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Children 3-6 years of age, when given an identification task where number was redundant to length or density, Solved the task on the basis of number. Surreptitious subtraction or addition elicited strong surprise as well as search behavior whereas displacements did not. Children who noticed the change in number or length and density gave unambiguous explanations of the nature of the intervening operations and were able to indicate how to reverse the effect. These findings are taken to show young children can treat small numbers as invariant. The results are discussed in terms of why children of the same age fail to conserve numbers in the standard conservation task and how complex number concepts might develop. [ABSTRACT FROM AUTHOR]

Let Cn be the n-dimensional complex number space of the complex variables z1,…, zn and be the unit hypersphere. Further, let G be the group of all holomorphic automorphisms of K, then G is a n(n + 2)-dimensional real Lie group. In [3] the author has proved that for any P∈∂K (the boundary of K) there exists a decomposition of G in the form , where G0 is the group of all analytic rotations about the origin and is a 2n-dimensional real Lie group, whose underlying topological space is K, which acts transitively on K and P is a fixed point of all elements of . [ABSTRACT FROM PUBLISHER]

Estimates involving polynomials can often naturally be given in terms of the discriminants of these polynomials or of the resultants of pairs of polynomials. Since the discriminant of a polynomial with multiple zeros vanishes as does the resultant of two polynomials with common zeros these results become trivial when applied to such polynomials or pairs of polynomials. Therefore it is often necessary to exclude polynomials with multiple zeros from a given investigation. In theoretical studies of a measure-theoretical nature this often does not affect the results; however for the purpose of constructing polynomials with specified properties it can be an advantage if it is not necessary to restrict the attention to polynomials without multiple zeros. [ABSTRACT FROM PUBLISHER]

It was proved in a recent paper† that if au α1, …, αn denote non-zero algebraic numbers and if‡ logαn, …, log αn and and 2πi are linearly independent over the rationals then log α1, …, log αn are linearly independent over the field of all algebraic numbers. Further it was shown that if α1 …, αn are positive real algebraic numbers other than 1 and if β1, …, βn denote real algebraic numbers with 1, β1 …, βn linearly independent over the rationals then is transcendental. [ABSTRACT FROM PUBLISHER]

The article focuses on the standards for evaluating the performance of outlet managers in companies with numerous outlets. The author discusses the differences of the profit potentials of the outlets and the effects of the environmental factors. The author states that some differences in measured contribution margins among outlets may be explained by differences in the characteristics of the locations of the outlets as well as the differences in the performance of the outlet managers. The article also presents guides for the resource allocation in selecting managers, location and facilities. [ABSTRACT FROM AUTHOR]