The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers.
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph.
University Electromagnetism:
Electric field and potential of a capacitor that is partly filled (vertically or horizontally) with dielectric material (connected or not to a battery)
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers.
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph.
University Electromagnetism:
Electric field and potential of a capacitor that is partly filled (vertically or horizontally) with dielectric material (connected or not to a battery)
Inductance of transmission line
Flux linkages of one conductor in a group of conductors
Inductance of composite conductor lines
Inductance of 3-phase overhead line
Bundled conductors
All about amateur radio RF transmission lines. This relates to Section 26 of the NZART Radio Syllabus and may be used to teach this section of the exam.
Microwave is a descriptive term used to identify EM waves in the frequency spectrum ranging approximately from 1 GHz to 30 GHz.
This corresponds to wavelength from 30 cm to 1 cm (λ = c/f).Sometimes higher frequency ranging upto 600 GHz are also called Microwaves
EWS
ECM
ESM
ECCM
Microwave Heating
Industrial Heating
Microwave oven
Industrial,Scientific,Medical
Linear Acclerators
Plasma Containment
Radio Astronomy
Whole body cancer theraphy
The fundamental theory of electromagnetic field is based on Maxwell.pdfinfo309708
The fundamental theory of electromagnetic field is based on Maxwell\'s equations. These
equations govern the electromagnetic fields, E, D, H, and there relations to the source, f and p_v.
In a source-free region, list the Maxwell\'s equations for time-harmonic fields: Given the Phaser
from of the electric field E? For the above given electric field, is B varying with time? Why?
Solution
Maxwell’s equations simplify considerably in the case of harmonic time dependence. Through
the inverse Fourier transform, general solutions of Maxwell’s equation can be built as linear
combinations of single-frequency solutions:† E(r, t)= E(r, )ejt d2 (1) Thus, we assume that all
fields have a time dependence ejt: E(r, t)= E(r)ejt, H(r, t)= H(r)ejt where the phasor amplitudes
E(r), H(r) are complex-valued. Replacing time derivatives by t j, we may rewrite Eq. in the
form:
× E = jB
× H = J + jD
· D =
· B = 0
(Maxwell’s equations) (2) In this book, we will consider the solutions of Eqs. (.2) in three
different contexts: (a) uniform plane waves propagating in dielectrics, conductors, and
birefringent media, (b) guided waves propagating in hollow waveguides, transmission lines, and
optical fibers, and (c) propagating waves generated by antennas and apertures
Next, we review some conventions regarding phasors and time averages. A realvalued sinusoid
has the complex phasor representation: A(t)= |A| cos(t + ) A(t)= Aejt (3) where A = |A|ej. Thus,
we have A(t)= Re A(t) = Re Aejt . The time averages of the quantities A(t) and A(t) over one
period T = 2/ are zero. The time average of the product of two harmonic quantities A(t)= Re Aejt
and B(t)= Re Bejt with phasors A, B is given by A(t)B(t) = 1T T0 A(t)B(t) dt = 12 Re AB] (4) In
particular, the mean-square value is given by: A2(t) = 1T T0 A2(t) dt = 12 Re AA]= 12|A|2 (5)
Some interesting time averages in electromagnetic wave problems are the time averages of the
energy density, the Poynting vector (energy flux), and the ohmic power losses per unit volume.
Using the definition) and the result (.4), we have for these time averages:
w = 1 2 Re 12E · E + 12H · H (energy density) P = 1/ 2 Re E × H (Poynting vector) dPloss dV =
1/ 2 Re Jtot · E (ohmic losses) (6) where Jtot = J + jD is the total current in the right-hand side of
Amp`ere’s law and accounts for both conducting and dielectric losses. The time-averaged
version of Poynting’s theorem is discussed in Problem 1.5. The expression (1.9.6) for the energy
density w was derived under the assumption that both and were constants independent of
frequency. In a dispersive medium, , become functions of frequency. In frequency bands where
(), () are essentially real-valued, that is, where the medium is lossless,that the timeaveraged
energy density generalizes to: w = 1/ 2 Re 1/2 d() d E · E + 1/2 d() d H · H (lossless case) (.7)
The derivation of (.7) is as follows. Starting with Maxwell’s equations (1.1.1) and without
assuming any particular constitutive relations, we obtain:.
