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THE SHELL MODEL - MIT OpenCourseWare

THE SHELL MODEL - MIT OpenCourseWare

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THE SHELL MODEL 22.02 Introduction To Applied Nuclear Physics Spring 2012 1. Atomic Shell Model ... Dy 50 82: 126 28 20 8: Nucleon number S: 2p (MeV) 4 3 2 1 0-1-2-3-4-5 5 0 50 100 150: 208: Pb: 114 184: W Ca: 64: Ni: 38: Ar: 14: C: 132: Te: 86: Kr: 102: Mo 50 82: 126 28 20 8: Image by MIT OpenCourseWare. After Krane.

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Lecture 3: Signals and systems: part II - MIT OpenCourseWare

Lecture 3: Signals and systems: part II - MIT OpenCourseWare

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The essen-tial idea, however, as discussed in Section 3.7 of the text, is that the important aspect of these functions, in particular of the impulse, is not what its value is at each instant of time but how it behaves under integration. Signals and Systems 3-2

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Periodic Table of the Elements - MIT OpenCourseWare

Periodic Table of the Elements - MIT OpenCourseWare

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Hf Hafnium 178.49 6.8251 40 Zr Zirconium 91.224 6.6339 39 Y Yttrium 88.90585 6.2173 38 Sr Strontium 87.62 5.6949 56 Ba Barium 137.327 5.2117 73 Ta Tantalum 180.9479 7.5496 54 Xe Xenon 131.293 12.1298 19 K Potassium 39.0983 4.3407 20 Ca Calcium 40.078 6.1132 21 Sc Scandium 44.955910 6.5615 22 Ti Titanium 47.867 6.8281 30 Zn Zinc 65.409 9.3942 31 ...

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Interactions of Photons with Matter - MIT OpenCourseWare

Interactions of Photons with Matter - MIT OpenCourseWare

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In Compton scattering, the incoming gamma-ray photon is deflected through an angle θ with respect to its original direction. The photon transfers a portion of its energy to the electron (assumed to be initially at rest), which is then known as a recoil electron, or a Compton electron. • All angles of scattering are possible.

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Lecture 6: Genome Assembly - MIT OpenCourseWare

Lecture 6: Genome Assembly - MIT OpenCourseWare

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Efficient de novo assembly of large genomes using compressed data structures Jared T Simpson and Richard Durbin Genome Res. 2012. 22: 549-556 SGA algorithm excludes redundant (transitive) edges

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Free Surface Water Waves - MIT OpenCourseWare

Free Surface Water Waves - MIT OpenCourseWare

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Therefore the dynamic pressure for all depths becomes px z t ) =ρηg (x t , ) cosh[ kz ( +H )] d ( ,, cosh(kH ) (7.39) V. Motion of Fluid Particles below a Wave We can define the motion of fluid particles underneat h a linear progressive wave to have a horizontal motion,ζp and a vertical motion, ηp, such that

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Lecture 8: Hashing I - MIT OpenCourseWare

Lecture 8: Hashing I - MIT OpenCourseWare

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Lecture 8 Hashing I 6.006 Fall 2011. Simple Uniform Hashing: An assumption (cheating): Each key is equally likely to be hashed to any slot of table, independent of where other keys are hashed. letn = # keys stored in table m = # slots in table load factor = n=m= expected # keys per slot = expected length of a chain. Performance

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Lecture 4 Notes: Arrays and Strings - MIT OpenCourseWare

Lecture 4 Notes: Arrays and Strings - MIT OpenCourseWare

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String literals such as “Hello, world!” are actually represented by C++ as a sequence of characters in memory. In other words, a string is simply a character array and can be manipulated as such. Consider the following program: 1 #include <iostream> 2 using namespace std; …

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18.445 HOMEWORK 4 SOLUTIONS - MIT OpenCourseWare

18.445 HOMEWORK 4 SOLUTIONS - MIT OpenCourseWare

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18.445. HOMEWORK 4 SOLUTIONS variables X and Y are said to be independent conditionally on A is for every non-negative measurable

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Feedback Linearization - MIT OpenCourseWare

Feedback Linearization - MIT OpenCourseWare

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Oct 29, 2003 · Department of Electrical Engineering and Computer Science 6.243j (Fall 2003): DYNAMICS OF NONLINEAR SYSTEMS by A. Megretski Lecture 13: Feedback Linearization1 Using control authority to transform nonlinear models into linear ones is one of the most commonly used ideas of practical nonlinear control design. Generally, the trick helps one

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Practice Right Hand Rule #1 - MIT OpenCourseWare

