Simple necessary and sufficient conditions for robust stability of the positive linear discrete-time systems with delays with linear uncertainty structure in two cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices, are established. The proposed conditions are compared with the suitable conditions for the standard systems. The considerations are illustrated by numerical examples.

The influence of bandwidth of OPA on frequency characteristics was investigated in this paper. The analysis of frequency properties was carried out for two exemplary structures. For operational amplifier it was assumed a typical frequency macromodel with 1-pole characteristic. Deformation of the frequency characteristic and the structure bandwidth in dependence on amplifiers bandwidth were analyzed. It was proved that shape of the characteristic to some degree depends on some elements values. The procedure was proposed for optimal choice of the values of (RC) elements, that ensures the characteristic is most approached to ideal one. Optimal values of these (RC) elements ensure that the characteristic of structures do not have any distortion in all frequencies, and these structures can be used in high frequency applications.

The paper outlines the Catholic and the Evangelical standpoint on the primate’s function served by the Bishop of Rome and its origin. The controversy revolves around the key phrase, iure divino and iure humano, which points to the divine or human origin of the primacy. In the Catholic perspective, Jesus Christ brought the Church into existence and provided this institution with permanent structural elements: primacy and apostolate. This thesis, considered an imperative of faith, is based on the texts of the Gospel which underscore the primacy of Saint Peter the Apostle among the Twelve and in the early Church. According to the Catholic ecclesiology, it was not only a private privilege enjoyed by Peter but a permanent element of the structure of the Church, which received the formal status of a dogma at the First Vatican Council. From the outset, the Reformation has assumed that primacy is an element shaped in the course of the historical development of the Church. The ecumenical dialogue between Catholicism and Lutheranism led to the establishment of a standpoint veering towards the consideration of the origin of primacy as a matter of lesser consequence. This step was taken in order to underscore the communal dimension of the Church, with its important function in unifying Christianity and presenting it to the world. The basic premise giving credence to this function is its foundation in the Gospel.

The article is a topic outline of the theology of the Church’s unity. It shows the spectrum of contemporary reflection on this attribute of the Church mentioned in the Nicene-Con-stantinople Symbol (credo in unam Ecclesiam). The reflection includes biblical categories, especially the idea of koinōnia/communio, emphasizing the Trinitarian basis for unity of the Church, and its concrete means – bonds of unity. Among these means of unity, particular attention is paid to the bond of faith, the sacraments and ecclesiastical governance, nota-bly the universal ministry of Christian unity. Individual Churches (denominations) have different visions of unity, but also these concepts are the subject of ecumenical dialogue. The most recent ecumenical vision on the Church, including its unity, is the document of the World Council of Churches Commission on Faith and Order, Towards a Common Vision of the Church (published in 2013). Christian Churches involved in the contemporary ecumenical dialogue are aware that the unity of the Church is a reality given and set, yet incomplete and imperfect, so to speak “on the way”. In this sense they can express their spero in unam Ecclesiam.

The article describes the Roman Catholic understanding of the ecumenical dialogue as stated in the Decree on ecumenism of the Second Vatican Council and in further documents of the RC Church. This ecumenical dialogue may be conducted only among Christian Churches and Church Communities as it aims the restoration of full visible unity of Christians.

The dialogue should primarily lead to the common rediscovery of the truth, and never to any kind of establishing the truth, of elaborating it or reaching the compromise. The true dialogue has nothing to do with negotiating the common position, where each party wants to force oneself upon another and to make the less concessions possible. This is because we cannot reduce the requirements of the Gospel to any kind of necessary minimum, a common basis recognized by all the churches and ecclesial communities.

Such a dialogue contains its inner dynamics, its existential dimension. The truth is personal, as Christ himself is the Truth, so the search for unity belongs to the proper essence of being a Christian. So the ecumenical dialogue is “an imperative of Christian conscience” (John Paul II), so it is something that inevitably ought to be taken and accomplished by Christians.

