Addition and Subtraction Formulas; Double and Half Angle Formulas

Trigonometry ◽  
2017 ◽  
pp. 89-106
Author(s):  
James Tanton
Keyword(s):  
Half Angle ◽  
Addition And Subtraction

Resolution Attainable With the Present Day STEM

1973 ◽  
Vol 31 ◽  
pp. 230-231 ◽  
Author(s):  
J. S. Wall ◽  
J. P. Langmore ◽  
H. Isaacson ◽  
A. V. Crewe
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Incident Beam ◽  
Scanning Transmission Electron Microscope ◽  
Aperture Size ◽  
Magnetic Lens ◽  
Peak Intensity ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Half Angle

The scanning transmission electron microscope (STEM) constructed by the authors employs a field emission gun and a 1.15 mm focal length magnetic lens to produce a probe on the specimen. The aperture size is chosen to allow one wavelength of spherical aberration at the edge of the objective aperture. Under these conditions the profile of the focused spot is expected to be similar to an Airy intensity distribution with the first zero at the same point but with a peak intensity 80 per cent of that which would be obtained If the lens had no aberration. This condition is attained when the half angle that the incident beam subtends at the specimen, 𝛂 = (4𝛌/Cs)¼

Low-workfunction field-emission source for high-resolution EELS

1987 ◽  
Vol 45 ◽  
pp. 132-133
Author(s):  
P. E. Batson
Keyword(s):  
High Resolution ◽  
Energy Loss ◽  
Electron Probe ◽  
Collection Efficiency ◽  
Electron Sources ◽  
Wien Filter ◽  
Half Angle ◽  
Thermal Emitter ◽  
Electron Energy Loss ◽  
Intrinsic Energy

In recent years,instrumentation for electron energy loss spectroscopy (EELS) has been steadily improved to increase energy resolution and collection efficiency. At present 0.40eV at 10mR collection half angle is available with commercial magnetic sectors (e.g. Gatan, Inc. and VG Microscopes, Ltd.), and 70meV at 10mR has been demonstrated by use of a Wien filter within a large deceleration field. When these high resolution spectrometers are coupled to the modern small electron probe instrument, we obtain a tool which promises to reveal local changes in bandstructure and bonding near defects and interfaces in heterogeneous materials.Unfortunately, typical electron sources have intrinsic energy widths which limit attainable spectroscopic resolution in the absence of some monochromation system. For instance, the W thermal emitter has a half width of about 1eV.

Thinking in Action and Beyond

2018 ◽  
Author(s):  
Terezinha Nunes
Keyword(s):  
Hard Of Hearing ◽  
Inverse Relation ◽  
Teaching Approaches ◽  
Multiplicative Reasoning ◽  
Mathematical Concepts ◽  
Logical Organization ◽  
The World ◽  
Mathematical Problems ◽  
Addition And Subtraction ◽  
Learning By Imitation

Before children learn to use language, they learn about the world in action and by imitation. This learning provides the basis for language acquisition. Learning by imitation and thinking in action continue to be significant throughout life. Mathematical concepts are grounded in children’s schemas of action, which are action patterns that represent a logical organization that can be applied to different objects. This chapter describes some of the conditions that allow deaf or hard-of-hearing (DHH) children to learn by imitation and use schemas of action successfully to solve mathematical problems. Three examples of concepts that can be taught by observation and thinking in action are presented: the inverse relation between addition and subtraction, the concepts necessary for learning to write numbers, and multiplicative reasoning. There is sufficient knowledge for the use of teaching approaches that can prevent DHH children from falling behind before they start school.

scholarly journals Addition and subtraction as a valuation mechanism for valuable buildings

2021 ◽  
Vol 1105 (1) ◽  
pp. 012096
Author(s):  
Basim Hasan Almajdi ◽  
Abbas Na’im Mohsin ◽  
Tabark Hussein Ali
Keyword(s):  
Addition And Subtraction

scholarly journals A New Approach for Design Optimization and Parametric Analysis of Symmetric Compound Parabolic Concentrator for Photovoltaic Applications

2021 ◽  
Vol 13 (9) ◽  
pp. 4606
Author(s):  
Faisal Masood ◽  
Perumal Nallagownden ◽  
Irraivan Elamvazuthi ◽  
Javed Akhter ◽  
Mohammad Azad Alam
Keyword(s):  
Parametric Analysis ◽  
Concentration Ratio ◽  
Synergistic Effects ◽  
Geometric Optimization ◽  
Design Parameters ◽  
Imaging Device ◽  
Compound Parabolic Concentrator ◽  
Photovoltaic Applications ◽  
Half Angle ◽  
The Impact

A compound parabolic concentrator (CPC) is a non-imaging device generally used in PV, thermal, or PV/thermal hybrid systems for the concentration of solar radiation on the target surface. This paper presents the geometric design, statistical modeling, parametric analysis, and geometric optimization of a two-dimensional low concentration symmetric compound parabolic concentrator for potential use in building-integrated and rooftop photovoltaic applications. The CPC was initially designed for a concentration ratio of “2×” and an acceptance half-angle of 30°. A MATLAB code was developed in house to provoke the CPC reflector’s profile. The height, aperture width, and concentration ratios were computed for different acceptance half-angles and receiver widths. The interdependence of optical concentration ratio and acceptance half-angle was demonstrated for a wide span of acceptance half-angles. The impact of the truncation ratio on the geometric parameters was investigated to identify the optimum truncation position. The profile of truncated CPC for different truncation positions was compared with full CPC. A detailed statistical analysis was performed to analyze the synergistic effects of independent design parameters on the responses using the response surface modeling approach. A set of optimized design parameters was obtained by establishing specified optimization criteria. A 50% truncated CPC with an acceptance half-angle of 21.58° and receiver width of 193.98 mm resulted in optimum geometric dimensions.

A Proposed Instructional Theory for Integer Addition and Subtraction

2012 ◽  
Vol 43 (4) ◽  
pp. 428-464 ◽  
Author(s):  
Michelle Stephan ◽  
Didem Akyuz
Keyword(s):  
Number Line ◽  
Teaching Experiment ◽  
Learning Trajectory ◽  
Realistic Mathematics Education ◽  
Instructional Theory ◽  
Education Theory ◽  
Addition And Subtraction ◽  
Support Students ◽  
Grade Classroom ◽  
Viable Model

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional sequence, which was based on a financial context, was designed using the Realistic Mathematics Education theory. Additionally, an empty, vertical number line (VNL) is posited as a potentially viable model to support students' organizing their addition and subtraction strategies. Particular emphasis is placed on the mathematical practices that were established in this setting. These practices indicate that students can successfully draw on their experiences with assets, debts, and net worths to create meaning for integer addition and subtraction.

Sign in / Sign up

Export Citation Format

Share Document