Fall 2008 midterm
•
0 likes•205 views
This document provides a midterm exam for a differential equations course. It includes 5 questions testing skills like finding integrating factors, determining linear dependence, using methods like variation of parameters, and applying concepts like damping to solve differential equations modeling physical systems. Students are instructed to complete the exam without notes in 75 minutes and solutions will be posted in a few days.
Report
Share
Report
Share
Download to read offline
Recommended
Fall 2008 midterm solutions
The document is a math exam containing 5 questions regarding differential equations. Question 1 has 3 parts asking about integrating factors, values of m, and solutions to a differential equation. Question 2 asks for the general solution to a given differential equation. Question 3 has 7 parts testing knowledge of rate equations, linear dependence, differential equation types, undetermined coefficients methods, uniqueness of solutions, damped motion, and Euler's method. Question 4 asks for the position function of a damped spring system. Question 5 asks to use the variation of parameters method to find the particular solution to a given nonhomogeneous differential equation.
19 2
This document discusses techniques for solving first order differential equations, including separation of variables and exact equations. It begins by introducing separation of variables as a method to solve equations of the form dy/dx = f(x)g(y) by dividing through and integrating both sides separately. Examples are provided. The document then discusses exact equations, which can be solved directly by integrating both sides. It provides examples and explains how the solution consists of a definite part satisfying the equation and an indefinite part satisfying a related equation with zero on the right side. The document concludes by explaining how to recognize exact equations based on their form.
Engineering Mathematics 2 questions & answers
1. The document contains a mock exam for the course EE203 Mathematical Methods for Engineers II. It consists of 6 questions testing various skills in ordinary and partial differential equations.
2. The questions cover skills like solving exact and homogeneous differential equations, using separation of variables, Laplace transforms, power series solutions, and Fourier series.
3. Sample solutions are provided for parts of some questions to illustrate the solution methods. Formulas for various transforms, series and other relevant mathematical tools are also provided.
Structural VAR: the AB model
Time series econometrics
VAR/ SVAR representation
structural shock identification
estimation of SVAR model in Eviews
Univariate Financial Time Series Analysis
An Introduction to Univariate Financial Time Series Analysis
Carlo Favero
Dept of Finance, Bocconi University
Normal density and discreminant analysis
This document provides an overview of Gaussian density and discriminant analysis. It discusses mathematical descriptions of discriminant functions and how they are used in classifiers to select classes. It also covers bi-variate and multi-variate normal density functions and how they relate to dependent and independent random variables. Specifically, it shows how the shape of the loci of bi-variate density functions depends on whether variables are independent or dependent. Finally, it discusses discriminant functions and how to determine decision boundaries between classes.
Ma2002 1.23 rm
1. The document discusses the convergence and stability of finite difference methods for solving ordinary and partial differential equations numerically.
2. It shows that the error of the finite difference solution converges to zero as the grid size decreases, establishing convergence of the method.
3. It analyzes the stability of explicit finite difference schemes for a test differential equation. The type of difference approximation used for the first derivative term depends on the sign of a constant, in order to satisfy the stability condition for the scheme.
11.solution of a singular class of boundary value problems by variation itera...
1) The document proposes an effective methodology called the variation iteration method to find solutions to singular second order linear and nonlinear boundary value problems.
2) The variation iteration method constructs a sequence of correction functionals to iteratively solve the boundary value problem. It is shown that the limit of the convergent iterative sequence obtained from this method is the exact solution.
3) The convergence of the iterative sequence generated by the variation iteration method is analyzed. It is established that the sequence converges to the exact solution under certain continuity conditions on the problem functions.
Recommended
Fall 2008 midterm solutions
The document is a math exam containing 5 questions regarding differential equations. Question 1 has 3 parts asking about integrating factors, values of m, and solutions to a differential equation. Question 2 asks for the general solution to a given differential equation. Question 3 has 7 parts testing knowledge of rate equations, linear dependence, differential equation types, undetermined coefficients methods, uniqueness of solutions, damped motion, and Euler's method. Question 4 asks for the position function of a damped spring system. Question 5 asks to use the variation of parameters method to find the particular solution to a given nonhomogeneous differential equation.
19 2
This document discusses techniques for solving first order differential equations, including separation of variables and exact equations. It begins by introducing separation of variables as a method to solve equations of the form dy/dx = f(x)g(y) by dividing through and integrating both sides separately. Examples are provided. The document then discusses exact equations, which can be solved directly by integrating both sides. It provides examples and explains how the solution consists of a definite part satisfying the equation and an indefinite part satisfying a related equation with zero on the right side. The document concludes by explaining how to recognize exact equations based on their form.
Engineering Mathematics 2 questions & answers
1. The document contains a mock exam for the course EE203 Mathematical Methods for Engineers II. It consists of 6 questions testing various skills in ordinary and partial differential equations.
2. The questions cover skills like solving exact and homogeneous differential equations, using separation of variables, Laplace transforms, power series solutions, and Fourier series.
3. Sample solutions are provided for parts of some questions to illustrate the solution methods. Formulas for various transforms, series and other relevant mathematical tools are also provided.
Structural VAR: the AB model
Time series econometrics
VAR/ SVAR representation
structural shock identification
estimation of SVAR model in Eviews
Univariate Financial Time Series Analysis
An Introduction to Univariate Financial Time Series Analysis
Carlo Favero
Dept of Finance, Bocconi University
Normal density and discreminant analysis
This document provides an overview of Gaussian density and discriminant analysis. It discusses mathematical descriptions of discriminant functions and how they are used in classifiers to select classes. It also covers bi-variate and multi-variate normal density functions and how they relate to dependent and independent random variables. Specifically, it shows how the shape of the loci of bi-variate density functions depends on whether variables are independent or dependent. Finally, it discusses discriminant functions and how to determine decision boundaries between classes.
Ma2002 1.23 rm
1. The document discusses the convergence and stability of finite difference methods for solving ordinary and partial differential equations numerically.
2. It shows that the error of the finite difference solution converges to zero as the grid size decreases, establishing convergence of the method.
3. It analyzes the stability of explicit finite difference schemes for a test differential equation. The type of difference approximation used for the first derivative term depends on the sign of a constant, in order to satisfy the stability condition for the scheme.
11.solution of a singular class of boundary value problems by variation itera...
1) The document proposes an effective methodology called the variation iteration method to find solutions to singular second order linear and nonlinear boundary value problems.
2) The variation iteration method constructs a sequence of correction functionals to iteratively solve the boundary value problem. It is shown that the limit of the convergent iterative sequence obtained from this method is the exact solution.
3) The convergence of the iterative sequence generated by the variation iteration method is analyzed. It is established that the sequence converges to the exact solution under certain continuity conditions on the problem functions.