Practice Right Hand Rule #1 - MIT OpenCourseWare

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Practice Right Hand Rule #2 Remember:F v B G GG B =q × What direction is the force on a positive charge when entering a uniform B field in the direction indicated? 1) up 2) down 3) left 4) right 5) into page 6) out of page 7) there is no net force q v B

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Paper 1: An Analysis of Hart’s ... - MIT OpenCourseWare

Paper 1: An Analysis of Hart’s ... - MIT OpenCourseWare

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Secondary rules on the other hand, set up the procedures through which primary rules can be introduced, modified, or enforced. Secondary rules can be thought of as rules about the rules (Hart, 76). Continuing with our football metaphor, an example of …

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Area of Part of a Circle - MIT OpenCourseWare

Area of Part of a Circle - MIT OpenCourseWare

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Area = y dx. This is awkward, because near the end the height of the region changes from a constant y = b to the height of the circle y = √ a2 − x2. What if we integrate with respect to y? That seems to work better; there is a single simple expression for the length of each horizontal strip: x = a2 − y2. b Area = x dy 0 b = 0 a2 − y2 dy

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Transportation Management - MIT OpenCourseWare

Transportation Management - MIT OpenCourseWare

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Intermodal 1% Pipeline 4% Rail 5% Barge 1% Trucking By Sub-Mode Private , 46% Truckload, 44% LTL, 10% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1975 1987 1999 2003 Trucking Rail Air Freight Barge Note that these modes are all technology based – ... Develop detailed rules and relationships

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The Binomial Distribution - MIT OpenCourseWare

The Binomial Distribution - MIT OpenCourseWare

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Excel Calculates Binomial Probabilities Use the function wizard icon or the Insert_Function Command to choose ... Calculations shown for Binomial (n=3, p=0.3) = 0.794 Note: this is equivalent to counting success = 1 and failure = 0. 15.063 Summer 2003 1010 Another example:

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Fundamentals of Lean - MIT OpenCourseWare

Fundamentals of Lean - MIT OpenCourseWare

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Lean Enterprise Value: The Central Concept Lean is a process of eliminating waste with the goal of creating value for enterprise stakeholders. Lean Enterprise Value, Murman et al ... Small & fragmented market, depleted workforce, scarce natural resources, little capital

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MOSFET Equivalent Circuit Models - MIT OpenCourseWare

MOSFET Equivalent Circuit Models - MIT OpenCourseWare

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Oct 18, 2005 · 2L µnCox(VGS −VT) 2[1 +λ(VDS −VDSsat)] Then: go = ∂ID ∂VDS | Q = W 2L µnCox(VGS −VT) 2λ ' λI D ∝ ID L Output resistance is inverse of output conductance: ro = 1 go ∝ L ID VT VGS go 0 0 saturation cut-off ID go 0 0 saturation

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Relative Motion using Rotating Axes - MIT OpenCourseWare

Relative Motion using Rotating Axes - MIT OpenCourseWare

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x y z is the time derivative of the vector V as seen by the rotating frame. The expression (5) above is known as Coriolis’ theorem. Given an arbitrary vector, it relates the derivative of that vector as seen by a fixed frame with the derivative of the same vector as seen by a rotating frame. Symbolically, we can write, ( ˙ ) xyz = (˙ ) x y

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Lecture 17: Interpolation - MIT OpenCourseWare

Lecture 17: Interpolation - MIT OpenCourseWare

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lates between sample points by holding each sample value until the next sam-pling instant. This generates a staircase-like approximation to the original sig-nal. Linear interpolation, also commonly referred to as a first-order hold, corresponds to connecting the sample points by straight line segments. Both

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Natural frequency and damping - MIT OpenCourseWare

Natural frequency and damping - MIT OpenCourseWare

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13. Natural frequency and damping ratio There is a standard, and useful, normalization of the second order homogeneous linear constant coefficient ODE mx¨+ bx˙ + kx = 0 under the assumption that both the “mass” m and the “spring con­ stant” k are positive. It is illustrated in the Mathlet Damping Ratio.

