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Articles 12781 - 12810 of 21751

Full-Text Articles in Engineering

Decentralized Neural Network Control Of A Class Of Large-Scale Systems With Unknown Interconnection, Wenxin Liu, Jagannathan Sarangapani, Donald C. Wunsch, Mariesa Crow Jan 2004

Decentralized Neural Network Control Of A Class Of Large-Scale Systems With Unknown Interconnection, Wenxin Liu, Jagannathan Sarangapani, Donald C. Wunsch, Mariesa Crow

Electrical and Computer Engineering Faculty Research & Creative Works

A novel decentralized neural network (DNN) controller is proposed for a class of large-scale nonlinear systems with unknown interconnections. The objective is to design a DNN for a class of large-scale systems which do not satisfy the matching condition requirement. The NNs are used to approximate the unknown subsystem dynamics and the interconnections. The DNN is designed using the back stepping methodology with only local signals for feedback. All of the signals in the closed loop (system states and weights estimation errors) are guaranteed to be uniformly ultimately bounded and eventually converge to a compact set.


Space-Time Fading Correlation Functions Of A 3-D Mimo Channel Model, Sang-Yick Leong, Y. Rosa Zheng, Chengshan Xiao Jan 2004

Space-Time Fading Correlation Functions Of A 3-D Mimo Channel Model, Sang-Yick Leong, Y. Rosa Zheng, Chengshan Xiao

Electrical and Computer Engineering Faculty Research & Creative Works

Space-time correlation functions between the links of MIMO Rayleigh fading channels are derived using a new three-dimensional (3-D) cylinder scattering model. Closed form, mathematically tractable formulas are obtained for the space-time correlation functions for general MIMO systems where the base station and mobile station antennas may be arranged in 3-D space. It is shown that the correlation functions computed by the 3-D cylinder model are of significant difference than those of the conventional 2-D Clarke''s isotropic scattering model for vertically placed antennas. The general formulas of the correlation functions includes the 2-D Clarke''s model and the 3-D SIMO, MISO models …


Supervisory Level Neural Network Identifier For A Small Power System With A Statcom And A Generator, Salman Mohagheghi, Ganesh K. Venayagamoorthy, Ronald G. Harley Jan 2004

Supervisory Level Neural Network Identifier For A Small Power System With A Statcom And A Generator, Salman Mohagheghi, Ganesh K. Venayagamoorthy, Ronald G. Harley

Electrical and Computer Engineering Faculty Research & Creative Works

A neural network based identifier is designed for effective control of a small power system. The power network in this work is considered from an external point of view, i.e., from a supervisory level. Such a neuroidentifier can serve as a general model of such a plant, and then used for different neural network based control schemes.


Swarm Intelligence For Digital Circuits Implementation On Field Programmable Gate Arrays Platforms, Ganesh K. Venayagamoorthy, Venu Gopal Gudise Jan 2004

Swarm Intelligence For Digital Circuits Implementation On Field Programmable Gate Arrays Platforms, Ganesh K. Venayagamoorthy, Venu Gopal Gudise

Electrical and Computer Engineering Faculty Research & Creative Works

Field programmable gate arrays (FPGAs) are becoming increasingly important implementation platforms for digital circuits. One of the necessary requirements to effectively utilize the FPGA's resources is an efficient placement and routing mechanism. This paper presents an optimization technique based on swarm intelligence for FPGA placement and routing. Mentor graphics technology mapping netlist file is used to generate initial FPGA placements and routings which are then optimized by particle swarm optimization (PSO). Results for the implementation of a binary coded decimal bidirectional counter and an arithmetic logic unit on a Xilinx FPGA show that PSO is a potential technique for solving …


Temperature Considerations In Solar Arrays, Steve Eugene Watkins, Min-Jung Wu, E. J. Timpson Jan 2004

Temperature Considerations In Solar Arrays, Steve Eugene Watkins, Min-Jung Wu, E. J. Timpson

Electrical and Computer Engineering Faculty Research & Creative Works

Temperature is an important consideration in the operation of photovoltaic (PV) arrays. In particular, daily and seasonal temperature variations are a limitation on the application of solar power to homes. At lower temperatures, PV systems produce more power. For higher temperatures, optimum operation requires modification of electrical load and removal of excess heat. Several technologies and approaches are available. To pursue this system optimization, PV cells were investigated at different temperatures. These investigations are compared with simulated theoretical results to draw more specific conclusions that can be applied to a solar house. A temperature reduction of 60⁰C improved the power …


