Advanced operation schemes: two-color, split & delay
|
|
|
- Ζεύς Κοτζιάς
- 6 χρόνια πριν
- Προβολές:
Transcript
1 Advanced operation schemes: two-color, split & delay Production of two FEL pulses of different wavelengths with a controllable temporal delay (and) Splitting the FEL pulse into two sequential pulses at SASE3
2 2 Outline Why do we need two color pulses? How can we produce and deliver them X-ray split and delay device Combination of the both Other schemes under study
3 3 Baseline SASE3 operation SASE3 undulator (21 segments) Experiment K electron beam SASE λ SASE3 undulator tuned to radiate at wavelength λ Single SASE pulse is transported to the SQS/SCS instrument
4 4 Two-color SASE3 operation SASE3 undulator (21 segments) + magnetic chicane K1 Magnetic Chicane K2 Experiment electron beam SASE variable delay SASE delay λ 2 > λ 1 Magnetic chicane = electron beam delay Electron beam is delayed in the magnetic chicane Delay can be chosen by tuning the magnetic field (up to ps with sub-fs precision) U2 radiation comes always after (e-beam is delayed only) If wavelengths differ significantly, shorter wavelength goes first (preferably). [1] G. Geloni, et al, Scheme for femtosecond-resolution pump probe experiments at XFELs with two-color ten GW-level X-ray pulses, arxiv: [2] T. Hara et al. Two-colour hard X-ray free-electron laser with wide tunability, doi: /ncomms3919. [3] A. A. Lutman et al. Experimental Demonstration of Femtosecond Two-Color X-Ray Free-Electron Lasers, doi: /physrevlett
5 5 Two-color SASE3 operation SASE3 undulator (21 segments) + magnetic chicane + optical delay Experiment K1 Optical delay K2 electron beam SASE relative delay SASE delay λ 1 < λ 2 Magnetic chicane + mirror chicane = arbitrary delay Electron beam is delayed in the magnetic chicane Photon beam gets delayed in the optical chicane Keep the mirrors fixed, tune using the magnetic chicane
6 6 Case study for SQS at 630/250 ev SASE3 undulator (21 segments) + magnetic chicane + optical delay 2 off 630eV 7 off 5 active segments 250eV 7 active segments Baseline 20pC e-beam after SASE1 Here we optimized for short pulses mm
7 7 First undulator (second pulse) 630 ev Mean Energy/pulse: 5e-5 J Mean #ph/pulse : 5e μm fwhm (1.5 fs) 50 μj 50 GW
8 8 Second undulator (first pulse) 250 ev Mean Energy/pulse: 7e-5 J Mean #ph/pulse : 1.75e12 1 μm fwhm (3 fs) 70 μj 30 GW
9 9 Two sources problem 630 ev 1.8e18 ph/cm 2 Two sources and one focusing system -> two images Two mirrors -> only one image without aberrations We can tune both KB mirrors to image the intermediate spot in both planes 250 ev 4.5e18 ph/cm 2 I1.5 Both KBs focused at S ev Interm. 250 ev S1 S1.5 S2
10 10 Concept of optical X-ray split and delay device (XBSD) for SASE3 (by AlexanderYaroslavtsev) Located upstream of both instruments M Separated asymmetric paths Two mirror coatings: B4C (up to 1500 ev) Ni or Ru (up to 3000 ev) Plane mirrors -> does not affect focusing M
11 Recombine any two Advanced operation schemes: two-color, split & delay Svitozar Serkez (on behalf of WP72, SCS, SQS) Concept of optical X-ray split and delay device (XBSD) for SASE3 (by AlexanderYaroslavtsev) Upgradeable with zero-order mirror (ZOM) G Recombination of different grating reflection orders at optical axis possible 0 th odrer λ 1 0 th odrers Grating Grating 1 st odrer λ 2 (mono) 1 st odrer λ 1 (mono) 1 st odrer λ 1 (mono) λ 1 pink beam λ 2 λ 1
