The In the paper, we investigate two single processor problems, which deal with the process of negotiation between a producer and a customer about delivery time of final products. This process is modelled by a due interval, which is a generalization of well known classical due date and describes a time interval, in which a job should be finished. In this paper we consider two diffierent mathematical models of due intervals. In both considered problems we should find such a schedule of jobs and such a determination of due intervals to each job, that the generalized cost function is minimized. The cost function is the maximum of the following three weighted parts: the maximum tardiness, the maximum earliness and the maximum due interval size. For the first problem we proved several properties of its optimal solution and next we show the mirror image property for both of considered problems, which helps us to provide an optimal solution for the second problem.

The paper concerns the two-machine non-preemptive flow shop scheduling problem with a total late work criterion

and a common due date (F2|dj = d|Y ). The late work performance measure estimates the quality of a solution with regard

to the duration of late parts of activities performed in the system, not taking into account the quantity of this delay. In the

paper, a few theorems are formulated and proven, describing features of an optimal solution for the problem mentioned, which is

NP-hard. These theorems can be used in exact exponential algorithms (as dominance relations reducing the number of solutions

enumerated explicitly), as well as in heuristic and metaheuristic methods (supporting the construction of sub-optimal schedules

of a good quality).

This paper presents a numerical investigation of fracture criterion influence on perforation of high-strength 30PM steel plates subjected to 7.6251 mm Armour Piercing (AP) projectile. An evaluation of four ductile fracture models is performed to identify the most suitable fracture criterion. Included in the paper is the Modified Johnson-Cook (MJC) constitutive model coupled separately with one of these fracture criteria: the MJC fracture model, the Cockcroft-Latham (CL), the maximum shear stress and the constant failure strain models. A 3D explicit Lagrangian algorithm that includes both elements and particles, is used in this study to automatically convert distorted elements into meshless particles during the course of the computation. Numerical simulations are examined by comparing with the experimental results. The MJC fracture model formulated in the space of the stress triaxiality and the equivalent plastic strain to fracture were found capable of predicting the realistic fracture patterns and at the same time the correct projectile residual velocities. However, this study has shown that CL one parameter fracture criterion where only one simple material test is required for calibration is found to give good results as the MJC failure criterion. The maximum shear stress fracture criterion fails to capture the shear plugging failure and material fracture properties cannot be fully characterized with the constant fracture strain.

In modern conditions of urban development, there is a need to improve the technology for determining the investment attractiveness of urban lands by developing a method and models for assessing its impact, which will be based on the construction of a two-level system of indicators, which will determine the integral investment criterion and develop guidelines for improving the investment attractiveness of urban lands. As a result of the research, the value of the integral indicator of urban land investment attractiveness was determined, which allowed to apply it in the system of normative monetary valuation of urban land and to develop methodological recommendations for improving the efficiency of its investment attractiveness assessment. A method for assessing the investment attractiveness of urban land, as the main element of technology, based on the determination of indicators for assessing the integral criterion for the development of guidelines for improving the urban land investment attractiveness is developed. By the value of the integral criterion, the integral indicators of the potential investment attractiveness of urban lands are determined, considering the changes in the normative monetary value of the lands of settlements and the level of investment attractiveness of the regional centers of Ukraine is determined.

The entropy production per unit time is calculated for the regular lamellae -, and for the regular rods formation, respectively. The entropy production is a function of some parameters which define the eutectic phase diagram, coefficient of the diffusion in the liquid, and some capillary parameters connected with the mechanical equilibrium located at the triple point of the solid/liquid interface. Minimization of the entropy production allowed to formulate mathematically the so-called Growth Law for both envisaged eutectic morphologies.

The (Zn) – single crystal strengthened by the E = (Zn) + Zn16Ti eutectic precipitate is subjected to directional growth by the Bridgman’s system and current analysis. Experimentally, the strengthening layers (stripes) are generated periodically in the (Zn) – single crystal as a result of the cyclical course of precipitation which accompanies the directional solidification. These layers evince diversified eutectic morphologies like irregular rods, regular lamellae, and regular rods. The L – shape rods of the Zn16Ti – intermetallic compound appear within the first range of the growth rates when the irregular eutectic structure is formed. Next, the branched rods transform into regular rods and subsequently the regular rods into regular lamellae transitions can be recorded. The regular lamellae exist only within a certain range of growth rates. Finally, the regular rods re-appear at some elevated growth rates.