Solution of a singular class of boundary value problems by variation iteratio...
1. The document proposes an effective methodology called the variation iteration method to find solutions to a general class of singular second-order linear and nonlinear boundary value problems.
2. The variation iteration method generates a sequence of correction functionals that converges to the exact solution of the boundary value problem.
3. The author applies the variation iteration method to solve a specific class of boundary value problems and derives the sequence of correction functionals. Convergence of the iterative sequence is also analyzed.
Ch07 8
The document discusses repeated eigenvalues in systems of linear differential equations. If some eigenvalues are repeated, there may not be n linearly independent solutions of the form x = ξert. Additional solutions must be sought that are products of polynomials and exponential functions. For a double eigenvalue r, the first solution is x(1) = ξert, where ξ satisfies (A-rI)ξ = 0. The second solution has the form x(2) = ξtert + ηert, where η satisfies (A-rI)η = ξ and η is called a generalized eigenvector.
Solution of a subclass of singular second order
This document discusses using the Taylor series method to solve a subclass of singular second order differential equations of Lane-Emden type.
The method is applied to solve boundary value problems that arise from modeling physical phenomena. The Taylor series method produces an analytic solution in the form of a polynomial function.
Several examples from literature are considered to demonstrate the suitability and viability of the Taylor series method for solving these types of differential equations.
11.solution of a subclass of singular second order
This document presents a method for solving a subclass of singular second order differential equations of Lane-Emden type using Taylor series. The method identifies conditions where the equations can be solved analytically as a polynomial function. Several examples from literature are provided and solved using the proposed Taylor series method to demonstrate its effectiveness. The method produces exact solutions in polynomial form and is shown to perform well on both linear and nonlinear boundary value problems.
201977 1-1-4-pb
In this paper, the L1 norm of continuous functions and corresponding continuous estimation of regression parameters are defined. The continuous L1 norm estimation problem of one and two parameters linear models in the continuous case is solved. We proceed to use the functional form and parameters of the probability distribution function of income to exactly determine the L1 norm approximation of the corresponding Lorenz curve of the statistical population under consideration.
Differential equation
This document discusses differential equations. It defines differential equations as equations relating an unknown function and one or more of its derivatives. It describes the order and degree of differential equations. Several examples of first order differential equations are given and solved using techniques like direct integration, variable separation, and solving homogeneous equations. The key steps for solving first order differential equations are outlined.
Week 1 [compatibility mode]
This document introduces ordinary differential equations (ODEs). It defines an ODE as an equation involving a dependent variable, independent variable, and one or more derivatives of the dependent variable. The document discusses order of ODEs, solving methods including general, particular, and exact solutions, and applications of ODEs. It was prepared by Annie ak Joseph for the 2008/2009 session.
Ch07 6
The document discusses complex eigenvalues and eigenvectors for systems of linear differential equations. It shows that if the matrix A has complex conjugate eigenvalue pairs r1 and r2, then the corresponding eigenvectors and solutions will also be complex conjugates. This leads to real-valued fundamental solutions that can express the general solution. An example demonstrates these concepts, finding the complex eigenvalues and eigenvectors and expressing the general solution in terms of real-valued functions. Spiral points, centers, eigenvalues, and trajectory behaviors are also summarized.
Section2 stochastic
1. The document discusses concepts related to expectation and variance of random variables including expected value, variance, moments, and examples of calculating these for different probability distributions like uniform, normal, exponential, and Rayleigh.
2. Problems at the end provide examples of computing expected value, variance, and cumulative distribution function for random variables following different distributions. Solutions show the calculations and formulas used.
3. Key formulas introduced include definitions of expected value and variance, the relationship between them, and formulas for calculating moments, expected value, and variance for specific distributions. Examples demonstrate applying the concepts and formulas to problems.
A study on singular perturbation correction to bond prices under affine term ...
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.
Lesson 14: Derivatives of Exponential and Logarithmic Functions (Section 021 ...
The exponential function is pretty much the only function whose derivative is itself. The derivative of the natural logarithm function is also beautiful as it fills in an important gap. Finally, the technique of logarithmic differentiation allows us to find derivatives without the product rule.
Ch07 7
The document discusses fundamental matrices and their properties. A fundamental matrix Ψ(t) is a matrix whose columns are fundamental solutions to the system x' = P(t)x. Ψ(t) satisfies the differential equation Ψ' = P(t)Ψ and is nonsingular. The general solution to the system can be written as x = Ψ(t)c, where c is a constant vector. For an initial value problem, the solution is x = Ψ(t)Ψ-1(t0)x0. The fundamental matrix Φ(t) corresponding to a set of fundamental solutions satisfying initial conditions is also discussed. Matrix exponential functions are introduced as the fundamental matrix
Nonlinear perturbed difference equations
The paper reports on an iteration algorithm to compute asymptotic solutions at any order for a wide class of nonlinear
singularly perturbed difference equations.
Third-kind Chebyshev Polynomials Vr(x) in Collocation Methods of Solving Boun...
This paper proposed the use of third-kind Chebyshev polynomials as trial functions in solving boundary value problems via collocation method. In applying this method, two different collocation points are considered, which are points at zeros of third-kind Chebyshev polynomials and equally-spaced points. These points yielded different results on each considered problem, thus possessing different level of accuracy. The
method is computational very simple and attractive. Applications are equally demonstrated through numerical examples to illustrate the efficiency and simplicity of the approach
Conformable Chebyshev differential equation of first kind
In this paper, the Chebyshev-I conformable differential equation is considered. A proper power series is examined; there are two solutions, the even solution and the odd solution. The Rodrigues’ type formula is also allocated for the conformable Chebyshev-I polynomials.
8th alg -l5.6--jan7
1) The document provides assignments and lesson material for solving linear inequalities and graphing linear inequalities on a coordinate plane.
2) It gives steps for graphing linear inequalities which include graphing the inequality line and testing points to determine which half-plane to shade.
3) Examples are worked through demonstrating how to graph inequalities such as y > 1/2x + 3, 3x - y < 2, and 3y > -18 on a coordinate plane by following the given steps.
How to Solve a Partial Differential Equation on a surface
Familiar techniques of separation of variables and Fourier series can be used to solve a variety of pde based on domains in the plane, however these techniques do not extend naturally to surface problems. Instead we look to take a computational approach. The talk will cover the basics of finite difference and finite element approximations of the one dimensional heat equation and show how to extend these ideas on to surfaces. If time allows, we will show numerical results of an optimal partition problem based on a sphere. No background knowledge of pde or computation is required.
Solution of second order nonlinear singular value problems
1) The document presents a method for finding solutions to second order nonlinear singular boundary value problems using Taylor series.
