Beam method - Compared with beam scattering homogenization, nonlinear focusing with multipole magnets is a more suitable homogenization method for laser-accelerated beams. As we are also aiming to mitigate the disadvantage of low average beam intensity generated by laser acceleration, the method of nonlinear field homogenization makes maximal use …

 
Summary. The beam propagation method (BPM) is a simple numerical algorithm for simulating the propagation of a coherent beam of light through a dielectric waveguide (or other structure). Figure 32.1 shows the split-step technique used in the BPM, in which the diffraction of the beam and the phase-shifting action of the guide are separated from .... What do these letters spell unscrambled

position or by an inverse synthetic aperture (ISAR) method with a rotated metal plate. 6.4.3 The beam waist, w 0, is the radius of the beam at the focal point where the amplitude is reduced by 8.7 dB relative to the center of the beam. This corresponds to the radius where the field is reduced by a factor of 1/e, where e = 2.7183. The crossed molecular beam (CMB) technique is a well-established method for studying the dynamics of gas phase collisions and reactions. The basic methodology ...Application to Cantilever Beams and Beams With Symmetric ... From the Load Di... Statically Indeterminate Beams Sample Problem 9 1 Bending Moment Diagrams by Parts Sample Problem 9.11 Sample Problem 9.1 Sample Problem 9.3 Method of Superposition Application of Moment-Area Theorems to Beams With Unsymme... Method of Superposition Maximum DeflectionComparing targeting reliability between Beam F3 method and 5.5 cm rule techniques (A,B) and comparing the group mean centroids to other published transcranial magnetic stimulation targets (C,D). (A) Scatter plot of all 162 technician measurements plotted on an MNI composite scalp for Beam F3 (red) and 5.5 cm rule (green). The black circles ...Atomic and molecular beams have played central roles in many experiments in physics and chemistry – from seminal tests of fundamental aspects of quantum mechanics to molecular reaction dynamics – and have found a wide range of applications [].Nowadays, sophisticated laser-based methods exist to perform sensitive and quantum state selective …Jim Beam Kentucky Coolers come in four crisp and cool malt-based flavors inspired by the brand's southern welcoming ethos and will be available na... Jim Beam Kentucky Coolers come in four crisp and cool malt-based flavors inspired by the b...Jul 13, 2023 · This beam deflection calculator will help you determine the maximum beam deflection of simply-supported and cantilever beams carrying simple load configurations. You can choose from a selection of load types that can act on any length of beam you want. The magnitude and location of these loads affect how much the beam bends. Understanding of the stresses induced in beams by bending loads took many years to develop. Galileo worked on this problem, but the theory as we use it today is usually credited principally to the great mathematician Leonard Euler (1707–1783). ... ("Apparent Horizontal Shear Strength of Reinforced Plastics by Short Beam Method," ASTM D2344 ...6.36. 2 Analysis of Building Frames to Vertical Loads Consider a building frame subjected to vertical loads as shown in Fig.36.3. Any typical beam, in this building frame is subjected to axial force, bending moment and shear force. Hence each beam is statically indeterminate to third degree and hence 3 assumptions are required to reduce this beam to …1. Introduction. The Gaussian beam migration (GBM) method is a research hotspot because it can produce good imaging results and have high computational efficiency (Červený et al., 1982; Popov, 1982, 2002; Červený and Pšenčík, 1983, 1984).Its implementation mainly includes the traditional frequency domain and the recent popular …Watch on. BEAM is a framework for discussing the usefulness of different types resources. Developed by Joseph Bizup as a more functional alternative to the traditional primary/secondary classification, BEAM stands for Background, Exhibit, Argument, and Method.May 4, 2023 · The deflected beam method requires only a fixed Faraday cup mounted downstream from a set of x–y deflectors . The measurement is made by rastering the beam across the cup face by scanning the x–y deflector voltages with a computer-controlled power supply, while an ammeter simultaneously records the current signal in the cup. 5.1 This test method is designed to produce shear property data for material specifications, research and development, quality assurance, and structural design and analysis. Either in-plane or interlaminar shear properties may be evaluated, depending upon the orientation of the material coordinate system relative to the loading axis.The short beam shear (SBS) test method combined with digital image correlation (DIC) deformation measurement is used in this work to study constitutive properties of the IM7/8552 carbon/epoxy ...Aug 24, 2023 · A beam with an overhang is subjected to a varying load, as shown in Figure 3.11a. Determine the