This document summarizes a study on the generalized thermoelastic problem of a semi-infinite thin rod subjected to a step in strain. The study obtained solutions for temperature distribution, strain, and stress for small time values using the Laplace transform method. The study formulated the problem using the equations of motion, energy, and constitutive relations for an isotropic linear elastic solid. Non-dimensional variables were introduced to simplify the governing equations.
A study on singular perturbation correction to bond prices under affine term ...Frank Fung
The document discusses applying the technique of singular perturbation to pricing fixed income derivatives. Singular perturbation provides a convenient way to account for stochastic interest rate volatility. The accuracy of a perturbation corrected Vasicek model is evaluated by comparing its yield curve fitting to an exact analytic Fong-Vasicek model. The perturbation scheme achieves comparable accuracy to the exact model while requiring much less computational time. The perturbation scheme is also extended to a CIR model, though the advantage in speed is diminished due to the need for numerical methods.
-type and -type four dimensional plane wave solutions of Einstein's field eq...inventy
In the present paper, we have studied - type and -type plane wave solutions of Einstein's field equations in general theory of relativity in the case where the zero mass scalar field coupled with gravitational field and zero mass scalar field coupled with gravitational & electromagnetic field and established the existence of these two types of plane wave solutions in . Furthermore we have considered the case of massive scalar field and shown that the non-existence of these two types of plane wave solutions in GR theory.
Natural frequencies of magnetoelastic longitudinal wave propagationAlexander Decker
This document summarizes research on the natural frequencies of longitudinal wave propagation in an orthotropic circular cylinder permeated by a magnetic field. It begins by introducing the topic and providing background. It then presents the basic equations that govern magnetoelastic wave propagation. Specifically, it outlines the equations of motion for an elastic solid in a magnetic field, including the Lorentz force term. It also presents Maxwell's equations in the quasi-static approximation. The document derives a frequency equation for this problem and describes numerically solving for the natural frequencies of the first three modes for different material properties and cylinder geometries.
Gravitation al field_equations_and_theory_of_dark matter_and_dark_energySérgio Sacani
1) The document derives new gravitational field equations and establishes a unified theory of dark matter and dark energy.
2) The key ideas are that the energy-momentum tensor need not be divergence-free, and the field equations obey the Euler-Lagrange equation of the Einstein-Hilbert functional under a divergence-free constraint on the metric.
3) The new field equations introduce a scalar potential φ. The scalar potential energy density represents a new type of energy that accounts for dark matter and dark energy based on the distribution of matter.
The document discusses nonabelian vortices in nematic liquid crystals. It describes how vortices are topologically classified based on the symmetry group π1(SO3/D2)=Q8. An ansatz is proposed for isolated nonabelian vortices characterized by elements of the quaternion group. The energetics of different classes of vortices are analyzed, showing some may dissociate into others depending on conditions. The non-abelian nature of biaxial nematic defects is suggested to lead to topological rigidity slowing phase ordering dynamics.
On estimating the integrated co volatility usingkkislas
This document proposes a method to estimate the integrated co-volatility of two asset prices using high-frequency data that contains both microstructure noise and jumps.
It considers two cases - when the jump processes of the two assets are independent, and when they are dependent. For the independent case, it proposes an estimator that is robust to jumps. For the dependent case, it proposes a threshold estimator that combines pre-averaging to remove noise with a threshold method to reduce the effect of jumps. It proves the estimators are consistent and establishes their central limit theorems. Simulation results are also presented to illustrate the performance of the proposed methods.
Finite element modelling of nonlocal dynamic systems, Modal analysis of nonlocal dynamical systems, Dynamics of damped nonlocal systems, Numerical illustrations
This document is an acknowledgements section from a Master's Thesis on the Anderson model. It thanks several people for their contributions:
- The instructor, Professor Martti Salomaa, for introducing the topic, providing guidance and sharing insights.
- Dr. Juha Fagerholm for helping develop computational code and advising on programming.
- Dr. Robert Joynt for teaching basics of superconductivity.
- Colleagues for assistance with LaTeX and other software.
- The whole laboratory for creating an inspiring work environment.
A study on singular perturbation correction to bond prices under affine term ...Frank Fung
The document discusses applying the technique of singular perturbation to pricing fixed income derivatives. Singular perturbation provides a convenient way to account for stochastic interest rate volatility. The accuracy of a perturbation corrected Vasicek model is evaluated by comparing its yield curve fitting to an exact analytic Fong-Vasicek model. The perturbation scheme achieves comparable accuracy to the exact model while requiring much less computational time. The perturbation scheme is also extended to a CIR model, though the advantage in speed is diminished due to the need for numerical methods.
-type and -type four dimensional plane wave solutions of Einstein's field eq...inventy
In the present paper, we have studied - type and -type plane wave solutions of Einstein's field equations in general theory of relativity in the case where the zero mass scalar field coupled with gravitational field and zero mass scalar field coupled with gravitational & electromagnetic field and established the existence of these two types of plane wave solutions in . Furthermore we have considered the case of massive scalar field and shown that the non-existence of these two types of plane wave solutions in GR theory.
