Conditions and parametric representations of approximate minimal elements of a set through scalarization

2006 ◽  
pp. 173-184 ◽  
Author(s):  
César Gutiérrez ◽  
Bienvenido Jiménez ◽  
Vicente Novo
Keyword(s):  
Minimal Elements

scholarly journals Euler Characteristic of the Truncated Order Complex of Generalized Noncrossing Partitions

10.37236/232 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
D. Armstrong ◽  
C. Krattenthaler
Keyword(s):  
Euler Characteristic ◽  
Order Complex ◽  
Reflection Groups ◽  
Noncrossing Partitions ◽  
Minimal Elements ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Phd Thesis

The purpose of this paper is to complete the study, begun in the first author's PhD thesis, of the topology of the poset of generalized noncrossing partitions associated to real reflection groups. In particular, we calculate the Euler characteristic of this poset with the maximal and minimal elements deleted. As we show, the result on the Euler characteristic extends to generalized noncrossing partitions associated to well-generated complex reflection groups.

On the Structure of Certain Nest Algebra Modules

1987 ◽  
Vol 39 (6) ◽  
pp. 1405-1412
Author(s):  
G. J. Knowles
Keyword(s):  
Operator Algebras ◽  
Adjoint Operator ◽  
Systematic Investigation ◽  
Unique Determination ◽  
Nest Algebra ◽  
Minimal Elements ◽  
Open Questions ◽  
Weakly Closed ◽  
Order Homomorphisms

Let be a nest algebra of operators on some Hilbert space H. Weakly closed -modules were first studied by J. Erdos and S. Power in [4]. It became apparent that many interesting classes of non self-adjoint operator algebras arise as just such a module. This paper undertakes a systematic investigation of the correspondence which arises between such modules and order homomorphisms from Lat into itself. This perspective provides a basis to answer some open questions arising from [4]. In particular, the questions concerning unique “determination” and characterization of maximal and minimal elements under this correspondence, are resolved. This is then used to establish when the determining homomorphism is unique.

scholarly journals On Minimal Copulas under the Concordance Order

2019 ◽  
Vol 184 (3) ◽  
pp. 762-780 ◽  
Author(s):  
Jae Youn Ahn ◽  
Sebastian Fuchs
Keyword(s):  
Optimization Problems ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Negative Dependence ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Minimal Elements ◽  
Measures Of Concordance ◽  
Concordance Order

AbstractIn the present paper, we study extreme negative dependence focussing on the concordance order for copulas. With the absence of a least element for dimensions $$d\ge 3$$d≥3, the set of all minimal elements in the collection of all copulas turns out to be a natural and quite important extreme negative dependence concept. We investigate several sufficient conditions, and we provide a necessary condition for a copula to be minimal. The sufficient conditions are related to the extreme negative dependence concept of d-countermonotonicity and the necessary condition is related to the collection of all copulas minimizing multivariate Kendall’s tau. The concept of minimal copulas has already been proved to be useful in various continuous and concordance order preserving optimization problems including variance minimization and the detection of lower bounds for certain measures of concordance. We substantiate this key role of minimal copulas by showing that every continuous and concordance order preserving functional on copulas is minimized by some minimal copula, and, in the case the continuous functional is even strictly concordance order preserving, it is minimized by minimal copulas only. Applying the above results, we may conclude that every minimizer of Spearman’s rho is also a minimizer of Kendall’s tau.

Naturally Ordered Transformation Semigroups Preserving an Equivalence Relation and a Cross-section

2011 ◽  
Vol 18 (03) ◽  
pp. 523-532 ◽  
Author(s):  
Lei Sun ◽  
Weina Deng ◽  
Huisheng Pei
Keyword(s):  
Cross Section ◽  
Equivalence Relation ◽  
Transformation Semigroup ◽  
Natural Order ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Minimal Elements ◽  
Full Transformation Semigroup

The paper is concerned with the so-called natural order on the semigroup [Formula: see text], where [Formula: see text] is the full transformation semigroup on a set X, E is a non-trivial equivalence on X and R is a cross-section of the partition X/E induced by E. We determine when two elements of TE(X,R) are related under this order, find elements of TE(X,R) which are compatible with ≤ on TE(X,R), and observe the maximal and minimal elements and the covering elements.

scholarly journals Laplacian coefficients of unicyclic graphs with the number of leaves and girth

2014 ◽  
Vol 8 (2) ◽  
pp. 330-345
Author(s):  
Jie Zhang ◽  
Xiao-Dong Zhang
Keyword(s):  
Linear Algebra ◽  
Minimal Elements ◽  
Unicyclic Graphs ◽  
Number Of Leaves

Motivated by Ilic and Ilic?s conjecture [A. Ilic, M. Ilic, Laplacian coefficients of trees with given number of leaves or vertices of degree two, Linear Algebra Appl., 431(2009)2195-2202.], we investigate properties of the minimal elements in the partial set (Ugn,l,?) of the Laplacian coefficients, where Ug n,l denote the set of n-vertex unicyclic graphs with the number of leaves l and girth g. These results are used to disprove their conjecture. Moreover, the graphs with minimum Laplacian-like energy in Ug n,l are also studied.

Weak minimal elements and weak minimal solutions of a nonconvex set-valued optimization problem

2019 ◽  
Vol 75 (1) ◽  
pp. 131-141
Author(s):  
M. Chinaie ◽  
F. Fakhar ◽  
M. Fakhar ◽  
H. R. Hajisharifi
Keyword(s):  
Optimization Problem ◽  
Minimal Elements

scholarly journals MyTH4-FERM myosins have an ancient and conserved role in filopod formation

2016 ◽  
Vol 113 (50) ◽  
pp. E8059-E8068 ◽  
Author(s):  
Karl J. Petersen ◽  
Holly V. Goodson ◽  
Ashley L. Arthur ◽  
G. W. Gant Luxton ◽  
Anne Houdusse ◽  
...  
Keyword(s):  
Mammalian Cells ◽  
Live Cell Imaging ◽  
Cell Imaging ◽  
Null Mutant ◽  
Minimal Elements ◽  
Social Amoeba ◽  
Functional Conservation ◽  
Functional Homolog ◽  
The Social ◽  
Functional Features

The formation of filopodia in Metazoa and Amoebozoa requires the activity of myosin 10 (Myo10) in mammalian cells and of Dictyostelium unconventional myosin 7 (DdMyo7) in the social amoeba Dictyostelium. However, the exact roles of these MyTH4-FERM myosins (myosin tail homology 4-band 4.1, ezrin, radixin, moesin; MF) in the initiation and elongation of filopodia are not well defined and may reflect conserved functions among phylogenetically diverse MF myosins. Phylogenetic analysis of MF myosin domains suggests that a single ancestral MF myosin existed with a structure similar to DdMyo7, which has two MF domains, and that subsequent duplications in the metazoan lineage produced its functional homolog Myo10. The essential functional features of the DdMyo7 myosin were identified using quantitative live-cell imaging to characterize the ability of various mutants to rescue filopod formation in myo7-null cells. The two MF domains were found to function redundantly in filopod formation with the C-terminal FERM domain regulating both the number of filopodia and their elongation velocity. DdMyo7 mutants consisting solely of the motor plus a single MyTH4 domain were found to be capable of rescuing the formation of filopodia, establishing the minimal elements necessary for the function of this myosin. Interestingly, a chimeric myosin with the Myo10 MF domain fused to the DdMyo7 motor also was capable of rescuing filopod formation in the myo7-null mutant, supporting fundamental functional conservation between these two distant myosins. Together, these findings reveal that MF myosins have an ancient and conserved role in filopod formation.

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