reactions at supports A and B. Fig. 3.11. Beam with an overhang. Solution. Free-body diagram. The free-body diagram of the entire beam is shown in Figure 3.11b. Computation of reactions. Observe that the distributed loading in the beam is triangular. The beam propagation method (BPM) for simulating the propagation of a coherent beam of light through dielectric waveguide was discussed. The beam in BPM travels for a short distance in a homogeneous, isotropic medium, which has the average refractive index of the guide but lacks the guide's features. It was found that the mask must adjust the ... Structural Analysis. Civil Engineering. ISBN: 9781337630931. Author: KASSIMALI, Aslam. Publisher: Cengage, SEE MORE TEXTBOOKS. Solution for Use the conjugate-beam method to determine the slope and deflection at point c of the beams shown in 50 kN 90 kN 6 m 9 m -9 m El = constant.Engineering Civil Engineering A 4m simple beam is loaded with a downward vertical load of 500N at a point 1m from the left support and a counter-clockwise moment of 100N-m at a point 1m from the right support. Use Area Moment Method. a) Calculate the deviation of the right support relative to the tangent drawn from the left support. b) Calculate the …Assume that α = 1.2 × 10−5 /∘C α = 1.2 × 10 − 5 / ∘ C. For the truss from problem 21 but with no external loads, determine the vertical deflection at point B ( ΔB Δ B) if members BD, DF and AD were each fabricated 10mm 10 m m too short and member DE was fabricated 5mm 5 m m too long. 5.10a Selected Problem Answers. 5.9 Virtual ...The conjugate beam method is suitable for learning by sophomores and juniors; and it has been taught, tested, and highlighted in the course MEEG 3013 Mechanics of Materials at the University of Arkansas for several years. In the analysis of beam deflections, this method is the one method most frequently preferred by the students. Publisher: PEARSON. Principles of Foundation Engineering (MindTap Cou... Civil Engineering. ISBN: 9781337705028. Author: Braja M. Das, Nagaratnam Sivakugan. Publisher: Cengage Learning. SEE MORE TEXTBOOKS. Solution for Use the conjugate-beam method to determine the slope and deflection at point D of the beam shown. at the reaction. If either, or both ends of a beam projects beyond the supports, it is called a simple beam with overhang. A beam with more than simple supports is a continuous beam. Figures 3.2a, 3.2b, and 3.2c show respectively, a simple beam, a beam with overhang, and a continuous beam. A cantilever beam is one in which one end is built into 5.1 This test method is designed to produce shear property data for material specifications, research and development, quality assurance, and structural design and analysis. Either in-plane or interlaminar shear properties may be evaluated, depending upon the orientation of the material coordinate system relative to the loading axis.Problem 7-7: A cantilever beam subjected to a point load and uniformly distributed load is shown in Figure 7-7(a). Use the method of conjugate beam to determine ...Jul 20, 2020 · By Edgar 2020-07-20 Engineering, Structural Analysis, Structural Engineering. T he Double Integration Method or better known as Macaulay’s Method is one way of determining the linear and angular deflection of beams. Here, we will have one comprehensive post detailing this procedure. This short video overviews the BEAM Method, an approach for thinking about how we use resources in academic writing.If you have any questions about this vide...Structural Analysis. Civil Engineering. ISBN: 9781337630931. Author: KASSIMALI, Aslam. Publisher: Cengage, SEE MORE TEXTBOOKS. Solution for Use the conjugate-beam method to determine the slope and deflection at point c of the beams shown in 50 kN 90 kN 6 m 9 m -9 m El = constant.Beam-Propagation Method can be used to obtain the eigenmodes of longitudinal-invariant structures. References Taflove, A. and Umashankar, K.R. ( 1989 ) Review of FD-TD numerical modeling of electromagnetic wave scattering and …Different verification method was used to illustrate a wide applicability of the ENBM. Our ENBM extends from the equivalent linear beam model allowing for the von Karman nonlinear strain–displacement relationship. Then, the Hamilton principle is applied to derive the governing partial differential equations of motion for the ENBM.Nov 20, 2016 · We have provided illustrated solved examples on calculation of slope and deflection of cantilever, simply supported beams and frames by diffferent methods like double integration, Macaulay's method, Conjugate Beam method, Moment area method and unit load method. All the steps of these examples are very well explained and it is expected that ... Aug 24, 2023 · 1.1 Structural Analysis Defined. A structure, as it relates to civil engineering, is a system of interconnected members used to support external loads. Structural analysis is the prediction of the response of structures to specified arbitrary external loads. During the preliminary structural design stage, a structure’s potential external load ... Jun 9, 2022 · Developed by Joseph Bizup , the BEAM method