These slides follow up on the slides with a tutorial on how to index ED patterns, 5 10a. From the result achieved in those slides, we now derive the reflection conditions and corresponding possible space groups.
5 10c exercise_index the aluminum tilt series_ex on saed do not know cell parsJoke Hadermann
This is a tutorial on how to index single crystal (electron) diffraction patterns when the cell parameters are not yet known. This follows after another tutorial for the case of known cell parameters, 5.10a.
This is a tutorial on indexing diffraction patterns, deriving reflection conditions from SAED, derving point groups from CBED and combining both to find the space group. The slides contain exercises, the page to work on is at the end of the presentation and should be printed first to be able to measure on that page.
Electron diffraction: Tutorial with exercises and solutions (EMAT Workshop 2017)Joke Hadermann
Electron diffraction patterns provide information about the structure of crystalline materials by revealing the diffraction of electrons from crystal planes. Reflections in patterns represent the constructive interference of electrons from different crystal planes, with their position and intensity indicating the d-spacing of planes and occupation/symmetry of the structure. By indexing patterns, determining the d-spacings of reflections and relating them to crystal planes via Braggs law, the zone axis and unit cell parameters can be determined.
TEM Winterworkshop 2011: electron diffractionJoke Hadermann
1) The purpose of the lecture is to teach how to index and determine cell parameters from SAED patterns, determine possible space groups and point groups, and solve simple structures from PED patterns.
2) Example materials used are aluminum and rutile-type SnO2. The slides and exercises for determining unknown cell parameters from SAED patterns are provided.
3) The document provides a step-by-step example of determining the cell parameters of aluminum from its SAED patterns, starting with no prior knowledge of the material. The correct cell is determined to be cubic with a=b=c=4.06 Angstroms.
This document provides information about integration in higher mathematics. It begins with an overview of integration as the opposite of differentiation. It then discusses using antidifferentiation to find integrals by reversing the power rule for differentiation. Several examples are provided to illustrate integrating polynomials. The document also discusses using integrals to find the area under a curve or between two curves. It provides examples of calculating areas bounded by graphs and the x-axis. Finally, it presents some exam-style integration questions for practice.
LU decomposition is a method to solve systems of linear equations by decomposing the coefficient matrix A into the product of a lower triangular matrix L and an upper triangular matrix U. It involves (1) decomposing A into L and U, (2) solving LZ = C for Z, and (3) solving UX = Z for X to find the solution vector X. The document provides an example using LU decomposition to solve a system of 3 linear equations.
The document provides an overview of various topics in analytic geometry, including circle equations, distance equations, systems of two and three variable equations, linear inequalities, rational inequalities, and intersections of inequalities. It defines key concepts, provides examples of how to solve different types of problems, and notes things to remember when working with inequalities.
This module teaches about circular functions and their graphical representations. Students will learn to define and calculate the six trigonometric functions of an acute angle in standard position. Specifically, the module will:
1) Describe the properties of sine and cosine functions
2) Teach how to draw the graphs of sine and cosine functions
3) Define the six trigonometric functions of an angle given its terminal point is not on the unit circle
4) Calculate trigonometric function values given certain conditions
5 10c exercise_index the aluminum tilt series_ex on saed do not know cell parsJoke Hadermann
This is a tutorial on how to index single crystal (electron) diffraction patterns when the cell parameters are not yet known. This follows after another tutorial for the case of known cell parameters, 5.10a.
This is a tutorial on indexing diffraction patterns, deriving reflection conditions from SAED, derving point groups from CBED and combining both to find the space group. The slides contain exercises, the page to work on is at the end of the presentation and should be printed first to be able to measure on that page.
Electron diffraction: Tutorial with exercises and solutions (EMAT Workshop 2017)Joke Hadermann
Electron diffraction patterns provide information about the structure of crystalline materials by revealing the diffraction of electrons from crystal planes. Reflections in patterns represent the constructive interference of electrons from different crystal planes, with their position and intensity indicating the d-spacing of planes and occupation/symmetry of the structure. By indexing patterns, determining the d-spacings of reflections and relating them to crystal planes via Braggs law, the zone axis and unit cell parameters can be determined.
TEM Winterworkshop 2011: electron diffractionJoke Hadermann
1) The purpose of the lecture is to teach how to index and determine cell parameters from SAED patterns, determine possible space groups and point groups, and solve simple structures from PED patterns.
2) Example materials used are aluminum and rutile-type SnO2. The slides and exercises for determining unknown cell parameters from SAED patterns are provided.
3) The document provides a step-by-step example of determining the cell parameters of aluminum from its SAED patterns, starting with no prior knowledge of the material. The correct cell is determined to be cubic with a=b=c=4.06 Angstroms.
This document provides information about integration in higher mathematics. It begins with an overview of integration as the opposite of differentiation. It then discusses using antidifferentiation to find integrals by reversing the power rule for differentiation. Several examples are provided to illustrate integrating polynomials. The document also discusses using integrals to find the area under a curve or between two curves. It provides examples of calculating areas bounded by graphs and the x-axis. Finally, it presents some exam-style integration questions for practice.
LU decomposition is a method to solve systems of linear equations by decomposing the coefficient matrix A into the product of a lower triangular matrix L and an upper triangular matrix U. It involves (1) decomposing A into L and U, (2) solving LZ = C for Z, and (3) solving UX = Z for X to find the solution vector X. The document provides an example using LU decomposition to solve a system of 3 linear equations.
The document provides an overview of various topics in analytic geometry, including circle equations, distance equations, systems of two and three variable equations, linear inequalities, rational inequalities, and intersections of inequalities. It defines key concepts, provides examples of how to solve different types of problems, and notes things to remember when working with inequalities.
This module teaches about circular functions and their graphical representations. Students will learn to define and calculate the six trigonometric functions of an acute angle in standard position. Specifically, the module will:
1) Describe the properties of sine and cosine functions
2) Teach how to draw the graphs of sine and cosine functions
3) Define the six trigonometric functions of an angle given its terminal point is not on the unit circle
4) Calculate trigonometric function values given certain conditions
The document summarizes key aspects of quadratic graphs:
1) A quadratic function takes the form of ax2 + bx + c, with examples given.
