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In this article, we will introduce the mathematical model of the diffusion process in a swelling medium that has already been modeled. The main purpose of this paper is introducing a new class of group transformations for solving the nonlinear emulsion equation. Thus, we introduce this method as the discrete group methods based on solvable class orbits. One of the crucial advantages of this method is that a transformation is sought, which reduces the equation being investigated to some standard form for which the methods of integration are known. In developing this approach, one may construct all canonical forms of solvable equations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to evaluate the feasibility of implementation of a passive safety feature in the form of an under-fuselage airbag in the rescue systems of small aircraft. The paper presents a multidisciplinary approach for the viability of the implementation. It presents the development of mathematical model for airbag performance analysis. The model is validated against the experimental data to account for various simplifications. Validated mathematical model is used to design a full-scale airbag for the chosen airplane to perform in the designed range. Weight penalty for increased safety is determined. [ABSTRACT FROM AUTHOR]

The paper investigates whether foam glass could reduce the structural thickness of the protection layer in the construction of the railway track (saving of natural materials - crushed aggregate) and, at the same time, also provide sufficient thermal protection of the frost-susceptible subgrade surface. It also discusses whether the incorporation of foam glass would have a relevant effect on the increase of the deformation resistance of the railway track structure at the level of the sub-ballast upper surface. Following these assumptions, the paper presents the results of experimental measurements of the deformation resistance of the modified structural composition of the sub-ballast layers (with an embedded foam glass layer) and their comparison with the results determined on a structure with a standard composition of the sub-ballast layers (crushed aggregate sub-ballast layer/protective layer). Also, numerical and mathematical analysis of the influence of the built-in thermal insulation foam glass layer on the reduction of the structural thickness of the protective crushed aggregate layer in terms of the effect of climatic factors is conducted in the paper. The mathematical model, developed by the research, provides the possibility of continuous monitoring of the change in the railway track structure freezing depending on climatic characteristics. [ABSTRACT FROM AUTHOR]

In this paper, we present a deterministic mathematical model for the study of overweight, and obesity in a population and its impact on the growth of the number of diabetics. For the construction of the model, we take into account social factors and the interactions between the elements of society. We find the basic reproduction number and prove the global stability of the disease-free equilibrium point. We present theoretical results and find the sensitivity indices to characterize the impact of parameters associated with overweight, obesity and diagnosed diabetes on the basic reproduction number. To validate the model, we perform computational simulations and study the basic reproduction number and compartments. We present the behavior of the compartments for a scenario and study the impact of the variation of parameters associated with overweight by social pressure and diabetes due to causes other than obesity. [ABSTRACT FROM AUTHOR]

This paper analyses the available mathematical models of flight simulators based on the Stewart platform. It was found that there is no model that describes the conditions for stable dynamic equilibrium operation of the Stewart platform as a function of a number of important motion parameters. In this context, a new physical model is proposed based on classical models of theoretical mechanics using the d’Alembert formalism, the concept of stable equilibrium of a mechanical system. This model mathematically separates the stable equilibrium of the flight simulator motion system from the general uniformly accelerated motion. The systems of equations obtained in the framework of the model connect the physical and geometrical parameters of the Stewart platform and make it possible to determine the reactions in the upper hinges of the platform support, the limit values of the position angles in the space of the base of the support of the Stewart platform, under which the condition of stable equilibrium operation of the Stewart platform is satisfied. The proposed physical model and the analytical relations obtained on its basis are of great practical importance: the operator controlling the operation of the Stewart platform-based flight simulator can control the range of parameters during training so as not to bring the flight simulator out of stable equilibrium. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to propose new mathematical models for simulation of biosensors and to construct and investigate discrete methods for the efficient solution of the obtained systems of nonlinear PDEs. The classical linear diffusion operators are substituted with nonlocal fractional powers of elliptic operators. The splitting type finite volume scheme is used as a basic template for the introduction of new mathematical models. Therefore the accuracy of the splitting scheme is investigated and compared with the symmetric Crank-Nicolson scheme. The dependence of the approximation error on the regularity of the solution is investigated. Results of computational experiments for different values of fractional parameters are presented and analysed. [ABSTRACT FROM AUTHOR]

This paper proposes virtual element methods for approximating the mathematical model consisting of coupled poroelastic and Advection-Diffusion-Reaction (ADR) equations. The space discretization relies on virtual element spaces containing piecewise linear polynomials as well as non-polynomials for displacement, pressure and concentrations, and piecewise constant for total pressure; a backward Euler scheme is employed for the approximation of time derivative. Using standard techniques of explicit schemes, the well-posedness of the resultant fully discrete scheme is derived. Moreover, under certain regularity assumptions on the mesh, optimal apriori error estimates are established by introducing suitable projection operators. Several numerical experiments are presented to validate the theoretical convergence rate and exhibit the proposed scheme’s performance. [ABSTRACT FROM AUTHOR]

