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Although parabolic approximations of sawlogs have become widespread, in current specialized literature, there are no parameter values of such approximations or dependencies for their calculation that could be used to analyze the influence of log dimensions on the volume yield of edged boards. The developed technique for determining the parameters of a truncated paraboloid, which approximates a sawlog, is based on Nilson’s formula for estimating its volume. Based on this, the equation of the generatrix of the truncated paraboloid as a function of the top diameter and the length of the sawlog (considering the species) and the formula for calculating its taper (in particular, total and main) are derived. The error of approximating sawlogs with a paraboloid was determined by comparing the taper estimate with literature data on the taper of Scots pine ( L.), Norway spruce ( (L.) H. Karst.), and common oak ( L.) sawlogs in Ukraine, Sweden, and Finland. This error ranges from -36% to -9%. Using the method of parametric identification of taper distributions based on literature data on their statistical characteristics (unbounded metalog distribution with four parameters and normal distribution were used), the probability that a sawlog has a taper smaller than its estimate was calculated. These probabilities range from 20% to 36%. The third quartiles of the sawlogs’ taper distributions are, respectively, between 200% and 150% of the taper estimate. Therefore, the obtained formulas for determining the parameters of the approximating paraboloid led to a rather conservative estimate of the taper (however, acceptable for use in log sawing planning), which confirms their suitability for analyzing the influence of log dimensions on the yield of edged boards.

There is a constant demand for higher equipment parameters, such as the pressure of a sealing medium and shaft rotation speed. However, as the parameters increase, it becomes more difficult to ensure hermetization efficiency. The rotor of a multi-stage machine rotates in non-contact seals. Seals’ parameters have a great influence on vibration characteristics. Non-contact seals are considered to be hydrostatodynamic supports that can effectively dampen rotor oscillations. The force coefficients of gap seals are determined by geometric and operational parameters. A purposeful choice of these parameters can influence the vibration state of the rotor. It is shown for the first time that the initially dynamically flexible rotor, in combination with properly designed seals, can become dynamically rigid. Analytical dependencies for the computation of the dynamic characteristics are obtained. The resulting equations make it possible to calculate the radial-angular vibrations of the rotor of a centrifugal machine in the seals and construct the amplitude–frequency characteristics. By purposefully changing the parameters of non-contact seals, an initially flexible rotor can be made rigid, and its vibration resistance increases. Due to this, the environmental safety of critical pumping equipment increases.

Problems of power quality and electric energy accounting often occur in networks with large pervasion of photovoltaic (PV) elements on rooftops of household and office buildings. In smart grids, including PV arrays electricity, which is sold back to the distribution network, requires approval of its parameters and quality control. Distributed power inverters generate higher harmonics which affect relay protection, automation systems, smart meters and power system’s reliability. In this article the influence of photovoltaic elements on the accuracy of electric energy metering and power quality questions are analysed.

This article deals with main characteristics of the oscillating system “central body – liquid” by means of its well-known representation in the form of a pendulum mathematical model. It makes possible to evaluate spread of specified disturbances at the general physical level and to determine the most dangerous frequencies that lead to increased amplitudes of fluid oscillations. We propose equations for single-frequency pendulums, which influence each other by means of resistance forces and added mass. Several examples with different natural frequencies of the body are considered. The calculation results showed that besides natural frequencies of the components, system has two more natural frequencies. So, system actually responds only to disturbances which frequencies are close to the natural frequency of the liquid layer. In this case, amplitudes of liquid and the body sharply increase. This fact indicates that in real technological processes frequency of dominant disturbance should be as far from the first resonant frequency of the liquid as possible. The further experimental and theoretical studies that take into account the influence of the following modes on the dynamic picture of the process are also of interest.

For the first time in the Ukrainian religious studies the article overviews the interrelation of the works of Merold Westphal, which reveal the specificity of the correlation of the ideas of S. Kierkegaard and E. Levinas. The peculiarities of S. Kierkegaard's and E. Levinas' interpretation of the biblical teaching Thou shalt love thy neighbour as thyself and its rethinking in the existential theology of M. Westphal are analyzed. The dichotomy I--Other is investigated in the context of realization of true Self and the search for the answer to the question that M. Westphal asks himself, which of the ideas will further unite people. It is shown that for E. Levinas it is infinity and ineffability that constitute the radical individual responsibility of each of us for our neighbour. S. Kierkegaard and his pseudonyms, according to M. Westphal, tell about the idea of Eternal, and mainly based on the more expressive Christian idea of true God. It is proven that M. Westphal justified the inadmissibility of the Levinas post-biblical incorporation of religion into ethics, when it is the truth that becomes the criterion of a subject, but not kindness, freedom, sincerity; it is objectivity, not subjectivity. He opposed him the categoricalness of the Kierkegaard's principle, according to which religion is unconditional prerequisite of ethics. Key words: Self, Other, faith, love, indirect communication, Religiousness C, revelation as immediacy, logic of solidarity, identity.

