Diagram Of System Research Articles

Critical Thinking Skills Development among Secondary School Students: An Analysis of Chemistry Textbook Grade X (2020)

The current study used qualitative analysis of the Chemistry textbook grade X through the facilitation of NVivo 12 software to analyze the textbook about critical thinking skills development. The textbook was selected through purposive sampling. The findings revealed that the textbook fostered critical thinking skills through several approaches relevant to chemistry concepts in to real-world, and their applications, asking open-ended questions, presenting merits and demerits of chemical processes, offering flow diagrams of industrial systems, comparing related concepts, and illustrating underlying chemical principles behind the phenomenon. The book urged students to apply chemistry principles critically in practical settings, evaluate them from different perspectives, rationalize complex processes thoroughly, and analyze their strengths and weaknesses in various approaches. Additionally, it invited them to discover the logic behind complex chemical systems and question what drives chemical behaviors at core levels. Moreover, explicit instruction on developing critical thinking skills should be better integrated into the curriculum with inquiry-based activities.

Development of decision-making technology for the provision of services in project implementation

The object of research is decision-making processes regarding the provision of services within the framework of cross-border projects. To achieve the aim of the research, an analysis of the service provision market was first conducted, its features have been revealed and problems arising in the processes of its functioning have been identified. The main problem is to find the optimal distribution of services between performers in the service management system. A mathematical model of the problem of single- and multi-criteria optimization has been developed, where the problem is decomposed into independent sub-problems. The problem is presented in the form of a linear programming problem. Various efficiency criteria of the found distributions are proposed. Depending on the number of criteria, the problem will be a single-criteria Boolean programming problem or a multi-criteria optimization problem. An iterative method for finding the optimal distribution of services has been created, and individual methods are laid out in the form of production rules, which is understandable and allows to gain new knowledge. Based on the obtained data, a decision-making technology has been developed regarding the distribution of service consumers between performers. At the same time, decision-making methods were used, which allow optimizing the processes of service provision. A systematic approach was used when designing information technology. This made it possible to create an effective and problem-relevant technology that helps in making informed decisions about the distribution of services between participants of cross-border projects. A structural and functional diagram of the decision support system has been developed. Its structural elements are detailed. The obtained results reflect a thorough analysis of the current state of the services market and the development of effective decision-making technology, which contributes to the optimization of work in the field of cross-border projects. This approach can be useful for various subjects involved in the implementation and coordination of international projects.

Experimental phase diagram study of the Eu2O3–Gd2O3–ZrO2 system at 1673 K and 1873 K and thermodynamic modeling of the ternary system

The phase relationships of Eu2O3 - Gd2O3 – ZrO2 system at 1873 K and 1673 K were investigated. To experimentally determine the phase relationships, the scanning electron microscopy, X-ray diffraction, and electron probe microanalyzer with wavelength dispersive spectrometer were employed. Our findings indicated that there were no ternary compounds. However, the binary pyrochlore phases (Eu2Zr2O7 and Gd2Zr2O7) formed a continuous solid solution, denotated as (Eu2-xGdx)Zr2O7 at 1673 K. Moreover, the solubility of Gd2O3 was observed to reach at least 28.0 mol.% along Eu2Zr2O7 - Gd2O3 composition line at 1873 K. Additionally, a continuous cubic solid solution was formed between C–Gd2O3 and C–Eu2O3 at 1673 K. The obtained experimental data were utilized to optimize the thermodynamic parameters for the Eu2O3 - Gd2O3 – ZrO2 system. Thermodynamic modeling was carried out to reproduce the present phase diagram experimental results and isothermal phase diagrams of this ternary system at 1673 and 1873 K were calculated.