Time Series Prediction With A Weighted Bidirectional Multi-Stream Extended Kalman Filter, Donald C. Wunsch, Xiao Hu Jan 2004

Time Series Prediction With A Weighted Bidirectional Multi-Stream Extended Kalman Filter, Donald C. Wunsch, Xiao Hu

Electrical and Computer Engineering Faculty Research & Creative Works

This paper describes the use of a multi-stream extended Kalman filter (EKF) to tackle the IJCNN 2004 challenge problem - time series prediction on CATS benchmark. A weighted bidirectional approach was adopted in the experiments to incorporate the forward and backward predictions of the time series. EKF is a practical, general approach to neural networks training. It consists of the following: 1) gradient calculation by backpropagation through time (BPTT); 2) weight updates based on the extended Kalman filter; and 3) data presentation using multi-stream mechanics.


Time Series Prediction With Recurrent Neural Networks Using A Hybrid Pso-Ea Algorithm, Nian Zhang, Ganesh K. Venayagamoorthy, Donald C. Wunsch, Xindi Cai Jan 2004

Time Series Prediction With Recurrent Neural Networks Using A Hybrid Pso-Ea Algorithm, Nian Zhang, Ganesh K. Venayagamoorthy, Donald C. Wunsch, Xindi Cai

Electrical and Computer Engineering Faculty Research & Creative Works

To predict the 100 missing values from the time series consisting of 5000 data given for the IJCNN 2004 time series prediction competition, we applied an architecture which automates the design of recurrent neural networks using a new evolutionary learning algorithm. This new evolutionary learning algorithm is based on a hybrid of particle swarm optimization (PSO) and evolutionary algorithm (EA). By combining the searching abilities of these two global optimization methods, the evolution of individuals is no longer restricted to be in the same generation, and better performed individuals may produce offspring to replace those with poor performance. The novel …


Laser Welding Control, Y.-S. Huang, Hai-Lung Tsai, P. Turner, P.-C. Wang Jan 2004

Laser Welding Control, Y.-S. Huang, Hai-Lung Tsai, P. Turner, P.-C. Wang

Mechanical and Aerospace Engineering Faculty Research & Creative Works

In laser welding of metallic workpieces, the energetic beam is moved over the workpiece surface to form a pool of molten weld metal that quickly solidifies behind the advance of the laser into a weld nugget. The laser beam produces a keyhole of plasma-containing vapor within the molten pool. Weld nugget porosity, due to entrapment of the vapor, is minimized by continually sensing radiation from the molten metal pool to determine pool depth and width and then controlling laser power and speed to continually produce a weld metal pool wide enough for the liquid to fully expel the vapor and …


Adaptive Load Frequency Control Of Nigerian Hydrothermal System Using Unsupervised And Supervised Learning Neural Networks, Ganesh K. Venayagamoorthy, U. O. Aliyu, S. Y. Musa Jan 2004

Adaptive Load Frequency Control Of Nigerian Hydrothermal System Using Unsupervised And Supervised Learning Neural Networks, Ganesh K. Venayagamoorthy, U. O. Aliyu, S. Y. Musa

Electrical and Computer Engineering Faculty Research & Creative Works

This work presents a novel load frequency control design approach for a two-area power system that relies on unsupervised and supervised learning neural network structure. Central to this approach is the prediction of the load disturbance of each area at every minute interval that is uniquely assigned to a cluster via unsupervised learning process. The controller feedback gains corresponding to each cluster center are determined using modal control technique. Thereafter, supervised learning neural network (SLNN) is employed to learn the mapping between each cluster center and its feedback gains. A real time load disturbance in either or both areas activates …


Enhanced Practical Photosynthetic Co₂ Mitigation, David J. Bayless, Morgan Lefay Vis-Chiasson, Gregory G. Kremer Dec 2003

Enhanced Practical Photosynthetic Co₂ Mitigation, David J. Bayless, Morgan Lefay Vis-Chiasson, Gregory G. Kremer

Mechanical and Aerospace Engineering Faculty Research & Creative Works

This process is unique in photosynthetic carbon sequestration. An on-site biological sequestration system directly decreases the concentration of carbon-containing compounds in the emissions of fossil generation units. In this process, photosynthetic microbes are attached to a growth surface arranged in a containment chamber that is lit by solar photons. A harvesting system ensures maximum organism growth and rate of CO2 uptake. Soluble carbon and nitrogen concentrations delivered to the cyanobacteria are enhanced, further increasing growth rate and carbon utilization.


