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Design Of A Frequency-Selective Surface Strain Sensor, Edward C. Kinzel Sep 2014

Design Of A Frequency-Selective Surface Strain Sensor, Edward C. Kinzel

Mechanical and Aerospace Engineering Faculty Research & Creative Works

Frequency Selective Surfaces (FSS) have long been used in the RF/microwave community to control radar cross-section. The scattering parameters of the FSS form a signature which is a function of the frequency, element size and spacing, as well as the local electromagnetic environment. This paper considers a FSS as a strain sensor on the surface of a structural element. By interrogating the FSS with a series of polarized far-field measurements in a bistatic configuration the biaxial plane strain, including shear, can be resolved.

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Calderón Preconditioned Pmchwt Equation For Layered Medium Problems, Yongpin P. Chen, Lijun Jiang, Sheng Sun, Weng Cho Chew Sep 2014

Calderón Preconditioned Pmchwt Equation For Layered Medium Problems, Yongpin P. Chen, Lijun Jiang, Sheng Sun, Weng Cho Chew

Electrical and Computer Engineering Faculty Research & Creative Works

Electromagnetic scattering by dielectric objects in the presence of a layered medium is investigated by applying the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equation combined with the layered medium Green's function. Due to the electric field integral equation (EFIE) operator involved, the spectrum of the PMCHWT equation is also undesired. When the surface is densely discretized, the condition of the resulting matrix is extremely bad. An effective Calderón preconditioner is developed in this paper to improve the convergence. Different from its free space counterpart, the Calderón identities for inhomogeneous medium need to be re-derived. It is shown from numerical examples that the convergence of …

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Differential Forms Inspired Finite Element Discretization For Waveguide Eigenvalue Problems, Qi I. Dai, Weng Cho Chew, Lijun Jiang Sep 2014

Differential Forms Inspired Finite Element Discretization For Waveguide Eigenvalue Problems, Qi I. Dai, Weng Cho Chew, Lijun Jiang

Electrical and Computer Engineering Faculty Research & Creative Works

A differential forms inspired finite element based discretization scheme for waveguide eigenvalue problems is presented. Naïve discretization of the governing variational expression involving only transverse fields with edge elements renders the discretized eigen-equation unsolvable. Motivated by differential forms, in the proposed scheme, electric and magnetic fields are discretized with curl-conforming basis functions on the primal and dual grids, respectively. Meanwhile, magnetic flux density and electric displacement fields are discretized with divergence-conforming basis functions on the primal and dual grids, respectively. Matrices in the resultant eigen-equation is well-conditioned and easy to solve, which is validated by several numerical examples.

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The Missouri Miner, September 18, 2014 Sep 2014

The Missouri Miner, September 18, 2014

The Missouri Miner Newspaper

No abstract provided.

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The Contour Deformation Method For Calculating The High Frequency Scattered Fields By The Fock Current On The Surface Of The 3-D Convex Cylinder, Yu Mao Wu, Li (Lijun) Jun Jiang, Weng Cho Chew Sep 2014

The Contour Deformation Method For Calculating The High Frequency Scattered Fields By The Fock Current On The Surface Of The 3-D Convex Cylinder, Yu Mao Wu, Li (Lijun) Jun Jiang, Weng Cho Chew

Electrical and Computer Engineering Faculty Research & Creative Works

In this work, the Fock currents on the convex cylinders are comprehensively studied. The contour deformation method is invoked to calculate the highly oscillatory Fock currents. The computational process is frequency independent in workload. Then, quadratic phase approximation is proposed to efficiently solve the highly oscillatory scattered field. Numerical results for the high frequency scattered far fields on the convex cylinders are given to validate the efficiency of the proposed method. Furthermore, the contour deformation method for computing the Fock currents offers a clear high frequency wave physical picture.

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Linearly Polarized Near Field Focused Slot-Array Waveguide, Meng Lin Chen, Shulabh Gupta, Zi Long Ma, Li (Lijun) Jun Jiang Sep 2014

Linearly Polarized Near Field Focused Slot-Array Waveguide, Meng Lin Chen, Shulabh Gupta, Zi Long Ma, Li (Lijun) Jun Jiang

Electrical and Computer Engineering Faculty Research & Creative Works

A 2-D slot array structure to achieve near-field beam focusing, with a linear polarization, is proposed and demonstrated using full-wave simulations. The proposed structure has a negligible cross-polarization and its far-field gain is lower by 10 dB compared to the non-focus case, indicating a good focusing in the near-field of the structure.

