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Lundström, Patrikorcid.org/0000-0001-6594-7041

Open this publication in new window or tab >>Algebra, trigonometri och analys### Lundström, Patrik

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##### Place, publisher, year, edition, pages

Lund: Studentlitteratur AB, 2023. p. 649 Edition: 1
##### Keywords

Algebra, Trigonometry, Algebra, Trigonometri, Analytisk trigonometri
##### National Category

Algebra and Logic
##### Identifiers

urn:nbn:se:hv:diva-21051 (URN)9789144166421 (ISBN)
#####

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Available from: 2023-12-11 Created: 2023-12-11 Last updated: 2024-01-03Bibliographically approved

University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.

Open this publication in new window or tab >>Corrigendum: Group gradations on Leavitt path algebras### Lundström, Patrik

### Öinert, Johan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_some",{id:"formSmash:j_idt204:1:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_otherAuthors",{id:"formSmash:j_idt204:1:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829Article in journal (Other academic) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

World Scientific, 2023
##### National Category

Algebra and Logic
##### Identifiers

urn:nbn:se:hv:diva-19880 (URN)10.1142/S0219498824920014 (DOI)000946343400001 ()2-s2.0-85150800283 (Scopus ID)
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Available from: 2023-04-24 Created: 2023-04-24 Last updated: 2024-04-12Bibliographically approved

University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.

Department of Mathematics and Natural Sciences, Blekinge Institute of Technology, Karlskrona (SWE).

The results that are stated in P. Nystedt and J. Öinert [Group gradations on Leavitt path algebras, J. Algebra Appl. 19(9) (2020) 2050165, Sec. 4] hold true, but due to an oversimplification some of the proofs are incomplete. The purpose of this note is to amend and complete the affected proofs.

Open this publication in new window or tab >>Double Calculus### Lundström, Patrik

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_some",{id:"formSmash:j_idt204:2:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_otherAuthors",{id:"formSmash:j_idt204:2:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Surveys in Mathematics and its Applications, ISSN 1843-7265, E-ISSN 1842-6298, Vol. 18, p. 27-48Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

continuous function; differentiable function; Riemann integral; the fundamental theorem of calculus
##### National Category

Mathematical Analysis
##### Identifiers

urn:nbn:se:hv:diva-20894 (URN)2-s2.0-85173464276 (Scopus ID)
#####

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##### Note

University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.

We present a streamlined, slightly modified version, in the two-variable situation, of a beautiful, but not so well known, theory by Bögel [1, 2], already from the 1930s, on an alternative higher dimensional calculus of real functions, a double calculus, which includes many two-variable extensions of classical results from single variable calculus, such as Rolle’s theorem, Lagrange’s mean value theorem, Cauchy’s mean value theorem, Fermat’s extremum theorem, the first derivative test, and the first and second fundamental theorems of calculus.

CC BY 4.0

Available from: 2023-12-28 Created: 2023-12-28 Last updated: 2023-12-28Open this publication in new window or tab >>Group gradations on Leavitt path algebras (vol 19, 2050165, 2020)### Lundström, Patrik

University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.### Oinert, Johan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_some",{id:"formSmash:j_idt204:3:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_otherAuthors",{id:"formSmash:j_idt204:3:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, article id 2492001Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

World Scientific, 2023
##### Keywords

s-unital ring; strongly graded ring; epsilon-strongly graded ring; Leavitt path algebra
##### National Category

Algebra and Logic
##### Identifiers

urn:nbn:se:hv:diva-19847 (URN)10.1142/S0219498824920014 (DOI)000946343400001 ()2-s2.0-85150800283 (Scopus ID)
#####

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Available from: 2023-12-20 Created: 2023-12-20 Last updated: 2024-04-29Bibliographically approved

Department of Mathematics and Natural Sciences, Blekinge Institute of Technology, SE-37179 Karlskrona (SWE).

The results that are stated in P. Nystedt and J. Oinert [Group gradations on Leavitt path algebras, J. Algebra Appl. 19(9) (2020) 2050165, Sec. 4] hold true, but due to an oversimplification some of the proofs are incomplete. The purpose of this note is to amend and complete the affected proofs.

