Search results for: weighted modulus of continuity

Authors: Rishikesh Yadav, Ramakanta Meher, Vishnu Narayan Mishra

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The main aim of this article is to investigate the statistical convergence of the summation of integral type operators and to obtain the weighted statistical convergence. The rate of statistical convergence by means of modulus of continuity and function belonging to the Lipschitz class are also studied. We discuss the convergence of the defined operators by graphical representation and put a better rate of convergence than the Szasz-Mirakjan-Kantorovich operators. In the last section, we extend said operators into bivariate operators to study about the rate of convergence in sense of modulus of continuity and by means of Lipschitz class by using function of two variables.

Keywords: The Szasz-Mirakjan-Kantorovich operators, statistical convergence, modulus of continuity, Peeters K-functional, weighted modulus of continuity

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Authors: Preeti Sharma

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This paper deals with the Stancu type generalization of Lupaş-Durrmeyer operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, 1]. Also, Voronovskaja type theorem is studied.

Keywords: Lupas-Durrmeyer operators, polya distribution, weighted approximation, rate of convergence, modulus of continuity

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Authors: Neha Bhardwaj

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In this paper, we consider positive linear operators and study the Voronovskaya type result of the operator then obtain an error estimate in terms of the higher order modulus of continuity of the function being approximated and its A-statistical convergence. Also, we compute the corresponding rate of A-statistical convergence for the linear positive operators.

Keywords: Poisson distribution, Voronovskaya, modulus of continuity, a-statistical convergence

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Authors: Tarul Garg, P. N. Agrawal

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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

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Authors: Salisu ibrahim, Abdalla Rababah

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In this research, we use Weighted G2-Multi-degree reduction of Bezier curve of degree n to a Bezier curve of degree m, m < n. The degree reduction of Bezier curves is used to represent a given Bezier curve of n by a Bezier curve of degree m, m < n. Exact degree reduction is not possible, and degree reduction is approximate process in nature. We derive a weighted degree reducing method that is geometrically continuous at the end points. Different norms will be considered, several error minimizations will be given. The proposed methods produce error function that are less than the errors of existing methods.

Keywords: Bezier curves, multiple degree reduction, geometric continuity, error function

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Authors: Fakharuddin Ibrahim, Jamaludin Md. Ali, Ahmad Ramli

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In this paper, we will discuss about the data interpolation by using the rational cubic Ball curve. To generate a curve with a better and satisfactory smoothness, the curve segments must be connected with a certain amount of continuity. The continuity that we will consider is of type G¹ continuity. The conditions considered are known as the G¹ Hermite condition. A simple application of the proposed method is to generate an Arabic font satisfying the required continuity.

Keywords: data interpolation, rational ball curve, hermite condition, continuity

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Authors: Shams Alyusof

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This work is to enrich the studies of the frames due to their prominent role in pure mathematics as well as in applied mathematics and many applications in computer science and engineering. Recently, there are remarkable studies of operators that preserve frames on some spaces, and this research could be considered as an extension of such studies. Indeed, this paper is to we characterize weighted composition operators that preserve frames in weighted Hardy spaces on the open unit disk. Moreover, it shows that this characterization does not apply to generalized weighted composition operators on such spaces. Nevertheless, this study could be extended to provide more specific characterizations.

Keywords: frames, generalized weighted composition operators, weighted Hardy spaces, analytic functions

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Authors: M. Abdelmalek

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In this work, we study the hypersurfaces of constant weighted mean curvature embedded in weighted manifolds. We give a condition about these hypersurfaces to be minimal. This condition is given by the ellipticity of the weighted Newton transformations. We especially prove that two compact hypersurfaces of constant weighted mean curvature embedded in space forms and with the intersection in at least a point of the boundary must be transverse. The method is based on the calculus of the matrix of the second fundamental form in a boundary point and then the matrix associated with the Newton transformations. By equality, we find the weighted elementary symmetric function on the boundary of the hypersurface. We give in the end some examples and applications. Especially in Euclidean space, we use the above result to prove the Alexandrov spherical caps conjecture for the weighted case.