2) When plotted, a quadratic function produces a smooth curve called a parabola.
3) There are two ways to solve quadratic graphs - using a table of values to find coordinates, or directly replacing x-values into the function.
Steps for each method are outlined along with an example.
The document provides information on various math topics including:
1. Graph transformations including stretching and compressing graphs along the x and y axes.
2. Similarity and congruency of triangles.
3. Differentiation including differentiating polynomials and finding derivatives.
4. Integration including integrating polynomials and using integration to find areas.
5. Kinematics equations for velocity, acceleration, and displacement.
6. The binomial distribution and Pascal's triangle for expanding binomial expressions.
7. Using the discriminant of a quadratic equation to determine the nature of its roots.
The Simplex Method is an algorithm for solving linear programming problems. It involves setting up the problem in standard form, constructing an initial simplex tableau, and then iteratively selecting pivot columns and performing row operations until an optimal solution is found. The method terminates when all indicators in the tableau are positive or zero, at which point the basic and non-basic variables can be identified to read the optimal solution.
1. The document discusses matrices and determinants. It defines different types of matrices such as rectangular, square, diagonal, scalar, row, column, identity, zero, upper triangular, and lower triangular matrices.
2. It explains how to calculate determinants of matrices. The determinant of a 1x1 matrix is the single element. The determinant of a 2x2 matrix is calculated using a formula. Determinants of higher order matrices are calculated by expanding along rows or columns.
3. It introduces concepts of minors, cofactors, and explains how the value of a determinant can be written in terms of its minors and cofactors. It also lists some properties and operations for determinants.
This module introduces functions and how to distinguish them from relations. It discusses:
1) Defining a function and differentiating it from a relation using arrow diagrams and the vertical line test.
2) Identifying the domain and range of a function using sets of ordered pairs.
3) Recognizing functional relationships in real-life situations where one variable depends on another in a one-to-one or many-to-one way.
The document contains notes on trigonometric graphs and functions. It discusses the amplitude and period of trigonometric graphs, defines radians and relates them to degrees, provides exact values of trigonometric functions at common angles, explains the four quadrants used to measure angles, and gives examples of solving trigonometric equations both graphically and algebraically using properties of the quadrants.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
- The document discusses various trigonometric identities and formulae, including basic identities, compound angles, double angles, and their applications.
- It provides examples of using trigonometric formulae to find unknown sides and angles, including solving trigonometric equations involving double angles.
- Three-dimensional trigonometry is also introduced, defining the angle between two planes and an example problem of finding unknown angles and lengths in a pyramid.
This document discusses Gaussian elimination, a method for numerically solving simultaneous linear equations. It begins by outlining the key concepts readers should understand, including performing naive Gaussian elimination, its pitfalls, and modifying it with partial pivoting. It then describes the two steps of the method: forward elimination of unknowns and back substitution. An example applying the method to a set of three equations is shown.
1) Cramer's rule can be used to solve systems of linear equations. It expresses the solution in terms of the determinants of the coefficient matrix and matrices with one column replaced by the constants vector.
2) If the determinant of the coefficient matrix is non-zero, there is a unique solution. If it is zero, there may be no solution or infinitely many solutions.
3) Three examples demonstrate applying Cramer's rule to find the unique solution, that there is no solution, and that there are infinitely many solutions, respectively.
The document discusses 3D coordinate systems. It explains that a 3D coordinate system adds a z-axis perpendicular to the x- and y-axes. There are two ways to orient the z-axis, resulting in right-hand and left-hand systems. Points in 3D space are identified by ordered triples (x,y,z). Graphs of equations in 3D are surfaces. Constant equations like x=k form planes parallel to coordinate planes.
The document describes the two phase method for solving linear programming problems. In phase I, artificial variables are introduced to obtain an initial basic feasible solution. The objective is to minimize the artificial variables subject to the original constraints. In phase II, the original objective function is optimized using the feasible solution from phase I as the starting point, without the artificial variables. Two examples are provided to illustrate the two phase method.
This module covers trigonometric equations and identities. Students will learn to:
1. State fundamental trigonometric identities like reciprocal, quotient, and Pythagorean identities.
2. Prove trigonometric identities algebraically by transforming one side into the other.
3. Use sum and difference formulas for sine and cosine to find values of trig functions of angles that are not special angles.
4. Solve simple trigonometric equations.
Worked examples are provided to simplify expressions using identities, prove identities by algebraic manipulation, and apply sum and difference formulas to find trig values of combined angles.
This document discusses techniques for evaluating integrals involving exponential functions. It introduces the formulas for integrating exponentials and differentiating them. Several important definite integrals are evaluated, such as the integral from 0 to infinity of e^-ax dx = 1/a. Graphs are used to visualize these integrals. The document then evaluates the more complex integral from negative infinity to positive infinity of e^-ax^2 dx using a change of variables technique. Finally, it discusses how these integrals can be used in kinetic theory and derives an important ratio and normalization factor for Maxwell's velocity distribution.
This document provides an overview of quadratic functions including:
- The graph of a quadratic function is a parabola.
- The general form of a quadratic function is f(x) = ax2 + bx + c.
- Key aspects that must be identified before sketching the graph are the nature of the turning point, y-intercept, x-intercepts, and axis of symmetry.
- Quadratic equations can be solved by factorizing, completing the square, or using the quadratic formula. The discriminant determines the nature of the roots.
The document defines key concepts related to coordinate grids and ordered pairs:
- A coordinate grid uses horizontal and vertical intersecting lines to locate points via distances from the lines.
- The x-axis is horizontal and the y-axis is vertical.
- Ordered pairs use the format (x,y) to give the location of a point by listing the distance from each axis.
- Points can be plotted on a four-quadrant grid by first finding the x value and then the y value, with negative numbers indicating left/below the origin.
