Search
- Filter Results
- Location
- Classification
- Include attachments
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Introduction_to_Electric_Power_Systems_(Kirtley)/12%3A_Permanent_magnet_Brushless_DC_motors/12.02%3A_Zeroth_Order_RatingIn determining the rating of a machine, we may consider two separate sets of parameters. The first set, the elementary rating parameters, consist of the machine inductances, internal flux linkage and ...In determining the rating of a machine, we may consider two separate sets of parameters. The first set, the elementary rating parameters, consist of the machine inductances, internal flux linkage and stator resistance. From these and a few assumptions about base and maximum speed it is possible to get a first estimate of the rating and performance of the motor. More detailed performance estimates, including efficiency in sustained operation, require estimation of other parameters.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Discrete_Stochastic_Processes_(Gallager)/07%3A_Random_Walks_Large_Deviations_and_Martingales/7.07%3A_Submartingales_and_Supermartingales\[ \begin{align} &\{ |Z_n|;\, n\geq \} \text{ is a submartingale} \\ &\{ Z_n^2; \, n\geq 1\} \text{ is a submartingale if } \mathsf{E}[Z_n^2]<\infty \\ &\{\exp (rZ_n); \, n\geq 1\} \text{ is a submart...\[ \begin{align} &\{ |Z_n|;\, n\geq \} \text{ is a submartingale} \\ &\{ Z_n^2; \, n\geq 1\} \text{ is a submartingale if } \mathsf{E}[Z_n^2]<\infty \\ &\{\exp (rZ_n); \, n\geq 1\} \text{ is a submartingale for } r \text{ such that } \mathsf{E}[\exp (rZ_n)]<\infty \end{align} \nonumber \]
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Book%3A_Continuum_Electromechanics_(Melcher)/02%3A_Electrodynamic_Laws_Approximations_and_Relations/2.21%3A_Problems\[ \begin{bmatrix} \varepsilon \hat{E}_x^{\alpha} \\ \varepsilon \hat{E}_x^{\beta} \\ \mu \hat{H}_x^{\alpha} \\ \mu \hat{H}_x^{\beta} \end{bmatrix} = \begin{bmatrix} j \frac{ \varepsilon k}{ \gamma} c...\[ \begin{bmatrix} \varepsilon \hat{E}_x^{\alpha} \\ \varepsilon \hat{E}_x^{\beta} \\ \mu \hat{H}_x^{\alpha} \\ \mu \hat{H}_x^{\beta} \end{bmatrix} = \begin{bmatrix} j \frac{ \varepsilon k}{ \gamma} coth\, (\gamma \Delta) & -j \frac{\varepsilon k}{\gamma} \frac{1}{sinh\, (\gamma \Delta)} & 0 & 0 \\ j \frac{ \varepsilon k}{ \gamma} sinh\, (\gamma \Delta) & -j \frac{\varepsilon k}{\gamma} \frac{1}{coth\, (\gamma \Delta)} & 0 & 0 \\ 0 & 0 & j \frac{\mu k}{\gamma} coth\, (\gamma \Delta) & -j \frac{…
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Book%3A_Continuum_Electromechanics_(Melcher)/05%3A_Charge_Migration_Convection_and_Relaxation/5.02%3A_Charge_Conservation_with_Material_ConvectionEach of \(n\) species contributing to the transfer of charge is described by an expression of the form of Equation \ref{9}. The evolution of one species is linked to the others through Gauss' law, whi...Each of \(n\) species contributing to the transfer of charge is described by an expression of the form of Equation \ref{9}. The evolution of one species is linked to the others through Gauss' law, which recognizes that the net charge from all of the species is the source for the electric field: In the remainder of this chapter, certain of the physical implications of these relations are explored, with emphasis on the interplay of the material convection and the charge transport processes.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Introduction_to_Nanoelectronics_(Baldo)/08%3A_References_and_Appendices/8.03%3A_Appendix_2_-_The_Hydrogen_AtomThe p orbitals are similar to the first excited state of the box, i.e. \((n_{x},n_{y},n_{z})=(2,1,1)\) is similar to a \(p_{x}\) orbital, \((n_{x},n_{y},n_{z})=(1,2,1)\) is similar to a \(p_{y}\) orbi...The p orbitals are similar to the first excited state of the box, i.e. \((n_{x},n_{y},n_{z})=(2,1,1)\) is similar to a \(p_{x}\) orbital, \((n_{x},n_{y},n_{z})=(1,2,1)\) is similar to a \(p_{y}\) orbital and \((n_{x},n_{y},n_{z})=(1,1,2)\) is similar to a \(p_{z}\) orbital.