平面凸体的完全不等式组

对于平面凸体，分别用A、p、r、R、d表示它的面积、周长、内径、外径、直径．本文分别给出了其中的三元组合(A，r，R)，(p，r．R)，(p，r，d)，(A，r，d)所满足的不等式，并给出了相应的极值集．     

On Partially Ordered Semigroups and an Abstract Set-Difference

In this paper we prove the independence of a system of five axioms (S1)–(S5), which was proposed in the book of Pallaschke and Urbański (Pairs of Compact Convex Sets, vol. 548, Kluwer Academic Publishers, Dordrecht, 2002) for partially ordered commutative semigroups. These five axioms (S1)–(S5) are stated in the introduction below. A partially ordered commutative semigroup satisfying these axioms is called a F-semigroup. By the use of a further axiom (S6) we define an abstract difference for the elements of a F-semigroup and prove some basic properties. The most interesting example of a F-semigroup are the nonempty compact convex sets of a topological vector space endowed with the Minkowski sum as operation and the inclusion as partial order. In Section 4 we apply the abstract difference to the problem of minimality of convex fractions. Dedicated to Boris Mordukhovich in honour of his 60th birthday.     

Very Colorful Theorems

We prove several colorful generalizations of classical theorems in discrete geometry. Moreover, the colorful generalization of Kirchberger’s theorem gives a generalization of the theorem of Tverberg on non-separated partitions.     

LS[7](3,5,11( exists

In this article, we employ trades to construct an instance of an LS[7](3,5,11) which is the smallest unresolved LS[7](3,k,v) [ 9 ]. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 312–316, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10021     

New orthogonal designs of order 56

Amicable sets of eight matrices are very useful in the construction of orthogonal designs using the Kharaghani array. In this article we use a simple procedure to construct many new amicable sets of eight matrices of order 7 and then new orthogonal designs of order 56. Some of these are restricted to be short amicable sets of two or four circulant matrices.. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 387–393, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10030     

Cubature grids

This article applies group theory to the problem of calculating accurate cubature grids for three‐dimensional (3D) integrals that have an exponential weighting factor. The nodes of a cubature are divided into structures, each with the full symmetry of the octahedral group. The sequence of structures is derived from a basis set of polynomials forming a Sturmian basis for the function space. Several cubatures, of up to eighth degree accuracy, are reported and their features discussed. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

On the cofinalities of Boolean algebras and the ideal of null sets

We will show that if the cofinality of the ideal of Lebesgue measure zero sets is equal to then there exists a Boolean algebra B of cardinality which is not a union of strictly increasing -sequence of its subalgebras. This generalizes a result of Just and Koszmider who showed that it is consistent with that such an algebra exists. Received November 21; accepted in final form April 12, 2001.     

Electronic structure calculations of Fe-rich ordered and disordered Fe-Al alloys

Tight Binding Linear Muffin-Tin Orbital (TB-LMTO) electronic calculations are presented for the magnetic and structural properties of ordered and disordered FeAl alloys. The total energy, bulk modulus, lattice parameter and magnetic moments of B2, D03 and B32 ordered structures and A2 disordered structure were calculated for different compositions. The different structures are obtained by varying the position of Fe and Al atoms in a BCC superstructure. In this way, we examine the order-disorder transition that takes place in these alloys. Disordered alloys present both larger Fe magnetic moment and lattice parameter than ordered ones. In this work comparison of the calculated quantities with available experimental results is provided and it can be concluded that the results are in quantitative agreement with the experimental trends. Received 7 May 2002 / Received in final form 20 September 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: eaf@we.lc.ehu.es