12 12 Two-color SASE + XBSD combination λ x == λ x (sase) (by AlexanderYaroslavtsev) Undulator mode XBSD mode Result N. of pulses N. of frequencies (boring) mono λ 1 (mono) Δt (fs ps) λ 1 (mono) 2 1 mono λ 1 mono + ZOM 0 th λ 1 Δt (fs ps) λ 1 (mono) 2 1 sase/mono pink λ 1 Δt (fs ps) λ sase mono XFEL baseline λ 1 (mono) Δt 1 (fs) λ 1 (mono) Δt 2 (fs ps) λ 1 (mono) Δt 1 (fs) λ 1 (mono) 4 1 mono λ 1 Δt 1 (fs) λ 1 mono + ZOM 0 th λ 1 Δt 1 (fs) λ 1 Δt 2 (fs ps) λ 1 (mono) Δt 1 (fs) λ 1 (mono) 4 1 sase/mono pink λ 1 Δt 1 (fs) λ 1 Δt 2 (fs ps) λ 1 Δt 1 (fs) λ sase mono + ZOM 1 st λ 1 (mono) Δt 2 (fs ps) λ 2 (mono) 2 2 mono λ 1 Δt 1 (fs) λ 2 mono + ZOM 0 th λ 1 Δt 1 (fs) λ 2 Δt 2 (fs ps) λ 2 (mono) 3 2 sase/mono pink λ 1 Δt 1 (fs) λ 2 Δt 2 (fs ps) λ 1 Δt 1 (fs) λ sase λ 1
13 13 Two-color SASE + XBSD combination λ x == λ x (sase) (by AlexanderYaroslavtsev) Undulator mode XBSD mode Result N. of pulses N. of frequencies mono λ 1 (mono) Δt (fs ps) λ 1 (mono) 2 1 mono XBCD scheme λ 1 mono + ZOM 0 th λ 1 Δt (fs ps) λ 1 (mono) 2 1 sase/mono pink λ 1 Δt (fs ps) λ sase mono λ 1 (mono) Δt 1 (fs) λ 1 (mono) Δt 2 (fs ps) λ 1 (mono) Δt 1 (fs) λ 1 (mono) 4 1 mono λ 1 Δt 1 (fs) λ 1 mono + ZOM 0 th λ 1 Δt 1 (fs) λ 1 Δt 2 (fs ps) λ 1 (mono) Δt 1 (fs) λ 1 (mono) 4 1 sase/mono pink λ 1 Δt 1 (fs) λ 1 Δt 2 (fs ps) λ 1 Δt 1 (fs) λ sase mono + ZOM 1 st λ 1 (mono) Δt 2 (fs ps) λ 2 (mono) 2 2 mono λ 1 Δt 1 (fs) λ 2 mono + ZOM 0 th λ 1 Δt 1 (fs) λ 2 Δt 2 (fs ps) λ 2 (mono) 3 2 sase/mono pink Two-color scheme interference terms λ 1 Δt 1 (fs) λ 2 Δt 2 (fs ps) λ 1 Δt 1 (fs) λ sase Δt 1 (fs) λ 2 λ 1
14 14 Two-color SASE + XBSD combination λ x == λ x (sase) (by AlexanderYaroslavtsev) Undulator mode XBSD mode Result N. of pulses N. of frequencies mono λ 1 (mono) Δt (fs ps) λ 1 (mono) 2 1 mono λ 1 mono + ZOM 0 th λ 1 Δt (fs ps) λ 1 (mono) 2 1 sase/mono pink λ 1 Δt (fs ps) λ sase mono λ 1 (mono) Δt 1 (fs) λ 1 (mono) Δt 2 (fs ps) λ 1 (mono) Δt 1 (fs) λ 1 (mono) 4 XBCD 1 mono scheme λ 1 Δt 1 (fs) λ 1 mono + ZOM 0 th λ 1 Δt 1 (fs) λ 1 Δt 2 (fs ps) λ 1 (mono) Δt 1 (fs) λ 1 (mono) 4 1 sase/mono pink λ 1 Δt 1 (fs) λ 1 Δt 2 (fs ps) λ 1 Δt 1 (fs) λ sase mono + ZOM 1 st λ 1 (mono) Δt 2 (fs ps) λ 2 (mono) 2 2 mono λ 1 Δt 1 (fs) λ 2 mono + ZOM 0 th λ 1 Δt 1 (fs) λ 2 Δt 2 (fs ps) λ 2 (mono) 3 2 sase/mono interference terms pink λ 1 Δt 1 (fs) λ 2 Δt 2 (fs ps) λ 1 Δt 1 (fs) λ sase λ 1 λ 1 λ 1 Δt 2 (fs ps)
15 15 Two-color SASE + XBSD combination λ x == λ x (sase) (by AlexanderYaroslavtsev) Undulator mode XBSD mode Result N. of pulses N. of frequencies mono λ 1 (mono) Δt (fs ps) λ 1 (mono) 2 1 mono λ 1 mono + ZOM 0 th λ 1 Δt (fs ps) λ 1 (mono) 2 1 sase/mono pink λ 1 Δt (fs ps) λ 1 Interference 2 2 sase terms mono λ 1 (mono) Δt 1 (fs) λ 1 (mono) Δt 2 (fs ps) λ 1 (mono) Δt 1 (fs) λ 1 (mono) 4 1 mono λ 1 Δt 1 (fs) λ 1 mono + ZOM 0 th λ 1 Δt 1 (fs) λ 1 Δt 2 (fs ps) λ 1 (mono) Δt 1 (fs) λ 1 (mono) 4 1 sase/mono pink λ 1 Δt 1 (fs) λ 1 Δt 2 (fs ps) λ 1 Δt 1 (fs) λ sase mono + ZOM 1 st λ 1 (mono) Δt 2 (fs ps) λ 2 (mono) 2 2 mono λ 1 Δt 1 (fs) λ 2 mono + ZOM 0 th λ 1 Δt 1 (fs) λ 2 Δt 2 (fs ps) λ 2 (mono) 3 2 sase/mono pink λ 1 Δt 1 (fs) λ 2 Δt 2 (fs ps) λ 1 Δt 1 (fs) λ sase Δt 1 (fs) λ 2 λ 1 λ 2 λ 1 λ 2 λ 1 Δt 2 (fs ps)
16 16 Coherent Anti-Stokes Raman Scattering (CARS) Correlation Spectroscopy Undulator mode XBSD mode Result N. of pulses N. of frequencies mono λ 1 (mono) Δt (fs ps) λ 1 (mono) 2 1 mono λ 1 mono + ZOM 0 th λ 1 Δt (fs ps) λ 1 (mono) 2 1 sase/mono pink λ 1 Δt (fs ps) λ sase mono λ 1 (mono) Δt 1 (fs) λ 1 (mono) Δt 2 (fs ps) λ 1 (mono) Δt 1 (fs) λ 1 (mono) 4 1 mono λ 1 Δt 1 (fs) λ 1 mono + ZOM 0 th λ 1 Δt 1 (fs) λ 1 Δt 2 (fs ps) λ 1 (mono) Δt 1 (fs) λ 1 (mono) 4 1 sase/mono pink λ 1 Δt 1 (fs) λ 1 Δt 2 (fs ps) λ 1 Δt 1 (fs) λ sase mono + ZOM 1 st λ 1 (mono) Δt 2 (fs ps) λ 2 (mono) 2 2 mono λ 1 Δt 1 (fs) λ 2 mono + ZOM 0 th λ 1 Δt 1 (fs) λ 2 Δt 2 (fs ps) λ 2 (mono) 3 2 sase/mono pink λ 1 Δt 1 (fs) λ 2 Δt 2 (fs ps) λ 1 Δt 1 (fs) λ sase Δt 2 λ 2 λ 1 λ 2 (mono) λ 1