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Applying Cem Techniques To Solve Nano-Scale Quantum Transport Problems, Jun Z. Huang, Weng Cho Chew, Li (Lijun) Jun Jiang Sep 2014

Applying Cem Techniques To Solve Nano-Scale Quantum Transport Problems, Jun Z. Huang, Weng Cho Chew, Li (Lijun) Jun Jiang

Electrical and Computer Engineering Faculty Research & Creative Works

Two widely used algorithms in computational electromagnetics (CEM) society, namely the asymptotic waveform evaluation (AWE) technique and the model order reduction (MOR) mode matching method, are employed to calculate electron wave propagation in novel nanoelectronic devices.

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Improved Field Projection In Equivalence Principle Algorithm With Rotated Cwbc Basis, Zu Hui Ma, Sheng Sun, Lijun Jiang, Weng Cho Chew, Mao Kun Li Sep 2014

Improved Field Projection In Equivalence Principle Algorithm With Rotated Cwbc Basis, Zu Hui Ma, Sheng Sun, Lijun Jiang, Weng Cho Chew, Mao Kun Li

Electrical and Computer Engineering Faculty Research & Creative Works

In this paper, a dual-basis testing method is utilized to enhance the field projection in the equivalence principle algorithm (EPA). Due to the presence of identity operators in the EPA formulation, the near-field calculation is less accurate with field projection errors. This issue can be effectively remedied by using the recently proposed dual-basis function of Rao-Wilton-Glisson basis function, named as rotated Chen-Wilton-Buffa-Christiansen basis function. Numerical result shows the validity of the proposed method.

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A Discontinuous Galerkin Time Domain-Boundary Integral Method For Analyzing Transient Electromagnetic Scattering, Ping Li, Li (Lijun) Jun Jiang, Yifei Shi, Hakan Bagci Sep 2014

A Discontinuous Galerkin Time Domain-Boundary Integral Method For Analyzing Transient Electromagnetic Scattering, Ping Li, Li (Lijun) Jun Jiang, Yifei Shi, Hakan Bagci

Electrical and Computer Engineering Faculty Research & Creative Works

This paper presents an algorithm hybridizing discontinuous Galerkin time domain (DGTD) method and time domain boundary integral (BI) algorithm for 3-D open region electromagnetic scattering analysis. The computational domain of DGTD is rigorously truncated by analytically evaluating the incoming numerical flux from the outside of the truncation boundary through BI method based on the Huygens' principle. The advantages of the proposed method are that it allows the truncation boundary to be conformal to arbitrary (convex/ concave) scattering objects, well-separated scatters can be truncated by their local meshes without losing the physics (such as coupling/multiple scattering) of the problem, thus reducing …

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Second-Harmonic Generation In Metal Nanoparticles Modeling By Surface Integral Equation, Xiaoyan Y.Z. Xiong, Li (Lijun) Jun Jiang, Yat Hei Lo, Weng Cho Chew Sep 2014

Second-Harmonic Generation In Metal Nanoparticles Modeling By Surface Integral Equation, Xiaoyan Y.Z. Xiong, Li (Lijun) Jun Jiang, Yat Hei Lo, Weng Cho Chew

Electrical and Computer Engineering Faculty Research & Creative Works

Metals are centrosymmetric materials which only posse local surface second-harmonic (SH) nonlinearities due to the symmetry broken at the surface. In this work the surface integral equation (SIE) is used for evaluating SH radiation generated from metal nanoparticles with arbitrary shapes. The whole SIE system is solved by employing the Galerkin testing procedure and Rao-Wilton-Gillson (RWG) basis functions. The mutual coupling between fundamental and second harmonic field is captured. The method is validated by comparisons with the analytic SH-Mie solution. This method paves the way for accurate and efficient design of general SH nonlinear nanoplasmonic structures.

