1. The document provides solutions to homework problems from a complex analysis class.
2. It shows the work to find harmonic conjugates and derivatives of complex functions, evaluate complex expressions, and take logarithms and exponents of complex numbers.
3. Key steps include using the Cauchy-Riemann equations to test if functions are analytic, decomposing complex expressions into polar form, and applying properties of logarithms and exponents to manipulate expressions.
This document contains mathematical formula tables from the University of Manchester. It provides formulas for topics including trigonometric identities, derivatives, integrals, Laplace transforms, and more. The tables are identical to version 2.0 tables from UMIST with the exception of the front cover. The tables contain over 30 pages of formulas organized by topic.
1. The document provides solutions to homework problems from a complex analysis class.
2. It shows the work to find harmonic conjugates and derivatives of complex functions, evaluate complex expressions, and take logarithms and exponents of complex numbers.
3. Key steps include using the Cauchy-Riemann equations to test if functions are analytic, decomposing complex expressions into polar form, and applying properties of logarithms and exponents to manipulate expressions.
This document contains mathematical formula tables from the University of Manchester. It provides formulas for topics including trigonometric identities, derivatives, integrals, Laplace transforms, and more. The tables are identical to version 2.0 tables from UMIST with the exception of the front cover. The tables contain over 30 pages of formulas organized by topic.
1. The function f(x) = ln(x + sqrt(x^2 + 1)) is analyzed. It is shown that f(x) is differentiable on R and strictly increasing, with f'(x) > 0 for all x in R.
2. The inverse function g(x) = f^(-1)(x) is shown to be 1/2(e^x - e^-x), which is also differentiable on R with g'(x) > 0.
3. It is proven that the area between the graphs of f(x) and x from x = 0 to x = 1 is √2/2 - ln(1+√2).
University of manchester mathematical formula tablesGaurav Vasani
This document contains mathematical formula tables covering a wide range of topics including:
- Greek alphabet
- Indices and logarithms
- Trigonometric, complex number, and hyperbolic identities
- Power series expansions
- Derivatives of common functions
- Integrals of common functions
- Laplace transforms
- And more advanced topics such as vector calculus, mechanics, and statistical distributions.
The detailed derivation of the derivatives in Table 2 of Marginalized Denoisi...Tomonari Masada
The detailed derivation of the derivatives in Table 2 of Marginalized Denoising Auto-encoders for Nonlinear Representations by M. Chen, K. Weinberger, F. Sha, and Y. Bengio
http://www.cse.wustl.edu/~mchen/papers/deepmsda.pdf
El text.life science6.matsubayashi191120RCCSRENKEI
This document discusses molecular dynamics (MD) simulations. It provides equations for modeling interactions in MD, such as bonds, angles, torsions, and nonbonded interactions. It describes algorithms like Verlet integration that are used to solve the equations of motion in MD. It also discusses ensembles like NVE, NVT, and NPT that are commonly used, and methods like Langevin dynamics and barostats that are applied to control temperature and pressure.
This document discusses Taylor series expansions and examples of their applications. Specifically, it provides 15 examples of how common functions can be expressed as Taylor series expansions around a point a, including expressions for sin(x), cos(x), log(1+x), exp(x), and trigonometric functions. Each Taylor series expansion is written out term-by-term with the little-o notation used to describe the remainder term.
1) This document provides formulas for integrals of common functions including polynomials, rational functions, radicals, logarithms, trigonometric functions, exponentials, and hyperbolic functions.
2) The integrals are organized into sections based on the type of function, with the formula provided along with conditions on parameters.
3) There are over 100 integrals presented in the table spanning multiple pages of formulas.
This document provides formulas for integrals of common functions. It includes integrals of polynomials, rational functions, functions with roots, logarithms, exponentials, trigonometric functions, hyperbolic functions, and products of various functions. There are over 100 formulas presented in a table format with the function and integral provided.
The document provides tables summarizing rules for deriving functions. It lists common functions and their derivatives, such as the derivative of a sum of functions being the sum of the individual derivatives. Examples are given such as the derivative of x4 + x3 being 4x3 + 3x2. Trigonometric functions and their inverses are also covered.