RESEARCH OF THE FEATURES OF DIGITAL SIGNAL FORMATION IN SATELLITE COMMUNICATION LINES

Context. Remote sensing of the Earth is now widely used in various fields. One of the challenges of remote sensing is the creation of inexpensive satellite systems operating in polar circular orbits. These systems require the development of a receptiontransmission system that allows tens of gigabits of video information to be transmitted to an earth receiving station within ten minutes. That is, there is a need to create a communication system that provides high speed data transmission from small satellites weighing up to 50 kg.
 Objective. The aim of the work is to study the features of digital signal formation in modern satellite communication lines and to develop a communication system with a high data transfer rate (usually 300 Mbit/s), which can be applied to small Earth Observation satellites.
 Method. Proposed concept for building a high-speed data transmitter from a remote sensing earth satellite using commercially available off-the-shelf technology. Calculations of the power flow density created at the input of the receiving earth station were performed to find out the possible power of the on-board transmitter.
 Results. A diagram of a communication system based on the DVB-S standard using the technology of commercially available off-the-shelf products has been developed. The high-speed data transmitter is implemented on a Xilinx® Zynq Ultrascale+ ™ MPSoC FPGA microchip, which is located on an Enclustra Mercury XU8 module with a high-performance dual 16-bit AD9174 DAC. The on-board transmitter with a power of up to 2 W meets the requirements of the ITU Radio Regulations for the power flux density on the surface of the Earth, which is created by the radiation of the space station EESS in the range 8025–8400 MHz. It is shown that the energy reserve of the communication line of 3 dB is achieved for various commands for coding and modulation changes with an increase in the elevation angle, which allows to increase the speed of information transmission.
 Conclusions. An original receiving-transmitting system was developed for use in small satellites for remote sensing of the Earth. It is shown that the function of adaptive modeling of ACM of the DVB-S standard allows you to automatically change the transmission parameters in real time depending on the changing conditions of the channel, providing opportunities for more flexible and effective data transmission in various conditions, which will allow to increase the volumes of information transmitted by communication session. The proposed system operates in the X-band and is built using commercially available off-the-shelf products. An antenna with double circular polarization is used as the emitter. Two physical channels represent two polarization modes: right circular polarization and left circular polarization, each of which has three frequency channels.

Complicated flow in tip flow field of a compressor tandem cascade using delayed detached eddy simulation

The complex flow characteristics in the tip region of a tandem cascade with tip clearance have been calculated and analyzed using Delayed Detached Eddy Simulation (DDES). The coherent mechanism of the vortex structures near the blade tip was discussed, and the unsteady behaviors and features in the tip flow field were analyzed. Additionally, the interaction between the tip leakage flow and the gap jet was revealed. The results show that, compared to the datum cascade, the blade tip load of the rear blade increases while that of the front blade decreases. Unsteady fluctuations of the tandem cascade are mainly caused by the interaction between the tip leakage flow and gap jet, and by the mixing of the vortex structures, but there is no essential change in the spectrum feature of the tip leakage flow. Finally, a detailed analysis of the development of vortices in the tip region is conducted by the topological structures of the flow field. Combined with the three-dimensional vortex structures, the schematic diagram of the vortex system of the datum single-row cascade and tandem cascade is summarized.

Determination and molecular simulation of ternary solid–liquid phase equilibrium of succinic acid + maleic acid + water from 283.15 K to 333.15 K

This study used the isothermal saturation gravimetric method to examine the solid–liquid phase equilibrium relationships composed of succinic acid + maleic acid + water spanning from 283.15 K to 333.15 K. The experimental data were utilized for the purpose of plotting the equilibrium phase diagrams of ternary systems in the studied temperature range. There were three crystalline regions in each isothermal ternary phase diagram, two saturation boundary curves, and a co-saturation point. To broaden the use of data from binary and ternary phase equilibrium measurements, Wilson and NRTL models were utilized for correlation and expectation, while relative average deviation (RAD) and root mean square deviation (RMSD) were utilized to evaluate the computational exactness. The results show that the theoretically calculated values were found to be in near agreement with the experimental values, and both models were able to obtain more precise theoretical data under different experimental conditions. In addition, molecular simulation was employed to elucidate the interaction between succinic acid, maleic acid, and water. This study provides accurate and reliable data for the separation of succinic acid and maleic acid mixture in water. These findings can be utilized to make sense of the dissolvability conduct of succinic acid and maleic acid in aqueous solution.

Steady-state selection in multi-species driven diffusive systems

We introduce a general method to determine the large-scale non-equilibrium steady-state properties of one-dimensional multi-species driven diffusive systems with open boundaries, generalizing thus the max-min current principle known for systems with a single type of particles. This method is based on the solution of the Riemann problem of the associated system of conservation laws. We demonstrate that the effective density of a reservoir depends not only on the corresponding boundary hopping rates but also on the dynamics of the entire system, emphasizing the interplay between bulk and reservoirs. We highlight the role of Riemann variables in establishing the phase diagram of such systems. We apply our method to three models of multi-species interacting particle systems and compare the theoretical predictions with numerical simulations.