Keywords: weighted mean curvature, weighted manifolds, ellipticity, Newton transformations

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Authors: Zhiming Ye, Dejiang Wang, Huiling Zhao

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Development of the technology demands a higher-level research on the mechanical behavior of materials. Structural members made of bi-modulus materials have different elastic modulus when they are under tension and compression. The stress and strain states of the point effect on the elastic modulus and Poisson ratio of every point in the bi-modulus material body. Accompanied by the uncertainty and nonlinearity of the elastic constitutive relation is the complicated nonlinear problem of the bi-modulus members. In this paper, the small displacement and large displacement finite element method for the bi-modulus members have been proposed. Displacement nonlinearity is considered in the elastic constitutive equation. Mechanical behavior of slender bi-modulus beam-column under different boundary conditions and loading patterns has been simulated by the proposed method. The influence factors on the ultimate bearing capacity of slender beam and columns have been studied. The results show that as the ratio of tensile modulus to compressive modulus increases, the error of the simulation employing the same elastic modulus theory exceeds the engineering permissible error.

Keywords: bi-modulus, ultimate capacity, beam-column, nonlinearity

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Authors: Olgha Giorgishvili

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The work is mainly concerned with the determination of modulus of deformation by laboratory method. It is known that a modulus of deformation is defining by laboratory and field methods. By laboratory method the modulus of deformation is defined in the compressive devices. Our goal is to conduct experiments by both methods and finally make to interpret the obtained results. In this article is considered the definition by new offered laboratory method of deformation modulus that is closer to the real deformation modulus. Finally, the obtained results gives the possibility to us to raise the issue of change the state norms for determining ground by laboratory method.

Keywords: building, soil mechanic, deformation moulus, compression methods

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Authors: Radmila Hajkova, Jiri Palecek, Hana Malachova, Alena Oulehlova

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Ensuring of continuity of business is the basic strategy of every company. Continuity of organization activities includes comprehensive procedures that help in solving unexpected situations of natural and anthropogenic character (for example flood, blaze, economic situations). Planning of continuity operations is a process that helps identify critical processes and implement plans for the security and recovery of key processes. The aim of this article demonstrates application of system approach to managing business continuity called business continuity management systems in military issues. This article describes the life cycle of business continuity management which is based on the established cycle PDCA (plan-do-check-act). After this is carried out by activities which are making by the University of Defence during activation of forces and means of the Integrated rescue system in case of emergencies - accidents at a nuclear power plant in Czech republic. Activities of various stages of deployment earmarked forces and resources are managed and evaluated by using MCMS application (military continuity management system).

Keywords: business continuity management system, emergency management, military, nuclear safety

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Authors: Win-Jin Chang, Haw-Long Lee, Yu-Ching Yang

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In this study, we use the atomic-scale finite element method to investigate the mechanical behavior of the armchair- and zigzag-structured nanoporous graphene sheets with the clamped-free-free-free boundary condition under tension and shear loadings. The effect of porosity on Young’s modulus and shear modulus of nanoporous graphene sheets is obvious. For the armchair- and zigzag-structured nanoporous graphene sheets, Young’s modulus and shear modulus decreases with increasing porosity. Young’s modulus and shear modulus of zigzag graphene are larger than that of armchair one for the same porosity. The results are useful for application in the design of nanoporous graphene sheets.

Keywords: graphene, nanoporous, Young's modulus, shear modulus

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Authors: Klara Krizova, Rudolf Hela

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The paper is focused on monitoring of dependencies of different composition concretes on elastic modulus values. To obtain a summary of elastic modulus development independence of concrete composition design variability was the objective of the experiment. Essential part of this work was initiated as a reaction to building practice when questions of elastic moduli arose at the same time and which mostly did not obtain the required and expected values from concrete constructions. With growing interest in this theme the elastic modulus questions have been developing further.