encourages students to think about sources in terms of the function rather than common features. It asks students to think about how writers use sources in writing. BEAM describes 4 ways that sources can be used. Students can be asked to try to use sources in each of the 4 ways, but requirements can ... Beam design is a wide subject that covers a vast area in structural engineering design. The beam is one of the primary elements of structures. ... Let’s see some of the methods available for the initial design of beams. The following method is discussed as per the British standards (BS 8110).Beams are frequently classified on the basis of supports or reactions. A beam supported by pins, rollers, ... An alternative method of developing Eq. 3.3 involves the definition of normal strain. An incremental element of a beam is shown both …The small pipe–roof–beam method has better adaptability to ultra-shallow buried subway stations. Five groups of similar model tests were carried out to explore the pipe–roof deformation, surface settlement, and beam strain caused by excavation using this method. Based on the test results, a 3D numerical model was established to study the ...Shilpi Saxena. Richa Mohan. R. Venkataramanan. Request PDF | On Jan 1, 2012, John Schultz published Focused Beam Methods Measuring Microwave Materials in Free Space | Find, read and cite all the ...Jan 13, 2020 · BEAM is a framework for discussing the usefulness of different types resources. Developed by Joseph Bizup as a more functional alternative to the traditional primary/secondary classification, BEAM stands for Background, Exhibit, Argument, and Method. BEAM Model (Joseph Bizup) Source Function. Explanation. Examples of Types of Sources. Where you might use it in your paper. B: Background. Factual and noncontroversial information, providing context. Encyclopedia articles, overviews in books, statistics, historical facts. Introduction.3. Using BEAM: An Example. Using sources to function in these roles is how you enter into the scholarly conversation with all the other research and writing that has covered your topic before. In the next few pages, you'll learn more about each role by analyzing how sources are used in the pop culture essay cited in the Example below.Assume that α = 1.2 × 10−5 /∘C α = 1.2 × 10 − 5 / ∘ C. For the truss from problem 21 but with no external loads, determine the vertical deflection at point B ( ΔB Δ B) if members BD, DF and AD were each fabricated 10mm 10 m m too short and member DE was fabricated 5mm 5 m m too long. 5.10a Selected Problem Answers. 5.9 Virtual ...Beam Theory. According to the beam theory, a beam is a structural member whose one dimension (length) is significantly larger than the other dimensions (width and height). From: …We have provided illustrated solved examples on calculation of slope and deflection of cantilever, simply supported beams and frames by diffferent methods like double integration, Macaulay's method, Conjugate Beam method, Moment area method and unit load method. All the steps of these examples are very well explained and it is expected that ...The general method of measuring damping using a vibrating cantilever beam is also referred to as the Oberst beam test in the ASTM E756 standard [9]. This.The maximum stress is then given by Equation 4.2.7 using this value of I and y = ˉy / 2 (the distance from the neutral axis to the outer fibers), along with the maximum bending moment M max. The result of these substitutions is. σx = (3d2c + 6abd + 3ab2)wL2 2c2d4 + 8abcd3 + 12ab2cd2 + 8ab3cd + 2a2b4. In this work, we experimentally study a two-dimensional THz beam-steering method based on a programmable metasurface with a crossbar architecture. Generating coding patterns through the modulo-addition of column and row coding matrices in the programmable devices are experimentally verified. We further explore the flexible THz beam steering in ...The slope at A , in the original beam will be equal to the shear force at A in the conjugate beam, thus, (clockwise direction) The deflection of B in the real beam will be equal to the bending moment at B in conjugate beam i.e. (downward direction) Example 4.8 Determine the deflection at the free end of the beam shown in Figure 4.10 using ... Aug 24, 2023 · The conjugate beam method, developed by Heinrich Muller-Breslau in 1865, is one of the methods used to determine the slope and deflection of a beam. The method is based on the principle of statics. A conjugate beam is defined as a fictitious beam whose length is the same as that of the actual beam, but with a loading equal to the bending moment ... Here are the steps used to draw the conjugate beam from the real beam:-. Step 1: Draw the bending moment diagram for the real beam. Step 2: Divide the magnitudes of bending moments by flexural rigidity and draw the M/EI diagram. Step 3: Draw the conjugate beam having the same length as a real beam. Step 4: Plot the loading same as the M/EI ... Problems 269. SUMMARY In this chapter we have discussed the geometric methods for determin-ing the slopes and deflections of statically determinate