The fundamental theory of electromagnetic field is based on Maxwell.pdfRBMADU
The fundamental theory of electromagnetic field is based on Maxwell\'s equations. These
equations govern the electromagnetic fields, E, D, H, and there relations to the source, f and p_v.
In a source-free region, list the Maxwell\'s equations for time-harmonic fields: Given the Phaser
from of the electric field E? For the above given electric field, is B varying with time? Why?
Solution
Maxwell’s equations simplify considerably in the case of harmonic time dependence. Through
the inverse Fourier transform, general solutions of Maxwell’s equation can be built as linear
combinations of single-frequency solutions:† E(r, t)= E(r, )ejt d2 (1) Thus, we assume that all
fields have a time dependence ejt: E(r, t)= E(r)ejt, H(r, t)= H(r)ejt where the phasor amplitudes
E(r), H(r) are complex-valued. Replacing time derivatives by t j, we may rewrite Eq. in the
form:
× E = jB
× H = J + jD
· D =
· B = 0
(Maxwell’s equations) (2) In this book, we will consider the solutions of Eqs. (.2) in three
different contexts: (a) uniform plane waves propagating in dielectrics, conductors, and
birefringent media, (b) guided waves propagating in hollow waveguides, transmission lines, and
optical fibers, and (c) propagating waves generated by antennas and apertures
Next, we review some conventions regarding phasors and time averages. A realvalued sinusoid
has the complex phasor representation: A(t)= |A| cos(t + ) A(t)= Aejt (3) where A = |A|ej. Thus,
we have A(t)= Re A(t) = Re Aejt . The time averages of the quantities A(t) and A(t) over one
period T = 2/ are zero. The time average of the product of two harmonic quantities A(t)= Re Aejt
and B(t)= Re Bejt with phasors A, B is given by A(t)B(t) = 1T T0 A(t)B(t) dt = 12 Re AB] (4) In
particular, the mean-square value is given by: A2(t) = 1T T0 A2(t) dt = 12 Re AA]= 12|A|2 (5)
Some interesting time averages in electromagnetic wave problems are the time averages of the
energy density, the Poynting vector (energy flux), and the ohmic power losses per unit volume.
Using the definition) and the result (.4), we have for these time averages:
w = 1 2 Re 12E · E + 12H · H (energy density) P = 1/ 2 Re E × H (Poynting vector) dPloss dV =
1/ 2 Re Jtot · E (ohmic losses) (6) where Jtot = J + jD is the total current in the right-hand side of
Amp`ere’s law and accounts for both conducting and dielectric losses. The time-averaged
version of Poynting’s theorem is discussed in Problem 1.5. The expression (1.9.6) for the energy
density w was derived under the assumption that both and were constants independent of
frequency. In a dispersive medium, , become functions of frequency. In frequency bands where
(), () are essentially real-valued, that is, where the medium is lossless,that the timeaveraged
energy density generalizes to: w = 1/ 2 Re 1/2 d() d E · E + 1/2 d() d H · H (lossless case) (.7)
The derivation of (.7) is as follows. Starting with Maxwell’s equations (1.1.1) and without
assuming any particular constitutive relations, we obtain:.
EMF ELECTROSTATICS:
Coulomb’s Law, Electric Field of Different Charge Configurations using Coulomb’s Law, Electric Flux, Field Lines, Gauss’s Law in terms of E (Integral Form and Point Form), Applications of Gauss’s Law, Curl of the Electric Field, Electric Potential, Calculation of Electric Field Through Electric Potential for given Charge Configuration, Potential Gradient, The Dipole, Energy density in the Electric field.