2) The method modifies the differential equation to handle singularities, then obtains recurrence relations for the Taylor series coefficients by taking derivatives at the singular point.
3) Examples are provided to demonstrate the method, yielding exact solutions for problems in astronomy modeling gas spheres and other physical applications.
First order linear differential equation
1. A differential equation relates an unknown function and its derivatives, and can be ordinary (involving one variable) or partial (involving partial derivatives).
2. Linear differential equations have dependent variables and derivatives that are of degree one, and coefficients that do not depend on the dependent variable.
3. Common methods for solving first-order linear differential equations include separation of variables, homogeneous equations, and exact equations.
Discrete-Chapter 12 Modeling Computation
This document discusses finite state machines and regular expressions. It provides definitions and examples of finite state machines with output and without output. It also defines regular expressions recursively and provides examples of describing regular language sets using regular expressions. The document contains several examples of constructing state diagrams and tables for finite state machines based on descriptions, and determining if strings belong to regular language sets defined by regular expressions.
My projet life
Mi proyecto de vida consiste en terminar mis estudios universitarios el próximo año y encontrar un trabajo estable. A largo plazo, me gustaría casarme y formar una familia cuando tenga unos 30 años. Mi mayor aspiración es jubilarme a una edad temprana para poder viajar y disfrutar de la vida.
More Related Content
What's hot
Solution of a singular class of boundary value problems by variation iteratio...
1. The document proposes an effective methodology called the variation iteration method to find solutions to a general class of singular second-order linear and nonlinear boundary value problems.
2. The variation iteration method generates a sequence of correction functionals that converges to the exact solution of the boundary value problem.
3. The author applies the variation iteration method to solve a specific class of boundary value problems and derives the sequence of correction functionals. Convergence of the iterative sequence is also analyzed.
Ch07 8
The document discusses repeated eigenvalues in systems of linear differential equations. If some eigenvalues are repeated, there may not be n linearly independent solutions of the form x = ξert. Additional solutions must be sought that are products of polynomials and exponential functions. For a double eigenvalue r, the first solution is x(1) = ξert, where ξ satisfies (A-rI)ξ = 0. The second solution has the form x(2) = ξtert + ηert, where η satisfies (A-rI)η = ξ and η is called a generalized eigenvector.
Solution of a subclass of singular second order
This document discusses using the Taylor series method to solve a subclass of singular second order differential equations of Lane-Emden type.
The method is applied to solve boundary value problems that arise from modeling physical phenomena. The Taylor series method produces an analytic solution in the form of a polynomial function.
Several examples from literature are considered to demonstrate the suitability and viability of the Taylor series method for solving these types of differential equations.
11.solution of a subclass of singular second order
This document presents a method for solving a subclass of singular second order differential equations of Lane-Emden type using Taylor series. The method identifies conditions where the equations can be solved analytically as a polynomial function. Several examples from literature are provided and solved using the proposed Taylor series method to demonstrate its effectiveness. The method produces exact solutions in polynomial form and is shown to perform well on both linear and nonlinear boundary value problems.
201977 1-1-4-pb
In this paper, the L1 norm of continuous functions and corresponding continuous estimation of regression parameters are defined. The continuous L1 norm estimation problem of one and two parameters linear models in the continuous case is solved. We proceed to use the functional form and parameters of the probability distribution function of income to exactly determine the L1 norm approximation of the corresponding Lorenz curve of the statistical population under consideration.
Differential equation
This document discusses differential equations. It defines differential equations as equations relating an unknown function and one or more of its derivatives. It describes the order and degree of differential equations. Several examples of first order differential equations are given and solved using techniques like direct integration, variable separation, and solving homogeneous equations. The key steps for solving first order differential equations are outlined.
Week 1 [compatibility mode]
This document introduces ordinary differential equations (ODEs). It defines an ODE as an equation involving a dependent variable, independent variable, and one or more derivatives of the dependent variable. The document discusses order of ODEs, solving methods including general, particular, and exact solutions, and applications of ODEs. It was prepared by Annie ak Joseph for the 2008/2009 session.
Ch07 6
The document discusses complex eigenvalues and eigenvectors for systems of linear differential equations. It shows that if the matrix A has complex conjugate eigenvalue pairs r1 and r2, then the corresponding eigenvectors and solutions will also be complex conjugates. This leads to real-valued fundamental solutions that can express the general solution. An example demonstrates these concepts, finding the complex eigenvalues and eigenvectors and expressing the general solution in terms of real-valued functions. Spiral points, centers, eigenvalues, and trajectory behaviors are also summarized.
Section2 stochastic
1. The document discusses concepts related to expectation and variance of random variables including expected value, variance, moments, and examples of calculating these for different probability distributions like uniform, normal, exponential, and Rayleigh.
2. Problems at the end provide examples of computing expected value, variance, and cumulative distribution function for random variables following different distributions. Solutions show the calculations and formulas used.
3. Key formulas introduced include definitions of expected value and variance, the relationship between them, and formulas for calculating moments, expected value, and variance for specific distributions. Examples demonstrate applying the concepts and formulas to problems.
A study on singular perturbation correction to bond prices under affine term ...
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.
Lesson 14: Derivatives of Exponential and Logarithmic Functions (Section 021 ...
The exponential function is pretty much the only function whose derivative is itself. The derivative of the natural logarithm function is also beautiful as it fills in an important gap. Finally, the technique of logarithmic differentiation allows us to find derivatives without the product rule.
Ch07 7
The document discusses fundamental matrices and their properties. A fundamental matrix Ψ(t) is a matrix whose columns are fundamental solutions to the system x' = P(t)x. Ψ(t) satisfies the differential equation Ψ' = P(t)Ψ and is nonsingular. The general solution to the system can be written as x = Ψ(t)c, where c is a constant vector. For an initial value problem, the solution is x = Ψ(t)Ψ-1(t0)x0. The fundamental matrix Φ(t) corresponding to a set of fundamental solutions satisfying initial conditions is also discussed. Matrix exponential functions are introduced as the fundamental matrix
Nonlinear perturbed difference equations
The paper reports on an iteration algorithm to compute asymptotic solutions at any order for a wide class of nonlinear
singularly perturbed difference equations.
Third-kind Chebyshev Polynomials Vr(x) in Collocation Methods of Solving Boun...
This paper proposed the use of third-kind Chebyshev polynomials as trial functions in solving boundary value problems via collocation method. In applying this method, two different collocation points are considered, which are points at zeros of third-kind Chebyshev polynomials and equally-spaced points. These points yielded different results on each considered problem, thus possessing different level of accuracy. The
method is computational very simple and attractive. Applications are equally demonstrated through numerical examples to illustrate the efficiency and simplicity of the approach
Conformable Chebyshev differential equation of first kind
In this paper, the Chebyshev-I conformable differential equation is considered. A proper power series is examined; there are two solutions, the even solution and the odd solution. The Rodrigues’ type formula is also allocated for the conformable Chebyshev-I polynomials.
