Recall that B is PA relative to A if B computes a member of every nonempty $\Pi ^0_1(A)$ class. This two-place relation is invariant under Turing equivalence and so can be thought of as a binary relation on Turing degrees. Miller and Soskova [23] introduced the notion of a $\Pi ^0_1$ class relative to an enumeration oracle A, which they called a $\Pi ^0_1{\left \langle {A}\right \rangle }$ class. We study the induced extension of the relation B is PA relative (...) to A to enumeration oracles and hence enumeration degrees. We isolate several classes of enumeration degrees based on their behavior with respect to this relation: the PA bounded degrees, the degrees that have a universal class, the low for PA degrees, and the ${\left \langle {\text {self}\kern1pt}\right \rangle }$ -PA degrees. We study the relationship between these classes and other known classes of enumeration degrees. We also investigate a group of classes of enumeration degrees that were introduced by Kalimullin and Puzarenko [14] based on properties that are commonly studied in descriptive set theory. As part of this investigation, we give characterizations of three of their classes in terms of a special sub-collection of relativized $\Pi ^0_1$ classes—the separating classes. These three can then be seen to be direct analogues of three of our classes. We completely determine the relative position of all classes in question. (shrink)

In their logical analysis of theorems about disjoint rays in graphs, Barnes, Shore, and the author (hereafter BGS) introduced a weak choice scheme in second-order arithmetic, called the $\Sigma ^1_1$ axiom of finite choice (hereafter finite choice). This is a special case of the $\Sigma ^1_1$ axiom of choice ( $\Sigma ^1_1\text {-}\mathsf {AC}_0$ ) introduced by Kreisel. BGS showed that $\Sigma ^1_1\text {-}\mathsf {AC}_0$ suffices for proving many of the aforementioned theorems in graph theory. While it is not known (...) if these implications reverse, BGS also showed that those theorems imply finite choice (in some cases, with additional induction assumptions). This motivated us to study the proof-theoretic strength of finite choice. Using a variant of Steel forcing with tagged trees, we show that finite choice is not provable from the $\Delta ^1_1$ -comprehension scheme (even over $\omega $ -models). We also show that finite choice is a consequence of the arithmetic Bolzano–Weierstrass theorem (introduced by Friedman and studied by Conidis), assuming $\Sigma ^1_1$ -induction. Our results were used by BGS to show that several theorems in graph theory cannot be proved using $\Delta ^1_1$ -comprehension. Our results also strengthen results of Conidis. (shrink)

In their environment, plants are continuously submitted to natural stimuli such as wind, rain, temperature changes, wounding, etc. These signals induce a cascade of events which lead to metabolic and morphogenetic responses. In this paper the different steps are described and discussed starting from the reception of the signal by a plant organ to the final morphogenetic response. In our laboratory two plants are studied: Bryonia dioica for which rubbing the internode results in reduced elongation and enhanced radial expansion and (...) Bidens pilosa for which the response occurs at distance, hence pricking the cotyledon of a plantlet induces the growth inhibition of both the hypocotyl and the axillary bud of the pricked cotyledon. Reception of the signal and transmission of the message. In Bryonia the signal is received by epidermal cells while in Bidens they are the cells adjacent to the midrib of the cotyledon which receive the mechanical signal. In both plants the message is transmitted via a wave of electric depolarization. This latter is composed of an action potential associated with a slow wave whose transmission rates are respectively 1cm s−1 and 1 mm s−1. Recent results have shown the involvement of Ca2+ in the triggering of the slow wave and the role of the H+ pump during the slow wave. Transient and fast biochemical responses. An entry of extraceilular Ca2+ into the cells and a transient increase in IP3 occur within seconds following the mechanical stimulus. At the same time, the membrane becomes more fluid, correlated with qualitative changes in phospholipids. The rapid increase in the concentration of peroxidated lipids may be correlated with ethylene biosynthesis which is stimulated after rubbing. Other parameters such as cytoplasmic pH, relative water content, hydric potential, membrane potential and modifications of K+, Mg2+-ATPase and Ca2+-ATPase activities, play a key role in the early responses induced by the traumatisms. Irreversible-biochemical responses. The mechanical stimulus performed on a Bryonia internode induces an acceleration of: i) enzymatic activities related to the lignification, ii) esterification of phenolic acids in the cell wall. Consequently the lignification process is accelerated. Storage of the information. After being received by the target cells the information can be stored during several days before being expressed. At the level of cotyledonary bud, the first message, previously stored, can be expressed or not by a second treatment. Bidens thus behaves as if it was able to “store” and to “retrieve” morphogenetic messages, using a sort of rudimentary memory. The nuclei of the bud cells of the pricked cotyledon show that these cells, initially in G2 phase, divide and then remain in the G1 phase. In Bryonia, calli derived from young stimulated internodes, keep thigmomorphogenetic characteristics during several weeks. In the last part of this paper the particularity of our plant model which permits a study of the transmission and storage of the message, is underlined. The links between the different steps induced by the stimulus are discussed. Special attention is devoted to second messengers and to the amplification of the message. (shrink)

We investigate what it means for a (Hausdorff, second-countable) topological group to be computable. We compare several potential definitions based on classical notions in the literature. We relate these notions with the well-established definitions of effective presentability for discrete and profinite groups, and compare our results with similar results in computable topology.

