Virial expansions and augmented van der Waals approach: Application to Lennard-Jones-like Yukawa fluid

We argue that recently proposed [Melnyk et al., Fluid Phase Equilibr., 2009, Vol. 279, 1] a criterion to split the pair interaction energy into two parts, one of which is forced to be responsible the most accurate as possible for excluded volume energy in the system, results in expressions for the virial coefficients that improve the performance of the virial equation of state in general, and at subcritical temperatures, in particular. As an example, application to the Lennard-Jones-like hard-core attractive Yukawa fluid is discussed.Comment: 12 pages, 6 figure

Mean spherical approximation for the Lennard-Jones-like two Yukawa model: Comparison against Monte Carlo data

Monte Carlo simulation studies are performed for the Lennard-Jones like two Yukawa (LJ2Y) potential to show how properties of this model fluid depend on the replacement of the soft repulsion by the hard-core repulsion. Different distances for the positioning of hard core have been explored. We have found, that for temperatures that are slightly lower and slightly higher of the critical point temperature for the Lennard-Jones fluid, placing the hard core at distances that are shorter than zero-potential energy is well justified by thermodynamic properties that are practically the same as in original LJ2Y model without hard core. However, going to extreme conditions with the high temperature one should be careful since presence of the hard core provokes changes in the properties of the system. The later is extremely important when the mean spherical approximation (MSA) theory is applied to treat the Lennard-Jones-like fluid.Comment: 11 pages, 13 figure

Automatic generation of tasks and their automatic solutions in application software

Досліджено проблему формалізації процесу побудови та розв’язання задач з метою підвищення якості передавань знань та практичних навиків. Проаналізовано відомі підходи до вирішення проблеми автоматичної генерації практичних задач та їх розв’язання. Запропоновано метод генерації множини задач та їх автоматичного розв’язання в прикладному програмному середовищі. Показано, що даний метод володіє низкою переваг перед існуючими, що підтверджується експериментальними дослідженнями.In this paper the problem of formalizing the process of building and solving tasks is analized, existing approaches to solve this problem is analized, described their main advantages and disadvantages. The method of automatic generation of tasks and their solutions in application software are proposed. This method has several advantages over existing, as evidenced by experiments

Competition between Two Kinds of Correlations in Literary Texts

A theory of additive Markov chains with long-range memory is used for description of correlation properties of coarse-grained literary texts. The complex structure of the correlations in texts is revealed. Antipersistent correlations at small distances, L 300 define this nontrivial structure. For some concrete examples of literary texts, the memory functions are obtained and their power-law behavior at long distances is disclosed. This property is shown to be a cause of self-similarity of texts with respect to the decimation procedure.Comment: 7 pages, 7 figures, Submitted to Physica

Non-additive properties of finite 1D Ising chains with long-range interactions

We study the statistical properties of Ising spin chains with finite (although arbitrary large) range of interaction between the elements. We examine mesoscopic subsystems (fragments of an Ising chain) with the lengths comparable with the interaction range. The equivalence of the Ising chains and the multi-step Markov sequences is used for calculating different non-additive statistical quantities of a chain and its fragments. In particular, we study the variance of fluctuating magnetization of fragments, magnetization of the chain in the external magnetic field, etc. Asymptotical expressions for the non-additive energy and entropy of the mesoscopic fragments are derived in the limiting cases of weak and strong interactions.Comment: 20 pages, 4 figure

Memory functions and Correlations in Additive Binary Markov Chains

A theory of additive Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to describe statistical properties of long-range correlated systems. The convenient characteristics of such systems, a memory function, and its relation to the correlation properties of the systems are examined. Various methods for finding the memory function via the correlation function are proposed. The inverse problem (calculation of the correlation function by means of the prescribed memory function) is also solved. This is demonstrated for the analytically solvable model of the system with a step-wise memory function.Comment: 11 pages, 5 figure

AWARENESS OF LYME BORRELIOSIS OF THE PATIENTS OF TERNOPIL REGIONAL TB DISPENSARY

Background. Lyme disease has many clinical features similar tothose in sarcoidosis and tuberculosis. Epidemiological data in the world, in particular in Ukraine, proves the increase in Lyme borreliosis incidence. Ternopil region is endemic with Lyme borreliosis. Objective. The research was aimed to investigate the prevalence of infection with Borrelia burgdorferi and epidemiology features of borreliosis among the patients of Ternopil Regional TB Dispensary. Methods. In total, 29 patients were admitted to Departments of Differential Diagnostic, TB Therapy and TB Surgery of Ternopil Regional TB Dispensary in October 2016-January 2017. All the surveyed answered the questions of an integrated international questionnaire, where they noted the area and a number of tick bites, described the removal method, noted the survey for borreliosis pathogen and complaints after tick bites. Results. It was established that 5 respondents had a history of tick bites episodes, but only in one case the patient was examined of borreliosis. Tick bites were noticed in 3 patients with sarcoidosis and 1 with tuberculosis (TB) and exudative pleurisy, respectively. Conclusions. The absence of appeals for medical care, lack of sufficient information on Lyme borreliosis and disuse of preventive measures for tick bites by the interviewed patients of Ternopil regional TB dispensary departments proves the need of improvement of health education on Lyme borreliosis (LB) among this category of population. 24 (82.7%) of 29 respondents did not remember the tick bite. The symptoms of (LB) are similar to those in sarcoidosis and tuberculosis (pleural lesions, heart, joints, nervous system, skin), and the presence of tick bites gives the reasons to examine these patients of Borrelia burgdorferi senso lato

Charge distribution in two-dimensional electrostatics

We examine the stability of ringlike configurations of N charges on a plane interacting through the potential $V(z_1,...,z_N)=\sum_i |z_i|^2-\sum_{i<j} ln|z_i-z_j|^2$. We interpret the equilibrium distributions in terms of a shell model and compare predictions of the model with the results of numerical simulations for systems with up to 100 particles.Comment: LaTe