an effective built in self test scheme for parallel multipliers an effective built in self test bist scheme for parallel multipliers array and tree is proposed the new scheme combines the advantages of deterministic and pseudorandom testing and avoids their drawbacks no modifications to the multiplier structure are required a guaranteed very high fault coverage of a comprehensive cellular fault model is achieved the results do not depend either on the gate level implementation of the multiplier cells or the architecture of the multiplier whether it is a carry propagate or carry save array multiplier or a tree multiplier or on the multiplier size a small deterministic test set of highly regular test vectors is used which exploits the inherent regularity of the multiplier architecture the regularity of the test vectors allows for their on chip generation with a very small hardware overhead which is equivalent to the hardware overhead of pseudorandom testing

exact equation for the pair connectedness function an exact integral equation for the pair connectedness function gdouble dagger 12 is derived on the basis of the author s earlier exact equation for the pair distribution function g 12 the new equation gives rise to a sequence of approximations for gdouble dagger 12 starting with the percus yevick approximation significant aspects of the first two approximations are noted as is the relevance of the blocking functions g gdouble dagger for ionic and chemically associating particles

design of testable multipliers for fixed width data paths the usage of multipliers in fixed width data dominated architectures also termed data paths poses serious testability problems due to truncation of their outputs the fault observability of the multipliers degrades and the resulting output patterns are inadequate to completely test functional blocks that are driven by them consequently the overall random pattern testability of data paths deteriorates substantially in this paper we propose new generic design schemes based on residue number system arithmetic to improve the overall testability of data paths the approach uses in the test mode the truncated least significant bits of the product to increase the variety of patterns at the output of a multiplier this in turn improves the fault detectability of multipliers and consequently have a remarkable impact on the overall testability of data paths the proposed techniques can be incorporated with a minimal performance degradation and area overhead and are independent of the multiplier architecture experimental analysis performed on four high level synthesis benchmarks exhibits a significant improvement in the overall testability of the corresponding data path implementations

continuum theory of percolation and association abstract the development of a general theory of clustering is sketched the primary focus is on the use of the pair connectedness function in problems of correlated clustering and on the ornstein zernike formalism that has been developed to evaluate this function and relate it to observed mesoscopic and macroscopic properties the treatment here stresses percolation which has already been found to be directly relevant to complex matter problems it goes on to show the way the general theory becomes a theory of chemical association when applied to chemically associating fluids in the complete association limit it becomes a site site theory of molecular fluids

sticky spheres and related systems some properties of a system of hard core particles with attractive wells in the baxter sticky sphere limit and a related limit are considered as is the approach to these limits a demonstration of the result of stell and williams that sticky spheres of equal diameter in the baxter limit are not thermodynamically stable is given and the way in which size polydispersity can be expected to restore thermodynamic stability is discussed the implications of these results for the py sticky sphere approximation and recent sticky sphere computer simulations are then examined it is concluded that the baxter py sticky sphere approximation for a monodisperse system may well be a reasonable one for a slightly polydisperse system of sticky spheres and that existing simulation results may also be relevant to such a system how polydisperse a system must be in quantitative terms in order for the py approximation to be useful remains to be seen however the question of whether the py sticky sphere approximation may prove to be useful and appropriate in describing monodisperse systems with pair potentials for which the attractive wells arenot extremely narrow is also considered it is noted that firm evidence concerning this question also appears to be lacking implications for systems near but not in the limit of zero attractive well width are also considered especially in terms of the relative size of the well width and the degree of size polydispersity in the repulsive cores the possible pertinence of such considerations to colloidal systems is observed the importance of taking into consideration the extremely long equilibration times that can be expected for systems with very narrow attractive wells is also pointed out in connection both with real colloidal systems and in computer simulations it is further observed that in the baxter limit sticky spheres described quantum mechanically are indistinguishable from hard spheres so described near the zero well width limit the quantal behavior hinges on the number of bound states and thus the well depth as well as the relative size of the de broglie thermal wavelength and the well width related results and investigations relevant to the issues described above are cited

