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sum
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Book Chapter
Series: AIPP Books, Principles
Published: August 2022
10.1063/9780735424876_014
EISBN: 978-0-7354-2487-6
ISBN: 978-0-7354-2484-5
...,” “GSg2,”… are used to denote segments, and two distinct points with a bar accent: “ P 1 P 2 ¯ ,” “ P 3 P 4 ¯ ,”… are used to denote the segments whose end points are the respective two points. Cosine and Sine of a Sum In this section, we will derive expressions...
Images
Published: March 2023
FIG. 2.2 The sum of the arbitrarily shaped areas over sides B and C equals the area over A, provided all three areas are similar. More about this image found in The sum of the arbitrarily shaped areas over sides B and ...
Images
in Visualization and Mathematization: How Digital Tools Provide Access to Formal Physics Ideas
> The International Handbook of Physics Education Research: Special Topics
Published: March 2023
FIG. 21.6 A modeled pendulum in Algodoo with dynamic vector arrows as they change throughout the pendulum swing—velocity in black, external forces on the bob in white, and the sum of all external forces in green (left). A constructed “car” in Algodoo with motors on the front and rear wheels ascends a slope (right). Dynamic vector arrows are displayed for the orange box, while the graph above shows the time dependence of the box's gravitational potential energy. More about this image found in A modeled pendulum in Algodoo with dynamic vector arrows a...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_001
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
... seem to have changed the pattern of resources. For example, in Kryjevskaia et al. (2011) , the “only peaks sum up” and the “peak for pulse” resources are not mentioned. Instead, two new resources appear that do sum up the pulse point by point but not correctly. The reasoning by which they do...
Book Chapter
Series: AIPP Books, Methods
Published: March 2023
10.1063/9780735425743_008
EISBN: 978-0-7354-2574-3
ISBN: 978-0-7354-2572-9
... † ) is executed. The qubit states at the end of the circuit form the binary representation of the sum of a and b. Proportional control of a dynamic system using a hybrid quantum/classical multiplication procedure As noted above, our prior work ( Nieman et al., 2022 ) integrated the QFT...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425514_024
EISBN: 978-0-7354-2551-4
ISBN: 978-0-7354-2548-4
... is the distance between the cluster centers. To identify the optimal number of clusters, a scree plot like that shown in Fig. 24.4 can be used. The scree diagram plots the remaining error sum of squares against the number of clusters. A weak “knee” is visible at two clusters. One can also examine the dendrogram...
Book Chapter
Book: Toward Better Photovoltaic Systems: Design, Simulation, Optimization, Analysis, and Operations
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425613_003
EISBN: 978-0-7354-2561-3
ISBN: 978-0-7354-2560-6
... was the sum of individual absolute errors. Other works have shown applications of these types of models that in most cases are known as single-diode and double-diode models see Paukshto and Lovetskiy, 2008 . In 2010, Kishor et al. (2010) showed an enhancement of a single-diode model by including...
Book Chapter
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425590_001
EISBN: 978-0-7354-2559-0
ISBN: 978-0-7354-2556-9
... = j) and u i , j = ∂ u i ∂ X j . The displacement gradient (or distortion) tensor ui,j, can be written as sum of a symmetric and an anti-symmetric tensor as follows: (1.12) u i , j = 1 2 ( u i , j + u j , i ) + 1...
Images
in High Breakdown Voltage β-Ga2O3 Schottky Diodes
> Ultrawide Bandgap β-Ga2O3 SemiconductorTheory and Applications
Published: February 2023
FIG. 8.27 Temperature-dependent reverse leakage characteristics of a near-ideal β-Ga2O3 SBD. The reverse leakage current (JR) is a sum of TE current (JTE) that captures over-the-barrier current and TFE current (JTFE) that captures below-the-barrier tunneling current under low-to-moderate surface electric fields at the Schottky interface. As the surface field increases or the temperature decreases, the dominant reverse leakage mechanism transitions from TE to TFE. Reprinted with permission from Li et al., J. Appl. Phys. 131 (1), 015702 (2022). Copyright 2022 AIP Publishing LLC. More about this image found in Temperature-dependent reverse leakage characteristics of a near-ideal β-Ga...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_015
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
..., the combination of the three types of knowledge—content, procedural, and epistemic—seems difficult to enact.” To sum up, there are many dimensions associated with physics teaching that can be considered: target audiences, learning goals, and their role in navigating/guiding the teaching and learning processes. We...
