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### Turning Inductive into Equational Specifications [chapter]

Stefan Berghofer, Lukas Bulwahn, Florian Haftmann
2009 Lecture Notes in Computer Science
Using the theorem prover Isabelle, we describe an approach to turn a class of systems of inductively defined predicates into a system of equations using data flow analysis; the translation is carried out  ...  Inductively defined predicates are frequently used in formal specifications.  ...  equational rewriting: The code generator turns a set of equational theorems into a program inducing the same equational rewrite system.  ...

### Cutting Out Continuations [chapter]

Graham Hutton, Patrick Bahr
2016 Lecture Notes in Computer Science
Our approach is calculational, uses standard equational reasoning techniques, and is widely applicable.  ...  In this article, we show how these two transformations can be fused together into a single transformation step that cuts out the need to first introduce and then eliminate continuations.  ...  turn, to apply the induction hypothesis for y, i.e. eval y e c = exec c u, we need to rewrite the term eval x (u : e ) c into the form exec c u for some control stack c , i.e. we need to solve the equation  ...

### High-Frequency LLC Resonant Converter with GaN Devices and Integrated Magnetics

Yu-Chen Liu, Chen Chen, Kai-De Chen, Yong-Long Syu, Meng-Chi Tsai
2019 Energies
transformer leakage inductance without increasing the amount of loss caused by the proximity effect.  ...  In this study, a light emitting diode (LED) driver containing an integrated transformer with adjustable leakage inductance in a high-frequency isolated LLC resonant converter was proposed as an LED lighting  ...  The turns ratio of the transformer was calculated using Equation (27) , and substituting the circuit specifications of this study (400 V input voltage and 300 V output voltage) yielded a transformer turns  ...

### Transient Numerical Analysis of Induction Heating of Graphite Cruciable at Different Frequency

B. Patidar, M.M.Hussain, A. Sharma, A.P. Tiwari
2016 Zenodo
Mathematical modeling of electromagnetism and heat transfer is done by using maxwell equations and classical heat transfer equation respectively.  ...  Mathematical modeling of Induction heating process is done by using 2D axisymmetric geometry. Induction heating is coupled field problem that includes electromagnetism and heat transfer.  ...  FEM converts continuous equations i.e eq (10) into discrete equation by discretizing geometry of solution domain  .Discretization can be done by using trigular, rectangular or hexagonal elements.  ...

### Transient Numerical Analysis of Induction Heating of Graphite Cruciable at Different Frequency

B. Patidar, M.M.Hussain, A. Sharma, A.P. Tiwari
2016 Zenodo
Mathematical modeling of electromagnetism and heat transfer is done by using maxwell equations and classical heat transfer equation respectively.  ...  Mathematical modeling of Induction heating process is done by using 2D axisymmetric geometry. Induction heating is coupled field problem that includes electromagnetism and heat transfer.  ...  FEM converts continuous equations i.e eq (10) into discrete equation by discretizing geometry of solution domain  .Discretization can be done by using trigular, rectangular or hexagonal elements.  ...

### Improving a model of the induction traction motor operation involving non-symmetric stator windings

Sergey Goolak, Borys Liubarskyi, Svitlana Sapronova, Viktor Tkachenko, Ievgen Riabov, Marina Glebova
2021 Eastern-European Journal of Enterprise Technologies
A model of the induction motor has been proposed that takes into consideration changes in the values of mutual inductance of phases and complete inductance of the magnetization circuit due to changes in  ...  Existing approaches to modeling an induction motor do not make it possible to fully take into consideration these changes.  ...  These equations were supplemented with equations that make it possible to take into consideration a change in the values of mutual inductances of phases and the main inductance of the magnetization circle  ...

### An evaluation of inductances of a squirrel-cage induction motor under mixed eccentric conditions

J. Faiz, I.T. Ardekanei, H.A. Toliyat
2003 IEEE transactions on energy conversion
This paper presents a more precise model for computation of three-phase squirrel cage induction machine inductances under different eccentric conditions.  ...  Meanwhile, the evaluated inductances are compared to those calculated using different approximate geometrical models and the best approximation is recommended for a geometrical modeling of induction motor  ...  Toliyat is with the Department of Electrical Engineering, Texas A&M University, Digital Object Identifier 10.1109/TEC.2003.811740 TABLE I SPECIFICATIONS I OF THE PROPOSED INDUCTION MOTOR turns and stator  ...