Potato virus Y (PVY) is an aphid-borne plant virus that causes substantial yield losses in potato production. Control measures of the viral infection are both limited and expensive. A proper use of mixed-cropping strategy can reduce the spread of PVY. In this paper, we formulate and analyze a mathematical model of PVY spread in a mixed-cropping system. Then, we extend the model to an optimal control problem by considering use of mineral oil, insecticide and farmer’s level of field inspection for infected plants. The analytic results show that the basic reproduction number ℜ0, a threshold parameter that decides properties of the dynamics. The disease free equilibrium is stable if ℜ0 < 1 and unstable when ℜ0 > 1. It is found that ℜ0, and hence, the disease dynamics is highly sensitive to the representative parameters of density the non-host plant and its quality in attracting vectors. The model exhibits forward bifurcation at ℜ0 = 1. The study of optimal control problem suggests that mixed-cropping combined with either mineral oil or insecticide is the best to control the disease. Furthermore, simulation results show that mixed-cropping can be used as an alternative strategy and can reduce the need of mineral oil or insecticide. [ABSTRACT FROM AUTHOR]

The hydrodynamic and thermodynamic processes of geothermal well extraction are investigated and presented in this paper. The paper presents mathematical models for a multi-level centrifugal pump and pipeline system. The mathematical models were used to evaluate gas (nitrogen) emission in water and its effects on hydrodynamic processes. Experimental studies and mathematical modelling showed that the gas content of the fluid increases the pressure and flow pulsations within a centrifugal pump. The variation in the height of the liquid column in extraction has an influence on characteristics of the multistage centrifugal pump used in wells. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of singularly perturbed convection-diffusion boundary-value problems with discontinuous convection coefficient which often occur as mathematical models for analyzing shock wave phenomena in gas dynamics. In general, interior layers appear in the solutions of this class of problems and this gives rise to difficulty while solving such problems using the classical numerical methods (standard central difference or standard upwind scheme) on uniform meshes when the perturbation parameter ε is small. To achieve better numerical approximation in solving this class of problems, we propose a new hybrid scheme utilizing a layer-resolving piecewise-uniform Shishkin mesh and the method is shown to be ε- uniformly stable. In addition to this, it is proved that the proposed numerical scheme is almost second-order uniformly convergent in the discrete supremum norm with respect to the parameter ε. Finally, extensive numerical experiments are conducted to support the theoretical results. Further, the numerical results obtained by the newly proposed scheme are also compared with the hybrid scheme developed in the paper [Z.Cen, Appl. Math. Comput., 169(1): 689-699, 2005]. It shows that the current hybrid scheme exhibits a significant improvement over the hybrid scheme developed by Cen, in terms of the parameter-uniform order of convergence. [ABSTRACT FROM AUTHOR]

The paper considers the theoretical explanation and construction of some mathematical models of the aircraft operational process in reference to maintenance organizations preferred by aviation experts and aircraft operators. The uncertainty of such operational multi-alternativeness is evaluated on the basis of subjective entropy of preferences demonstrated by aircraft operators and aviation experts. When applying the maximum principle of subjective entropy, the optimal distributions of the preferences are obtained. The proposed concept allows finding the optimal distribution of the aircraft fleet according to the available maintenance alternatives. To optimize the above mentioned distribution, one may take into account the possible development and improvement of maintenance organizations and so called “shadow” components. The paper also discusses a significant approach that helps to evaluate the effectiveness of organizations functioning in the area of aviation. This evaluation can be carried out at both global and continental levels as well as state, operator, and airline levels. The respective modeling has been performed and is illustrated with diagrams. [ABSTRACT FROM PUBLISHER]

An issue of improving flight safety during landing with an inertial navigation system (INS) and a failed barometric altimeter is considered. In this paper, we propose a specific algorithm for in-flight calibration of the vertical channel of INS. Accordingly, the baro-inertial integration algorithm using a discrete five-state Kalman filter will be performed during a particular flight maneuver before landing. As a result, it is possible to estimate not only the bias of vertical accelerometer but also its scale factor, which is too small to be defined by a usual in-flight calibration algorithm. After applying the proposed algorithm, the flight management system can provide a safe landing with a standalone INS. The algorithm's performance is assessed by simulating complete mathematical models of aircraft motion and control systems. The impact of calibrated bias and scale factor of vertical accelerometer on the altitude estimation error is provided through an analysis. [ABSTRACT FROM AUTHOR]

The paper presents the solution methodology of a multi-objective probabilistic fractional programming problem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In first step, multi-objective probabilistic fractional programming problem is converted to deterministic multi-objective fractional mathematical programming problem. In the second step, it is converted to its equivalent multi-objective mathematical programming problem. Finally, -constraint method is applied to find the best compromise solution. A numerical example and application are presented to demonstrate the procedure of proposed mathematical model. [ABSTRACT FROM AUTHOR]

