This method, Newton raphson helps to approximate the root of a non linear equation.
The presentation also tells about the Advantages and disadvantages of the method.
This document discusses base excitation in vibration analysis and provides examples. It begins by introducing base excitation as an important class of vibration analysis that involves preventing vibrations from passing through a vibrating base into a structure. Examples of base excitation include vibrations in cars, satellites, and buildings during earthquakes. The document then provides mathematical models and equations to analyze single degree of freedom base excitation systems. Graphs of transmissibility ratios are presented and examples are worked through, such as calculating car vibration amplitude at different speeds. Rotating unbalance is also covered as another source of vibration excitation.
L5 determination of natural frequency & mode shapeSam Alalimi
The document summarizes several computational/numerical methods for determining natural frequencies and mode shapes of vibrating systems, including:
- Standard matrix iteration method, which involves solving the eigenvalue problem of the equation of motion.
- Rayleigh's method, which predicts the fundamental natural frequency using an energy method and the Rayleigh quotient.
- Dunkerly's method, which predicts the fundamental natural frequency based on the natural frequencies of individual components.
- Holzer's method, which determines natural frequencies and mode shapes by assuming harmonic motion and setting the equation of motion to zero at each node.
Examples are provided to demonstrate applying these methods to calculate natural frequencies and mode shapes of simple multi-degree of
This document provides equations and calculations for determining the mean cycles to failure (x-bar) and standard deviation of cycles to failure (s_x) for a sample of fatigue test data. The sample data consists of the number of cycles to failure (x) and applied force (f) for 10 tests. The mean x-bar is calculated as the sum of the product of f and x divided by the sum of f, which equals 122.9 kcycles. The standard deviation s_x is calculated using the variance formula, which equals 30.3 kcycles.
This document discusses Newton's forward and backward difference interpolation formulas for equally spaced data points. It provides the formulations for calculating the forward and backward differences up to the kth order. For equally spaced points, the forward difference formula approximates a function f(x) using its kth forward difference at the initial point x0. Similarly, the backward difference formula approximates f(x) using its kth backward difference at x0. The document includes an example problem of using these formulas to estimate the Bessel function and exercises involving interpolation of the gamma function and exponential function.
What is a multiple dgree of freedom (MDOF) system?
How to calculate the natural frequencies?
What is a mode shape?
What is the dynamic stiffness matrix approach?
#WikiCourses
https://wikicourses.wikispaces.com/Lect04+Multiple+Degree+of+Freedom+Systems
https://eau-esa.wikispaces.com/Topic+Multiple+Degree+of+Freedom+%28MDOF%29+Systems
This document provides an overview of modeling systems using Laplace transforms. It discusses:
1) Converting time functions to the frequency domain using Laplace transforms and inverse Laplace transforms
2) Finding transfer functions (TF) from differential equations to model systems
3) Using partial fraction expansions to simplify transfer functions for inverse Laplace transforms
4) Examples of using Laplace transforms to solve differential equations and model various mechanical and electrical systems.
This document discusses the Z-transform and its inverse. It begins by defining the Z-transform as a mapping from a discrete-time signal to a power series. The region of convergence (ROC) is introduced as the set of values where the Z-transform has a finite value. Common properties of the ROC are described. Rational Z-transforms containing poles and zeros are covered. The inverse Z-transform is discussed using inspection and partial fraction expansion methods. The relationship between the Z-transform of a system's impulse response and its transfer function is explained. Finally, the four-step process for analyzing discrete-time linear time-invariant systems in the transform domain using the Z-transform is outlined.
This document discusses base excitation in vibration analysis and provides examples. It begins by introducing base excitation as an important class of vibration analysis that involves preventing vibrations from passing through a vibrating base into a structure. Examples of base excitation include vibrations in cars, satellites, and buildings during earthquakes. The document then provides mathematical models and equations to analyze single degree of freedom base excitation systems. Graphs of transmissibility ratios are presented and examples are worked through, such as calculating car vibration amplitude at different speeds. Rotating unbalance is also covered as another source of vibration excitation.