Book Chapter
Series: AIPP Books, Methods
Published: March 2023
10.1063/9780735425743_003
EISBN: 978-0-7354-2574-3
ISBN: 978-0-7354-2572-9
...-profile of the system can be obtained by summing the σ-profiles of the components, as follows: (3.7) p s ( σ ) = ∑ i ∈ s x i p i ( σ ) It is worth noting that in thermodynamic theory the macroscopic thermodynamic properties of a mixed system can be inferred...
Book Chapter
Series: AIPP Books, Methods
Published: March 2023
10.1063/9780735425743_011
EISBN: 978-0-7354-2574-3
ISBN: 978-0-7354-2572-9
... at every time instant; the probability is based on the ratio of the individual event over the sum of overall reaction rates ( r t , u p p e r = Σ r s i + r m ). Then, having this rate distribution, a random number, ξ p 1 ∈ ( 0 , 1 ] , is generated...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_005
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
... individually and then added together through integration. They found that students using the dependence and parts-of-a-whole cue could make progress even with unseen problems, but found evidence that a naive view of the limit concept may prevent students from viewing integrals as sums. Nguyen and Rebello (2011...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_014
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
...' meta-affective learning “by attending to how we frame instruction and assessment, by giving them opportunities to engage in genuine sensemaking and by explicitly addressing the affective challenges inherent in doing so” (p. 90). In sum, as this body of work shows, positioning affect as a target...
Book Chapter
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425590_006
EISBN: 978-0-7354-2559-0
ISBN: 978-0-7354-2556-9
... in the paraelectric (cubic) phase. The total free energy of a ferroic is expressed as the sum of various contributions such as bulk, electric, magnetic, elastic, and gradient. The bulk term is described using a Landau polynomial of degree six or eight where the polynomial is given as a series expansion...
Book Chapter
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735424395_002
EISBN: 978-0-7354-2439-5
ISBN: 978-0-7354-2436-4
... for the three triangles, the same constant q was used. FIG. 2.1 Derivation of Pythagoras theorem using scaling law. The area of ΔABC is the sum of the areas of the two inner triangles: (2.3) Area of Δ ABC = Area of Δ ADC + Area of Δ CDB (2.4) δ L 1 2 = δ L 2...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425712_008
EISBN: 978-0-7354-2571-2
ISBN: 978-0-7354-2568-2
... the specified models (model abstraction) by comparing different specified models. For example, noticing that an impulsive force model is best handled with momentum, energy, and impulse or noticing that the sum of the momentum vectors before a collision is identical to the sum of the momentum vectors after...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_004
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
... the ability to move, the sum of which, force vive absolue, remains constant. However, with the triumphal success of Newtonian mechanics that subsisted without an explicit notion of energy, the idea of a force vive absolute lost significance, only to be revived through the work of Joseph–Louis...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425712_007
EISBN: 978-0-7354-2571-2
ISBN: 978-0-7354-2568-2
... Sinusoidal 20.41 15.84 Sum of sinusoidal 2.04 1.98 Other (e.g., tanx) 8.16 1.98 Repeated but non-periodic mathematical relations 0.00 2.97 Other mathematical relations 2.04 5.94 Schematic representations Periodic models Circular motions Trigonometric circle 18.37 0.00...
Book Chapter
Book: Toward Better Photovoltaic Systems: Design, Simulation, Optimization, Analysis, and Operations
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425613_002
EISBN: 978-0-7354-2561-3
ISBN: 978-0-7354-2560-6
... of silicon, are consumed. In addition, other toxic chemicals, e.g., diborane and phosphine, are necessary for the doping of silicon. Other materials like aluminum and copper are also necessary for the production of other components in the system. Therefore, all hazardous materials should be summed up when...
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