Micro turbojets can be used for propulsion of civilian and military aircraft, consequently their investigation and control is essential. Although these power plants exhibit nonlinear behaviour, their control can be based on linearized mathematical models in a narrow neighbourhood of a selected operating point and can be extended by using robust control laws like H∞ or Linear Quadratic Integrating (LQI). The primary aim of the present paper is to develop a novel parametric linear mathematical model based on state space representation for micro turbojet engines and the thrust parameter being Turbofan Power Ratio (TPR). This parameter is used by recent Rolls-Royce commercial turbofan engines but can be applied for single stream turbojet power plants as well, as it has been proven by the authors previously. An additional goal is to perform the identification for a particular type based on measurements of a real engine. This model has been found suitable for automatic control of the selected engine with respect of TPR, this has been validated by simulations conducted in MATLAB® Simulink® environment using acquired data from transient operational modes. [ABSTRACT FROM AUTHOR]

A conflict is an infringement of minimum separation between at least two aircraft. The model is based on these assumptions: aircraft fly on level straight line routes, only an infringement of the lateral separation is considered, deviations are excluded, aircraft at the same flight level fly the same average speed, and aircraft fly towards an intersection and may change direction after intersection. Hence, conflicts mainly occur owing to a loss of minimum separation between aircraft flying at the same flight level. Calculation of average number of potential conflicts is designated for long time interval; hence, aircraft velocity deviations are negligible. The mathematical model in this paper is intended to compare different alternatives of intersection configuration of air traffic services routes. The comparison is based on the results: an average number of potential conflicts per hour on intersection of routes, index of conflicts intensity, and intersection capacity. [ABSTRACT FROM AUTHOR]

For decades, the General Motors (GM) car following model has received a great deal of attention and provided a basic framework to describe the interactions between vehicles on the road. It is based on the stimulus-response assumption that the following vehicle responds to the relative speed between the lead vehicle and itself. However, some of the empirical findings show that the assumption of GM model is not always true and need some modification. For example, the acceleration of the following vehicle is very sensitive to the sign of the relative speed and because of no term in the model that directly represents the leader's acceleration, the follower's response to the leader's acceleration can be retarded. This paper offers a new car-following model that can be considered as a variant of the GM model that can better capture car following behavior. The new model treats the follower's acceleration as a proportion of a weighted sum of the leader's acceleration and the relative speed between the lead and following vehicles. This paper compares the new model with the original GM model numerically and the characteristics of the new parameters in the model are investigated. It is also shown that the new model overcomes the shortcomings of the original GM model identified in this paper and gives us more instruments to capture the real-world car-following behavior. [ABSTRACT FROM PUBLISHER]

Reduced-order models based on Proper orthogonal decomposition are known to suffer from a lack of accuracy due to the truncation effect introduced by keeping only the most energetic modes. In this paper, we propose a new regularized calibration method aiming at minimizing a weighted average of normalized error, and a term measuring the change of the coefficients from their value obtained by Galerkin projection. We also determine the optimal value of the regularization parameter by analogy of the L-curve method. This paper is a sequel of [8] in which we compared various methods of calibration and introduced a Tikhonov-based regularization method. The proposed approach is assessed for a two dimensional wake flow around a cylinder, characteristic of the configurations of interest. [ABSTRACT FROM AUTHOR]

The article examines the dependencies of individual sectoral stock price indices of OMX Baltic security market on macroeconomic indicators, using econometric methods. Regression models are constructed using quarterly time series of 2000–2011 years while the methodology is backed with the findings of Lithuanian and foreign scientists from an extensive overview of specific literature. Regression equations, obtained in the paper, allows us to identify the key macroeconomic and global indicators that statistically significantly affect the Baltic securities market and to quantify their impact on the stock price indices of individual sectors in the Baltic countries. Econometric analysis of OMX Baltic security market proves the hypothesis that the set of macroeconomic regressors may vary considerably depending on the individual sector's price indices, especially in the case of small open economy with immature stock markets. The paper provides investors who are shaping their portfolios taking into account the macroeconomic forecasts with additional opportunities on the basis of sectoral stock price indices regression equations. [ABSTRACT FROM AUTHOR]

Making operational plans for Yard Cranes (YCs) to enhance port efficiency has become vital issues for the container terminals. This paper discusses the load-scheduling problem of multiple YCs. The problem is to schedule two YCs at different container blocks, which serve the loading operations of one quay crane so as to minimize the total distance of visiting paths and the make-span at stack area. We consider the container handling time, the YC visiting time, and the waiting time of each YC when evaluating the make-span of the loading operation by YCs. Both the container bay visiting sequences and the number of containers picked up at each visit of the two YCs are determined simultaneously. A mathematical model, which considers interference between adjacent YCs, is provided by means of time-space network to formulate the problem and a two-stage hybrid algorithm composed of greedy algorithm and dynamic programming is developed to solve the proposed model. Numerical experiments were conducted to compare performances of the algorithm in this study with actual scheduling rules. [ABSTRACT FROM AUTHOR]