Natural frequencies of magnetoelastic longitudinal wave propagationAlexander Decker
This document summarizes research on the natural frequencies of longitudinal wave propagation in an orthotropic circular cylinder permeated by a magnetic field. It begins by introducing the topic and providing background. It then presents the basic equations that govern magnetoelastic wave propagation. Specifically, it outlines the equations of motion for an elastic solid in a magnetic field, including the Lorentz force term. It also presents Maxwell's equations in the quasi-static approximation. The document derives a frequency equation for this problem and describes numerically solving for the natural frequencies of the first three modes for different material properties and cylinder geometries.
Gravitation al field_equations_and_theory_of_dark matter_and_dark_energySérgio Sacani
1) The document derives new gravitational field equations and establishes a unified theory of dark matter and dark energy.
2) The key ideas are that the energy-momentum tensor need not be divergence-free, and the field equations obey the Euler-Lagrange equation of the Einstein-Hilbert functional under a divergence-free constraint on the metric.
3) The new field equations introduce a scalar potential φ. The scalar potential energy density represents a new type of energy that accounts for dark matter and dark energy based on the distribution of matter.
The document discusses nonabelian vortices in nematic liquid crystals. It describes how vortices are topologically classified based on the symmetry group π1(SO3/D2)=Q8. An ansatz is proposed for isolated nonabelian vortices characterized by elements of the quaternion group. The energetics of different classes of vortices are analyzed, showing some may dissociate into others depending on conditions. The non-abelian nature of biaxial nematic defects is suggested to lead to topological rigidity slowing phase ordering dynamics.
On estimating the integrated co volatility usingkkislas
This document proposes a method to estimate the integrated co-volatility of two asset prices using high-frequency data that contains both microstructure noise and jumps.
It considers two cases - when the jump processes of the two assets are independent, and when they are dependent. For the independent case, it proposes an estimator that is robust to jumps. For the dependent case, it proposes a threshold estimator that combines pre-averaging to remove noise with a threshold method to reduce the effect of jumps. It proves the estimators are consistent and establishes their central limit theorems. Simulation results are also presented to illustrate the performance of the proposed methods.
Finite element modelling of nonlocal dynamic systems, Modal analysis of nonlocal dynamical systems, Dynamics of damped nonlocal systems, Numerical illustrations
This document is an acknowledgements section from a Master's Thesis on the Anderson model. It thanks several people for their contributions:
- The instructor, Professor Martti Salomaa, for introducing the topic, providing guidance and sharing insights.
- Dr. Juha Fagerholm for helping develop computational code and advising on programming.
- Dr. Robert Joynt for teaching basics of superconductivity.
- Colleagues for assistance with LaTeX and other software.
- The whole laboratory for creating an inspiring work environment.
Suppression of correlated electron escape in double ionization in strong lase...Jakub Prauzner-Bechcicki
1) The document discusses selection rules in double ionization of atoms and the suppression of correlated electron escape in double ionization of metastable helium.
2) It examines using a symmetric subspace and quantum simulations to model double ionization, showing suppression for a 800nm single-cycle laser pulse.
3) Double ionization of molecules like N2 and O2 is also discussed, with the conclusion that similar suppression may occur for oriented O2.
1) The document summarizes research on the ground state of strongly coupled quark matter with a finite isospin chemical potential.
2) A Ginzburg-Landau theory approach is used to qualitatively analyze the phase transition near the critical point in a model-independent way.
3) It is found that at zero isospin chemical potential, the chiral condensation transition becomes first-order at high densities due to the formation of spatial inhomogeneities. At finite isospin chemical potential, charged pion condensation can occur in addition to chiral condensation.
A current perspectives of corrected operator splitting (os) for systemsAlexander Decker
This document discusses operator splitting methods for solving systems of convection-diffusion equations. It begins by introducing operator splitting, where the time evolution is split into separate steps for convection and diffusion. While efficient, operator splitting can produce significant errors near shocks.
The document then examines the nonlinear error mechanism that causes issues for operator splitting near shocks. When a shock develops in the convection step, it introduces a local linearization that neglects self-sharpening effects. This leads to splitting errors.
To address this, the document discusses corrected operator splitting, which uses the wave structure from the convection step to identify where nonlinear splitting errors occur. Terms are added to the diffusion step to compensate for
This document contains a quantum mechanics formula sheet from fiziks, an institute that provides coaching for physics exams. It covers various topics in quantum mechanics over 12 sections, including wave-particle duality, mathematical tools, the Schrodinger equation, angular momentum, perturbation theory, and identical particles. It also provides contact information for fiziks' head office and branch office in New Delhi, India.
This document presents a systematic study of static vacuum solutions to Einstein's equations with a negative cosmological constant that asymptotically approach the generalized Kottler solution. It discusses three approaches to describing the asymptotic structure: three-dimensional conformal compactification, four-dimensional conformal completion, and a coordinate approach. It shows that under reasonable assumptions, the conformal boundary at infinity is connected. It also defines several notions of mass for these spacetimes and derives inequalities relating the mass and horizon area that could help prove uniqueness of the generalized Kottler black hole solutions.
The document discusses the dynamic response of structures with uncertain properties. It begins with an introduction discussing how stochasticity impacts dynamic response and efficient quantification of uncertainty. It then covers stochastic single degree of freedom and multiple degree of freedom damped systems. Equivalent damping factors are derived for single degree systems with random natural frequencies. The spectral function approach is also introduced for representing multiple degree of freedom stochastic systems in the frequency domain.