The document provides an overview of the simplex method for solving linear programming problems with more than two decision variables. It describes key concepts like slack variables, surplus variables, basic feasible solutions, degenerate and non-degenerate solutions, and using tableau steps to arrive at an optimal solution. Examples are provided to illustrate setting up and solving problems using the simplex method.
The Big M Method is used to solve linear programming problems with inequality constraints. It involves multiplying inequality constraints to make the right hand side positive, introducing surplus and slack variables, and adding a large penalty term M to the objective for any artificial variables. The example problem is solved using this method in multiple iterations of the simplex algorithm to find the optimal solution.
The document describes the two phase simplex method for solving linear programming problems (LPP) with greater than or equal to constraints. In phase I, an auxiliary LPP is constructed by introducing artificial variables and slack/surplus variables. The objective is to minimize the artificial variables using the simplex method. If an artificial variable is positive or zero in the optimal basis, phase II is executed to solve the original LPP. Phase I provides a starting feasible solution for phase II to obtain the actual optimal solution.
The document is a lesson on conic sections from Holt Algebra 2. It introduces the four types of conic sections - circles, ellipses, hyperbolas, and parabolas - and explains that they are formed by the intersection of a plane and a double right cone. Examples are provided on graphing each type of conic section on a calculator and identifying their characteristics like center, intercepts, vertices or direction of opening. The lesson also explains how to find the center and radius of a circle using the midpoint and distance formulas.
The document summarizes key aspects of quadratic graphs:
1) A quadratic function takes the form of ax2 + bx + c, with examples given.
2) When plotted, a quadratic function produces a smooth curve called a parabola.
3) There are two ways to solve quadratic graphs - using a table of values to find coordinates, or directly replacing x-values into the function.
Steps for each method are outlined along with an example.
The document provides information on various math topics including:
1. Graph transformations including stretching and compressing graphs along the x and y axes.
2. Similarity and congruency of triangles.
3. Differentiation including differentiating polynomials and finding derivatives.
4. Integration including integrating polynomials and using integration to find areas.
5. Kinematics equations for velocity, acceleration, and displacement.
6. The binomial distribution and Pascal's triangle for expanding binomial expressions.
7. Using the discriminant of a quadratic equation to determine the nature of its roots.
The Simplex Method is an algorithm for solving linear programming problems. It involves setting up the problem in standard form, constructing an initial simplex tableau, and then iteratively selecting pivot columns and performing row operations until an optimal solution is found. The method terminates when all indicators in the tableau are positive or zero, at which point the basic and non-basic variables can be identified to read the optimal solution.
1. The document discusses matrices and determinants. It defines different types of matrices such as rectangular, square, diagonal, scalar, row, column, identity, zero, upper triangular, and lower triangular matrices.
2. It explains how to calculate determinants of matrices. The determinant of a 1x1 matrix is the single element. The determinant of a 2x2 matrix is calculated using a formula. Determinants of higher order matrices are calculated by expanding along rows or columns.
3. It introduces concepts of minors, cofactors, and explains how the value of a determinant can be written in terms of its minors and cofactors. It also lists some properties and operations for determinants.
This module introduces functions and how to distinguish them from relations. It discusses:
1) Defining a function and differentiating it from a relation using arrow diagrams and the vertical line test.
2) Identifying the domain and range of a function using sets of ordered pairs.
3) Recognizing functional relationships in real-life situations where one variable depends on another in a one-to-one or many-to-one way.
The document contains notes on trigonometric graphs and functions. It discusses the amplitude and period of trigonometric graphs, defines radians and relates them to degrees, provides exact values of trigonometric functions at common angles, explains the four quadrants used to measure angles, and gives examples of solving trigonometric equations both graphically and algebraically using properties of the quadrants.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
- The document discusses various trigonometric identities and formulae, including basic identities, compound angles, double angles, and their applications.
- It provides examples of using trigonometric formulae to find unknown sides and angles, including solving trigonometric equations involving double angles.
- Three-dimensional trigonometry is also introduced, defining the angle between two planes and an example problem of finding unknown angles and lengths in a pyramid.
This document discusses Gaussian elimination, a method for numerically solving simultaneous linear equations. It begins by outlining the key concepts readers should understand, including performing naive Gaussian elimination, its pitfalls, and modifying it with partial pivoting. It then describes the two steps of the method: forward elimination of unknowns and back substitution. An example applying the method to a set of three equations is shown.
1) Cramer's rule can be used to solve systems of linear equations. It expresses the solution in terms of the determinants of the coefficient matrix and matrices with one column replaced by the constants vector.
2) If the determinant of the coefficient matrix is non-zero, there is a unique solution. If it is zero, there may be no solution or infinitely many solutions.
3) Three examples demonstrate applying Cramer's rule to find the unique solution, that there is no solution, and that there are infinitely many solutions, respectively.
The document discusses 3D coordinate systems. It explains that a 3D coordinate system adds a z-axis perpendicular to the x- and y-axes. There are two ways to orient the z-axis, resulting in right-hand and left-hand systems. Points in 3D space are identified by ordered triples (x,y,z). Graphs of equations in 3D are surfaces. Constant equations like x=k form planes parallel to coordinate planes.
The document describes the two phase method for solving linear programming problems. In phase I, artificial variables are introduced to obtain an initial basic feasible solution. The objective is to minimize the artificial variables subject to the original constraints. In phase II, the original objective function is optimized using the feasible solution from phase I as the starting point, without the artificial variables. Two examples are provided to illustrate the two phase method.
This module covers trigonometric equations and identities. Students will learn to:
1. State fundamental trigonometric identities like reciprocal, quotient, and Pythagorean identities.
2. Prove trigonometric identities algebraically by transforming one side into the other.
3. Use sum and difference formulas for sine and cosine to find values of trig functions of angles that are not special angles.
4. Solve simple trigonometric equations.
Worked examples are provided to simplify expressions using identities, prove identities by algebraic manipulation, and apply sum and difference formulas to find trig values of combined angles.
