Search results for: psychometric properties

Authors: M.Jalali Azizpour, S.Norouzi, H.mohammadi Majd, M.M.Rabieh, D.Sajedipour, A. Jaderi

Abstract:

The mechanical and tribological properties in WC-Co coatings are strongly affected by hardness and elasticity specifications. The results revealed the effect of spraying distance on microhardness and elasticity modulus of coatings. The metallurgical studies have been made on coated samples using optical microscopy, scanning electron microscopy (SEM).

Keywords: Elasticity modulus, HVOF, Micro-indentation, Thermal spray, WC-Co

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Authors: Ginalber L. O. Serra

Abstract:

This work proposes a recursive weighted ELS algorithm for system identification by applying numerically robust orthogonal Householder transformations. The properties of the proposed algorithm show it obtains acceptable results in a noisy environment: fast convergence and asymptotically unbiased estimates. Comparative analysis with others robust methods well known from literature are also presented.

Keywords: Stochastic Systems, Robust Identification, Parameter Estimation, Systems Identification.

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Authors: Karim Abouelmehdi, Loubna Dali, Elmoutaoukkil Abdelmajid, Hoda Elsayed Eladnani Fatiha, Benihssane Abderahim

Abstract:

The security of cloud services is the concern of cloud service providers. In this paper, we will mention different classifications of cloud attacks referred by specialized organizations. Each agency has its classification of well-defined properties. The purpose is to present a high-level classification of current research in cloud computing security. This classification is organized around attack strategies and corresponding defenses.

Keywords: Cloud computing, security, classification, risk.

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Authors: Xiang Liu, Ciprian Coman

Abstract:

The wrinkling of a thin elastic bi-annular plate with piecewise-constant mechanical properties, subjected to radial stretching, is considered. The critical wrinkling stretching loading and the corresponding wrinkling patterns are extensively investigated, together with the roles played by both the geometrical and mechanical parameters.

Keywords: bi-annular plate, wrinkling pattern, critical stretching loading.

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Authors: Kaylash Chaudhary, Ansgar Fehnker

Abstract:

There are many virtual payment systems available to conduct micropayments. It is essential that the protocols satisfy the highest standards of correctness. This paper examines the Netpay Protocol [3], provide its formalization as automata model, and prove two important correctness properties, namely absence of deadlock and validity of an ecoin during the execution of the protocol. This paper assumes a cooperative customer and will prove that the protocol is executing according to its description.

Keywords: Model, Verification, Micropayment.

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Authors: Eric Muñoz de la Torre, Julián González Trinidad, Efrén González Ramírez

Abstract:

Rain varies greatly in its duration, intensity, and spatial coverage, it is important to have sub-daily rainfall data for various applications, including risk prevention, however, the ground measurements are limited by the low and irregular density of rain gauges. An alternative to this problem is the Satellite Precipitation Products (SPPs) that use passive microwave and infrared sensors to estimate rainfall, as IMERG, however, these SPPs have to be validated before their application. The aim of this study is to evaluate the performance of the IMERG: Integrated Multi-satellitE Retrievals for Global Precipitation Measurement final run V06B SPP in a semi-arid region of Mexico, using four rain gauges sub-daily data of October 2019 and June to September 2021, using the Minimum inter-event Time (MIT) criterion to separate unique rain events with a dry period of 10 hrs for the purpose of evaluating the rainfall properties (depth, duration and intensity). Point to pixel analysis, continuous, categorical, and volumetric statistical metrics were used. Results show that IMERG is capable to estimate the rainfall depth with a slight overestimation but is unable to identify the real duration and intensity of the rain events, showing moderate overestimations and underestimations, respectively. The study zone presented 80 to 85% of convective rain events, the rest were stratiform rain events, classified by the depth magnitude variation of IMERG pixels and rain gauges. IMERG showed poorer performance at detecting the first ones but had a good performance at estimating stratiform rain events that are originated by Cold Fronts.

Keywords: IMERG, rainfall, rain gauge, remote sensing, statistical evaluation.

