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It is our real pain to write this article, remembering years of friendship and scientific collaboration with Stefan Sokołowski, who passed away on the 24th of June 2024. He was a strong man in his faith and convictions, a kind and helpful friend, attentive and open-minded in discussions, creative, profound and sophisticated in understanding the flow of life and science. He left an unforgettable mark on our hearts and personal memories. His way of thinking left an imprint on students, young scientists and co-workers. We accompany all that with warm farewell applause as an appreciation of Stefan’s way and effects throughout his life.

This brief essay commemorates Karl Heinzinger, one of the pioneers in the field of computer modelling of fluid systems, particularly of water and aqueous electrolyte solutions in the bulk phase and near interfaces. Karl Heinzinger died peacefully on January 14, 2023, after a short illness. We express our deepest condolences to his family, colleagues, and friends.

The analysis of scientific researches concerning professional training and qualification certification of engineers-land surveyors in Ukraine and abroad is carried out. The need to study, borrow the experience of one of the countries of the European Union and further adapt this certification in Ukraine is substantiated. Qualification requirements for certification of land surveying engineers in Ukraine and Poland are considered. A comparison of the qualification exam for a certified land surveyor is given. An analysis of the comparison of similar and different indicators for obtaining a certificate of land surveying engineer in Ukraine and Poland. Emphasis is placed on the quality of qualification selection of certified land surveyors. The proposals in the revision of the requirements for obtaining a qualification certificate of a land surveyor in Ukraine are given. In the future, the revision of the qualification certification requirements will help create objective equal opportunities for land relations specialists, improve the quality of land management documentation, as well as facilitate the adaptation of certification with our western neighbors - the European Union. Key words: certificate of land surveyor, certification, land management, surveying engineers, foreign experience, professional practice.

The papers in this special issue of ``Condensed Matter Physics'' have been submitted with the dedication to Professor Dr. Yuriy Kalyuzhnyi on the occasion of his 70th birthday.

There is indeed a finite-size issue in computer simulations of the correlation decay in a quasi-one-dimensional system of hard disks. The correlation function obtained from the exact canonical NVT partition function shows a decay which is much slower and more complex than the exponential one, presented in the Comment.

The simplicity of a quasi-one-dimensional system of hard disks enables us to get a much deeper and more quantitative insight into the solid-to-fluid transformation and identify it as caging-uncaging transition. Both computer simulation data and theoretical results show that density decrease induces progressively larger number of uncaged disk pairs which exchange their transverse positions through windows in the initial crystalline zigzag array. At low densities windows dominate and disks are moving independently (pairs “dissociate”). Along with the simulation data on the transversal excitation modes and pair correlation function this shows that the solid-to-liquid transformation is a continuous Kosterlitz-Thouless-type transition.

It is a pleasure to be involved in the preparation of the festschrifts honoring the 60th birthday of our good friend and colleague Professor Myroslav Holovko. Myroslav Holovko was born in 1943 in a small village of Chernijiv located in a beautiful area close to the Ukrainian Carpathians. After graduating in 1965 from the Ivano-Frankivsk Institute of Pedagogy he became a Ph.D. student at the Physics Department of the Lviv State University under the supervision of Professor Ihor Yukhnovskii. In 1969 Yukhnovskii became the head of Lviv Department of statistical theory of condensed states at the Institute for Theoretical Physics of the Ukrainian Academy of Sciences. From its early beginning the Lviv group experienced support and strong interest from another great Ukrainian - N.N.Bogolyubov, who was at that time Director of the Institute for Theoretical Physics. Yukhnovskii's group was a fantastic place for young people to grow up as scientists. At that time the group consisted of talented, ambitious and very enthusiastic young scientists selected among the best students who graduated mainly, but not exclusively, from Lviv University. It is interesting to note that Hartmut Krienke, who celebrated his 60th birthday last July was also a member of the Yukhnovskii's group, although Krienke came to Lviv from Rostock (Eastern Germany). Thanks to the outstanding personality of Prof. Yukhnovskii, a warm and friendly atmosphere in the group was combined with exceptionally high research standards.