primitive model for highly asymmetric electrolytes associative mean spherical approximation abstract we study the primitive model of highly asymmetric electrolytes consiting of a mixture of m n sticky charged hard spheres where m of these components represent polyions and n represent counterions it is assumed that the species representing polyions are highly charged and large in size while the counterions are small in size and have at most two charges a two density version of the mean spherical approximation associative msa explicitly accounting for the effects of the asymmetry is discussed and solved analytically the approximation is based on the recently developed multidensity integral equation theory for highly asymmetric electrolyte solutions kalyuzhnyi et al chem phys lett 215 1993 518 j chem phys 102 1995 5770 the analytic solution and the thermodynamic excess functions are given in terms of a single screening parameter t the excess entropy has the same remarkably simple form smsa t 3 3 sticky terms as found in previous work

single precision multiplier with reduced circuit complexity for signal processing applications when two numbers are multiplied a double wordlength product is produced in applications where only the single precision product is required the double wordlength result is rounded to single precision hence in single precision applications it is not necessary to compute the least significant part of the product exactly instead it is only necessary to estimate the carries generated in the computation of the least significant part that will ripple into the most significant part of the product this will produce a single precision multiplier with significantly reduced circuit complexity three novel methods for realizing this class of reduced complexity single precision multipliers are introduced and their performance analyzed

on piterbarg s max discretisation theorem for homogeneous gaussian random fields abstract motivated by the papers of piterbarg 17 and husler 7 in this paper the asymptotic relation between the maximum of a continuous dependent homogeneous gaussian random field and the maximum of this field sampled at discrete time points is studied it is shown that for the weakly dependent case these two maxima are asymptotically independent dependent or coincide when the grid of the discrete time points is a sparse grid pickands grid or dense grid respectively while for the strongly dependent case these two maxima are asymptotically totally dependent if the grid of the discrete time points is sufficiently dense and asymptotically dependent if the grid points are sparse or pickands grids

computations over finite monoids and their test complexity abstract we consider the test pattern generation problem for circuits which compute expressions over some algebraic structure the relation between algebraic properties of this structure and test complexity i e the best possible test size is analyzed here this relation is looked at in detail for the family of all finite monoids the test complexity of a monoid with respect to a problem is measured by the number of tests needed to check the best testable circuit in a certain computational model solving the problem two important computations over finite monoids namely expression evaluation and parallel prefix computation are considered the relation between algebraic properties of a monoid and its test complexity with respect to these problems is studied in both cases it can be shown that the set of all finite monoids partitions into exactly three classes with constant logarithmic and linear test complexity respectively these classes are characterized using algebraic properties for example groups are exactly the monoids with constant test complexity for each class we provide circuits with optimal test sets and efficient methods which decide the membership problem for a given finite monoid m i e determine the test complexity for m

new approach to percolation lattice system results results of an integral equation approach to pair connectedness are given for lattice models with emphasis on site percolation the lowest order approximation is expressible in terms of the lattice green function and is isomorphic to a polya random walk it yields percolation exponents gamma 2 nu 1 for d 3 and gamma 1 nu 1 2 for d or 4 d dimension for simple hypercubic lattices it also yields usefully sharp estimates for the site percolation threshold probability pp a first correction is described

extreme values and high boundary crossings of locally stationary gaussian processes we consider the large values of a locally stationary gaussian process which satisfies berman s condition on the long range dependence we present some limit results on the exceedances of the process above a certain general smooth high boundary this allows deriving the limiting distribution of the maximum up to time t for example in the case of a standardized process with a constant boundary or in the case of a nonstandardized process with a smooth trend

