Asymptotic expansions andL ∞-error estimates for mixed finite element methods for second order elliptic problems

Summary Asymptotic expansions for mixed finite element approximations of the second order elliptic problem are derived and Richardson extrapolation can be applied to increase the accuracy of the approximations. A new procedure, which is called the error corrected method, is presented as a further application of the asymptotic error expansion for the first order BDM approximation of the scalar field. The key point in deriving the asymptotic expansions for the error is an establishment ofL ¹-error estimates for mixed finite element approximations for the regularized Green's functions. As another application of theL ¹-error estimates for the regularized Green's functions, we shall present maximum norm error estimates for mixed finite element methods for second order elliptic problems.     

Comparison theorems forL-monosplines of minimal norm

Summary LetLM _N be the set of allL-monosplines withN free knots, prescribed by a pair (x;E) of pointsx = {x _i } ₁ ⁿ ,a <x ₁ < ... <x _n <b and an incidence matrixE = (e _ij ) _i=1 ⁿ , _r-1 ^j=0 with Denote byLM _N ^O the subset ofLM _N consisting of theL-monosplines withN simple knots (n=N). We prove that theL-monosplines of minimalL _p-norms inLM _N belong toLM _N ^O .The results are reformulated as comparison theorems for quadrature formulae.     

Pair formation in age-structured populations

The modelling problems associated with pair formation in age-structured populations are discussed in this paper. The author also formulates a class of models for pair formation in human populations and derives some results on persistent distributions.     

Lattice-point examples for a question of Erdős

Here we establish a set of eight points in general position in the plane, i.e. no three on a line, no four on a circle, and they determine 7 distinct distances, so that, thei-th distance occursi times,i = 1, 2, , 7. The points are embedded in a triangular net, and the distances are not ordered by size or in any other way. We shall show that some known and unknown examples forn < 8 with the above properties may also be lattice points of a similar net.Research (partially) supported by the Hungarian National Foundation for Scientific Research (OTKA) grant, no. 1808.     

On theR-order of coupled sequences arising in single-step type methods

Summary As shown in preceding papers of the authors, the verification of anR-convergence order for sequences coupled by a system (1.1) of basic inequalities can be reduced to the positive solvability of system (3.3) of linear inequalities. Further, the bestR-order implied by (1.1) is equal to the minimal spectral radius of certain matrices composed from the exponents occuring in (1.1). Now, these results are proven in a unified and essentially simpler way. Moreover, they are somewhat extended in order to facilitate applications to concrete methods.     

Methods of integral geometry and recovering a function with compact support from its projections in unknown directions

A method for recovering a function with compact support on a plane from its Radon transform is suggested. In particular, from the given projections of a function in unknown directions, these directions may be recovered (up to a rotation or a reflection), if there are 7 of them. This result may be applied in tomography.     

Normal subgroups and elementary theories of lattice-ordered groups

We show that any lattice-ordered group (l-group) G can be l-embedded into continuously many l-groups H _i which are pairwise elementarily inequivalent both as groups and as lattices with constant e. Our groups H _i can be distinguished by group-theoretical first-order properties which are induced by lattice-theoretically nice properties of their normal subgroup lattices. Moreover, they can be taken to be 2-transitive automorphism groups A(S _i ) of infinite linearly ordered sets (S _i , ) such that each group A(S _i ) has only inner automorphisms. We also show that any countable l-group G can be l-embedded into a countable l-group H whose normal subgroup lattice is isomorphic to the lattice of all ideals of the countable dense Boolean algebra B.     

氮杂冠醚与碱金属离子配位反应的研究

滴定量效法是研究反应热化学和热力学的重要手段之一．用这种方法对冠醚与金属离子的配位反应热力学性质进行研究一直受到很大关注【且S习．但是对氨杂冠林，尤其是一系列结构相似的氨杂冠醚体系进行系统的热力学性质研究的报导不多．前文K则曾报导了用自组装的消定量热计对银（I）－a吹体系和铜（11）·N，N’一问位取代革基乙二胺体系的配位反应热化学研究结果·本文报导从（对位取代革基）k杂15冠5卜RPW15CS，R＝CIZH；CHa；CHso）与碘化钠和碘化钾在25T、无水乙过溶液中进行配位反应的消定量效研究结果．讨论了配体上取代基的电…