Search results for: direct vs. indirect values.

Authors: A. Raminfard, S. M. Shahrtash

Abstract:

In this paper, a new efficient method for load balancing in low voltage distribution systems is presented. The proposed method introduces an improved Leap-frog method for optimization. The proposed objective function includes the difference between three phase currents, as well as two other terms to provide the integer property of the variables; where the latter are the status of the connection of loads to different phases. Afterwards, a new algorithm is supplemented to undertake the integer values for the load connection status. Finally, the method is applied to different parts of Tabriz low voltage network, where the results have shown the good performance of the proposed method.

Keywords: Load balancing, improved leap-frog method, optimization algorithm, low voltage distribution systems.

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Authors: M. Bahgat, F. M. Awan, H. A. Hanafy, O. N. Alzeghaibi

Abstract:

Strontium hexaferrite (SrFe12O19; Sr-ferrite) is one of the well-known materials for permanent magnets. In this study, Mtype strontium ferrite was prepared by following the conventional ceramic method from steelmaking by-product. Initial materials; SrCO3 and by-product, were mixed together in the composition of SrFe12O19 in different Sr/Fe ratios. The mixtures of these raw materials were dry-milled for 6h. The blended powder was presintered (i.e. calcination) at 1000°C for different times periods, then cooled down to room temperature. These pre-sintered samples were re-milled in a dry atmosphere for 1h and then fired at different temperatures in atmospheric conditions, and cooled down to room temperature. The produced magnetic powder has a dense hexagonal grain shape structure. The calculated energy product values for the produced samples ranged from 0.3 to 2.4 MGOe.

Keywords: Ceramic route, Hard magnetic materials, Strontium ferrite.

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Authors: Ali Reza Tahavvor, Saeed Hosseini, Nazli Jowkar, Behnam Amiri

Abstract:

Heat transfer of leaves is a crucial factor in optimal operation of metabolic functions in plants. In order to quantify this phenomenon in different leaves and investigate the influence of leaf shape on heat transfer, natural convection for pine, orange and olive leaves was simulated as representatives of different groups of leaf shapes. CFD techniques were used in this simulation with the purpose to calculate heat transfer of leaves in similar environmental conditions. The problem was simulated for steady state and threedimensional conditions. From obtained results, it was concluded that heat fluxes of all three different leaves are almost identical, however, total rate of heat transfer have highest and lowest values for orange leaves, and pine leaves, respectively.

Keywords: Computational fluid dynamic, heat flux, heat transfer, natural convection.

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Authors: Stoyan Nedeltchev, Markus Schubert

Abstract:

By means of the ultrafast X-ray tomography facility, data were obtained at different superficial gas velocities U_G in a bubble column (0.1 m in ID) operated with an air-deionized water system at ambient conditions. Raw reconstructed images were treated by both the information entropy (IE) and the reconstruction entropy (RE) algorithms in order to identify the main transition velocities in a bubble column. The IE values exhibited two well-pronounced minima at U_G=0.025 m/s and U_G=0.085 m/s identifying the boundaries of the homogeneous, transition and heterogeneous regimes. The RE extracted from the central region of the column’s cross-section exhibited only one characteristic peak at U_G=0.03 m/s, which was attributed to the transition from the homogeneous to the heterogeneous flow regime. This result implies that the transition regime is non-existent in the core of the column.

Keywords: Bubble column, ultrafast X-ray tomography, information entropy, reconstruction entropy.

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Authors: Jieer Wu, Zheshu Ma

Abstract:

Nondestructive testing in engineering is an inverse Cauchy problem for Laplace equation. In this paper the problem of nondestructive testing is expressed by a Laplace-s equation with third-kind boundary conditions. In order to find unknown values on the boundary, the method of fundamental solution is introduced and realized. Because of the ill-posedness of studied problems, the TSVD regularization technique in combination with L-curve criteria and Generalized Cross Validation criteria is employed. Numerical results are shown that the TSVD method combined with L-curve criteria is more efficient than the TSVD method combined with GCV criteria. The abstract goes here.

Keywords: ill-posed, TSVD, Laplace's equation, inverse problem, L-curve, Generalized Cross Validation.

