A note on continued fractions of quadratic irrationals

Quadratic irrationals √D have a periodic representation in terms of continued fractions. In this paper some relations between n-th approximations of quadratic irrationals are proved. Results are applied to Newton\u27s approximations of quadratic irrationals

Hamiltonian walks on Sierpinski and n-simplex fractals

We study Hamiltonian walks (HWs) on Sierpinski and $n$--simplex fractals. Via numerical analysis of exact recursion relations for the number of HWs we calculate the connectivity constant $\omega$ and find the asymptotic behaviour of the number of HWs. Depending on whether or not the polymer collapse transition is possible on a studied lattice, different scaling relations for the number of HWs are obtained. These relations are in general different from the well-known form characteristic of homogeneous lattices which has thus far been assumed to hold for fractal lattices too.Comment: 22 pages, 6 figures; final versio

Seroepizootiološko-epidemiološka istraživanja i mapiranje infekcije Zapadnog Nila u Republici Srbiji

The disease caused by the West Nile virus (WNV) has been known since 1937 when it was described for the first time in Uganda. After spreading to Europe and the Middle East, the disease has changed its primary location. Today WN infection is a significant health problem in the world. As a result of the current epizootiological and epidemiological situation in Europe studies on the occurrence of WND were introduced in Serbia, also. The investigation on the presence of WNV antibodies was intensified in the period from 2008 to 2012. In this period a total of 3618 serum samples were tested from 18 localities (2736 animal sera from 8 different species and 882 human sera samples). The method applied was gel immunodiffusion and the representative samples were confirmed by the plaque reduction test (PRNT-90). Out of the total number of samples WNV antibodies were present in 3.97% horses, 0.93% dogs, 0.31% poultry and 1.36% man. In one horse serum sample there was a positive reaction with a positive control serum, thus indicating the presence of WNV antigen. The results have confirmed that WNV antibodies are present in 9 out of 18 tested locations in the Republic of Serbia. The percentage of seropositive samples varies from 0.42% in Pozarevac (horses and humans) up to 6.45% in Novi Pazar (dogs). Out of the investigated species the highest seropositivity was recorded in horses (3.97%), and lowest in poultry (0.31%). WNV is present and widespread in the Republic of Serbia, thus enabling distribution mapping.Bolest koju izaziva virus Zapadnog Nila (WNV) je poznata još od 1937. kada je po prvi put opisana u Ugandi. Posle širenja virusa u Evropu i na Bliski istok, bolest je promenila prvobitnu lokaciju. Danas je WN infekcija značajan zdravstveni problem u svetu. Kao rezultat trenutne epizootiološko-epidemiološke situacije u Evropi, uvedena su istraživanja prisustva WNV i u Srbiji. Istraživanja prisustva antitela za WNV intenzivirana su u periodu od 2008. do 2012. godine. U ovom periodu ukupno je ispitano 3618 seruma sa 18 lokaliteta (2736 seruma životinja, od 8 različitih vrsta i 882 seruma ljudi). Korišćen je metod imunodifuzije u gelu a reprezentativni uzorak potvrđen je testom neutralizacije plaka (PRNT- 90). Od ukupnog broja uzoraka na prisustvo antitela za WNV bilo je pozitivno 3,97% konja, 0,93% pasa, 0,31% domaće živine i 1,36% ljudi. U serumu jednog konja pojavila se pozitivna reakcija sa pozitivnim kontrolnim serumom, ukazujući na prisustvo antigena WNV. Dobijeni rezultati su potvrdili da su antitela za WNV prisutna u 9 od 18 ispitivanih lokacija u Republici Srbiji. Procenat seropozitivnih varira od 0.42% u Požarevcu (konji i ljudi) do 6,45% u Novom Pazaru (psi). Od ispitivanih vrsta najveća seropozitivnost je registrovana kod konja (3,97%), a najniža kod živine (0,31%). Raspoloživi podaci ukazuju da je WNV prisutan i značajno raširen u Republici Srbiji, što je omogućilo i mapiranje njegovog širenja

Transition density of diffusion on Sierpinski gasket and extension of Flory's formula

Some problems related to the transition density u(t,x) of the diffusion on the Sierpinski gasket are considerd, based on recent rigorous results and detailed numerical calculations. The main contents are an extension of Flory's formula for the end-to-end distance exponent of self-avoiding walks on the fractal spaces, and an evidence of the oscillatory behavior of u(t,x) on the Sierpinski gasket.Comment: 11 pages, REVTEX, 2 postscript figure

Correlation between the morphology of unheated staircase and energy performance of residential buildings

As a side effect of the need for greater energy efficiency of buildings, there is a problem of decrease of the available interior space affected by the reduction in U-value of parts of thermal building envelope, i.e. an increase in thickness of insulating layer, which is especially present in unheated staircase. Having in mind that present methods of calculation of transmission heat losses through elements of thermal envelope include the adjustment factor which regulates designed temperature conditions if the temperature at the colder side of the element of the thermal envelope differs from that of the external environment, this paper strives to demonstrate that in the case of unheated staircases, this fixed value should be reconsidered and treated as a variable depending on the morphology, i.e. form, size and position of the staircase within the building. This problem has been analyzed on the example of Serbian housing stock and relevant national thermal regulations. Three morphological types of unheated staircases have been distinguished within which three models have been defined and examined with respect to variations in number of floors and percentage of glazing. Average temperatures of staircase volume and temperature correction factors were calculated in following temperature modes: stationary that excluded solar gains and ventilation heat losses and gains, and dynamic with variations in air exchange rates and insolation conditions, expressing in all of the cases variations in calculated values of temperature correction factors in comparison to the prescribed fixed value

Semi-flexible compact polymers in two dimensional nonhomogeneous confinement

© 2019 IOP Publishing Ltd. We have studied the compact phase conformations of semi-flexible polymer chains confined in two dimensional nonhomogeneous media, modelled by fractals that belong to the family of modified rectangular (MR) lattices. Members of the MR family are enumerated by an integer p  and fractal dimension of each member of the family is equal to 2. The polymer flexibility is described by the stiffness parameter s, while the polymer conformations are modelled by weighted Hamiltonian walks (HWs). Applying an exact recurrence equations method, we have found that partition function Z N for closed HWs consisting of N steps scales as , where constants and depend on both p  and s. We have calculated numerically the stiffness dependence of the polymer persistence length, as well as various thermodynamic quantities (such as free and internal energy, specific heat and entropy) for a large set of members of the MR family. Analysis of these quantities has shown that semi-flexible compact polymers on MR lattices can exist only in the liquid-like (disordered) phase, whereas the crystal (ordered) phase has not appeared. Finally, behavior of the examined system at zero temperature has been discussed