L5 determination of natural frequency & mode shapeSam Alalimi
The document summarizes several computational/numerical methods for determining natural frequencies and mode shapes of vibrating systems, including:
- Standard matrix iteration method, which involves solving the eigenvalue problem of the equation of motion.
- Rayleigh's method, which predicts the fundamental natural frequency using an energy method and the Rayleigh quotient.
- Dunkerly's method, which predicts the fundamental natural frequency based on the natural frequencies of individual components.
- Holzer's method, which determines natural frequencies and mode shapes by assuming harmonic motion and setting the equation of motion to zero at each node.
Examples are provided to demonstrate applying these methods to calculate natural frequencies and mode shapes of simple multi-degree of
This document provides equations and calculations for determining the mean cycles to failure (x-bar) and standard deviation of cycles to failure (s_x) for a sample of fatigue test data. The sample data consists of the number of cycles to failure (x) and applied force (f) for 10 tests. The mean x-bar is calculated as the sum of the product of f and x divided by the sum of f, which equals 122.9 kcycles. The standard deviation s_x is calculated using the variance formula, which equals 30.3 kcycles.
This document discusses Newton's forward and backward difference interpolation formulas for equally spaced data points. It provides the formulations for calculating the forward and backward differences up to the kth order. For equally spaced points, the forward difference formula approximates a function f(x) using its kth forward difference at the initial point x0. Similarly, the backward difference formula approximates f(x) using its kth backward difference at x0. The document includes an example problem of using these formulas to estimate the Bessel function and exercises involving interpolation of the gamma function and exponential function.
What is a multiple dgree of freedom (MDOF) system?
How to calculate the natural frequencies?
What is a mode shape?
What is the dynamic stiffness matrix approach?
#WikiCourses
https://wikicourses.wikispaces.com/Lect04+Multiple+Degree+of+Freedom+Systems
https://eau-esa.wikispaces.com/Topic+Multiple+Degree+of+Freedom+%28MDOF%29+Systems
This document provides an overview of modeling systems using Laplace transforms. It discusses:
1) Converting time functions to the frequency domain using Laplace transforms and inverse Laplace transforms
2) Finding transfer functions (TF) from differential equations to model systems
3) Using partial fraction expansions to simplify transfer functions for inverse Laplace transforms
4) Examples of using Laplace transforms to solve differential equations and model various mechanical and electrical systems.
This document discusses the Z-transform and its inverse. It begins by defining the Z-transform as a mapping from a discrete-time signal to a power series. The region of convergence (ROC) is introduced as the set of values where the Z-transform has a finite value. Common properties of the ROC are described. Rational Z-transforms containing poles and zeros are covered. The inverse Z-transform is discussed using inspection and partial fraction expansion methods. The relationship between the Z-transform of a system's impulse response and its transfer function is explained. Finally, the four-step process for analyzing discrete-time linear time-invariant systems in the transform domain using the Z-transform is outlined.
Z-transforms can be used to evaluate discrete functions, similar to how Laplace transforms are used for continuous functions. The z-transform of a discrete function f(n) is defined as the sum of f(n) multiplied by z to the power of -n, from n=0 to infinity. Some standard z-transform results include formulas for exponential, sinusoidal, and polynomial functions. Z-transforms have properties of linearity and shifting, and can be used to solve differential equations with constant coefficients and in applications of signal processing.
Z-transforms can be used to analyze systems described by difference equations. The Z-transform relates the terms of a discrete-time sequence to a complex function of a complex variable z. Some key applications of Z-transforms include analyzing Fibonacci series, Newton's interpolation formula, and compound interest problems. Important results for Z-transforms include theorems regarding shifting, constants, initial values, final values, and convolution. Z-transforms are also connected to other transforms like the Fourier transform and Laplace transform through relationships like the discrete-time Fourier transform and bilinear transform.
This document contains a presentation on Newton's second law of motion. The presentation topics include the relation between force, mass and acceleration, applications of Newton's second law, equations of motion, and an introduction to kinetics of particles. The document provides definitions and explanations of key concepts such as force, mass, acceleration, momentum, impulse, and kinetics. It also includes sample problems demonstrating applications of Newton's second law and equations of motion, along with step-by-step solutions. The presentation was made by Danyal Haider and Kamran Shah and covers fundamental principles of classical mechanics.
