Search results for: differential shrinkage

Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

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We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: integral images, differential images, differential filters, image fusion

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Authors: Yulu Zhang, Atushi Teramoto, Taka-Aki Ohkubo

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In this study, the effect of expansive additives on autogenous shrinkage and delayed expansion of ultra-high strength mortar was explored. The specimens made for the study were composed of ultra-high strength mortar, which was mixed with ettringite-lime composite type expansive additive. Two series of experiments were conducted with the specimens. The experimental results confirmed that the autogenous shrinkage of specimens was effectively decreased by increasing the proportion of the expansive additive. On the other hand, for the specimens, which had 7% expansive additive, and were cured for seven days at a constant temperature of 20°C, and then cured for a long time in either in an underwater, moist (Relative humidity: 100%) or dry air (Relative humidity: 60%) environment, excessively large expansion strain occurred. Specifically, typical turtle shell-like swelling expansion cracks were confirmed in the specimens that underwent long-term curing in an underwater and moist environment. According to the result of hydration analysis, the formation of expansive substances, calcium hydroxide and alumina, ferric oxide, tri-sulfate contribute to the occurrence of delayed expansion.

Keywords: ultra-high strength mortar, expansive additive, autogenous shrinkage, delayed expansion

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Authors: Teoman Ozer, Ozlem Orhan

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This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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Authors: Sonam Behl, Raju, Ginu Rajan, Paul Farrar, B. Gangadhara Prusty

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Reinforcing dental composites with micro-sized fibres can significantly improve the physio-mechanical properties of dental composites. The short fibres can be oriented randomly within dental composites, thus providing quasi-isotropic reinforcing efficiency unlike unidirectional/bidirectional fibre reinforced composites enhancing anisotropic properties. Thus, short fibres reinforced dental composites are getting popular among practitioners. However, despite their popularity, resin-based dental composites are prone to failure on account of shrinkage during photo polymerisation. The shrinkage in the structure may lead to marginal gap formation, causing secondary caries, thus ultimately inducing failure of the restoration. The traditional methods to evaluate polymerisation shrinkage using strain gauges, density-based measurements, dilatometer, or bonded-disk focuses on average value of volumetric shrinkage. Moreover, the results obtained from traditional methods are sensitive to the specimen geometry. The present research aims to evaluate the real-time shrinkage strain at selected locations in the material with the help of optical fibre Bragg grating (FBG) sensors. Due to the miniature size (diameter 250 µm) of FBG sensors, they can be easily embedded into small samples of dental composites. Furthermore, an FBG array into the system can map the real-time shrinkage strain at different regions of the composite. The evaluation of real-time monitoring of shrinkage values may help to optimise the physio-mechanical properties of composites. Previously, FBG sensors have been able to rightfully measure polymerisation strains of anisotropic (unidirectional or bidirectional) reinforced dental composites. However, very limited study exists to establish the validity of FBG based sensors to evaluate volumetric shrinkage for randomly oriented fibres reinforced composites. The present study aims to fill this research gap and is focussed on establishing the usage of FBG based sensors for evaluating the shrinkage of dental composites reinforced with randomly oriented fibres. Three groups of specimens were prepared by mixing the resin (80% UDMA/20% TEGDMA) with 55% of silane treated BaAlSiO₂ particulate fillers or by adding 5% of micro-sized fibres of diameter 5 µm, and length 250/350 µm along with 50% of silane treated BaAlSiO₂ particulate fillers into the resin. For measurement of polymerisation shrinkage strain, an array of three fibre Bragg grating sensors was embedded at a depth of 1 mm into a circular Teflon mould of diameter 15 mm and depth 2 mm. The results obtained are compared with the traditional method for evaluation of the volumetric shrinkage using density-based measurements. Degree of conversion was measured using FTIR spectroscopy (Spotlight 400 FT-IR from PerkinElmer). It is expected that the average polymerisation shrinkage strain values for dental composites reinforced with micro-sized fibres can directly correlate with the measured degree of conversion values, implying that more C=C double bond conversion to C-C single bond values also leads to higher shrinkage strain within the composite. Moreover, it could be established the photonics approach could help assess the shrinkage at any point of interest in the material, suggesting that fibre-Bragg grating sensors are a suitable means for measuring real-time polymerisation shrinkage strain for randomly fibre reinforced dental composites as well.

Keywords: dental composite, glass fibre, polymerisation shrinkage strain, fibre-Bragg grating sensors

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Authors: Ahmad Saadiq, Neeraj Sahu

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The partial or full replacement of natural coarse aggregate by recycled concrete aggregate (RCA) is of great benefit to the environment, as the demand of natural coarse aggregate reduces. In the modern construction and practice, the use of RCA is limited to backfilling and road construction. The establishment of RCA for its wide application can only be done after having an understanding of the use of RCA in conventional concrete. To have an insight to this, various tests to determine the compressive strength, elastic strength, workability, durability and drying shrinkage tests can be done and the test results may be different from that obtained from natural coarse aggregates, by using natural coarse aggregate in concrete. This paper gives a comprehensive review of the said tests done on RCA concrete. The results obtained from the tests indicate that RCA concrete gives comparable compressive strength, stiffness, and workability relative to the corresponding results obtained from the natural coarse aggregates. However, the durability and drying shrinkage had more variance but well within recommended limits.