17 Wavelength Advanced operation schemes: two-color, split & delay Svitozar Serkez (on behalf of WP72, SCS, SQS) Coherent Anti-Stokes Raman Scattering (CARS) Correlation Spectroscopy λ 2 0 th odrers (2 pulses) Grating 1 st odrer λ 1 (mono) λ 1 (mono) λ 1 1 st odrer λ 2 (mono) Δt 2 λ 2 λ 1 Time Δt 2 sample Δt 1 =0 λ 1 λ 2 λ 1 (mono) λ 1 λ 2 Two pulses of different wavelengths are generated in the undulator Grating is tuned to monochromatize one of the pulses in 1 st order reflection 0 th order reflection carries both SASE pulses and is recombined with ZOM Monochromatic pulse is delayed in XBSD by Δt 2 Story continues in talk by Justine Schlappa later today ω 1 ω 1 ω 2 Δt 2 ω out δω Ω
18 delay, ps Advanced operation schemes: two-color, split & delay Svitozar Serkez (on behalf of WP72, SCS, SQS) Comparison of delay ranges Two-color scheme: XBSD: λ 2 > λ 1 optical delay out: depends on electron beam energy up to (0 1 ps) depends on photon energy, estimated (-7 7 ps) up to 4 ps per single scan 8 6 optical delay in: estimated ( fs) stage position z, mm Example of the delay ranges 1000 ev, 5 fs pulse
19 19 Other schemes Circular polarizarion at SASE3 see S.Serkez, et al., Circular polarization opportunities at the SASE3 undulator line of the European XFEL, arxiv: Self-seeding see S.Serkez, Design and Optimization of the Grating Monochromator for Soft X-Ray Self-Seeding FELs, doi: /desy-thesis Ongoing R&D on attosecond pulse generation
20 20 End words Two-color scheme: robust, easy to set-up same pulse duration tunable delay, scan possible large max. range, up to ev, independent scan possible for both wavelengths XBSD: introduces tunable delay, scan possible does not affect baseline focusing can create two identical pulses allows delivery of SASE and monochromatic pulses with a given delay (with ZOM) Combination of the two: gives large added values, see Table Other schemes are under active study If you are interested please let us know
21 21 Thank you WP72, SCS, SQS, WP78, MPY(DESY)
Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)
Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts
Matrices and Determinants
Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z
HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:
HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying
Tunable Diode Lasers. Turning Laser Diodes into Diode Lasers. Mode selection. Laser diodes
Tunable Diode Lasers Turning Laser Diodes into Diode Lasers Laser diodes Mode selection FP diodes high power at low cost AR diodes for best performance Compact and robust Littrow setup Highest power from
CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS
CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =
(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)
Q1. (a) A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be excited. (i) What is meant by an excited atom? (1) (ii)
Finite Field Problems: Solutions
Finite Field Problems: Solutions 1. Let f = x 2 +1 Z 11 [x] and let F = Z 11 [x]/(f), a field. Let Solution: F =11 2 = 121, so F = 121 1 = 120. The possible orders are the divisors of 120. Solution: The
3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β
3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle
X-Y COUPLING GENERATION WITH AC/PULSED SKEW QUADRUPOLE AND ITS APPLICATION
X-Y COUPLING GENERATION WITH AC/PULSED SEW QUADRUPOLE AND ITS APPLICATION # Takeshi Nakamura # Japan Synchrotron Radiation Research Institute / SPring-8 Abstract The new method of x-y coupling generation
EE512: Error Control Coding
EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3
Ó³ Ÿ , º 6(190) Ä1142. DESY, ƒ ³ Ê, ƒ ³ Ö European XFEL, GmbH, ƒ ³ Ê, ƒ ³ Ö ±Êʳ-,
Ó³ Ÿ. 2014.. 11, º 6(190).. 1134Ä1142 Œ ˆŠ ˆ ˆ Š ƒ Š ˆŒ Š ˆ ˆŸ ŒˆŠ Š œ ˆ Ÿ Š. Ò a,1,. μ ±μ a,. ƒ Íμ a,. ³ÖÉ a,. Ê μ a, Œ. ±μ a,,2, Ÿ. ƒ Õ É,. Õ,3,. μ ±μ,. É,. ²,. Ò,4 a Ñ Ò É ÉÊÉ Ö ÒÌ ² μ, Ê DESY, ƒ ³
DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.
DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec
Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1.
Exercises 0 More exercises are available in Elementary Differential Equations. If you have a problem to solve any of them, feel free to come to office hour. Problem Find a fundamental matrix of the given
1. Αφετηρία από στάση χωρίς κριτή (self start όπου πινακίδα εκκίνησης) 5 λεπτά µετά την αφετηρία σας από το TC1B KALO LIVADI OUT
Date: 21 October 2016 Time: 14:00 hrs Subject: BULLETIN No 3 Document No: 1.3 --------------------------------------------------------------------------------------------------------------------------------------
Instruction Execution Times
1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables
CE 530 Molecular Simulation
C 53 olecular Siulation Lecture Histogra Reweighting ethods David. Kofke Departent of Cheical ngineering SUNY uffalo kofke@eng.buffalo.edu Histogra Reweighting ethod to cobine results taken at different
What happens when two or more waves overlap in a certain region of space at the same time?
Wave Superposition What happens when two or more waves overlap in a certain region of space at the same time? To find the resulting wave according to the principle of superposition we should sum the fields
Section 8.3 Trigonometric Equations
99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.
ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή
6.1. Dirac Equation. Hamiltonian. Dirac Eq.
6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2
Reminders: linear functions
Reminders: linear functions Let U and V be vector spaces over the same field F. Definition A function f : U V is linear if for every u 1, u 2 U, f (u 1 + u 2 ) = f (u 1 ) + f (u 2 ), and for every u U
2 Composition. Invertible Mappings
Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,
derivation of the Laplacian from rectangular to spherical coordinates
derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used
Srednicki Chapter 55
Srednicki Chapter 55 QFT Problems & Solutions A. George August 3, 03 Srednicki 55.. Use equations 55.3-55.0 and A i, A j ] = Π i, Π j ] = 0 (at equal times) to verify equations 55.-55.3. This is our third
CMOS Technology for Computer Architects
CMOS Technology for Computer Architects Iakovos Mavroidis Giorgos Passas Manolis Katevenis Lecture 13: On chip SRAM Technology FORTH ICS / EURECCA & UoC GREECE ABC A A E F A BCDAECF A AB C DE ABCDAECF
10 MERCHIA. 10. Starting from standing position (where the SIGN START ) without marshal (self start) 5 minutes after TC4 KALO LIVADI OUT
Date: 22 October 2016 Time: 09:00 hrs Subject: BULLETIN No 5 Document No: 1.6 --------------------------------------------------------------------------------------------------------------------------------------
Example Sheet 3 Solutions
Example Sheet 3 Solutions. i Regular Sturm-Liouville. ii Singular Sturm-Liouville mixed boundary conditions. iii Not Sturm-Liouville ODE is not in Sturm-Liouville form. iv Regular Sturm-Liouville note
PHOS π 0 analysis, for production, R AA, and Flow analysis, LHC11h
PHOS π, ask PHOS π analysis, for production, R AA, and Flow analysis, Henrik Qvigstad henrik.qvigstad@fys.uio.no University of Oslo --5 PHOS π, ask ask he task we use, AliaskPiFlow was written prior, for
Second Order Partial Differential Equations
Chapter 7 Second Order Partial Differential Equations 7.1 Introduction A second order linear PDE in two independent variables (x, y Ω can be written as A(x, y u x + B(x, y u xy + C(x, y u u u + D(x, y
department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι
She selects the option. Jenny starts with the al listing. This has employees listed within She drills down through the employee. The inferred ER sttricture relates this to the redcords in the databasee
Written Examination. Antennas and Propagation (AA ) April 26, 2017.
