Cyclic Maximal Ideals of Rings of Differential Operators over Power Series Rings

In [3], Bratti and Takagi conjectured that a first order differential operator S=11 +...+ nn+ with 1,..., n, {x1,..., xn} does not generate a cyclic maximal left (or right) ideal of the ring of differential operators. This is contrary to the case of the Weyl algebra, i.e., the ring of differential operators over the polynomial ring [x1,..., xn]. In this case, we know that such cyclic maximal ideals do exist. In this article, we prove several special cases of the conjecture of Bratti and Takagi.

Towards a maximal extension of Pelczynski`s decomposition method in Banach spaces

l Suppose that X, Y. A and B are Banach spaces such that X is isomorphic to Y E) A and Y is isomorphic to X circle plus B. Are X and Y necessarily isomorphic? In this generality. the answer is no, as proved by W.T. Cowers in 1996. In the present paper, we provide a very simple necessary and sufficient condition on the 10-tuples (k, l, m, n. p, q, r, s, u, v) in N with p+q+u >= 3, r+s+v >= 3, uv >= 1, (p,q)$(0,0), (r,s)not equal(0,0) and u=1 or v=1 or (p. q) = (1, 0) or (r, s) = (0, 1), which guarantees that X is isomorphic to Y whenever these Banach spaces satisfy X(u) similar to X(p)circle plus Y(q), Y(u) similar to X(r)circle plus Y(s), and A(k) circle plus B(l) similar to A(m) circle plus B(n). Namely, delta = +/- 1 or lozenge not equal 0, gcd(lozenge, delta (p + q - u)) divides p + q - u and gcd(lozenge, delta(r + s - v)) divides r + s - v, where 3 = k - I - in + n is the characteristic number of the 4-tuple (k, l, m, n) and lozenge = (p - u)(s - v) - rq is the discriminant of the 6-tuple (p, q, r, s, U, v). We conjecture that this result is in some sense a maximal extension of the classical Pelczynski`s decomposition method in Banach spaces: the case (1, 0. 1, 0, 2. 0, 0, 2. 1. 1). (C) 2009 Elsevier Inc. All rights reserved.

Seasonality and growth rings in lianas of Bignoniaceae

Lianas are one of the most important components of tropical forest, and yet one of the most poorly known organisms. Therefore, our paper addresses questions on the environmental and developmental aspects that influence the growth of lianas of Bignoniaceae, tribe Bignonieae. In order to better understand their growth, we studied the stem anatomy, seasonality of formation and differentiation of secondary tissues, and the influence of the cambial variant in xylem development on a selected species: Tynanthus cognatus. Afterwards, we compared the results found in T. cognatus with 31 other species of Bignonieae to identify general patterns of growth in lianas of this tribe. We found that cambial activity starts toward the end of the rainy season and onset of the dry season, in contrast to what is known for tropical trees and shrubs. Moreover, their pattern of xylem formation and differentiation is strongly influenced by the presence of massive wedges of phloem produced by a variant cambium. Thus, the variant cambium is the first to commence its activity and only subsequently does cambial activity progress towards the center of the regular region, leading to the formation of confluent growth rings. In summary, we conclude that: the cambium responds to environmental changes; the xylem growth rings are annual and produced in a brief period of about 2 months, something that may explain why lianas possess narrow stems; and furthermore, phloem wedges greatly influence cambial activity.

Exercise changes the size of cardiac neurons and protects them from age-related neurodegeneration

Aging leads to changes in cardiac structure and function. Evidence suggests that the practice of regular exercise may prevent disturbances in the cardiovascular system during aging. We studied the effects of aging on the morphology and morphometry of cardiac neurons in Wistar rats and investigated whether a lifelong moderate exercise program could exert a protective effect toward some deleterious effects of aging. Aging caused a significant decline (28%) in the number of NADH-diaphorase-stained cardiac Animals submitted to a daily session of 60 min, 5 day/week, at 1.1 km/h of running in treadmill over the entire life span exhibited a reversion of the observed decline in the number of cardiac neurons. However, most interesting was that the introduction of this lifelong exercise protocol dramatically altered the sizes of cardiac neurons. There was a notable increase in the percentage of small neurons in the rats of the exercise group compared to the sedentary animals. This is the first time that a protective effect of lifelong regular aerobic exercise has been demonstrated on the deleterious effects of aging in cardiac neurons. (C) 2009 Elsevier GmbH. All rights reserved.

M-deformations of A-simple germs from R(n) to R(n+1)

All A-simple corank-1 germs from R(n) to R(n+1), where n not equal 4, have an M-deformation, that is a deformation in which the maximal numbers of isolated stable singular points are simultaneously present in the image.

A transformational language for mutant description

Mutation testing has been used to assess the quality of test case suites by analyzing the ability in distinguishing the artifact under testing from a set of alternative artifacts, the so-called mutants. The mutants are generated from the artifact under testing by applying a set of mutant operators, which produce artifacts with simple syntactical differences. The mutant operators are usually based on typical errors that occur during the software development and can be related to a fault model. In this paper, we propose a language-named MuDeL (MUtant DEfinition Language)-for the definition of mutant operators, aiming not only at automating the mutant generation, but also at providing precision and formality to the operator definition. The proposed language is based on concepts from transformational and logical programming paradigms, as well as from context-free grammar theory. Denotational semantics formal framework is employed to define the semantics of the MuDeL language. We also describe a system-named mudelgen-developed to support the use of this language. An executable representation of the denotational semantics of the language is used to check the correctness of the implementation of mudelgen. At the very end, a mutant generator module is produced, which can be incorporated into a specific mutant tool/environment. (C) 2008 Elsevier Ltd. All rights reserved.

Classification of quantum relativistic orientable objects

Extending our previous work `Fields on the Poincare group and quantum description of orientable objects` (Gitman and Shelepin 2009 Eur. Phys. J. C 61 111-39), we consider here a classification of orientable relativistic quantum objects in 3 + 1 dimensions. In such a classification, one uses a maximal set of ten commuting operators (generators of left and right transformations) in the space of functions on the Poincare group. In addition to the usual six quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). Spectra of internal and external symmetry operators are interrelated, which, however, does not contradict the Coleman-Mandula no-go theorem. We believe that the proposed approach can be useful for the description of elementary spinning particles considered as orientable objects. In particular, it gives a group-theoretical interpretation of some facts of the existing phenomenological classification of spinning particles.

PARALLEL ALGORITHMS FOR MAXIMAL CLIQUES IN CIRCLE GRAPHS AND UNRESTRICTED DEPTH SEARCH

We present parallel algorithms on the BSP/CGM model, with p processors, to count and generate all the maximal cliques of a circle graph with n vertices and m edges. To count the number of all the maximal cliques, without actually generating them, our algorithm requires O(log p) communication rounds with O(nm/p) local computation time. We also present an algorithm to generate the first maximal clique in O(log p) communication rounds with O(nm/p) local computation, and to generate each one of the subsequent maximal cliques this algorithm requires O(log p) communication rounds with O(m/p) local computation. The maximal cliques generation algorithm is based on generating all maximal paths in a directed acyclic graph, and we present an algorithm for this problem that uses O(log p) communication rounds with O(m/p) local computation for each maximal path. We also show that the presented algorithms can be extended to the CREW PRAM model.