Open this publication in new window or tab >>Non-Unital Ore Extensions### Lundström, Patrik

University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.### Öinert, Johan

### Richter, Johan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_some",{id:"formSmash:j_idt204:4:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_otherAuthors",{id:"formSmash:j_idt204:4:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 172, no 2, p. 217-229Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

non-unital ring, Ore extension, simple ring, outer derivation
##### National Category

Algebra and Logic
##### Identifiers

urn:nbn:se:hv:diva-20692 (URN)10.4064/cm8941-11-2022 (DOI)000917921400001 ()2-s2.0-85163993902 (Scopus ID)
#####

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Available from: 2023-09-06 Created: 2023-09-06 Last updated: 2024-01-12Bibliographically approved

Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences, Karlskrona (SWE).

Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences, Karlskrona (SWE).

We study Ore extensions of non-unital associative rings. We provide a characterization of simple non-unital differential polynomial rings R[x; delta], under the hy-pothesis that R is s-unital and ker(delta) contains a non-zero idempotent. This result gener-alizes a result by oinert, Richter and Silvestrov from the unital setting. We also present a family of examples of simple non-unital differential polynomial rings.

Open this publication in new window or tab >>Simplicity of Leavitt Path Algebras via Graded Ring Theory### Lundström, Patrik

University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.### Öinert, Johan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_some",{id:"formSmash:j_idt204:5:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_otherAuthors",{id:"formSmash:j_idt204:5:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 108, no 3, p. 428-437Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Cambridge University Press, 2023
##### Keywords

Leavitt path algebra; graded ring; simple ring; centre
##### National Category

Algebra and Logic
##### Identifiers

urn:nbn:se:hv:diva-19848 (URN)10.1017/S0004972723000114 (DOI)000943276000001 ()2-s2.0-85177820296 (Scopus ID)
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##### Note

Department of Mathematics and Natural Sciences, Blekinge Institute of Technology, SE-37179 Karlskrona (SWE).

Suppose that R is an associative unital ring and that E= (E-0, E-1, r, s) is a directed graph. Using results from graded ring theory, we show that the associated Leavitt path algebra L-R(E) is simple if and only if R is simple, E-0 has no nontrivial hereditary and saturated subset, and every cycle in E has an exit. We also give a complete description of the centre of a simple Leavitt path algebra.

CC-BY 4.0

Available from: 2023-12-20 Created: 2023-12-20 Last updated: 2023-12-20Open this publication in new window or tab >>Primitives of continuous functions via polynomials### Lundström, Patrik

University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_some",{id:"formSmash:j_idt204:6:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_otherAuthors",{id:"formSmash:j_idt204:6:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_otherAuthors",multiple:true}); 2022 (English)In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211, p. 1-5Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Taylor & Francis Group, 2022
##### Keywords

Primitive function; integral; polynomial
##### National Category

Mathematical Analysis
##### Identifiers

urn:nbn:se:hv:diva-19316 (URN)10.1080/0020739X.2022.2129499 (DOI)000867511300001 ()2-s2.0-85139849437 (Scopus ID)
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Available from: 2022-10-28 Created: 2022-10-28 Last updated: 2024-03-21Bibliographically approved

In standard books on calculus the existence of primitive functions of continuous functions is proved, in one way or another, using Riemann sums. In this note we present a completely different self-contained, however probably folkloristic, proof of this existence. Our proof combines, on the one hand, the so-called Stone Weierstrass theorem on uniform approximation of continuous functions on the unit interval by polynomials, and, on the other hand, a classical result from calculus on the existence of limits of differentiated sequences of functions. The sought for primitive is then constructed as the limit of primitives of the polynomials approximating the original function.