The ecumenical dialogue however is not the goal for itself. Neither it is only mutual recognition of Christian Communities or even common prayer. The common aimis the restoration of full visible unity of divided Churches. On the way of ecumenism we cannot limit to the prayer or the ecumenical dialogue. On the contrary – we should develop all the possible ways of collaboration, because unity of action leads to the full unity of faith. Neither the unity nor uniformity of doctrine or churchly traditions, but only the unity in one faith is the far-reaching goal of the ecumenical dialogue.

The documents of the RC Church give also clear hints how to lead the ecumenical dialogues: the dialoguing parties must be expert in theology, seeking the truth, not a victory, moving from easier topics to the more diffcult ones, trying to use the language free of polemical connotations.

Before the Second Vatican Council the Catholic Church didn’t lead any offcial ecumenical dialogue, what didn’t mean the lack of any ecumenical encounters. The first ones, however, were unoffcial and did not engage the offcial Church authority. Widespread engagement in the ecumenical dialogues in the time of popes Paul VI and John Paul II can be justly perceived as a direct fruit of the Second Vatican council and its Decree on ecumenism.

During the decades the commissions of dialogue have already elaborated thousands of pages of common statements and agreed declarations. The Churches must be however aware, that without strong effort of reception of these documents in their midst, the fruits of the dialogues will have no infuence on the reconciliation of Christians in one faith.

Even if there may be some kind of deception because of slowness of ecumenical process, we can be certain that meetings in the dialogue enabled Christians of various Churches an Church Communities to grow towards full, visible unity wanted by our Lord for His disciples.

Sobór Watykański II, który był największym wydarzeniem we współczesnej historii chrześcijaństwa, zainicjował proces otwarcia i reformy Kościoła katolickiego na niespotykaną dotąd skalę. Przez trzy lata dyskutowano na temat najważniejszych tematów, zarówno natury czysto teologicznej i eklezjalnej, jak i pastoralnej i misyjnej. Jednym z tych soborowych tematów było także ożywienie braterskich relacji między katolikami i nie-katolikami. W artykułe dokonano analizy jednego z najważniejszych teologicznych tematów, który niestety pozostał w wyniku soborowej i postsoborowej dyskusji przeszkodą w rzeczywistym dialogu o przywróceniu jedności między katolikami a prawosławnymi. Jest nim prymat papieski, który prawosławni postrzegają jako wynik ludzkiej inwencji, pozbawionej solidnych biblijnych i patrystycznych podstaw. Ternin ten pojawił się po 1054 roku jako podstawowa cecha polityki religijnej związanej z prymatem Rzymu. Kościół prawosławny wierzy w możliwość przywrócenia jedności chrześcijan, jednak nie zgadza się na interkomunię bez uprzedniego osiągnięcia jedności w wierze. Stąd też oczekuje się od Kościoła katolickiego decyzji porzucenia roszczenia prymatu i papieskiej nieomylności bądź też ich przekształcenia zgodnie tradycją pierwszych wieków. Również oczekuje się redefinicji relacji między biskupem Rzymu a kolegium katolickich biskupów w sensie rzeczywistej i efektywnej synodlaności.

The paper examines from the thermodynamic point of view operation of coal fired power unit cooperating with the cryogenic oxygen unit, with a particular emphasis on the characteristic performance parameters of the oxygen unit. The relatively high purity technical oxygen produced in the oxygen unit is then used as the oxidant in the fluidized bed boiler of the modern coal fired power unit with electric power output of approximately 460 MW. The analyzed oxygen unit has a classical two-column structure with an expansion turbine (turboexpander), which allows the use of relatively low pressure initially compressed air. Multivariant calculations were performed, the main result being the loss of power and efficiency of the unit due to the need to ensure adequate driving power to the compressor system of the oxygen generating plant.

As we know the idea of papacy defined during the First Vatican Council is one of the biggest problems for the unity of Christian Churches. The author of this article attempts to re-interpret the statements of the Council relating to this matter. It will be done against the background of the theology of faith that definitely relates the content of faith (fides quae) to the fides qua. In this way, certain statements regarding faith, also referring to the pope, are relativized, but not in the sense of elimination, but in the sense of their intense reference to the center of biblical faith. We have also the possibility to give every time a new shape of papacy, understood as a “ministry of unity”.