Nonlinear vibration characteristics of axially moving anisotropic membrane with gas-thermal-elastic coupling

In the actual printing production process, the printing electronic motion membrane is susceptible to transverse vibration caused by interference from air drag, temperature changes, and other external conditions, resulting in membrane wrinkles, slippage, and other phenomena in the transmission process. We studied the bifurcation and chaos movement properties of anisotropic membranes under air drag and temperature. According to D’Alembert’s theory and von Kármán’s principle, the nonlinear dynamic differential formulas of axially moving anisotropic membranes with gas-thermal-elastic coupling are established. The Galerkin method is applied to discretize the formulas to obtain the state equation of the system. Finally, numerical simulations are performed by applying the fourth-order Runge–Kutta method to analyze the bifurcation and chaos of the system in terms of orthotropic coefficient, dimensionless air drags, and dimensionless temperature. The bifurcation diagrams, Lyapunov exponent diagrams, displacement time-history diagrams, phase-trajectory plane diagrams, and Poincaré diagrams of the membrane system are obtained. The results show that the anisotropic coefficient, dimensionless air drag, and dimensionless temperature significantly impact the investigated nonlinear dynamic of the anisotropic membrane, which provides a theoretical basis for production efficiency and high-quality printing equipment.

Development of A Precision Wind Generator Control System

The issues of developing a precision control system for a wind generator are considered. A comparative analysis with other devices was carried out, as a result of which all the shortcomings of these systems were taken into account. The type of generator, the operating mode of the wind generator, the system for regulating the angle of rotation of the blades and the cost of the control system are the most important factors in the development of this system. Methods for eliminating the shortcomings of similar devices are proposed and justified in order to eliminate them when developing a circuit for a new device. The diagram of the control system of a wind power plant in the MATLAB environment is presented. The functional and structural components of the developed device are indicated and the operating methods of each of its parts are described. Distinctive features and advantages of this device are considered

Научно-технологические основы разработки месторождений подземных вод с принудительным самоизливом

Introduction. A two-well borehole system is proposed, providing for the extraction of groundwater by forced self-discharge. The essence is to create conditions for the emergence of a down hole energy source in the form of hydraulic shocks, alternating hydraulic impulses affecting aquifers and ensuring the rise of water to a height. Materials and methods of research. A block diagram of a two-well circulation system of wells consisting of an above-ground tank, an injection well with a ledge, a water-lifting well connected by an intermediate trunk. The objects of the study are the shape of the above–ground tank, its connection with the injection well, the location of the ledge and the conditions for conducting a water circulation channel from the ledge to the above-ground tank. Methods – calculation of the energy characteristics of a two-well system, experiments to study the mechanism of the origin of incomplete hydraulic shock, boundary values of the modes of water movement in the system and the coefficient of injection of rocks. They were carried out on the installation with the possibility of visual observation of the processes taking place in the system. Results. When an incomplete hydraulic shock occurs on the ledge of the injection well, the flow is divided into core and lateral components. The water flow from the tank into the well was in the range of 20–60 l/min. The origin of incomplete hydraulic shock occurred at a water flow rate of 20 l/min, with an increase in pressure up to 7.0 atmospheres. The boundary values of the laminar flow mode of water flow are 60 l/min. The height of the water rise (H) mainly depends on the depth of origin of incomplete hydraulic shock (H1). The ejection coefficient of rocks decreases with increasing flow rate of the working flow. Discussion. The results of the study are due to the design features of the elements of the two-well circulation system of wells. The operating conditions of the system are the type of communication ground tank – injection well – aquifer, the location of the ledge, the execution of the water circulation channel from the ledge to the entrance to the ground tank with one diameter, the preservation of the laminar flow regime of water, the exclusion of pressure loss and water leakage in the intermediate trunk. Conclusions. The conditions for the origin of a down hole energy source in the form of renewable hydraulic shocks, which have a hydro impulsive effect on aquifers, have been established. A block diagram of the injection and circulation system of wells for the extraction of groundwater by forced self-discharge has been formed. Resume. The validity of the idea of injection-forced self-discharge of groundwater is proved by the results of research. The results are applicable in the development of groundwater with low-pressure and non-pressure aquifers. The objects of future research are the optimal ratios of the diameter of the injection well and the passage section of the ledge, the expansion of the boundary values of the flow transition from laminar to turbulent motion, and an increase in the ejection coefficient.