1. The document contains solutions to calculus integration problems.
2. One problem involves finding the limit as b approaches infinity of the integral from 0 to b of (x+1)(x+2) dx. The solution uses partial fractions to decompose the integrand and finds the limit is ln(2).
3. Another problem involves factorizing the integrand (x2 + 2x + 2) as (x+2)(x+1) and again using partial fractions to solve the integral.
jhkl,l.มือครูคณิตศาสตร์พื้นฐาน ม.4 สสวท เล่ม 2fuyhfgTonn Za
This document summarizes a book titled "The Development of the Thai Language Teaching Materials for Grade 3-4 Students" by Dr. Somchai Srisa-an.
The book was published in 2001 to provide Thai language teaching materials for grades 3-4. It includes 4 chapters, with each chapter focusing on a different grade level (grade 3, chapter 1 and grade 4, chapter 4).
The summary highlights that the book aims to develop Thai language skills for students in grades 3-4 and provides teaching materials tailored to each grade level. It also seeks to appropriately introduce students to the Thai language in order to enhance their language abilities and prepare them for further study.
The binomial theorem describes the expansion of binomial expressions of the form (x + y)n into a sum of terms involving integers and powers of x and y. It expresses the coefficient of each term using binomial coefficients. The general form of the binomial expansion is (x + y)n = xn + n xn-1 y + n(n-1)/2! xn-2 y2 + ... + yn. Fourier series can be used to represent periodic functions as an infinite sum of sines and cosines of integer multiples of the fundamental frequency. The coefficients of the Fourier series capture the frequency content of the original function.
1. The document contains mathematical formulas and equations related to geometry, trigonometry, and calculus.
2. Formulas are provided for calculating the surface area and volume of spheres, cylinders, cones, and other shapes.
3. Trigonometric functions like sine, cosine, and tangent are defined in terms of right triangles and angles in radians.
1) The document discusses maximizing a function f(uA) of a single variable uA on a bounded domain U.
2) It is found that f(uA) is maximized when uA = (2/5)2/3, giving a maximum value of 3/5.
3) The point (uA, uB) = ((2/5)2/3, 3/5) is therefore the optimal solution.
The document contains step-by-step workings and solutions to algebra problems involving inequalities, equations, polynomials, and subtraction of polynomials. Specifically, it solves an inequality, equation, identifies values for constants a and b in a polynomial based on remainders, and subtracts one polynomial from another.
Matematika diskrit: fungsi pembangkit part 3radar radius
1) The document discusses Taylor series and functions. It provides examples of calculating the Taylor series for functions like ex, 1/(1-x), and others.
2) It also discusses function generators in basic form (FPB) and exported form (FPE). An example is worked out to determine the coefficients for the FPB and FPE of a given function.
3) Determining the coefficients for different function generators is demonstrated, such as for p(x)=x2ex and p(x)=x/(1-x).
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Model Based Fault Detection, Identification and Accommodation in Antilock Bra...Behzad Samadi
1) The document presents a model-based fault detection and identification approach for antilock braking systems (ABS). It develops nonlinear dynamic models for vehicle motion and tire forces.
2) Kalman filtering techniques are used to estimate vehicle states and tire forces based on sensor measurements, and residuals between measurements and estimates are monitored to detect and identify faults.
3) The approach extends previous work by including additional tire force states and their dynamics in the estimation model to improve fault detection performance.
Similar to Lie-Trotter-Suzuki分解、特にフラクタル分解について (20)
quantum chemistry on quantum computer handson by Q# (2019/8/4@MDR Hongo, Tokyo)Maho Nakata
The document describes the Hamiltonian operator (H) and its application to the Hartree-Fock wavefunction (|ΦHF⟩) to obtain energy eigenvalues (E0, E1, etc.). The Hartree-Fock wavefunction can be expressed as a linear combination of Slater determinants (|Ψ0⟩, |Ψ1⟩, etc.). Applying the exponential of the Hamiltonian operator over time (eiHt) to |ΦHF⟩ yields the time-dependent Hartree-Fock wavefunction.
