A new fast direct algorithm for implementing a finite element method (FEM) of order on rectangles as applied to boundary value problems for Poisson-type equations is described that extends a well-known algorithm for the case of difference schemes or bilinear finite elements (n = 1). Its core consists of fast direct and inverse algorithms for expansion in terms of eigenvectors of one-dimensional eigenvalue problems for an nth-order FEM based on the fast discrete Fourier transform. The amount of arithmetic operations is logarithmically optimal in the theory and is rather attractive in practice. The algorithm admits numerous further applications (including the multidimensional case).
A perfect 2-matching in an undirected graph G=(V,E) is a function x:E→0,1,2 such that for each node v∈V the sum of values x(e) on all edges e incident to v equals 2. If supp(x)=e∈E∣x(e)≠0 contains no triangles then x is called triangle-free. Polyhedrally speaking, triangle-free 2-matchings are harder than 2-matchings, but easier than usual 1-matchings. Given edge costs c:E→R + , a natural combinatorial problem consists in finding a perfect triangle-free matching of minimum total cost. For this problem, Cornuéjols and Pulleyblank devised a combinatorial strongly-polynomial algorithm, which can be implemented to run in O(VElogV) time. (Here we write V, E to indicate their cardinalities |V|, |E|.) If edge costs are integers in range [0,C] then for both 1- and 2-matchings some faster scaling algorithms are known that find optimal solutions within O(Vα(E,V)logVElog(VC)) and O(VElog(VC)) time, respectively, where α denotes the inverse Ackermann function. So far, no efficient cost-scaling algorithm is known for finding a minimum-cost perfect triangle-free2-matching. The present paper fills this gap by presenting such an algorithm with time complexity of O(VElogVlog(VC)).
We address the following question: When an affine cone over a smooth Fano threefold admits an effective action of the additive group? In this paper we deal with Fano threefolds of index 1 and Picard number 1. Our approach is based on a geometric criterion from our previous paper, which relates the existence of an additive group action on the cone over a smooth projective variety X with the existence of an open polar cylinder in X. Non-trivial families of Fano threefolds carrying a cylinder were found in loc. cit. Here we provide new such examples.
We show that affine cones over smooth cubic surfaces do not admit non-trivial Ga-actions.
This paper identifies a new reason for giving preferences to the disadvantaged using a model of contests. There are two forces at work: the e§ort e§ect working against giving preferences and the selection e§ect working for them. When education is costly and easy to obtain (as in the U.S.), the selection e§ect dominates. When education is heavily subsidized and limited in supply (as in India), preferences are welfare reducing. The model also shows that unequal treatment of identical agents can be welfare improving, providing insights into when the counterintuitive policy of rationing educational access to some subgroups is welfare improving.
Анализируя опубликованную в этом же номере журнала работу Р. Харре, автор высказывает предположение, что Р. Харре рассматривает не абстрактную возможность, а реальные условия, при которых возможность актуализируется. В терминах Харре, потенциал человеческих возможностей может увеличиваться или уменьшаться в зависимости от того, какое воздействие на него оказывает культурный социум.
Standard Modern Russian has phonological contrast between palatal- ized and velarized consonants. One of the most prominent changes attributed recently to this part of its phonetic system is the dramatic aƵrication of pala- talized dental stops which are now pronounced in most phonetic contexts as aƵricates [tsj], [dzj]. The paper proposes the hypothesis that a fast spread of palatalized dental stops’ aƵrication in Standard Modern Russian is triggered by the need to more eƵectively distinguish palatalized plosives in situations that do not provide the primary acoustic cue (formant transition of adjacent vowel) for their diƵerentiation to the listener. Palatalized dental plosives still should be treated phonologically as stops since in the context of homorganic nasal or stop they are not aƵricated (and often unreleased), while the fricative part of dental aƵricates in the same position still preserved in pronunciation of all the subjects studied.