Abstract:
A real Banach algebra of Newton interpolating series, used to approximate the solutions of multipoint boundary value problems for ODE's, is studied.

Abstract:
This study presents nonlinear differential equations capable to generate continuous functions similar to pulse sequences. First are studied some basic properties of second-order differential equations with time-dependent coefficients generating bounded oscillating functions similar to test-functions (the function and its derivative being equal to zero at the same time moments). The necessary intercorrelations between the phase of generated oscillations and the time-dependent coefficients is presented, being shown also that the external command function should be set to a constant value at these time moments so as to determine the amplitude and the sign of generated oscillations. Then some possibilities of using previous differential equation for generating positive-definite functions with null values for the function and its derivative at the same time moments and with constant slope for its amplitude are presented, being shown that the corresponding external command function should present also alternating components. Finally all previous results are used for determining a set of second-order differential equations with time dependent coefficients and a set of external command and corrective functions for generating a pulse sequence useful for modelling time series.

Abstract:
This study presents mathematical aspects of wave equation considered on closed space intervals. It is shown that a solution of this equation can be represented by a certain superposition of traveling waves with null values for the amplitude and for the time derivatives of the resulting wave in the endpoints of this interval. Supplementary aspects connected with the possible existence of initial conditions for a secondorder differential system describing the amplitude of these localized oscillations are also studied, and requirements necessary for establishing a certain propagation direction for the wave (rejecting the possibility of reverse radiation) are also presented. Then it is shown that these aspects can be extended to a set of adjacent closed space intervals, by considering that a certain traveling wave propagating from an endpoint to the other can be defined on each space interval and a specific mathematical law (which can be approximated by a differential equation) describes the amplitude of these localized traveling waves as related to the space coordinates corresponding to the middle point of the interval. Using specific differential equations, it is shown that the existence of such propagating law for the amplitude of localized oscillations can generate periodical patterns and can explain fracture phenomena inside materials as well.

Abstract:
We derive orthogonality relations for discrete q-ultraspherical polynomials and their duals by means of operators of representations of the quantum algebra su_q(1,1). Spectra and eigenfunctions of these operators are found explicitly. These eigenfunctions, when normalized, form an orthonormal basis in the representation space.

Abstract:
This study presents the calcophilous vegetal associations developed on the limy rocky areas, very common in Padurea Craiului Mountains. These associations are affiliated with the coenotaxonomical system based on the dominant species and analyzed from an ecological, phytogeographical and of bioforms point of view, based on phytocaenological tables. Meadows installed on limestone rockeries make up 7 vegetal associations: Festucetum pallentis, Asplenio rutaemurariae-Melicetum, Seslerietum rigidae, Seslerietum heufflerianae, Sedo hispanici-Poaetum nemoralis, Asplenietum trichomano-rutae-murariae, and Pparietarietum officinalis. These associations belong to 4 vegetation classes. The most widespread are Festuca palentis meadows. They are important for protecting the soil against erosion, as they develop mostly on slopes with a high inclination, sometimes on scree, and rocky outposts. Generally these meadows have no economic importance.

Abstract:
he article analyzes The Letters for a Provincial, addressed by Mircea Eliade to a hypothetical provincial in order to prepare access to the capital city. The letters are written so as to dislocate the provincial from a cultural model built on fake values and prejudices. From a mere pretext, the letters are turned into a symbolic act through which the historian of religions assumes, on the one hand, the destiny of a messenger of a new humanism, and, on the other hand, transforms the modern areligious man into a destination point for whom the provincial is the archetype. Thus, in all of Eliade’s works one can trace the same pattern of dislocation of the partial man, disconnected from archetypes and milestones, in order to re-install him on the road towards the Center, through anthropology structured on cosmic reintegration, alchemy or androgyny in the books of the Romanian period, recovery of the eternal recursion in the Western treatises, and also through the theory of the irecognoscibility of the miracle, in his last essays. The end of the article proposes an answer from the present provincial, who for Eliade was still in the future, an answer showing that the messages of the historian of religions are not reaching him, because he has lost the road towards the Center; moreover, he is situated in an ill-fated extraterritoriality, that is made possible through the great integrations at a horizontal level, and his chance would be the return to the story.