This document discusses dynamics of structures with uncertainties. It begins with an introduction to stochastic single degree of freedom systems and how natural frequency variability can be modeled using probability distributions. It then discusses how to extend this approach to stochastic multi degree of freedom systems using stochastic finite element formulations and modal projections. Key challenges with statistical overlap of eigenvalues are noted. The document provides mathematical models of equivalent damping in stochastic systems and examples of stochastic frequency response functions.
This document summarizes research on the dynamics and structure of Janus particles under shear flow. Direct numerical simulations were used to model Janus particles, which are spheres composed of two distinct hemispheres. Simulation conditions such as shear rate, temperature, particle volume fraction, and interaction strength were varied. Initial binary simulations showed that at high shear rates or low interaction strengths, shear forces can overcome attraction and break particle pairs apart. Larger multi-particle simulations found that at low shear, flow helps break up and reform aggregates, while at high shear, clusters rapidly decay. Radial distribution functions were also analyzed to characterize particle structures under shear.
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Mathematical formulation of inverse scattering and korteweg de vries equationAlexander Decker
This document summarizes the mathematical formulation of inverse scattering and the Korteweg-de Vries (KdV) equation. It begins by defining inverse scattering as determining solutions to differential equations based on known asymptotic solutions, specifically by solving the Marchenko equation. It then discusses how the KdV equation describes shallow water waves and solitons, and how the inverse scattering transform method can be used to determine soliton solutions from arbitrary initial conditions. The document outlines the procedure, including deriving the scattering data from an initial potential function and using its time evolution to reconstruct solutions to the KdV equation at later times. It provides examples using reflectionless potentials, specifically obtaining the single-soliton solution from an initial sech^2
Effective properties of heterogeneous materialsSpringer
1) The document discusses the multipole expansion method (MEM) for analyzing the microstructure and effective properties of composite materials.
2) MEM reduces boundary value problems for heterogeneous materials to systems of linear algebraic equations. It expresses fields like temperature and stress as expansions of basis functions related to inclusion geometry.
3) MEM has been applied to analyze conductivity and elasticity problems in composites with spherical, spheroidal, circular, and elliptic inclusions. It provides analytical solutions for local fields and exact expressions for effective properties involving only dipole moments.
International Journal of Mathematics and Statistics Invention (IJMSI) inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Dynamic stiffness and eigenvalues of nonlocal nano beams - new methods for dynamic analysis of nano-scale structures. This lecture gives a review and proposed new techniques.
Peridynamic simulation of delamination propagation in fiber-reinforced compositeYILE HU
This document outlines a peridynamic simulation of delamination propagation in fiber-reinforced composites. It introduces peridynamic theory and the bond-based peridynamic model for composites. It describes the micromodulus, critical stretch criteria, and energy-based approaches for modeling failure. It also discusses explicit and implicit solvers, as well as the use of GPU computing to simulate crack propagation examples like double cantilever beam and transverse crack tension tests.
Stability analysis for nonlinear impulsive optimal control problemsAI Publications
We consider the generic stability of optimal control problems governed by nonlinear impulsive evolution equations. Under perturbations of the right-hand side functions of the controlled system, the results of stability for the impulsive optimal control problems are proved given set-valued theory.
Presentation at "Emerging problems in particle phenomenology" workshop held at CUNY on April 11, 2010. Has sensitivity of Jets+MET searches for 7 TeV LHC.
The document discusses residual stresses that arise during welding due to localized heating and rapid cooling. It analyzes how welding conditions like travel speed, specimen size, constraints, and preheating can affect residual stress distributions. A finite element model is used to simulate butt welding and predict residual stresses in the weld and base metal. The results show that transverse and longitudinal residual stresses are highest near the weld and decrease with increasing distance. Faster travel speeds, larger specimen sizes, and preheating can reduce residual stresses, while external constraints decrease transverse shrinkage and associated stresses.
STUDIES ON INTUTIONISTIC FUZZY INFORMATION MEASURESurender Singh
This document discusses studies on measures of intuitionistic fuzzy information. It begins with introductions and definitions related to fuzzy sets, intuitionistic fuzzy sets, and measures of fuzzy entropy. It then discusses special t-norm operators and proposes a measure of intuitionistic fuzzy entropy based on these t-norms. The measure is defined using a function of the membership, non-membership, and hesitancy degrees of an intuitionistic fuzzy set. Several desirable properties of such a measure are outlined, including sharpness, maximality, resolution, symmetry, and valuation. The document provides mathematical foundations and definitions to propose and analyze a measure of intuitionistic fuzzy entropy.
Lesson 12: Linear Approximation (Section 41 handout)Matthew Leingang
The line tangent to a curve, which is also the line which best "fits" the curve near that point. So derivatives can be used for approximating complicated functions with simple linear ones. Differentials are another set of notation for the same problem.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This document summarizes a research paper on a GSM-based power meter reading and control system. The system uses GSM technology to remotely read electricity meter readings and send the readings to users and the electricity department via SMS. It also allows remote control of power to appliances to reduce unnecessary power consumption. The system takes meter readings daily and sends them to the electricity billing system to generate accurate monthly bills without human errors. The hardware and software designs are presented along with block diagrams of the meter-side and server-side systems. The research aims to automate energy billing and enable remote power monitoring and control.