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Authors: Subramaniam Chandran

Abstract:

This paper explores the social and political imperatives in the sphere of public policy relating to social justice. In India, the colonial legacy and post-colonial social and political pressures sustained the appropriation of 'caste' category in allocating public resources to the backward class of citizens. For several reasons, 'economic' category could not be placed in allocating resources. This paper examines the reasons behind the deliberative exercises and formulating policies and seeks an alternative framework in realizing social justice in terms of a unified category. This attempt can be viewed as a reconciliation of traditional and modern values for a viable alternative in public policy making.

Keywords: Social justice, caste, public policy, communal quota

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Authors: Mihai Lungu

Abstract:

The paper presents the design of a mini-UAV attitude controller using the backstepping method. Starting from the nonlinear dynamic equations of the mini-UAV, by using the backstepping method, the author of this paper obtained the expressions of the elevator, rudder and aileron deflections, which stabilize the UAV, at each moment, to the desired values of the attitude angles. The attitude controller controls the attitude angles, the angular rates, the angular accelerations and other variables that describe the UAV longitudinal and lateral motions. To design the nonlinear controller, by using the backstepping technique, the nonlinear equations and the Lyapunov analysis have been directly used. The designed controller has been implemented in Matlab/Simulink environment and its effectiveness has been tested with a campaign of numerical simulations using data from the UAV flight tests. The obtained results are very good and they are better than the ones found in previous works.

Keywords: Attitude angles, Backstepping, Controller, UAV.

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Authors: Eunji Choi, Borang Park, Youngjae Choi, Jinwoo Moon

Abstract:

In this study, a predictive model for estimating the metabolism (MET) of human body was developed for the optimal control of indoor thermal environment. Human body images for indoor activities and human body joint coordinated values were collected as data sets, which are used in predictive model. A deep learning algorithm was used in an initial model, and its number of hidden layers and hidden neurons were optimized. Lastly, the model prediction performance was analyzed after the model being trained through collected data. In conclusion, the possibility of MET prediction was confirmed, and the direction of the future study was proposed as developing various data and the predictive model.

Keywords: Deep learning, indoor quality, metabolism, predictive model.

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Authors: M.Sushanth Babu, P.Krishna, U.Venu, M.Ranjith

Abstract:

In this paper, we evaluate the choice of suitable quantization characteristics for both the decoder messages and the received samples in Low Density Parity Check (LDPC) coded systems using M-QAM (Quadrature Amplitude Modulation) schemes. The analysis involves the demapper block that provides initial likelihood values for the decoder, by relating its quantization strategy of the decoder. A mapping strategy refers to the grouping of bits within a codeword, where each m-bit group is used to select a 2m-ary signal in accordance with the signal labels. Further we evaluate the system with mapping strategies like Consecutive-Bit (CB) and Bit-Reliability (BR). A new demapper version, based on approximate expressions, is also presented to yield a low complexity hardware implementation.

Keywords: Low Density parity Check, Mapping, Demapping, Quantization, Quadrature Amplitude Modulation

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Authors: Sérgio S. de Jesus, Edgar Leonardo Martínez, Aulus R.R. Binelli, Aline Santana, Rubens Maciel Filho

Abstract:

The speed profiles, gas holdup (e_G) and global oxygen transfer coefficient (k_La) from a stirred airlift bioreactor using water as the fluid model, was investigated by computational fluid dynamics modeling. The parameters predicted by the computer model were validated with the experimental dates. The CFD results were very close to those obtained experimentally. During the simulation it was verified a prevalent impeller effect at low speeds, propelling a large volume of fluid against the walls of the vessel, which without recirculation, results in low values of e_G and k_La; however, by increasing air velocity, the impeller effect is smaller with the air flow being greater, in the region of the riser, causing fluid recirculation, which explains the increase in e_G and k_La.

Keywords: CFD, Hydrodynamics, Mass transfer, Stirred airlift bioreactor.

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Authors: Porntip Ruengtam

Abstract:

This article is an extension of previous research presenting the relevant factors related to environmental perceptions, residential community, and the design of a healing environment, which have effects on the well-being and requirements of Thai elderly. Research methodology began with observations and interviews in three case studies in terms of the management processes and environment design of similar existing projects in Thailand. The interview results were taken to summarize with related theories and literature. A questionnaire survey was designed for data collection to confirm the factors of requirements in a residential community intended for the Thai elderly. A structural equation model (SEM) was formulated to explain the cause-effect factors for the requirements of a residential community for Thai elderly. The research revealed that the requirements of a residential community for Thai elderly were classified into three groups when utilizing a technique for exploratory factor analysis. The factors were comprised of (1) requirements for general facilities and activities, (2) requirements for facilities related to health and security, and (3) requirements for facilities related to physical exercise in the residential community. The results from the SEM showed the background of elderly people had a direct effect on their requirements for a residential community from various aspects. The results should lead to the formulation of policies for design and management of residential communities for the elderly in order to enhance quality of life as well as both the physical and mental health of the Thai elderly.