Superplastic Forming Of Micro Components, Rajiv S. Mishra Dec 2003

Superplastic Forming Of Micro Components, Rajiv S. Mishra

Materials Science and Engineering Faculty Research & Creative Works

A method for forming a miniaturized shaped component. Bulk superplastic material is contacted with a flat rotating surface of a rotating tool to frictionally heat the bulk superplastic material with the bulk superplastic material positioned between the flat rotating surface of the tool and a micro fabricated tool die. The bulk superplastic material is forced into the microfabricated die once the bulk superplastic material is heated to a temperature between a glass transition temperature and a crystallization temperature.


Web Crippling And Combined Bending And Web Crippling Of Cold-Formed Steel Beam Headers, Sutton F. Stephens, Roger A. Laboube Dec 2003

Web Crippling And Combined Bending And Web Crippling Of Cold-Formed Steel Beam Headers, Sutton F. Stephens, Roger A. Laboube

Civil, Architectural and Environmental Engineering Faculty Research & Creative Works

Beam headers are commonly used in walls framed with cold-formed steel studs to span openings in bearing walls. This paper presents the results of an experimental study conducted at the University of Missouri-Rolla to establish the web crippling strength of both box- and I-beam headers for an interior-one-flange (IOF) loading condition. the beam header specimens were tested as a system consisting of two C-sections together with top and bottom track sections. the header configuration used in this study are defined in the Standard for Cold-Formed Steel Framing, Header Design (2000). Tested as a system, it was found that the web …


Viewing The Learning Process: Assessment Via Usability Testing, Vicki M. Eller, Steve Eugene Watkins, Richard H. Hall Dec 2003

Viewing The Learning Process: Assessment Via Usability Testing, Vicki M. Eller, Steve Eugene Watkins, Richard H. Hall

Business and Information Technology Faculty Research & Creative Works

Learning through Computer-Based Activities Provides a Multi-Modal Approach in Which the User Can Select the Educational Media and Process. Effective Development of These Activities Requires an Understanding of User Interactivity. Traditional Assessment, Such as Test Scores and Subjective Surveys, Looks at End Results and Attitudes. This Method Does Not Monitor the Learning Process. in Particular Developer Needs to Accommodate Diverse Usage Preferences and Choices. Hence, Assessment Should Involve Usability Measures that Are Quantitative and Qualitative. Usability Testing Records Usage Patterns and User Reactions. a Usability Laboratory Was Created at the University of Missouri-Rolla. It is Supplements the Traditional Assessment for …


Steel Stud Brick Veneer Design Guide, American Iron And Steel Institute Nov 2003

Steel Stud Brick Veneer Design Guide, American Iron And Steel Institute

American Iron and Steel Institute (AISI) Specifications, Standards, Manuals and Research Reports (1946 - present)

The following Design Guide has been developed under the direction of the American Iron and Steel Institute Committee on Specifications for the Design of Cold- Formed Steel Structural Members. The development of the Guide was sponsored by the American Iron and Steel Institute. The AISI Committee on Specifications wishes to acknowledge and expresses gratitude to Mr. Thomas Trestain of T. W. J. Trestain Structural Engineering who was the author of this Guide.

With anticipated improvements in understanding of the behavior of cold-formed steel and the continuing development of new technology, this material might become dated. It is possible that AISI …


Design And Characterization Of Null Convention Self-Timed Multipliers, Satish K. Bandapati, Scott C. Smith, Minsu Choi Nov 2003

Design And Characterization Of Null Convention Self-Timed Multipliers, Satish K. Bandapati, Scott C. Smith, Minsu Choi

Electrical and Computer Engineering Faculty Research & Creative Works

Self-timed multipliers, designed using the delay-insensitive null convention logic (NCL) paradigm, were analyzed. NCL require less power, generate less noise, produce less electromagnetic interference, and allow easier reuse of components. Simulation results show a large variance in circuit performance in terms of power, area, and speed. NCL paradigm also represent bit-serial, iterative, and fully parallel multiplication architectures. They reduce the effort required to ensure correct operation under all timing scenarios, compared to equivalent synchronous designs.