QIQB(大阪大学先導的学際研究機構量子情報・量子生命研究部門)セミナー でのスライドを加筆したもの。量子コンピュータを用いた量子化学計算の現在の状況と展望を述べた.
伝統的なゲート式位相推定による方法とvariational eigen solverによるものと2つ。ごく最近虚時間発展法の実装もされており、それは別スライドで概観した。
The document discusses the application of the Bravyi-Kitaev transformation to quantum chemistry calculations on a quantum computer. It notes that while quantum computers could perform quantum chemistry simulations much faster than classical computers, actually implementing the calculations requires many unitary circuits. The Bravyi-Kitaev transformation reduces the number of circuits needed by encoding qubits in a different way, making the calculations more efficient for a real quantum computer.
PubChem QC project. In this project we calculate all molecules in the PubChem Project. Currently 1,100,000 molecules are available at http://pubchemqc.riken.jp/ . Results are in public domain.
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
Describing and Interpreting an Immersive Learning Case with the Immersion Cub...Leonel Morgado
Current descriptions of immersive learning cases are often difficult or impossible to compare. This is due to a myriad of different options on what details to include, which aspects are relevant, and on the descriptive approaches employed. Also, these aspects often combine very specific details with more general guidelines or indicate intents and rationales without clarifying their implementation. In this paper we provide a method to describe immersive learning cases that is structured to enable comparisons, yet flexible enough to allow researchers and practitioners to decide which aspects to include. This method leverages a taxonomy that classifies educational aspects at three levels (uses, practices, and strategies) and then utilizes two frameworks, the Immersive Learning Brain and the Immersion Cube, to enable a structured description and interpretation of immersive learning cases. The method is then demonstrated on a published immersive learning case on training for wind turbine maintenance using virtual reality. Applying the method results in a structured artifact, the Immersive Learning Case Sheet, that tags the case with its proximal uses, practices, and strategies, and refines the free text case description to ensure that matching details are included. This contribution is thus a case description method in support of future comparative research of immersive learning cases. We then discuss how the resulting description and interpretation can be leveraged to change immersion learning cases, by enriching them (considering low-effort changes or additions) or innovating (exploring more challenging avenues of transformation). The method holds significant promise to support better-grounded research in immersive learning.
Immersive Learning That Works: Research Grounding and Paths ForwardLeonel Morgado
We will metaverse into the essence of immersive learning, into its three dimensions and conceptual models. This approach encompasses elements from teaching methodologies to social involvement, through organizational concerns and technologies. Challenging the perception of learning as knowledge transfer, we introduce a 'Uses, Practices & Strategies' model operationalized by the 'Immersive Learning Brain' and ‘Immersion Cube’ frameworks. This approach offers a comprehensive guide through the intricacies of immersive educational experiences and spotlighting research frontiers, along the immersion dimensions of system, narrative, and agency. Our discourse extends to stakeholders beyond the academic sphere, addressing the interests of technologists, instructional designers, and policymakers. We span various contexts, from formal education to organizational transformation to the new horizon of an AI-pervasive society. This keynote aims to unite the iLRN community in a collaborative journey towards a future where immersive learning research and practice coalesce, paving the way for innovative educational research and practice landscapes.
Current Ms word generated power point presentation covers major details about the micronuclei test. It's significance and assays to conduct it. It is used to detect the micronuclei formation inside the cells of nearly every multicellular organism. It's formation takes place during chromosomal sepration at metaphase.
When I was asked to give a companion lecture in support of ‘The Philosophy of Science’ (https://shorturl.at/4pUXz) I decided not to walk through the detail of the many methodologies in order of use. Instead, I chose to employ a long standing, and ongoing, scientific development as an exemplar. And so, I chose the ever evolving story of Thermodynamics as a scientific investigation at its best.