network forming fluids yukawa square well m point model thermal and connectivity properties of the yukawa square well m point yswmp model of the network forming fluid are studied using solution of the multidensity ornstein zernike and connectedness ornstein zernike equations supplemented by the associative mean spherical approximation amsa the model is represented by the multicomponent mixture of yukawa hard spheres with m s a square well sites located on the surface of each hard sphere to validate the accuracy of the theory computer simulation is used to calculate the structure thermodynamic and connectivity properties of the one component ysw4p version of the model which is compared against corresponding theoretical data in addition connectivity properties of the model were studied using flory stockmayer fs theory predictions of the amsa for the thermal properties of the model radial distribution functions rdf internal energy pressure fractions of the particles in different bonding states are in good agreement with computer simulation predictions similarly good agreement was found for the connectedness rdf crdf except for the statepoints located close to the percolation threshold where the theory fails to reproduce the long range behavior of the crdf results of both theories amsa and fs for the mean cluster size are reasonably accurate only at low degrees of association predictions of the fs theory for the percolation lines are in a good agreement with computer simulation predictions amsa predictions of percolation are much less accurate where corresponding percolation lines are located at a temperatures approximately 25 lower then those calculated using computer simulation

extremes of locally stationary gaussian random fields the main result of this contribution is the derivation of the exact asymptotic behavior of the supremum of a class of a t locally stationary gaussian random fields we present two applications of our result the first one deals with the extremes of aggregate multifractional brownian motions whereas the second one establishes the exact asymptotics of the supremum of the x process generated by multifractional brownian motions

fast multiplication without carry propagate addition conventional schemes for fast multiplication accumulate the partial products in redundant form carry save or signed digit and convert the result to conventional representation in the last step this step requires a carry propagate adder which is comparatively slow and occupies a significant area of the chip in a vlsi implementation a report is presented on a multiplication scheme left to right carry free lrcf that does not require this carry propagate step the lrcf scheme performs the multiplication most significant bit first and produces a conventional sign and magnitude product most significant n bits by means of an on the fly conversion the resulting implementation is fast and regular and is very well suited for vlsi the lrcf scheme for general radix r and a radix 4 signed digit implementation are presented

testing iterative logic arrays for sequential faults with a constant number of patterns shows that a constant number of test vectors are sufficient for fully testing a k dimensional ila for sequential faults if the cell function is bijective the authors then present an efficient algorithm to obtain such a test sequence by extending the concept of c testability and m testability to sequential faults the constant length test sequence can be obtained a pipelined array multiplier is shown to be c testable with only 53 test vectors for exhaustively testing the sequential faults

does modeling a structural break improve forecast accuracy mean square forecast error loss implies a bias variance trade off that suggests that structural breaks of small magnitude should be ignored in this paper we provide a test to determine whether modeling a structural break improves forecast accuracy the test is near optimal even when the date of a local to zero break is not consistently estimable the results extend to forecast combinations that weight the post break sample and the full sample forecasts by our test statistic in a large number of macroeconomic time series we find that structural breaks that are relevant for forecasting occur much less frequently than existing tests indicate

test generation for iterative logic arrays based on an n cube of cell states model the authors present a novel approach to the test generation problem for a more general class of two dimensional iterative logic arrays ilas than considered by previous researchers for certain ilas it is possible to find a test set whose size remains fixed irrespective of the size of the ila while for others it varies with array size given an arbitrary ila cell truth table and a cell interconnection structure the goal is to determine if a fixed size test can be found if not then a test set whose size grows as slowly as possible with the size of the array should be found the authors propose a new model called the n cube of cell states model for representing the cell truth table and interconnection structure the test generation problem is shown to be related to certain properties of cycles in a set of graphs obtained from this model by careful analysis of these cycles efficient testing schedules can be obtained the proposed technique can be applied to unilateral as well as regular bilateral ilas in which the bilateral direction of signal flow are restricted to lie along the horizontal axis

detecting relevant changes in time series models summary most of the literature on change point analysis by means of hypothesis testing considers hypotheses of the form h0 1 2versush1 1 2 where 1 and 2 denote parameters of the process before and after a change point the paper takes a different perspective and investigates the null hypotheses of no relevant changes i e h0 1 2 where is an appropriate norm this formulation of the testing problem is motivated by the fact that in many applications a modification of the statistical analysis might not be necessary if the difference between the parameters before and after the change point is small a general approach to problems of this type is developed which is based on the cumulative sum principle for the asymptotic analysis weak convergence of the sequential empirical process must be established under the alternative of non stationarity and it is shown that the resulting test statistic is asymptotically normally distributed the results can also be used to establish similarity of the parameters i e h1 1 2 at a controlled type 1 error and to estimate the magnitude 1 2 of the change with a corresponding confidence interval several applications of the methodology are given including tests for relevant changes in the mean variance parameter in a linear regression model and distribution function among others the finite sample properties of the new tests are investigated by means of a simulation study and illustrated by analysing a data example from portfolio management