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Authors: Dongxiao Sun-Waterhouse, Shiji Nair, Reginald Wibisono, Sandhya S. Wadhwa, Carl Massarotto, Duncan I. Hedderley, Jing Zhou, Sara R. Jaeger, Virginia Corrigan

Abstract:

Attempts to add fibre and polyphenols (PPs) into popular beverages present challenges related to the properties of finished products such as smoothies. Consumer acceptability, viscosity and phenolic composition of smoothies containing high levels of fruit fibre (2.5-7.5 g per 300 mL serve) and PPs (250-750 mg per 300 mL serve) were examined. The changes in total extractable PP, vitamin C content, and colour of selected smoothies over a storage stability trial (4°C, 14 days) were compared. A set of acidic aqueous model beverages were prepared to further examine the effect of two different heat treatments on the stability and extractability of PPs. Results show that overall consumer acceptability of high fibre and PP smoothies was low, with average hedonic scores ranging from 3.9 to 6.4 (on a 1-9 scale). Flavour, texture and overall acceptability decreased as fibre and polyphenol contents increased, with fibre content exerting a stronger effect. Higher fibre content resulted in greater viscosity, with an elevated PP content increasing viscosity only slightly. The presence of fibre also aided the stability and extractability of PPs after heating. A reduction of extractable PPs, vitamin C content and colour intensity of smoothies was observed after a 14-day storage period at 4°C. Two heat treatments (75°C for 45 min or 85°C for 1 min) that are normally used for beverage production, did not cause significant reduction of total extracted PPs. It is clear that high levels of added fibre and PPs greatly influence the consumer appeal of smoothies, suggesting the need to develop novel formulation and processing methods if a satisfactory functional beverage is to be developed incorporating these ingredients.

Keywords: Apple fibre, apple and blackcurrant polyphenols, consumer acceptability, functional foods, stability.

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Authors: Zue Chin Chang

Abstract:

RF magnetron sputtering is used on the ceramic targets, each of which contains zinc oxide (ZnO), zinc oxide doped with aluminum (AZO) and zinc oxide doped with gallium (GZO). The XRD analysis showed a preferred orientation along the (002) plane for ZnO, AZO, and GZO films. The AZO film had the best electrical properties; it had the lowest resistivity of 6.6 × 10-4 cm, the best sheet resistance of 2.2 × 10-1 Ω/square, and the highest carrier concentration of 4.3 × 1020 cm-3, as compared to the ZnO and GZO films.

Keywords: Aging, films, Microstructure, Photoelectric Property.

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Authors: Nawin Raj, Zhenquan Li

Abstract:

Streamtube is used to visualize expansion, contraction and various properties of the fluid flow. These are useful in fluid mechanics, engineering and geophysics. The streamtube constructed in this paper only reveals the flow expansion rate along streamline. Based on the mass conservative streamline, we will show how to construct the streamtube.

Keywords: Flow visualization, mass conservative, streamline, streamtube.

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Authors: Dong Xie, Jun Zhao, Yiming Weng

Abstract:

The objective of this study was to synthesize and characterize the poly(alkenoic acid)s with different molecular structures, use these polymers to formulate a dental cement restorative, and study the effect of molecular structures on reaction kinetics, viscosity, and mechanical strengths of the formed polymers and cement restoratives. In this study, poly(alkenoic acid)s with different molecular structures were synthesized. The purified polymers were formulated with commercial Fuji II LC glass fillers to form the experimental cement restoratives. The reaction kinetics was studied via 1HNMR spectroscopy. The formed restoratives were evaluated using compressive strength, diametral tensile strength, flexural strength, hardness and wear-resistance tests. Specimens were conditioned in distilled water at 37oC for 24 h prior to testing. Fuji II LC restorative was used as control. The results show that the higher the arm number and initiator concentration, the faster the reaction was. It was also found that the higher the arm number and branching that the polymer had, the lower the viscosity of the polymer in water and the lower the mechanical strengths of the formed restorative. The experimental restoratives were 31-53% in compressive strength, 37- 55% in compressive modulus, 80-126% in diametral tensile strength, 76-94% in flexural strength, 4-21% in fracture toughness and 53-96% in hardness higher than Fuji II LC. For wear test, the experimental restoratives were only 5.4-13% of abrasive and 6.4-12% of attritional wear depths of Fuji II LC in each wear cycle. The aging study also showed that all the experimental restoratives increased their strength continuously during 30 days, unlike Fuji II LC. It is concluded that polymer molecular structures have significant and positive impact on mechanical properties of dental cement restoratives.

Keywords: Poly(alkenoic acid)s, molecular structures, dental cement, mechanical strength.