The paper considers theoretical explanation and construction of some mathematical models of a transportation mean operational process in reference to maintenance optimal periodicity. The important finding is that the objectively existing engineering transportation means maintenance optimal periodicity is determined in the different from the probabilistic methods way. There is a scientifically proven explanation for the mentioned above periodicity optimization with the help of the specially introduced hybrid-optional effectiveness functions distribution. The developed doctrine uses the entropy paradigm conditional extremization approach. This contribution allows obtaining the wanted optimal periodicities sidestepping the related states probabilities determination and their further extremization. The essential breakthrough of the developed doctrine is that the optional objective effectiveness functions, in such a case, are the corresponding combinations of the intensities of the studied system's possible transitions from state to state, which relates with the set of the considered operational options. Corresponding limit solutions for the zero-to-zero ratio indeterminate forms are analyzed. Theoretical speculations are illustrated with the example calculation experiments. The necessary diagrams are plotted. [ABSTRACT FROM AUTHOR]

The paper builds on the ideas of previous research concerning the theoretical explanation of the aircraft operational process with regard to the preferences for maintenance organization by experts and aircraft operators, and describes the designed mathematical models. The problem of conditional extremization is considered. The uncertainty of aircraft technical operation multi-alternativeness is evaluated using the subjective entropy of the aircraft operators' and experts' preferences. By applying the subjective entropy extremization principle in view of its maximum, we obtain the conditional optimal distributions of the preferences. The proposed approach allows finding the optimal distribution of the aircraft fleet for the available maintenance alternatives, taking into consideration the restricted possible influences or shadow components of maintenance organizations. The concepts discussed here are important for evaluating the effectiveness of the aviation industry by making allowance for shadow parameters, if needed. The designed model is illustrated with diagrams. [ABSTRACT FROM AUTHOR]

Decision makers usually prefer to express their preferences by linguistic variables. Classic fuzzy sets allowed expressing these preferences using a single linguistic value. Considering inevitable hesitancy of decision makers, hesitant fuzzy linguistic term sets allowed them to express individual evaluation using several linguistic values. Therefore, these sets improve the ability of humans to determine believes using their own language. Considering this feature, in this paper a method upon linear assignment method is proposed to solve group decision making problems using this kind of information, when criteria weights are known or unknown. The performance of the proposed method is illustrated in a numerical example and the results are compared with other methods to delineate the models efficiency. Following a logical and well-known mathematical logic along with simplicity of execution are the main advantages of the proposed method. [ABSTRACT FROM AUTHOR]

The paper describes proecological solution dedicated for organizing logistics services in urban areas. Proposed solution is based on cross-docking processes combined with consolidation centres. Authors proposed new method of estimating economic and social benefits from implementing centrally managed cooperation of logistics operators using common city consolidation hubs. Developed mathematical model bases on Vehicle Routing Problem (VRP) with vehicles of different types, limited loading capacities and multiply depots characterized by limited throughput. Proposed approach was supported by case study of integration of distribution processes in Warsaw (Poland) performed by three medium-size logistics operators. The central management of distribution was investigated in variants assuming using existing warehouses and with new configuration of logistics network developed with using SIMMAG 3D tools. As it was proved for analysed case, total costs of distribution in the city after implementation of centrally managed distribution were reduced by 8.1% for variant with current depots and by 26.5% for variant with new logistics network, while emission of carbon monoxide (CO) was reduced respectively by 7.8 and 16.7%. [ABSTRACT FROM AUTHOR]

In this paper we derive the closed-form solutions for the Lucas-Uzawa growth model with the aid of the partial Hamiltonian approach and then compare our results with those derived in literature. The partial Hamiltonian approach provides two first integrals [9] in the case where there are no parameter restrictions and these two first integrals are utilized to construct three sets of closed form solutions for all the variables in the model. We begin by using the two first integrals to find two closed form solutions, one of which is new to the literature. We then use only one of the first integrals to derive a third solution that is the same as that found in the previous literature. We continue by analyzing the newly derived solution in detail also show that all three solutions converge to the same long run balanced growth path. The special case when the share of capital is equal to the inverse of the intertemporal elasticity of substitution is also investigated in detail. [ABSTRACT FROM PUBLISHER]