This document discusses refrigeration and air conditioning systems. It covers topics like principles of refrigeration, vapor compression systems, vapor absorption systems, refrigerants and their properties, refrigeration system components, reciprocating compressors, and principles of air conditioning. Specifically, it describes air refrigeration cycles like open and closed cycles, the reversed Carnot cycle for air refrigeration, and how the coefficient of performance is maximized by decreasing the higher temperature and increasing the lower temperature in the reversed Carnot cycle.
Sliding Mode Control (SMC) is a type of Variable Structure Control that uses a discontinuous control law to drive the system states towards a switching surface, called the sliding surface, in finite time, resulting in robust behavior to disturbances and uncertainties. The summary discusses:
1) SMC involves selecting a sliding surface and designing discontinuous feedback gains such that the system trajectory intersects and stays on the sliding surface.
2) For a sliding mode to exist, the system state trajectory velocity must always be directed towards the sliding surface in its vicinity.
3) Using Lyapunov stability analysis, sufficient conditions are presented to guarantee the existence of a sliding mode and that the sliding surface is reached in finite
Its states Periodic function, Fourier series for disontinous function, Fourier series, Intervals, Odd and even functions, Half range fourier series etc. Mostly used as active learning assignment in Degree 3rd sem students.
Z TRANSFORM PROPERTIES AND INVERSE Z TRANSFORMTowfeeq Umar
The document discusses various methods for computing the inverse z-transform including inspection, partial fraction expansion, and power series expansion. It provides examples to illustrate each method. The inverse z-transform finds the original time domain sequence from its z-transform. Key properties like linearity, time shifting, and convolution are also covered.
The document provides an overview of Fourier transforms. It begins by introducing Fourier series which deals with continuous-time periodic signals and results in discrete frequency spectra. It then discusses how the Fourier integral and continuous Fourier transform can deal with aperiodic signals by providing continuous spectra. The continuous Fourier transform represents a function as an integral of its frequencies, while the inverse transform uses this representation to recover the original function. The properties of the Fourier transform discussed include linearity, time scaling, time reversal, time shifting, and frequency shifting. Real functions have special properties where the Fourier transform is always real or pure imaginary. Examples are provided to illustrate how to calculate the Fourier transform of simple functions.
Modern control engineering 5th ed solution manual (2010)Omar Elfarouk
The document is a solution manual from Pearson Education that contains repeated copyright notices stating that the publication is protected by copyright and written permission must be obtained from Pearson Education for any prohibited reproduction, storage, transmission, or other use. The notices provide contact information for Pearson Education's Rights and Permissions Department.
Exercise 1a transfer functions - solutionswondimu wolde
This document provides information about the course EE4107 - Cybernetics Advanced, including:
- An overview of transfer functions and how they are represented mathematically using numerators and denominators related to zeros and poles.
- How transfer functions can be derived from differential equations using Laplace transforms.
- Functions in MathScript that can be used to define transfer functions and analyze system responses.
- Examples of converting differential equations into transfer functions by taking the Laplace transform.
The z-transform provides a method to analyze discrete-time signals and systems using complex variable theory. It is defined as the summation of a sequence multiplied by z to the power of the time index from negative infinity to positive infinity. The region of convergence consists of values of z where this summation converges. It is determined by the locations of the zeros and poles of the z-transform function. Examples show how different sequences lead to different regions of convergence bounded by these zeros and poles.
The document discusses the region of convergence (ROC) of the z-transform. It states that the ROC is a region in the complex z-plane where the z-transform converges. If the ROC includes the unit circle, then the discrete-time Fourier transform exists and the signal is stable. The ROC can be inside the unit circle, outside the unit circle, or it can be an annular region that includes the unit circle. Examples are provided to illustrate different ROCs for left-sided, right-sided, and two-sided sequences.
Laplace Transformation & Its ApplicationChandra Kundu
This document presents an overview of the Laplace transform and its applications. It begins with an introduction to Laplace transforms as a mathematical tool to convert differential equations into algebraic expressions. It then provides definitions and properties of both the Laplace transform and its inverse. Examples are given of how Laplace transforms can be used to solve ordinary and partial differential equations, as well as applications in electrical circuits and other fields. The document concludes by noting some limitations of the Laplace transform method and references additional resources.