MA 243 Calculus III Fall 2015 Dr. E. JacobsAssignmentsTh.docxinfantsuk
MA 243 Calculus III Fall 2015 Dr. E. Jacobs
Assignments
These assignments are keyed to Edition 7E of James Stewart’s “Calculus” (Early Transcendentals)
Assignment 1. Spheres and Other Surfaces
Read 12.1 - 12.2 and 12.6
You should be able to do the following problems:
Section 12.1/Problems 11 - 18, 20 - 22 Section 12.6/Problems 1 - 48
Hand in the following problems:
1. The following equation describes a sphere. Find the radius and the coordinates of the center.
x2 + y2 + z2 = 2(x + y + z) + 1
2. A particular sphere with center (−3, 2, 2) is tangent to both the xy-plane and the xz-plane.
It intersects the xy-plane at the point (−3, 2, 0). Find the equation of this sphere.
3. Suppose (0, 0, 0) and (0, 0, −4) are the endpoints of the diameter of a sphere. Find the
equation of this sphere.
4. Find the equation of the sphere centered around (0, 0, 4) if the sphere passes through the
origin.
5. Describe the graph of the given equation in geometric terms, using plain, clear language:
z =
√
1 − x2 − y2
Sketch each of the following surfaces
6. z = 2 − 2
√
x2 + y2
7. z = 1 − y2
8. z = 4 − x − y
9. z = 4 − x2 − y2
10. x2 + z2 = 16
Assignment 2. Dot and Cross Products
Read 12.3 and 12.4
You should be able to do the following problems:
Section 12.3/Problems 1 - 28 Section 12.4/Problems 1 - 32
Hand in the following problems:
1. Let u⃗ =
⟨
0, 1
2
,
√
3
2
⟩
and v⃗ =
⟨√
2,
√
3
2
, 1
2
⟩
a) Find the dot product b) Find the cross product
2. Let u⃗ = j⃗ + k⃗ and v⃗ = i⃗ +
√
2 j⃗.
a) Calculate the length of the projection of v⃗ in the u⃗ direction.
b) Calculate the cosine of the angle between u⃗ and v⃗
3. Consider the parallelogram with the following vertices:
(0, 0, 0) (0, 1, 1) (1, 0, 2) (1, 1, 3)
a) Find a vector perpendicular to this parallelogram.
b) Use vector methods to find the area of this parallelogram.
4. Use the dot product to find the cosine of the angle between the diagonal of a cube and one of
its edges.
5. Let L be the line that passes through the points (0, −
√
3 , −1) and (0,
√
3 , 1). Let θ be the
angle between L and the vector u⃗ = 1√
2
⟨0, 1, 1⟩. Calculate θ (to the nearest degree).
Assignment 3. Lines and Planes
Read 12.5
You should be able to do the following problems:
Section 12.5/Problems 1 - 58
Hand in the following problems:
1a. Find the equation of the line that passes through (0, 0, 1) and (1, 0, 2).
b. Find the equation of the plane that passes through (1, 0, 0) and is perpendicular to the line in
part (a).
2. The following equation describes a straight line:
r⃗(t) = ⟨1, 1, 0⟩ + t⟨0, 2, 1⟩
a. Find the angle between the given line and the vector u⃗ = ⟨1, −1, 2⟩.
b. Find the equation of the plane that passes through the point (0, 0, 4) and is perpendicular to
the given line.
3. The following two lines intersect at the point (1, 4, 4)
r⃗ = ⟨1, 4, 4⟩ + t⟨0, 1, 0⟩ r⃗ = ⟨1, 4, 4⟩ + t⟨3, 5, 4⟩
a. Find the angle between the two lines.
b. Find the equation of the plane that contains every point o ...