This document discusses techniques for evaluating integrals involving exponential functions. It introduces the formulas for integrating exponentials and differentiating them. Several important definite integrals are evaluated, such as the integral from 0 to infinity of e^-ax dx = 1/a. Graphs are used to visualize these integrals. The document then evaluates the more complex integral from negative infinity to positive infinity of e^-ax^2 dx using a change of variables technique. Finally, it discusses how these integrals can be used in kinetic theory and derives an important ratio and normalization factor for Maxwell's velocity distribution.
This document provides an overview of quadratic functions including:
- The graph of a quadratic function is a parabola.
- The general form of a quadratic function is f(x) = ax2 + bx + c.
- Key aspects that must be identified before sketching the graph are the nature of the turning point, y-intercept, x-intercepts, and axis of symmetry.
- Quadratic equations can be solved by factorizing, completing the square, or using the quadratic formula. The discriminant determines the nature of the roots.
The document defines key concepts related to coordinate grids and ordered pairs:
- A coordinate grid uses horizontal and vertical intersecting lines to locate points via distances from the lines.
- The x-axis is horizontal and the y-axis is vertical.
- Ordered pairs use the format (x,y) to give the location of a point by listing the distance from each axis.
- Points can be plotted on a four-quadrant grid by first finding the x value and then the y value, with negative numbers indicating left/below the origin.
The document provides an overview of the simplex method for solving linear programming problems with more than two decision variables. It describes key concepts like slack variables, surplus variables, basic feasible solutions, degenerate and non-degenerate solutions, and using tableau steps to arrive at an optimal solution. Examples are provided to illustrate setting up and solving problems using the simplex method.
The Big M Method is used to solve linear programming problems with inequality constraints. It involves multiplying inequality constraints to make the right hand side positive, introducing surplus and slack variables, and adding a large penalty term M to the objective for any artificial variables. The example problem is solved using this method in multiple iterations of the simplex algorithm to find the optimal solution.
The document describes the two phase simplex method for solving linear programming problems (LPP) with greater than or equal to constraints. In phase I, an auxiliary LPP is constructed by introducing artificial variables and slack/surplus variables. The objective is to minimize the artificial variables using the simplex method. If an artificial variable is positive or zero in the optimal basis, phase II is executed to solve the original LPP. Phase I provides a starting feasible solution for phase II to obtain the actual optimal solution.
The document is a lesson on conic sections from Holt Algebra 2. It introduces the four types of conic sections - circles, ellipses, hyperbolas, and parabolas - and explains that they are formed by the intersection of a plane and a double right cone. Examples are provided on graphing each type of conic section on a calculator and identifying their characteristics like center, intercepts, vertices or direction of opening. The lesson also explains how to find the center and radius of a circle using the midpoint and distance formulas.
Integrability and weak diffraction in a two-particle Bose-Hubbard model jiang-min zhang
We report a bound state, which is embedded in the continuum spectrum, of the one-dimensional two-particle (Bose or Fermion) Hubbard model with an impurity potential. The state has the Bethe-ansatz form, although this model is nonintegrable. Moreover, for a wide region in parameter space, its energy is located in the continuum band. A remarkable advantage of this state with respect to similar states in other systems is the simple analytical form of the wave function and eigenvalue. This state can be tuned in and out of the continuum continuously.
This document discusses complex variables and their applications. It introduces complex numbers using the form z = x + iy and defines complex arithmetic operations like addition, multiplication, and conjugation. Euler's formula e^{i\theta} = cos(\theta) + i\sin(\theta) is presented and used to derive trigonometric identities. De Moivre's theorem and finding roots of complex numbers are also covered.
This document discusses two methods for developing the underlying equations of finite element analysis (FEA): the method of weighted residuals and calculus of variations. It focuses on describing the method of weighted residuals, which takes the governing equations in their strong form and transforms them into weaker statements. This is done by approximating the solution over the problem domain using shape functions with unknown constants, then minimizing the residuals through an integral approach to determine the constants. Two specific weighted residual methods are outlined: collocation, which sets residuals to zero at discrete points, and subdomain, which integrates the residual over subdivided regions.
The document discusses membrane harmonics and the Helmholtz equation. It begins by considering the one-dimensional Helmholtz equation on an interval, finding the eigenfunctions and eigenvalues. It then extends this to the two-dimensional case on a rectangle using separation of variables, obtaining eigenfunctions that are products of sine waves and eigenvalues that are sums of the one-dimensional eigenvalues.
The document discusses solving second order linear differential equations with constant coefficients. It introduces the process of finding the complementary function, which is the general solution to the homogeneous equation. The complementary function contains two arbitrary constants. The document provides examples of finding the complementary function when the auxiliary equation has real roots, equal roots, and complex roots. When the auxiliary equation has complex roots k1 and k2, the complementary function is written as eαx(A cos βx + B sin βx), where α and β are the real and imaginary parts of k1 and k2.
1. The document provides the weightage or marks distribution for different units in Class XI. The highest weightage is given to Algebra with 37 marks, followed by Sets and Functions with 29 marks.
2. The document then provides definitions and derivations of some fundamental trigonometric identities involving sine, cosine, tangent, cotangent, secant and cosecant functions. Key identities such as sin^2(θ) + cos^2(θ) = 1 are derived from basic definitions.
3. Suggestions are provided for proving trigonometric identities which include starting from one side and making it look like the other side, using pythagorean identities, and expressing everything in terms of sine and
The document is a compilation of word problems involving various areas of mathematics such as algebra, geometry, trigonometry, and statistics. It contains an introduction outlining the purpose and structure of the compilation, followed by chapters with sample word problems and step-by-step solutions for topics like equations in one and two variables, plane and solid figures, right triangles, and permutation/combination problems. The compilation is intended to demonstrate how to integrate mathematics concepts into real-world situations.