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"Green" On-Chip Inductors In Three-Dimensional Integrated Circuits, Umamaheswara Rao Tida, Varun Mittapalli, Cheng Zhuo, Yiyu Shi Sep 2014

"Green" On-Chip Inductors In Three-Dimensional Integrated Circuits, Umamaheswara Rao Tida, Varun Mittapalli, Cheng Zhuo, Yiyu Shi

Electrical and Computer Engineering Faculty Research & Creative Works

Through-silicon-vias (TSVs) are the enabling technique for three-dimensional integrated circuits (3D ICs). However, their large area significantly reduces the benefits that can be obtained by 3D ICs. On the other hand, a major limiting factor for the implementation of many on-chip circuits such as DC-DC converters and resonant clocking is the large area overhead induced by spiral inductors. Several works have been proposed in the literature to make inductors out of idle TSVs. In this paper, we will demonstrate the effectiveness of such TSV inductors in addressing both challenges. Experimental results show that by replacing conventional spiral inductors with TSV …

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Quantification Of Information Flow In A Smart Grid, Li Feng, Bruce Mcmillin Sep 2014

Quantification Of Information Flow In A Smart Grid, Li Feng, Bruce Mcmillin

Computer Science Faculty Research & Creative Works

The key to computer security is the notion of information flow. Information flow occurs either explicitly or implicitly in a system. In cyber-physical systems (CPSs), complicated interactions occur frequently between computational components and physical components. Thus, detecting and quantifying information flow in these systems is more difficult than it is in purely cyber systems. In CPSs, failures and attacks are either from the physical infrastructure, or from cyber part of data management and communication protocol, or a combination of both. As the physical infrastructure is inherently observable, aggregated physical observations can lead to unintended cyber information leakage. The computational portion …

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Augmented Equivalence Principle Algorithm For Domain Decomposition Method For Low Frequency Scattering, Circuits, And Casimir Force Calculations, P. R. Atkins, Z. H. Ma, L. E. Sun, M. K. Li, L. (Lijun) J. Jiang, M. S. Tong, W. C. Chew Sep 2014

Augmented Equivalence Principle Algorithm For Domain Decomposition Method For Low Frequency Scattering, Circuits, And Casimir Force Calculations, P. R. Atkins, Z. H. Ma, L. E. Sun, M. K. Li, L. (Lijun) J. Jiang, M. S. Tong, W. C. Chew

Electrical and Computer Engineering Faculty Research & Creative Works

A broadband integral-equation-based domain decomposition method (DDM) using augmented equivalence principle algorithm (A-EPA) is introduced for solving large scale electromagnetic scattering, circuits, and Casimir force problems. The root cause of the low frequency breakdown problem of EPA algorithm without augmentation technique is analyzed. Numerical examples validate the method for various applications in scattering, circuits, and Casimir force calculations.

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An Ibc Enhanced Dgtd Scheme For Transient Analysis Of Em Interactions With Graphene, Ping Li, Li (Lijun) Jun Jiang, Hakan Baʇci Sep 2014

An Ibc Enhanced Dgtd Scheme For Transient Analysis Of Em Interactions With Graphene, Ping Li, Li (Lijun) Jun Jiang, Hakan Baʇci

Electrical and Computer Engineering Faculty Research & Creative Works

A discontinuous Galerkin time-domain (DGTD) method is proposed for analyzing electromagnetic field interactions on graphene from microwave to terahertz frequencies. An impedance boundary condition (IBC) is utilized to model the graphene within the DGTD framework. The numerical flux is reformulated to take into account the IBC. Highly dispersive surface conductivity of graphene present in the resulting flux expression is approximated in terms of rational functions using the fast-relaxation vector-fitting technique. Via inverse Laplace transform, this facilitates the time domain matrix equations into an integral form for time variable t, finite integral technique (FIT) with recursive convolution method is employed to …

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Analysis Of Scattering By Pec Objects In Layered Medium With Calderón Preconditioner, Yongpin P. Chen, Min Meng, Sheng Sun, Lijun Jiang, Weng Cho Chew Sep 2014

Analysis Of Scattering By Pec Objects In Layered Medium With Calderón Preconditioner, Yongpin P. Chen, Min Meng, Sheng Sun, Lijun Jiang, Weng Cho Chew

Electrical and Computer Engineering Faculty Research & Creative Works

Electromagnetic scattering by perfect electrically conducting (PEC) objects in a layered medium is studied in this paper. The layered medium Green's function is adopted as the kernel of the electric field integral equation (EFIE) so that the effects from the multilayered background can be accounted for automatically. However, the spectrum of the EFIE with this kernel, is unfortunately undesirable. This leads to slow convergence of the iterative solution. To improve the convergence, the Calderón identities are derived and leveraged to precondition the EFIE. By utilizing Buffa-Christiansen (BC) basis function in discretizing the preconditioning operator, the preconditioner can be made completely …

