formalizes the Zassenhaus butterfly lemma and the Schreier refinement theorem, and defines the composition series.</abstract>

The Jordan-Hölder Theorem

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Formalized Mathematics

  Pioneering Journal in the field of formalized and mechanically checked mathematics. Excellent articles on latest research in formal methods and computer-checked mathematics. Full-length original research articles in English. Archival issues available at the journal's home page fm.mizar.org/.   To build a uniform and extensible computer-checked repository of mathematical knowledge.  Reconstruction of mathematics based on mechanization of mathematical reasoning.  To check a wide range of mathematical theorems using a computer in an automatic fashion.  General mathematics: especially topology, lattice theory, functional analysis.  Applications: computer-aided verification of software and hardware, computer-aided teaching of mathematics.   Why subscribe and read   Pioneering source of high quality research in formalized and mechanically checked mathematics.  The oldest journal in the field, a medium for the publication of research reporting pioneering findings of broad mathematical significance that are likely to advance the direction and thinking of the field.  Long-term experience in publishing original articles on mechanizing mathematics and various aspects of automated reasoning, since 1990.   Why submit   Fair and constructive peer review by international experts in the field (three referees are designated for the assessment of each manuscript) - double-blind review process.  New publishing technology: articles automatically translated from a formal language into English and automatically typeset, available in both forms - electronic and printed.  Articles abstracted by online indexing services and databases.   Rejection Rate   59% of submitted articles.  The rejection percentage is described in detail in the following paper, pp.239-240: dx.doi.org/10.1007/978-3-540-73086-6_20 Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. Back Issues fm.mizar.org/   Other Files  Addenda 2008Formalized Mathematics Bibliography File.Formalized Mathematics External Bibliography File.  "In years: 2016-2017, the English version of Formalized Mathematics was financed under agreements 548/P-DUN/2016 and 548/1/P-DUN/2016 with the funds from the Polish Minister of Science and Higher Education for the dissemination of science." 

Formalized Mathematics

Volume 15 (2007): Issue 2 (January 2007)

Combinatorial Grassmannians

Riemann Indefinite Integral of Functions of Real Variable

Partial Differentiation on Normed Linear Spaces Rⁿ

Regular Expression Quantifiers — m to n Occurrences

The Jordan-Hölder Theorem

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Formalized Mathematics

Volume 15 (2007): Issue 2 (January 2007)

Combinatorial Grassmannians

Riemann Indefinite Integral of Functions of Real Variable

Partial Differentiation on Normed Linear Spaces Rn

Regular Expression Quantifiers — m to n Occurrences

The Jordan-Hölder Theorem

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Partial Differentiation on Normed Linear Spaces Rⁿ