The document presents a method for solving fuzzy assignment problems using triangular and trapezoidal fuzzy numbers. It formulates the fuzzy assignment problem into a crisp linear programming problem that can be solved using the Hungarian method. The paper also uses Robust's ranking method to transform fuzzy costs into crisp values, allowing conventional solution methods to be applied. It aims to provide a more realistic approach to assignment problems by considering costs as fuzzy numbers rather than deterministic values.
Suppression of correlated electron escape in double ionization in strong lase...Jakub Prauzner-Bechcicki
1) The document discusses selection rules in double ionization of atoms and the suppression of correlated electron escape in double ionization of metastable helium.
2) It examines using a symmetric subspace and quantum simulations to model double ionization, showing suppression for a 800nm single-cycle laser pulse.
3) Double ionization of molecules like N2 and O2 is also discussed, with the conclusion that similar suppression may occur for oriented O2.
1) The document summarizes research on the ground state of strongly coupled quark matter with a finite isospin chemical potential.
2) A Ginzburg-Landau theory approach is used to qualitatively analyze the phase transition near the critical point in a model-independent way.
3) It is found that at zero isospin chemical potential, the chiral condensation transition becomes first-order at high densities due to the formation of spatial inhomogeneities. At finite isospin chemical potential, charged pion condensation can occur in addition to chiral condensation.
A current perspectives of corrected operator splitting (os) for systemsAlexander Decker
This document discusses operator splitting methods for solving systems of convection-diffusion equations. It begins by introducing operator splitting, where the time evolution is split into separate steps for convection and diffusion. While efficient, operator splitting can produce significant errors near shocks.
The document then examines the nonlinear error mechanism that causes issues for operator splitting near shocks. When a shock develops in the convection step, it introduces a local linearization that neglects self-sharpening effects. This leads to splitting errors.
To address this, the document discusses corrected operator splitting, which uses the wave structure from the convection step to identify where nonlinear splitting errors occur. Terms are added to the diffusion step to compensate for
This document contains a quantum mechanics formula sheet from fiziks, an institute that provides coaching for physics exams. It covers various topics in quantum mechanics over 12 sections, including wave-particle duality, mathematical tools, the Schrodinger equation, angular momentum, perturbation theory, and identical particles. It also provides contact information for fiziks' head office and branch office in New Delhi, India.
This document presents a systematic study of static vacuum solutions to Einstein's equations with a negative cosmological constant that asymptotically approach the generalized Kottler solution. It discusses three approaches to describing the asymptotic structure: three-dimensional conformal compactification, four-dimensional conformal completion, and a coordinate approach. It shows that under reasonable assumptions, the conformal boundary at infinity is connected. It also defines several notions of mass for these spacetimes and derives inequalities relating the mass and horizon area that could help prove uniqueness of the generalized Kottler black hole solutions.
The document discusses the dynamic response of structures with uncertain properties. It begins with an introduction discussing how stochasticity impacts dynamic response and efficient quantification of uncertainty. It then covers stochastic single degree of freedom and multiple degree of freedom damped systems. Equivalent damping factors are derived for single degree systems with random natural frequencies. The spectral function approach is also introduced for representing multiple degree of freedom stochastic systems in the frequency domain.
This document discusses dynamics of structures with uncertainties. It begins with an introduction to stochastic single degree of freedom systems and how natural frequency variability can be modeled using probability distributions. It then discusses how to extend this approach to stochastic multi degree of freedom systems using stochastic finite element formulations and modal projections. Key challenges with statistical overlap of eigenvalues are noted. The document provides mathematical models of equivalent damping in stochastic systems and examples of stochastic frequency response functions.
This document summarizes research on the dynamics and structure of Janus particles under shear flow. Direct numerical simulations were used to model Janus particles, which are spheres composed of two distinct hemispheres. Simulation conditions such as shear rate, temperature, particle volume fraction, and interaction strength were varied. Initial binary simulations showed that at high shear rates or low interaction strengths, shear forces can overcome attraction and break particle pairs apart. Larger multi-particle simulations found that at low shear, flow helps break up and reform aggregates, while at high shear, clusters rapidly decay. Radial distribution functions were also analyzed to characterize particle structures under shear.
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Mathematical formulation of inverse scattering and korteweg de vries equationAlexander Decker
This document summarizes the mathematical formulation of inverse scattering and the Korteweg-de Vries (KdV) equation. It begins by defining inverse scattering as determining solutions to differential equations based on known asymptotic solutions, specifically by solving the Marchenko equation. It then discusses how the KdV equation describes shallow water waves and solitons, and how the inverse scattering transform method can be used to determine soliton solutions from arbitrary initial conditions. The document outlines the procedure, including deriving the scattering data from an initial potential function and using its time evolution to reconstruct solutions to the KdV equation at later times. It provides examples using reflectionless potentials, specifically obtaining the single-soliton solution from an initial sech^2
Effective properties of heterogeneous materialsSpringer
1) The document discusses the multipole expansion method (MEM) for analyzing the microstructure and effective properties of composite materials.
2) MEM reduces boundary value problems for heterogeneous materials to systems of linear algebraic equations. It expresses fields like temperature and stress as expansions of basis functions related to inclusion geometry.
3) MEM has been applied to analyze conductivity and elasticity problems in composites with spherical, spheroidal, circular, and elliptic inclusions. It provides analytical solutions for local fields and exact expressions for effective properties involving only dipole moments.
