Displaying similar documents to “Configurations of rank- 40 r extremal even unimodular lattices ( r = 1 , 2 , 3 )”

A new approach to construct uninorms via uninorms on bounded lattices

Zhen-Yu Xiu, Xu Zheng (2024)

Kybernetika

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In this paper, on a bounded lattice L , we give a new approach to construct uninorms via a given uninorm U * on the subinterval [ 0 , a ] (or [ b , 1 ] ) of L under additional constraint conditions on L and U * . This approach makes our methods generalize some known construction methods for uninorms in the literature. Meanwhile, some illustrative examples for the construction of uninorms on bounded lattices are provided.

Modular lattices from finite projective planes

Tathagata Basak (2014)

Journal de Théorie des Nombres de Bordeaux

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Using the geometry of the projective plane over the finite field 𝔽 q , we construct a Hermitian Lorentzian lattice L q of dimension ( q 2 + q + 2 ) defined over a certain number ring 𝒪 that depends on q . We show that infinitely many of these lattices are p -modular, that is, p L q ' = L q , where p is some prime in 𝒪 such that | p | 2 = q . The Lorentzian lattices L q sometimes lead to construction of interesting positive definite lattices. In particular, if q 3 mod 4 is a rational prime such that ( q 2 + q + 1 ) is norm of some element in...

Construction of uninorms on bounded lattices

Gül Deniz Çaylı, Funda Karaçal (2017)

Kybernetika

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In this paper, we propose the general methods, yielding uninorms on the bounded lattice ( L , , 0 , 1 ) , with some additional constraints on e L { 0 , 1 } for a fixed neutral element e L { 0 , 1 } based on underlying an arbitrary triangular norm T e on [ 0 , e ] and an arbitrary triangular conorm S e on [ e , 1 ] . And, some illustrative examples are added for clarity.

Cambrian fans

Nathan Reading, David E. Speyer (2009)

Journal of the European Mathematical Society

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For a finite Coxeter group W and a Coxeter element c of W ; the c -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of W . Its maximal cones are naturally indexed by the c -sortable elements of W . The main result of this paper is that the known bijection cl c between c -sortable elements and c -clusters induces a combinatorial isomorphism of fans. In particular, the c -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for...

Wallman-type compaerifications and function lattices

Alessandro Caterino, Maria Cristina Vipera (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Let F C ( X ) be a vector sublattice over which separates points from closed sets of X . The compactification e F X obtained by embedding X in a real cube via the diagonal map, is different, in general, from the Wallman compactification ω ( Z ( F ) ) . In this paper, it is shown that there exists a lattice F z containing F such that ω ( Z ( F ) ) = ω ( Z ( F z ) ) = e F X . In particular this implies that ω ( Z ( F ) ) e F X . Conditions in order to be ω ( Z ( F ) ) = e F X are given. Finally we prove that, if α X is a compactification of X such that C l α X ( α X X ) is 0 -dimensional, then there is an...

On the real X -ranks of points of n ( ) with respect to a real variety X n

Edoardo Ballico (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let  X n be an integral and non-degenerate m -dimensional variety defined over . For any P n ( ) the real X -rank r X , ( P ) is the minimal cardinality of S X ( ) such that P S . Here we extend to the real case an upper bound for the X -rank due to Landsberg and Teitler.

A localization property for B p q s and F p q s spaces

Hans Triebel (1994)

Studia Mathematica

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Let f j = k a k f ( 2 j + 1 x - 2 k ) , where the sum is taken over the lattice of all points k in n having integer-valued components, j∈ℕ and a k . Let A p q s be either B p q s or F p q s (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on n . The aim of the paper is to clarify under what conditions f j | A p q s is equivalent to 2 j ( s - n / p ) ( k | a k | p ) 1 / p f | A p q s .

𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More precisely, we prove that for a ¯ -closed form f in 𝒞 0 , q k ( X D , E ) , 1 q n - 2 , n 3 , with compact support and for ε with 0 < ε < 1 there...

Structural aspects of truncated archimedean vector lattices: good sequences, simple elements

Richard N. Ball (2021)

Commentationes Mathematicae Universitatis Carolinae

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The truncation operation facilitates the articulation and analysis of several aspects of the structure of archimedean vector lattices; we investigate two such aspects in this article. We refer to archimedean vector lattices equipped with a truncation as truncs. In the first part of the article we review the basic definitions, state the (pointed) Yosida representation theorem for truncs, and then prove a representation theorem which subsumes and extends the (pointfree) Madden representation...

C * -points vs P -points and P -points

Jorge Martinez, Warren Wm. McGovern (2022)

Commentationes Mathematicae Universitatis Carolinae

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In a Tychonoff space X , the point p X is called a C * -point if every real-valued continuous function on C { p } can be extended continuously to p . Every point in an extremally disconnected space is a C * -point. A classic example is the space 𝐖 * = ω 1 + 1 consisting of the countable ordinals together with ω 1 . The point ω 1 is known to be a C * -point as well as a P -point. We supply a characterization of C * -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space...

Generalized versions of Ilmanen lemma: Insertion of C 1 , ω or C loc 1 , ω functions

Václav Kryštof (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove that for a normed linear space X , if f 1 : X is continuous and semiconvex with modulus ω , f 2 : X is continuous and semiconcave with modulus ω and f 1 f 2 , then there exists f C 1 , ω ( X ) such that f 1 f f 2 . Using this result we prove a generalization of Ilmanen lemma (which deals with the case ω ( t ) = t ) to the case of an arbitrary nontrivial modulus ω . This generalization (where a C l o c 1 , ω function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.