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Authors: Hussain Al-Qassem

Abstract:

In this paper we study the boundedness properties of certain oscillatory integrals with polynomial phase. We obtain sharp estimates for these oscillatory integrals. By the virtue of these estimates and extrapolation we obtain Lp boundedness for these oscillatory integrals under rather weak size conditions on the kernel function.

Keywords: Fourier transform, oscillatory integrals, Orlicz spaces, Block spaces, Extrapolation, Lp boundedness.

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Authors: Andrey V. Timofeev

Abstract:

A method is proposed for stable detection of seismoacoustic sources in C-OTDR systems that guarantee given upper bounds for probabilities of type I and type II errors. Properties of the proposed method are rigorously proved. The results of practical applications of the proposed method in a real C-OTDRsystem are presented.

Keywords: Guaranteed detection, C-OTDR systems, change point, interval estimation.

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Authors: D. Allison, A. Didenko, G. Miller

Abstract:

The link between coordinate transformations in the plane and their effects on the graph of a function can be difficult for students studying college level mathematics to comprehend. To solidify this conceptual link in the mind of a student Microsoft Excel can serve as a convenient graphing tool and pedagogical aid. The authors of this paper describe how various transformations and their related functional symmetry properties can be graphically displayed with an Excel spreadsheet.

Keywords: Mathematics education, Microsoft Excel spreadsheet, technology.

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Authors: Jonathan Bohn, Jorge Rebaza, Kaitlin Speer

Abstract:

The dynamics of a predator-prey model with continuous threshold policy harvesting functions on the prey is studied. Theoretical and numerical methods are used to investigate boundedness of solutions, existence of bionomic equilibria, and the stability properties of coexistence equilibrium points and periodic orbits. Several bifurcations as well as some heteroclinic orbits are computed.

Keywords: Predator-prey models, threshold harvesting, dynamicalsystems

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Authors: Morteza Amirabadi, Vahid Fayaz , Fereshteh Felegary, Hossien Hossienkhani

Abstract:

The most suitable Semiconductor detector, Cadmium Zinc Teloraid , has unique properties because of high Atomic number and wide Brand Gap . It has been tried in this project with different processes such as Lead , Diffusion , Produce and Recombination , effect of Trapping and injection carrier of CdZnTe , to get hole and then present a complete answer of it . Then we should investigate the movement of carrier ( Electron – Hole ) by using above answer.

Keywords: Semiconcuctor detector, Trapping, Recommbination, Diffusion

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Authors: G. Wagner, R. Herrmann

Abstract:

Cytotoxic platinum compounds play a major role in the chemotherapy of a large number of human cancers. However, due to the severe side effects for the patient and other problems associated with their use, there is a need for the development of more efficient drugs and new methods for their selective delivery to the tumours. One way to achieve the latter could be in the use of nanoparticular substrates that can adsorb or chemically bind the drug. In the cell, the drug is supposed to be slowly released, either by physical desorption or by dissolution of the particle framework. Ideally, the cytotoxic properties of the platinum drug unfold only then, in the cancer cell and over a longer period of time due to the gradual release. In this paper, we report on our first steps in this direction. The binding properties of a series of cytotoxic Pt(II) oxadiazoline compounds to mesoporous silica particles has been studied by NMR and UV/vis spectroscopy. High loadings were achieved when the Pt(II) compound was relatively polar, and has been dissolved in a relatively nonpolar solvent before the silica was added. Typically, 6-10 hours were required for complete equilibration, suggesting the adsorption did not only occur to the outer surface but also to the interior of the pores. The untreated and Pt(II) loaded particles were characterised by C, H, N combustion analysis, BET/BJH nitrogen sorption, electron microscopy (REM and TEM) and EDX. With the latter methods we were able to demonstrate the homogenous distribution of the Pt(II) compound on and in the silica particles, and no Pt(II) bulk precipitate had formed. The in vitro cytotoxicity in a human cancer cell line (HeLa) has been determined for one of the new platinum compounds adsorbed to mesoporous silica particles of different size, and compared with the corresponding compound in solution. The IC50 data are similar in all cases, suggesting that the release of the Pt(II) compound was relatively fast and possibly occurred before the particles reached the cells. Overall, the platinum drug is chemically stable on silica and retained its activity upon prolonged storage.