A Four-Level Crossing Dc/Dc Converter Based Drive System, X. Kou, Keith Corzine Nov 2003

A Four-Level Crossing Dc/Dc Converter Based Drive System, X. Kou, Keith Corzine

Electrical and Computer Engineering Faculty Research & Creative Works

This paper introduces a novel crossing front-end dc/dc converter for a four-level drive system which provides a voltage boost as well as dc capacitor bank voltage regulation. The primary advantage of the proposed converter is that it simplifies the control of the four-level diode-clamped inverter since capacitor voltage balancing is not required by the inverter control. Furthermore, the inverter modulation index can be varied up to its physical limitation. An average-value model of the converter is derived and used for insight and analysis of the converter operation. Detailed simulations of the four-level drive system demonstrate the effectiveness of the proposed …


Melanoma And Seborrheic Keratosis Differentiation Using Texture Features, Srinivas V. Deshabhoina, Scott E. Umbaugh, William V. Stoecker, Randy Hays Moss, Subhashini K. Srinivasan Nov 2003

Melanoma And Seborrheic Keratosis Differentiation Using Texture Features, Srinivas V. Deshabhoina, Scott E. Umbaugh, William V. Stoecker, Randy Hays Moss, Subhashini K. Srinivasan

Chemistry Faculty Research & Creative Works

Purpose: To explore texture features in two-dimensional images to differentiate seborrheic keratosis from melanoma.

Methods: A systematic approach to consistent classification of skin tumors is described. Texture features, based on the second-order histogram, were used to identify the features or a combination of features that could consistently differentiate a malignant skin tumor (melanoma) from a benign one (seborrheic keratosis). Two hundred and seventy-one skin tumor images were separated into training and test sets for accuracy and consistency. Automatic induction was applied to generate classification rules. Data analysis and modeling tools were used to gain further insight into the feature space. …


Kinetics Of Wet Air Oxidation Of Phenol Over A Novel Catalyst, Jing Guo, Muthanna H. Al-Dahhan Oct 2003

Kinetics Of Wet Air Oxidation Of Phenol Over A Novel Catalyst, Jing Guo, Muthanna H. Al-Dahhan

Chemical and Biochemical Engineering Faculty Research & Creative Works

The Wet Air Oxidation Kinetics of an Aqueous Solution of Phenol Was Studied over Extrudates of an Al-Fe Pillared Clay Catalyst in the Temperature Range of 90-150°C and Air Pressure Range of 0.8-2.5 MPa. the Variables Studied Included Reaction Temperature, Air Pressure, Solution PH, Initial Phenol Concentration, and Catalyst Loading. the Obtained Findings Are Compared with Those Obtained using Hydrogen Peroxide Oxidation. a Group of Kinetic Models Considering Both the Power-Law and Langmuir-Hinshelwood Approaches Was Evaluated to Describe the Catalytic Kinetics of the Phenol Disappearance. the Nonlinear Dependence of the Phenol Conversion Rate on the Catalyst Concentration Was Taken into …


Computation Of Effectiveness Factors For Partially Wetted Catalyst Pellets Using The Method Of Fundamental Solution, E. Palmisano, P. A. Ramachandran, K. Balakrishnan, M. (Muthanna) H. Al-Dahhan Oct 2003

Computation Of Effectiveness Factors For Partially Wetted Catalyst Pellets Using The Method Of Fundamental Solution, E. Palmisano, P. A. Ramachandran, K. Balakrishnan, M. (Muthanna) H. Al-Dahhan

Chemical and Biochemical Engineering Faculty Research & Creative Works

Trickle Bed Reactors Are Widely Used in Many Process Industries. the Catalyst Particles Are Often Incompletely Wetted Especially in the Trickling Flow Regime and Hence to Design These Reactors, the Effectiveness Factor of Partially Wetted Catalyst Needs to Be Calculated Accurately. Numerical Solutions by Traditional Methods Are Time Consuming and Not Very Accurate, Especially for Some Commonly Used Complex Catalyst Shapes Such as Trilobes, Quadrilobes Etc. the Paper Presents a Novel Numerical Solution for These Problems based on the Method of Fundamental Solutions. the Advantage of the Method is that It Involves Only Boundary Collocation and Can Be Applied to …


Preliminary Work On The Antibacterial Effect Of Strontium In Glass Ionomer Cements, A. Guida, Mark R. Towler, J. G. Wall, R. G. Hill, S. Eramo Oct 2003

Preliminary Work On The Antibacterial Effect Of Strontium In Glass Ionomer Cements, A. Guida, Mark R. Towler, J. G. Wall, R. G. Hill, S. Eramo

Chemical and Biochemical Engineering Faculty Research & Creative Works

The antibacterial effect of strontium in glass ionomer cements (GIC) was discussed. The glass transition temperatures were found to decrease with the increasing fluorine content consistent with the fluorine replacing bridging oxygens. However no significant correlation was found between the fluoride release and the antibacterial activity.