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Introduction_to_Nanoelectronics_(Baldo)/06%3A_The_Electronic_Structure_of_Materials/6.17%3A_Tight_Binding_Calculations_in_Periodic_molecules_and_crystalsWe now repeat the polyacetylene calculation, but this time we impose periodic boundary conditions and assume molecular wavefunctions of the Bloch form. The solutions are almost identical to the previo...We now repeat the polyacetylene calculation, but this time we impose periodic boundary conditions and assume molecular wavefunctions of the Bloch form. The solutions are almost identical to the previous calculation in the absence of periodic boundary conditions, but there are some subtle yet important differences in the dispersion relation.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Introduction_to_Nanoelectronics_(Baldo)/06%3A_The_Electronic_Structure_of_Materials/6.14%3A_Bloch_functions-_wavefunctions_in_periodic_moleculesUnder the tight binding approximation, the wavefunction of the unit cell is itself constructed from a linear combination of frontier atomic orbitals. Figure \(\PageIndex{1}\): The molecular orbitals o...Under the tight binding approximation, the wavefunction of the unit cell is itself constructed from a linear combination of frontier atomic orbitals. Figure \(\PageIndex{1}\): The molecular orbitals of periodic molecules are linear combinations of the wavefunctions of the unit cells. Now, the molecular orbitals will be composed of linear combinations of the wavefunction of the unit cell, i.e.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Operational_Amplifiers%3A_Theory_and_Practice_(Roberge)/12%3A_Advanced_Applications/12.05%3A_FURTHER_EXAMPLESSuccessful design almost always involves combining bits and pieces, a concept here, a topology there, to ultimately arrive at the optimum solution. In this section we will see how some of the ideas in...Successful design almost always involves combining bits and pieces, a concept here, a topology there, to ultimately arrive at the optimum solution. In this section we will see how some of the ideas introduced earlier are combined into relatively more sophisticated configurations. The three examples that are presented are all "real world" in that they reflect actual requirements that the author has encountered recently in his own work.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Programming_and_Computation_Fundamentals/Principles_of_Computer_System_Design_(Saltzer_and_Kaashoek)/03%3A_Atomicity_-_All-or-nothing_and_Before-or-after/3.02%3A_AtomicityDefinition of all-or-nothing atomicity and before-and-after atomicity. Examples of their use in layered applications and in concurrent threads.
- https://eng.libretexts.org/Bookshelves/Industrial_and_Systems_Engineering/Book%3A_Dynamic_Systems_and_Control_(Dahleh_Dahleh_and_Verghese)/10%3A_Discrete-Time_Linear_State-Space_Models/10.02%3A_Linear_Time-Invariant_ModelsWhat this series establishes, on comparison with the definition of the \(\mathcal{Z}\)-transform, is that the inverse transform of \(z(zI - A)^{-1}\) is the matrix sequence whose value at time \(k\) i...What this series establishes, on comparison with the definition of the \(\mathcal{Z}\)-transform, is that the inverse transform of \(z(zI - A)^{-1}\) is the matrix sequence whose value at time \(k\) is \(A^{k}\) for \(k \geq 0\) the sequence is 0 for time instants \(k < 0\). Also since the inverse transform of a product such as \((z I-A)^{-1} B U(z)\) is the convolution of the sequences whose transforms are \((z I-A)^{-1} B\) and \(U(z)\) respectively, we get
- https://eng.libretexts.org/Bookshelves/Industrial_and_Systems_Engineering/Book%3A_Dynamic_Systems_and_Control_(Dahleh_Dahleh_and_Verghese)/04%3A_Matrix_Norms_and_Singular_Value_Decomposition/4.04%3A_Relationship_to_Matrix_Norms\sup _{x \neq 0} \frac{\|A x\|_{2}}{\|x\|_{2}} &=\sup _{x \neq 0} \frac{\left\|U \Sigma V^{\prime} x\right\|_{2}}{\|x\|_{2}} \\ &=\sup _{y \neq 0} \frac{\left(\sum_{i=1}^{r} \sigma_{i}^{2}\left|y_{i}\...\sup _{x \neq 0} \frac{\|A x\|_{2}}{\|x\|_{2}} &=\sup _{x \neq 0} \frac{\left\|U \Sigma V^{\prime} x\right\|_{2}}{\|x\|_{2}} \\ &=\sup _{y \neq 0} \frac{\left(\sum_{i=1}^{r} \sigma_{i}^{2}\left|y_{i}\right|^{2}\right)^{\frac{1}{2}}}{\left(\sum_{i=1}^{r}\left|y_{i}\right|^{2}\right)^{\frac{1}{2}}} \\ \|\Sigma y\|_{2} &=\left(\sum_{i=1}^{n}\left|\sigma_{i} y_{i}\right|^{2}\right)^{\frac{1}{2}} \\