Written Examination Antennas and Propagation (AA. 6-7) April 6, 7. Problem ( points) Let us consider a wire antenna as in Fig. characterized by a z-oriented linear filamentary current I(z) = I cos(kz)ẑ
Every set of first-order formulas is equivalent to an independent set
Every set of first-order formulas is equivalent to an independent set May 6, 2008 Abstract A set of first-order formulas, whatever the cardinality of the set of symbols, is equivalent to an independent
Strain gauge and rosettes
Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified
Bayesian modeling of inseparable space-time variation in disease risk
Bayesian modeling of inseparable space-time variation in disease risk Leonhard Knorr-Held Laina Mercer Department of Statistics UW May, 013 Motivation Ohio Lung Cancer Example Lung Cancer Mortality Rates
Coupling of a Jet-Slot Oscillator With the Flow-Supply Duct: Flow-Acoustic Interaction Modeling
1th AIAA/CEAS Aeroacoustics Conference, May 006 interactions Coupling of a Jet-Slot Oscillator With the Flow-Supply Duct: Interaction M. Glesser 1, A. Billon 1, V. Valeau, and A. Sakout 1 mglesser@univ-lr.fr
Partial Differential Equations in Biology The boundary element method. March 26, 2013
The boundary element method March 26, 203 Introduction and notation The problem: u = f in D R d u = ϕ in Γ D u n = g on Γ N, where D = Γ D Γ N, Γ D Γ N = (possibly, Γ D = [Neumann problem] or Γ N = [Dirichlet
Statistical Inference I Locally most powerful tests
Statistical Inference I Locally most powerful tests Shirsendu Mukherjee Department of Statistics, Asutosh College, Kolkata, India. shirsendu st@yahoo.co.in So far we have treated the testing of one-sided
ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011
Διάρκεια Διαγωνισμού: 3 ώρες Απαντήστε όλες τις ερωτήσεις Μέγιστο Βάρος (20 Μονάδες) Δίνεται ένα σύνολο από N σφαιρίδια τα οποία δεν έχουν όλα το ίδιο βάρος μεταξύ τους και ένα κουτί που αντέχει μέχρι
Sampling Basics (1B) Young Won Lim 9/21/13
Sampling Basics (1B) Copyright (c) 2009-2013 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any
ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α. Διαβάστε τις ειδήσεις και εν συνεχεία σημειώστε. Οπτική γωνία είδησης 1:.
ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α 2 ειδήσεις από ελληνικές εφημερίδες: 1. Τα Νέα, 13-4-2010, Σε ανθρώπινο λάθος αποδίδουν τη συντριβή του αεροσκάφους, http://www.tanea.gr/default.asp?pid=2&artid=4569526&ct=2 2. Τα Νέα,
C.S. 430 Assignment 6, Sample Solutions
C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order
Aτοµική Δοµή LASER. Τροχιές ηλεκτρονίων Ατοµικά Φάσµατα Άτοµο Bohr
Τροχιές ηλεκτρονίων Ατοµικά Φάσµατα Άτοµο Bohr Aτοµική Δοµή LASER Ενεργειακά Επίπεδα και Φάσµατα Αρχή της Αντιστοιχίας Πυρηνική Κίνηση Ατοµική Διέγερση Laser Light Amplification by Stimulated Emission
Assalamu `alaikum wr. wb.
LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump
the total number of electrons passing through the lamp.
1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy
ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. του φοιτητή του Τμήματος Ηλεκτρολόγων Μηχανικών και. Τεχνολογίας Υπολογιστών της Πολυτεχνικής Σχολής του. Πανεπιστημίου Πατρών
ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΕΡΓΑΣΤΗΡΙΟ ΗΛΕΚΤΡΟΜΗΧΑΝΙΚΗΣ ΜΕΤΑΤΡΟΠΗΣ ΕΝΕΡΓΕΙΑΣ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ του φοιτητή του
The challenges of non-stable predicates
The challenges of non-stable predicates Consider a non-stable predicate Φ encoding, say, a safety property. We want to determine whether Φ holds for our program. The challenges of non-stable predicates
Higher Derivative Gravity Theories
Higher Derivative Gravity Theories Black Holes in AdS space-times James Mashiyane Supervisor: Prof Kevin Goldstein University of the Witwatersrand Second Mandelstam, 20 January 2018 James Mashiyane WITS)
Lecture 2. Soundness and completeness of propositional logic
Lecture 2 Soundness and completeness of propositional logic February 9, 2004 1 Overview Review of natural deduction. Soundness and completeness. Semantics of propositional formulas. Soundness proof. Completeness
Current Status of PF SAXS beamlines. 07/23/2014 Nobutaka Shimizu
Current Status of PF SAXS beamlines 07/23/2014 Nobutaka Shimizu BL-6A Detector SAXS:PILATUS3 1M WAXD:PILATUS 100K Wavelength 1.5Å (Fix) Camera Length 0.25, 0.5, 1.0, 2.0, 2.5 m +WAXD Chamber:0.75, 1.0,
CT Correlation (2B) Young Won Lim 8/15/14
CT Correlation (2B) 8/5/4 Copyright (c) 2-24 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version.2 or any
SCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions
SCHOOL OF MATHEMATICAL SCIENCES GLMA Linear Mathematics 00- Examination Solutions. (a) i. ( + 5i)( i) = (6 + 5) + (5 )i = + i. Real part is, imaginary part is. (b) ii. + 5i i ( + 5i)( + i) = ( i)( + i)
Problem Set 9 Solutions. θ + 1. θ 2 + cotθ ( ) sinθ e iφ is an eigenfunction of the ˆ L 2 operator. / θ 2. φ 2. sin 2 θ φ 2. ( ) = e iφ. = e iφ cosθ.