Virtual digital representation of a physical object or system, created with precision through computer simulations, data analysis, and various digital technologies can be used as training set for real life situations. The principal aim behind creating a virtual representation is to furnish a dynamic, data-fueled, and digital doppelgänger of the physical asset. This digital counterpart serves multifaceted purposes, including the optimization of performance, the continuous monitoring of its well-being, and the augmentation of informed decision-making processes. Main advantage of employing a digital twin is its capacity to facilitate experimentation and assessment of diverse scenarios and conditions, all without impinging upon the actual physical entity. This capability translates into substantial cost savings and superior outcomes, as it allows for the early identification and mitigation of issues before they escalate into significant problems in the tangible world. Within our research endeavors, we've meticulously constructed a digital twin utilizing the Unity3D software. This digital replica faithfully mimics vehicles, complete with functioning headlamp toggles. Our lighting system employs polygons and normal vectors, strategically harnessed to generate an array of dispersed and reflected light effects. To ensure realism, we've meticulously prepared the scene to emulate authentic road conditions. For validation and testing, we integrated our model with the YOLO (You Only Look Once) neural network. A specifically trained compact YOLO model demonstrated impressive capabilities by accurately discerning the status of real vehicle headlamps. On average, it achieved an impressive recognition probability of 80%, affirming the robustness of our digital twin.

The aim of the article is to present the selected results of analytical investigations concerning

possible directions of reducing the unit production costs in the mining company together with some

results of practical calculations. The investigations emphasize the role of the rate of utilising the

production capacity leading to reducing the unit production costs. The main component having an

essential influence on the unit production costs are the fixed unit costs. Two basic indices of a crucial

meaning for searching for possibilities leading to decreasing the unit production costs are assumed.

The first index (w1) is a measure of the rate of utilising the production capacity, the second one (w2)

concerns the fixed costs coincided with the unit of the production capacity. Theoretical considerations

concerning the mathematical modelling of the unit production costs as the values depending on the

rate of utilising the production capacity and the fixed costs coincided with the production capacity

unit, are presented in the first part of the paper. The rationalisation criteria of the mine unit production

costs are formulated. These criteria can constitute the elements of restructuring program for the mining

company. The calculation example with the use of the practical input data shows the impact of the

rate of utilising the production capacity on the mine unit production costs. In the example two variants

of annual working time are taken into account. Results of appropriate calculations are presented and

analysed in an aspect of reducing unit costs of production as a result of increasing rate of utilising the

mine production capacity.

Calculations were performed of the thermal system of a power plant with installed water pressure tanks. The maximum rise in the block electric power resulting from the shut-off of low-pressure regenerative heaters is determined. At that time, the boiler is fed with hot water from water pressure tanks acting as heat accumulators. Accumulation of hot water in water tanks is also proposed in the periods of the power unit small load. In order to lower the plant electric power in the off-peak night hours, water heated in low-pressure regenerative heaters and feed water tank to the nominal temperature is directed to water pressure tanks. The water accumulated during the night is used to feed the boiler during the period of peak demand for electricity. Drops in the power block electric power were determined for different capacities of the tanks and periods when they are charged. A financial and economic profitability analysis (of costs and benefits) is made of the use of tanks for a 200 MW power unit. Operating in the automatic system of frequency and power control, the tanks may also be used to ensure a sudden increase in the electric power of the unit. The results of the performed calculations and analyses indicate that installation of water pressure tanks is well justified. The investment is profitable. Water pressure tanks may not only be used to reduce the power unit power during the off-peak night hours and raise it in the periods of peak demand, but also to increase the power capacity fast at any time. They may also be used to fill the boiler evaporator with hot water during the power unit start-up from the cold state.

The article presents the results of thermodynamic analysis of the supercritical coal-fired power plant with gross electrical output of 900 MW and a pulverized coal boiler. This unit is integrated with the absorption-based CO2separation installation. The heat required for carrying out the desorption process, is supplied by the system with the gas turbine. Analyses were performed for two variants of the system. In the first case, in addition to the gas turbine there is an evaporator powered by exhaust gases from the gas turbine expander. The second expanded variant assumes the application of gas turbine combined cycle with heat recovery steam generator and backpressure steam turbine. The way of determining the efficiency of electricity generation and other defined indicators to assess the energy performance of the test block was showed. The size of the gas turbine system was chosen because of the need for heat for the desorption unit, taking the value of the heat demand 4 MJ/kg CO2. The analysis results obtained for the both variants of the installation with integrated CO2separation plant were compared with the results of the analysis of the block where the separation is not conducted.