This document discusses methods for finding the roots of polynomial equations, including Muller's method, Bairstow's method, and the Bairstow algorithm. It provides details on how each method works, such as deriving the coefficients of a parabola through three points for Muller's method or using synthetic division and solving simultaneous equations to estimate changes in values for Bairstow's method. An example is also shown applying Bairstow's method to find the roots of a 5th order polynomial equation.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This document discusses applications of quadratic equations and functions in various contexts. It provides examples of optimization problems involving finding the minimum number of bacteria given a quadratic function for bacterial growth and calculating dimensions of shapes like triangles given their properties. It also includes a word problem asking to maximize the total play area for twins by optimizing the dimensions of their playpen given the available fence length.
Futher pure mathematics 3 hyperbolic functionsDennis Almeida
This document provides an overview of hyperbolic functions including:
- Their definition in terms of exponential functions compared to circular/trigonometric functions defined using the unit circle.
- Graphs and properties of the six main hyperbolic functions (sinh, cosh, tanh, sech, coth, cosech) derived using exponential definitions and relationships between functions.
- Typical session structure includes introducing hyperbolic functions, defining the six functions, proving identities, and example exam questions.
My paper for Domain Decomposition Conference in Strobl, Austria, 2005Alexander Litvinenko
We did a first step in solving, so-called, skin problem. We developed an efficient H-matrix preconditioner to solve diffusion problem with jumping coefficients
This document discusses integrals involving exponential functions. It shows that integrating the exponential function results in dividing the constant in the exponent. It evaluates the important definite integral from 0 to infinity of e^-ax, which equals 1/a. It also evaluates the double integral from -infinity to infinity of e^-a(x^2+y^2), which equals sqrt(pi/a). Taking derivatives of these integrals generates related integrals involving x and x^4 that are useful in kinetic theory of gases.
I am Stuart M. I am a Chemistry Exam Helper at liveexamhelper.com. I hold a Masters' Degree in Chemistry, from the University of Greenwich, UK. I have been helping students with their exams for the past 6 years. You can hire me to take your exam in Chemistry.
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Solution of the Special Case "CLP" of the Problem of Apollonius via Vector Ro...James Smith
Using ideas developed in detail in http://www.slideshare.net/JamesSmith245/rotations-of-vectors-via-geometric-algebra-explanation-and-usage-in-solving-classic-geometric-construction-problems-version-of-11-february-2016, this document solves one of the special cases of the famous Problem of Apollonius. A new Appendix presents alternative solutions.
See also:
http://www.slideshare.net/JamesSmith245/solution-of-the-ccp-case-of-the-problem-of-apollonius-via-geometric-clifford-algebra
http://www.slideshare.net/JamesSmith245/rotations-of-vectors-via-geometric-algebra-explanation-and-usage-in-solving-classic-geometric-construction-problems-version-of-11-february-2016
http://www.slideshare.net/JamesSmith245/resoluciones-de-problemas-de-construccin-geomtricos-por-medio-de-la-geometra-clsica-y-el-lgebra-geomtrica-vectorial
This document provides an introduction to elementary quantum mechanics. It begins by defining Hilbert spaces and establishing complex exponentials as an orthonormal basis for L2 spaces. It then discusses Fourier series and using a linear combination of complex exponentials to represent L2 functions. Next, it introduces the Fourier transform and Parseval's identity. It derives the one-dimensional Schrodinger equation and discusses its physical interpretation. Finally, it formally defines quantum mechanics as a Hilbert space with a Hamiltonian and presents the Heisenberg uncertainty principle.
This document discusses numerical methods for solving partial differential equations. It begins by classifying second-order PDEs as elliptic, parabolic, or hyperbolic based on the coefficients. Finite difference approximations for derivatives are presented. Explicit and implicit methods for solving the heat equation are described, including the Bender-Schmidt explicit method and Crank-Nicholson implicit method. Poisson's equation is also discussed. Examples of applying these methods to specific PDEs are included.
Similar to 5 10b exercise_determine the diffraction symbol of ca_f2_ex on saed (20)
Complementarity of advanced TEM to bulk diffraction techniquesJoke Hadermann
Lecture contains some examples of how advanced TEM techniques can help solve the structure if for some reason bulk diffraction techniques do not allow to propose a model.
Scheelite CGEW/MO for luminescence - Summary of the paperJoke Hadermann
This document summarizes a research paper that studied the incommensurate modulation and luminescence properties of CaGd2(1-x)Eu2x(MoO4)4(1-y)(WO4)4y phosphors. The researchers found that these materials exhibit incommensurate modulation of the cation ordering due to vacancies in the scheelite structure, which requires description in superspace. Replacing Mo6+ with W6+ switched the modulation from 3+2D to 3+1D, despite their similar sizes. Variations in Eu content changed luminescence intensity but not the modulation periodicity. The results contradict prior reports of simple ordered structures.
Mapping of chemical order in inorganic compoundsJoke Hadermann
Presentations of some of the possibilities of observing cation and anion order in perosvkite based structures in order to solve their structure or to solve other questions, when they could not be solved by bulk diffraction techniques. The examples include a (Pb,Bi)FeO3-d compound, a solid oxide fuel cell compound Sr(Nb,Co,Fe)O3-d and several brownmillerite related compounds, as well as a "relaxor ferromagnetic". This was an invited lecture given at the Spring meeting of the British Crystallographic Association in 2014.
New oxide structures using lone pairs cations as "chemical scissors"Joke Hadermann
Lone pair cations like Bi3+ and Pb2+ allow for asymmetric coordination environments which can be used to create crystallographic shear planes in perovskite structures. Shear planes involve shifting one part of the structure relative to the other. This results in a new class of anion-deficient perovskite structures called the AnBnO3n-2 homologous series. Unlike other homologous series, these structures have electrically and magnetically active interfaces between perovskite blocks, resulting in frustrated magnetic structures. The orientation and spacing of shear planes can be controlled through composition.
This lecture was given at the 2nd International School on Aperiodic Crystals in Bayreuth, Germany. It is an updated version of the lecture given on the 1st school, that can be found between my lectures as "TEM for incommensurately modulated materials".