Chemistry 362 Dr Jean M Standard Problem Set 9 Solutions The ˆ L 2 operator is defined as Verify that the angular wavefunction Y θ,φ) Also verify that the eigenvalue is given by 2! 2 & L ˆ 2! 2 2 θ 2 +
Variational Wavefunction for the Helium Atom
Technische Universität Graz Institut für Festkörperphysik Student project Variational Wavefunction for the Helium Atom Molecular and Solid State Physics 53. submitted on: 3. November 9 by: Markus Krammer
Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1
Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1 A Brief History of Sampling Research 1915 - Edmund Taylor Whittaker (1873-1956) devised a
TMA4115 Matematikk 3
TMA4115 Matematikk 3 Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet Trondheim Spring 2010 Lecture 12: Mathematics Marvellous Matrices Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet
Engineering Tunable Single and Dual Optical. Emission from Ru(II)-Polypyridyl Complexes. Through Excited State Design
Engineering Tunable Single and Dual Optical Emission from Ru(II)-Polypyridyl Complexes Through Excited State Design Supplementary Information Julia Romanova 1, Yousif Sadik 1, M. R. Ranga Prabhath 1,,
CRASH COURSE IN PRECALCULUS
CRASH COURSE IN PRECALCULUS Shiah-Sen Wang The graphs are prepared by Chien-Lun Lai Based on : Precalculus: Mathematics for Calculus by J. Stuwart, L. Redin & S. Watson, 6th edition, 01, Brooks/Cole Chapter
ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ
ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΛΕΝΑ ΦΛΟΚΑ Επίκουρος Καθηγήτρια Τµήµα Φυσικής, Τοµέας Φυσικής Περιβάλλοντος- Μετεωρολογίας ΓΕΝΙΚΟΙ ΟΡΙΣΜΟΙ Πληθυσµός Σύνολο ατόµων ή αντικειµένων στα οποία αναφέρονται
Notes on the Open Economy
Notes on the Open Econom Ben J. Heijdra Universit of Groningen April 24 Introduction In this note we stud the two-countr model of Table.4 in more detail. restated here for convenience. The model is Table.4.
Thin Film Chip Resistors
FEATURES PRECISE TOLERANCE AND TEMPERATURE COEFFICIENT EIA STANDARD CASE SIZES (0201 ~ 2512) LOW NOISE, THIN FILM (NiCr) CONSTRUCTION REFLOW SOLDERABLE (Pb FREE TERMINATION FINISH) Type Size EIA PowerRating
PMD Compensator and PMD Emulator * * * Yu Mimura Kazuhiro Ikeda Tatsuya Hatano * * * Takesi Takagi Sugio Wako Hiroshi Matsuura
PMD PMD PMD Compensator and PMD Emulator * * * Yu Mimura Kazuhiro Ikeda Tatsuya Hatano * * * Takesi Takagi Sugio Wako Hiroshi Matsuura D- WDM: Dense-Wavelength Division Multiplexing 4 Gbps Polarization
Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1
Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test
Aluminum Electrolytic Capacitors (Large Can Type)
Aluminum Electrolytic Capacitors (Large Can Type) Snap-In, 85 C TS-U ECE-S (U) Series: TS-U Features General purpose Wide CV value range (33 ~ 47,000 µf/16 4V) Various case sizes Top vent construction
상대론적고에너지중이온충돌에서 제트입자와관련된제동복사 박가영 인하대학교 윤진희교수님, 권민정교수님
상대론적고에너지중이온충돌에서 제트입자와관련된제동복사 박가영 인하대학교 윤진희교수님, 권민정교수님 Motivation Bremsstrahlung is a major rocess losing energies while jet articles get through the medium. BUT it should be quite different from low energy
A. Two Planes Waves, Same Frequency Visible light
Interference 1 A. Two Planes Waves, Same Frequency EE 1 rr, tt = EE 0,1 cccccc αα 1 ωω tt αα 1 kk 1. rr + εε 1 EE 2 rr, tt = EE 0,2 cccccc αα 2 ωω tt αα 2 kk 2. rr + εε 2 ωω = 4.3 7.5 10 14 HHHH Visible
Concrete Mathematics Exercises from 30 September 2016
Concrete Mathematics Exercises from 30 September 2016 Silvio Capobianco Exercise 1.7 Let H(n) = J(n + 1) J(n). Equation (1.8) tells us that H(2n) = 2, and H(2n+1) = J(2n+2) J(2n+1) = (2J(n+1) 1) (2J(n)+1)
Calculating the propagation delay of coaxial cable
Your source for quality GNSS Networking Solutions and Design Services! Page 1 of 5 Calculating the propagation delay of coaxial cable The delay of a cable or velocity factor is determined by the dielectric
ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας»
ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΩΝ ΤΗΣ ΠΡΟΣΧΟΛΙΚΗΣ ΑΓΩΓΗΣ ΚΑΙ ΤΟΥ ΕΚΠΑΙ ΕΥΤΙΚΟΥ ΣΧΕ ΙΑΣΜΟΥ «ΠΑΙ ΙΚΟ ΒΙΒΛΙΟ ΚΑΙ ΠΑΙ ΑΓΩΓΙΚΟ ΥΛΙΚΟ» ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που εκπονήθηκε για τη
Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013
Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering
D Alembert s Solution to the Wave Equation
D Alembert s Solution to the Wave Equation MATH 467 Partial Differential Equations J. Robert Buchanan Department of Mathematics Fall 2018 Objectives In this lesson we will learn: a change of variable technique
Solutions to Exercise Sheet 5
Solutions to Eercise Sheet 5 jacques@ucsd.edu. Let X and Y be random variables with joint pdf f(, y) = 3y( + y) where and y. Determine each of the following probabilities. Solutions. a. P (X ). b. P (X
ω ω ω ω ω ω+2 ω ω+2 + ω ω ω ω+2 + ω ω+1 ω ω+2 2 ω ω ω ω ω ω ω ω+1 ω ω2 ω ω2 + ω ω ω2 + ω ω ω ω2 + ω ω+1 ω ω2 + ω ω+1 + ω ω ω ω2 + ω
0 1 2 3 4 5 6 ω ω + 1 ω + 2 ω + 3 ω + 4 ω2 ω2 + 1 ω2 + 2 ω2 + 3 ω3 ω3 + 1 ω3 + 2 ω4 ω4 + 1 ω5 ω 2 ω 2 + 1 ω 2 + 2 ω 2 + ω ω 2 + ω + 1 ω 2 + ω2 ω 2 2 ω 2 2 + 1 ω 2 2 + ω ω 2 3 ω 3 ω 3 + 1 ω 3 + ω ω 3 +
Homework 8 Model Solution Section
MATH 004 Homework Solution Homework 8 Model Solution Section 14.5 14.6. 14.5. Use the Chain Rule to find dz where z cosx + 4y), x 5t 4, y 1 t. dz dx + dy y sinx + 4y)0t + 4) sinx + 4y) 1t ) 0t + 4t ) sinx
forms This gives Remark 1. How to remember the above formulas: Substituting these into the equation we obtain with
Week 03: C lassification of S econd- Order L inear Equations In last week s lectures we have illustrated how to obtain the general solutions of first order PDEs using the method of characteristics. We
1) Abstract (To be organized as: background, aim, workpackages, expected results) (300 words max) Το όριο λέξεων θα είναι ελαστικό.
UΓενικές Επισημάνσεις 1. Παρακάτω θα βρείτε απαντήσεις του Υπουργείου, σχετικά με τη συμπλήρωση της ηλεκτρονικής φόρμας. Διευκρινίζεται ότι στα περισσότερα θέματα οι απαντήσεις ήταν προφορικές (τηλεφωνικά),
ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 24/3/2007
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Όλοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα μικρότεροι του 10000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Αν κάπου κάνετε κάποιες υποθέσεις
From the finite to the transfinite: Λµ-terms and streams
From the finite to the transfinite: Λµ-terms and streams WIR 2014 Fanny He f.he@bath.ac.uk Alexis Saurin alexis.saurin@pps.univ-paris-diderot.fr 12 July 2014 The Λµ-calculus Syntax of Λµ t ::= x λx.t (t)u
Specification. code ±1.0 ±1.0 ±1.0 ±1.0 ±0.5 approx (g)
High CV-value Long Life > 10 years at 50 C Low ESR and ESL High stability, 10 years shelf life Optimized designs available on request RoHS Compliant application Basic design Smoothing, energy storage,
Solutions to the Schrodinger equation atomic orbitals. Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz
Solutions to the Schrodinger equation atomic orbitals Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz ybridization Valence Bond Approach to bonding sp 3 (Ψ 2 s + Ψ 2 px + Ψ 2 py + Ψ 2 pz) sp 2 (Ψ 2 s + Ψ 2 px + Ψ 2 py)
Study of In-vehicle Sound Field Creation by Simultaneous Equation Method
Study of In-vehicle Sound Field Creation by Simultaneous Equation Method Kensaku FUJII Isao WAKABAYASI Tadashi UJINO Shigeki KATO Abstract FUJITSU TEN Limited has developed "TOYOTA remium Sound System"
ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ. Ψηφιακή Οικονομία. Διάλεξη 10η: Basics of Game Theory part 2 Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Ψηφιακή Οικονομία Διάλεξη 0η: Basics of Game Theory part 2 Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών Best Response Curves Used to solve for equilibria in games
Galatia SIL Keyboard Information
Galatia SIL Keyboard Information Keyboard ssignments The main purpose of the keyboards is to provide a wide range of keying options, so many characters can be entered in multiple ways. If you are typing
A Bonus-Malus System as a Markov Set-Chain. Małgorzata Niemiec Warsaw School of Economics Institute of Econometrics
