optimal codes for minimax criterion on error detection nonlinear quadratic codes that are optimal for the minimax error detection are presented characteristic functions for these codes are asymptotically bent for a given block size n and the number of codewords mod c mod these codes minimize max q e e not 0 where q e is the conditional error masking probability given the error pattern e the codewords are blocks of n symbols from gf q encoding and decoding procedures for the codes are described

eigenvalues and eigenfunctions of the laplacian via inverse iteration with shift in this paper we present an iterative method inspired by the inverse iteration with shift technique of finite linear algebra designed to find the eigenvalues and eigenfunctions of the laplacian with homogeneous dirichlet boundary condition for arbitrary bounded domains r n this method which has a direct functional analysis approach does not approximate the eigenvalues of the laplacian as those of a finite linear operator it is based on the uniform convergence away from nodal surfaces and can produce a simple and fast algorithm for computing the eigenvalues with minimal computational requirements instead of using the ubiquitous rayleigh quotient of finite linear algebra also an alternative expression for the rayleigh quotient in the associated infinite dimensional sobolev space which avoids the integration of gradients is introduced and shown to be more efficient the method can also be used in order to produce the spectral decomposition of any given function u l 2

computing the first eigenvalue of the p laplacian via the inverse power method abstract in this paper we discuss a new method for computing the first dirichlet eigenvalue of the p laplacian inspired by the inverse power method in finite dimensional linear algebra the iterative technique is independent of the particular method used in solving the p laplacian equation and therefore can be made as efficient as the latter the method is validated theoretically for any ball in r n if p 1 and for any bounded domain in the particular case p 2 for p 2 the method is validated numerically for the square

on some nonlinear elliptic equations involving derivatives of the nonlinearity the existence of weak solutions of the dirichlet problem for nonlinear elliptic equations of the type x j a ij x u x i b j u a x u f is proved for nonlinearities b j which are only continuous the proof is based on the observation that an l a priori estimate is valid which is independent of b j the second part contains several uniqueness results and counterexamples showing that uniqueness may fail in general

vector sets for exhaustive testing of logic circuits l d universal sets are useful for exhaustively testing logic circuits with a large number of functional components designed so that every functional component depends on at most d inputs randomized and deterministic constructions of l d universal test sets are presented and lower and upper bounds on the optimal sizes of such sets are proven it is also proven that the design of an optimal exhaustive test set for an arbitrary logic circuit is an np complete problem

a combinatorial approach to x tolerant compaction circuits test response compaction for integrated circuits ics with scan based design for testability dft support in the presence of unknown logic values xs is investigated from a combinatorial viewpoint the theoretical foundations of x codes employed in an x tolerant compaction technique called x compact are examined through the formulation of a combinatorial model of x compact novel design techniques are developed for x codes to detect a specified maximum number of errors in the presence of a specified maximum number of unknown logic values while requiring only small fan out the special class of x codes that results leads to an avoidance problem for configurations in combinatorial designs general design methods and nonconstructive existence theorems to estimate the compaction ratio of an optimal x compactor are also derived

design of test sequences for vlsi self testing using lfsr consider a shift register sr of length n and a collection of designated subsets of 0 1 n 1 the problem is how to add feedback to the sr such that the resulting linear feedback shift register lfsr exercises almost exhaustively each of the designated subsets and is of small period several previously known results for maximum length lfsr are extended to more general lfsr and in particular a previously known algorithm is simplified and extended applications to the problems of vlsi self testing are discussed and illustrated

vector space theoretic analysis of additive cellular automata and its application for pseudoexhaustive test pattern generation a novel scheme for utilizing the regular structure of three neighborhood additive cellular automata cas for pseudoexhaustive test pattern generation is introduced the vector space generated by a ca can be decomposed into several cyclic subspaces a cycle corresponding to an m dimensional cyclic subspace has been shown to pseudoexhaustively test an n input circuit n or m such a cycle is shown to supply a m 1 bit exhaustive pattern including the all zeros m 1 tuple schemes have been reported specifying how one or more subsets of m 1 cell positions of an n cell ca can be identified to generate exhaustive patterns in an m dimensional cyclic subspace

design of universal test sequences for vlsi a test sequence is called s t universal if it exercises every function depending on t or fewer inputs on a very large scale integration vlsi chip with s inputs randomized and deterministic procedures are deseribed for the design of s t universal sequences and for the signature analysis of the test outputs

recursive pseudoexhaustive test pattern generation a recursive technique for generating exhaustive patterns is presented the method is optimal i e in one experiment it covers exhaustively every block of k adjacent inputs in the first 2 sup k vectors implementation methods based on characteristic functions of test vectors are provided they include a parallel pattern generator employing an exclusive or array and two serial generators that can be easily adopted in a scan based built in self test environment