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Lecture 9 - MOSFET (I) - MIT OpenCourseWare

Lecture 9 - MOSFET (I) - MIT OpenCourseWare

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Oct 06, 2005 · the current-voltage characteristics of a MOSFET? 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 9-3 1. MOSFET: layout, cross-section, symbols source gate body drain inversion layer gate oxide channel polysilicon gate p p n n p+ n+ n+ n+ p +n n+ n n+ gate length g a t e w i d t h STI edge

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First-Order Logic - MIT OpenCourseWare

First-Order Logic - MIT OpenCourseWare

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talk about things, and so there's a new kind of syntactic element. There's a new kind of syntactic element called a term. And the term, as we'll see when we do the semantics, is a name for a thing. It's an expression that somehow names a thing in …

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18.03SCF11 text: Complex Eigenvalues - MIT OpenCourseWare

18.03SCF11 text: Complex Eigenvalues - MIT OpenCourseWare

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1 + i x 2 is a solution, we have (x 1 + i x 2) = A (x 1 + i x 2) = Ax 1 + i Ax 2. Equating real and imaginary parts of this equation, x 1 = Ax, x 2 = Ax 2, which shows exactly that the real vectors x 1 and x 2 are solutions to x = Ax. Example. Find the corresponding two real solutions to …

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Probability mass function (PMF) - MIT OpenCourseWare

Probability mass function (PMF) - MIT OpenCourseWare

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We assu e ~]xi Px(x) < oo X . Expec a ·on of a Ber o Iii r.v X= 1, 0, w.p. P w.p 1 - p If X is the indicator of an event A, X IA : xpec ation of a ·rorm r v. • nifor on0,1, ... ,n Px(x) ~ 1 n+l 0 1 E[X •••••• n X X . Expectation as a population average • n students ...

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Time Series Analysis I - MIT OpenCourseWare

Time Series Analysis I - MIT OpenCourseWare

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Useful models of covariance stationary time series have. Modest nite values of p and/or include. Moving average models depending on a parsimonious number of parameters. MIT 18.S096. Time Series Analysis Time Series Analysis. Stationarity and Wold Representation Theorem

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Tissue Repair, Fibrosis, and Healing - MIT OpenCourseWare

Tissue Repair, Fibrosis, and Healing - MIT OpenCourseWare

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Proteoglycans and Hyaluronan: Hydrated Gels Proteoglycans have a core of protein to which glycosaminoglycans are attached Glycoproteins are globular proteins with branched monosaccharide chains Proteoglycans such as syndecan can be transmembrane proteins with ligand binding capacity.

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Problem Set 1 Solutions - MIT OpenCourseWare

Problem Set 1 Solutions - MIT OpenCourseWare

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recurrence becomes S(n) = S ... Solution: Notice that the x-coordinates of the vertices form a unimodal array and we can use part (a) to find the vertex with the maximum x-coordinate inΘ(lgn) time. (c) Give an algorithm to find the vertex with the maximum y …

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Negotiation: Theory and Practice - MIT OpenCourseWare

Negotiation: Theory and Practice - MIT OpenCourseWare

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Conflict and Conflict Management. in The Handbook of Industrial and Organizational Psychology. Edited by Marvin Dunnette. Chicago, IL: Rand McNally, 1976. Prof. Mary P. Rowe—MIT, Cambridge, MA 02139 8 of 44

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Chapter 6 - Water Waves - MIT OpenCourseWare

Chapter 6 - Water Waves - MIT OpenCourseWare

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Chapter 6 - Water Waves 6.1 Exact (Nonlinear) Governing Equations for Surface Gravity Waves, Assuming Potential Flow Free surface definition B(x, y = η ( x,z,t) or F(x, y,z,t) = 0 x y y z Unknown variables Velocity field: Position of free surface: Pressure field: Governing equations Continuity: Bernoulli for 1P-Flow: Far way, no disturbance ...

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15.760: National Cranberry Case - MIT OpenCourseWare

15.760: National Cranberry Case - MIT OpenCourseWare

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=5400 -600/hr 2200/600 = 3.67hrs = 20:40 pm No more trucks 3200/450 = 7.1 = trucks begin waiting at 14:06 pm 8.67 hrs x (2200/2)/75 = 127 hours 7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00 1:00 3:00 Plant is empty after 5400/600 = 9 hours after 19:00 or 4 am the next morning Total run time = 12600/600 = 21 hours ...

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Estimation with Minimum Square Error - MIT OpenCourseWare

Estimation with Minimum Square Error - MIT OpenCourseWare

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the probability mass of Y below it and the other half above, is the value of yb that minimizes the mean absolute deviation, E[ |Y − yb| ]. Also, the mode of Y , which is the value of y at which the PDF fY (y) is largest, turns out to minimize the expected value of an all-or-none cost function, i.e., a cost that is unity when the

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6.092 Lecture 4: Classes and Objects - MIT OpenCourseWare

6.092 Lecture 4: Classes and Objects - MIT OpenCourseWare

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Defining Classes Using Classes References vs Values Static types and methods. Today’s Topics Object oriented programming Defining Classes Using Classes ... Classes and Instances // class Definition public class Baby {…} // class Instances Baby shiloh = …

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Lecture 6:Regression Analysis - MIT OpenCourseWare

Lecture 6:Regression Analysis - MIT OpenCourseWare

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Maximum Likelihood Estimation Generalized M Estimation. Specifying Estimator Criterion in (2) Least Squares. Maximum Likelihood. Robust (Contamination-resistant) Bayes (assume j are r.v.’s with known prior distribution) Accommodating incomplete/missing data Case Analyses for (4) Checking Assumptions. Residual analysis Model errors i are ...