A new solution to the diffusion equation is provided to describe the micro-field of the solute concentration in the liquid adjacent to the front of the growing eutectic structure. The solution is based on the mass balance in the considered system. Moreover, the existence of the protrusion of the leading eutectic phase over the wetting one is required by the mass balance. The appearance of the d – protrusion in the growing eutectic is well confirmed by the experimental observations of the frozen solid/liquid interface. The mentioned solution satisfies the concept of the eutectic coupled growth according to which undercooling of the leading phase is less than undercooling of the wetting eutectic phase. Also, the Ti – solute micro-segregation / redistribution is analyzed within the matrix of the single crystal. The micro-segregation is described as a result of the solution to the adequate, newly developed differential equation. The definition for the solute redistribution is given by the subsequently / separately formulated relationship. This definition takes into account both extent -, and intensity of the solute redistribution.

Finally, the entropy production is calculated for the regular lamellae -, and for the regular rods formation, respectively. The entropy production is a function of some parameters which define the eutectic phase diagram, coefficient of the diffusion in the liquid, and some capillary parameters connected with the mechanical equilibrium located at the triple point of the solid/liquid interface. Branches formation is related to the marginal stability. A new criterion is formulated and subjected to successful verification. It is: in the structural – thermodynamic competition the winner is this kind of the pattern for which minimum entropy production has a lower value.

In the longwall exploitation system, the main gates are subject of the most intensive movements of the rock mass, where the proximity of the excavation front is a key factor. The paper presents the results of a research on the constants mb and s of Hoek-Brown failure criterion for the rocks surrounding the gallery: shale, sandy shale, coal and medium-grained sandstone, in relation to the distance to longwall face. The research comprised numerical modeling based on convergence monitoring records. The convergence measurements were carried out on three stations in a selected maingate in a coal mine from Upper Silesia Coal Basin near Jastrzębie-Zdrój, concurrently with changing distance to the longwall face. The measured were the width, the height and the heave of the floor of the gate. The measurements showed that the convergence at the longwall-maingate crossing was 1.5-3 times greater than in the locations much further from the longwall face. It was demonstrated that this effect was due to continuously changing properties of the rock-mass surrounding the gallery that can be expressed as decreasing empirical parameters mb i s of Hoek-Brown’s criterion. These parameters are decreasing exponentially together with the distance to the longwall face The consistency between the theoretical and factual curve varies between 70% to 98%. The change of each of the parameters can be described by general equation P = a· exp(–b·d), where a, b are constants, and d is the distance to the excavation face. The authors highlight that during the measurements period the horizontal stress was 1.45 to 1.61 times greater than the concurrent vertical stress. The so high horizontal stress causes heave of unsupported gallery floor which is commonly observed in the mines in Silesia.

The paper refers to previous publications of the author, focused on criteria of casting feeding, including the thermal criterion proposed by

Niyama. On the basis of this criterion, present in the post-processing of practically all the simulation codes, danger of casting compactness

(in the sense of soundness) in form of a microporosity, caused by the shrinkage phenomena, is predicted. The vast majority of publications

in this field concerns shrinkage and feeding phenomena in the cast steel castings – these are the alloys, in which parallel expansion

phenomenon does not occur as in the cast irons (graphite crystallization). The paper, basing on the simulation-experimental studies,

presents problems of usability of a classic, definition-based approach to the Niyama criterion for the cast iron castings, especially of

greater massiveness, for prediction of presence of zones of dispersed porosity, with relation to predictions of the shrinkage type defects.

The graphite expansion and its influence on shrinkage compensation during solidification of eutectic is also discussed.

Turbine blades have complex geometries with free form surface. Blades have different thickness at the trailing and leading edges as well

as sharp bends at the chord-tip shroud junction and sharp fins at the tip shroud. In investment casting of blades, shrinkage at the tip-shroud

and cord junction is a common casting problem. Because of high temperature applications, grain structure is also critical in these castings

in order to avoid creep. The aim of this work is to evaluate the effect of different process parameters, such as, shell thickness, insulation

and casting temperature on shrinkage porosity and grain size. The test geometry used in this study was a thin-walled air-foil structure

which is representative of a typical hot-gas-path rotating turbine component. It was observed that, in thin sections, increased shell

thickness helps to increase the feeding distance and thus avoid interdendritic shrinkage. It was also observed that grain size is not

significantly affected by shell thickness in thin sections. Slower cooling rate due to the added insulation and steeper thermal gradient at

metal mold interface induced by the thicker shell not only helps to avoid shrinkage porosity but also increases fill-ability in thinner

sections.