Each group of selections in this text book is preceded by about ten pages of commentary by Harrington. These commentaries can be read either before the selections as a preparation setting forth the issues, or after the selections as an elucidation, isolating the selection's central concerns. All the selections, with the exception of Kierkegaard's, are from twentieth century thinkers. The contributors include Tillich, Herberg, G. E. Wright, Bultmann, D. M. Bailie, J. J. C. Smart, Wisdom, Hare, Sartre, Barth and Vahanian. (...) The book is divided into three main parts. The first part is basically doctrinal, exploring Biblical themes and contemporary views of revelation, God, man, Jesus, crucifixion, resurrection, and incarnation. The second part deals with aspects of the philosophy of religion including the connection between philosophy and theology, religious language, the existence of God, theistic proofs, and epistemological considerations. The third part, under the heading of "Challenges to Contemporary Man," is a potpourri of theological glamor issues including Existentialism and the death of God. Very often Harrington's commentary provides the reader with the classical aspects of the problem which the contemporary contributer is dealing with. There is a topically organized bibliography of suggested reading. There is no index.--S. O. H. (shrink)

By considering the irreducible representations of the Lorentz group, an analysis of the different spin-2 waves is presented. In particular, the question of the helicity is discussed. It is concluded that, although from the point of view of representation theory there are no compelling reasons to choose between spin-2 waves with helicity σ=±1 or σ=±2, consistency arguments of the ensuing field theories favor waves with helicity σ=±1.

Actuality of the conducted research is practically oriented character. Without the use of information and communication technologies in the field of higher education, it is impossible to carry out qualitative training of specialists in engineering, the results of which are necessary for the implementation of a national strategy for modernizing the economy and forming a progressive state of European type. Formulation of the task - the specificity of the use of ICT in the system of higher education has not been (...) studied sufficiently. ICT form a complex environment, which includes a lot of information objects and the links between them. It can be argued that the structural and functional analysis of the use of ICT in higher education is the basis of the theoretical justification in the formation of technical professionalism of future engineers. ICTs form a complex system, which includes not only technical and software-hardware capabilities, but also psycho-pedagogical, organizational, methodological. Without taking into account all of these components, as well as the needs of the subjects of the educational process, the use of ICT tools may be accompanied by risks and negatively affect the quality of high education. An analysis of recent research and publications-is actively exploring the experience of using ICT in high school, it is possible to distinguish the work of foreign specialists D. Stevenson, G. Reinhold, E. Wenger, S. Papierta, I. Zakharova, E. Patarakina, A. Khutorskogo, E. Polat The founders of this scientific direction in our country were M. I. Zhaldak, Y. I.Mashbits. The recent significant increase in the number of studies, the subject of which was the use of information and communication technologies in the educational process. Tsitemi in Ukraine is dedicated to the study of such scholars as V. Yu. Bykov, Ya.V. Bulakhova, O.M. Bondarenko, V.F. Zabolotny, G.O. Kozlakova, O. Moiko, O. Naumenko, Yu.Burovitskaya, I. Stavyts'ka, O.P. Pinchuk, O.V. Shestopal and others. Selection of unexplored parts of the general problem. The use of information technologies in the educational process is the foundation of innovative development of the educational system. The rapid development of ICT provides not only significant pace of innovative progress, but also requires the definition of information resources that guarantee the quality of learning, the choice of techniques that are in line with the general strategy for the formation of professional competences. Therefore, the problem of choosing an approach to the process of learning with the use of ICTs remains one of the main tasks of education. Research methods. In theory and practice, the study of the application of information and communication technologies in high school uses empirical methods of collecting and analyzing information based on the results of the survey of 120 students. Presenting main material. The essence of professionalism of future specialists of the technical direction is revealed. The scientific point of view on the professionalism of the engineer is presented. The peculiarities of formation of the basis of technical professionalism of future engineers in the process of studying at a higher school are theoretically grounded. The quantitative and qualitative analysis of the results of empirical researches of this problem is presented. The practical significance of the research topic is that the innovative approaches to the training of specialists in engineering specialties are differentiated, which differentiate in the educational concepts of teaching in higher educational institutions of European countries. (shrink)