Keywords: concrete, compressive strength, modulus of elasticity, EuroCode 2

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Authors: Ruchi, A. M. Acu, Purshottam N. Agrawal

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The purpose of this paper to introduce the Durrmeyer type modification of q-generalized-Bernstein operators which include the Bernstein polynomials in the particular α = 0. We investigate the rate of convergence by means of the Lipschitz class and the Peetre’s K-functional. Also, we define the bivariate case of Durrmeyer type modification of q-generalized-Bernstein operators and study the degree of approximation with the aid of the partial modulus of continuity and the Peetre’s K-functional. Finally, we introduce the GBS (Generalized Boolean Sum) of the Durrmeyer type modification of q- generalized-Bernstein operators and investigate the approximation of the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, Peetre’s K-functional, Lipschitz class, mixed modulus of smoothness

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Authors: Shih-Wen Hsiao, Chu-Hsuan Lee, Rong-Qi Chen

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When it comes to last, it is regarded as the critical foundation of shoe design and development. Not only the last relates to the comfort of shoes wearing but also it aids the production of shoe styling and manufacturing. In order to enhance the efficiency and application of last development, a computer aided methodology for customized last form designs is proposed in this study. The reverse engineering is mainly applied to the process of scanning for the last form. Then the minimum energy is used for the revision of surface continuity, the surface of the last is reconstructed with the feature curves of the scanned last. When the surface of a last is reconstructed, based on the foundation of the proposed last form reconstruction module, the weighted arithmetic mean method is applied to the calculation on the shape morphing which differs from the grading for the control mesh of last, and the algorithm of subdivision is used to create the surface of last mesh, thus the feet-fitting 3D last form of different sizes is generated from its original form feature with functions remained. Finally, the practicability of the proposed methodology is verified through later case studies.

Keywords: 3D last design, customization, reverse engineering, weighted morphing, shape blending

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Authors: Xianjia Meng, Chuanyong Qu

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Compact bone produces fatigue damage under the inevitable physiological load. The accumulation of fatigue damage can change the bone’s micro-structure at different scales and cause the catastrophic failure eventually. However, most tests were limited to the macroscopic modulus of bone and there is a need to assess the microscopic modulus during fatigue progress. In this paper, nano-identation was used to investigate the bone specimen subjected to four point bending. The microscopic modulus of the same area were measured at different degrees of damage including fracture. So microscopic damage can be divided into three stages: first, the modulus decreased rapidly and then They fell slowly, before fracture the decline became fast again. After fracture, the average modulus decreased by 20%. The results of inner and outer planes explained the influence of compressive and tensile loads on modulus. Both the compressive and tensile moduli decreased with the accumulation of damage. They reached the minimum at ending and increased after fracture. The modulus evolution under different strains were revealed by the side. They all fell slowly and then fast with the accumulation of damage. The fractured results indicated that the elastic modulus decreased obviously at the high strain while decreased less at the low strain. During the fatigue progress, there was a significant difference in modulus at low degree of damage. However, the dispersed modulus tended to be similar at high degree of damage, but they became different again after the failure.

Keywords: fatigue damage, fracture, microscopic modulus, bone, nano-identation

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Authors: Klara Krizova, Rudolf Hela

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The topic of the article focuses on the evaluation of selected technological factors and their influence on resulting elasticity modulus of concrete. A series of various factors enter into the manufacturing process which, more or less, influences the elasticity modulus. This paper presents the results of concrete in which the influence of water coefficient and the size of maximum fraction of the aggregate on the static elasticity modulus were monitored. Part of selected results of the long-term programme was discussed in which a wide scope of various variants of proposals for the composition of concretes was evaluated.

Keywords: mix design, water-cement ratio, aggregate, modulus of elasticity

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Authors: Donald Zullick, Cihan Varol

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This research paper begins with a look at current work in business continuity as it relates to the cloud and small to medium business (SMB). While cloud services are an emerging paradigm that is quickly making an impact on business, there has been no substantive research applied to SMB. Seeing this lapse, we have taken a fusion of continuity and cloud research with application to the SMB market. It is an initial reflection with base framework guidelines as a starting point for implementation. In this approach, our research ties together existing work and fill the gap with an SMB outlook.

Keywords: business continuity, cloud services, medium size business, risk assessment, small business

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Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell

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The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: bonded rubber, quasi-static test, shape factor, apparent Young’s modulus

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Authors: Jiří F. Urbánek, Jiří Barta

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Societal security, continuity scenarios, and methodological cycling approach understands in this article. Namely, societal security organizational challenges ask implementation of international standards BS 25999-2 and global ISO 22300 which is a family of standards for business continuity management system. Efficient global organization system is distinguished of high entity´s complexity, connectivity, and interoperability, having not only cooperative relations in a fact. Competing business have numerous participating ´enemies´, which are in apparent or hidden opponent and antagonistic roles with prosperous organization systems, resulting to a crisis scene or even to a battle theater. Organization business continuity scenarios are necessary for such ´a play´ preparedness, planning, management, and overmastering in real environments.