8th alg -l5.6--jan7
1) The document provides assignments and lesson material for solving linear inequalities and graphing linear inequalities on a coordinate plane.
2) It gives steps for graphing linear inequalities which include graphing the inequality line and testing points to determine which half-plane to shade.
3) Examples are worked through demonstrating how to graph inequalities such as y > 1/2x + 3, 3x - y < 2, and 3y > -18 on a coordinate plane by following the given steps.
How to Solve a Partial Differential Equation on a surface
Familiar techniques of separation of variables and Fourier series can be used to solve a variety of pde based on domains in the plane, however these techniques do not extend naturally to surface problems. Instead we look to take a computational approach. The talk will cover the basics of finite difference and finite element approximations of the one dimensional heat equation and show how to extend these ideas on to surfaces. If time allows, we will show numerical results of an optimal partition problem based on a sphere. No background knowledge of pde or computation is required.
Solution of second order nonlinear singular value problems
1) The document presents a method for finding solutions to second order nonlinear singular boundary value problems using Taylor series.
2) The method modifies the differential equation to handle singularities, then obtains recurrence relations for the Taylor series coefficients by taking derivatives at the singular point.
3) Examples are provided to demonstrate the method, yielding exact solutions for problems in astronomy modeling gas spheres and other physical applications.
First order linear differential equation
1. A differential equation relates an unknown function and its derivatives, and can be ordinary (involving one variable) or partial (involving partial derivatives).
2. Linear differential equations have dependent variables and derivatives that are of degree one, and coefficients that do not depend on the dependent variable.
3. Common methods for solving first-order linear differential equations include separation of variables, homogeneous equations, and exact equations.
Discrete-Chapter 12 Modeling Computation
This document discusses finite state machines and regular expressions. It provides definitions and examples of finite state machines with output and without output. It also defines regular expressions recursively and provides examples of describing regular language sets using regular expressions. The document contains several examples of constructing state diagrams and tables for finite state machines based on descriptions, and determining if strings belong to regular language sets defined by regular expressions.
What's hot (20)
Solution of a singular class of boundary value problems by variation iteratio...
Solution of a singular class of boundary value problems by variation iteratio...
11.solution of a subclass of singular second order
11.solution of a subclass of singular second order
A study on singular perturbation correction to bond prices under affine term ...
A study on singular perturbation correction to bond prices under affine term ...
Lesson 14: Derivatives of Exponential and Logarithmic Functions (Section 021 ...
Lesson 14: Derivatives of Exponential and Logarithmic Functions (Section 021 ...
Third-kind Chebyshev Polynomials Vr(x) in Collocation Methods of Solving Boun...
Third-kind Chebyshev Polynomials Vr(x) in Collocation Methods of Solving Boun...
Conformable Chebyshev differential equation of first kind
Conformable Chebyshev differential equation of first kind
How to Solve a Partial Differential Equation on a surface
How to Solve a Partial Differential Equation on a surface
Solution of second order nonlinear singular value problems
Solution of second order nonlinear singular value problems
Viewers also liked
My projet life
Mi proyecto de vida consiste en terminar mis estudios universitarios el próximo año y encontrar un trabajo estable. A largo plazo, me gustaría casarme y formar una familia cuando tenga unos 30 años. Mi mayor aspiración es jubilarme a una edad temprana para poder viajar y disfrutar de la vida.
Idolcdpunit5
Classical Greece emphasized simplicity, balance, symmetry, and restraint in their art and literature. They defined the good life through seeking perfection, moderation in all things, and control over chaos. These values were expressed in sculptures like the Kritios Boy and Michelangelo's David through their idealized forms, balanced proportions, and restrained poses.
Skills development journal
The document describes the process of designing the front cover and contents page for a skills development journal. For the front cover, the designer started with a background color, inserted a masthead and person cut out, added a white text box with stress marks, headlines, a barcode, and enlarged the word "stress". Lastly, a price was added and the cover was saved as a JPEG file. For the contents page, the designer added a white and orange background, blue border sections, page numbers, the word "Regulars", descriptions of regular features, and page numbers before saving as a JPEG file.
Cyriak
Cyriak is a highly successful surrealist animator based near Brighton, England. He is known for creating bizarre and nightmarish animations that take ordinary objects and situations and transforms them in strange and imaginative ways. For example, he took a single picture of his face and animated it into sea creatures, wheeled animals, plants, and a spaceship. While his personal work is considered underground, he has also worked with bands, artists, and the BBC on music videos and television program elements. His creative style is truly unique and difficult to compare to any other influences, making him his own influence.
Viewers also liked (6)
Similar to Fall 2008 midterm
Engineering Mathematics 2 questions & answers(2)
1. The document contains a mock exam for the course EE203 Mathematical Methods for Engineers II. It consists of 6 questions testing various skills in ordinary and partial differential equations.
2. The questions cover skills like solving exact and homogeneous differential equations, using separation of variables, Laplace transforms, power series solutions, and Fourier series.
3. Sample solutions are provided for parts of some questions to illustrate the solution methods. Formulas for various transforms, series and other relevant mathematical tools are also provided.
Assignment6
This document contains instructions for 5 assignment questions involving numerical integration and solving differential equations. Question 1 involves using the quad function to evaluate several integrals. Question 2 involves using quad to evaluate Fresnel integrals and plot the results. Question 3 involves using Monte Carlo methods to estimate volumes and double integrals. Question 4 involves using Euler's method to solve an initial value problem and analyze errors. Question 5 involves using lsode to solve a system of differential equations modeling atmospheric circulation and experimenting with initial conditions.
Miran Anwar, mth 235 ss21 1 Hw17-5.2-SDE-2x2PP. Due 042620
Miran Anwar, mth 235 ss21 1: Hw17-5.2-SDE-2x2PP. Due: 04/26/2021 at 11:00pm EDT.
See in LN, § 5.2, See Example 5.2.4.
1. (10 points)
Note: You have only 5 attempts to solve this problem.
Consider the system of differential equations x′ = A x, where x =
[
x1
x2
]
and the 2×2 matrix A has eigenpairs
λ± = α±β i, α = 0.25, β = 2,
v± = a±b i, a =
[
2
1
]
, b =
[
−1/2
1
]
,
Draw on paper the solution x(t) = eαt
(
a cos(βt)−b sin(βt)
)
on the x1x2-plane and then answer the ques-
tions below.
(a) Based on your graph, select the correct solution curve from the interactive graph below.