### Impacts of rotor inter-turn short circuit fault upon performance of wound rotor induction machines

2016 Electric power systems research
The obtained inductances are compared with that of the FEM and effect of the SC turns on the inductances are investigated.  ...  Current of SC turns is also the signal that is considered here.  ...  These equations are classified into two categories.  ...

### Compiling a 50-year journey

GRAHAM HUTTON, PATRICK BAHR
2017 Journal of functional programming
In this article, we revisit this example in a modern context, and show how such a compiler can now be calculated directly from a specification of its correctness using simple equational reasoning techniques  ...  John McCarthy and James Painter (1967) published the first paper on compiler verification, in which they showed how to formally prove the correctness of a compiler that translates arithmetic expressions into  ...  We consider each unbound variable in turn: • For c, the simplest option is to put it into the argument c as we did in the base case, by adding a new constructor.  ...

### Steady-State Current Characteristics for Squirrel Cage Induction Motor according to Design Variables of Rotor Bars using Time Difference Finite Element Analysis

Young Sun Kim
2017 Journal of Magnetics
Additionally, we calculated the steady-state current with a method combining an electromagnetic field equation and a circuit equation.  ...  The introduction of power-source-containing harmonics into the induction motor winding lowers its efficiency and increases its temperature, greatly affecting its operation characteristics.  ...  Introduction Induction motors can be largely categorized into winding-type and squirrel-cage-type induction motors.  ...

### Optimized Multiport DC/DC Converter for Vehicle Drivetrains: Topology and Design Optimization

Duong Tran, Sajib Chakraborty, Yuanfeng Lan, Joeri Van Mierlo, Omar Hegazy
2018 Applied Sciences
of input current ripples and losses distribution between optimized and conventional designs are also analyzed in detailed, which validates the perspective of the proposed optimization method, taking into  ...  into Equation (A2) an expression of the maximum air-gap for the maximum number of turns can be derived in Equation (A6): g = K u W a J w µ 0 B max (A6) It is clear that is a function of only the material  ...  Figure 9 . 9 Inductance value in function of air-gap and number of turns. Figure 9 . 9 Inductance value in function of air-gap and number of turns. Appl.  ...

### A Complete Flow of Miniaturizing Coil Antennas Based on Matching Circuit

Xiaokun Yang, Zhao Ding, Zhengping Zhang
2021 Electronics
The inductances of a three-turn and five-turn CA are calculated and tabulated based on the dynamic equation, Equation (1) , as shown in Table 1 (unit: nH).  ...  In fact, the rela inductance value and variable parameters of the CA can be formulat equation, Equation (1)  : The conventional CA's inductance is about 1 to 2 uH, as it has 3-turn metallic loops  ...

### A ground-complete axiomatisation of finite-state processes in a generic process algebra

JOS C. M. BAETEN, MARIO BRAVETTI
2008 Mathematical Structures in Computer Science
Vice-versa we show that every process admits a specification in terms of such a restricted form of recursion.  ...  More precisely, we provide a syntactical characterization (allowing as many terms as possible) for the equations involved in recursion operators, which guarantees that transition systems generated by the  ...  The axiom Dec is used to decompose recursive specifications E made up of multiple (finitely-many) equations into several recursive specifications made up of single equations.  ...

### Some Tips on Writing Proof Scores in the OTS/CafeOBJ Method [chapter]

Kazuhiro Ogata, Kokichi Futatsugi
2006 Lecture Notes in Computer Science
We have been developing a tool called Gateau  that takes propositions used for case splitting and state predicates used to strengthen the basic induction hypothesis, and generates the proof score  ...  Simultaneous Induction The first thing to do is to use simultaneous induction to break the proof into the four (sub-)goals (one is the base case and the others are the three induction cases) and the four  ...  Write S in CafeOBJ as an algebraic specification. The specification consists of sorts (or types), operators on the sorts, and equations that define (properties of) the operators.  ...

### Mathematical Model of an Inductive Measuring Cell for Contactless Conductometry [article]

Yury S. Semenov
2013 arXiv   pre-print
It is sample-coil capacity that makes inductive cell applicable for measurement of electrical conductivity of low conductive samples (specific conductance is less than 1S/m).  ...  The model can be used to calculate impedance of inductive cell for different characteristics of sample, materials and dimensions of cell without numerical solving of partial differential equations.  ...  The limit at high specific conductance (more than about 100 ) allow to split the model into two parts.  ...
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