In this study, a procedure for optimal selection of measurement points using the D-optimality criterion to find the best calibration curves of measurement sensors is proposed. The coefficients of calibration curve are evaluated by applying the classical Least Squares Method (LSM). As an example, the problem of optimal selection for standard pressure setters when calibrating a differential pressure sensor is solved. The values obtained from the D-optimum measurement points for calibration of the differential pressure sensor are compared with those from actual experiments. Comparison of the calibration errors corresponding to the D-optimal, A-optimal and Equidistant calibration curves is done.

The paper concerns the problem of choosing a criterion for transmission line when lumped parameters analysis is required. First, the formal introduction of transmission line scheme is presented. Secondly, a new criterion for lumped-parameter analysis of transmission line is proposed. The criterion has clear physical meaning and simple mathematical form. The proposed criterion takes into account not only wave length, but also the dissipation of transmission line. The criterion can be easily adjusted to some requirements, such as needed level of no-load output voltage change.

Experimental observations of the steel morphology as well as measurements of the solutes concentration in the macro-scale were made on the basis of the vertical cut at the mid-depth of the 15-tons steel forging ingot serially produced in one of the steel plant in Poland. Experimental observations of the morphology accompanied by the measurements of the Peclet Number were also made on the cross-section of the continuously cast brass ingots serially produced in the copper / brass industry in Poland. The performed measurements allowed to work out some maps of the alloying elements segregation for the longitudinal section of the steel static ingot and a Growth Law for the columnar grains formation in the brass ingots. The marginal stability criterion has been applied to the last mentioned development / description. Some suggestions for the micro-segregation measurement mode in the columnar structure are derived.

The subject of the study are alumina foams produced by gelcasting method. The results of micro-computed tomography of the foam samples are used to create the numerical model reconstructing the real structure of the foam skeleton as well as the simplified periodic open-cell structure models. The aim of the paper is to present a new idea of the energy-based assessment of failure strength under uniaxial compression of real alumina foams of various porosity with use of the periodic structure model of the same porosity. Considering two kinds of cellular structures: the periodic one, for instance of fcc type, and the random structure of real alumina foam it is possible to justify the hypothesis, computationally and experimentally, that the same elastic energy density cumulated in the both structures of the same porosity allows to determine the close values of fracture strength under compression. Application of finite element computations for the analysis of deformation and failure processes in real ceramic foams is time consuming. Therefore, the use of simplified periodic cell structure models for the assessment of elastic moduli and failure strength appears very attractive from the point of view of practical applications.

Automation of data processing of contactless diagnostics (detection) of the technical condition of the majority of nodes and aggregates of railway transport (RWT) minimizes the damage from failures of these systems in operating modes. This becomes possible due to the rapid detection of serious defects at the stage of their origin. Basically, in practice, the control of the technical condition of the nodes and aggregates of the RWT is carried out during scheduled repairs. It is not always possible to identify incipient defects. Consequently, it is not always possible to warn personnel (machinists, repairmen, etc.) of significant damage to the RWT systems until their complete failure. The difficulties of obtaining diagnostic information is that there is interdependence between the main nodes of the RWT. This means that if physical damage occurs at any of the RWT nodes, in other nodes there can also occur malfunctions.

As the main way to improve the efficiency of state detection of the nodes and aggregates of RWT, we see the direction of giving the adaptability property for an automated data processing system from various contactless diagnostic information removal systems. The global purpose can be achieved, in particular, through the use of machine learning methods and failure recognition (recognition objects). In order to improve the operational reliability and service life of the main nodes and aggregates of RWT, there are proposed an appropriate model and algorithm of machine learning of the operator control system of nodes and aggregates. It is proposed to use the Shannon normalized entropy measure and the Kullback-Leibler distance information criterion as a criterion of the learning effectiveness of the automated detection system and operator node state control of RWT. The article describes the application of the proposed method on the example of an automatic detection system (ADS) of the state of a traction motor of an electric locomotive. There are given the test data of the model and algorithm in the MATLAB environment.