O the volume growth of the hyperbolic regular $$\varvec{}$$-simplex

In this paper we give lower and upper bounds for the volume growth of a regular hyperbolic simplex, namely for the ratio of the n-dimensional volume of a regular simplex and the \((n-1)\)-dimensional volume of its facets. In addition to the methods of U. Haagerup and M. Munkholm we use a third volume form based on the hyperbolic orthogonal coordinates of a body. In the case of the ideal, regular simplex our upper bound gives the best known upper bound. On the other hand, also in the ideal case our general lower bound, improved the best known one for \(n=3\).     

Measuring centrality by a generalization of degree

Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have been developed. This paper proposes a new parametric family of centrality measures called generalized degree. It is based on the idea that a relationship to a more interconnected node contributes to centrality in a greater extent than a connection to a less central one. Generalized degree improves on degree by redistributing its sum over the network with the consideration of the global structure. Application of the measure is supported by a set of basic properties. A sufficient condition is given for generalized degree to be rank monotonic, excluding counter-intuitive changes in the centrality ranking after certain modifications of the network. The measure has a graph interpretation and can be calculated iteratively. Generalized degree is recommended to apply besides degree since it preserves most favourable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish among their importance.     

Advances in nucleic acid architectures for electrochemical sensing

Nucleic acid–based electrochemical sensors are ideally suited to the detection of molecular targets for which enzymatic detection or direct electrochemical oxidation – reduction reactions are not possible. Moreover, the versatility of nucleic acids in their ability to bind a great variety of target types, from small molecules to single-entity mesoscopic targets, makes them attractive receptors for the development of electrochemical biosensors. In this brief opinion piece, we discuss field advances from the past two years. We hope the works highlighted here will inspire the community to pursue creative designs enabling the detection of larger and more complex targets with a specific focus on analytical validation and translation into preclinical or clinical applications.     

Analytical and statistical studies of Rodriguez–Velazquez indices

Journal of Mathematical Chemistry - In this work we perform analytical and statistical studies of the Rodríguez–Velázquez (RV) indices on graphs G. The topological RV(G) indices,...     

Synthesis and Investigation of Piezophotocatalytic Properties of Polyvinylidene Fluoride Nanofibers Modified with Titanium Dioxide

Moscow University Chemistry Bulletin - A piezoactive nanofiber composite PVDF film with TiO2 nanoparticles included in it was synthesized by electrospinning. The composition, morphology and...     

Effect of soil properties on radioactivity concentrations and dose assessment

This study evaluated the correlation between radioactivity concentrations and soil properties, and determined the total annual effective dose near an underground geologic repository for transuranic wastes. Soil samples were collected from two historical monitoring areas (Near Field and Cactus Flats). Alpha-particle spectrometry was used for the analysis of ²⁴¹Am, ^239+240Pu and ²³⁸U, while ¹³⁷Cs, ⁴⁰K, ²³²Th and ²²⁶Ra were detected by gamma ray spectrometry. Higher radioactivity concentrations and stronger positive correlations between radioactivity concentrations and soil properties were obtained in Cactus Flats compared to Near Field. The total annual effective dose was lower than the recommended limit of 1 mSv y^??1.

     

The Hungarian periconceptional service as a model for community genetics

OBJECTIVES: This review describes the methods and results of the Hungarian periconceptional service consisting of counselling, examinations and medical interventions. (The term periconceptional is used instead of preconceptional because the early postconceptional period is also involved to this service.) METHODS: The service was based on three steps: check-up examination of reproductive health (i.e., preconceptional screenings), a 3-month preparation for conception, dispensed and/or supervised by qualified nurses, and a better protection in early pregnancy for the most sensitive early development of the embryo for voluntary and eligible couples. RESULTS: Experiences from the coordinating centre of the Hungarian periconceptional service are summarized between February 1, 1984, and January 31, 1999, thus 15 years. Participants with positive family histories, case histories and subjects with genito-urinary infections had a more effective flow towards secondary care. Infertile couples were diagnosed and treated sooner. The periconceptional service is effective for the introduction of periconceptional folic acid-containing multivitamin supplementation and for the reduction of smoking and alcohol consumption in females in the preconceptional period. The rate of major congenital abnormalities (20.6 per 1,000) was significantly lower than expected. CONCLUSIONS: The periconceptional service is feasible and has many benefits. Thus, proper preparation for conception is the earliest and probably the most important effort to prevent genetic diseases.     

Stress relaxation,creep, and internal stresses in high density polyethylene filled with calcium carbonate

The effect of filling high density polyethylene (HDPE) with calcium carbonate (up to 50% by weight) on the stress relaxation and the creep in uniaxial extension at room temperature was investigated. The addition of CaCO₃ was found to have a strong influence on the flow behaviour of HDPE. In particular, it was observed that the internal stress level, calculated from relaxation data, increased markedly with the filler content. The reduction in creep rate of the filled samples suggested that the CaCO₃-particles induce a change in the structure of the HDPE-interphase close to the filler surface. This was supported by dynamic mechanical measurements performed at low temperatures on swollen HDPE-CaCO₃ samples.     

Bistable Boundary Reactions in Two Dimensions

In a bounded domain \({\Omega \subset \mathbb R^2}\) with smooth boundary we consider the problem

$\Delta u = 0 \quad {\rm{in }}\, \Omega, \qquad \frac{\partial u}{\partial \nu} = \frac1\varepsilon f(u) \quad {\rm{on }}\,\partial\Omega,$

where ν is the unit normal exterior vector, ε > 0 is a small parameter and f is a bistable nonlinearity such as f(u) = sin(π u) or f(u) = (1 ? u ²)u. We construct solutions that develop multiple transitions from ?1 to 1 and vice-versa along a connected component of the boundary ?Ω. We also construct an explicit solution when Ω is a disk and f(u) = sin(π u).