beams. The dif-ferential equation for the deflection of beams can be expressed as d 2y M ¼ (6.9) dx 2 EI The direct integration method essentially involves writing expression(s) for M/EI for the beam in terms of x and …Dec 13, 2018 · Called the BEAM method, the new technique is based on EEG (electroencephalography), an existing technology in the field of neurology that uses electrodes to measure the brain’s electrical activity. During an EEG test, a provider determines where to place the electrodes on the scalp based on a grid system called the “international 10-20 ... The slope at A , in the original beam will be equal to the shear force at A in the conjugate beam, thus, (clockwise direction) The deflection of B in the real beam will be equal to the bending moment at B in conjugate beam i.e. (downward direction) Example 4.8 Determine the deflection at the free end of the beam shown in Figure 4.10 using ... Structural Analysis Questions and Answers – Analysis of Beams-2. This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Analysis of Beams-2”. A and C are fixed supports. B is a roller. A distributed load is acting on beam BC with peak at C being 6N/ft. AB is 8 ft. while BC is 6ft. Take EI as constant.This short video overviews the BEAM Method, an approach for thinking about how we use resources in academic writing.If you have any questions about this vide...This method is somewhat more refined than the traditional 2-D grid method. For this modeling approach, beam element internal forces obtained from this method need to be eccentrically transformed to obtain the composite girder internal forces (bending moment and shear) used in the bridge design. •Feb 2, 2021 · @OP I reccomend sending vouch copies to users who KNOW what beam methods are out there. Don't give it to some 50+ random, You don't profit from it when all they're gonna do is give a biased review. I do know MANY "beaming" method that are out there. I have asked for a vouch copy because I have heard of A LOT, i'm interested in their 3rd beam ... The Conjugate beam has the same length as the Real beam. But in load in the conjugate beam will be the bending moment of real beam divided by EI at the same point. It is the most common and familiar method for civil engineers to analyze slope and displacement of the beam. This method was developed by H. Müller-Breslau in 1865 A.D. Supports. Loads. Calculation. Beam Length L,(m): Length Unit: Force Unit: Go to the Supports. 10 (m) Calculate the reactions at the supports of a beam - statically determinate and statically indeterminate, automatically plot the Bending Moment, Shear Force and Axial Force Diagrams. Fig. 1 (a) shows a schematic of the W-DCB method. One end of the test specimen was fixed, where the notch end of the test specimen was loaded by a wedge indenter. Consequently, during the translational movement of the wedge indenter along the notch direction, friction must occur at the contact position (approximate line contact) between the wedge …The beam propagation method (BPM) for simulating the propagation of a coherent beam of light through dielectric waveguide was discussed. The beam in BPM travels for a short distance in a homogeneous, isotropic medium, which has the average refractive index of the guide but lacks the guide's features. It was found that the mask must adjust the ... The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed (APS) thermal barrier coatings (TBCs). As APS TBCs are typical multilayer porous ceramic …7 de mar. de 2013 ... The “Smart Beam” method for wood framework, jointly developed by Nippon Steel & Sumitomo Metal Corporation and TATSUMI, a leading maker of metal ...The model is used extensively in a method that is presented allowing for the calculation of bidimensional growth rates from Focused Beam Reflectance Measurement or in situ microscopy measurements ...The modified Winkler foundation beam (MEFB method) presented in this paper can be used to analyze the deflection of the diaphragm-cross wall system during excavation. As shown in the figure, the predicted wall deflections using the MEFB method were similar to the 3D analysis results and field observations, but much smaller than the results ...beam, in engineering, originally a solid piece of timber, as a beam of a house, a plow, a loom, or a balance. In building construction, a beam is a horizontal member spanning an opening and carrying a load that may be a brick or stone wall above the opening, in which case the beam is often called a lintel (see post-and-lintel system).The load may be a …View Stat Details. Problem 656 Find the value of EIδ at the point of application of the 200 N·m couple in Fig. P-656.Engr. Christian Otto Mohr. The length of a conjugate beam is always equal to the length of the actual beam. The load on the conjugate beam is the M/EI diagram of the loads on the actual beam. A simple support for the real beam remains simple support for the conjugate beam. A fixed end for the real beam becomes free end for the conjugate beam.Laser welding is a highly precise and efficient method of joining materials together. It utilizes a high-powered laser beam to create a concentrated heat source that melts and fuses the materials, resulting in a strong and durable bond.Dec 25, 2016 · Any exact method, such as slope-deflection method, moment distribution method or direct stiffness method may be used to analyse this rigid frame. However, in order to estimate the preliminary size of different members, approximate methods are used to obtain approximate design values of moments, shear and axial forces in various members. 