Keywords: business continuity, societal security, crisis scenarios cycles, interoperability

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Authors: Sujith Rajashekar Swamy, Meghana Rajashekara Swamy

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Although T1-weighted gadolinium-enhanced imaging (T1-Gd) has its established clinical role in diagnosing brain lesions of infectious and metastatic origins, the use of post-contrast susceptibility-weighted imaging (SWI) has been understudied. This observational study aims to explore and compare the prominence of brain parenchymal lesions between T1-Gd and SWI-Gd images. A cross-sectional study design was utilized to analyze 58 patients with brain parenchymal lesions using T1-Gd and SWI-Gd scanning techniques. Our results indicated that SWI-Gd enhanced the conspicuity of metastatic as well as infectious brain lesions when compared to T1-Gd. Consequently, it can be used as an adjunct to T1-Gd for post-contrast imaging, thereby avoiding additional contrast administration. Improved conspicuity of brain lesions translates directly to enhanced patient outcomes, and hence SWI-Gd imaging proves useful to meet that endpoint.

Keywords: susceptibility weighted, T1 weighted, brain lesions, gadolinium contrast

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Authors: O. Giorgishvili

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For calculation of foundations one of the important characteristics is the module of deformation (E0). As we all know, the main goal of calculation of the foundations of buildings on deformation is to arrange the base settling and difference in settlings in such limits that do not cause origination of cracks and changes in design levels that will be dangerous to standard operation in the buildings and their individual structures. As is known from the literature and the practical application, the modulus of deformation is determined by two basic methods: laboratory method, soil test on compression (without the side widening) and soil test in field conditions. As we know, the deformation modulus of soil determined by field method is closer to the actual modulus deformation of soil, but the complexity of the tests to be carried out and the financial concerns did not allow determination of ground deformation modulus by field method. Therefore, we determine the ground modulus of deformation by compression method without side widening. Concerning this, we introduce a new way for determination of ground modulus of deformation by laboratory order that occurs by side widening and more accurately reflects the ground modulus of deformation and more accurately reflects the actual modulus of deformation and closer to the modulus of deformation determined by the field method. In this regard, we bring a new approach on the ground deformation detection laboratory module, which is done by widening sides. The tests and the results showed that the proposed method of ground deformation modulus is closer to the results that are obtained in the field, which reflects the foundation's work in real terms more accurately than the compression of the ground deformation module.

Keywords: build, deformation modulus, foundations, ground, laboratory research

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Authors: K. Krizova

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This objective of this article is to present concrete that differs by the size of the aggregate used. The set of concrete contained six concrete recipes manufactured as traditional vibrated concrete containing identical basic components of concrete. The experiment focused on monitoring the resulting properties of hardened concrete, specifically the primary strength and modulus of the concrete elasticity and the developing parameters from 7 to 180 days were assessed.

Keywords: aggregate, cement, concrete, elasticity modulus

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Authors: Jiri Palecek, Radmila Hajkova, Alena Oulehlova, Hana Malachova

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The increase of emergency incidents and crisis situations requires proactive crisis management of authorities and for its solution. Application business continuity management systems help the crisis management authorities quickly and responsibly react to events and to plan more effectively and efficiently powers and resources. The main goal of this article is describing Military Continuity Management System (MCMS) based on the principles of Business Continuity Management System (BCMS) for dealing with floods in the territory of the selected municipalities. There are explained steps of loading, running and evaluating activities in the software application MCMS. Software MCMS provides complete control over the tasks, contribute a comprehensive and responsible approach solutions to solution floods in the municipality.