Analysis of the most probable exit path in the synthetic gene network with genetic toggle

In this paper, the most probable exit path is applied to understand the switching of a bistable synthetic gene network with genetic toggle in Escherichia coli from a new perspective. It is worth mentioning that the most probable exit path is a deterministic indicator for researching stochastic system, and its role is analogous to the phase diagram and time history diagram of deterministic system. Firstly, the large deviation theory proves that when a dynamic system has a stable equilibrium point, the cumulative effect of its long-term action can make its sample trajectory reach another region with a probability of 1 from the attractive region under weak random disturbance. The concept of the most probable exit path is given by defining Freidlin-Wentzell action functional. Moreover, considering the noise intensity, Onsager-Machlup action functional is defined to obtain the most probable exit path of the system subject to random disturbance. Based on the Onsager-Machlup action functional, it can be observed that the impact of two types of noise intensities on the most probable exit path for the transition of the system. In addition, based on vector field decomposition, energy landscape is used to analyze the global stability of the system. Finally, this article intuitively demonstrates the switching process of the system with genetic toggle. The analysis of Onsager-Machlup action functional reveals that two independent noises have opposite effects on the system switching. The increase in the intensity of the second Gaussian noise is conductive to more accurately observing the most probable exit path of the system. According to the energy landscape, the reduction of noise intensity is not conductive to switching of the system with genetic toggle.

Borax preparation from Na-B-Si-containing solution by carbonation and multi-step crystallization

The Na-B-Si-containing solution was derived from ludwigite ore through a two-step process involving soda-ash roasting and subsequent grind-leaching. This study employed a carbonation-crystallization approach to comprehensively utilize the valuable components in the solution, aiming to produce borax while simultaneously generating sodium carbonate and silica. The initial carbonation precipitation achieved a high desilication ratio of 95.54 % through nano-sized silica particle formation. Meanwhile, the boron conversion ratio reached 94 %, with negligible boron loss due to efficient metaborate-to-borate transformation. To guide the crystallization separation of Na2CO3 and Na2B4O7, phase diagrams of the ternary system (Na2CO3 + Na2B4O7 + H2O) were experimentally constructed at 308.15 k and 333.15 k. Crystallization was then conducted at 278.15 K for 2 h, yielding a Na2B4O7·10H2O product with 96.45 % purity. The remaining filtrate was evaporated and crystallized to obtain the Na2CO3 product, which can be reused in the previous roasting process.

Phase diagram of a rigid rod system with attractive end groups

We present a molecular dynamics study into the thermotropic liquid crystalline phase behaviour of a coarse-grained model of a rigid bolaamphiphilic molecule. The model consists of 11 spherical beads held in a fixed linear arrangement, where the two opposing terminal beads are self-attracting, mimicking hydrophilic segments and the remaining internal beads, as well as cross-bead interactions, are softly repulsive, mimicking hydrophobic organic segments. The effect of the model’s end bead self-attraction strength on liquid crystalline phase behaviour is studied. Coexistence points between the smectic A, nematic and isotropic phases exhibited by the model are determined following a thermodynamic integration pathway, using equations of state constructed by multiple histogram reweighting of simulation data. Variants of Gibbs–Duhem integration are used to trace pressure–temperature coexistence curves. Under isobaric conditions, the effect of increasing the end-group self-attraction on the nematic–isotropic coexistence temperature is relatively small; however, the nematic phase stability is reduced at the expense of a significant increase in the smectic A–nematic coexistence temperature. Lower temperature simulations show the approximate smectic A–crystalline transition temperature to be only weakly dependent on the strength of the end-group self-attraction.