• Select One
• Curve 1
• Curve 2
• Curve 3
• Curve 4
• None
(b) Use the graph below to find lim
t→+∞
‖x(t)‖, where ‖x(t)‖ is the length of the solution vector x(t).
• Select One
• Zero
• Infinity
• None
(c) Introduce the unit vectors u1 = a/‖a‖ and u2 = b/‖b‖. Use the graph below to find the lim
t→+∞
u(t),
where u(t) =
x(t)
‖x(t)‖
, is a unit vector in the direction of the solution vector x(t).
[Select One/U1/-U1/U2/-U2/None]
(d) Use the graph below to find lim
t→−∞
‖x(t)‖.
1
• Select One
• Zero
• Infinity
• None
(e) Use the graph below to find the lim
t→−∞
u(t), where u(t) =
x(t)
‖x(t)‖
.
[Select One/U1/-U1/U2/-U2/None]
(f) Characterize the zero solution, x0 = 0.
• Select One
• Source Node
• Source Spiral
• Sink Node
• Sink Spiral
• Saddle
• Center
• None
Comments on the graph below:
• The graph is interactive.
• You can click on the boxes to turn on and off possible solution curves.
• For each possible solution we display: the possible solution curve, the possible solution vector
x(t), and the associated unit vector u(t) = x(t)/‖x(t)‖.
• You can move the time slider to see how each possible solution vector x(t) and unit vector u(t)
change in time.
• You can turn on or off the ellipse formed by vectors a and b.
1
See in LN, § 5.2, See Example 5.2.4.
2. (10 points)
Note: You have only 5 attempts to solve this problem.
Consider the system of differential equations x′ = A x, where x =
[
x1
x2
]
and the 2×2 matrix A has eigenpairs
λ± = α±β i, α = 0.45, β = 2,
v± = a±b i, a = −
[
2
1
]
, b = −
[
−1/2
1
]
,
Draw on paper the solution x(t) = eαt
(
a sin(βt)+ b cos(βt)
)
on the x1x2-plane and then answer the ques-
tions below.
2
(a) Based on your graph, select the correct solution curve from the interactive graph below.
• Select One
• Curve 1
• Curve 2
• Curve 3
• Curve 4
• None
(b) Use the graph below to find lim
t→+∞
‖x(t)‖, where ‖x(t)‖ is the length of the solution vector x(t).
• Select One
• Zero
• Infinity
• None
(c) Introduce the unit vectors u1 = a/‖a‖ and u2 = b/‖b‖. Use the graph below to find the lim
t→+∞
u(t),
where u(t) =
x(t)
‖x(t)‖
, is a unit vector in the direction of the solution vector x(t).
[Select One/U1/-U1/U2/-U2/None]
(d) Use the graph below to find lim
t→−∞
‖x(t)‖.
• Select One
• Zero
• Infinity
• None
(e) Use the graph below to find the lim
t→−∞
u(t), where u(t) =
x(t)
‖x(t)‖
.
[ ...
Design of Linear Control Systems(0).ppt
This document discusses ordinary differential equations (ODEs) and their applications in modeling dynamic systems. It covers first-order and second-order ODEs, including analytic and numerical solution methods. Specific cases like underdamped, overdamped, critically damped, and undamped systems are examined. The concepts of natural frequency, damping frequency, and damping factor are introduced for characterizing oscillatory systems modeled by second-order linear ODEs.
Exam i(practice)
This document contains a practice exam for Math 220 with 16 multi-part questions covering topics such as functions, inequalities, trigonometry, logarithms, and graphing. The exam instructs students to show their work to receive partial credit and enough work to receive full credit. It tests skills like finding domains of functions, solving inequalities, determining equations of lines and circles, properties of functions, evaluating trigonometric and logarithmic expressions, solving equations, and graphing functions.
Constant strain triangular
constant strain triangular which is used in analysis of triangular in finite element method with the help of shape function and natural coordinate system.
ISI MSQE Entrance Question Paper (2008)
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2008. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
Ch03 6
The document discusses solving nonhomogeneous differential equations using the method of undetermined coefficients. It begins by introducing nonhomogeneous and homogeneous equations. It then presents the method of undetermined coefficients, which involves finding a particular solution to the nonhomogeneous equation assuming a known solution to the corresponding homogeneous equation. Several examples are worked through, finding particular solutions when the nonhomogeneous term is exponential, sine, polynomial, product, and sum functions.
Mth 4101-2 b
1. This document contains 11 multi-part math problems involving systems of equations and inequalities. The problems cover topics such as solving systems graphically, algebraically, and determining if ordered pairs are solutions. They also involve word problems about ages, expenses, and splitting amounts into parts.
2. Key steps addressed include setting up tables of values, identifying line types, finding the solution set intersection, using substitution or elimination methods, stating yes or no for ordered pairs, and drawing graphs of solution sets for systems of inequalities.
3. The problems progress from simpler systems to more complex ones involving multiple equations or inequalities, requiring skills like algebraic manipulation, graphical analysis, and translating word problems into mathematical systems.
IIT JEE Maths 1984
This document contains an unsolved mathematics past paper from 1984 containing multiple choice and multiple answer questions on topics including limits, probability, trigonometry, and geometry. The paper tests fundamental concepts and problem solving abilities in mathematics. It contains 11 sections with over 50 total questions assessing a range of mathematical skills.
Ch03 2
This document discusses fundamental solutions of linear homogeneous differential equations. It introduces the concept of a fundamental set of solutions - two solutions whose Wronskian is nonzero at some point. Any linear combination of a fundamental set with arbitrary constants forms the general solution. The principle of superposition and Wronskian determinant are used to show whether a given set of solutions spans all solutions. Examples demonstrate finding fundamental solutions and using them to solve initial value problems. Theorems establish existence and properties of fundamental solutions, including their role in solving initial value problems uniquely.
M112rev
This document provides a review of exercises for a Math 112 final exam. It contains 31 multi-part exercises covering topics like graphing, logarithms, trigonometry, and word problems. The review is intended to help students practice problems similar to what may appear on the exam. The exam will have two parts, one allowing a calculator and one not.
Finite Element Method.ppt
The finite element method involves four main steps: (1) discretizing the solution region into finite elements, (2) deriving the governing equations for each element using variational methods or Galerkin's method, (3) assembling the element equations into a global system of equations, and (4) solving the resulting system of equations. The method approximates an unknown field variable within each element using shape functions that are interpolations of the variable's values at the element nodes. This allows the governing PDE to be transformed into an equivalent variational problem or functional that is minimized over each element.
Differential equations
1. Differential equations are equations involving derivatives of an unknown function and can be of different orders. Separable differential equations can be expressed as the product of a function of x and a function of y.