Keywords: Elderly, environmental design, residential community, structural equation modeling.

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Authors: B. Medjahed, M. A. Didi, B. Guezzen

Abstract:

In the present work, emulsion liquid membrane (ELM) technique was applied for the extraction of cadmium(II) present in aqueous samples. Aliquat 336 (Chloride tri-N-octylmethylammonium) was used as carrier to extract cadmium(II). The main objective of this work is to investigate the influence of various parameters affected the ELM formation and its stability and testing the performance of the prepared ELM on removal of cadmium by using synthetic solution with different concentrations. Experiments were conducted to optimize pH of the feed solution and it was found that cadmium(II) can be extracted at pH 6.5. The influence of the carrier concentration and treat ratio on the extraction process was investigated. The obtained results showed that the optimal values are respectively 3% (Aliquat 336) and a ratio (feed: emulsion) equal to 1:1.

Keywords: Cadmium, carrier, emulsion liquid membrane, surfactant.

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Authors: Seema Kapoor, Baljinder K. Gill, V. K. Rattan

Abstract:

Isobaric vapor-liquid equilibrium measurements are reported for the binary mixture of Methyl acetate and Isopropylbenzene at 97.3 kPa. The measurements have been performed using a vapor recirculating type (modified Othmer's) equilibrium still. The mixture shows positive deviation from ideality and does not form an azeotrope. The activity coefficients have been calculated taking into consideration the vapor phase nonideality. The data satisfy the thermodynamic consistency tests of Herington and Black. The activity coefficients have been satisfactorily correlated by means of the Margules, NRTL, and Black equations. A comparison of the values of activity coefficients obtained by experimental data with the UNIFAC model has been made.

Keywords: Binary mixture, Isopropylbenzene, Methyl acetate, Vapor-liquid equilibrium.

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Authors: H. Jusoh, N. Sapari, R.Z. Raja Azie

Abstract:

Iron in groundwater is one of the problems that render the water unsuitable for drinking. The concentration above 0.3 mg/L is common in groundwater. The conventional method of removal is by precipitation under oxic condition. In this study, iron removal under anaerobic conditions was examined by batch experiment as a main purpose. The process involved by purging of groundwater samples with H2S to form iron sulfide. Removal up to 83% for 1 mg/L iron solution was achieved. The removal efficiency dropped to 82% and 75% for the higher initial iron concentrations 3.55 and 5.01 mg/L, respectively. The average residual sulfide concentration in water after the process was 25*g/L. The Eh level during the process was -272 mV. The removal process was found to follow the first order reaction with average rate constant of 4.52 x 10-3. The half-life for the concentrations to reduce from initial values was 157 minutes.

Keywords: Anaerobic, chemical kinetics, hydrogen sulfide, iron, rate constant

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Authors: Luc Conti, Dimitry Dumont-Fillon, Harald van Lintel, Eric Chappel

Abstract:

Flow control valves comprise a silicon flexible membrane that deflects against a substrate, usually made of glass, containing pillars, an outlet hole, and anti-stiction features. However, there is a strong interest in using silicon instead of glass as substrate material, as it would simplify the process flow by allowing the use of well controlled anisotropic etching. Moreover, specific devices demanding a bending of the substrate would also benefit from the inherent outstanding mechanical strength of monocrystalline silicon. Unfortunately, direct Si-Si bonding is not easily achieved with highly structured wafers since residual stress may prevent the good adhesion between wafers. Using a thermoplastic polymer, such as parylene, as intermediate layer is not well adapted to this design as the wafer-to-wafer alignment is critical. An alternative anodic bonding method using an intermediate borosilicate layer has been successfully tested. This layer has been deposited onto the silicon substrate. The bonding recipe has been adapted to account for the presence of the SOI buried oxide and intermediate glass layer in order not to exceed the breakdown voltage. Flow control valves dedicated to infusion of viscous fluids at very high pressure have been made and characterized. The results are compared to previous data obtained using the standard anodic bonding method.