design of testable structures defined by simple loops a methodology is given for generating combinational structures from high level descriptions using assignment statements if statements and single nested loops of register transfer rt level operators the generated structures are cellular and are interconnected in a tree structure a general algorithm is given to test cellular tree structures with a test length which grows only linearly with the size of the tree it is proved that this test length is optimal to within a constant factor ways of making the structures self checking are also indicated

the general solution of the binding mean spherical approximation for pairing ions the mean spherical approximation msa for an arbitrary mixture of charged hard spheres with saturating bonds is solved in the wertheim formalism only pairs are allowed it is shown that the general solution is given in terms of two scaling parameters and the set of binding fractions one of the scales is the screening parameter and the other is a coupling parameter analogous to that of the simple msa but that now is found solving a cubic equation therefore the full solution requires solvingm 2 nonlinear algebraic equations for a system withm components a brief discussion of the thermodynamics is given

testing in two dimensional iterative logic arrays abstract the test methods of two dimensional 2 d iterative logic arrays ilas composed of combinational cells are considered an ila which can be tested by a test whose size is a constant independent of the number of cells in the ila is referred to as a c testable ila an ila which can be tested in a number of vectors linear to the number of cells is referred to as a linear testable ila the fault model assumed is that faults in a cell can change a cell behavior in any arbitrary way as long as the cell remains a combinational circuit at the array level two fault models are considered in the single cell fault model scfm only one cell can be faulty and in the multiple cell fault model mcfm any number of cells can be faulty previous papers have shown the testing methods of c testable and linear testable one dimensional ilas under scfm and mcfm in this paper we extend those methods and use the concept of divide and conquer to generate test sets for 2 d ilas under scfm and mcfm the sufficient conditions and test complexities are derived futhermore some practical circuits are used for example

fault detection and design complexity in c testable vlsi arrays an extension of a previous approach to fault detection and c testability of orthogonal iterative arrays is presented the state transition table of a basic cell is analyzed five new states are added to it it is proved that even though the number of additional states in the proposed approach is greater than previous approaches five states compared to four the required number of test vectors is considerably reduced by a factor of approximately 4 9 an approach to implement the proposed c testability approach into logic design is also presented complexity of this implementation is analyzed

continuum percolation of the four bonding site associating fluids wertheim s integral equation theory for associating fluids is reformulated for the study of the connectedness properties of associating hard spheres with four bonding sites the association interaction is described as a square well saturable attraction between these sites the connectedness version of the ornstein zernike oz integral equation is supplemented by the py like closure relation and solved analytically within an ideal network approximation in which the network is represented as resulting from the crossing of ideal polymer chains the pair connectedness functions and the mean cluster size are calculated and discussed the condition for the percolation transition and the analytical form of the percolation threshold are derived the connection of the percolation with the gas liquid phase transition is discussed

a minimum test set for multiple fault detection in ripple carry adders previous papers have shown that a ripple carry adder composed of several full adder cells can be completely tested by a minimum test set of size 8 independent of the number of cells in the ripple carry adder under single faulty cell assumption the fault model assumed is that faults in a cell can change the cell behavior in any arbitrary way as long as the cell remains a combinational circuit in this paper we assume that any number of cells can be faulty at any time a minimum test set of size 11 which can detect arbitrary length ripple carry adders under this fault model is presented for general n p adders in which each cell is a p bit adder a minimum test set of size 3 22p 1 is also presented

extremes of α t locally stationary gaussian processes with non constant variances abstract with motivation from 9 in this paper we derive the exact tail asymptotics of t locally stationary gaussian processes with non constant variance functions we show that some certain variance functions lead to qualitatively new results

