Tariffs, rent extraction and manipulation of competition

Tariffs;Models

Small families of complex lines for testing holomorphic extendibility

Let B be the open unit ball in C^2 and let a, b be two points in B. It is known that for every positive integer k there is a function f in C^k(bB) which extends holomorphically into B along any complex line passing through either a or b yet f does not extend holomorphically through B. In the paper we show that there is no such function in C^\infty (bB). Moreover, we obtain a fairly complete description of pairs of points a, b in C^2 such that if a function f in C^\infty(bB) extends holomorphically into B along each complex line passing through either a or b that meets B, then f extends holomorphically through B.Comment: 17 pages, an error in the last step of the proof of the main theorem has been correcte

Torsion-free, divisible, and Mittag-Leffler modules

We study (relative) K-Mittag-Leffler modules, with emphasis on the class K of absolutely pure modules. A final goal is to describe the K-Mittag-Leffler abelian groups as those that are, modulo their torsion part, aleph_1-free, Cor.6.12. Several more general results of independent interest are derived on the way. In particular, every flat K-Mittag-Leffler module (for K as before) is Mittag-Leffler, Thm.3.9. A question about the definable subcategories generated by the divisible modules and the torsion-free modules, resp., has been left open, Quest.4.6

The Couple to Couple League Approach to Natural Family Planning Instruction

Material appearing below is an advertisement for Couple to Couple League, which teaches the full sympto-thermal method of natural family planning to groups of learner couples through a cadre of well-trained teaching couples

Comparison of Support Vector Machine and Back Propagation Neural Network in Evaluating the Enterprise Financial Distress

Recently, applying the novel data mining techniques for evaluating enterprise financial distress has received much research alternation. Support Vector Machine (SVM) and back propagation neural (BPN) network has been applied successfully in many areas with excellent generalization results, such as rule extraction, classification and evaluation. In this paper, a model based on SVM with Gaussian RBF kernel is proposed here for enterprise financial distress evaluation. BPN network is considered one of the simplest and are most general methods used for supervised training of multilayered neural network. The comparative results show that through the difference between the performance measures is marginal; SVM gives higher precision and lower error rates.Comment: 13 pages, 1 figur

(2,m,n)-groups with Euler characteristic equal to −2asb-2^as^b

We study those $(2, m, n)$-groups which are almost simple and for which the absolute value of the Euler characteristic is a product of two prime powers. All such groups which are not isomorphic to $PSL_2 (q)$ or $PGL_2(q)$ are completely classified