The freezing mechanism suggested for a fluid composed of hard disks [Huerta et al., Phys. Rev. E, 2006, 74, 061106] is used here to probe the fluid-to-solid transition in a hard-dumbbell fluid composed of overlapping hard disks with a variable length between disk centers. Analyzing the trends in the shape of second maximum of the radial distribution function of the planar hard-dumbbell fluid it has been found that the type of transition could be sensitive to the length of hard-dumbbell molecules. From the NpT Monte Carlo simulations data we show that if a hard-dumbbell length does not exceed 15% the fluid-to-solid transition scenario follows the case of a hard-disk fluid, i.e., the isotropic hard-dumbbell fluid experiences freezing. However, for a hard-dumbbell length larger than 15% fluid-to-solid transition may change to continuous transition, i.e., such an isotropic hard-dumbbell fluid will avoid freezing.

We argue that recently proposed [Melnyk et al., Fluid Phase Equilibr., 2009, 279, 1] a criterion to split the pair interaction potential into two parts, one of which is forced to be responsible for excluded volume in the system, results in the expressions for 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.

The idea of this special issue was derived a year ago. The year 2014 was a significant anniversary both generally and personally. Personally, it was 80 years since the oldest of us, Douglas Henderson, was born. More generally, it was a hundred years since another important paper in the theory of liquids by Ornstein and Zernike appeared. With this in mind, we felt it is timely for a collection of expert contributions to fill at least some of the gaps on the way to answer that magic question What is "liquid"? We are thankful for all colleagues who joined us in this project.

We discuss the photograph procured from the archives of the V.Stefanyk Lviv National Scientific Library of Ukraine dated by 1904 which shows Marian Smoluchowski together with professors and graduate students of the Philosophy department of the Lviv University. The personalia includes both the professors and the graduates depicted on the photograph with the emphasis on the graduates as being much less known and studied. The photograph originates from the collection of the Shevchenko Scientific Society, therefore a brief historical background on the activities of physicists in this society around that period of time is provided as well.

The freezing mechanism, recently suggested for a monodisperse hard-disk fluid [Huerta et al, Phys. Rev. E, 2006, Vol. 74, 061106] is extended here to an equimolar binary hard-disk mixtures. We are showing that for diameter ratios, smaller than 1.15 the global orientational order parameter of the binary mixture behaves like in the case of a monodisperse fluid. Namely, by increasing the disk number density there is a tendency to form a crystalline-like phase. However, for diameter ratios larger than 1.15 the binary mixtures behave like a disordered fluid. We use some of the structural and thermodynamic properties to compare and discuss the behavior as a function of diameter ratio and packing fraction.

The year 2012 marks the 140th birth anniversary of Marian Smoluchowski (28.05.1872-5.09.1917), a man who "made ground-breaking contribution to the theory of Brownian motion, the theory of sedimentation, the statistical nature of the Second Law, the theory and practice of density fluctuations (critical opalescence). During his final years of scientific creativity his pioneering theory of coagulation and diffusion-limited reaction rate appeared. These outstanding achievements present true gems which dominate the description of soft matter physics and chemical physics as well as the related areas up till now!" This quotation was taken from the lecture by Peter Hanggi given at international conference Statistical Physics: Modern Trends and Applications that took place in Lviv, Ukraine on July 3-6, 2012 (see conference web-page for more details) and was dedicated to the commemoration of Smoluchowski's work. This and forthcoming issues of the Condensed Matter Physics contain papers presented at this conference.

Exponential approximation based on the first order mean spherical approximation (FMSA) is applied to the study of the structure and thermodynamics of hard-core repulsive Yukawa fluids. The proposed theory utilizes an exponential enhancement of the analytical solution of the FMSA due to Tang and Lu [J. Chem. Phys., 1993, Vol. 99, 9828] for the radial distribution function. From comparison with computer simulation data we have shown that at low density and low temperature conditions, where original FMSA theory fails, the FMSA-based exponential theory predicts a significant improvement.

