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A detailed theoretical study of the dynamical behaviour of a quantitative trait under stabilizing selection is given for an effectively infinite sexual population. The trait is controlled by a finite number of loci and the exact equation obeyed by the distribution of allelic effects in gametes is derived and investigated. Results are derived for the effects of selection over one generation when the population is initially in linkage equilibrium, allelic effects are normally distributed, but the strength of selection is arbitrary. When weak stabilizing selection is operative, a more general analysis is presented. This includes explicitly identifying the linkage disequilibrium generating aspect of selection. In addition, the way quantities may be obtained from summing over effective one-locus haploid loci, is derived from the explicit dynamics. Numerical tests of dynamical results over 10 4 generations and equilibrium results are pre- sented.

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Let m ≠ 0, ±1 and n ≥ 2 be integers. The ring of algebraic integers of the pure fields of type (nm) is explicitly known for n = 2, 3,4. It is well known that for n = 2, an integral basis of the pure quadratic fields can be given parametrically, by using the remainder of the square-free part of m modulo 4. Such characterisation of an integral basis also exists for cubic and quartic pure fields, but for higher degree pure fields there are only results for special cases.

In this paper we explicitly give an integral basis of the field (nm), where m ≠ ±1 is square-free. Furthermore, we show that similarly to the quadratic case, an integral basis of (nm) is repeating periodically in m with period length depending on n.

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We give a description of the terms in the Ringel-Hall product of preinjective Kronecker modules. We characterize in this way all the short exact sequences of preinjective modules. As an application we also give an explicit solution to the column completion challenge for pencils with only minimal indices for columns (corresponding to preinjective modules) and to the row completion challenge for pencils with only minimal indicies for rows (corresponding to preprojective modules).

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It is a well-known result of Solecki that every nonlocally compact Polish group with a two-sided invariant metric contains continuum many pairwise disjoint sets which are Haar ambivalent. Inspired by a recent result of Zajíček, we give such an explicit and natural collection in the space of continuous functions on the interval. Our collection involves functions which have infinite derivatives and knot points.

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Zero-one-sequences f length n with at least k -1 zeros between tw successive ones are c nsidered.The limit f the mean value f the number f nes in such sequences,as n tends t in .nity,is determined using nly the explicit f rmula f r the terms f linear recurrences.This determinati n is simpler than the ne due to Kiss and Zay.

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We study the set of the representable numbers in base with ρ>1 and n∊ℕ and with digits in an arbitrary finite real alphabet A. We give a geometrical description of the convex hull of the representable numbers in base q and alphabet A and an explicit characterization of its extremal points. A characterizing condition for the convexity of the set of representable numbers is also shown.

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In this paper, we study the k-th order Kantorovich type modication of Szász—Mirakyan operators. We first establish explicit formulas giving the images of monomials and the moments up to order six. Using this modification, we present a quantitative Voronovskaya theorem for differentiated Szász—Mirakyan operators in weighted spaces. The approximation properties such as rate of convergence and simultaneous approximation by the new constructions are also obtained.

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Although Aristotle's hymn to Areta is not an explicit expression of his moral, theological and political views, it fits them perfectly. According to the fictional thread of the poem the performers, Aristotle and his friends execute both a poetical and onthological immortalization of their friend, Hermias, when they commemorate him turning themselves into a mouthpiece of the Muses. This act of immortalization is seen as a process imagined as being fulfilled both in the present and the future recitals of the poem.

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An explicit characterization of each of the separation properties T i, i=0,1, , and T 2 at a point p is given in the topological category of Cauchy spaces. Moreover, specific relationships that arise among the various T i, i=0,1, , and T 2 structures at p are examined in this category. Finally, we investigate the relationships between generalized separation properties and separation properties at a point p in this category.

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According to Hermeneutics ch. 4, the analysis of non-assertive sentences such as wishes, commands, etc. belongs to rhetoric or poetics. They are, however, examined neither in the Rhetoric, nor in the Poetics, where in ch. 20 their treatment is explicitly excluded from the art of poetry and referred to that of delivery or performance. In this paper an explanation is given for this discrepancy, based on an interpretation of Aristotle's rejection of Protagoras' criticism of Homer.

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