Monotonic solutions of a quadratic integral equation of fractional order

In the paper we indicate an error made in the proof of the main result of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112-119]. Moreover, we provide correct proof of a slightly modified version of the mentioned result. The main tool used in our proof is the technique associated with the Hausdorff measure of noncompactness.     

On existence and asymptotic stability of solutions of a nonlinear integral equation

We prove an existence theorem for a nonlinear integral equation being a Volterra counterpart of an integral equation arising in the traffic theory. The method used in the proof allows us to obtain additional characterization in terms of asymptotic stability of solutions of an equation in question.     

C-N Bond Formation by Consecutive Continuous-Flow Reductions towards A Medicinally Relevant Piperazine Derivative

A new, continuous-flow consecutive reduction method was developed for the C-N bond formation in the synthesis of the key intermediate of the antipsychotic drug cariprazine. The two-step procedure consists of a DIBAL-H mediated selective ester reduction conducted in a novel, miniature alternating diameter reactor, followed by reductive amination using catalytic hydrogenation on 5% Pt/C. The connection of the optimized modules was accomplished using an at-line extraction to prevent precipitation of the aluminum salt byproducts.     

Electron-electron interaction in strong electromagnetic fields: the two-electron contribution to the ground-state energy in He-like uranium

Radiative recombination transitions into the ground state of cooled bare and hydrogenlike uranium ions were measured at the storage ring ESR. By comparing the corresponding x-ray centroid energies, this technique allows for a direct measurement of the electron-electron contribution to the ionization potential in the heaviest He-like ions. For the two-electron contribution to the ionization potential of He-like uranium we obtain a value of 2248+/-9 eV. This represents the most accurate determination of two-electron effects in the domain of high-Z He-like ions, and the accuracy reaches already the size of the specific two-electron radiative QED corrections.     

On existence and local attractivity of solutions of a quadratic Volterra integral equation of fractional order

In the paper we study the existence of solutions of a nonlinear quadratic Volterra integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on an unbounded interval. Moreover, we show that solutions of this integral equation are locally attractive.     

Functions related to convexity and smoothness of normed spaces

We introduce a few functions related to convexity and smoothness of normed spaces. Those functions turn out to be moduli of convexity or smoothness or play an intermediate role. We calculate the exact formulas for introduced functions in some classical Banach spaces. An application to geometry of normed spaces is also indicated.     

Shaking table experimental study on the effectiveness of polymer bearings for seismic isolation of structures

Seismic isolation has been recognised to be a very effective way of protecting structures from damage during earthquakes. It allows us to extend the natural period of the structure and therefore avoid resonance with the ground motion. Moreover, by increasing damping in the isolation devices, more energy can be dissipated and thus the structural response can be further reduced. The aim of this paper is to show the results of the study focused on verification of the applicability of the innovative method of seismic isolation by installing bearings made of a polymer mass, which is an especially designed flexible elastoplastic two-component grout based on polyurethane resin. In the study, a model structure was tested experimentally on a shaking table under earthquake excitation. First, the structure was fixed directly to the table and its response was recorded. Then, the response of the structure with polymer bearings installed at its base was observed and both responses were compared. The results of the study show that equipping the structure with the polymer bearings can considerably reduce the structural response under earthquake excitation. The innovative method considered in the study has been verified to be an effective seismic isolation technique. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Using micro-synchrotron radiation induced X-ray emission distribution maps to determine correlation between elements in prostate tissue

Elemental maps obtained by micro-synchrotron radiation induced X-ray emission technique can be manipulated in several ways to extract useful information. In this paper the method of displaying the correlation between two or three elements in one correlation map is described. Such types of maps give precise information about the overlap between the elements without distorting the original data.     

Transparent prioritisation,budgeting and resource allocation with multi-criteria decision analysis and decision conferencing

Managers in both for-profit and not-for-profit organisations continually face the task of allocating resources by balancing costs, benefits and risks and gaining commitment by a wide constituency of stakeholders to those decisions. This task is complex and difficult because many options are present, benefits and risks are rarely expressed as single objectives, multiple stakeholders with different agendas compete for limited resources, individually optimal resource allocations to organisational units are rarely collectively optimal, and those dissatisfied with the decisions taken may resist implementation. We first explain three current approaches to resource allocation taken from corporate finance, operational research and decision analysis, and we identify a common mistake organisations make in allocating resources. The paper then presents a technical process, multi-criteria portfolio analysis, for balancing the conflicting elements of the problem, and a social process, decision conferencing, which engages all the key players during the modelling process, ensuring their ownership of the model and the subsequent implementation. This socio-technical process improves communication within the organisation, develops shared understanding of the portfolio and generates a sense of common purpose about those projects that will best realise the organisation’s objectives. The paper concludes with lessons we have learned from actual practice. The authors want to thank Allergan and FCT (Portuguese Science Foundation) for their support.