On the Maximal Multiplicative Family for the Class of Quasicontinuous Functions

1989 ◽  
Vol 15 (2) ◽  
pp. 437
Author(s):  
Grande
Keyword(s):  
Quasicontinuous Functions ◽  
Multiplicative Family

scholarly journals Uncorrelated genetic drift of gene frequencies and linkage disequilibrium in some models of linked overdominant polymorphisms

1974 ◽  
Vol 24 (3) ◽  
pp. 281-294 ◽  
Author(s):  
Joseph Felsenstein
Keyword(s):  
Linkage Disequilibrium ◽  
Covariance Matrix ◽  
Genetic Drift ◽  
Conditional Distribution ◽  
Large Population ◽  
Multivariate Normal ◽  
Gene Frequencies ◽  
Constant Variance ◽  
Population Sizes ◽  
Multiplicative Family

SUMMARYFor large population sizes, gene frequencies p and q at two linked over-dominant loci and the linkage disequilibrium parameter D will remain close to their equilibrium values. We can treat selection and recombination as approximately linear forces on p, q and D, and we can treat genetic drift as a multivariate normal perturbation with constant variance-covariance matrix. For the additive-multiplicative family of two-locus models, p, q and D are shown to be (approximately) uncorrelated. Expressions for their variances are obtained. When selection coefficients are small the variances of p and q are those previously given by Robertson for a single locus. For small recombination fractions the variance of D is that obtained for neutral loci by Ohta & Kimura. For larger recombination fractions the result differs from theirs, so that for unlinked loci r2 ≃ 2/(3N) instead of 1/(2N). For the Lewontin-Kojima and Bodmer symmetric viability models, and for a model symmetric at only one of the loci, a more exact argument is possible. In the asymptotic conditional distribution in these cases, various of p, q and D are uncorrelated, depending on the type of symmetiy in the model.

scholarly journals Some continuous operations on pairs of cliquish functions

2009 ◽  
Vol 44 (1) ◽  
pp. 15-25
Author(s):  
Zbigniew Grande ◽  
Ewa Strońska
Keyword(s):  
Continuous Operation ◽  
Quasicontinuous Functions ◽  
Real Functions ◽  
Real Anal

Abstract The algebraic or lattice operations in the classes of cliquish or quasicontinuous functions are well known [Z. Grande: On the maximal multiplicativefamily for the class of quasicontinuous functions, Real Anal. Exchange 15 (1989-1990), 437-441, Z. Grande, L. Soltysik: Some remarks on quasicontinuousreal functions, Problemy Mat. 10 (1990), 79-86]. This also pertains to the symmetrical quasicontinuity or symmetrical cliquishness [Z. Grande: On the maximaladditive and multiplicative families for the quasicontinuities of Piotrowskiand Vallin, Real Anal. Exchange 32 (2007), 511-518]. In this article, we examine the superpositions F(f, g), where F is a continuous operation and f, g are cliquish (symmetrically cliquish) or f is continuous (f is symmetrically quasicontinuous with continuous sections) and g is quasicontinuous (symmetrically quasicontinuous).

scholarly journals DARBOUX QUASICONTINUOUS FUNCTIONS

1997 ◽  
Vol 23 (2) ◽  
pp. 631 ◽  
Author(s):  
Rosen
Keyword(s):  
Quasicontinuous Functions

Quasicontinuous functions, minimal usco maps and topology of pointwise convergence

2010 ◽  
Vol 60 (4) ◽  
Author(s):  
Dušan Holý ◽  
Ladislav Matejíčka
Keyword(s):  
Pointwise Convergence ◽  
Rocky Mountain ◽  
Set Valued Mapping ◽  
Upper Semicontinuous Functions ◽  
Quasicontinuous Functions ◽  
Minimal Usco Map ◽  
Pointwise Limit ◽  
Topology Of Pointwise Convergence ◽  
Semicontinuous Functions

AbstractIn [HOLÁ, Ľ.—HOLÝ, D.: Pointwise convergence of quasicontinuous mappings and Baire spaces, Rocky Mountain J. Math.] a complete answer is given, for a Baire space X, to the question of when the pointwise limit of a sequence of real-valued quasicontinuous functions defined on X is quasicontinuous. In [HOLÁ, Ľ.—HOLÝ, D.: Minimal USCO maps, densely continuous forms and upper semicontinuous functions, Rocky Mountain J. Math. 39 (2009), 545–562], a characterization of minimal USCO maps by quasicontinuous and subcontinuous selections is proved. Continuing these results, we study closed and compact subsets of the space of quasicontinuous functions and minimal USCO maps equipped with the topology of pointwise convergence. We also study conditions under which the closure of the graph of a set-valued mapping which is the pointwise limit of a net of set-valued mappings, is a minimal USCO map.

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