Keywords: Anodic bonding, evaporated glass, microfluidic valve, drug delivery.

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Authors: Bertha Sânduleasa, Aniela Matei, Mihaela Ghenţa, Nicolina Racoceanu

Abstract:

The increasing divorce and fertility rates outside of marriage, the changing values in the last decades have led to a high prevalence of single parent families. Currently, worldwide, singleparent families represent about a quarter of all families. Recent changes occurring in the structure of single-parent families and also the multitude of factors that influence the quality of life of these families require the development of new research tools in order to provide foundations for social policies addressed to this type of family. The purpose of this paper is to present an analysis concerning the quality of life for single parent families in Romania, based on data collected through a research methodology developed by the authors within a scientific research project funded by a national grant called Partnerships in priority areas.

Keywords: Family policies, quality of life, single-parent families, work-life balance.

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Authors: M. A. Basunia

Abstract:

Thirty three re-wetting tests were conducted at different combinations of temperatures (5.7- 46.30C) and relative humidites (48.2-88.6%) with barley. Two most commonly used thinlayer drying and rewetting models i.e. Page and Diffusion were compared for their ability to the fit the experimental re-wetting data based on the standard error of estimate (SEE) of the measured and simulated moisture contents. The comparison shows both the Page and Diffusion models fit the re-wetting experimental data of barley well. The average SEE values for the Page and Diffusion models were 0.176 % d.b. and 0.199 % d.b., respectively. The Page and Diffusion models were found to be most suitable equations, to describe the thin-layer re-wetting characteristics of barley over a typically five day re-wetting. These two models can be used for the simulation of deep-bed re-wetting of barley occurring during ventilated storage and deep bed drying.

Keywords: Thin-layer, barley, re-wetting parameters, temperature, relative humidity.

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Authors: Michal Cerny

Abstract:

We consider linear regression models where both input data (the values of independent variables) and output data (the observations of the dependent variable) are interval-censored. We introduce a possibilistic generalization of the least squares estimator, so called OLS-set for the interval model. This set captures the impact of the loss of information on the OLS estimator caused by interval censoring and provides a tool for quantification of this effect. We study complexity-theoretic properties of the OLS-set. We also deal with restricted versions of the general interval linear regression model, in particular the crisp input – interval output model. We give an argument that natural descriptions of the OLS-set in the crisp input – interval output cannot be computed in polynomial time. Then we derive easily computable approximations for the OLS-set which can be used instead of the exact description. We illustrate the approach by an example.

Keywords: Linear regression, interval-censored data, computational complexity.

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Authors: H.-G. Herrmann, M. Schwarz, J. Summa, F. Grossmann

Abstract:

In this work, different non-destructive testing methods for the characterization of defects and interfaces are presented. It is shown that, by means of active thermography, defects in the interface and in the carbon fiber reinforced polymer (CFRP) itself can be detected and determined. The bonding of metal and thermoplastic can be characterized very well by ultrasonic testing with electromagnetic acoustic transducers (EMAT). Mechanical testing is combined with passive thermography to correlate mechanical values with the defect-size. There is also a comparison between active and passive thermography. Mechanical testing shows the influence of different defects. Furthermore, a correlation of defect-size and loading to rupture was performed.

 

Keywords: Defect evaluation, EMAT, mechanical testing, thermography.

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Authors: A.K.Jayanthy, N.Sujatha, M.Ramasubba Reddy

Abstract:

Microcirculation is essential for the proper supply of oxygen and nutritive substances to the biological tissue and the removal of waste products of metabolism. The determination of blood flow in the capillaries is therefore of great interest to clinicians. A comparison has been carried out using the developed non-invasive, non-contact and whole field laser speckle contrast imaging (LSCI) based technique and as well as a commercially available laser Doppler blood flowmeter (LDF) to evaluate blood flow at the finger tip and elbow and is presented here. The LSCI technique gives more quantitative information on the velocity of blood when compared to the perfusion values obtained using the LDF. Measurement of blood flow in capillaries can be of great interest to clinicians in the diagnosis of vascular diseases of the upper extremities.

