A local implicit function theorem and application to systems of differential equations

A local implicit function theorem is proved which assumes certain injectivity rather than differentiability. Moreover, there is given a result on solvability of noncanonic systems of differential equations which arise in optimal control and network theory.     

Calculation of quasi-static electromechanical coupling coefficientsfor electrostrictive ceramic materials

The quasi-static coupling coefficients, k₁₃ and k₃₃, for electrostrictive ceramics are computed analytically. The calculation is based on a three-dimensional constitutive relation that models both electrostriction and nonlinear dielectric behaviors. The results show that the coupling factors depend on the amplitudes of the applied ac field and the dc bias, as well as the mechanical prestress. For an actuator without bias voltage or prestress, the coupling coefficients approach an asymptotic value with increasing electric field. The primary coefficients, k₁₃ and k₃₃ , for a lead magnesium niobate, Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃BaTiO ₃(PMN-PT-BT), based relaxor ferroelectric are computed as an example. The results show that the coupling coefficients for PMN-PT-BT materials are roughly comparable with those of existing piezoelectrics. These coefficients are important parameters for material section and power source design for transducer devices     

Towards mechanical metamathematics

Metamathematics is a source of many interesting theorems and difficult proofs. This paper reports the results of an experiment to use the Boyer-Moore theorem prover to proof-check theorems in metamathematics. We describe a First Order Logic due to Shoenfield and outline some of the theorems that the prover was able to prove about this logic. These include the tautology theorem which states that every tautology has a proof. Such proofs can be used to add new proof procedures to a proof-checking program in a sound and efficient manner.     

A time-domain differential solver for electromagnetic scatteringproblems

The authors' objective is to extend computational fluid dynamics (CFD) based upwind schemes to solve numerically the Maxwell equations for scattering from objects with layered non-metallic sections. After a discussion on the character of the Maxwell equations it is shown that they represent a linearly degenerate set of hyperbolic equations. To show the feasibility of applying CFD-based algorithms, first the transverse magnetic (TM) and the transverse electric (TE) waveforms of the Maxwell equations are considered. A finite-volume scheme is developed with appropriate representations for the electric and magnetic fluxes at a cell interface, accounting for variations in material properties in both space and time. This process involves a characteristic subpath integration known as the `Riemann solver'. An explicit-Lax-Wendroff upwind scheme, which is second-order accurate in both space and time, is employed to solve the TM and TE equations. A body-fitted coordinate transformation is introduced to treat arbitrary cross-sectioned bodies with computational grids generated using an elliptic grid solver procedure. For treatment of layered media, a multizonal representation is employed satisfying appropriate zonal boundary conditions in terms of flux conservation. The computational solution extending from the object to a far-field boundary located a few wavelengths away constitutes the near-field solution. A Green's function based near-field-to-far-field transformation is employed to obtain the bistatic radar cross section (RCS) information     

Protocol Verification via Projections

The method of projections is a new approach to reduce the complexity of analyzing nontrivial communication protocols. A protocol system consists of a network of protocol entities and communication channels. Protocol entities interact by exchanging messages through channels; messages in transit may be lost, duplicated as well as reordered. Our method is intended for protocols with several distinguishable functions. We show how to construct image protocols for each function. An image protocol is specified just like a real protocol. An image protocol system is said to be faithful if it preserves all safety and liveness properties of the original protocol system concerning the projected function. An image protocol is smaller than the original protocol and can typically be more easily analyzed. Two protocol examples are employed herein to illustrate our method. An application of this method to verify a version of the high-level data link control (HDLC) protocol is described in a companion paper.     

Euclidean Reconstruction and Reprojection Up to Subgroups

International Journal of Computer Vision - The necessary and sufficient conditions for being able to estimate scene structure, motion and camera calibration from a sequence of images are very...     

Computation of Current Distributions using FEMLAB

An efficient method for the computation of current density and surface concentration distributions in electrochemical processes is analyzed using the commercial mathematical software FEMLAB. To illustrate the utility of the software, the procedure is applied to some realistic problems encountered in electrochemical engineering, such as current distribution in a continuous moving electrode, parallel plate electrode, hull cell, curvilinear hull cell, thin layer galvanic cell, through‐hole plating, and a recessed disc electrode. The model equations of the above cases are considered and their implementations into the software, FEMLAB, are analyzed. The technique is attractive because it involves a systematic way of coupling equations to perform case studies.