Electron crystallography for lithium based battery materialsJoke Hadermann
This lecture was given at the IUCr (International Union of Crystallography) meeting in Madrid, 2011. Contents are focussed on the use of precession electron diffraction for functional materials, mainly lithium based battery materials, but also a perovskite was included, since a large part of the audience worked on that subject.
Solving the Structure of Li Ion Battery Materials with Precession Electron Di...Joke Hadermann
Very short summary of the paper "Solving the Structure of Li Ion Battery Materials with Precession
Electron Diffraction: Application to Li2CoPO4F", published in Chem. Mater.
Tem for incommensurately modulated materialsJoke Hadermann
This presentation is a teaching lecture given on the International School on Aperiodic Crystals and explains how to index electron diffraction patterns taken from incommensurately modulated materials, with exercises, and gives some examples of HAADF-STEM and HRTEM images on incommensurately modulated materials.
Modulated materials with electron diffractionJoke Hadermann
This lecture was given at the International School of Crystallography in Erice 2011, on the topic of Electron Crystallography. It explains the very basics of how to index commensurately and incommensurately modulated materials. It was meant for a 40 minute lecture.
Direct space structure solution from precession electron diffraction data: Re...Joke Hadermann
The presentation shows the main points from the publication "Direct space structure solution from precession electron diffraction data: Resolving heavy and light scatterers in Pb13Mn9O25" about how thee structure of Pb13Mn9O25 was solved using transmission electron microscopy.
Determining a structure with electron crystallography - Overview of the paper...Joke Hadermann
The route to a solved structure (in this case Pb13Mn9O25) on the basis of precession electron diffraction, combined with HAADF-STEM, HRTEM, EELS and EDX is shown.
Summary of the paper "Solving the Structure of Li Ion Battery Materials with Precession
Electron Diffraction: Application to Li2CoPO4F"
Cation Ordering In Tunnel Compounds Determined By TemJoke Hadermann
1) The document discusses tunnel manganites, which are compounds containing manganese oxide frameworks that form tunnel structures. These frameworks can accommodate various guest cations in their tunnels.
2) Several examples of tunnel manganite frameworks are described, including pyrolusite, ramsdellite, hollandite, and more complex examples. The document also discusses the types of guest cations that can occupy the tunnels.
3) New examples of tunnel manganites are presented, including SrMn3O6, CaMn3O6, and a todorokite compound with rock salt-type tunnel contents. Composite structural models are discussed that can be used to describe ordering of guest cations
Dr. Firoozeh Kashani-Sabet is an innovator in Middle Eastern Studies and approaches her work, particularly focused on Iran, with a depth and commitment that has resulted in multiple book publications. She is notable for her work with the University of Pennsylvania, where she serves as the Walter H. Annenberg Professor of History.
Discovery of An Apparent Red, High-Velocity Type Ia Supernova at 𝐳 = 2.9 wi...Sérgio Sacani
We present the JWST discovery of SN 2023adsy, a transient object located in a host galaxy JADES-GS
+
53.13485
−
27.82088
with a host spectroscopic redshift of
2.903
±
0.007
. The transient was identified in deep James Webb Space Telescope (JWST)/NIRCam imaging from the JWST Advanced Deep Extragalactic Survey (JADES) program. Photometric and spectroscopic followup with NIRCam and NIRSpec, respectively, confirm the redshift and yield UV-NIR light-curve, NIR color, and spectroscopic information all consistent with a Type Ia classification. Despite its classification as a likely SN Ia, SN 2023adsy is both fairly red (
�
(
�
−
�
)
∼
0.9
) despite a host galaxy with low-extinction and has a high Ca II velocity (
19
,
000
±
2
,
000
km/s) compared to the general population of SNe Ia. While these characteristics are consistent with some Ca-rich SNe Ia, particularly SN 2016hnk, SN 2023adsy is intrinsically brighter than the low-
�
Ca-rich population. Although such an object is too red for any low-
�
cosmological sample, we apply a fiducial standardization approach to SN 2023adsy and find that the SN 2023adsy luminosity distance measurement is in excellent agreement (
≲
1
�
) with
Λ
CDM. Therefore unlike low-
�
Ca-rich SNe Ia, SN 2023adsy is standardizable and gives no indication that SN Ia standardized luminosities change significantly with redshift. A larger sample of distant SNe Ia is required to determine if SN Ia population characteristics at high-
�
truly diverge from their low-
�
counterparts, and to confirm that standardized luminosities nevertheless remain constant with redshift.