on the reynolds lubrication equation let be a bounded open set in r 2 with smooth boundary is the region where two solid bodies are in contact these two solids are moving and the average of their velocities is denoted by v v 1 v 2 the pressure p p x which develops in a fluid layer confined between these two bodies satisfies the so called reynolds lubrication equation 1 h 3 p 6 v h in 2 p p a on here is the density of the fluid 0 its dynamic viscosity h h x is the distance between the two bodies and p a 0 is the given ambient pressure we will assume all along that h is a lipschitz continuous function such that 3 0 h 1 h x h 2 a e x x y 4 h x ha e x x y where h 1 h 2 h are positive constants when the fluid is incompressible i e is a positive constant existence and uniqueness for a solution to 1 2 is a trivial matter since the equation is linear in the compressible case when 5 p the problem becomes more challenging the paper is organized as follows in section 1 we investigate the problem of existence of a solution for 1 2 when is given by 5 in section 2 we consider a case where 1 2 reduces to a one dimensional problem and we study the question of uniqueness as well as the shape of the solution finally in a third section we give some extensions of the results of section 2 in higher dimension

the weighted syndrome sums approach to vlsi testing with the advent of vlsi testing has become one of the most costly complicated and time consuming problems the method of syndrome testing is applicable toward vlsi testing since it does not require test generation and fault simulation it can also be considered as a vehicle for self testing in order to employ syndrome testing in vlsi we electronically partition the chip into macros in test mode the macros are then syndrome tested in sequence

high order iterative methods without derivatives for solving nonlinear equations the new second order and third order iterative methods without derivatives are presented for solving nonlinear equations the iterative formulae based on the homotopy perturbation method are deduced and their convergences are provided finally some numerical experiments show the efficiency of the theoretical results for the above methods

approximation of the least rayleigh quotient for degree p homogeneous functionals abstract we present two novel methods for approximating minimizers of the abstract rayleigh quotient u u p here is a strictly convex functional on a banach space with norm and is assumed to be positively homogeneous of degree p 1 minimizers are shown to satisfy u j p u 0 for a certain r where j p is the subdifferential of 1 p p the first approximation scheme is based on inverse iteration for square matrices and involves sequences that satisfy u k j p u k 1 0 k n the second method is based on the large time behavior of solutions of the doubly nonlinear evolution j p v t v t 0 a e t 0 and more generally p curves of maximal slope for we show that both schemes have the remarkable property that the rayleigh quotient is nonincreasing along solutions and that properly scaled solutions converge to a minimizer of u u p these results are new even for hilbert spaces and their primary application is in the approximation of optimal constants and extremal functions for inequalities in sobolev spaces

built in test for circuits with scan based on reseeding of multiple polynomial linear feedback shift registers we propose a new scheme for built in test bit that uses multiple polynomial linear feedback shift registers mp lfsr s the same mp lfsr that generates random patterns to cover easy to test faults is loaded with seeds to generate deterministic vectors for difficult to test faults the seeds are obtained by solving systems of linear equations involving the seed variables for the positions where the test cubes have specified values we demonstrate that mp lfsr s produce sequences with significantly reduced probability of linear dependence compared to single polynomial lfsr s we present a general method to determine the probability of encoding as a function of the number of specified bits in the test cube the length of the lfsr and the number of polynomials theoretical analysis and experiments show that the probability of encoding a test cube with s specified bits in an s stage lfsr with 16 polynomials is 1 10 sup 6 we then present the new bit scheme that allows for an efficient encoding of the entire test set here the seeds are grouped according to the polynomial they use and an implicit polynomial identification reduces the number of extra bits per seed to one bit the paper also shows methods of processing the entire test set consisting of test cubes with varied number of specified bits experimental results show the tradeoffs between test data storage and test application time while maintaining complete fault coverage

existence and uniqueness for several non linear elliptic problems arising in lubrication theory we consider the non linear elliptic equation a x p p b x p with positive dirichlet boundary data the coefficients a and b are taken from models used in lubrication theory andin particular are not d negative values of p we prove some general existence anduniqueness results for a family of mod els which extendrelatedresults in the literature these results allow us to prove existence uniqueness andpositivity of the solution to advanced compressible lubrication models such as the kinetic based fukui kaneko model and the second order slip model we also consider a spring like model of compliant foil compressible bearing andweaken some hypotheses of previous results on more classical mod els such as the standard reynolds model and the first order slip model