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1 Difference equations - MIT OpenCourseWare

1 Difference equations - MIT OpenCourseWare

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1 Difference equations. 5. The samples grow quickly. Their growth is too rapid to fbe logarithmic, unless f[n] is an unusual function like (log n) 20. Their growth is probably also too rapid for f[n] to be a polynomial in n, unless f[n] is. n. a high-degree polynomial. A likely al­ ternative is exponential growth.o T test

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Chapter 9 Backward Induction - MIT OpenCourseWare

Chapter 9 Backward Induction - MIT OpenCourseWare

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Repeat this procedure until the origin is the only remaining node. Theoutcomeisthemoves thatarepicked inthe way. Sinceamove ispicked ateach information set, the result is a strategy profile. For an illustration of the procedure, consider the game in the following figure. ... 14.12 Economic Applications of Game Theory

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2D Rigid Body Dynamics - MIT OpenCourseWare

2D Rigid Body Dynamics - MIT OpenCourseWare

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Kinematics of Two-Dimensional Rigid Body Motion Even though a rigid body is composed of an infinite number of particles, the motion of these particles is constrained to be such that the body remains a rigid body during the motion. In particular, the only degrees of freedom of a 2D rigid body are translation and rotation. Parallel Axes

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Statistics for Applications PsetSol3 - MIT OpenCourseWare

Statistics for Applications PsetSol3 - MIT OpenCourseWare

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the following data on Haptoglobin Type in a sample of 190 people Haptoglobin Type Hp1-1 Hp1-2 Hp2-2 10 68 112 This is precisely the same problem as Example 8.5.1.A of the text and class notes which corresponds to count data: (X 1,X 2,X 3) ∼ Multinomial(n = 3,p = ((1 − θ)2, 2θ(1 − θ),θ2) distribution. (a).

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Institute Technology DC” - MIT OpenCourseWare

Institute Technology DC” - MIT OpenCourseWare

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Figure 3: Axial View of Internal Magnet Motor A second morphology for an internal magneti motor is shown in Figure 3. This geometry has been proposed for highly salient synchronous machines without permanent magnets: such machines would run on the saliency torque and are called synchronous reluctance motors. however,

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Tangent Plane to a Level - MIT OpenCourseWare

Tangent Plane to a Level - MIT OpenCourseWare

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Tangent Plane to a Level Surface 1. Find the tangent plane to the surface x. 2 + 2y. 2 + 3z. 2 = 36 at the point P = (1, 2, 3). Answer: In order to use gradients we introduce a new variable

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Experiment 2: Faraday Ice Pail - MIT OpenCourseWare

Experiment 2: Faraday Ice Pail - MIT OpenCourseWare

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Michael Faraday used a metal ice pail as a conducting object to study how charges distributed themselves when a charged object was brought inside the pail. Suppose we lower a positively charged metal ball into the pail without touching it to the pail. When we do this, positive charges move as far away from the ball as possible – to the outer

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Problem Set 1 Solutions - MIT OpenCourseWare

Problem Set 1 Solutions - MIT OpenCourseWare

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Solution: The correct order of these functions is f 1(n);f 4(n);f 3(n);f 2(n). The vari-able n never appears in the formula for f 1(n), so despite the multiple exponentials, f 1(n) is constant. Hence, it is asymptotically smaller than f 4(n), which does grow with n. We may rewrite p the formula for f 4(n) to be f 4(n) = n n = n1:5. The value of ...

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SIGNALS, INFERENCE for to and - MIT OpenCourseWare

SIGNALS, INFERENCE for to and - MIT OpenCourseWare

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SIGNALS, SYSTEMS, and INFERENCE — Class Notes for 6.011: Introduction to Communication, Control and Signal Processing Spring 2010 Alan V. Oppenheim and George C. Verghese

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V13.3 Stokes’ Theorem - MIT OpenCourseWare

V13.3 Stokes’ Theorem - MIT OpenCourseWare

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To prove (3), we turn the left side into a line integral around C′, and the right side into a double integral over R, both in the xy-plane. Then we show that these two integrals are equal by Green’s theorem. To calculate the line integrals around C and C′, we parametrize these curves. Let C′ : x = x(t), y = y(t), t0 ≤ t ≤ t1

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