A perturbation approach based on the first-order mean spherical approximation (FMSA) is proposed. It consists in adopting a hard-sphere plus short-range attractive Yukawa fluid as the novel reference system, over which the perturbative solution of the Ornstein-Zernike equation is performed. A choice of the optimal range of the reference attraction is discussed. The results are compared against conventional FMSA/HS theory and Monte-Carlo simulation data for compressibility factor and vapor-liquid phase diagrams of the medium-ranged Yukawa fluid. Proposed theory keeps the same level of simplicity and transparency, as the conventional FMSA/HS approach does, but shows to be more accurate.

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.

Virial coefficients B2 through B4 and the vapor-liquid equilibria for the EXP6 and 2-Yukawa (2Y) fluids have been determined using numerical integrations and Gibbs ensemble simulations, respectively. The chosen 2Y models have been recently determined as an appropriate reference fluid for the considered EXP6 models.

The Planer-Smoluchowski Soft Matter (PSSM) Workshop on Liquid Crystals and Colloidal Dispersions was held on June 22, 2009 in historic city of Lviv in Ukraine.

Brief review of the literature on the history of thermotropic liquid crystal discovery and the role of the observations reported by Julius Planer in his note published almost 150 years ago.

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The research reveals the main reasons that prevent the extension of commercial apricot plantations in Ukraine and worldwide. This brief description includes eight cultivars from Ukrainian and foreign breeding programmes. The trials conducted in the Right-Bank subzone of the Western Forest Steppe of Ukraine. The plants from Ukrainian breeding programme 'Melitopolskyi Ranni?', 'Botsadivskyi', 'Siaivo', 'Kumir', 'Osoblyvyi Denysiuka', as well as the foreign one - 'Robada', 'Harogem', 'HJA-19', were distinguished by high adaptability to the complex of adverse overwintering factors in the above-mentioned region. These samples did not lose the acquired level of frost resistance under the influence of provoking thaws. A comprehensive assessment of drought resistance, based on water-holding capacity, turgor recovery degree, water deficiency, and leaves' hydration of the presented varieties, established that all variants of the experiment were not inferior to the best popular cultivars. According to the the biological feature of buds' formation at an early age, the cultivars 'Robada' and 'HJA-19' were characterized as early-fruiting. The yield and quality indicators for the 2021-2022 years of research were evaluated. Average fruit weight was noted in all samples, with the cultivar 'Siaivo' exceeding the average. To improve the assortment and enrich the apricot gene pool collections with the best samples suitable for cultivation in the Forest-Steppe Zone of Ukraine, according to the results of the study, the following researched cultivars were included in the collection of valuable samples of the common apricot gene pool of the Institute of Horticulture of the National Academy of Sciences of Ukraine: 'Melitopolskyi Ranni?,' 'Botsadivskyi,' 'Siaivo,' and 'Osoblyvyi Denysiuka'. These cultivars are sources of productivity and adaptability to abiotic factors of cultivation (winter and frost resistance, drought resistance). They are certified by the National Center of Plant Genetic Resources of Ukraine. [ABSTRACT FROM AUTHOR]

The main purpose of the article is to develop a multifactorial model for rapid assessment of the efficiency of biological wastewater treatment reactors. A mathematical model of the process of biological wastewater treatment has been developed based on: changes in the concentration of organic contaminants in the bioreactor over time, taking into account the uneven flow of wastewater to the treatment plant, the process of substrate entering the bioreactor (different amounts may enter at different times). The software implementation of the proposed algorithm for solving the corresponding model problem in Python is carried out. The results of computer experiments on the study of the efficiency of wastewater treatment in biological treatment reactors for different operating conditions of facilities are presented. In particular, such processes were considered with taking into account the unevenness of the load, because the maximum cleaning loads are in the morning and in the evening. The task was solved to simulate a real situation and show how cleaning takes place at the maximum load at a certain time of the day. The results obtained will be useful for calculations in the design of biological treatment facilities or in the reconstruction of existing bioreactors for their prospective operation under new operating conditions. [ABSTRACT FROM AUTHOR]