Keywords: Blood flow, Laser Doppler flowmeter, LSCI, speckle

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Authors: Jana M. Havigerová, Jiří Haviger

Abstract:

Paper deals with the topic of questions as important components of information behavior in the school. By analyzing the Corpus Schola2010, the state of contemporary education in terms of questioning is proven unsatisfactory: 80% of the questions are asked by teachers; most of teacher-s questions are asked at the beginning of the first grade, than their number decreases and is settling down on 80±10 questions per lesson. The average number of questions within one lesson per one pupil is generally less than one whole question. The highest values are achieved in the first, sixth, eighth and tenth grade,, i.e. in the transition years in which pupils are moving into higher levels of education and every following year it declines. We can state Czech school do not support questioning and question skill of their pupils, thereby typical Czech schools are neglecting the development of thinking, reasoning and cooperation of their pupils.

Keywords: information behavior, questions, primary and secondary education, Czech Republic

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Authors: Nasser AlShawaaf, Soo Hee Lee

Abstract:

Arts globalisation represents a different phenomenon than arts commercialisation which was facilitated by local cultural policies. This study examines the causes and effects of globalisation of art museums in France. Building on art literature, we conducted a literature review of cultural policies. Our findings show that the cultural policies of the French government since the 1980s of cultural democratisation, cultural decentralisation, and implementing market principles on the cultural sector are leading to arts globalisation. Although globalisation is producing economic benefits and enhancing cultural reach, however, the damages include artistic values and creativity, cultural heritage and representation, and the museum itself. Art museums and host cities could overcome negative consequences through a hybrid collection display and develop local collections gradually.

Keywords: Cultural policy, cultural decentralisation, cultural globalisation, art museums, contextual analysis, France.

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Authors: Salam K. Al-Dawery

Abstract:

Despite of few research works on municipal sludge, still there is a lack of actual data. Thus, this work was focused on the conditioning and rheology of fresh activated sludge. The effect of cationic polyelectrolyte has been investigated at different concentrations and pH values in a comparative fashion. Yield stress is presented in all results indicating the minimum stress that necessary to reach flow conditions. Connections between particle-particle is the reason for this yield stress, also, the addition of polyelectrolyte causes strong bonds between particles and water resulting in the aggregation of particles which required higher shear stress in order to flow. The results from the experiments indicate that the cationic polyelectrolytes have significant effluence on the sludge characteristic and water quality such as turbidity, SVI, zone settling rate and shear stress.

Keywords: Rheology, Polyelectrolyte, Settling volume index, Turbidity.

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Authors: Ruwaida Abdul Rasid, Kevin J. Hughes, Peter J. Heggs, Mohamed Pourkashanian

Abstract:

Heightened concerns over the amount of carbon emitted from coal-related processes are generating shifts to the application of biomass. In co-gasification, where coal is gasified along with biomass, the biomass may be fed together with coal (cofeeding) or an independent biomass gasifier needs to be integrated with the coal gasifier. The main aim of this work is to evaluate the biomass introduction methods in coal co-gasification. This includes the evaluation of biomass concentration input (B0 to B100) and its gasification performance. A process model is developed and simulated in Aspen HYSYS, where both coal and biomass are modelled according to its ultimate analysis. It was found that the syngas produced increased with increasing biomass content for both co-feeding and independent schemes. However, the heating values and heat duties decreases with biomass concentration as more CO2 are produced from complete combustion.

Keywords: Aspen HYSYS, biomass, coal, co-gasification modelling and simulation.

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Authors: Ahmet Tekcan, Arzu Özkoç

Abstract:

Let D = 1 be a positive non-square integer and let δ = √D or 1+√D 2 be a real quadratic irrational with trace t =δ + δ and norm n = δδ. Let γ = P+δ Q be a quadratic irrational for positive integers P and Q. Given a quadratic irrational γ, there exist a quadratic ideal Iγ = [Q, δ + P] and an indefinite quadratic form Fγ(x, y) = Q(x−γy)(x−γy) of discriminant Δ = t 2−4n. In the first section, we give some preliminaries form binary quadratic forms, quadratic irrationals and quadratic ideals. In the second section, we obtain some results on γ, Iγ and Fγ for some specific values of Q and P.

Keywords: Quadratic irrationals, quadratic ideals, indefinite quadratic forms, extended modular group.