Keywords: Cytotoxicity, mesoporous silica, nanoparticles platinum compounds.

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Authors: N.Subramanian, C.Murugesan

Abstract:

This paper is devoted to the study of the general properties of Orlicz space of entire sequence of fuzzy numbers by using infinite matrices.

Keywords: Fuzzy numbers, infinite matrix, Orlicz space, entiresequence.

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Authors: D. H. Gahane, B. M. Bahirwar, S. V. Moharil

Abstract:

Efficient luminescence is reported for the first time in Eu2+ activated double Chlorides A2BCl4 (A=Alkali metal, B=Alkaline earth element). A simple wet-chemical preparation is described. Emission intensities are comparable to that of the commercial phosphor. Excitation covers near UV region. These phosphors may be useful for applications like solid state lighting, scintillation detectors and X-ray storage using photo-stimulable phosphors.

Keywords: Alkaline Earth, Chloride, Luminescence.

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Authors: Salima Kouici, Abdelkader Khelladi

Abstract:

In this work, we begin with the presentation of the Tθ family of usual similarity measures concerning multidimensional binary data. Subsequently, some properties of these measures are proposed. Finally the impact of the use of different inter-elements measures on the results of the Agglomerative Hierarchical Clustering Methods is studied.

Keywords: Binary data, similarity measure, Tθ measures, Agglomerative Hierarchical Clustering.

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Authors: Vinod B. Suryawanshi, Ajit D. Kelkar

Abstract:

Composite materials, due to their unique properties such as high strength to weight ratio, corrosion resistance, and impact resistance have huge potential as structural materials in automotive, construction and transportation applications. However, these properties often come at higher cost owing to complex design methods, difficult manufacturing processes and raw material cost. Traditionally, tapered laminated composite structures are manufactured using autoclave manufacturing process by ply drop off technique. Autoclave manufacturing though very powerful suffers from high capital investment and higher energy consumption. As per the current trends in composite manufacturing, Out of Autoclave (OoA) processes are looked as emerging technologies for manufacturing the structural composite components for aerospace and defense applications. However, there is a need for improvement among these processes to make them reliable and consistent. In this paper, feasibility of using out of autoclave process to manufacture the variable thickness cantilever beam is discussed. The minimum weight design for the composite beam is obtained using constant stress beam concept by tailoring the thickness of the beam. Ply drop off techniques was used to fabricate the variable thickness beam from glass/epoxy prepregs. Experiments were conducted to measure bending stresses along the span of the cantilever beam at different intervals by applying the concentrated load at the free end. Experimental results showed that the stresses in the bean at different intervals were constant. This proves the ability of OoA process to manufacture the constant stress beam. Finite element model for the constant stress beam was developed using commercial finite element simulation software. It was observed that the simulation results agreed very well with the experimental results and thus validated design and manufacturing approach used.

Keywords: Beams, Composites, Constant Stress, Structures.

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Authors: D.R Prince Williams

Abstract:

In this paper, we introduce the notion θ-Euclidean k-fuzzy ideal in semirings and to study the properties of the image and pre image of a θ -Euclidean k-fuzzy ideal in a semirings under epimorphism.

Keywords: semiring, fuzzy ideal, k–fuzzy ideal, θ -Euclidean Lfuzzyideal, θ -Euclidean fuzzy k–ideal, θ -Euclidean k-fuzzy ideal.

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Authors: Anuoluwapo S. Taiwo, David S. Ayre, Morteza Khorami, Sameer S. Rahatekar

Abstract:

This investigation aims to characterize the effect of corncob (CC), an agricultural waste, for potential use as a filler material, reducing cement in natural fibre-reinforced cement composite boards used for building applications in low-cost housing estates in developing countries. The CC is readily and abundantly available in many West African States. However, this agricultural waste product has not been put to any effective use. Hence, the objective of the current research is to convert this massive agro-waste resource into a potential material for use as filler materials reducing cement contents in fibre-cement board production. Kraft pulp fibre-reinforced cement composite boards were developed with the incorporation of the CC powder at varying percentages of 1-4% as filler materials to reduce the cement content, using a laboratory-simulated vacuum de-watering process. The mechanical properties of the developed cement boards were characterized through a three-point bending test, while the fractured morphology of the cement boards was examined through a Scanning Electron Microscope (SEM). Results revealed that the flexural strength of the composite board improved significantly with an optimum enhancement of 39% when compared to the reference sample without CC replacement, however, the flexural behaviour (ductility) of the composite board was slightly affected by the addition of the CC powder at higher percentage. SEM observation of the fractured surfaces revealed good bonding at the fibre-matrix interface as well as a ductile-to-brittle fracture mechanism. Overall, the composite board incorporated with 2% CC powder as filler materials had the optimum properties, satisfying the minimum requirements of relevant standards for fibre cement flat sheets.