2. The general solution or family of solutions to a differential equation represents all possible solutions. Specific solutions satisfy initial conditions.
3. Models of natural growth and decay can be represented by differential equations where the rate of change is proportional to the amount present, following an exponential solution. The logistic growth model includes limitations on growth.
4. Mixing problems can be modeled using differential equations to determine properties of mixtures over time as different substances enter and exit a container.
Differential equations
1. Differential equations are equations involving derivatives of an unknown function and can be of different orders. Separable differential equations can be expressed as the product of a function of x and a function of y.
2. The general solution or family of solutions to a differential equation represents all possible solutions as determined by initial or boundary conditions. Initial value problems find a particular solution satisfying given initial conditions.
3. Models of natural growth and decay can be represented by differential equations where the rate of change is proportional to the amount present, with solutions in the form of exponential functions. The logistic growth model accounts for limiting factors with a carrying capacity.
Eigenvalues and eigenvectors
The document discusses eigenvalues and eigenvectors. It defines an eigenvalue problem as finding scale constants (λ) and nonzero vectors (X) such that when a square matrix (A) multiplies a vector (X), it produces a vector in the same direction but scaled by λ. The characteristic polynomial is used to find the eigenvalues by setting its determinant equal to 0. Once the eigenvalues are obtained, the corresponding eigenvectors can be found by solving the homogeneous system (A - λI)X = 0. Examples are provided to demonstrate finding the eigenvalues and eigenvectors of different matrices.
MRS EMMAH.pdf
1. The document discusses ordinary and partial differential equations. Ordinary differential equations contain one independent variable, while partial differential equations contain more than one independent variable.
2. It defines the order and degree of differential equations, and provides examples to illustrate these concepts. Linear differential equations are classified and examples are given. Non-linear differential equations are also discussed.
3. Differential equations can arise from geometric, physical, and primitive problems. Examples include the motion of a falling object, projectile motion, electric circuits, vibration problems, and heat transfer. Primitives and how they relate to differential equations are explained.
GATE Mathematics Paper-2000
This document contains a mathematics exam with 30 multiple choice questions covering various topics in calculus, linear algebra, differential equations, real analysis, and probability. The exam has 75 total marks and is divided into sections on vectors and matrices, differential equations, real analysis, and probability. It provides the questions, response options, and asks test takers to select the correct option(s) and write them in the answer booklet.
Second order homogeneous linear differential equations
1) The document discusses second order linear homogeneous differential equations, which have the general form P(x)y'' + Q(x)y' + R(x)y = 0.
2) It describes methods for finding the general solution including reduction of order, and discusses the solutions when the coefficients are constants.
3) The general solution depends on the nature of the roots of the auxiliary equation: distinct real roots, repeated real roots, or complex roots.
The two dimensional wave equation
The document discusses solving the 2D wave equation using separation of variables and superposition. It separates the wave equation into ordinary differential equations for the spatial and temporal parts. The solutions to the spatial equations give normal modes, which are combined using superposition to satisfy the initial conditions. As an example, the document finds the solution for a rectangular membrane with a given initial shape.
Similar to Fall 2008 midterm (20)
Miran Anwar, mth 235 ss21 1 Hw17-5.2-SDE-2x2PP. Due 042620
Miran Anwar, mth 235 ss21 1 Hw17-5.2-SDE-2x2PP. Due 042620
Second order homogeneous linear differential equations
Second order homogeneous linear differential equations
Recently uploaded
20240607 QFM018 Elixir Reading List May 2024
Everything I found interesting about the Elixir programming ecosystem in May 2024
Things to Consider When Choosing a Website Developer for your Website | FODUU
Choosing the right website developer is crucial for your business. This article covers essential factors to consider, including experience, portfolio, technical skills, communication, pricing, reputation & reviews, cost and budget considerations and post-launch support. Make an informed decision to ensure your website meets your business goals.
“I’m still / I’m still / Chaining from the Block”
“An Outlook of the Ongoing and Future Relationship between Blockchain Technologies and Process-aware Information Systems.” Invited talk at the joint workshop on Blockchain for Information Systems (BC4IS) and Blockchain for Trusted Data Sharing (B4TDS), co-located with with the 36th International Conference on Advanced Information Systems Engineering (CAiSE), 3 June 2024, Limassol, Cyprus.
Building Production Ready Search Pipelines with Spark and Milvus
Spark is the widely used ETL tool for processing, indexing and ingesting data to serving stack for search. Milvus is the production-ready open-source vector database. In this talk we will show how to use Spark to process unstructured data to extract vector representations, and push the vectors to Milvus vector database for search serving.
TrustArc Webinar - 2024 Global Privacy Survey
How does your privacy program stack up against your peers? What challenges are privacy teams tackling and prioritizing in 2024?
In the fifth annual Global Privacy Benchmarks Survey, we asked over 1,800 global privacy professionals and business executives to share their perspectives on the current state of privacy inside and outside of their organizations. This year’s report focused on emerging areas of importance for privacy and compliance professionals, including considerations and implications of Artificial Intelligence (AI) technologies, building brand trust, and different approaches for achieving higher privacy competence scores.
See how organizational priorities and strategic approaches to data security and privacy are evolving around the globe.
This webinar will review:
- The top 10 privacy insights from the fifth annual Global Privacy Benchmarks Survey
- The top challenges for privacy leaders, practitioners, and organizations in 2024
- Key themes to consider in developing and maintaining your privacy program
AI 101: An Introduction to the Basics and Impact of Artificial Intelligence
Imagine a world where machines not only perform tasks but also learn, adapt, and make decisions. This is the promise of Artificial Intelligence (AI), a technology that's not just enhancing our lives but revolutionizing entire industries.
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...Edge AI and Vision Alliance
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/building-and-scaling-ai-applications-with-the-nx-ai-manager-a-presentation-from-network-optix/
Robin van Emden, Senior Director of Data Science at Network Optix, presents the “Building and Scaling AI Applications with the Nx AI Manager,” tutorial at the May 2024 Embedded Vision Summit.
In this presentation, van Emden covers the basics of scaling edge AI solutions using the Nx tool kit. He emphasizes the process of developing AI models and deploying them globally. He also showcases the conversion of AI models and the creation of effective edge AI pipelines, with a focus on pre-processing, model conversion, selecting the appropriate inference engine for the target hardware and post-processing.
van Emden shows how Nx can simplify the developer’s life and facilitate a rapid transition from concept to production-ready applications.He provides valuable insights into developing scalable and efficient edge AI solutions, with a strong focus on practical implementation.Monitoring and Managing Anomaly Detection on OpenShift.pdf
Monitoring and Managing Anomaly Detection on OpenShift
Overview
Dive into the world of anomaly detection on edge devices with our comprehensive hands-on tutorial. This SlideShare presentation will guide you through the entire process, from data collection and model training to edge deployment and real-time monitoring. Perfect for those looking to implement robust anomaly detection systems on resource-constrained IoT/edge devices.