International Journal of Mathematics and Statistics Invention (IJMSI) inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Dynamic stiffness and eigenvalues of nonlocal nano beams - new methods for dynamic analysis of nano-scale structures. This lecture gives a review and proposed new techniques.
Peridynamic simulation of delamination propagation in fiber-reinforced compositeYILE HU
This document outlines a peridynamic simulation of delamination propagation in fiber-reinforced composites. It introduces peridynamic theory and the bond-based peridynamic model for composites. It describes the micromodulus, critical stretch criteria, and energy-based approaches for modeling failure. It also discusses explicit and implicit solvers, as well as the use of GPU computing to simulate crack propagation examples like double cantilever beam and transverse crack tension tests.
Stability analysis for nonlinear impulsive optimal control problemsAI Publications
We consider the generic stability of optimal control problems governed by nonlinear impulsive evolution equations. Under perturbations of the right-hand side functions of the controlled system, the results of stability for the impulsive optimal control problems are proved given set-valued theory.
Presentation at "Emerging problems in particle phenomenology" workshop held at CUNY on April 11, 2010. Has sensitivity of Jets+MET searches for 7 TeV LHC.
The document discusses residual stresses that arise during welding due to localized heating and rapid cooling. It analyzes how welding conditions like travel speed, specimen size, constraints, and preheating can affect residual stress distributions. A finite element model is used to simulate butt welding and predict residual stresses in the weld and base metal. The results show that transverse and longitudinal residual stresses are highest near the weld and decrease with increasing distance. Faster travel speeds, larger specimen sizes, and preheating can reduce residual stresses, while external constraints decrease transverse shrinkage and associated stresses.
STUDIES ON INTUTIONISTIC FUZZY INFORMATION MEASURESurender Singh
This document discusses studies on measures of intuitionistic fuzzy information. It begins with introductions and definitions related to fuzzy sets, intuitionistic fuzzy sets, and measures of fuzzy entropy. It then discusses special t-norm operators and proposes a measure of intuitionistic fuzzy entropy based on these t-norms. The measure is defined using a function of the membership, non-membership, and hesitancy degrees of an intuitionistic fuzzy set. Several desirable properties of such a measure are outlined, including sharpness, maximality, resolution, symmetry, and valuation. The document provides mathematical foundations and definitions to propose and analyze a measure of intuitionistic fuzzy entropy.
Lesson 12: Linear Approximation (Section 41 handout)Matthew Leingang
The line tangent to a curve, which is also the line which best "fits" the curve near that point. So derivatives can be used for approximating complicated functions with simple linear ones. Differentials are another set of notation for the same problem.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This document summarizes a research paper on a GSM-based power meter reading and control system. The system uses GSM technology to remotely read electricity meter readings and send the readings to users and the electricity department via SMS. It also allows remote control of power to appliances to reduce unnecessary power consumption. The system takes meter readings daily and sends them to the electricity billing system to generate accurate monthly bills without human errors. The hardware and software designs are presented along with block diagrams of the meter-side and server-side systems. The research aims to automate energy billing and enable remote power monitoring and control.
The document presents a method for solving fuzzy assignment problems using triangular and trapezoidal fuzzy numbers. It formulates the fuzzy assignment problem into a crisp linear programming problem that can be solved using the Hungarian method. The paper also uses Robust's ranking method to transform fuzzy costs into crisp values, allowing conventional solution methods to be applied. It aims to provide a more realistic approach to assignment problems by considering costs as fuzzy numbers rather than deterministic values.
This document analyzes stresses in a rotating circular disc with a central hole and symmetrical array of non-central holes using finite element analysis. It investigates the effect of geometric parameters such as R2/R1 ratio of inner to outer disc radius, d/2R1 ratio of hole diameter to disc radius, Rb/(R2-R1) ratio of pitch circle radius to annular width, and number of holes N. Stress concentration factors are derived for these parameters. As number of holes increases, the stress concentration factor decreases. Results are verified against analytical solutions. Contour plots show highest stresses occur near holes.
This document discusses dispersion compensation techniques for optical code division multiple access (OCDMA) systems using dispersion compensation fiber (DCF) and fiber gratings. It compares the performance of an 8-user OCDMA system using DCF versus fiber gratings. The results show that DCF more effectively compensates for dispersion, as evidenced by a lower bit error rate and higher Q factor, making it a better dispersion compensation method for OCDMA systems compared to fiber gratings.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
This document proposes integrating iris recognition with RFID cards to develop a high-security access environment. It discusses:
1) How iris recognition works, including iris segmentation, normalization, feature extraction using wavelets, and identification by comparing templates.
2) Details of the RFID card used, including its microcontroller and memory, and the design of an RFID card programmer.
3) The proposed method of integrating iris recognition by storing the extracted iris features and a signature in the RFID card, and comparing them during authentication.
4) Preliminary test results comparing combinations of wavelet coefficients to find the best approach. Performance metrics like reading time, writing time, and memory utilization are evaluated.