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Reduced-Permittivity Meandered Single-Beam Full-Space Scanning Phase-Reversal Leaky-Wave Antenna, Shulabh Gupta, Li (Lijun) Jun Jiang, Christophe Caloz Sep 2014

Reduced-Permittivity Meandered Single-Beam Full-Space Scanning Phase-Reversal Leaky-Wave Antenna, Shulabh Gupta, Li (Lijun) Jun Jiang, Christophe Caloz

Electrical and Computer Engineering Faculty Research & Creative Works

A meandered version of the phase-reversal leaky-wave antenna is introduced to reduce the permittivity requirement εeff > 4 for single-beam full-space scanning.

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Phytomonitoring Of Chlorinated Ethenes In Trees: A Four-Year Study Of Seasonal Chemodynamics In Planta, Matt A. Limmer, Amanda J. Holmes, Joel Gerard Burken Sep 2014

Phytomonitoring Of Chlorinated Ethenes In Trees: A Four-Year Study Of Seasonal Chemodynamics In Planta, Matt A. Limmer, Amanda J. Holmes, Joel Gerard Burken

Civil, Architectural and Environmental Engineering Faculty Research & Creative Works

Long-Term Monitoring (LTM) of Groundwater Remedial Projects is Costly and Time-Consuming, Particularly When using Phytoremediation, a Long-Term Remedial Approach. the Use of Trees as Sensors of Groundwater Contamination (I.e., Phytoscreening) Has Been Widely Described, Although the Use of Trees to Provide Long-Term Monitoring of Such Plumes (Phytomonitoring) Has Been More Limited Due to Unexplained Variability of Contaminant Concentrations in Trees. to Assess This Variability, We Developed an in Planta Sampling Method to Obtain High-Frequency Measurements of Chlorinated Ethenes in Oak (Quercus Rubra) and Baldcypress (Taxodium Distichum) Trees Growing above a Contaminated Plume during a 4-Year Trial. the Data Set Revealed …

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Uncertainty Quantification Of Em-Circuit Systems Using Stochastic Polynomial Chaos Method, Ping Li, Li (Lijun) Jun Jiang Sep 2014

Uncertainty Quantification Of Em-Circuit Systems Using Stochastic Polynomial Chaos Method, Ping Li, Li (Lijun) Jun Jiang

Electrical and Computer Engineering Faculty Research & Creative Works

Uncertainties in realistic lumped and distributive circuit systems are of great importance to today's high yield manufacture demand. However, evaluating the stochastic effect in the time domain for the hybrid electromagnetics (EM)-circuit system was seldom done, especially when Monte Carlo is too expensive to be feasible. In this work, an adaptive hierarchical sparse grid collocation (ASGC) method is presented to quantify the impacts of stochastic inputs on hybrid electromagnetics (EM)-circuit or EM scattering systems. The ASGC method approximates the stochastic observables of interest using interpolation functions over series collocation points. Instead of employing a full-tensor product sense, the collocation points …

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Effective Roughness Dielectric In A Pcb: Measurement And Full-Wave Simulation Verification, Tracey Vincent, Marina Koledintseva, Antonio Ciccomancini, Scott Hinaga Sep 2014

Effective Roughness Dielectric In A Pcb: Measurement And Full-Wave Simulation Verification, Tracey Vincent, Marina Koledintseva, Antonio Ciccomancini, Scott Hinaga

Electrical and Computer Engineering Faculty Research & Creative Works

Surface roughness topography of printed circuit boards (PCBs) needs to be included in SI simulations in order to accurately predict the insertion loss of the structure. An effective roughness dielectric (ERD) model can be used to substitute an inhomogeneous interface between copper foil and laminate dielectric in a PCB. Herein, this approach is tested for verification using 3D full-wave numerical simulations. These effective roughness dielectric layers with the appropriate complex permittivity are included in the modeling of strip line examples. The parameters of an ambient laminate dielectric free of conductor roughness effects in the strip line are determined using differential …

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Efficient Caching And Incrementalization Of Object Queries On Collections In Programming Codes, Venkata Krishna Suhas Nerella, Sanjay Madria, Thomas Weigert Sep 2014