The paper presents thermodynamic analysis of the gas-steam unit of the 65 MWe combined heat and power station. Numerical analyses of the station was performed for the nominal operation conditions determining the Brayton and combined cycle. Furthermore, steam utilization for the gas turbine propulsion in the Cheng cycle was analysed. In the considered modernization, steam generated in the heat recovery steam generator unit is directed into the gas turbine combustion chamber, resulting in the Brayton cycle power increase. Computational flow mechanics codes were used in the analysis of the thermodynamic and operational parameters of the unit.

The shell and coil heat exchangers are commonly used in heating, ventilation, nuclear industry, process plant, heat recovery and air conditioning systems. This type of recuperators benefits from simple construction, the low value of pressure drops and high heat transfer. In helical coil, centrifugal force is acting on the moving fluid due to the curvature of the tube results in the development. It has been long recognized that the heat transfer in the helical tube is much better than in the straight ones because of the occurrence of secondary flow in planes normal to the main flow nside the helical structure. Helical tubes show good performance in heat transfer enhancement, while the uniform curvature of spiral structure is inconvenient in pipe installation in heat exchangers. Authors have presented their own construction of shell and tube heat exchanger with intensified heat transfer. The purpose of this article is to assess the influence of the surface modification over the performance coefficient and effectiveness. The experiments have been performed for the steady-state heat transfer. Experimental data points were gathered for both laminar and turbulent flow, both for co current- and countercurrent flow arrangement. To find optimal heat transfer intensification on the shell-side authors applied the number of transfer units analysis.

Among the technologies which allow to reduce greenhouse gas emissions, mainly of carbon dioxide, special attention deserves the idea of 'zero-emission' technology based on boilers working in oxy-combustion technology. In the paper a thermodynamic analysis of supercritical power plant fed by lignite was made. Power plant consists of: 600 MW steam power unit with live steam parameters of 650°C/30 MPa and reheated steam parameters of 670°C/6 MPa; circulating fluidized bed boiler working in oxy-combustion technology; air separation unit and installation of the carbon dioxide compression. Air separation unit is based on high temperature membrane working in three-end technology. Models of steam cycle, circulation fluidized bed boiler, air separation unit and carbon capture installation were made using commercial software. After integration of these models the net electricity generation efficiency as a function of the degree of oxygen recovery in high temperature membrane was analyzed.

The results of investigations conducted on the prototype of vapour driven micro-CHP unit integrated with a gas boiler are presented. The system enables cogeneration of heat and electric energy to cover the energy demand of a household. The idea of such system is to produce electricity for own demand or for selling it to the electric grid – in such situation the system user will became the prosumer. A typical commercial gas boiler, additionally equipped with an organic Rankine cycle (ORC) module based on environmentally acceptable working fluid can be regarded as future generation unit. In the paper the prototype of innovative domestic cogenerative ORC system, consisting of a conventional gas boiler and a small size axial vapour microturbines (in-house designed for ORC and the commercially available for Rankine cycle (RC)), evaporator and condenser were scrutinised. In the course of study the fluid working temperatures, rates of heat, electricity generation and efficiency of the whole system were obtained. The tested system could produce electricity in the amount of 1 kWe. Some preliminary tests were started with water as working fluid and the results for that case are also presented. The investigations showed that domestic gas boiler was able to provide the saturated/superheated ethanol vapour (in the ORC system) and steam (in the RC system) as working fluids.

The paper presents the results of the numerical analyses for the steam turbine rotor, dedicated for the newly-designed 900 MW steam unit with supercritical steam parameters (650 °C, 30.0 MPa). Basing on the design calculations, an optimal design solution was determined. Review of the available literature on materials for turbine rotors with supercritical steam parameters was done. Then the start-ups of the turbine were simulated. Thermal and strength states were analyzed. As a result, an optimal start-up characteristic was obtained.