Detection Of Weak Transitions In Signal Dynamics Using Recurrence Time Statistics, J. B. Gao, Yinhe Cao, Lingyun Gu, J. G. Harris, J. C. Principe Oct 2003

Detection Of Weak Transitions In Signal Dynamics Using Recurrence Time Statistics, J. B. Gao, Yinhe Cao, Lingyun Gu, J. G. Harris, J. C. Principe

Electrical and Computer Engineering Faculty Research & Creative Works

Signal detection in noisy and nonstationary environments is very challenging. In this Letter, we study why the two types of recurrence times [Phys. Rev. Lett. 83 (1999) 3178] may be very useful for detecting weak transitions in signal dynamics. We particularly emphasize that the recurrence times of the second type may be more powerful in detecting transitions with very low energy. These features are illustrated by studying a number of speech signals with fricatives and plosives. We have also shown that the recurrence times of the first type, nevertheless, has the distinguished feature of being more robust to the noise …


Commentary On The Specifications For The Design, Testing, And Utilization Of Industrial Steel Storage Racks, Rack Manufacturers Institute Oct 2003

Commentary On The Specifications For The Design, Testing, And Utilization Of Industrial Steel Storage Racks, Rack Manufacturers Institute

Rack Manufacturers Institute (RMI) Specifications and Manuals (1984 - 2012)

No abstract provided.


Configuration For Micro Ph Sensor, Young-Jin Kim, Young-Chul Lee, Byung-Ki Sohn, Chang-Soo Kim, Jung-Hee Lee Oct 2003

Configuration For Micro Ph Sensor, Young-Jin Kim, Young-Chul Lee, Byung-Ki Sohn, Chang-Soo Kim, Jung-Hee Lee

Electrical and Computer Engineering Faculty Research & Creative Works

A fully integrated pH sensor with a built-in reference electrode is proposed. An iridium oxide microelectrode and a pH-insensitive field-effect transistor are used as a pH sensor and a reference electrode, respectively. The sensitivity of the proposed device matches well with the estimated value to within 0.3 mV/pH deviation.


Resolution Of Multiple Ssdna Structures In Free Solution Electrophoresis, Eve F. Fabrizio, Ali Nadim, James D. Sterling Oct 2003

Resolution Of Multiple Ssdna Structures In Free Solution Electrophoresis, Eve F. Fabrizio, Ali Nadim, James D. Sterling

Business and Information Technology Faculty Research & Creative Works

By using high concentrations of buffer, electroosmotic flow within uncoated channels of a microfluidic chip was minimized, allowing the free solution electrophoretic separation of DNA. More importantly, because of the ability to efficiently dissipate heat within these channels, field strengths as high as 600 V/cm could be applied with minimal Joule heating (< 2 °C). As a result of the higher field strengths, separations within an 8-cm-long channel were achieved within a few minutes. However, when the electrophoretic separation of single-stranded DNA (ssDNA) less than 22 bases in length was performed, containing the fluorophore Texas Red as an end label, more than the expected single peak was observed at this high electric field. On the other hand, the free solution electrophoresis of a double-stranded DNA (dsDNA) consisting of a random sequence did exhibit the expected single peak. The appearance of these multiple peaks for ssDNA is shown to be dependent upon the base content and sequence of the ssDNA as well as on the chemical structure of the fluorophore used to tag the DNA for detection. Specifically, the peaks can be attributed to different secondary structures that result either from hydrophobic interactions between the DNA bases and an uncharged fluorescent dye or from G-quadruplexes within guanine-rich strands.