Research Directions of the Energy Transformation Impact on the Economy in the Aspect of Asset Analysis

The challenges of climate change encourage immediate solutions by creating the conditions for energy transformation. This process is significantly related to capital investments and the conversion of existing assets to clean energy sources. Due to the need to save resources, workplaces, and public favor, specific studies involving different data groups are necessary. This article presents key data sources for analyzing the impact of energy transformation on Lithuanian regions—governance, potential, and existing power indicators. The economic, social, and governance data combined in the article will allow us to determine the perspectives of sustainable energy transformation in the regions. The article showed that in certain regions there may be major, complex problems that hinder the breakthrough of the energy system. Cluster analysis and a generic system diagram were used for the research, which showed that municipalities have a wide potential for energy transformation. The research emphasizes the governance component as a key success factor. After reorganizing the management of municipal enterprises, further actions can be initiated, since emerging competences allow progress to be made efficiently and with less time spent. The asset analysis methodology presented in the article allows for the identification of the main groups of assets that can be converted in the short term for the purpose of energy transformation, according to sustainable development principles. These decisions provide an opportunity for decision-makers to consistently implement energy transformation decisions.

Dynamic diffusive interfacial transport (D-DIT): A novel quantitative swelling technique for developing binary phase diagrams of aqueous surfactant systems.

Current methods to develop surfactant phase diagrams are time-intensive and fail to capture the kinetics of phase evolution. Here, the design and performance of a quantitative swelling technique to study the dynamic phase behavior of surfactants are described. The instrument combines cross-polarized optical and short-wave infrared imaging to enable high-resolution, high-throughput, and in situ identification of phases and water compositions. Data across the entire composition spectrum for the dynamics and phase evolution of a binary aqueous non-ionic surfactant solution at two isotherms are presented. This instrument provides pathways to develop non-equilibrium phase diagrams of surfactant systems-critical to predicting the outcomes of formulation and processing. It can be applied to study time-dependent material relationships across a diverse range of materials and processes, including the dissolution of surfactant droplets and the drying of aqueous polymer films.

Сравнительный анализ принципов проектирования электрогидравлических рулевых машин скоростных судов

The composition and control principles of steering electro-hydraulic machines of a simple and follower type, intended for rudder shifting of small and high-speed vessels are considered. An analysis of the functioning of existing steering gears for the specified group of vessels was carried out. Deficiencies in the work associated with the element base and composition of the control and electric drive systems of the analyzed steering machines have been formed. The features of the operation of hydraulic systems with drive electric motors of pumps made on direct current, revealed as a result of experiments, are shown. Variants of technical solutions for improving the energy performance of the electric drive are proposed. A comparative analysis of the operation of steering machines with AC and DC drives has been carried out. An assessment of steering machines operation in normal and emergency modes is given. Structural diagrams of control systems of simple and follow-up action are proposed, taking into account the operating features identified during the analysis and the requirements of the Russian classification society. The possibility of implementing an SM electric drive built using a frequency converter – asynchronous motor system powered by an alternating current network and an emergency source has been shown. Options for the implementation of electric drives for pumps of hydraulic stations with a high-voltage battery are proposed. The possibility of creating domestic installations for steering and other ship mechanisms, according to the proposed structural diagrams of control systems for hydraulic stations for high-speed ships, is shown. Recommendations are given for the construction of steering gears for high-speed vessels with a total displacement of up to 100 tons using domestic electrical equipment.

Экономическая эффективность применения систем мониторинга крутильных колебаний на судах

A torsional vibration monitoring system is being investigated, and an assessment of the economic efficiency of its implementation on ships is made. A schematic diagram of the torsional vibration monitoring system is illustrated and a photograph of an experimental sample of the monitoring system is provided. An assessment of the economic efficiency of the implementation of torsional vibration monitoring systems on ships is being carried out to prevent the occurrence of emergency situations with marine propulsion systems. The rules of classification societies, scientific and technical literature in the field of torsional oscillations and industrial economics, and the authors' own research were used as materials. The methods used are analysis and computational experiment. Data on the economic costs of the shipowner in the event of emergency situations in case of fatigue failures of elements of ship's engine and propulsion systems were obtained. An assessment of the costs for the development, installation and maintenance of a torsional vibration monitoring system on ships was made; as well as an approximate assessment of the volume of the Russian domestic market for installation and maintenance of torsional vibration monitoring systems on ships. It is noted that the cost of the consequences of propeller shaft failures ranges from several million to tens of millions of rubles. It is concluded that the development and implementation of torsional vibration monitoring systems will reduce the cost of the shipowner for a routine assessment of the technical condition of torsional vibration dampers and reduce the risks of costly accidents with shipboard engine complexes.

Spectroscopic and Computational Study of ZnCl2-Methanol Low-Melting-Temperature Mixtures.