1. The document defines the Laplace transform, Z-transform, and their relationship to continuous-time and discrete-time signals.
2. Tables are provided that list common transforms and their corresponding functions in the s-domain, z-domain, and time/discrete-time domains.
3. Important properties and theorems of the Z-transform are outlined, including linearity, shifting, derivatives, and the inverse z-transform.
Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-IIRai University
This document provides an overview of Unit II - Complex Integration from the Engineering Mathematics-IV course at RAI University, Ahmedabad. It covers key topics such as:
1) Complex line integrals and Cauchy's integral theorem which states that the integral of an analytic function around a closed curve is zero.
2) Cauchy's integral formula which can be used to evaluate integrals and find derivatives of analytic functions.
3) Taylor and Laurent series expansions of functions, including their regions of convergence.
4) The residue theorem which can be used to evaluate real integrals involving trigonometric or rational functions.
The document describes the Newton-Raphson method for finding the roots of nonlinear equations. It provides the derivation of the method, outlines the algorithm as a 3-step process, and gives an example of applying it to find the depth a floating ball submerges in water. The advantages are that it converges fast if it converges and requires only one initial guess. Drawbacks include potential issues with division by zero, root jumping, and oscillations near local extrema.
This document discusses using recurrence relations to model problems involving counting techniques. It provides examples of modeling problems related to bacteria population growth, rabbit population growth, the Tower of Hanoi puzzle, and valid codeword enumeration. For each problem, it defines the recurrence relation and initial conditions, derives a closed-form solution, and proves its correctness using mathematical induction. Recurrence relations provide a way to define sequences and solve problems recursively by relating terms to previous terms in the sequence.
Radix sort is a non-comparative sorting algorithm that sorts data based on the individual digit positions of integer keys. It works by performing multiple passes over the data, where each pass groups keys by a specific digit (from least to most significant). A stable sorting method is used to group the keys in each pass. This results in a running time of O(dn) for d digit positions and n keys.
Z-transforms can be used to evaluate discrete functions, similar to how Laplace transforms are used for continuous functions. The z-transform of a discrete function f(n) is defined as the sum of f(n) multiplied by z to the power of -n, from n=0 to infinity. Some standard z-transform results include formulas for exponential, sinusoidal, and polynomial functions. Z-transforms have properties of linearity and shifting, and can be used to solve differential equations with constant coefficients and in applications of signal processing.
Z-transforms can be used to analyze systems described by difference equations. The Z-transform relates the terms of a discrete-time sequence to a complex function of a complex variable z. Some key applications of Z-transforms include analyzing Fibonacci series, Newton's interpolation formula, and compound interest problems. Important results for Z-transforms include theorems regarding shifting, constants, initial values, final values, and convolution. Z-transforms are also connected to other transforms like the Fourier transform and Laplace transform through relationships like the discrete-time Fourier transform and bilinear transform.
This document contains a presentation on Newton's second law of motion. The presentation topics include the relation between force, mass and acceleration, applications of Newton's second law, equations of motion, and an introduction to kinetics of particles. The document provides definitions and explanations of key concepts such as force, mass, acceleration, momentum, impulse, and kinetics. It also includes sample problems demonstrating applications of Newton's second law and equations of motion, along with step-by-step solutions. The presentation was made by Danyal Haider and Kamran Shah and covers fundamental principles of classical mechanics.
This document discusses refrigeration and air conditioning systems. It covers topics like principles of refrigeration, vapor compression systems, vapor absorption systems, refrigerants and their properties, refrigeration system components, reciprocating compressors, and principles of air conditioning. Specifically, it describes air refrigeration cycles like open and closed cycles, the reversed Carnot cycle for air refrigeration, and how the coefficient of performance is maximized by decreasing the higher temperature and increasing the lower temperature in the reversed Carnot cycle.
Sliding Mode Control (SMC) is a type of Variable Structure Control that uses a discontinuous control law to drive the system states towards a switching surface, called the sliding surface, in finite time, resulting in robust behavior to disturbances and uncertainties. The summary discusses:
1) SMC involves selecting a sliding surface and designing discontinuous feedback gains such that the system trajectory intersects and stays on the sliding surface.