Keywords: aggregate, compressive strength, durability, modulus of elasticity, recycled concrete, shrinkage, workability

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Reena Aggarwal, Neha Kestwal

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The Himalayan Nettle (Girardinia diversifolia) has been used for centuries as fibre and food source by Himalayan communities. Himalayan Nettle is a natural cellulosic fibre that can be handled in the same way as other cellulosic fibres. The Uttarakhand Bamboo and Fibre Development Board based in Uttarakhand, India is working extensively with the nettle fibre to explore the potential of nettle for textile production in the region. The fiber is a potential resource for rural enterprise development for some high altitude pockets of the state and traditionally the plant fibre is used for making domestic products like ropes and sacks. Himalayan Nettle is an unconventional natural fiber with functional characteristics of shrink resistance, degree of pathogen and fire resistance and can blend nicely with other fibres. Most importantly, they generate mainly organic wastes and leave residues that are 100% biodegradable. The fabrics may potentially be reused or re-manufactured and can also be used as a source of cellulose feedstock for regenerated cellulosic products. Being naturally bio- degradable, the fibre can be composted if required. Though a lot of research activities and training are directed towards fibre extraction and processing techniques in different craft clusters villagers of different clusters of Uttarkashi, Chamoli and Bageshwar of Uttarakhand like retting and Degumming process, very little is been done to analyse the crucial properties of nettle fiber like shrinkage and wash fastness. These properties are very crucial to obtain desired quality of fibre for further processing of yarn making and weaving and in developing these fibers into fine saleable products. This research therefore is focused towards various on-field experiments which were focused on shrinkage properties conducted on cotton, nettle and cotton/nettle blended yarn samples. The objective of the study was to analyze the scope of the blended fiber for developing into wearable fabrics. For the study, after conducting the initial fiber length and fineness testing, cotton and nettle fibers were mixed in 60:40 ratio and five varieties of yarns were spun in open end spinning mill having yarn count of 3s, 5s, 6s, 7s and 8s. Samples of 100% Nettle 100% cotton fibers in 8s count were also developed for the study. All the six varieties of yarns were tested with shrinkage test and results were critically analyzed as per ASTM method D2259. It was observed that 100% Nettle has a least shrinkage of 3.36% while pure cotton has shrinkage approx. 13.6%. Yarns made of 100% Cotton exhibits four times more shrinkage than 100% Nettle. The results also show that cotton and Nettle blended yarn exhibit lower shrinkage than 100% cotton yarn. It was thus concluded that as the ratio of nettle increases in the samples, the shrinkage decreases in the samples. These results are very crucial for Uttarakhand people who want to commercially exploit the abundant nettle fiber for generating sustainable employment.

Keywords: Himalayan nettle, sustainable, shrinkage, blending

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Authors: Hasan Ziari, Hassan Fazaeli, Seyed Javad Vaziri Kang Olyaei, Asma Sadat Dabiri

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The presence of cracks in concrete pavements is a place for the ingression of corrosive substances, acids, oils, and water into the pavement and reduces its long-term durability and level of service. One of the causes of early cracks in concrete pavements is the plastic shrinkage. This shrinkage occurs due to the formation of negative capillary pressures after the equilibrium of the bleeding and evaporation rates at the pavement surface. These cracks form if the tensile stresses caused by the restrained shrinkage exceed the tensile strength of the concrete. Different climate conditions change the rate of evaporation and thus change the balance time of the bleeding and evaporation, which changes the severity of cracking in concrete. The present study examined the relationship between the balance time of bleeding and evaporation and the area of cracking in the concrete slabs using the standard method ASTM C1579 in 27 different environmental conditions by using continuous video recording and digital image analyzing. The results showed that as the evaporation rate increased and the balance time decreased, the crack severity significantly increased so that by reducing the balance time from the maximum value to its minimum value, the cracking area increased more than four times. It was also observed that the cracking area- balance time curve could be interpreted in three sections. An examination of these three parts showed that the combination of climate conditions has a significant effect on increasing or decreasing these two variables. The criticality of a single factor cannot cause the critical conditions of plastic cracking. By combining two mild environmental factors with a severe climate factor (in terms of surface evaporation rate), a considerable reduction in balance time and a sharp increase in cracking severity can be prevented. The results of this study showed that balance time could be an essential factor in controlling and predicting plastic shrinkage cracking in concrete pavements. It is necessary to control this factor in the case of constructing concrete pavements in different climate conditions.

Keywords: bleeding and cracking severity, concrete pavements, climate conditions, plastic shrinkage

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Authors: Lev Idels, Arcady Ponosov

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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

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Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Lina Wu, Ye Li

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An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.

Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms

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Authors: Hanizam Awang, Muhammad Hafiz Ahmad

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An experimental study was conducted on foamed concrete with synthetic and natural fibres consisting of AR-glass, polypropylene, steel, kenaf and oil palm fibre. The foamed concrete mixtures produced had a target density of 1000 kg/m3 and a mix ratio of (1:1.5:0.45). The fibres were used as additives. The inclusion of fibre was maintained at a volumetric fraction of 0.25 and 0.4 %. The water absorption, thermal and shrinkage were determined to study the effect of the fibre on the durability properties of foamed concrete. The results showed that AR-glass fibre has the lowest percentage value of drying shrinkage compared to others.

Keywords: foamed concrete, fibres, durability, construction, geological engineering

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Zaoiai Said, Makani Abdelkadir, Tafraoui Ahmed

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Concrete material suffers from a relatively low tensile strength and deformation capacity is limited. Such defects of the concrete are very fragile and sensitive to shrinkage cracking materials. The Self- Compacting Concrete (SCC) are highly fluid concretes whose implementation without vibration. This material replaces traditional vibrated concrete mainly seen techno-economic interest it presents. The SCC has several advantages which are at the origin of their development crunching. The research is therefore to conduct a comparison in terms of rheological and mechanical performance between different formulations to find the optimal dosage for rubber granulates. Through this research, we demonstrated that it is possible to make different settings SCC composition having good rheological and mechanical properties. This study also showed that the substitution of natural coarse aggregates (NA) by coarse rubber aggregates (RA) in the composition of the SCC, contributes to a slight variation of workability in the fresh state parameters still remaining in the field of SCC required by the AFGC recommendations. The experimental results show that the compressive strengths of SCC decreased slightly by substituting NA by RA. Finally, the decrease in free shrinkage is proportional to the percentage of RA incorporated into the composition of concrete. This reduction is mainly due to the improvement of the deformability of these materials.

Keywords: self-compacting concrete, coarse rubber aggregate, rheological characterization, mechanical performance, shrinkage

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Authors: Zhan Chen, Wenquan Bi

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This paper focuses on examining the strength of Midori against impossible differential attack. The Midori family of light weight block cipher orienting to energy-efficiency is proposed in ASIACRYPT2015. Using a 6-round property, the authors implement an 11-round impossible differential attack on Midori64 by extending two rounds on the top and three rounds on the bottom. There is enough key space to consider pre-whitening keys in this attack. An impossible differential path that minimises the key bits involved is used to reduce computational complexity. Several additional observations such as partial abort technique are used to further reduce data and time complexities. This attack has data complexity of 2 ⁶⁹·² chosen plaintexts, requires 2 ¹⁴·⁵⁸ blocks of memory and 2 ⁹⁴·⁷ 11- round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: Redha Yeghnem, Laid Boulefrakh, Sid Ahmed Meftah, Abdelouahed Tounsi, El Abbas Adda Bedia

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In this study, the time-dependent behavior of damaged reinforced concrete shear wall structures strengthened with composite plates having variable fibers spacing was investigated to analyze their seismic response. In the analytical formulation, the adherent and the adhesive layers are all modeled as shear walls, using the mixed finite element method (FEM). The anisotropic damage model is adopted to describe the damage extent of the RC shear walls. The phenomenon of creep and shrinkage of concrete has been determined by Eurocode 2. Large earthquakes recorded in Algeria (El-Asnam and Boumerdes) have been tested to demonstrate the accuracy of the proposed method. Numerical results are obtained for non uniform distributions of carbon fibers in epoxy matrices. The effects of damage extent and the delay mechanism creep and shrinkage of concrete are highlighted. Prospects are being studied.

Keywords: RC shear wall structures, composite plates, creep and shrinkage, damaged reinforced concrete structures, finite element method

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: N. Dahraoui, M. Boulakroune, D. Benatia

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In this paper, the improvement by deconvolution of the depth resolution in Secondary Ion Mass Spectrometry (SIMS) analysis is considered. Indeed, we have developed a new Tikhonov-Miller deconvolution algorithm where a priori model of the solution is included. This is a denoisy and pre-deconvoluted signal obtained from: firstly, by the application of wavelet shrinkage algorithm, secondly by the introduction of the obtained denoisy signal in an iterative deconvolution algorithm. In particular, we have focused the light on the effect of the iterations number on the evolution of the deconvoluted signals. The SIMS profiles are multilayers of Boron in Silicon matrix.

Keywords: DRF, in-depth resolution, multiresolution deconvolution, SIMS, wavelet shrinkage

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Authors: Katerina Kormusheva

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Pricing plays a pivotal role in the marketing discipline as it directly influences consumer perceptions, purchase decisions, and overall market positioning of a product or service. This paper seeks to expand current knowledge in the area of discriminatory and differential pricing, a main area of marketing research. The methodology includes developing a framework and a model for determining how many price points to implement in differential pricing. We focus on choosing the levels of differentiation, derive a function form of the model framework proposed, and lastly, test it empirically with data from a large-scale marketing pricing experiment of services in telecommunications.

Keywords: marketing, differential pricing, price points, optimization

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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