This document summarizes a study assessing groundwater quality in rural areas near Vijayawada, India. The study analyzed physicochemical parameters like pH, turbidity, conductivity, alkalinity, hardness, nitrates and more from groundwater samples from four villages. Most parameters were within permissible limits, except for higher hardness levels. The highest conductivity, pH, chlorides, alkalinity were found in samples from Nidamanuru village, possibly due to agricultural and industrial pollution from nearby areas entering the groundwater. The study aims to evaluate groundwater quality for drinking and other uses in the region.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
The document describes a new architecture for a high-speed multiplier accumulator (MAC) unit. The MAC uses a modified Booth encoding algorithm to reduce the number of partial products generated during multiplication. It also uses a hybrid carry save adder structure to improve performance. Additionally, it incorporates a spurious power suppression technique (SPST) to reduce power consumption during the addition process. The MAC accumulates intermediate results as sums and carries rather than using the final adder output to improve output rate. Analysis shows the proposed MAC requires fewer hardware resources, has lower delay, and reduced power compared to previous designs.
This document describes a microcontroller based speed control system for a DC geared motor through an RS-232 interface with a PC. The system uses pulse width modulation to control the speed of the motor. It includes hardware components like a power supply module, microcontroller, LCD display, motor driver IC, and MAX232 level converter. The software development involves coding in C language, compiling the code, and burning the hex file onto the microcontroller using a programmer. The system allows variable speed control of the DC motor through a GUI on the PC. It provides a platform for industrial applications requiring precision speed control of DC motors.
This document summarizes a research paper that proposes a novel seven-level inverter for grid-connected photovoltaic systems. The inverter uses a hybrid cascaded configuration with a novel pulse width modulation technique to generate seven output voltage levels from the DC supply. Simulation results using MATLAB/Simulink are presented to validate the operation of the proposed inverter. The inverter is capable of improving power quality by reducing harmonic distortion compared to traditional two-level inverters.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Este documento apresenta os resultados financeiros da TPI - Triunfo Participações e Investimentos S.A. no quarto trimestre de 2012 e no ano de 2012. Destaca o crescimento da receita líquida, do tráfego em rodovias e portos, e do EBITDA ajustado. Apresenta também os principais investimentos realizados e a estrutura de endividamento da companhia.
O documento discute três gêneros de parasitas que infectam peixes: Chilodonella spp, Trichodina spp e Dactylogyrus spp. Trichodina spp se fixa nas brânquias dos peixes e se alimenta de bactérias, proliferando em ambientes eutróficos ou de má qualidade da água e causando patologias. Dactylogyrus spp e Chilodenella spp também infectam as brânquias, causando perda de apetite, respiração acelerada e morte dos
El documento describe las diferentes clases de amigos que encontramos en la vida y cómo algunos permanecen con nosotros por mucho tiempo mientras que otros solo pasan brevemente. Compara amigos con las hojas de un árbol, donde algunos están cerca nuestro como la familia, otros son amigos cercanos, y otros son amigos distantes que aparecen ocasionalmente. Aunque algunos amigos se van con el tiempo, dejan recuerdos felices que nos alimentan como personas.
1. Se realizó la reunión constitutiva del Foro Federal de Legisladores por la Infancia en San Juan, Argentina, con la participación de legisladores de varias provincias y niveles de gobierno.
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1. D. Raju / International Journal of Engineering Research and Applications
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Vol. 2, Issue 4, July-August 2012, pp.621-630
Generalized Thermoelastic Problem Concerning Semi–Infinite Rods
Problem Of Step In Strain
D. Raju
Vidya Jyothi Institute of Technology, AzizNagar Gate, Hyderabad-500 075,
Andhra Pradesh, India.
Abstract
In this paper, we have solved a generalized thermoelasticity problem concerning to semi – infinite
thin rods subjected to step in strain. We obtained the solutions for small values of time.
AMS Mathematics Subject Classification: 34 B 40.
Key Words: Generalized thermoelasticity, Temperature distribution, Strain – Acceleration, Relaxation Constant,
Stress-Strain relations.
1. Introduction
Transient heat transfer problems usually involve the solution of the classical Fourier heat Conduction
equation, which is of parabolic character, as a consequence a perturbed heat signal propagates with an infinite
velocity through the medium. That is, if an isotropic homogeneous elastic continuum is subjected to a mechanical or
thermal disturbance, the effect of the disturbance will be felt instantaneously at distances infinitely far from its
source. Such a behaviour is physically inadmissible and contradicts the existing theories of heat transport
mechanisms.
Nonconventional thermoelasticity theories in which the parabolic heat transport equation is replaced by a hyperbolic
heat transport equation do not suffer from the above said drawbacks and they admit Wave – like thermal signals
propagating with finite speeds. A wave like thermal signal is referred to as second Sound – the first sound being the
usual sound wave. Thermoelasticity theories admitting such signals are known as thermoelasticity theories with
Second Sound or Generalized thermoelasticity theories or hyperbolic thermoelasticity. A bibliographical review of
the literature on the above theory was given by Chandrasekharaiah, D.S [2] in his review article, and
“Thermoelasticity with second sound“.
Tisza, L [4] predicted the possibility of extremely small heat propagation rates (Second Sound) in liquid Helium –
II. Chester, M [5] discussed the possibility of existence of Second Sound in solids. The experiments on Sodium
Helium by Ackerman, C.C et.al [1] and by Mc Nelly, T et.al [7] on Sodium fluoride, have shown that second sound
occurs in solids also. The second sound effect indicates that heat can be transported by wave type mechanism rather
than usual diffusion process. All these researches lead to the reformulation of the existing Fourier heat conduction
equation in to a damped wave type equation, which is hyperbolic.