2) For a sliding mode to exist, the system state trajectory velocity must always be directed towards the sliding surface in its vicinity.
3) Using Lyapunov stability analysis, sufficient conditions are presented to guarantee the existence of a sliding mode and that the sliding surface is reached in finite
Its states Periodic function, Fourier series for disontinous function, Fourier series, Intervals, Odd and even functions, Half range fourier series etc. Mostly used as active learning assignment in Degree 3rd sem students.
Z TRANSFORM PROPERTIES AND INVERSE Z TRANSFORMTowfeeq Umar
The document discusses various methods for computing the inverse z-transform including inspection, partial fraction expansion, and power series expansion. It provides examples to illustrate each method. The inverse z-transform finds the original time domain sequence from its z-transform. Key properties like linearity, time shifting, and convolution are also covered.
The document provides an overview of Fourier transforms. It begins by introducing Fourier series which deals with continuous-time periodic signals and results in discrete frequency spectra. It then discusses how the Fourier integral and continuous Fourier transform can deal with aperiodic signals by providing continuous spectra. The continuous Fourier transform represents a function as an integral of its frequencies, while the inverse transform uses this representation to recover the original function. The properties of the Fourier transform discussed include linearity, time scaling, time reversal, time shifting, and frequency shifting. Real functions have special properties where the Fourier transform is always real or pure imaginary. Examples are provided to illustrate how to calculate the Fourier transform of simple functions.
Modern control engineering 5th ed solution manual (2010)Omar Elfarouk
The document is a solution manual from Pearson Education that contains repeated copyright notices stating that the publication is protected by copyright and written permission must be obtained from Pearson Education for any prohibited reproduction, storage, transmission, or other use. The notices provide contact information for Pearson Education's Rights and Permissions Department.
Exercise 1a transfer functions - solutionswondimu wolde
This document provides information about the course EE4107 - Cybernetics Advanced, including:
- An overview of transfer functions and how they are represented mathematically using numerators and denominators related to zeros and poles.
- How transfer functions can be derived from differential equations using Laplace transforms.
- Functions in MathScript that can be used to define transfer functions and analyze system responses.
- Examples of converting differential equations into transfer functions by taking the Laplace transform.
The z-transform provides a method to analyze discrete-time signals and systems using complex variable theory. It is defined as the summation of a sequence multiplied by z to the power of the time index from negative infinity to positive infinity. The region of convergence consists of values of z where this summation converges. It is determined by the locations of the zeros and poles of the z-transform function. Examples show how different sequences lead to different regions of convergence bounded by these zeros and poles.
The document discusses the region of convergence (ROC) of the z-transform. It states that the ROC is a region in the complex z-plane where the z-transform converges. If the ROC includes the unit circle, then the discrete-time Fourier transform exists and the signal is stable. The ROC can be inside the unit circle, outside the unit circle, or it can be an annular region that includes the unit circle. Examples are provided to illustrate different ROCs for left-sided, right-sided, and two-sided sequences.
Laplace Transformation & Its ApplicationChandra Kundu
This document presents an overview of the Laplace transform and its applications. It begins with an introduction to Laplace transforms as a mathematical tool to convert differential equations into algebraic expressions. It then provides definitions and properties of both the Laplace transform and its inverse. Examples are given of how Laplace transforms can be used to solve ordinary and partial differential equations, as well as applications in electrical circuits and other fields. The document concludes by noting some limitations of the Laplace transform method and references additional resources.
1. The document defines the Laplace transform, Z-transform, and their relationship to continuous-time and discrete-time signals.
2. Tables are provided that list common transforms and their corresponding functions in the s-domain, z-domain, and time/discrete-time domains.
3. Important properties and theorems of the Z-transform are outlined, including linearity, shifting, derivatives, and the inverse z-transform.
Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-IIRai University
This document provides an overview of Unit II - Complex Integration from the Engineering Mathematics-IV course at RAI University, Ahmedabad. It covers key topics such as:
1) Complex line integrals and Cauchy's integral theorem which states that the integral of an analytic function around a closed curve is zero.