In order to gain an overall view on all relevant connections of the elements in a public transportation system, a systematic approach is advisable to follow, which applies well-proven methodology. In case a structure contains both hierarchical and non-hierarchical connections, the formerly recommended methodologies are: ISM-AHP, ISM-ANP, ANP. This paper however proposes a different approach: AHP-ISM, which aims to keep the AHP hierarchy, but simul- taneously to amend that with the non-hierarchical types of linkages within the structure. By that, those connections that were verified in the AHP procedure can be considered dominant, but also weaker linkages might provide impor- tant additional information about the whole structure. The additional ISM procedure is suitable for two purposes: the most influential elements of the AHP structure can be selected, moreover also direct and indirect impacts of element improvement might be followed in the structure by considering both types of connections within the system, using the directed graph of ISM. The introduced AHP-ISM model is applicable for analyzing public transportation systems – as shown in the paper – but also generally applicable for any AHP applications, which are not strictly but dominantly hierarchically structured. [ABSTRACT FROM AUTHOR]

This paper considers the technological development of an additional network for Vilnius City public transport. Several types of scenarios for the development of Vilnius City tram line were analysed. This paper describes the situation pertaining to Vilnius City transport system as well as the traffic parameters, which are used for a multiple attribute ranking of a tram line development in Vilnius City. The multiple attribute criteria methods have been chosen to perform the ranking of three development scenarios and to estimate the best alternative based on the traffic conditions of Vilnius City. The experts of different decision-making groups have performed the importance analysis of traffic parameters, which were chosen for the assessment of alternative scenarios for the tram line development. The transport system experts were used to determine the relative weights of indicators. Two methods – TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and SAW (Simple Additive Weighting)–were used and compared to determine the best transport development alternative based on traffic parameters. Two multi-criteria methods were applied in this research to perform the ranking of more accurate alternatives and to make the comparison of calculation results. [ABSTRACT FROM AUTHOR]

Prestressed stayed compression members are frequently required as very slender load-bearing structural components by both investors and architects. Behavior of these members depends on their geometrical and material properties, prestressing and boundary conditions. In the paper are discussed respective critical buckling loads and post-buckling paths with regards to 2D and 3D GMNIA (geometrically and materially nonlinear analysis with imperfections) using ANSYS software. Former tests and recent detailed analyses of other authors are commented with respect to the 3D analysis, level of imperfections, boundary conditions at central crossarm (fixed or sliding stays) and nonlinear stainless steel material. [ABSTRACT FROM AUTHOR]

The paper deals with the location selection problem of the garage at the parcel of a single-family residential house. The mathematical model for this real life problem is constructed within MCDM framework. The significance of the chosen criteria was evaluated by AHP approach. The formulated MCDM problem is solved applying WASPAS extension, namely WASPAS-SVNS. The applied single-valued neutrosophic set allows to modeling uncertainty of the initial information explicitly. A numerical example is considered in order to verify the proposed approach. [ABSTRACT FROM AUTHOR]

Regarding to the high importance of project selection in the project life cycle, solving bid/no-bid problems, especially in the construction industry, is a subject of most recent research. Portfolio selection has been the most interesting area in the last two decades in management research but there is poor investigation in the construction industry. Taking into account the risk, which is inherent in the construction industry and especially in the project selection phase is inevitable. This paper intends to propose a model for project selection and developing two main concepts including company portfolio and risk. The main innovation of this paper is presenting a new framework, which attempts to optimize project selection based on the endurable risk level of a company with regard to the existing portfolio. Considering the user-friendly characteristic of the model, this paper has applied the fuzzy multi criteria decision-making approaches. Finally, the model is implemented in a real case study. [ABSTRACT FROM PUBLISHER]

The periodic zeta-functionζ(s; a),s=σ+itis defined forσ >1 by the Dirichlet series with periodic coefficients and is meromorphically continued to the whole complex plane. It is known that the functionζ(s; a), for some sequences a of coefficients, is universal in the sense that its shiftsζ(s+iτ; a),τ∈ℝ, approximate a wide class of analytic functions. In the paper, a weighted universality theorem for the functionζ(s; a) is obtained. [ABSTRACT FROM AUTHOR]

This paper describes the construction of second derivative general linear methods in Nordsieck form with stability properties determined by quadratic stability functions. This is achieved by imposing the so–called inherent quadratic stability conditions. After satisfying order and inherent quadratic stability conditions, the remaining free parameters are used to find the methods withL–stable property. Examples of methods withp=q=s=r −1 up to order four are given. [ABSTRACT FROM PUBLISHER]

In this paper we investigate a logistic equation with a new free boundary condition appearing in ecology, we aim to describe the spreading of a new or invasive species by studying the asymptotic behavior of the radially symmetric solutions of the problem. We will obtain a trichotomy result: spreading (the solution converges to a stationary solution defined on the half–line), transition (the solution converges to a stationary solution with compact support) and vanishing (the solution converges to 0 within a finite time). Besides we can also obtain a dichotomy result (either spreading or vanishing happens). Moreover, in the spreading case, we give the sharp estimate of the asymptotic spreading speed of the free boundary. [ABSTRACT FROM PUBLISHER]