'Uncertainty and chance' is a subject with a broad span, in that there is no academic discipline or walk of life that is not beset by uncertainty and chance. In this book a range of approaches is represented by authors from varied disciplines: natural sciences, mathematics, social sciences and medical sciences. At one extreme, this volume is concerned with the foundations of probability. At the other extreme, we have scholars who acknowledge the concept of chance and uncertainty but do not (...) cope with it by means of systematic measurement or quantative analysis. (shrink)

To localize wheat ESTs on chromosomes, 882 homoeologous group 6-specific ESTs were identified by physically mapping 7965 singletons from 37 cDNA libraries on 146 chromosome, arm, and sub-arm aneuploid and deletion stocks. The 882 ESTs were physically mapped to 25 regions flanked by 23 deletion breakpoints. Of the 5154 restriction fragments detected by 882 ESTs, 2043 were localized to group 6 chromosomes and 806 were mapped on other chromosome groups. The number of loci mapped was greatest on chromosome 6B and (...) least on 6D. The 264 ESTs that detected orthologous loci on all three homoeologs using one restriction enzyme were used to construct a consensus physical map. The physical distribution of ESTs was uneven on chromosomes with a tendency toward higher densities in the distal halves of chromosome arms. About 43% of the wheat group 6 ESTs identified rice homologs upon comparisons of genome sequences. Fifty-eight percent of these ESTs were present on rice chromosome 2 and the remaining were on other rice chromosomes. Even within the group 6 bins, rice chromosomal blocks identified by 1-6 wheat ESTs were homologous to up to 11 rice chromosomes. These rice-block contigs were used to resolve the order of wheat ESTs within each bin. (shrink)

Como casi todos los conceptos fi losófi cos, el de «validez normativa» tiene altos grados de ambigüedad y de vaguedad. En este trabajo me encargo de analizar la postura de distintos autores que han tratado de dar respuesta a la pregunta ¿qué significa que una norma sea «válida»? Para ello, tomo como hilo conductor la obra de Ernesto Garzón Valdés. Esto se debe a que los trabajos de Ernesto Garzón dedicados a este tema, le ofrecen al lector un análisis crítico (...) y comprensivo de algunas de las posturas teóricas más relevantes sobre el concepto de validez normativa. Asimismo, trabajar a través de su obra tiene un doble benefi cio: por un lado, no sólo nos permite conocer a fondo la postura teórica de autores que pertenecen a distintas corrientes del pensamiento, como Hans Kelsen, H.L.A. Hart, Francisco Suárez o von Wright por ejemplo, sino que, por el otro, nos permite conocer la postura del mismo Garzón y sus críticas a los diferentes modelos conceptuales. (shrink)

If G is an omega-stable group with a normal definable subgroup H, then the Sylow-2-subgroups of G/H are the images of the Sylow-2-subgroups of G. /// Sei G eine omega-stabile Gruppe und H ein definierbarer Normalteiler von G. Dann sind die Sylow-2-Untergruppen von G/H Bilder der Sylow-2-Untergruppen von G.

Exposure of man to chemical agents can occur intentionally, as in the treatment of disease, or inadvertently because the environment contains a wide range of synthetic or naturally occurring chemicals. The alkylating agents are a diverse group of compounds (Fig. 1) and comprise a good example of such xenobiotics, since much is known about their occurrence, and their biological effects include carcinogenicity, mutagenicity, toxicity and teratogenicity.Exposure to potentially carcinogenic alkylating agents such as nitrosamines may occur occupationally, from cigarette smoke, from (...) certain foodstuffs and even endogenously through the ingestion of the appropriate precursor chemicals.1 At the other extreme, the cytotoxic effects of agents such as the chloroethylating nitrosamides or mustards have been exploited in the design of certain antitumour drugs.2 The effectiveness of antitumour agents and the other, mostly adverse, biological effects of alkylating agents have been ascribed to their ability to damage cellular macromolecules, in particular DNA. This review concentrates on investigations carried out over the past two years on the role of DNA damage in carcinogenesis, but we shall see how recent advances in this area of research have also led to a better understanding of the mechanisms of the cytotoxic effects of alkylating antitumour agents. (shrink)

It is found that a coherent state of the cavity field can be generated in a micromaser with injected atoms in a coherent superposition of the upper and lower states. The dependence of the density matrix elements of the field on the number of injected atoms indicates that due to the same initial atomic coherence the emission of separately injected single atoms in the cavity is a cooperative process.