Keywords: Kraft pulp fibre, fibre-cement board, agricultural waste, sustainability, building applications.

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Authors: M. Nabeel Rashin, J. Hemalatha

Abstract:

Novel Coconut oil nanofluids of various concentrations have been prepared through ultrasonically assisted sol-gel method. The structural and morphological properties of the copper oxide nanoparticle have been analyzed with respectively and it revealed the monoclinic end-centered structure of crystallite and shuttle like flake morphology of agglomerates. Ultrasonic studies have been made for the nanofluids at different temperatures. The molecular interactions responsible for the changes in acoustical parameter with respect to concentration and temperature are discussed.

Keywords: Cutting Fluid, Molecular Interaction, Nanofluids, Ultrasonic

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Authors: Emre Kara, Şura Karakuzu, Ahmet F. Geylan, Metehan Demir, Kadir Koç, Halil Aykul

Abstract:

The material selection in the design of the sandwich structures is very crucial aspect because of the positive or negative influences of the base materials to the mechanical properties of the entire panel. In the literature, it was presented that the selection of the skin and core materials plays very important role on the behavior of the sandwich. Beside this, the use of the correct adhesive can make the whole structure to show better mechanical results and behavior. In the present work, the static three-point bending tests were performed on the sandwiches having an aluminum alloy foam core, the skins made of three different types of fabrics and two different commercial adhesives (flexible polyurethane and toughened epoxy based) at different values of support span distances by aiming the analyses of their flexural performance in terms of absorbed energy, peak force values and collapse mechanisms. The main results of the flexural loading are: force-displacement curves obtained after the bending tests, peak force and absorbed energy values, collapse mechanisms and adhesion quality. The experimental results presented that the sandwiches with epoxy based toughened adhesive and the skins made of S-Glass Woven fabrics indicated the best adhesion quality and mechanical properties. The sandwiches with toughened adhesive exhibited higher peak force and energy absorption values compared to the sandwiches with flexible adhesive. The use of these sandwich structures can lead to a weight reduction of the transport vehicles, providing an adequate structural strength under operating conditions.

Keywords: Adhesive and adhesion, Aluminum foam, Bending, Collapse mechanisms.

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Authors: Salma H. Abu Hafsa, A. Mendonca, B. Brehm-Stecher, A. A. Hassan, S. A. Ibrahim

Abstract:

Enterococci are important inhabitants of the animal intestine and are widely used in probiotic products. A probiotic strain is expected to possess several desirable properties in order to exert beneficial effects. Therefore, the objective of this study was to isolate, characterize and identify Enterococcus sp. from chicken cecal and fecal samples to determine potential probiotic properties. Enterococci were isolated from chicken ceca and feces of thirty three clinically healthy chickens from a local farm. In vitro studies were performed to assess antibacterial activity of the isolated LAB (using agar well diffusion and cell free supernatant broth technique against Salmonella enterica serotype Enteritidis), survival in acidic conditions, resistance to bile salts, and their survival during simulated gastric juice conditions at pH 2.5. Isolates were identified by biochemical carbohydrate fermentation patterns using an API 50 CHL kit and API ZYM kits and by sequenced 16S rDNA. An isolate belonging to E. faecium species exhibited inhibitory effect against S. enteritidis. This isolate producing a clear zone as large as 10.30 mm or greater and was able to grow in the coculture medium and at the same time, inhibited the growth S. enteritidis. In addition, E. faecium exhibited significant resistance under highly acidic conditions at pH 2.5 for 8 h and survived well in bile salt at 0.2% for 24 h and showing ability to survive in the presence of simulated gastric juice at pH 2.5. Based on these results, E. faecium isolate fulfills some of the criteria to be considered as a probiotic strain and therefore, could be used as a feed additive with good potential for controlling S. Enteritidis in chickens. However, in vivo studies are needed to determine the safety of the strain.