The paper analyzes the possibilities of using computer aided modelling programs for developing new cars to achieve better dynamical properties of control over vehicles. The article shortly reviews the behaviour of young and experienced drivers and models describing it. The paper covers the process of turning car steering wheel, considers acceptable values of lateral acceleration comfortable for a car driver and all car passengers and presents computer aided modelling program CarSim used for displaying single and double lane change manoeuvres at various speeds on dry asphalt. The given charts, including data about steering wheel angle and lateral acceleration values indicate single and double lane change manoeuvres performed by a car. Also, the values of longitudinal and lateral forces of each wheel during the double lane change manoeuvre are provided. [ABSTRACT FROM AUTHOR]

Numerical modelling of bond is a challenging due to a number of physical and mechanical phenomena arising from interaction of ribbed reinforcing bars and concrete. In present paper 2D and 3D approaches for bond analysis are compared in terms of global load-displacement behaviour of RC element, formation of microcracks and deterioration of concrete in front of the ribs. Nonlinear Finite element software ATENA was used for both 2D and 3D analysis. It was shown that differences between two approaches are minor and simpler 2D models may be used for the analysis of bond in RC structures. [ABSTRACT FROM AUTHOR]

A vector of residual forces of the ideally elastic-plastic structure at shakedown is obtained by solving the static analysis problem. A unique distribution of the residual forces is determined if the analysis is based on the minimum complementary deformation energy principle. However, the residual displacements developing in the shakedown process of ideally elastic-plastic structures under variable repeated loads can vary non-monotonically. Nevertheless mathematical models for the optimization problems of steel structures at shakedown must include the conditions for strength (safety) and stiffness (serviceability). Residual displacements determined by the plastic deformations are included in the stiffness conditions; therefore to improve the optimal solution it is necessary to determine upper and lower bounds of the residual displacement variations. This paper describes an improved methodology for estimating the variation bounds of the residual displacements at shakedown. [ABSTRACT FROM AUTHOR]

This paper presents a numerical method for solving systems of partial differential equations describing flow in porous media with an embedded and inclined conduit pipe. This work considers a coupled continuum pipe-flow/Darcy model. The numerical schemes presented are based on combinations of the quasi-Wilson element on anisotropic mesh and the conforming finite element on regular mesh. The existence and uniqueness of the approximation solution are obtained. Optimal error estimates in bothL2andH1norms are obtained independent of the regularity condition on the mesh. Numerical examples show the accuracy and efficiency of the proposed scheme. [ABSTRACT FROM PUBLISHER]

A rapidly developing and equality-based society needs a reliable and attractive public transport system. With booming mobility in Lithuania, a great importance has been attached to the sustainable development concept, and public transport has been given priority in the urban transport system. Accessibility and comfort of public transport are essential indicators that guarantee equal travelling opportunities for all people. Transport modelling is the only economical and sufficiently reliable way to carry out a forward assessment of the impact of innovations to be applied to the overall system without involvement of passengers. This paper considers estimation of the origin–destination (O–D) matrix and its size correction. The public transport (PT) system of Vilnius City was taken as a basis for the research. Modelling of Vilnius City public transport was carried out with the help of VISUM software. Modelling of the public transport route network in Vilnius is aimed at improving the quality of life of inhabitants of the city. The O–D matrix is one of the key elements in modelling. Reliability of modelling results is based on reliability and size of the matrix. Although many scientists analyse the problem of estimating an O–D matrix, this paper focuses on the size of the O–D matrix required in order to give reliable results in PT modelling. During the first step, the matrix of 230 transport districts is estimated, which is reduced by 10 percent with every following step. The aim of this article is to find the break point in the size of O–D matrix where the reliability of PT modeling results falls. [ABSTRACT FROM AUTHOR]

Current network techniques used for project scheduling presume that there is only one logical sequence of activities. However, in reality, the precedence logic of activities is not necessarily unchangeable. There are two types of relations between activities: fixed (hard) and soft. Current scheduling methods do not differentiate between these two types of relations and require a planner to choose one particular logical sequence based on some assumptions. The paper presents a model that allows for “weakening” the links between activities, i.e. that permits concurrent execution of activities or reversing their order, but this may require additional resource-consuming works or expenditures. The model involves two subtypes of soft logic: REVERSED and CANCELED to represent the soft relations between activities. Its mathematical form is a mixed linear integer programming model of minimizing the project duration without exceeding the allowed budget. The paper presents an example of practical application of the method to scheduling interior finishing works. The results support the argument that using soft logic relations between construction activities provides more flexibility in reducing project duration, activities timing and resource allocation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyze the Bickel-Rosenblatt test for simple hypothesis in case of weakly dependent data. Although the test has nice theoretical properties, it is not clear how to implement it in practice. Choosing different bandwidth sequences first we analyze percentage rejections of the test statistic under H0 by some empirical simulation analysis. This can serve as an approximate rule for choosing the bandwidth in case of simple hypothesis for practical implementation of the test. In the recent paper [12] a version of Neyman goodness-of-fit test was established for weakly dependent data in the case of simple hypotheses. In this paper we also aim to compare and discuss the applicability of these tests for both independent and dependent observations. [ABSTRACT FROM AUTHOR]