2) Cauchy's integral formula which can be used to evaluate integrals and find derivatives of analytic functions.
3) Taylor and Laurent series expansions of functions, including their regions of convergence.
4) The residue theorem which can be used to evaluate real integrals involving trigonometric or rational functions.
The document describes the Newton-Raphson method for finding the roots of nonlinear equations. It provides the derivation of the method, outlines the algorithm as a 3-step process, and gives an example of applying it to find the depth a floating ball submerges in water. The advantages are that it converges fast if it converges and requires only one initial guess. Drawbacks include potential issues with division by zero, root jumping, and oscillations near local extrema.
This document discusses using recurrence relations to model problems involving counting techniques. It provides examples of modeling problems related to bacteria population growth, rabbit population growth, the Tower of Hanoi puzzle, and valid codeword enumeration. For each problem, it defines the recurrence relation and initial conditions, derives a closed-form solution, and proves its correctness using mathematical induction. Recurrence relations provide a way to define sequences and solve problems recursively by relating terms to previous terms in the sequence.
Radix sort is a non-comparative sorting algorithm that sorts data based on the individual digit positions of integer keys. It works by performing multiple passes over the data, where each pass groups keys by a specific digit (from least to most significant). A stable sorting method is used to group the keys in each pass. This results in a running time of O(dn) for d digit positions and n keys.
1. The document discusses SignWriting, a writing system for sign languages that is supported by the Center for Sutton Movement Writing.
2. SignWriting uses a grid-based system of glyphs and can be encoded in Unicode, with some sign languages encoded in Plane 15 and others in Plane 16.
3. The Center for Sutton Movement Writing aims to provide standardized, stable, and free specifications for encoding various sign languages in fonts and Unicode for wide accessibility across operating systems and devices.
CELEBRACION DE ELEVAR A LOS ALTARES A SS JUAN Y JUAN
ROGAMOS A DIOS POR SS Y QUE INTERCEDAN POR SU SANTA IGLESIA EN TIERRA, POR SS FRANCISCO, POR LOS FIELES...QUE SE PIERDEN
MIRA LOS VIDEOS EN YOU TUBE DEL GRUPO DE CREENCIA LAICA::
http://www.youtube.com/channel/UCiL56e1l8ztiGqQH67UaZPQ
The document provides contact information for two Cambodia teams promoting World Capital Market 777 (WCM777). It lists mobile numbers, Skype, email addresses, and social media pages. It then shows numerous pages advertising WCM777's cloud services, digital products, investment opportunities, and multi-level compensation plan with bonuses for recruiting others and product sales. WCM777 is presented as a global financial network and investment bank.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms for those who already suffer from conditions like anxiety and depression.
Natural selection occurs through a 5 step process: 1) Variation exists within populations, 2) Organisms compete for limited resources, 3) Organisms produce more offspring than can survive, 4) Genetic traits are passed to offspring, 5) Those organisms with traits most beneficial to survival and reproduction are more likely to survive and reproduce. The document also lists key terms related to biological evolution such as mass extinction, homologous structures, and vestigial structures.
Assessment of business plan session 24 28 november 2014 step by stepGodfrey Tshimauswu
1) The document outlines the step-by-step process for assessing business plans from 2015/16-2017/18 over five days from November 24-28, 2014 in all districts.
2) Session leaders from Social Work and Community Development will lead the process and ensure logistics and documentation are in place, and compile required reports. Panels will be set up to conduct assessments.
3) A daily and comprehensive final report will be compiled to track the number of NPOs assessed and recommended or not recommended for funding, along with any challenges.
Salesforce training with placement in chennaiFTworks
Salesforce training with placement is provided by funtech in chennai. Training will be done with real time projects. Funtech is a training arm of FT works which is a software development company. Get trained by a Software company
The document summarizes several sources on the use of herbal medicine related to women's health and pregnancy. Graham Pinn states that herbal medicine is commonly used to treat menopausal symptoms. Simon Mills and Kerry Bone illustrate how the female reproductive system changes with age. Chong Yun Liu, Angela Tseng and Sue Yang describe symptoms and causes of chronic cervicitis. Rudolf Fritz Weiss recommends treatments for dysmenorrhoea. Two additional sources discuss uses of Vitex agnus-castus and issues with using ginger during pregnancy. Finally, two sources address the importance of consulting healthcare providers when using herbs during pregnancy and avoiding certain herbs.