Efficient Caching And Incrementalization Of Object Queries On Collections In Programming Codes, Venkata Krishna Suhas Nerella, Sanjay Madria, Thomas Weigert

Computer Science Faculty Research & Creative Works

Object oriented programming languages raised the level of abstraction by incorporating first class query constructs explicitly into program codes. These query constructs allow programmers to express operations over collections as object queries. They also provide optimal query execution, utilizing query optimization strategies from the database domain. However, when a query is repeated in the program, it is executed as a new query. Existing approaches, however, such as Java Query Language (JQL), which caches such query constructs on collections have high run time overhead. Therefore, this paper presents an approach to reduce the run time execution of programs involving explicit queries …

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Effect Of Placement Characteristics On Scc Lateral Pressure Variations, A. F. Omran, Y. M. Elaguab, Kamal Khayat Sep 2014

Effect Of Placement Characteristics On Scc Lateral Pressure Variations, A. F. Omran, Y. M. Elaguab, Kamal Khayat

Civil, Architectural and Environmental Engineering Faculty Research & Creative Works

Lateral pressure exerted by fresh concrete on vertical formwork systems controls significantly the design of the formwork systems. Several factors including, material properties, placement conditions, and formwork characteristics can affect formwork lateral pressure. This paper presents the results of an extensive experimental work aimed at studying the influence of concrete temperature (10-32 °C), casting depth (up to 13 m), placement rate (2-30 m/h), waiting period between successive lifts, as well as concrete thixotropy on lateral pressure characteristics. The increase of concrete temperature is shown to accelerate the stiffening rate of the concrete leading to reduction in initial lateral pressure. For …

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The Missouri Miner, September 11, 2014 Sep 2014

The Missouri Miner, September 11, 2014

The Missouri Miner Newspaper

No abstract provided.

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Variable Selection For Regression Problems Using Gaussian Mixture Models To Estimate Mutual Information, Emil Eirola, Amaury Lendasse, Juha Karhunen Sep 2014

Variable Selection For Regression Problems Using Gaussian Mixture Models To Estimate Mutual Information, Emil Eirola, Amaury Lendasse, Juha Karhunen

Engineering Management and Systems Engineering Faculty Research & Creative Works

Variable Selection is a Crucial Part of Building Regression Models and is Preferably Done as a Filtering Method Independently from the Model Training. Mutual Information is a Popular Relevance Criterion for This, But It is Not Trivial to Estimate Accurately from a Limited Amount of Data. in This Paper, a Method is Presented Where a Gaussian Mixture Model is Used to Estimate the Joint Density of the Input and Output Variables, and Subsequently Used to Select the Most Relevant Variables by Maximizing the Mutual Information Which Can Be Estimated using the Model.

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Finite Horizon Stochastic Optimal Control Of Nonlinear Two-Player Zero-Sum Games Under Communication Constraint, Hao Xu, S. Jagannathan Sep 2014

Finite Horizon Stochastic Optimal Control Of Nonlinear Two-Player Zero-Sum Games Under Communication Constraint, Hao Xu, S. Jagannathan

Electrical and Computer Engineering Faculty Research & Creative Works

In this paper, the finite horizon stochastic optimal control of nonlinear two-player zero-sum games, referred to as Nonlinear Networked Control Systems (NNCS) two-player zero-sum game, between control and disturbance input players in the presence of unknown system dynamics and a communication network with delays and packet losses is addressed by using neuro dynamic programming (NDP). The overall objective being to find the optimal control input while maximizing the disturbance attenuation. First, a novel online neural network (NN) identifier is introduced to estimate the unknown control and disturbance coefficient matrices which are needed in the generation of optimal control input. Then, …

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The Delta Test: The 1-Nn Estimator As A Feature Selection Criterion, Emil Eirola, Amaury Lendasse, Francesco Corona, Michel Verleysen Sep 2014

The Delta Test: The 1-Nn Estimator As A Feature Selection Criterion, Emil Eirola, Amaury Lendasse, Francesco Corona, Michel Verleysen

Engineering Management and Systems Engineering Faculty Research & Creative Works

Feature Selection is Essential in Many Machines Learning Problem, But It is Often Not Clear on Which Grounds Variables Should Be Included or Excluded. This Paper Shows that the Mean Squared Leave-One-Out Error of the First Nearest-Neighbour Estimator is Effective as a Cost Function When Selecting Input Variables for Regression Tasks. a Theoretical Analysis of the Estimator's Properties is Presented to Support its Use for Feature Selection. an Experimental Comparison to Alternative Selection Criteria (Including Mutual Information, Least Angle Regression, and the Rrelieff Algorithm) Demonstrates Reliable Performance on Several Regression Tasks.