The goal of this paper is to find a solution for route planning in a transport network where the network type can be arbitrary: a network of bus routes, a network of tram rails, a road network or any other type of a transport network. Furthermore, the costs of network elements are uncertain. The concept is based on the Dempster-Shafer theory and Dijkstras algorithm which helps with finding the best routes. The paper focuses on conventional studies without considering traffic accidents or other exceptional circumstances. The concept is presented by an undirected graph. In order to model conventional real transport, the influencing factors of traffic congestion have been applied in the abstract model using uncertain probabilities described by probability intervals. On the basis of these intervals, the cost intervals of each road can be calculated. Taking into account the uncertain values of costs, an algorithm has been outlined for determining the best routes from one node to all other nodes comparing cost intervals and using decision rules that can be defined by the end user, and if necessary, node by node. The suggested solution can be applied for both one type of network as well as for a combination of a few of those. [ABSTRACT FROM AUTHOR]

The paper investigates the general buckling of an axially loaded column using the finite element method with different slenderness ratios of axes x-x and z-z. The paper deals with three different modes of buckling. The conducted numerical experiments have suggested correction factors and appropriate buckling modes of the built-up columns. The obtained modelling results were compared with data on analytical calculations made according to Lithuanian national codes STR and Eurocode 3. The FEM analysis of the built-up column has showed that both codes (STR and EC3) are giving safe enough results for a considered type of conditions for column support. [ABSTRACT FROM AUTHOR]

Different types of planar broadband slow-wave systems are used for designing microwave devices. The papers published by Lithuanian scientists analyze and investigate the models of helical and meander slow-wave systems. The article carefully examines the applications of meander slow-wave systems and presents the areas where similar systems, e.g. mobile devices, RFID, wireless technologies are used and reviewed nowadays. The paper also focuses on the examples of the papers discussing antennas, filters and couplers that contain designed and fabricated meander slow-wave systems. [ABSTRACT FROM AUTHOR]

This paper presents estimation of the traffic accident costs in Serbia, based on original dominant costs model. Dominant costs model uses human capital approach and this model is developed for simple and quick calculation of the traffic accidents costs, because other simple methods as 1 million rules, are not suitable for estimation of the traffic accident costs in the countries with a low GDP per capita. Knowing the costs of traffic accidents is of crucial importance for establishing traffic safety to the level defined by the size of costs made as a consequence of unsafely. So, politicians, decision makers and stakeholders in the field of traffic safety often need quick estimation of the traffic accident costs and economic effects of the particular measures which are applied for decreasing the number and severity of traffic accidents. The estimation of the level of the traffic accidents costs in Serbia, based on the official data (from the Ministry of Interior of the Republic of Serbia) about traffic accidents in Serbia for 2008 is shown in this paper and the comparison between predicted and calculated value of the traffic accident costs for 2009 is also presented. [ABSTRACT FROM PUBLISHER]

Th e cost optimal design of the majority of distribution and servicing systems consists of decisions on a number and on the locations of facilities from which customers' demands are satisfied however, there are severe difficulties in solving exact procedures because the underlying mathematical model is NP-hard. Th ese decisions should respect some additional conditions as a limited capacity of located facilities. Th e objective is to minimize the overall costs of the system and to satisfy all customers' demands. In this paper, we enrich the set of constraints by a new requirement called sub-pool compactness. Th is property of customer subset influences the quality of vehicle routes s ubsequently formed in a sub-set of customers served by the same facility. Th is paper formulates the problem of the enriched capacitated facility location considering compactness condition, formalizes and studies the property of compactness and suggests the compound method solving this problem. [ABSTRACT FROM AUTHOR]

Statistical data on traffic accidents in 2008 in Lithuania is presented. Referring to statistical data, 'grounding on an obstacle' makes one-tenth of all registered traffic accidents - 9.4% (an obstacle may be a road guardrail, a lamp post, a tree, a bar, a gate, etc.). Road guardrails of various types are installed on the shoulders and dividing strips of urban and suburban roads. They are as follows: reinforced concrete guardrails, cable guardrails and metal guardrails. Metal guardrails, consisting of Σ-shape metal posts and a protective W-shape horizontal beam, are most popular. The authors of the present paper examine the deformation processes of the elements of the above mentioned guardrail. A mathematical model of metal road guardrail was developed. Metal road guardrail was modelled using one-dimensional first-order finite elements, taking into account only elastic deformations, as well as the effect of soil on the buried post section of the guardrail. Based on the developed mathematical model of metal road guardrail, the deflections of its elements caused by the impact of a vehicle moving at varying speed were determined. The obtained values of deflections of guardrail elements (a protective W-shape horizontal beam and a Σ-shape post) presented in paper do not exceed the admissible values (of beam deflections). [ABSTRACT FROM AUTHOR]