Keywords: business continuity management, floods plan, flood activity, level of flood activity

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Authors: M. Madigoe, R. Modiba

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High alloyed beta (β) phase-stabilized titanium alloys are known to have a low elastic modulus comparable to that of the human bone (≈30 GPa). The β phase in titanium alloys exhibits an elastic Young’s modulus of about 60-80 GPa, which is nearly half that of α-phase (100-120 GPa). In this work, a theoretical investigation of structural stability and thermodynamic stability, as well as the elastic properties of a quaternary Ti-Nb-Ta-Zr alloy, will be presented with an attempt to lower Young’s modulus. The structural stability and elastic properties of the alloy were evaluated using the first-principles approach within the density functional theory (DFT) framework implemented in the CASTEP code. The elastic properties include bulk modulus B, elastic Young’s modulus E, shear modulus cʹ and Poisson’s ratio v. Thermodynamic stability, as well as the fraction of β phase in the alloy, was evaluated using the Thermo-Calc software package. Thermodynamic properties such as Gibbs free energy (Δ?⁰?) and enthalpy of formation will be presented in addition to phase proportion diagrams. The stoichiometric compositions of the alloy is Ti-Nbx-Ta5-Zr5 (x = 5, 10, 20, 30, 40 at.%). An optimum alloy composition must satisfy the Born stability criteria and also possess low elastic Young’s modulus. In addition, the alloy must be thermodynamically stable, i.e., Δ?⁰? < 0.

Keywords: elastic modulus, phase proportion diagram, thermo-calc, titanium alloys

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Authors: David Idiata

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This paper is directed at using the UKCP09 climate change projection tool to predict the effect of climate change on the dynamic modulus of asphalt concrete is Southern England knowing that there is a pressing challenge directly facing infrastructure in the urban cities in the world today due to climate change. Climate change causes change in the environment which in turn impacts on the long-term structural performance of structures. From the projection values obtained, it was discovered that as the temperature increases, the dynamic modulus reduces and this effect was more on the South West which have temperature range of 36.8 oC to 48.3 oC and dynamic modulus range of 2,212 MPa to 1256 MPa.

Keywords: dynamic modulus, asphalt concrete, UKCP09, Southern England

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Authors: M. Guler, E. Guler

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We report some elastic parameters of cubic fluorite type neptunium dioxide (NpO2) with a recent EAM type interatomic potential through geometry optimization calculations. Typical cubic elastic constants, bulk modulus, shear modulus, young modulus and other relevant elastic parameters were also calculated during research. After calculations, we have compared our results with the available theoretical data. Our results agree well with the previous theoretical findings of the considered quantities of NpO2.

Keywords: NpO2, elastic properties, bulk modulus, mechanical properties

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Authors: Reza Ziaie Moayed, Javad Shamsi Soosahab

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Helical piles are being used extensively in engineering applications all over the world. There are insufficient studies on the helical piles' behavior in anisotropic soils. In this paper, numerical modeling was adopted to investigate the effect of elastic modulus anisotropy on helical pile behavior resting on anisotropic sand by using a finite element limit analysis. The load-displacement behavior of helical piles under compression and tension loads is investigated in different relative densities of soils, and the effect of the ratio of horizontal elastic modulus with respect to vertical elastic modulus (EH/EV) is evaluated. The obtained results illustrate that in sandy soils, the anisotropic ratio of elastic modulus (EH/EV) has notable effect on bearing capacity of helical piles in different relative density. Therefore, it may be recommended that the effect of anisotropic condition of soil elastic modulus should be considered in helical piles behavior.

Keywords: helical piles, bearing capacity, numerical modeling, soil anisotropy

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Authors: Muhammad Swilam

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Solutions for the wrong division problem of the Extended Multi-Modulus Divider (EMMD) that occurs during modulus extension (i.e. switching the modulus value between two different ranges of division ratios), in open loop fractional dividers and fractional multiplying delay locked loop, is proposed. A detailed study for the MMD with Sigma-Delta is also presented. Moreover, extensive simulations for the divider are presented to ensure and verify its functionality and compared with the conventional dividers.

Keywords: extended multi-modulus divider (EMMD), fractional multiplying delay locked loop, open loop fractional divider, sigma delta modulator

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Authors: E. Güler, M. Güler

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We present some elastic parameters of cubic fluorite type uranium dioxide (UO2) with a recent EAM type interatomic potential through geometry optimization calculations. Typical cubic elastic constants, bulk modulus, shear modulus, young modulus and other related elastic parameters were calculated during research. After calculations, we compared our results not only with the available theoretical data but also with previous experimental results. Our results are consistent with experiments and compare well the former theoretical results of the considered parameters of UO2.

Keywords: UO2, elastic constants, bulk modulus, mechanical properties

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