Higher parameters of centrifugal machines are constantly required, such as the pressure of the medium to be sealed and the speed of rotation of the shaft. However, as the parameters increase, it becomes more and more difficult to ensure the effectiveness of sealing. In addition, sealing systems affect the overall safety of equipment operation, especially vibration. In order to harmonize the sealing functions and increase the dynamic rigidity of the rotors of centrifugal machines, a method for modeling complex sealing systems has been developed. Non-contact seals are considered as hydrostatic–dynamic bearings that can effectively dampen rotor oscillations. A general approach to the analysis of non-contact seals as automatic control systems and an algorithm for constructing their dynamic characteristics at the design stage were proposed for the first time. Models of “rotor-gap seal”, impulse seal and “rotor–hydraulic face” systems, and seal-supports of a shaftless pump have been studied to assess the effect of these seal systems on the oscillatory characteristics of the rotor. Analytical dependencies are obtained for calculating the dynamic characteristics and stability limits of seals as hydromechanical systems. The directions for improving the safety of operation of critical pumping equipment due to a targeted increase in the rigidity of non-contact seals are determined, which leads to an increase in the vibration resistance of the rotor and the environ-mental safety of centrifugal machines. The paper proposes a method for designing sealing systems based on the configuration of sealing components in order to achieve harmonization between sealing and vibration reliability, taking into account oscillatory processes due to hydrodynamic sealing characteristics.

This paper reports the peculiarities of the Dnipropetrovsk region’s geological structure and related mineral resources used as building materials. The basis of the region’s resource potential is explored and active deposits of building stone, decorative stone (granite), molding sand, building sand, carbonate rocks (mainly limestone), brick and tile raw materials, gypsum, mineral paints, etc. The resources of building and decorative stones are confined to the formations of the Precambrian age, while the formation of clay and sand deposits is mainly dated to the Paleogene, Neogene and Quaternary age and is associated with the processes of chemical and mechanical weathering of granites, granodiorites, gneisses and other crystalline rocks. Carbonate rocks, which are important for metallurgy and other industries, are found in the territory of the region among Palaeozoic (Carboniferous) and Neogene depositios. The industrial reserves of construction minerals, the main enterprises developing deposits of the Dnipropetrovsk region are given. Based on the results of the research, a conclusion was made regarding the potential readiness of the mineral and raw material base of building materials and the main market players to participate in the post-war reconstruction of the regions of Ukraine logistically close to Dnipropetrovsk region.

The purpose of the study is to review the philosophical foundations of the religious doctrine by Berdyaev based on a comparative analysis of the epistemological, anthropological, and ontological backgrounds for his thinking. The study combines methods and theories from various cultural, religious, and historical-philosophical approaches, which made it possible to reveal the peculiarities of Berdyaev's rethinking of traditional Christianity in the context of the crisis of Western culture. The scientific novelty proves a fundamental break in his conception with classical metaphysics as the basis of Christian orthodoxy. Human freedom, spirituality as a system-forming principle of human existence, which humanize anthropologism and de-objectification as a priori of the general system of the world-understanding, form that new type of the religious-metaphysical basis of \"modern Orthodoxy\" that Berdyaev sought to establish as a new model of Christianity in the world. The conclusions emphasize that the specifics of \"existential Christianity\" by Berdyaev consisted in establishing a special commensurability between man and God, and in the thesis about the \"eternal humanity\" of God, beyond which, in his deep conviction, one can hardly understand and interpret the very possibility of Revelation.

Merold Westphal is a living legend for contemporary foreign researchers and compatriots, and his views are called \"prophetic\". [...]the collection \"Gazing Through a Prism Darkly: Reflections on Merold Westphal's Hermeneutical Epistemology\" (2009) starts with an article of the editor of this edition - Keith Putt \"The Benefit of the Doubt: Merold Westphal's Prophetic Philosophy of Religion\", in which Westphal is recognized as \"one of the most creative and influential phenomenologies of religion of the past two decades\" (Putt 2009, 3). The humanist tradition looked for the truth beyond the philosophical and theological methodology in the tragedies of Aeschylus and Sophocles; the epics of Homer and Virgil; the histories of Herodotus, Thucydides, Tacitus and Julius Caesar, the philosophical treaties of Plato, Aristotle and the Stoics. Since Gadamer, as Westphal emphasizes, does not specify where exactly to look for the truth beyond scientific method, this proves that he does not exclude from the list above even scriptural texts such as the Bible, especially in such important interpretations as the Septuagint, the Vulgate, the Luther Bible and so on. In Gadamer's opinion, they provide us with a certain kind of pleasure, unselfish pleasure that that does not seek to own or rule over that which pleases. [...]the pleasure of reading is different from kinds of pleasure that we get from eating, drinking, having sex, having high social status or owning property. According to Westphal's interpretation, the Bible appears as a work of art that embodies the truth beyond any research method and correlates with the constant formation and dynamics of human existence and the existence of the Christian community in the historical and cultural process.

The structure of weed phytocenoses in maize crops is determined by the adaptive capacity of weeds and the specific characteristics of crop area distribution in rotation systems. The main factors driving weed dominance include herbicide resistance, a broad germination range, morphological plasticity, and the presence of neotenic traits. The use of shallow non-inversion mulching tillage methods (such as chisel plowing and flat-cut loosening) in maize cultivation increases weed infestation levels by 1.4–1.8 times, necessitating additional applications of pre-emergence and post-emergence herbicides to control weeds and prevent yield reduction. Research indicates that plow tillage and chisel plowing provide a slight advantage in maize grain productivity on unfertilized soils and under fertilization with N30P30K30. This advantage arises from improved nutrient availability and reduced weed infestation levels. However, with increased nitrogen application (N60P30K30), shallow flat-cut loosening becomes more effective, yielding similar results to plow tillage and chisel plowing, thus mitigating earlier disadvantages. At low overall weed infestation levels (9.0–12.6 plants/m²), primary soil tillage methods have no significant impact on maize grain quality. The application of mineral fertilizers, particularly nitrogen, increases protein content in maize grain while reducing carbohydrate levels, particularly starch.