For examination of road accidents often calculations are being performed according to mathematical equations having many variables, real values of which are of stochastic nature and they depend on many accident factors. Therefore it is important to know limits of determination of final values of every being analysed parameter of car movement and their probabilistic characteristics. This paper presents some cases of simulation of some road situations by mathematical methods of calculations, which now are widely used for evaluation of accuracy of values of the calculated parameter (in this paper -- the braking distance). Also here is presented some analysis of these methods. The paper presents the following cases of car braking: braking with making attempts to prevent a collision with another car, braking through impact-to-pedestrian prevention and conventional (rectilinear) car braking. The main attention in the analysis of the mentioned road situations is paid to veracity of the car braking distance, i.e. to limits of variation of values of this parameter and also to influence of accidental factors on the final result which is being looked for. Some conclusions on the expediency of application of the described methods of calculations to analysis of road accidents are present. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop a mathematical model that could guide certain speed limits for vehicles on roads. Excessive speeds on roads have been a major indirect cause of deaths on highways due to the sudden impact of vehicles that lead to accidents. The model presented here is developed on a measure of impact force of two vehicles engaged in a head-on collision. A hypothetical case study was investigated based on the impact of force on the human body. The results showed a variation of speed with occupation position distance. The paper also examines the role of seatbelt as a safety feature for vehicle occupants. Practically, developing a quantitative approach for evaluating the impacts of speed would help road regulatory authorities in reducing accidents and deaths on roads. It would also assist them in tracking "road traffic offenders" by setting controls to which road users must conform. [ABSTRACT FROM AUTHOR]

The error estimation for quadrature formulas based on equally spaced nodes is discussed in this paper. The error estimates use embedded formulas and they are obtained for Newton-Cotes and Hermitian quadrature formulas. The coefficients of these formulas and error estimates are presented. The locally adaptive integration procedures implementing the truncation error estimation method proposed in this paper were developed in MATLAB and results of appropriate comparative tests are presented. [ABSTRACT FROM AUTHOR]

For the needs of this paper, certain area of issues associated with the infiltration process and neural networks were selected. In the scope of infiltration process, the measurements and analysis of air infiltration through the buildings have shown how difficult this process is in terms of strict mathematical models formulation. In the scope of neural networks, attention was given to multi-layer perceptrons and systems composed of them. It must be noted that, due to the novelty of this method, a detailed description of the neuron network theory was presented in this paper as well as a thorough discussion of the neuron modelling process. The work was carried out in two stages, with the first stage covering the development of detailed methodology for the construction of neural model and the second stage in which a developed methodology was applied to modelling real objects. [ABSTRACT FROM AUTHOR]

The paper is devoted to construction and development of new method for numerical solution of hyperbolic type equations [14, 17]. In the previous papers [4, 5, 6, 7, 8, 9] authors have investigated theoretically and tested experimentally 26 different finite-difference schemes on 4 point patterns for the simplest hyperbolic equation: linear advection equation. This equation has the main features of every hyperbolic equation and is the important part of many mathematical models. In other cases the advection operator is the important part of the full operator of the problem. All 26 schemes have been compared experimentally on the special representative set of tests. Nevertheless to simplicity of the equation, almost all schemes have different disadvantages. They are discussed in detail in the cited papers. So, the investigation of new schemes for this equation is still an important task. In [4, 5, 6, 7, 8, 9] some new schemes were constructed for solving this advection equation. The nonlinear monotone Babenko scheme (‘square’) proved to be the best among all 26 schemes. So, it is a big interest to generalize this scheme to more difficult equations. The impotent example is a quasi-linear advection equation. In this paper our basic aim is to construct a quasi-monotone nonlinear Babenko scheme for solving the quasi-linear advection equation and to test it experimentally. The monotonisation of the scheme is done by adding the artificial diffusion with limiters. We also present advanced results of comparative analysis of the new scheme with other known schemes. We have considered explicit and implicit upwind approximation schemes [4, 6, 13, 16] which is firstorder accurate in time and space, the Lax­Wendroff scheme [4] which is the first order accurate in time and second order accurate in space. We also analyze the monotonised ‘Cabaret’ scheme proposed in [10, 11 ]. It is second order accurate in time and space, and its monotonisation is based on apriori knowledge of the dependence region of the exact solution. The authors of this scheme called it by ‘jumping advection’. The considered schemes are compared numerically by using a set of tests, which is similar to one used in [4, 5, 6, 8]. [ABSTRACT FROM AUTHOR]