Morse, P.M and Feshbach, H [6] postulated that the governing transient heat conduction must depend upon the
velocity of the propagation of heat C. They assumed that the equation,
2
1 T 1 T 2
T
2 2
C t h t
Which is hyperbolic, must be the correct governing differential equation for heat conduction problems.
Here, we have studied the application of the generalized theory of thermoelasticity to semi–infinite thin
rods when the rods are subjected to Step in strain. Since the specimen is very thin and long the problem is treated as
one dimensional.
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Vol. 2, Issue 4, July-August 2012, pp.621-630
The solutions of problems of this type usually do not permit closed forms unless certain
relaxations in the constraints are made. In order to obtain a closed form solution Lord, H.W. and Schulman Y [3]
neglected the strain – acceleration term in the field equations, on the assumption that, for most materials, the
relaxation constant and coupled parameter have very small values (< < 1) and that their product has naturally very
insignificant value.
Since the problems of this type are amenable to integral transform methods, Laplace
transform is used and the solutions are obtained for small values of time.
2. Formulation of the problem:
Consider a long thin rod in which the only non zero stress component is the axial one 1 . The equation of
motion reduces to
2
u
1 1
(1)
0 2
x t
1
Where u1 is the displacement in the axial direction x1 , 0 is the undeformed density and t is the
time. The energy equation of isotropic linear thermoelasticity is given by,
2
T 2T e 2 e
0 2
3 2 T
T
0 E 0 0 2
k C (2)
t t t t
2
x
1
The constitutive equation for the isotropic linear elastic solid can be written as
(3 2 ) e 3 (3 2 )T (3)
1
For the case of thin rod
u
1
E ET ( 4)
1
x
1
From (2) and (3), we get
2
T T 2T 1 21
0 2 0 2
k C T (5)
0 0
t t
2
x t t
1
Where,
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Vol. 2, Issue 4, July-August 2012, pp.621-630
2
3 (3 2 ) T
0
C C
E
0
Here,
u
1
e (6)
x
1
From equations (1) and (4), we get
23 3
u
T u
1 1
E E
0
(7)
2 3 2
x x t x
1 1 1
Using the following non dimensional variables,
1
x
1 u vt E 2
k ( C T )
o 1
1
x , u , , v , a , ,
a a a 0 0 C v ( T E )
o
E
2
o C o v
β = Relaxation constant =
k
2
To E
=Coupling Constant =
(8)
o C
We get the field equations as,
....
IV II II
u (1 ) u
u
(1 ) (1 ) u 0
u (9)
and similar equations to and also. Here, primes denote differentiation with respect to x and
superposed dots denote differentiation with respect to time . The following auxiliary relations can be obtained
from the foregoing equations.
From equation (7), we get
I II
u u
(10)
From equation (4), we get
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Vol. 2, Issue 4, July-August 2012, pp.621-630
I
u (10 a )
From the above two equations, we get
.. ..
II
(11)
From equation (5), we get
. .. . ..
II
(12)
From equations (10), (10 a) and (12), we get,
III I I
(1 ) (1 ) u
(1 )u u
(13)
Applying Laplace transform to equation (9), we get
IV 2 II 3
u [(1 ) p p ]u (1 ) p (1 p ) u 0 (14)
( p ) d
u ( x , p ) u ( x , ). e
Where,
o
while applying Laplace transform, we have used the initial conditions
. .. ...
u ( x , 0) u ( x , 0) u ( x , 0) u ( x , 0) 0
If 1 , 2
2
2 are the roots of the characteristic equation of (14), we get
2 2
1 2 p[(1 ) p 1]
1
2 2 2 2
1 2 p[(1 ) p 1] 4 p (1 )(1 p )] (15)
Solving, we get
1
2
1 2
(1 ) p 1 ((1 ) p 1) 4 p (1 )(1 p )
p 2
1,2
2
(16)
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For large values of p, we get
p 1
1,2 k O
p (17)
1,2
V
1,2
2 1
2
1
2
Where, v
1,2
1/ 2 2
4K V [1 (1 2 ) ] and (1 ) 4
1,2 1,2
As we see v1 < v2, we get
1 3 3/2 1
p [ p 1 2 ] O
p
2 2
1 2
1
2
For small values of p, we get 1 p , 2 0 (18)
3. Problem of step in strain
The boundary and initial conditions are,
u 0
for 0
(0, ) (19)
x
x0 0
for 0
(0, ) 0
We know the governing equation satisfied by displacement u is (equation 9)
. II ... ....