Abstract:
This article analyses the concept of “the loss of time” in the essays of Mircea Eliade. This concept is shown to be an instrument of knowledge and a form of freedom that saves the human being from falling into historicity, and opens a point of access towards authenticity. The article critically discusses the temporal alternatives of the modern human being: capitalized time, free time, and personal time. The loss of time is subsequently shown to be both a technique for obtaining salvation, and a domination technique de- scribed in scientific works. Finally, the invitation of losing time is seen as a re-activation of an a priori structure that makes possible the “humanitarian engagement” of Eliade in order to re-actualize the sacred at the conscious level of the modern human being, as well as an attempt at revalorization of parusia for the religious Christian.

Abstract:
The article analyzes The Letters for a Provincial, addressed by Mircea Eliade to a hypothetical provincial in order to prepare access to the capital city. The letters are written so as to dislocate the provincial from a cultural model built on fake values and prejudices. From a mere pretext, the letters are turned into a symbolic act through which the historian of religions assumes, on the one hand, the destiny of a messenger of a new humanism, and, on the other hand, transforms the modern areligious man into a destination point for whom the provincial is the archetype. Thus, in all of Eliade’s works one can trace the same pattern of dislocation of the partial man, disconnected from archetypes and milestones, in order to re-install him on the road towards the Center, through anthropology structured on cosmic reintegration, alchemy or androgyny in the books of the Romanian period, recovery of the eternal recursion in the Western treatises, and also through the theory of the irecognoscibility of the miracle, in his last essays. The end of the article proposes an answer from the present provincial, who for Eliade was still in the future, an answer showing that the messages of the historian of religions are not reaching him, because he has lost the road towards the Center; moreover, he is situated in an ill-fated extraterritoriality, that is made possible through the great integrations at a horizontal level, and his chance would be the return to the story.

Abstract:
A protocol for assuring the authenticity of information broadcasted over long periods of time is proposed. The protocol is based on time synchronization and uses one-way chains constructed with the squaring function which gives the possibility to construct a one-way chain of whose length is unbounded in practice. Although the computational cost is somewhat increased, compared to the use of hash chains, these computational requirements are affordable for the addressed scenario. In brief, the protocol assures information authenticity at the reduced cost of almost one modular multiplication for each broadcasted packet. Time synchronization issues are discussed and the security of the protocol is equivalent to the integer factorization problem since the squaring function is used in the construction of the one-way chain. A failure mode analysis of the protocol is done; this is an aspect of novelty and applies to other protocols based on time synchronization as well. Also, a formal proof on the security of the protocol is sketched.

Abstract:
In the biomedical domain, authors publish their experiments and findings using a quasi-standard coarse-grained discourse structure, which starts with an introduction that sets up the motivation, continues with a description of the materials and methods, and concludes with results and discussions. Over the course of the years, there has been a fair amount of research done in the area of scientific discourse analysis, with a focus on performing automatic recognition of scientific artefacts/conceptualisation zones from the raw content of scientific publications. Most of the existing approaches use Machine Learning techniques to perform classification based on features that rely on the shallow structure of the sentence tokens, or sentences as a whole, in addition to corpus-driven statistics. In this article, we investigate the role carried by the deep (dependency) structure of the sentences in describing their rhetorical nature. Using association rule mining techniques, we study the presence of dependency structure patterns in the context of a given rhetorical type, the use of these patterns in exploring differences in structure between the rhetorical types, and their ability to discriminate between the different rhetorical types. Our final goal is to provide a series of insights that can be used to complement existing classification approaches. Experimental results show that, in particular in the context of a fine-grained multi-class classification context, the association rules emerged from the dependency structure are not able to produce uniform classification results. However, they can be used to derive discriminative pair-wise classification mechanisms, in particular for some of the most ambiguous types.