Conducted over a period of >200 years, Thermodynamics R&D, and application, benefitted from the highest levels of professionalism, collaboration, and technical thoroughness. New layers of application, methodology, and practice were made possible by the progressive advance of technology. In turn, this has seen measurement and modelling accuracy continually improved at a micro and macro level.
Perhaps most importantly, Thermodynamics rapidly became a primary tool in the advance of applied science/engineering/technology, spanning micro-tech, to aerospace and cosmology. I can think of no better a story to illustrate the breadth of scientific methodologies and applications at their best.
The cost of acquiring information by natural selectionCarl Bergstrom
This is a short talk that I gave at the Banff International Research Station workshop on Modeling and Theory in Population Biology. The idea is to try to understand how the burden of natural selection relates to the amount of information that selection puts into the genome.
It's based on the first part of this research paper:
The cost of information acquisition by natural selection
Ryan Seamus McGee, Olivia Kosterlitz, Artem Kaznatcheev, Benjamin Kerr, Carl T. Bergstrom
bioRxiv 2022.07.02.498577; doi: https://doi.org/10.1101/2022.07.02.498577
(June 12, 2024) Webinar: Development of PET theranostics targeting the molecu...Scintica Instrumentation
Targeting Hsp90 and its pathogen Orthologs with Tethered Inhibitors as a Diagnostic and Therapeutic Strategy for cancer and infectious diseases with Dr. Timothy Haystead.
ESR spectroscopy in liquid food and beverages.pptxPRIYANKA PATEL
With increasing population, people need to rely on packaged food stuffs. Packaging of food materials requires the preservation of food. There are various methods for the treatment of food to preserve them and irradiation treatment of food is one of them. It is the most common and the most harmless method for the food preservation as it does not alter the necessary micronutrients of food materials. Although irradiated food doesn’t cause any harm to the human health but still the quality assessment of food is required to provide consumers with necessary information about the food. ESR spectroscopy is the most sophisticated way to investigate the quality of the food and the free radicals induced during the processing of the food. ESR spin trapping technique is useful for the detection of highly unstable radicals in the food. The antioxidant capability of liquid food and beverages in mainly performed by spin trapping technique.
Mending Clothing to Support Sustainable Fashion_CIMaR 2024.pdfSelcen Ozturkcan
Ozturkcan, S., Berndt, A., & Angelakis, A. (2024). Mending clothing to support sustainable fashion. Presented at the 31st Annual Conference by the Consortium for International Marketing Research (CIMaR), 10-13 Jun 2024, University of Gävle, Sweden.
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
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!
19. exp(x + y)A = exp xA + exp xA
exp[x(A + B)] = exp[sx(A + B)]exp[(1 − 2s)x(A + B)]exp[sx(A + B)]
S3(x) ≡ S2(sx)S2((1 − 2s)x)S2(sx) = e
s
2 xA
esxB
e
1 − s
2 xA
e(1−2s)xB
e
1 − s
2 xA
esxB
e
s
2 xA
S3(x) ≡ e
s
2 xA
esxB
e
1 − s
2 xA
e(1−2s)xB
e
1 − s
2 xA
esxB
e
s
2 xA
= ex(A+B)
+ O(x4
)
20. S3(x) ≡ S2(sx)S2((1 − 2s)x)S2(sx) = e
s
2 xA
esxB
e
1 − s
2 xA
e(1−2s)xB
e
1 − s
2 xA
esxB
e
s
2 xA
S2(x) ≡ e
x
2 A
exB
e
x
2 A
= ex(A+B)+x3
R3+x5
R5+⋯
= ex(A+B)+x3
R3+O(x5
)
R2, R4
O(x4
)
S3(x) = S2(sx)S2((1 − 2s)x)S2(sx)
= esx(A+B)+s3
x3
R3+O(x5
)
e(1−2s)x(A+B)+(1−2s)3
x3
R3+O(x5
)
esx(A+B)+s3
x3
R3+O(x5
)
= ex(A+B)+[2s3
+ (1 − 2s)3
]R3+O(x5
)
R3
2s3
+ (1 − 2s)3
= 0