A colleague of yours has given you mathematical expressions for the f.pdfarjuntiwari586
A colleague of yours has given you mathematical expressions for the following electromagnetic
fields that they have measured. i. E(x, y, z, t)z squareroot x+ u_t sinc (x + u-p t) U (x + u_pt),
where u_p = 1/squareroot epsilon_0 mu_0, and U (pi) is the unit step function. ii. H(x, y, z, t) =
zH_ye -(z -ct/2) cos (z - ct/2), where c = 3 times 10^8 m/sec iii. E (x, y, z, t) = x cos (pi y) cos
(z^2 - u_p t) v. E (r, theta, z, t) = E_0 cos (omega t - beta r) In all of these cases, analyze and
state each of the following properties of these EM fields; (a) Which of the fields are plane
waves? In each case, give a detailed explanation of your reasoning and state which plane (i.e. xz-
plane, ... etc.) the waves are measured. (b) Which of the plane waves are uniform plane waves?
Why? (c) Calculate what the velocity of each of the uniform plane waves is, which direction it is
propagating in, and which waves are travelling in free space? (d) List the plane waves (either
uniform or non-uniform) that are time harmonic and explain why? (e) In the case of the uniform
plane waves, state (write down in differential form) which one of Maxwell\'s equations and
whose law it is to find the corresponding magnetic or electric field. Calculate the magnetic or
electric field intensity from this law. Assume that the uniform plane waves are propagating in a
linear, homogeneous, isotropic (LHI) media that is lossless.
Solution
The Relation Between Expressions for Time-Dependent Electromagnetic Fields Given by
Jefimenko and by Panofsky and Phillips Kirk T. McDonald Joseph Henry Laboratories,
Princeton University, Princeton, NJ 08544 (Dec. 5, 1996; updated May 7, 2016) Abstract The
expressions of Jefimenko for the electromagnetic fields E and B in terms of source charge and
current densities and J, which have received much recent attention in the American Journal of
Physics, appeared previously in sec. 14.3 of the book Classical Electricity and Magnetism by
Panofsky and Phillips. The latter develop these expressions further into a form that gives greater
emphasis to the radiation fields. This Note presents a derivation of the various expressions and
discusses an apparent paradox in applying Panofsky and Phillips’ result to static situations. 1
Introduction A general method of calculation of time-dependent electromagnetic fields was
given by Lorenz in 1867 [1], in which the retarded potentials were first introduced.1 These are
(x, t) = [(x , t )] R d3x , and A(x, t) = 1 c [J(x , t )] R d3x , (1) where and A are the scalar and
vector potentials in Gaussian units ,2 and J are the charge and current densities, R = |R| with R =
xx , and a pair of brackets, [ ], implies the quantity within is to be evaluated at the retarded time t
= t R/c with c being the speed of light in vacuum. Lorenz did not explicitly display the electric
field E and the magnetic field B, although he noted they could be obtained via E = 1 c A t , and
B = × A. (3) Had Lorenz’ work been better received by Max.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
"Impact of front-end architecture on development cost", Viktor TurskyiFwdays
I have heard many times that architecture is not important for the front-end. Also, many times I have seen how developers implement features on the front-end just following the standard rules for a framework and think that this is enough to successfully launch the project, and then the project fails. How to prevent this and what approach to choose? I have launched dozens of complex projects and during the talk we will analyze which approaches have worked for me and which have not.
Search and Society: Reimagining Information Access for Radical FuturesBhaskar Mitra
The field of Information retrieval (IR) is currently undergoing a transformative shift, at least partly due to the emerging applications of generative AI to information access. In this talk, we will deliberate on the sociotechnical implications of generative AI for information access. We will argue that there is both a critical necessity and an exciting opportunity for the IR community to re-center our research agendas on societal needs while dismantling the artificial separation between the work on fairness, accountability, transparency, and ethics in IR and the rest of IR research. Instead of adopting a reactionary strategy of trying to mitigate potential social harms from emerging technologies, the community should aim to proactively set the research agenda for the kinds of systems we should build inspired by diverse explicitly stated sociotechnical imaginaries. The sociotechnical imaginaries that underpin the design and development of information access technologies needs to be explicitly articulated, and we need to develop theories of change in context of these diverse perspectives. Our guiding future imaginaries must be informed by other academic fields, such as democratic theory and critical theory, and should be co-developed with social science scholars, legal scholars, civil rights and social justice activists, and artists, among others.