IV II
u (1 )u u (1 ) u (1 ) u 0
Proceeding as in previous problems, applying Laplace transform and using boundary conditions
(19), we get
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6. D. Raju / International Journal of Engineering Research and Applications
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Vol. 2, Issue 4, July-August 2012, pp.621-630
1
u 1 2 2 ( 2 x )
2 2 [(1 ) p p 1 ] e
0 p ( 2 1 )
2 2 ( x)
[(1 ) p p 2 ] e 1 ( 20)
Taking inverse transform for large values of p, we get
for
x
0
v2
k2 x
e 1 2k 1 2 1 x
1 2 1 1 2
1
v1
v1 v 1
v1
2
x x
for
v2 v1
k1x
1 1 2 1 x
I
u e 2k
1 2 2 1 2
1
v1
v2 v 2
0
2
v2
k x
e 2 1 2k 1 2 1 x
1 2 1 1 2
1
v2
v1 v 1
v1
2
for
x
v1
(21)
From equation (13), the temperature distribution is given by,
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Vol. 2, Issue 4, July-August 2012, pp.621-630
1 2 2 2 2
[(1 ) v1 v2 1 v1 v2 ]
for
x
v2
k2 x 2 2 2
2 2
2 k 2 v2 1 v1 v1 1 v 2
2
x
e
1
2 2
2
1 v 2 v1 v1 1 1 v 2 2 k1v1 v1
2
v2
v1
1 2
1 v 2
2 v1 v1
2
2
1
1 v1 v 2 1 v1 v 2
2 2 2 2
x x
for
v2 v1
k x
2 2
2 k1v1 1 v 2 v 2 1 v1
2
e 1
0 1 2
2 2
2
1 v1 v 2 v 2 1 1 v1 2 k 2 v2 v 2
2
x
2 2 v1
v2
1 2
1 v
2
1 v2 v2
2 2
1
2 2
2 k1v2 1 v1 v1 1 v 2 2
e 2
k x
x
1
2 2
2
2 2
2
1 v 2 v1 v1 1 1 v 2 2 k 2 v1 v1
2
v2
v1
1 2
1 v 2
2 v1 v1
2 2
1
1 v1 v 2 1 v1 v 2
2 2 2 2
x
for
v1
(22)
For most of the materials the parameters and have smaller values so that the product is far less
than Unity. Based on this assumption, Lord, H.W. and Shulman, Y [3] neglected the term containing , which is
the term involving strain acceleration. Here we want to study the effect of dropping this term from the field
equations.
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Vol. 2, Issue 4, July-August 2012, pp.621-630
Neglecting the term containing , we get the field equations as
.. II . II ... ....
IV
u (1 ) u u (1 ) u u 0 (23)
..
I II
u u (24)
I
u (25)
.. ..
II
(26)
. .. . ..
II
(27)
and,
. .. I .I
III
u u u (28)
Applying Laplace transform, we get
IV 2 II 3
u [(1 ) p p ]u [1 p ] p u 0 (29)
If 1 and 2 are the characteristic roots of (29), we have
2 2
1 2 p[(1 ) p 1] ,
2 2 3
1 2 (1 p ) p
2 2 2 1
1 2 p[(1 ) p 1] 4 p (1 p )] 2
p 2 1 1
1,2 2 2
2 [(1 ) p 1 [(1 ) p 1) 4 p (1 p ) ] 30
For large values of p,
p 1
1,2 K1,2 O
V1,2
p
Where,
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2 1
2 1 2
v1,2
12
4 K1,2 V [1 (1 2 )
1,2 ]
2
(1 ) (31)
For the problem of velocity impact, from equation (29), taking the regularity boundary condition
at infinity into account, we get
( 1x) ( 2 x)
u ( x, p ) A e e
Here A and B are constants and are determined using boundary conditions.
I
u
1
2 (12 p 2 ) e( 2 x ) 1 (2 p 2 ) e( 1x )
2
2 2 2
v0 p ( 2 1 )
For large values of p, we get
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Vol. 2, Issue 4, July-August 2012, pp.621-630
0,
x
for
v2
v e k2 x
1 2 1 v 2
2
2
2 2 2
1
1 v 2
1
1
2 k1v1 k 2 v2 1 v
1
x
v 2
v1 v 2
for
x
x
v2 v1
u
I
v0
k1x
2 1 2 1 v 2
2
v e
1
2
1 v 2 k 2 v2 k1v1 1 v
2
2
x
v1
1
1
2 2 2 k2x 1 2 1 v
2
2
v1 v 2
v2 e
1 v2
1
1
2 k1v1 k 2 v2 1 v
1
x
v 2
x
for
v1
32
Acknowledgement:
First, I thank Dr.D.Rama Murthy, (Rtd) Professor of Mathematics, U.C.S, Osmania University, Hyderabad,
for his valuable suggestions in preparing this paper.
References
[1] C.C. Ackerman, B. Bentman, H.A.Fairbank, and R.A.Guyer, Second Sound in Solid Helium – 3,
Phys.Rev.Letters, Vol. 16 (1966), p.p. 789.
[2] D.S. Chandrasekaraiah, Thermoelasticity with Second Sound – A Review, Trans. ASME, Appl. Mech.Rev,
Vol. 39 (1986), p.p. 355.
[3] H.W .Lord and Y. Shulman, A Generalized Dynamical Theory of Thermoelasticity, J.Mech.Phys.Solids,
Vol. 15 (1996), p.p. 299.
[4] L.Tisza, Heat Propagation Rates In Helium – II, J.Phys.Radium, Paris, Vol. 1 (1940), p.p. 350.
[5] M. Chester, Second Sound in Solids, Phys.Rev.Letters, 131, 2013, (1963).
[6] P.M .Morse, and H.Feshbach, Methods of Theoretical Physics, Mc Graw – Hill, New York, 865, (1953).
[7] T. McNally, et.al, Heat Pulses in NaF, Phys.Rev.Letters, Vol. 24 (1970), p.p. 100.
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