This software helps companies score opportunities based on data to focus on the most promising accounts, which can generate more revenue while saving money on long sales cycles and extensive travel. A free trial is available without requiring a credit card.
Surgical disaster in temporomandibular joint: Case reportlpfeilsticker
This case report describes a surgical disaster that occurred during treatment of a young woman's congenital bilateral temporomandibular joint ankylosis. During surgery to remove the ankylosis and place prosthetic joints, the patient suffered iatrogenic injuries including facial nerve palsy, deafness on the right side, and a cerebrospinal fluid leak from trauma to the structures of the external, middle, and inner ear on the right side. Computed tomography scans showed extensive destruction of the lateral skull base region involving the middle and inner ear and middle fossa floor on the right side. The patient was left with permanent deafness on the right side, limited mouth opening, and right facial palsy.
How to Develop and Implement Effective Research Tools from Ilm Ideas on Slide...ilmideas
This document discusses various aspects of research design and methodology. It addresses how to properly frame research questions, select appropriate sampling strategies, and consider challenges that may arise. Specific examples are provided on framing research on public-private partnerships in education, remedial teacher education, and the impact of a schooling program. Key points covered include how to minimize sampling error through randomization, representativeness, and accounting for clustering. The importance of statistical power in hypothesis testing and detecting real effects is also emphasized.
1. The document defines various functions and relations using set-builder and function notation.
2. Examples of linear, quadratic, and polynomial functions are provided with their domain and range restrictions.
3. Common transformations of basic quadratic functions like y=x^2 are demonstrated, such as shifting the graph left or right and changing the sign of coefficients.
11 x1 t09 03 rules for differentiation (2013)Nigel Simmons
The document outlines differentiation rules:
1) The derivative of a constant function is 0.
2) The derivative of a function with respect to x multiplied by a constant k is the derivative of the function multiplied by k.
3) The derivative of a polynomial function is found by taking the derivative of each term.
4) The derivative of a function divided by x is the derivative of the function minus the function divided by x squared.
jhkl,l.มือครูคณิตศาสตร์พื้นฐาน ม.4 สสวท เล่ม 2fuyhfgTonn Za
This document summarizes a book titled "The Development of the Thai Language Teaching Materials for Grade 3-4 Students" by Dr. Somchai Srisa-an.
The book was published in 2001 to provide Thai language teaching materials for grades 3-4. It includes 4 chapters, with each chapter focusing on a different grade level (grade 3, chapter 1 and grade 4, chapter 4).
The summary highlights that the book aims to develop Thai language skills for students in grades 3-4 and provides teaching materials tailored to each grade level. It also seeks to appropriately introduce students to the Thai language in order to enhance their language abilities and prepare them for further study.
This document provides solutions to calculating the derivative functions of various given functions. It includes:
1) Finding the derivative functions of polynomials, rational functions, exponential functions, logarithmic functions, trigonometric functions, and composite functions.
2) The solutions provide the step-by-step work and final derivative function for each problem.
3) There are over 25 problems covered across multiple pages with the aim of teaching calculation of derivative functions.
This document contains an instructor's resource manual for limits concepts with examples and problem sets. It includes definitions of limits, worked examples of limit calculations, and limit problems to solve.
This document contains an instructor's resource manual for limits concepts with examples and problem sets. It includes definitions of limits, worked examples of limit calculations, and limit problems to solve.
1. The document provides examples of limits calculations and concepts.
2. Key steps in limit calculations are presented such as evaluating one-sided limits separately if they differ and using algebraic manipulation to simplify expressions before taking the limit.
3. Problem sets with solutions demonstrate various types of limits, including one-sided limits, limits at infinity, limits of rational functions, and limits of trigonometric functions.
1) The document provides definitions and formulas for calculating derivatives, including the derivative of a function at a point, the derivative function, and common derivatives of basic functions like polynomials, exponentials, logarithms, trigonometric functions, and inverse trigonometric functions.