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualityInflectra
In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
Learn about:
• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
Whether you're a developer, tester, or QA professional, this webinar will give you valuable insights into how AI is shaping the future of software delivery.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
Let's dive deeper into the world of ODC! Ricardo Alves (OutSystems) will join us to tell all about the new Data Fabric. After that, Sezen de Bruijn (OutSystems) will get into the details on how to best design a sturdy architecture within ODC.
3. Gauss’ and Faraday’s Laws for E Div = micro-flux per unit of volume Rot = micro-circulation per unit of area B c dS Faraday’s Law : S E S V dV Gauss’ Law :
4. Gauss’ and Maxwell’s Law for B S V dV B Gauss’ Law : j S L Maxwell’s Fix for Ampere’s Law :
5. Maxwell’s Equations and the Wave Equation This is a 3-Dimensional Wave Equation v = 2.99… x 10 8 m/s = light velocity In vacuum ( = 0 and j = 0): }
6. Harmonic Solution of the Wave Equation: Plane Waves E may have 3 components: E x E y E z Choose x-axis // E E y = E z = 0 (Polarization direction = x-axis). Does a plane-wave expression for E x satisfy the wave equation? E x = E x0 exp{ i ( t-kz )} : E x0 = amplitude + polarization vector +z-axis = direction of propagation Insertion into wave equation: k 2 = 0 0 2 = 2 / c 2 k = / c = 2 / k = wave number ; = wavelength (in 3D-case: k = wave vector ) Analogously: B y = B y0 exp{ i ( t-kz )}
7. Plane waves (1): orientation of fields -i k e z .E = 0 -i k e z .H = 0 -i k e z x E = -i H -i k e z x H = E +i E (1) div E = 0 (2) div B = 0 (3) rot E = - d B/ dt (4) rot H = j f + d D /dt j f = E Consequences: (1)+(2): E and H e z (3)+(4): E H If E chosen // x-axis, then H // y-axis Suppose : E // x-axis; .. propagation // +z-axis: k // e z .. E x = E x0 exp i ( t-kz ) x z y E Propag- ation H
8. Plane waves (2): complex wave vector e z x e z x E = -E i k 2 = ( + i ). Result: k complex: k = k Re + i k Im exp (-i kz ) = exp (-i k Re z ) . exp ( k Im z ) (1) -i k e z .E = 0 (2) -i k e z .H = 0 (3) -i k e z x E = -i H (4) -i k e z x H = E +i E (1)+(2): E and H e z (3)+(4): E H Suppose : E // x-axis; .. propagation // +z-axis: k // e z .. E x = E x0 exp i ( t-kz ) x z y E Propag- ation H } harmonic } k Im < 0 : absorption >0 : amplification (“laser”)
9. Plane waves (3): B-E correspondence Faraday: rot E = - d B/ dt Maxwell (for j =0): rot H = d D /dt: similar result Suppose : E // x-axis; B // y-axis; .. propagation // +z-axis: k // e z .. E x = E x0 exp i ( t-kz ) .. B y = B y0 exp i ( t-kz ) x z y E Propag- ation B
10. The Poynting vector S Definition (for free space) : S = E x H = H (-d B /dt) - E ( j f + d D /dt) Apply Divergence Theorem to integrate over wave surface A: S = energy outflux per m 2 = Intensity [W/m 2 ] S = ( E H ) = H ( E ) - E ( H ) = { Change in Electro- magnetic field energy { Joule heating losses [J/s] { Outflux of energy [J/s] = [W] Direction of S : // k E H k S
![Electromagnetic Waves ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)