A Bonus-Malus System as a Markov Set-Chain Małgorzata Niemiec Warsaw School of Economics Institute of Econometrics Contents 1. Markov set-chain 2. Model of bonus-malus system 3. Example 4. Conclusions
Elements of Information Theory
Elements of Information Theory Model of Digital Communications System A Logarithmic Measure for Information Mutual Information Units of Information Self-Information News... Example Information Measure
EE434 ASIC & Digital Systems Arithmetic Circuits
EE434 ASIC & Digital Systems Arithmetic Circuits Spring 25 Dae Hyun Kim daehyun@eecs.wsu.edu Arithmetic Circuits What we will learn Adders Basic High-speed 2 Adder -bit adder SSSSSS = AA BB CCCC CCCC =
Proforma E. Flood-CBA#2 Training Seminars. Περίπτωση Μελέτης Ποταμός Έ βρος, Κοινότητα Λαβάρων
Proforma E Flood-CBA#2 Training Seminars Περίπτωση Μελέτης Ποταμός Έ βρος, Κοινότητα Λαβάρων Proforma A B C D E F Case Η λογική Study Collecting information regarding the site that is to be assessed. Collecting
The Simply Typed Lambda Calculus
Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and
Lecture 21: Scattering and FGR
ECE-656: Fall 009 Lecture : Scattering and FGR Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA Review: characteristic times τ ( p), (, ) == S p p
ΙΕΥΘΥΝΤΗΣ: Καθηγητής Γ. ΧΡΥΣΟΛΟΥΡΗΣ Ι ΑΚΤΟΡΙΚΗ ΙΑΤΡΙΒΗ
ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΠΟΛΥΤΕΧΝΙΚΗ ΣΧΟΛΗ ΤΜΗΜΑ ΜΗΧΑΝΟΛΟΓΩΝ ΚΑΙ ΑΕΡΟΝΑΥΠΗΓΩΝ ΜΗΧΑΝΙΚΩΝ ΕΡΓΑΣΤΗΡΙΟ ΣΥΣΤΗΜΑΤΩΝ ΠΑΡΑΓΩΓΗΣ & ΑΥΤΟΜΑΤΙΣΜΟΥ / ΥΝΑΜΙΚΗΣ & ΘΕΩΡΙΑΣ ΜΗΧΑΝΩΝ ΙΕΥΘΥΝΤΗΣ: Καθηγητής Γ. ΧΡΥΣΟΛΟΥΡΗΣ Ι ΑΚΤΟΡΙΚΗ
Lanczos and biorthogonalization methods for eigenvalues and eigenvectors of matrices
Lanzos and iorthogonalization methods for eigenvalues and eigenvetors of matries rolem formulation Many prolems are redued to solving the following system: x x where is an unknown numer А a matrix n n
Fractional Colorings and Zykov Products of graphs
Fractional Colorings and Zykov Products of graphs Who? Nichole Schimanski When? July 27, 2011 Graphs A graph, G, consists of a vertex set, V (G), and an edge set, E(G). V (G) is any finite set E(G) is
Resurvey of Possible Seismic Fissures in the Old-Edo River in Tokyo
Bull. Earthq. Res. Inst. Univ. Tokyo Vol. 2.,**3 pp.,,3,.* * +, -. +, -. Resurvey of Possible Seismic Fissures in the Old-Edo River in Tokyo Kunihiko Shimazaki *, Tsuyoshi Haraguchi, Takeo Ishibe +, -.
Ο πιο φωτεινός φωτισμός φθορισμού στον κόσμο
Lighting Ο πιο φωτεινός φωτισμός φθορισμού στον κόσμο MASTER TL5 Υψηλής Φωτεινής Ροής Αυτός ο λαμπτήρας TL5 (διάμετρος σωλήνα 16 mm) προσφέρει υψηλή φωτεινή ροή. Ο λαμπτήρας έχει βελτιστοποιηθεί για εγκαταστάσεις
Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.
Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action
Chapter 6: Systems of Linear Differential. be continuous functions on the interval
Chapter 6: Systems of Linear Differential Equations Let a (t), a 2 (t),..., a nn (t), b (t), b 2 (t),..., b n (t) be continuous functions on the interval I. The system of n first-order differential equations
k A = [k, k]( )[a 1, a 2 ] = [ka 1,ka 2 ] 4For the division of two intervals of confidence in R +
[a 1, a 2 ] = [ka 1,ka 2 ] 4For the division of two intervals of confidence in R +](/thumbs/73/69566903.jpg "k A = [k, k]( )[a 1, a 2 ] = [ka 1,ka 2 ] 4For the division of two intervals of confidence in R +")
Chapter 3. Fuzzy Arithmetic 3- Fuzzy arithmetic: ~Addition(+) and subtraction (-): Let A = [a and B = [b, b in R If x [a and y [b, b than x+y [a +b +b Symbolically,we write A(+)B = [a (+)[b, b = [a +b
Ο πιο φωτεινός φωτισμός φθορισμού στον κόσμο
Lighting Ο πιο φωτεινός φωτισμός φθορισμού στον κόσμο Αυτός ο λαμπτήρας TL5 (διάμετρος σωλήνα 16 mm) προσφέρει υψηλή φωτεινή. Ο λαμπτήρας έχει βελτιστοποιηθεί για εγκαταστάσεις που απαιτούν υψηλή φωτεινή,
Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in
Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in : tail in X, head in A nowhere-zero Γ-flow is a Γ-circulation such that