This paper presents a universal approximation of the unit circle by a polygon that can be used in signal processing algorithms. Optimal choice of the values of three parameters of this approximation allows one to obtain a high accuracy of approximation. The approximation described in the paper has a universal character and can be used in many signal processing algorithms, such as DFT, that use the mathematical form of the unit circle. One of the applications of the described approximation is the DFT linear interpolation method (LIDFT). Applying the results of the presented paper to improve the LIDFT method allows one to significantly decrease the errors in estimating the amplitudes and frequencies of multifrequency signal components. The paper presents the derived formulas, an analysis of the approximation accuracy and the region of best values for the approximation parameters.

Efficiency, functionality and performance of the grain grinding process are significantly influenced by phenomena that are difficult to describe and occur in the working area of the grinder. In a machine-based, multi-disc grinding of grain biomaterials, the design of the quasi-cutting unit, volumes, sections of transport/grinding holes, their motion and the design features of the discs (the grinding unit) must facilitate the functions of grinding in the inter-hole space (with minimum energy-consumption of the process and maximum efficiency) and minimising undesirable phenomena related to mixing and transport. The pre-requisite for optimisation of the quasi-cutting unit design is a mathematical model. Among many aspects of the problem, this study describes a sample procedure resulting in a filling model for a biomass grain quasi-cutting unit including an initial verification of the same under conditions of the evaluation of maize and triticale grain grinding efficiency, using an innovative multi-hole 5-disc and 7-disc grinder.

The Variable Frequency Drive (VFD) is used to control the speed of the pumpmotor to attain the desired flow rate and fluid level in a fluid system. An AC drive provides efficient flow control by varying the pump-motor speed. The comparison of energy requirements and costs in a system where a throttling device is used for flow control on a centrifugal pump with the power used when an variable frequency drive (VFD) is used to control the same flow, evidently shows potential savings. In this system, AC Motor Frequency drive and static pressure transmitter, turbine type flowmeter and Analog/Digital cards, micro-control unit and computer connection are designed specially to control flow rate, fluid flow type (turbulence or laminar) and water level at the different conditions with different PID parameters.

The Arab Republic of Egypt – the most important Middle Eastern Arabic country, is one of the oldest countries in the world, believed by some to be the cradle of civilization. Patriotic songs are very popular in it. They can be heard in times of peace and when the country may be facing some difficulties. They are shown on television, played on the radio, broadcast during official ceremonies, and used in social media, coffee shops, and weddings. In recent years, there has been something of a phenomenon around songs titled Taḥyā Maṣr. Notwithstanding the main messages – for Egypt to “live long” and show the artist’s love for their country – other messages and differences in how the singer expresses their love can be found. An analysis of six songs released in the years 2013–2018 under the same title, Taḥyā Maṣr, will be presented in this article. Any clear distinctions between them and the reasons for their being made under the same title will be shown.

The paper presents the results of laboratory tests concerning the cutting process of basket willow by means of disc cutting unit. A disc for cutting wood with diameter of 600mm was used in the tests. The influence of plant’s moisture and the rotary speed of the disc of cutting unit on the unitary energy were determined. The most favorable values of the operating parameters of the cutting unit were selected according to the minimum energy requirement in the cutting process of the tested plant.

The national total expenditure of a country is precipitated on several factors of which revenue generated could be one and very significant. This paper therefore examines the contribution of some selected sources of Nigerian government revenue to total national expenditure. Statistical and econometric techniques used for the data analysis are unit root test, cointegration test, combined estimators’ analysis, the error correction model (ECM) and the feasible generalized linear (FGLS) estimators. Results showed that the variables are non stationary but are stationary at first difference. The long-run relationship of total expenditure on oil revenue, non-oil revenue, federation account and federal retained revenue revealed that the variables are co-integrated and required the use of combined estimators. The effect of non-oil revenue and federal retained revenue is very significant. Investigations on the short-run modeling necessitated the use of FGLS estimators. The effect of ECM and federal retained revenue is very significant. Consequently, other sources of revenue apart from federal retained revenue need to be enhanced and tailored towards improving economic growth and development through national expenditure.