Key Topics Covered
1. Introduction to Anomaly Detection
- Understand the fundamentals of anomaly detection and its importance in identifying unusual behavior or failures in systems.
2. Understanding Edge (IoT)
- Learn about edge computing and IoT, and how they enable real-time data processing and decision-making at the source.
3. What is ArgoCD?
- Discover ArgoCD, a declarative, GitOps continuous delivery tool for Kubernetes, and its role in deploying applications on edge devices.
4. Deployment Using ArgoCD for Edge Devices
- Step-by-step guide on deploying anomaly detection models on edge devices using ArgoCD.
5. Introduction to Apache Kafka and S3
- Explore Apache Kafka for real-time data streaming and Amazon S3 for scalable storage solutions.
6. Viewing Kafka Messages in the Data Lake
- Learn how to view and analyze Kafka messages stored in a data lake for better insights.
7. What is Prometheus?
- Get to know Prometheus, an open-source monitoring and alerting toolkit, and its application in monitoring edge devices.
8. Monitoring Application Metrics with Prometheus
- Detailed instructions on setting up Prometheus to monitor the performance and health of your anomaly detection system.
9. What is Camel K?
- Introduction to Camel K, a lightweight integration framework built on Apache Camel, designed for Kubernetes.
10. Configuring Camel K Integrations for Data Pipelines
- Learn how to configure Camel K for seamless data pipeline integrations in your anomaly detection workflow.
11. What is a Jupyter Notebook?
- Overview of Jupyter Notebooks, an open-source web application for creating and sharing documents with live code, equations, visualizations, and narrative text.
12. Jupyter Notebooks with Code Examples
- Hands-on examples and code snippets in Jupyter Notebooks to help you implement and test anomaly detection models.
UiPath Test Automation using UiPath Test Suite series, part 6
Welcome to UiPath Test Automation using UiPath Test Suite series part 6. In this session, we will cover Test Automation with generative AI and Open AI.
UiPath Test Automation with generative AI and Open AI webinar offers an in-depth exploration of leveraging cutting-edge technologies for test automation within the UiPath platform. Attendees will delve into the integration of generative AI, a test automation solution, with Open AI advanced natural language processing capabilities.
Throughout the session, participants will discover how this synergy empowers testers to automate repetitive tasks, enhance testing accuracy, and expedite the software testing life cycle. Topics covered include the seamless integration process, practical use cases, and the benefits of harnessing AI-driven automation for UiPath testing initiatives. By attending this webinar, testers, and automation professionals can gain valuable insights into harnessing the power of AI to optimize their test automation workflows within the UiPath ecosystem, ultimately driving efficiency and quality in software development processes.
What will you get from this session?
1. Insights into integrating generative AI.
2. Understanding how this integration enhances test automation within the UiPath platform
3. Practical demonstrations
4. Exploration of real-world use cases illustrating the benefits of AI-driven test automation for UiPath
Topics covered:
What is generative AI
Test Automation with generative AI and Open AI.
UiPath integration with generative AI
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Artificial Intelligence for XMLDevelopment
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
Generating privacy-protected synthetic data using Secludy and Milvus
During this demo, the founders of Secludy will demonstrate how their system utilizes Milvus to store and manipulate embeddings for generating privacy-protected synthetic data. Their approach not only maintains the confidentiality of the original data but also enhances the utility and scalability of LLMs under privacy constraints. Attendees, including machine learning engineers, data scientists, and data managers, will witness first-hand how Secludy's integration with Milvus empowers organizations to harness the power of LLMs securely and efficiently.
20240605 QFM017 Machine Intelligence Reading List May 2024
Everything I found interesting about machines behaving intelligently during May 2024
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Discover the seamless integration of RPA (Robotic Process Automation), COMPOSER, and APM with AWS IDP enhanced with Slack notifications. Explore how these technologies converge to streamline workflows, optimize performance, and ensure secure access, all while leveraging the power of AWS IDP and real-time communication via Slack notifications.
Mind map of terminologies used in context of Generative AI
Mind map of common terms used in context of Generative AI.
GraphRAG for Life Science to increase LLM accuracy
GraphRAG for life science domain, where you retriever information from biomedical knowledge graphs using LLMs to increase the accuracy and performance of generated answers
Your One-Stop Shop for Python Success: Top 10 US Python Development Providers
Simplify your search for a reliable Python development partner! This list presents the top 10 trusted US providers offering comprehensive Python development services, ensuring your project's success from conception to completion.
20240609 QFM020 Irresponsible AI Reading List May 2024
Everything I found interesting about the irresponsible use of machine intelligence in May 2024
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAU
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-und-domino-lizenzkostenreduzierung-in-der-welt-von-dlau/
DLAU und die Lizenzen nach dem CCB- und CCX-Modell sind für viele in der HCL-Community seit letztem Jahr ein heißes Thema. Als Notes- oder Domino-Kunde haben Sie vielleicht mit unerwartet hohen Benutzerzahlen und Lizenzgebühren zu kämpfen. Sie fragen sich vielleicht, wie diese neue Art der Lizenzierung funktioniert und welchen Nutzen sie Ihnen bringt. Vor allem wollen Sie sicherlich Ihr Budget einhalten und Kosten sparen, wo immer möglich. Das verstehen wir und wir möchten Ihnen dabei helfen!
Wir erklären Ihnen, wie Sie häufige Konfigurationsprobleme lösen können, die dazu führen können, dass mehr Benutzer gezählt werden als nötig, und wie Sie überflüssige oder ungenutzte Konten identifizieren und entfernen können, um Geld zu sparen. Es gibt auch einige Ansätze, die zu unnötigen Ausgaben führen können, z. B. wenn ein Personendokument anstelle eines Mail-Ins für geteilte Mailboxen verwendet wird. Wir zeigen Ihnen solche Fälle und deren Lösungen. Und natürlich erklären wir Ihnen das neue Lizenzmodell.
Nehmen Sie an diesem Webinar teil, bei dem HCL-Ambassador Marc Thomas und Gastredner Franz Walder Ihnen diese neue Welt näherbringen. Es vermittelt Ihnen die Tools und das Know-how, um den Überblick zu bewahren. Sie werden in der Lage sein, Ihre Kosten durch eine optimierte Domino-Konfiguration zu reduzieren und auch in Zukunft gering zu halten.
Diese Themen werden behandelt
- Reduzierung der Lizenzkosten durch Auffinden und Beheben von Fehlkonfigurationen und überflüssigen Konten
- Wie funktionieren CCB- und CCX-Lizenzen wirklich?