SDSS1335+0728: The awakening of a ∼ 106M⊙ black hole⋆Sérgio Sacani
Context. The early-type galaxy SDSS J133519.91+072807.4 (hereafter SDSS1335+0728), which had exhibited no prior optical variations during the preceding two decades, began showing significant nuclear variability in the Zwicky Transient Facility (ZTF) alert stream from December 2019 (as ZTF19acnskyy). This variability behaviour, coupled with the host-galaxy properties, suggests that SDSS1335+0728 hosts a ∼ 106M⊙ black hole (BH) that is currently in the process of ‘turning on’. Aims. We present a multi-wavelength photometric analysis and spectroscopic follow-up performed with the aim of better understanding the origin of the nuclear variations detected in SDSS1335+0728. Methods. We used archival photometry (from WISE, 2MASS, SDSS, GALEX, eROSITA) and spectroscopic data (from SDSS and LAMOST) to study the state of SDSS1335+0728 prior to December 2019, and new observations from Swift, SOAR/Goodman, VLT/X-shooter, and Keck/LRIS taken after its turn-on to characterise its current state. We analysed the variability of SDSS1335+0728 in the X-ray/UV/optical/mid-infrared range, modelled its spectral energy distribution prior to and after December 2019, and studied the evolution of its UV/optical spectra. Results. From our multi-wavelength photometric analysis, we find that: (a) since 2021, the UV flux (from Swift/UVOT observations) is four times brighter than the flux reported by GALEX in 2004; (b) since June 2022, the mid-infrared flux has risen more than two times, and the W1−W2 WISE colour has become redder; and (c) since February 2024, the source has begun showing X-ray emission. From our spectroscopic follow-up, we see that (i) the narrow emission line ratios are now consistent with a more energetic ionising continuum; (ii) broad emission lines are not detected; and (iii) the [OIII] line increased its flux ∼ 3.6 years after the first ZTF alert, which implies a relatively compact narrow-line-emitting region. Conclusions. We conclude that the variations observed in SDSS1335+0728 could be either explained by a ∼ 106M⊙ AGN that is just turning on or by an exotic tidal disruption event (TDE). If the former is true, SDSS1335+0728 is one of the strongest cases of an AGNobserved in the process of activating. If the latter were found to be the case, it would correspond to the longest and faintest TDE ever observed (or another class of still unknown nuclear transient). Future observations of SDSS1335+0728 are crucial to further understand its behaviour. Key words. galaxies: active– accretion, accretion discs– galaxies: individual: SDSS J133519.91+072807.4
JAMES WEBB STUDY THE MASSIVE BLACK HOLE SEEDSSérgio Sacani
The pathway(s) to seeding the massive black holes (MBHs) that exist at the heart of galaxies in the present and distant Universe remains an unsolved problem. Here we categorise, describe and quantitatively discuss the formation pathways of both light and heavy seeds. We emphasise that the most recent computational models suggest that rather than a bimodal-like mass spectrum between light and heavy seeds with light at one end and heavy at the other that instead a continuum exists. Light seeds being more ubiquitous and the heavier seeds becoming less and less abundant due the rarer environmental conditions required for their formation. We therefore examine the different mechanisms that give rise to different seed mass spectrums. We show how and why the mechanisms that produce the heaviest seeds are also among the rarest events in the Universe and are hence extremely unlikely to be the seeds for the vast majority of the MBH population. We quantify, within the limits of the current large uncertainties in the seeding processes, the expected number densities of the seed mass spectrum. We argue that light seeds must be at least 103 to 105 times more numerous than heavy seeds to explain the MBH population as a whole. Based on our current understanding of the seed population this makes heavy seeds (Mseed > 103 M⊙) a significantly more likely pathway given that heavy seeds have an abundance pattern than is close to and likely in excess of 10−4 compared to light seeds. Finally, we examine the current state-of-the-art in numerical calculations and recent observations and plot a path forward for near-future advances in both domains.
BIRDS DIVERSITY OF SOOTEA BISWANATH ASSAM.ppt.pptxgoluk9330
Ahota Beel, nestled in Sootea Biswanath Assam , is celebrated for its extraordinary diversity of bird species. This wetland sanctuary supports a myriad of avian residents and migrants alike. Visitors can admire the elegant flights of migratory species such as the Northern Pintail and Eurasian Wigeon, alongside resident birds including the Asian Openbill and Pheasant-tailed Jacana. With its tranquil scenery and varied habitats, Ahota Beel offers a perfect haven for birdwatchers to appreciate and study the vibrant birdlife that thrives in this natural refuge.
Compositions of iron-meteorite parent bodies constrainthe structure of the pr...Sérgio Sacani
Magmatic iron-meteorite parent bodies are the earliest planetesimals in the Solar System,and they preserve information about conditions and planet-forming processes in thesolar nebula. In this study, we include comprehensive elemental compositions andfractional-crystallization modeling for iron meteorites from the cores of five differenti-ated asteroids from the inner Solar System. Together with previous results of metalliccores from the outer Solar System, we conclude that asteroidal cores from the outerSolar System have smaller sizes, elevated siderophile-element abundances, and simplercrystallization processes than those from the inner Solar System. These differences arerelated to the formation locations of the parent asteroids because the solar protoplane-tary disk varied in redox conditions, elemental distributions, and dynamics at differentheliocentric distances. Using highly siderophile-element data from iron meteorites, wereconstruct the distribution of calcium-aluminum-rich inclusions (CAIs) across theprotoplanetary disk within the first million years of Solar-System history. CAIs, the firstsolids to condense in the Solar System, formed close to the Sun. They were, however,concentrated within the outer disk and depleted within the inner disk. Future modelsof the structure and evolution of the protoplanetary disk should account for this dis-tribution pattern of CAIs.
Microbial interaction
Microorganisms interacts with each other and can be physically associated with another organisms in a variety of ways.
One organism can be located on the surface of another organism as an ectobiont or located within another organism as endobiont.
Microbial interaction may be positive such as mutualism, proto-cooperation, commensalism or may be negative such as parasitism, predation or competition
Types of microbial interaction
Positive interaction: mutualism, proto-cooperation, commensalism
Negative interaction: Ammensalism (antagonism), parasitism, predation, competition
I. Mutualism:
It is defined as the relationship in which each organism in interaction gets benefits from association. It is an obligatory relationship in which mutualist and host are metabolically dependent on each other.
Mutualistic relationship is very specific where one member of association cannot be replaced by another species.
Mutualism require close physical contact between interacting organisms.
Relationship of mutualism allows organisms to exist in habitat that could not occupied by either species alone.
Mutualistic relationship between organisms allows them to act as a single organism.
Examples of mutualism:
i. Lichens:
Lichens are excellent example of mutualism.
They are the association of specific fungi and certain genus of algae. In lichen, fungal partner is called mycobiont and algal partner is called
II. Syntrophism:
It is an association in which the growth of one organism either depends on or improved by the substrate provided by another organism.
In syntrophism both organism in association gets benefits.
Compound A
Utilized by population 1
Compound B
Utilized by population 2
Compound C
utilized by both Population 1+2
Products
In this theoretical example of syntrophism, population 1 is able to utilize and metabolize compound A, forming compound B but cannot metabolize beyond compound B without co-operation of population 2. Population 2is unable to utilize compound A but it can metabolize compound B forming compound C. Then both population 1 and 2 are able to carry out metabolic reaction which leads to formation of end product that neither population could produce alone.