Characterizing Debris Clouds Created In Oblique Orbital Debris Particle Impact, D. Depczuk, William P. Schonberg Oct 2003

Characterizing Debris Clouds Created In Oblique Orbital Debris Particle Impact, D. Depczuk, William P. Schonberg

Civil, Architectural and Environmental Engineering Faculty Research & Creative Works

The problem of pollution within Earth's orbital environment has gained considerable recognition over the past decades. Determining adequate passive protection schemes is an unending process that attempts to meet different objectives for widely varying types of missions. Significant amounts of resources have been expended toward development of numerical and analytical models that model the response of a variety of target systems under high-speed orbital debris impacts. the objective of the study whose results are presented herein was to improve upon an existing oblique hypervelocity impact model that characterizes the various secondary debris clouds created in such an impact. This was …


Modeling And Analysis Of Fault Tolerant Multistage Interconnection Networks, Minsu Choi, Nohpill Park, Fabrizio Lombardi Oct 2003

Modeling And Analysis Of Fault Tolerant Multistage Interconnection Networks, Minsu Choi, Nohpill Park, Fabrizio Lombardi

Electrical and Computer Engineering Faculty Research & Creative Works

Performance and reliability are two of the most crucial issues in today's high-performance instrumentation and measurement systems. High speed and compact density multistage interconnection networks (MINs) are widely-used subsystems in different applications. New performance models are proposed to evaluate a novel fault tolerant MIN arrangement, thereby assuring performance and reliability with high confidence level. A concurrent fault detection and recovery scheme for MINs is considered by rerouting over redundant interconnection links under stringent real-time constraints for digital instrumentation as sensor networks. A switch architecture for concurrent testing and diagnosis is proposed. New performance models are developed and used to evaluate …


Electromagnetic Compatibility Issues In Mobile Computing, Antonio Orlandi, James L. Drewniak Oct 2003

Electromagnetic Compatibility Issues In Mobile Computing, Antonio Orlandi, James L. Drewniak

Electrical and Computer Engineering Faculty Research & Creative Works

No abstract provided.


Statistical Approach To The Emi Modeling Of Large Asics By A Single Noise-Current Source, Giulio Antonini, James L. Drewniak, Marco Leone, Antonio Orlandi, Vittorio Ricchiuti Oct 2003

Statistical Approach To The Emi Modeling Of Large Asics By A Single Noise-Current Source, Giulio Antonini, James L. Drewniak, Marco Leone, Antonio Orlandi, Vittorio Ricchiuti

Electrical and Computer Engineering Faculty Research & Creative Works

Large and complex ASICs are source of propagating noise inside the powerbus planes. A lumped noise source model is proposed and validated by means of a statistics based method.


Suitability Of Pulse Train™, A Novel Digitally Implemented Real-Time Control Technique, For Bifred Converter, Mehdi Ferdowsi, Ali Emadi, Mark Telefus, Anatoly Shteynberg Oct 2003

Suitability Of Pulse Train™, A Novel Digitally Implemented Real-Time Control Technique, For Bifred Converter, Mehdi Ferdowsi, Ali Emadi, Mark Telefus, Anatoly Shteynberg

Electrical and Computer Engineering Faculty Research & Creative Works

Pulse TrainTM, a new control scheme, is presented and applied to a BIFRED converter operating in discontinuous conduction mode (DCM), which avoids the light-load high-voltage stress problem. In contrast to the conventional control techniques, the principal idea of Pulse Train is to regulate the output voltage using a series of high and low energy pulses generated by the current of the inductor. In this paper, applicability of the proposed technique to both the input and magnetizing inductances of BIFRED converter is investigated. Analysis of BIFRED converter operating in DCM as well as the output voltage ripple estimation are …


Self-Consistent Modification To The Electron Density Of States Due To Electron-Phonon Coupling In Metals, Fatih Dogan, Frank Marsiglio Oct 2003

Self-Consistent Modification To The Electron Density Of States Due To Electron-Phonon Coupling In Metals, Fatih Dogan, Frank Marsiglio

Materials Science and Engineering Faculty Research & Creative Works

The "standard" theory of a normal metal consists of an effective electron band which interacts with phonons and impurities. The effects due to the electron-phonon interaction are often delineated within the Migdal approximation; the properties of many simple metals are reasonably well described with such a description. On the other hand, if the electron-phonon interaction is sufficiently strong, a polaron approach is more appropriate. The purpose of this paper is to examine to what degree the Migdal approximation is self-consistent, as the coupling strength increases. We find that changes in the electron density of states become significant for very large …