Keywords: Acid tolerance, antimicrobial activity, Enterococcus faecium, probiotic.

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Authors: M. Nekri, A. Khelladi

Abstract:

The world wide web network is a network with a complex topology, the main properties of which are the distribution of degrees in power law, A low clustering coefficient and a weak average distance. Modeling the web as a graph allows locating the information in little time and consequently offering a help in the construction of the research engine. Here, we present a model based on the already existing probabilistic graphs with all the aforesaid characteristics. This work will consist in studying the web in order to know its structuring thus it will enable us to modelize it more easily and propose a possible algorithm for its exploration.

Keywords: Clustering coefficient, preferential attachment, small world, Web community.

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Authors: Y. Liu, M. K. Bera, L. M. Kyaw, G. Q. Lo, E. F. Chor

Abstract:

The electrical and structural properties of Hf/Al/Ni/Au (20/100/25/50 nm) ohmic contact to n-GaN are reported in this study. Specific contact resistivities of Hf/Al/Ni/Au based contacts have been investigated as a function of annealing temperature and achieve the lowest value of 1.09´10-6 Ω·cm2 after annealing at 650 oC in vacuum. A detailed mechanism of ohmic contact formation is discussed. By using different chemical analyses, it is anticipated that the formation of Hf-Al-N alloy might be responsible to form low temperature ohmic contacts for the Hf-based scheme to n-GaN.

Keywords: Gallium nitride, ohmic contact, Hafnium

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Authors: W. Thepsuwan, N. Monmaturapoj

Abstract:

Calcium phosphate cement (CPC) is one of the most attractive bioceramics due to its moldable and shape ability to fill complicated bony cavities or small dental defect positions. In this study, CPC was produced by using mixture of tetracalcium phosphate (TTCP, Ca4O(PO4)2) and dicalcium phosphate anhydrous (DCPA, CaHPO4) in equimolar ratio (1/1) with aqueous solutions of acetic acid (C2H4O2) and disodium hydrogen phosphate dehydrate (Na2HPO4.2H2O) in combination with sodium alginate in order to improve theirs moldable characteristic. The concentration of the aqueous solutions and sodium alginate were varied to investigate the effect of different aqueous solutions and alginate on properties of the cements. The cement paste was prepared by mixing cement powder (P) with aqueous solution (L) in a P/L ratio of 1.0g/0.35ml. X-ray diffraction (XRD) was used to analyses phase formation of the cements. Setting time and compressive strength of the set CPCs were measured using the Gilmore apparatus and Universal testing machine, respectively. The results showed that CPCs could be produced by using both basic (Na2HPO4.2H2O) and acidic (C2H4O2) solutions. XRD results show the precipitation of hydroxyapatite in all cement samples. No change in phase formation among cements using difference concentrations of Na2HPO4.2H2O solutions. With increasing concentration of acidic solutions, samples obtained less hydroxyapatite with a high dicalcium phosphate dehydrate leaded to a shorter setting time. Samples with sodium alginate exhibited higher crystallization of hydroxyapatite than that of without alginate as a result of shorten setting time in a basic solution but a longer setting time in an acidic solution. The stronger cement was attained from samples using the acidic solution with sodium alginate; however the strength was lower than that of using the basic solution.

Keywords: Calcium phosphate cements, TTCP, DCPA, hydroxyapatite, properties.

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Authors: Andrey V. Timofeev

Abstract:

This paper presents development results of the method of seismoacoustic activity monitoring based on usage vibrosensitive properties of optical fibers. Analysis of Rayleigh backscattering radiation parameters changes, which take place due to microscopic seismoacoustic impacts on the optical fiber, allows to determine seismoacoustic emission sources positions and to identify their types. Results of using this approach are successful for complex monitoring of railways.

Keywords: C-OTDR systems, monitoring of railways, Rayleigh backscattering.

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Authors: Zhaohao Wang, Lan Shu

Abstract:

In this paper, we generalize some propositions in [C.Z. Wang, D.G. Chen, A short note on some properties of rough groups, Comput. Math. Appl. 59(2010)431-436.] and we give some equivalent conditions for rough subgroups. The notion of minimal upper rough subgroups is introduced and a equivalent characterization is given, which implies the rough version of Lagranges Theorem.

Keywords: Lower approximations, Upper approximations, Rough sets, Rough groups, Lagrange

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