easily testable iterative logic arrays iterative logic arrays ilas are studied with respect to two testing problems first a variety of conditions is presented meeting these conditions guarantees an upper bound on the size of the test set for the ila under consideration second techniques for designing optimally testable ilas are presented the arrays treated are in some cases more general than those that have been reported by other researchers they include multidimensional and inhomogeneous arrays octagonally connected arrays and bilateral arrays are also discussed the results indicate that the characteristics of the individual cell functions e g whether they are bijective are a good guide to the test complexity of the overall array matrix multiplication as an example is shown to have several different optimally testable implementations the results are useful for combinational and pipelined arrays and for certain systolic arrays

approximations of mean spherical type for lattice percolation models the authors develop a general class of approximations of mean spherical msa type as a method for studying lattice percolation problems they review the msa and test certain extensions of it on lattice spin models the relations between thermal spin models and percolation models are then reviewed in order to identify natural extensions of the msa to percolation models these extensions are used to treat both site and bond percolation models in one low density formulation of msa the threshold for bond percolation on a lattice is found to equal the value at the origin of the corresponding lattice green s function this formula gives accurate results for all lattices studied and in all space dimensions d or 3 an accurate treatment is also given of the general site bond problem the entire percolation locus for this problem agrees closely with the results of simulation they also introduce a new method for studying percolation transitions which is a hybrid of the kikuchi cluster approximation scheme and the msa the method is shown to give good values for percolation thresholds while preserving the valuable features of the standard msa in particular it provides a convenient means of computing the pair connectedness function they also explore extensions of their approximations to treat directed site and bond percolation

fluids with highly directional attractive forces ii thermodynamic perturbation theory and integral equations the formalism of statistical thermodynamics developed in the preceding paper is used as a basis for deriving tractable approximations the system treated is one where repulsion and highly directional attraction due to a single molecular site combine to allow the formation of dimers but no highers mers we derive thermodynamic perturbation theory using the system interacting with only the repulsive potential as a reference system two distinct integral equations for the pair correlation are derived the first one treats both parts of the interaction approximately the other one employs the repulsive reference system used in perturbation theory we show that each of these integral equations permits the calculation of an important thermodynamic function directly from the solution at a single state of density and temperature in the first case this applies to a pressure consistent with the compressibility relation in the second to the excess helmholtz free energy over the reference system

overcomplete free energy functional for d 1 particle systems with next neighbor interactions we deduce an overcomplete free energy functional for d 1 particle systems with next neighbor interactions where the set of redundant variables are the local block densities i of i interacting particles the idea is to analyze the decomposition of a given pure system into blocks of i interacting particles by means of a mapping onto a hard rod mixture this mapping uses the local activity of component i of the mixture to control the local association of i particles of the pure system thus it identifies the local particle density of component i of the mixture with the local block density i of the given system consequently our overcomplete free energy functional takes on the hard rod mixture form with the set of block densities i representing the sequence of partition functions of the local aggregates of particle numbers i the system of equations for the local particle density of the original system is closed via a subsidiary condition for the block densities in terms of analoguous to the uniform isothermal isobaric technique all our results are expressible in terms of effective pressures we illustrate the theory with two standard examples the adhesive interaction and the square well potential for the uniform case our proof of such an overcomplete format is based on the exponential boundedness of the number of partitions of a positive integer hardy ramanujan formula and on varadhan s theorem on the asymptotics of a class of integrals

testability of convergent tree circuits the testing properties of a class of regular circuits called convergent trees are investigated convergent trees include such practical circuits as comparators multiplexers and carry lookahead adders the conditions for the testability of these tree circuits are derived for a functional fault model the notion of l testability is introduced where the number of tests for a p level tree is directly proportional to p rather than exponential in p convergent trees that are c testable testable with a fixed number of tests regardless of the tree s size are also characterized two design techniques are also introduced that modify arbitrary tree modules in order to achieve land c testability finally we apply these techniques to the design of a large carry lookahead adder

