A mean value theorem for systems of integrals

More than a century ago, G. Kowalewski stated that for each n continuous functions on a compact interval [a,b], there exists an n-point quadrature rule (with respect to Lebesgue measure on [a,b]), which is exact for given functions. Here we generalize this result to continuous functions with an arbitrary positive and finite measure on an arbitrary interval. The proof relies on a version of Caratheodory's convex hull theorem for a continuous curve, that we also prove in the paper. As applications, we give a representation of the covariance for two continuous functions of a random variable, and a most general version of Gruess' inequality.Comment: 7 page

Metoda merenja moždanih ERP potencijala zasnovana na merenju harmonika epohe

U radu je predložena metoda merenja moždanih ERP potencijala zasnovana na merenju harmonika epohe. Predložena metoda je zasnovana na pristupu takozvanog stohastičkog digitalnog merenja na intervalu (SDMI), a hardver sa kojim se ova metoda može implementirati je zasnovan na brzim A/D konvertorima i FPGA strukturi. Metoda je ispitana brojnim simulacijama i eksperimentima i pokazano je da SDMI manjeg broja epoha, sa zadovoljavajućom tačnošću, meri latenciju ERP-a, što je korisno kod vremenski kraćih merenja, kada tačno merenje amplitude ERP komponente nije od značaja

The influence of the solar flux at 2.8 GHz on outbreaks of gypsy moth (Lymantria dispar L.) (Lepidoptera: Lymantriidae) in Serbia

The connection between the solar flux at 2.8 GHz (based on mean monthly values) and the outbreaks of gypsy moths (Lymantria dispar L.) in Serbia was investigated. The researches included six outbreaks from 1952 to 2007. The average values of the solar flux ranged between 83.8 and 101.8 sfu during the outbreaks, whereas they were between 147.9 and 188.3 sfu for the periods without outbreaks. The results of the research showed that the increase in the number of gypsy moths appears when the values of the solar flux at 2.8 GHz range from 70 to 120 sfu

Influence of mental disorders on working ability assessment

Background/Aim. There is an increasing need for evaluation of working ability due to lower level of social protection of workers and growing number of patients with mental diseases in Bosnia and Herzegovina (B&H). The aim of this study was to establish the influence of mental diseases on the occurrence of disability of I and III categories in B&H during the period from January 1st 2005 to December 31st 2006. Methods. This study involved 1 792 examinees with the complete loss of working ability (I disability category) (n = 921). Disability category III consisted of persons with limited working ability (n = 871). The instruments of research in this multricentric and retrospective study were the forms P-6 and D-2 for the years of service in B&H, and the form IN for persons with years of service abroad and personal features questionnaire (EPQ). Results. The study included 1 494 men (78.5%) and 298 women (21.5%). Univariant analysis represented very high statistical significance (p = 0.001) concerning: age (χ2 = 65.428), years of service (χ2=28.438), drinking (χ2 = 33.234), smoking (χ2=70.880), father’s education (χ2 = 58.124), migrations (χ2 = 14.874), sick leave (χ2 = 29.190), medical treatment (χ2 = 95.073) and rehabilitation (χ2 = 29.453). Multivariant analysis represented the influence on disability category I by parameters such as: years of service, sick leave, psychoticism and depression (p = 0.001). Hospital treatment and fatigation had influence on disability in both groups. Mental diseases are the leading cause in disability category I in 14.98% and in disability category III in 9.3% persons. Leading diseases in both disability categories were depression and schizophrenia followed by alcoholism, anxiety, brain organ psychosyndrome (BOPS) and other diseases. Conclusion. The following parameters have highest influence on the disability category: the years of service, sick leave, psychoticism, depression, and long-lasting disease, medical treatments and fatigation on the disability category III

HYBRID GPS/SINS SYSTEM - AN OVERVIEW

This paper describes a hybrid navigation system consisting of an integrated GPS/INS system. The integration of the navigation systems has been performed to improve the accuracy of the navigation parameters and it is a current trend in the world. The need for continuous navigation, during the change of position of the GPS receiver, during the closing time of the GPS receiving antenna, and during the appearance of interference, has imposed a solution that is achieved by the integration of GPS / INS. The role of SINS, which is part of the integrated GPS / INS navigation system, is to determine the navigation parameters at intervals between two adjacent measurements of GPS receivers, i.e., at times when there is no GPS navigation information for any reason. In this way, GPS and INS, when used together, complement and correct each other, significantly increasing the reliability and accuracy of the hybrid navigation system