Alcoholic electrolyte mixtures have wide applications in industries. In this study, a series of mixtures composed of ZnCl2 and methanol (MeOH) with ZnCl2 mol % from 6.7 to 25 were prepared, and their spectral, structural, and thermodynamic properties were studied using infrared (IR) spectroscopy, differential scanning calorimetry (DSC), and density functional theory (DFT) calculations. The DFT-assisted analysis of excess spectra, supported by 2D-correlation spectroscopy, led to the identification of the major constituents of ZnCl2-MeOH mixtures, namely, MeOH monomer, MeOH dimer, and ZnCl2-3MeOH complex, produced after dissociation of MeOH trimer which represents the bulk methanol. The Hirshfeld charge analysis showed that in the competition between the O-H···Cl hydrogen bond (H-bond) and Zn ← O coordination bond to transfer charge in ZnCl2-MeOH complexes, the latter always dominates, making MeOH positively charged. The phase diagram of the binary system showed the presence of V-shaped glass transition temperatures (Tg), characteristic of low-melting mixture solvents (LoMMSs). The present study provides insights into the microscopic properties of the system and sheds light on the understanding of the general principles to prepare deep-eutectic solvents (DESs) or LoMMSs using inorganic salts and alcoholic compounds.

Eutectic Resolves Lysolipid Paradox in Thermoresponsive Liposomes.

A better molecular understanding of the temperature-triggered drug release from lysolipid-based thermosensitive liposomes (LTSLs) is needed to overcome the recent setbacks in developing this important drug delivery system. Enhanced drug release was previously rationalized in terms of detergent-like effects of the lysolipid monostearyl lysophosphatidylcholine (MSPC), stabilizing local membrane defects upon LTSL lipid melting. This is highly surprising and here referred to as the 'lysolipid paradox,' because detergents usually induce the opposite effect─they cause leakage upon freezing, not melting. Here, we aim at better answers to (i) why lysolipid does not compromise drug retention upon storage of LTSLs in the gel phase, (ii) how lysolipids can enhance drug release from LTSLs upon lipid melting, and (iii) why LTSLs typically anneal after some time so that not all drug gets released. To this end, we studied the phase transitions of mixtures of dipalmitoylphosphatidylcholine (DPPC) and MSPC by a combination of differential scanning and pressure perturbation calorimetry and identified the phase structures with small- and wide-angle X-ray scattering (SAXS and WAXS). The key result is that LTSLs, which contain the standard amount of 10 mol % MSPC, are at a eutectic point when they release their cargo upon melting at about 41 °C. The eutectic present below 41 °C consists of a MSPC-depleted gel phase as well as small domains of a hydrocarbon chain interdigitated gel phase containing some 30 mol % MSPC. In these interdigitated domains, the lysolipid is stored safely without compromising membrane integrity. At the eutectic temperature, both the MSPC-depleted bilayer and interdigitated MSPC-rich domains melt at once to fluid bilayers, respectively. Intact, fluid membranes tolerate much less MSPC than interdigitated domains─where the latter have melted, the high local MSPC content causes transient pores. These pores allow for fast drug release. However, these pores disappear, and the membrane seals again as the MSPC distributes more evenly over the membrane so that its local concentration decreases below the pore-stabilizing threshold. We provide a pseudobinary phase diagram of the DPPC-MSPC system and structural and volumetric data for the interdigitated phase.

Stability and modal evolution characteristics of pipe-in-pipe system with internal intermediate support

In this paper, the stability of the pipe-in-pipe (PIP) conveying fluid system with intermediate supports are studied. The focus of the study is mainly on the influence of the intermediate supports on the critical velocity boundary. The governing equations of the coupled system are established according to Hamilton’s principle, and the modal functions in analytical solution form and the frequency equation in implicit function form are obtained by using the Laplace transform technique. In the numerical discussion part, the influence of the stiffness and position of the support on frequencies, modal functions, and critical flow velocity of the system is discussed. In the stability region diagrams of the cantilever PIP system, it is found that when the position and stiffness of the support change, the minimum critical flow velocity is frequently converted between different modes, and there are two different types of critical flow velocity conversion phenomena (CFVC). And high-order flutter instability, ‘jump’ phenomenon, S-shaped critical velocity boundary and modal conversion phenomenon are discussed in detail. In addition, the effective and negative regions of the support in the cantilever PIP and simply supported PIP systems are given.