2) Examples are given of calculating derivatives using the definition of the derivative, for functions like f(x)=3x^2, f(x)=x+1, and f(x)=1/x.
3) Rules are listed for calculating the derivatives of sums, products, quotients of functions using properties of derivatives.
Solutions manual for fundamentals of business math canadian 3rd edition by je...Pollockker
This document provides the solutions manual for the 3rd Canadian edition of the textbook "Fundamentals of Business Math" by Jerome. It contains solutions to exercises in Chapter 2 on reviewing and applying algebra. The exercises cover basic, intermediate, and advanced algebra problems involving operations with variables, exponents, percentages, and compound interest.
The document provides tables summarizing rules for deriving functions. It lists common functions and their derivatives, such as the derivative of a sum of functions being the sum of the individual derivatives. Examples are given such as the derivative of x4 + x3 being 4x3 + 3x2. Trigonometric functions and their inverses are also covered.
The document contains the solutions to several calculus problems:
1) Finding the total amount spent in an economy where dollars recirculate at 90% each time.
2) Calculating the speed needed to shoot a basketball into a hoop from a given distance and height.
3) Taking derivatives and integrals to solve optimization problems.
The document discusses the discrete Fourier transform (DFT) and its application to signals with different numbers of points. It provides the equations to calculate the DFT of 2-point, 4-point and 8-point signals. For a 4-point signal x(n) with points x(0), x(1), x(2), x(3), it shows the calculation of the DFT X(k) at points X(0), X(1), X(2), X(3).
This document provides information about calculator models and functions. It begins with a list of calculator models, followed by examples of math expressions and their equivalent forms on different lines. The remainder of the document contains examples of calculations and statistical functions performed on a calculator.
This document contains mathematical formulas and calculations related to probability and statistics. It includes formulas for variance, standard deviation, t-tests, chi-squared tests, conditional probability, binomial probability, and Poisson probability. An example calculates the probability of having 1 boy out of 5 children.
The document provides exercises on calculating derivatives using various rules including the sum and difference rule, product rule, and quotient rule. It includes 15 problems calculating derivatives of given functions and finding numerical derivatives at given values. The answers provide the step-by-step work to arrive at the derivatives using the appropriate rules.
1. This document provides a review of concepts and sample problems related to multiple integrals. It covers topics such as iterated integrals, changing the order of integration, and evaluating double integrals over various regions.
2. The problem set contains 14 problems evaluating double integrals over different regions using techniques like iterated integration and changing the order of integration.
3. Multiple integrals are used to find volumes, masses, moments, and other physical quantities over regions in 2D and 3D space. The document demonstrates how to set up and evaluate multiple integrals to solve applied problems.
This document contains mathematical equations and calculations related to limits, derivatives, and functions. Some key details:
- It evaluates several limits as the variable approaches various values.
- It finds derivatives of functions using limit definitions.
- It solves equations related to finding maximum/minimum values and points of inflection for functions.
1. The document provides solutions to math problems involving sets, logic, trigonometry, vectors, and calculus.
2. It gives step-by-step workings and explanations for solving equations derived from geometric and algebraic expressions.
3. The problems cover a wide range of mathematical concepts and the document shows the thought process and reasoning for arriving at the answers.
1. The document provides solutions to math problems involving sets, logic, trigonometry, vectors, and calculus.
2. Several problems are solved involving intersections of sets, logical statements, trigonometric identities, and vector operations.
3. Solutions include determining the intersection of two sets, evaluating logical statements, simplifying trigonometric expressions, and calculating the cross product of two vectors.
ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
6. SStteepp 22
6
Calculate the next estimate of the root
x = x - f(x )
i
f'(x )
i
i+1 i
Find the absolute relative approximate error
x 100
= x - x
i i
1
1
x
i
a
+
Î +
7. SStteepp 33
Find if the absolute relative approximate error is greater
than the pre-specified relative error tolerance.
If so, go back to step 2, else stop the algorithm.
Also check if the number of iterations has exceeded the
maximum number of iterations.
7
8. EExxaammppllee
Solve the given equation using Newton’s method using 3 iterations:
8
f ( x) = x3-0.165x2+3.993x10-4