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Authors: Kouassi Dongo, Christian Zurbrügg, Gueladio Cissé1, Brigit Obrist, Marcel Tanner, Jean Biémi

Abstract:

This study analyzed environmental health risks and people-s perceptions of risks related to waste management in poor settlements of Abidjan, to develop integrated solutions for health and well-being improvement. The trans-disciplinary approach used relied on remote sensing, a geographic information system (GIS), qualitative and quantitative methods such as interviews and a household survey (n=1800). Mitigating strategies were then developed using an integrated participatory stakeholder workshop. Waste management deficiencies resulting in lack of drainage and uncontrolled solid and liquid waste disposal in the poor settlements lead to severe environmental health risks. Health problems were caused by direct handling of waste, as well as through broader exposure of the population. People in poor settlements had little awareness of health risks related to waste management in their community and a general lack of knowledge pertaining to sanitation systems. This unfortunate combination was the key determinant affecting the health and vulnerability. For example, an increased prevalence of malaria (47.1%) and diarrhoea (19.2%) was observed in the rainy season when compared to the dry season (32.3% and 14.3%). Concerted and adapted solutions that suited all the stakeholders concerned were developed in a participatory workshop to allow for improvement of health and well-being.

Keywords: Abidjan, environmental health risks, informalsettlements, vulnerability, waste management.

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Authors: Bing-Jing Li, Sih-Yin Wang, Tse-Chun Yeh, Yuan-Bin Chen

Abstract:

Microwave dielectric ceramic materials of (Mg1-xNix)2(Ti0.95Sn0.05)O4 for x = 0.01, 0.03, 0.05, 0.07 and 0.09 were prepared and sintered at 1250–1400 ºC. The microstructure and microwave dielectric properties of the ceramic materials were examined and measured. The observations shows that the content of Ni2+ ions has little effect on the crystal structure, dielectric constant, temperature coefficient of resonant frequency (τf) and sintering temperatures of the ceramics. However, the quality values (Q×f) are greatly improved due to the addition of Ni2+ ions. The present study showed that the ceramic material prepared for x = 0.05 and sintered at 1325ºC had the best Q×f value of 392,000 GHz, about 23% improvement compared with that of Mg2(Ti0.95Sn0.05)O4.

Keywords: (Mg1-xNix)2(Ti0.95Sn0.05)O4, microwave dielectric ceramics, high quality factor, high frequency wireless communication.

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Authors: M.Imanova, G.Mehdiyeva, V.Ibrahimov

Abstract:

Solution of some practical problems is reduced to the solution of the integro-differential equations. But for the numerical solution of such equations basically quadrature methods or its combination with multistep or one-step methods are used. The quadrature methods basically is applied to calculation of the integral participating in right hand side of integro-differential equations. As this integral is of Volterra type, it is obvious that at replacement with its integrated sum the upper limit of the sum depends on a current point in which values of the integral are defined. Thus we receive the integrated sum with variable boundary, to work with is hardly. Therefore multistep method with the constant coefficients, which is free from noted lack and gives the way for finding it-s coefficients is present.

Keywords: Volterra integro-differential equations, multistepmethods, finite-difference methods, initial value problem

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Authors: Shagufta Tabassum, V. P. Pawar

Abstract:

The study of static dielectric properties in a binary mixture of 1,2 dichloroethane (DE) and n,n dimethylformamide (DMF) polar liquids has been carried out in the frequency range of 10 MHz to 30 GHz for 11 different concentration using time domain reflectometry technique at 10ºC temperature. The dielectric relaxation study of solute-solvent mixture at microwave frequencies gives information regarding the creation of monomers and multimers as well as interaction between the molecules of the binary mixture. The least squares fit method is used to determine the values of dielectric parameters such as static dielectric constant (ε₀), dielectric constant at high frequency (ε_∞) and relaxation time (τ).

Keywords: Excess parameters, relaxation time, static dielectric constant, time domain reflectometry.

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Authors: Soma Roychowdhury

Abstract:

This paper deals with a periodic-review substitutable inventory system for a finite and an infinite number of periods. Here an upward substitution structure, a substitution of a more costly item by a less costly one, is assumed, with two products. At the beginning of each period, a stochastic demand comes for the first item only, which is quality-wise better and hence costlier. Whenever an arriving demand finds zero inventory of this product, a fraction of unsatisfied customers goes for its substitutable second item. An optimal ordering policy has been derived for each period. The results are illustrated with numerical examples. A sensitivity analysis has been done to examine how sensitive the optimal solution and the maximum profit are to the values of the discount factor, when there is a large number of periods.

Keywords: Multi-period model, inventory, random demand, upward substitution.

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