Examples of syntrophism:
i. Methanogenic ecosystem in sludge digester
Methane produced by methanogenic bacteria depends upon interspecies hydrogen transfer by other fermentative bacteria.
Anaerobic fermentative bacteria generate CO2 and H2 utilizing carbohydrates which is then utilized by methanogenic bacteria (Methanobacter) to produce methane.
ii. Lactobacillus arobinosus and Enterococcus faecalis:
In the minimal media, Lactobacillus arobinosus and Enterococcus faecalis are able to grow together but not alone.
The synergistic relationship between E. faecalis and L. arobinosus occurs in which E. faecalis require folic acid
Signatures of wave erosion in Titan’s coastsSérgio Sacani
The shorelines of Titan’s hydrocarbon seas trace flooded erosional landforms such as river valleys; however, it isunclear whether coastal erosion has subsequently altered these shorelines. Spacecraft observations and theo-retical models suggest that wind may cause waves to form on Titan’s seas, potentially driving coastal erosion,but the observational evidence of waves is indirect, and the processes affecting shoreline evolution on Titanremain unknown. No widely accepted framework exists for using shoreline morphology to quantitatively dis-cern coastal erosion mechanisms, even on Earth, where the dominant mechanisms are known. We combinelandscape evolution models with measurements of shoreline shape on Earth to characterize how differentcoastal erosion mechanisms affect shoreline morphology. Applying this framework to Titan, we find that theshorelines of Titan’s seas are most consistent with flooded landscapes that subsequently have been eroded bywaves, rather than a uniform erosional process or no coastal erosion, particularly if wave growth saturates atfetch lengths of tens of kilometers.
Sexuality - Issues, Attitude and Behaviour - Applied Social Psychology - Psyc...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
2. You will need this table (from IT volume A)
Figure out reflection
conditions for these
sets.
For shortening the exercise, let's suppose we already know that it is cubic (the fact that a=b=c is not enough to declare
that it is cubic, it needs the right symmetry elements! If we do not know this, the difference will be that we will also take
the tabes for orthorhombic, etc and will just end up with more possibilities to check further.
3. hkl:
h+k+l=2n
h+k, k+l, h+l=2n
h+k=2n
Step 1: determine the reflection conditions from the patterns.
200
131
200
151
200111
200020
[001] [015]
-
[013]
-
[011]
-
We indexed these patterns in an earlier exercise in the lecture "How to index SAED patterns". Which general reflection
condition can you derive from these patterns?
4. hkl:
h+k+l=2n
h+k, k+l, h+l=2n
h+k=2n
Step 1: determine the reflection conditions from the patterns.
-
For these patterns
both would be
good....!?
200
131
200
151
200111
200020
[001] [015]
-
[013]
-
[011]
-
Both the second and third answer are in agreement with these patterns! This means you cannot determine the general
condition from these patterns. In real life you would need to go back to the microscope and get extra patterns from other
zones.
6. This means we do not have sufficient information!
we miss [012], which will make the difference.
-
By coincidence
200
042
For these patterns
both would be
good....!?
hkl:
h+k+l=2n
h+k, k+l, h+l=2n
h+k=2n
An extra pattern that can bring the solution here is for example the [01-2] shown in this slide. Determine which of the two
conditions still agrees with this pattern.
7. 200
042 hkl:
h+k+l=2n
h+k, k+l, h+l=2n
h+k=2n
200
042
This means we do not have sufficient information!
we miss [012], which will make the difference.
-
By coincidence
For these patterns
both would be
good....!?
Now only hkl: h+k=2n, k+l=2n, h+l=2n fits. Which means that this is the correct reflection condition. The correct reflection
conditions should fit all zones of the same material!
8. It is possible to draw the wrong
conclusions if you do not have
enough zones!
9. 0kl:
k=2n
k,l=2n
k+l=2n
Step 1: determine the reflection conditions from the patterns.
200
131
200
151
200111
200020
[001] [015]
-
[013]
-
[011]
-
200
042
After the general condition, determine the special conditions.
10. Step 1: determine the reflection conditions from the patterns.
0kl:
k=2n
k,l=2n
k+l=2n
200
131
200
151
200111
200020
[001] [015]
-
[013]
-
[011]
-
200
042
13. 00l:
no condition
l=2n
l=4n
Step 1: determine the reflection conditions from the patterns.
200
131
200
151
200111
200020
[001] [015]
-
[013]
-
[011]
-
200
042
And afterwards, the serial conditions. The International table asks for the condition 00l, and we cannot see these reflections.
But remember, in cubic there is equivalence: h00, 0k0 and 00l are interchangeable.
Again, if we did not know it was cubic, we would need to also check the tables of the other crystal classes, check more
combinations and need for that more zones. This however all goes in the same way, so to learn the concepts now, assuming
that cubic is known is perfectly ok.
14. 00l:
no condition
l=2n
l=4n
Step 1: determine the reflection conditions from the patterns.
200
131
200
151
200111
200020
[001] [015]
-
[013]
-
[011]
-
200
042
Possible! It
might be double
diffraction!
Do not forget about the possibility of double diffraction!
15. Step 2: look up the matching extinction
symbol in the International Tables of
Crystallography.
?
?
17. 200 and 020 could be due to double diffraction...
200
131
200
151
200111
200020
[001] [015]
-
[013]
-
[011]
-
Tilt around 200 until all other reflections gone
except h00 axis:
18. 200 and 020 could be due to double diffraction...
Tilt around 200 until all other reflections gone except h00 axis:
200 does not disappear
It is not double diffraction
00l: l=2n
not 00l: l=4n
19. Step 2: look up the matching extinction symbol in
the International Tables of Crystallography.
20. From the reflection conditions you get
the diffraction symbol:
F - - -
This still leaves 5 possible space groups:
F23 Fm3 F432 F43m Fm3m
Only difference: rotation axes and mirror planes
Cannot be derived from reflection conditions
need CBED