the extinction versus the blow up global and non global existence of solutions of source types of degenerate parabolic equations with a singular absorption abstract we consider nonnegative solutions of degenerate parabolic equations with a singular absorption term and a source nonlinear term t u u x p 2 u x x u u 0 f u x t in i 0 t with the homogeneous zero boundary condition on i x 1 x 2 an open bounded interval in r through this paper we assume that p 2 and 0 1 to show the local existence result we prove first a sharp pointwise estimate for u x one of our main goals is to analyze conditions on which local solutions can be extended to the whole time interval t 0 the so called global solutions or by the contrary a finite time blow up 0 0 arises such that lim t 0 u t l i moreover we prove that any global solution must vanish identically after a finite time if provided that either the initial data or the source term is small enough finally we show that the condition f 0 x t 0 x t i 0 is a necessary and sufficient condition for the existence of solution of equations of this type

pseudoexhaustive test pattern generator with enhanced fault coverage a method of pseudoexhaustive test pattern generation is proposed that is suitable above all for circuits using random access scan two linear feedback shift registers are used to generate scan addresses and test patterns to be scanned into these addresses it is shown that the method gives better results than random testing

bounds on the linear span of bent sequences recently olsen scholtz and welch presented families of binary sequences called bent function sequences which can be generated through nonlinear operations on m sequences these families of sequences possess asymptotically optimum correlation properties and large equivalent linear span els upper and lower bounds to the els of bent function sequences are derived the upper bound improves upon key s upper bound and the lower bound obtained through construction and exceeds left stackrel n 2 n 4 right cdot 2 n 4 where n is the length of the shift register generating the m sequence an interesting general result contained in the derivation is the exhibition of a class of nonlinear sequences whose els is guaranteed to be large

existence of equilibria in articulated bearings the existence of equilibrium solutions for a lubricated system consisting of an articulated body sliding over a flat plate is considered though this configuration is very common it corresponds to the popular tilting pad thrust bearings the existence problem has only been addressed in extremely simplified cases such as planar sliders of infinite width our results show the existence of at least one equilibrium for a quite general class of nonplanar slider shapes we also extend previous results concerning planar sliders

multiple seed tpg structures linear feedback shift registers lfsrs are popular mechanisms for built in test pattern generation tpg they are normally used with a primitive characteristic polynomial because in that case only one initialization state seed is required we show that if the characteristic polynomial is nonprimitive irreducible the required seeds can still be efficiently generated we establish a formula that shows how the seeds of any nonprimitive irreducible polynomial relate to each other this leads to an efficient hardware implementation with small hardware overhead irrespective of the number of seeds and enhances the choices available for the design of appropriate tpg structures in the case of pseudoexhaustive tpg that were previously limited to primitive characteristic polynomials only

computing the first eigenpair of the p laplacian in annuli abstract we propose a method for computing the first eigenpair of the dirichlet p laplacian p 1 in the annulus a b x r n a x b n 1 for each t a b we use an inverse iteration method to solve two radial eigenvalue problems one in the annulus a t with the corresponding eigenvalue t and boundary conditions u a 0 u t and the other in the annulus t b with the corresponding eigenvalue t and boundary conditions u t 0 u b next we adjust the parameter t using a matching procedure to make t coincide with t thereby obtaining the first eigenvalue p hence by a simple splicing argument we obtain the positive l normalized radial first eigenfunction u p the matching parameter is the maximum point of u p in order to apply this method we derive estimates for t and t and we prove that these functions are monotone and locally lipschitz continuous moreover we derive upper and lower estimates for the maximum point which we use in the matching procedure and we also present a direct proof that u p converges to the l normalized distance function to the boundary as p we also present some numerical results obtained using this method

asymptotics for the principal eigenvalue of the p laplacian on the ball as p approaches 1 abstract using the estimates of the principal eigenvalue of the p laplacian on the ball from below and from above we provide its asymptotic analysis as p 1

estimates of the principal eigenvalue of the p laplacian abstract we provide estimates from below and from above for the principal eigenvalue of the p laplacian on a bounded domain we apply these estimates to study the asymptotic behavior of the principal eigenvalue for p

exhaustive generation of bit patterns with applications to vlsi self testing one has a shift register of length n and a collection of designated subsets of 0 1 n 1 the problem is to devise a method for feeding a string of bits into the shift register in such an order that for each designated subset s k1 kr if one keeps track of the bit patterns appearing at the corresponding positions k1 krof the shift register all 2r possible bit patterns will ultimately appear at those positions a simple and efficient solution to this problem derived from the connections between polynomials over finite fields and linear feedback shift registers is presented applications of this solution to the problem of vlsi self testing are discussed and illustrated