Open this publication in new window or tab >>Arc length of function graphs via Taylor’s formula### Nystedt, Patrik

University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_some",{id:"formSmash:j_idt204:7:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_otherAuthors",{id:"formSmash:j_idt204:7:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_otherAuthors",multiple:true}); 2021 (English)In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 52, no 2, p. 310-323Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Taylor's formula, the fundamental theorem of calculus, Riemann sums, arc length
##### National Category

Mathematical Analysis
##### Research subject

ENGINEERING, Mathematics
##### Identifiers

urn:nbn:se:hv:diva-15157 (URN)10.1080/0020739X.2020.1751320 (DOI)000527605900001 ()2-s2.0-85083643127 (Scopus ID)
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Available from: 2020-05-04 Created: 2020-05-04 Last updated: 2022-01-19Bibliographically approved

We use Taylor’s formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subdivisions which are equally spaced. As a means for generating interesting examples of exact arc length calculations in calculus courses, we recall two large classes of functions f with the property that (Formula presented.) has a primitive, including classical examples by Neile, van Heuraet and Fermat, as well as more recent ones induced by Pythagorean triples of functions. We also discuss potential benefits for our proposed definition of arc length in introductory calculus courses. © 2020, © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

Open this publication in new window or tab >>Elementär optimeringslära### Lundström, Patrik

University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_some",{id:"formSmash:j_idt204:8:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_otherAuthors",{id:"formSmash:j_idt204:8:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_otherAuthors",multiple:true}); 2021 (Swedish)Book (Other academic)
##### Abstract [sv]

##### Place, publisher, year, edition, pages

Lund: Studentlitteratur AB, 2021. p. 331
##### Keywords

Mathematical optimization, Optimering
##### National Category

Mathematics Educational Sciences
##### Identifiers

urn:nbn:se:hv:diva-16608 (URN)9789144141855 (ISBN)
#####

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Available from: 2021-07-07 Created: 2021-07-07 Last updated: 2021-07-07Bibliographically approved

Elementär optimeringslära inleds med en repetition av grundläggande matematikkunskaper om algebra, ekvationer, matriser, funktioner och derivata. Därefter behandlas linjär optimering, först i två variabler med fokus på geometrisk förståelse och därefter, i det allmänna fallet, med simplexmetoden. Denna metod tillämpas i boken även inom det spännande matematikområdet spelteori. Boken redogör för olika metoder för optimering av allmänna tvåvariabelfunktioner, dels över kompakta områden, dels med Lagranges sats givet ett bivillkor och dels med Hessianen. Boken tar avslutningsvis upp optimering på grafer med Kruskals, Prims och Dijkstras algoritmer.

Open this publication in new window or tab >>Graded modules over object-unital groupoid graded rings### Cala, Juan

### Lundström, Patrik

University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.### Pinedo, Hector

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_some",{id:"formSmash:j_idt204:9:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_otherAuthors",{id:"formSmash:j_idt204:9:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_otherAuthors",multiple:true}); 2021 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 50, no 2, p. 444-462Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Taylor & Francis Group, 2021
##### Keywords

finitely gererated, finitely presented, free, groupoid graded module, injective, projective, pure sequences, small and flat modules, 16D10, 16D40, 16D50, 16D90
##### National Category

Algebra and Logic
##### Identifiers

urn:nbn:se:hv:diva-17455 (URN)10.1080/00927872.2021.1959601 (DOI)000686088500001 ()2-s2.0-85113240292 (Scopus ID)
#####

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#####

##### Note

Escuela de Matemáticas, Universidad Industrial de Santander, Bucaramanga (COL).

Escuela de Matemáticas, Universidad Industrial de Santander, Bucaramanga (COL).

In this article, we analyze the category(Formula presented) of unitary G-graded modules over object unital G -graded rings R, being G a groupoid. Here we consider the forgetful functor G - R- mod and determine many properties (Formula presented.) for which the following implications are valid for modules M in (Formula presented.) M is (Formula presented.) (Formula presented.) U(M) is (Formula presented.) U(M) is (Formula presented.) (Formula presented.) M is (Formula presented.) We treat the cases when (Formula presented.) is any of the properties: direct summand, projective, injective, free and semisimple. Moreover, graded versions of results concerning classical module theory are established, as well as some structural properties (Formula presented.).

To see the correct formulas in the abstract; see the original article.

Available from: 2021-11-08 Created: 2021-11-08 Last updated: 2022-04-04Bibliographically approved