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A Generalized Proportionate Adaptive Algorithm Based On Convex Optimization, Jianming Liu, Steven L. Grant Sep 2014

A Generalized Proportionate Adaptive Algorithm Based On Convex Optimization, Jianming Liu, Steven L. Grant

Electrical and Computer Engineering Faculty Research & Creative Works

A general framework is proposed to derive proportionate adaptive algorithms for sparse system identification. The proposed algorithmic framework employs the convex optimization and covers many traditional proportionate algorithms. Meanwhile, based on this framework, some novel proportionate algorithms could be derived too. In the simulations, we compare the new derived proportionate algorithm with the traditional ones and demonstrate that it could provide faster convergence rate and tracking performance for both white and colored input in sparse system identification.

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Near Optimal Event-Based Control Of Nonlinear Discrete Time Systems In Affine Form With Measured Input And Output Data, Avimanyu Sahoo, Hao Xu, S. Jagannathan Sep 2014

Near Optimal Event-Based Control Of Nonlinear Discrete Time Systems In Affine Form With Measured Input And Output Data, Avimanyu Sahoo, Hao Xu, S. Jagannathan

Electrical and Computer Engineering Faculty Research & Creative Works

In this paper, an event-based near optimal control of uncertain nonlinear discrete time systems is presented by using input-output data and approximate dynamic programming (ADP). The nonlinear system dynamics in affine form are transformed into an input-output form. Then, three neural networks (NN) with event sampled input-output vector are used, namely, the identifier NN to relax the knowledge of the system dynamics, a critic NN to approximate the value function which is the solution to the Hamilton-Jacobi Bellman (HJB) equation, and an actor NN to approximate the optimal control policy, in an online manner without utilizing value or policy iterations. …

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Coherent-State Path Integrals In The Continuum, G. Kordas, Simeon I. Mistakidis, A. I. Karanikas Sep 2014

Coherent-State Path Integrals In The Continuum, G. Kordas, Simeon I. Mistakidis, A. I. Karanikas

Physics Faculty Research & Creative Works

We Discuss The Time Continuous Path Integration In The Coherent-State Basis In A Way That Is Free From Inconsistencies. Employing This Notion We Reproduce Known And Exact Results Working Directly In The Continuum. Such A Formalism Can Set The Basis To Develop Perturbative And Nonperturbative Approximations Already Known In The Quantum-Field-Theory Community. These Techniques Can Be Proven Useful In A Great Variety Of Problems Where Bosonic Hamiltonians Are Used.

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Interaction Of Positronium With Helium Atoms - The Classical Treatment Of The 5-Body Collision System, Károly Tokési, Robert D. Dubois, Takeshi Mukoyama Sep 2014

Interaction Of Positronium With Helium Atoms - The Classical Treatment Of The 5-Body Collision System, Károly Tokési, Robert D. Dubois, Takeshi Mukoyama

Physics Faculty Research & Creative Works

The interaction between positronium and a helium atom is studied using the 5-body classical trajectory Monte Carlo method. We present the total cross sections for the dominant channels, namely for single ionization of the target, and ionization of the projectile, resulting from pure ionization and also from electron transfer (capture or loss) processes for 1-5.7 a.u. incident velocities of the positronium atom. Our results were compared with the calculated data using hydrogen projectiles having the same velocities as well as with the experimental data in collisions between H and He [R.D. DuBois, Á. Kövér, Phys. Rev. A 40, 3605 (1989)]. …

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On Second Order Elliptic Equations And Variational Inequalities With Anisotropic Principal Operators, Vy Khoi Le Sep 2014

On Second Order Elliptic Equations And Variational Inequalities With Anisotropic Principal Operators, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

This paper is about boundary value problems of the form where ƨ is a convex function of ξ.∈ RN rather than a function of the norm|ξ|. The problem is formulated appropriately in an anisotropic Orlicz-Sobolev space associated with ƨ. We study the existence of solutions and some other properties of the above problem and its corresponding variational inequality in such space.

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