18) using Gauss–Legendre quadrature method to find the needed loading); Ref. [47] and Ref. [48] focused on straight beams and ICBs subjected to a vertical load at the beam end respectively; Ref. [49] proposed a genetic-algorithm-based shooting method for the case of an in-plane load and a transversal load exerted at the beam tip; although …The short beam shear (SBS) test method combined with digital image correlation (DIC) deformation measurement is used in this work to study constitutive properties of the IM7/8552 carbon/epoxy ...7.1 Introduction. The serviceability requirements limit the maximum deflection …... beam (VFB) method. Three formulae are already known: (a) and (b) perform the back-projection in the parallel-beam geometry and (c) performs the back ...Mar 24, 2021 · 5.1 This test method is designed to produce shear property data for material specifications, research and development, quality assurance, and structural design and analysis. Either in-plane or interlaminar shear properties may be evaluated, depending upon the orientation of the material coordinate system relative to the loading axis. The beam-bending method permits measurement of liquid permeability in the nanoDarcy range in a few minutes to a few hours. This technique has been applied successfully to determine the permeability, as well as the viscoelastic properties, of isotropic materials with low permeability, such as gels, porous glass, and cement paste.Apr 16, 2021 · A cantilever beam shown in Figure 7.10a is subjected to a concentrated moment at its free end. Using the moment-area method, determine the slope at the free end of the beam and the deflection at the free end of the beam. \(EI\) = constant. \(Fig. 7.10\). Cantilever beam. Solution (\(M/EI\)) diagram. H.C. Wainwright analyst Amit Dayal maintained a Buy rating on Beam Global (BEEM – Research Report) today and set a price target of $30.00.... H.C. Wainwright analyst Amit Dayal maintained a Buy rating on Beam Global (BEEM – Research R...Jul 4, 2023 · BEAM Model (Joseph Bizup) A source may serve more than one function. For instance, a journal article could provide you with background information, exhibits, argument, and method. However, some sources are focused on a single function. For example, an encyclopedia entry is likely to only serve as background information. The single cantilever beam method has proved a useful method to measure the interfacial adhesion. Fig. 1 shows schematic illustration of the SCB method. A beam is adhered on a rigid body by an adhesive with a foundation modulus κ.Crack length is a and the ligament is c.Load P is applied at the end of cantilever, and the resultant displacement is δ.It is assumed …Beam (structure) A statically determinate beam, bending (sagging) under a uniformly distributed load. A beam is a structural element that primarily resists loads applied laterally to the beam's axis (an element designed to carry primarily axial load would be a strut or column). Its mode of deflection is primarily by bending.The Attachment the Beam originates from. A Beam 's Attachment0 is the first control point on the Beam 's cubic Bézier curve. The orientation of Attachment0, alongside the Beam 's Beam.CurveSize0, property determine the position of the second control point. For the Attachment where the Beam ends see Beam.Attachment1. Classify the beams shown in Figure 3.1 through Figure 3.5 as stable, determinate, or indeterminate, and state the degree of indeterminacy where necessary. Fig. 3.1. Beam. ... Note: When using equation 3.4 to classify a frame with a closed loop, as given here, the loop has to be cut open by the method of section, ...Apr 16, 2021 · Sign Convention •Draw the curvature diagram for the real beam. •Draw the conjugate beam for the real beam. The conjugate beam has the same length as the real beam. A rotation at any... •Apply the curvature diagram of the real beam as a distributed load on the conjugate beam. •Using the equations of ... Aug 12, 2020 · Using the geometry in the elastic curve, we know that: Now, let’s consider the conjugate beam of the said beam. To construct it, first, we draw the moment diagram by parts (section at B). Next, divide the diagram by the flexural rigidity (EI). Then, treat this as a fictional load applied at the same beam. The built-in beams shown in the figure below are statically indeterminate. To determine the stresses and deflections of such beams, the most direct method is to solve the Euler-Bernoulli beam equation with appropriate boundary conditions. But direct analytical solutions of the beam equation are possible only for the simplest cases.