Joint Crystal Structure and Computational Study of Hydrogen Bonds of Ethylenediamine

The hydrogen bonds of coordinated ethylenediamine (en) play important roles in catalytic activity [1], the aim of this work was to study geometrical parameters and strength of these interactions. The search of crystal structures archived in Cambridge Structural Database (CSD) was performed in order to find crystal structures containing at least one coordinated en to a transition metal, and at least one free water molecule interacting with en via NH···O hydrogen bond. All calculations were performed at M06L-GD3/def2-TZVPP/BSSE level of theory since it was confirmed that this level gives a good agreement with the CCSD(T)/CBS level. The distribution of dOH (Fig. 1) showed the maximum is at 2.0 Å - 2.1 Å, with a relatively large number of structures with distances shorter than 2.0 Å. The distribution of α (Fig 1.) revealed the maximum at 150⁰ - 160. The dOH and α are correlated, i.e. shorter distances correspond to larger angles. Most of en complexes contain cobalt, followed with palladium, nickel, and copper and most of them are in octahedral geometry. The coordination of en to the metal ions strengthens its hydrogen bonds with a water molecule. Namely, the energy of hydrogen bond of noncoordianted ethylenediamine is -2.3 kcal/mol, while the interaction energies for neutral metal complexes are in the range of -4.0 kcal/mol to -6.7 kcal/mol. Increasing of charge of complexes increases the energy of hydrogen bond. For singly charged complexes energy spans from -8.5 to -11.8 kcal/mol; for doubly charged complexes it spans from -15.6 kcal/mol to -19.9 kcal/mol; while triply charged complex has the strongest interaction of -28.0 kcal/mol [2]. In addition, the energies of hydrogen bond have a good correlation with the electrostatic potential on interacting hydrogen atom

CLIMATE REGIONALIZATION OF SERBIA ACCORDING TO KÖPPEN CLIMATE CLASSIFICATION

The paper presents a concise overview of the theoretical framework on which climate classifications are based. Beside short review of climate classifications, namely climatic regionalization for Serbia (or wider area including Serbia), main deficiency of these research was ascertained (which primarily relate to the period on the basis of which climate regionalization was carried out). The criteria of the Köppen climate classification are presented, on the basis of which the climate regionalization of Serbia has been carried out. The methodology of making maps of air temperatures and precipitation amounts has been described, on the basis of which a map of the climate regions of Serbia has been created. Spatial distribution of the types and subtypes of the climates in Serbia has been briefly described. It has been pointed to the constraints of the climate regionalization that arise from the theoretical bases of the climate classifications, but also from nature of the collected data and the applied methodology

USER DEFINED GEOMETRIC FEATURE FOR THE CREATION OF THE FEMORAL NECK ENVELOPING SURFACE

There is a growing demand for application of personalized bone implants (endoprostheses or macro-scaffolds, and fixators) which conform the anatomy of patient. Hence the need for a CAD procedure that enables fast and sufficiently accurate digital reconstruction of the traumatized bone geometry. Research presented in this paper addresses digital reconstruction of the femoral neck fracture. The results point out that User-Defined (geometric) Feature (UDF) concept is the most convenient to use in digital reconstruction of numerous variants of the same topology, such as in this kind of bone region. UDF, named FemoNeck, is developed to demonstrate capability of the chosen concept. Its geometry, controlled by a dozen of parameters, can be easily shaped according to anatomy of femoral neck region of the specific patient. That kind of CAD procedure should use minimally required set of geometric (anatomical) parameters, which can be easily captured from X-ray or Computed Tomography (CT) images. For the statistical analysis of geometry and UDF development we used CT scans of proximal femur of 24 Caucasian female and male adults. The validation of the proposed method was done by applying it for remodeling four femoral necks of four different proximal femurs and by comparing the geometrical congruency between the raw polygonal models gained directly from CT scan and reconstructed models

REVIEW OF BONE SCAFFOLD DESIGN CONCEPTS AND DESIGN METHODS

The paper brings out a review of existing, state-of-the-art approaches to designing the geometry of the scaffolds that are used for tissue engineering with a special emphasis on the macro scaffolds aimed for bone tissue recovery. Similar concepts of different authors are organized into groups. The focus of the paper is on determining the existing concepts as well as their advantages and disadvantages. Besides the review of scaffolds' geometry solutions, the analysis of the existing designs points to some serious misconceptions regarding the scaffold role within the (bone) tissue recovery. In the last section of the paper, the main requirements regarding geometry, that is, architecture and corresponding mechanical properties and permeability are reconsidered