210,398 research outputs found
Rota-Baxter operators on the polynomial algebras, integration and averaging operators
No full textThe concept of a Rota–Baxter operator is an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota–Baxter operators and integrals in the case of the polynomial algebra k[x]
k[x]
. We consider two classes of Rota–Baxter operators, monomial ones and injective ones. For the first class, we apply averaging operators to determine monomial Rota–Baxter operators. For the second class, we make use of the double product on Rota–Baxter algebras
Yang-Baxter maps and the discrete KP hierarchy
No full textWe present a systematic construction of the discrete KP hierarchy in terms of Sato–Wilson-type shift operators. Reductions of the equations in this hierarchy to 1+1-dimensional integrable lattice systems are considered, and the problems that arise with regard to the symmetry algebra underlying the reduced systems as well as the ultradiscretizability of these systems are discussed. A scheme for constructing ultradiscretizable reductions that give rise to Yang–Baxter maps is explained in two explicit examples
Baxter, M P, NX68141
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/370732Surname: BAXTER
Given Name(s) or Initials: M P
Military Service Number or Last Known Location: NX68141
Missing, Wounded and Prisoner of War Enquiry Card Index Number: 18499181087
Item: [2016.0049.03059] "Baxter, M P, NX68141
Baxter, M C, 36841
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/370712Surname: BAXTER
Given Name(s) or Initials: M C
Military Service Number or Last Known Location: 36841
Missing, Wounded and Prisoner of War Enquiry Card Index Number: SEA-3063181067
Item: [2016.0049.03039] "Baxter, M C, 36841
Lloyd M. Baxter, U.S. Army Air Forces
No full textThis is a portrait of Lloyd M. Baxter, U.S. Army Air Forces. He is wearing a summer service uniform; a nametag reading "Lloyd M. Baxter, 4SE, ASN 12014027" is clipped to his left breast pocket. He is smiling slightly at the camera. This portrait was likely taken in a photography studio
Lloyd M. Baxter, U.S. Army Air Forces
No full textThis is a portrait of Lloyd M. Baxter, U.S. Army Air Forces. He is wearing a summer service uniform; a nametag reading "Lloyd M. Baxter, 4SE, ASN 12014027" is clipped to his left breast pocket. He is smiling slightly at the camera. This portrait was likely taken in a photography studio
Slicings of parallelogram polyominoes: Catalan, schröder, baxter, and other sequences
No full textWe provide a new succession rule (i.e. generating tree) associated with Schröder numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schröder and Baxter generalizations of parallelogram polyominoes, called slicings, which grow according to these succession rules. In passing, we also exhibit Schröder subclasses of Baxter classes, namely a Schröder subset of triples of non-intersecting lattice paths, a new Schröder subset of Baxter permutations, and a new Schröder subset of mosaic floorplans. Finally, we define two families of subclasses of Baxter slicings: the m-skinny slicings and the m-rowrestricted slicings, for m ∈ N. Using functional equations and the kernel method, their generating functions are computed in some special cases, and we conjecture that they are algebraic for any m
Slicings of parallelogram polyominoes: Catalan, schröder, baxter, and other sequences
No full textWe provide a new succession rule (i.e. generating tree) associated with Schröder numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schröder and Baxter generalizations of parallelogram polyominoes, called slicings, which grow according to these succession rules. In passing, we also exhibit Schröder subclasses of Baxter classes, namely a Schröder subset of triples of non-intersecting lattice paths, a new Schröder subset of Baxter permutations, and a new Schröder subset of mosaic floorplans. Finally, we define two families of subclasses of Baxter slicings: the m-skinny slicings and the m-rowrestricted slicings, for m ∈ N. Using functional equations and the kernel method, their generating functions are computed in some special cases, and we conjecture that they are algebraic for any m
- …