Conjugate beam method. The conjugate-beam methods is an engineering method to derive the slope and displacement of a beam. A conjugate beam is defined as an imaginary beam with the same dimensions (length) as that of the original beam but load at any point on the conjugate beam is equal to the bending moment at that point divided by EI.. Bs microbiology

beam method

BEAM Method. Developed by Joseph Bizup, the BEAM method encourages you to think about sources in terms of the function rather than common features.It asks students to think about how writers use sources in writing. You might have had discussions about the differences in scholarly, academic articles vs. popular magazine or newspaper articles; but the reality is, depending on your research, you ...Conjugate beam method is only used to find deflection due to bending forces applied on structure. This means that conjugate beam method cannot be used to find deflection due to shear, torsion, axial force, temperature change, etc. For beams having non-prismatic cross-section, the slope and deflection can be easily obtained by …BEAM: Method Sources. While argument sources help you frame your paper within the larger scholarly discussion about your topic and exhibits provide a focal point, method …Conjugate-Beam Method – 2 This set of Structural Analysis MCQs focuses on “Conjugate-Beam Method – 2”. B is a hinge support and C is roller support. A and D are free ends. A load of 60 KN acts in downward direction at point D. Sign conventions are as usual.Simple and robust method for determination of laser fluence thresholds for material modifications: an extension of Liu’s approach to imperfect beams. [version 2; peer review: 2 approved, 1 approved with reservations] Mario Garcia-Lechuga 1,2, David Grojo 1. Author details. This article is included in the Materials Engineering gateway.BEAM Method Overview In discussing the usefulness of different types of sources, we find it is helpful to use the BEAM method, developed by Joseph Bizup, BEAM stands for: B ackground, E xhibit, A rgument, M ethod. Background: using a source to provide general information to explain the topic.Knife Edge measurement of Gaussian Beam • Consider a Gaussian shaped beam ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛− ⎟⎟= ⎠ ⎞ ⎜⎜ ⎝ ⎛− = 2 2 2 2 2 0 w 2r exp w 2P w 2r I(r) I exp π Where P = total power in the beam w = 1/e2 beam radius at point w(z) • This is in cylindrical coordinates • r is the radius of the central areaEngineering Civil Engineering A 4m simple beam is loaded with a downward vertical load of 500N at a point 1m from the left support and a counter-clockwise moment of 100N-m at a point 1m from the right support. Use Area Moment Method. a) Calculate the deviation of the right support relative to the tangent drawn from the left support. b) Calculate the …The built-in beams shown in the figure below are statically indeterminate. To determine the stresses and deflections of such beams, the most direct method is to solve the Euler-Bernoulli beam equation with appropriate boundary conditions. But direct analytical solutions of the beam equation are possible only for the simplest cases.BEAM stands for: Background, Exhibit, Argument, Method. Background: using a source to provide general information to explain the topic. For example, the use of a Wikipedia page on the Pledge of Allegiance to explain the relevant court cases and changes the Pledge has undergone.Figure 8.2: Potential energy of a beam element and the entire beam. In the above de nition Wis negative. The concept of the energy stored elastically Uhas been introduced earlier. For a 3-D body U= Z V 1 2 ˙ ij ijdv (8.5) and for a beam U= Z l 0 1 2 MKdx+ Z l 0 1 2 N dx (8.6) For plates, the bending and membrane energies are given by Eqs. (4. ....

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