- Verstehen des DLAU-Tools und wie man es am besten nutzt
- Tipps für häufige Problembereiche, wie z. B. Team-Postfächer, Funktions-/Testbenutzer usw.
- Praxisbeispiele und Best Practices zum sofortigen Umsetzen
OpenID AuthZEN Interop Read Out - Authorization
During Identiverse 2024 and EIC 2024, members of the OpenID AuthZEN WG got together and demoed their authorization endpoints conforming to the AuthZEN API
CAKE: Sharing Slices of Confidential Data on Blockchain
Presented at the CAiSE 2024 Forum, Intelligent Information Systems, June 6th, Limassol, Cyprus.
Synopsis: Cooperative information systems typically involve various entities in a collaborative process within a distributed environment. Blockchain technology offers a mechanism for automating such processes, even when only partial trust exists among participants. The data stored on the blockchain is replicated across all nodes in the network, ensuring accessibility to all participants. While this aspect facilitates traceability, integrity, and persistence, it poses challenges for adopting public blockchains in enterprise settings due to confidentiality issues. In this paper, we present a software tool named Control Access via Key Encryption (CAKE), designed to ensure data confidentiality in scenarios involving public blockchains. After outlining its core components and functionalities, we showcase the application of CAKE in the context of a real-world cyber-security project within the logistics domain.
Paper: https://doi.org/10.1007/978-3-031-61000-4_16
Recently uploaded (20)
Things to Consider When Choosing a Website Developer for your Website | FODUU
Things to Consider When Choosing a Website Developer for your Website | FODUU
Building Production Ready Search Pipelines with Spark and Milvus
Building Production Ready Search Pipelines with Spark and Milvus
AI 101: An Introduction to the Basics and Impact of Artificial Intelligence
AI 101: An Introduction to the Basics and Impact of Artificial Intelligence
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
Monitoring and Managing Anomaly Detection on OpenShift.pdf
Monitoring and Managing Anomaly Detection on OpenShift.pdf
UiPath Test Automation using UiPath Test Suite series, part 6
UiPath Test Automation using UiPath Test Suite series, part 6
Generating privacy-protected synthetic data using Secludy and Milvus
Generating privacy-protected synthetic data using Secludy and Milvus
20240605 QFM017 Machine Intelligence Reading List May 2024
20240605 QFM017 Machine Intelligence Reading List May 2024
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Mind map of terminologies used in context of Generative AI
Mind map of terminologies used in context of Generative AI
GraphRAG for Life Science to increase LLM accuracy
GraphRAG for Life Science to increase LLM accuracy
Your One-Stop Shop for Python Success: Top 10 US Python Development Providers
Your One-Stop Shop for Python Success: Top 10 US Python Development Providers
20240609 QFM020 Irresponsible AI Reading List May 2024
20240609 QFM020 Irresponsible AI Reading List May 2024
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAU
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAU
CAKE: Sharing Slices of Confidential Data on Blockchain
CAKE: Sharing Slices of Confidential Data on Blockchain
Fall 2008 midterm
- 1. Hi Everyone! Here’s the Fall 2008 midterm for you to try. TRY IT!!! i.e. put away all your notes and textbooks, and give yourself 75 minutes. We’ll post solutions in a few days, but try it before you look at them!!! 1. (4 marks each; total 12 marks) Answer each question in the space provided. You MUST show all of your work. a) Consider the following linear first-order differential equation: xy 3 y sin x3 . What is the appropriate integrating factor to help solve this equation? (Just find the integrating factor, but do NOT actually solve the equation). m b) Find all values of m so that x is a solution of the differential equation x 2 y 2 xy 2 y 0 c) Find the general solution of the differential equation ( D 1)( D 2 9)( D 2 16) 2 y 0 .
- 2. MATH2860U Midterm October, 2008 2 2. (7 marks) Find the general solution of the differential equation 1 dy (4 x 3 y 2 e x ) 2 x 4 y 0 y dx
- 3. MATH2860U Midterm October, 2008 3 3. (Total 12 marks) Write your final answer on the line provided. You do NOT have to show your work, but it is suggested for parts f and g (for part marks in case the final answer is wrong). For all other parts, ONLY the final answer will be marked. a) (2 marks) Suppose that we have a radioactive series in which element A decays to element B then C with rate constants k1 , k 2 as shown below ( k1 , k 2 positive). dA The differential equation governing the amount of element A is k1 A . dt What are the differential equations governing the amount of element B and element C? Differential Equation for Element B: _________________________________ Differential Equation for Element C: _________________________________ b) (1 mark) Determine whether the functions y1 x 2 and y 2 x 2 1 are linearly dependent or linearly independent. (Answer: “Dependent” or “Independent”) Answer : ________________________________________ c) (1 mark) Which of the following statements describes the differential equation x 3 y (cos x) y x 2 e x 0 ? i. Linear and homogeneous ii. Linear and nonhomogeneous iii. Nonlinear Answer: _________________________________ d) (3 marks) For the equation y y 12 y 6 x 2 2e4 x , if it is known 4 x that yc c1e c2 e , what is the appropriate form to be assumed for the 3x particular solution, if solving using the method of undetermined coefficients? You do NOT have to solve for the values of the constants A, B, C, etc. y p is of the form: _________________________________
- 4. MATH2860U Midterm October, 2008 4 e) (1 mark) Without attempting to solve the ODE, determine whether the ODE y x 4 y 2 is guaranteed to have a unique solution through the point (2,0). Answer “True” or “False”. Answer: _________________________________ f) (2 marks) Suppose an LRC circuit is critically damped. Increasing the resistance of the resistor will result in what type of motion? i) underdamped motion. ii) overdamped motion. iii) pure resonant motion iv) both a and c Answer: _________________________________ g) (2 marks) Consider the differential equation y y x x subject to the 2 initial condition y(3) = 7. Use Euler’s Method with a step size of h = 0.2 to approximate y(3.2). Answer: _________________________________
- 5. MATH2860U Midterm October, 2008 5 4. (9 marks) A horizontal spring with a mass of 2 kg has damping constant 8, and a force of 6 N is required to keep the spring stretched 0.5 m beyond its natural length. The spring is stretched 1m beyond its natural length (i.e. to the right) and then released with zero velocity. Find the position x(t) of the mass at any time t. Note: There is no external force F(t) applied to the spring.
- 6. MATH2860U Midterm October, 2008 6 5. (10 marks total) Use variation of parameters to obtain the particular solution of the given differential equation y y 12 y 8e NOTE: You must use variation of 2x parameters; other methods will NOT receive any marks. Hint: You may use the fact that yc c1e 4 x c2e3 x for this differential equation.