the classical fluid of associating hard rods in an external field two models of one dimensional fluids of associating hard rods in an arbitrary external field are investigated in the first model particles can only form dimers while in the second model which has been solved previously by percus aggregates of any size coexist in both cases the grand canonical potential and the external potential are found exactly as functionals of the density it is shown that wertheim s thermodynamic perturbation theory of polymerization provides a straightforward route to the exact solution by expanding the functional space to include more density parameters this suggests that wertheim s theory should be used also for studying the structure and not only the thermo dynamics of real associating fluids

on the testability of one dimensional ilas for multiple sequential faults it is shown that one dimensional unilateral iterative logic arrays ilas of combinational cells are c testable for multiple sequential faults provided the fault free cell functions satisfy appropriate conditions the test sequence is of length o m sup 2 n sup 2 mn sup 3 k where n resp m is the number of signal values that can be applied to the horizontal resp vertical cell input and k

estimating and testing linear models with multiple structural changes this paper develops the statistical theory for testing and estimating multiple change points in regression models the rate of convergence and limiting distribution for the estimated parameters are obtained several test statistics are proposed to determine the existence as well as the number of change points a partial structural change model is considered the authors study both fixed and shrinking magnitudes of shifts in addition the models allow for serially correlated disturbances mixingales an estimation strategy for which the location of the breaks need not be simultaneously determined is discussed instead the authors method successively estimates each break point

nonparametric sequential signal change detection under dependent noise a nonparametric version of the sequential signal detection problem is studied our signal model includes a class of time limited signals for which we collect data in the sequential fashion at discrete points in the presence of correlated noise for such a setup we introduce a novel signal detection algorithm relying on the postfiltering smooth correction of the classical whittaker shannon interpolation series given a finite frame of noisy samples of the signal we design a detection algorithm being able to detect a departure from a reference signal as quickly as possible our detector is represented as a normalized partial sum continuous time stochastic process for which we obtain a functional central limit theorem under weak assumptions on the correlation structure of the noise particularly our results allow for noise processes such as arma and general linear processes as well as mixing processes the established limit theorems allow us to design monitoring algorithms with the desirable level of the probability of false alarm and able to detect a change with probability approaching one

a testable design of iterative logic arrays testable design of unilateral iterative logic arrays ila of combinational cells under the assumption of a single cell failure is considered the concepts of one step testability and one step c testability are introduced methods to modify the basic cell flow table so as to facilitate fault detection and location are given it is shown that if no directly observable outputs from each cell are available then it is possible to augment the cell flow table by the addition of a fixed number 4 of columns and a row so that a faulty cell can be located by a test of length proportional to log2p where p is the number of cells in the array however if directly observable outputs are available from each cell then the test length is shown to be independent of the array length to locate a faulty cell

the continuum potts model and continuum percolation abstract recently integral equations have been developed for continuum percolation models by relating them to the one state limit of a continuum potts model cpm in this paper we use the cpm formalism to develop series expansions for the main quantities of continuum percolation theory this provides necessary background for the work with integral equations and also sheds light on the basic structure of percolation theory we develop virial series for the mean number of clusters nc and the mean cluster size s a basic relation between these series is developed using a correlation function new to percolation theory which we denote h x we develop the virial theorem for continuum percolation which relates the mean number of clusters to the two point blocking function a geometric interpretation of this theorem is offered in the case of random sphere percolation for a general correlated percolation model the virial theorem involves our new correlation function h x we use the cpm formalism to give computationally efficient expressions for the general coefficient in the virial expansion of all of these quantities the combinatorial weighting factors that appear in these expansions are discussed in detail for completeness we prove the equivalence of our formulas to the others that have appeared in the literature we do this in the hope of providing a useful reference for further work in continuum percolation

extremes of vector valued gaussian processes with trend abstract let x t x 1 t x n t t t r be a centered vector valued gaussian process with independent components and continuous trajectories and h t h 1 t h n t t t be a vector valued continuous function we investigate the asymptotics of p sup t t min 1 i n x i t h i t u as u as an illustration to the derived results we analyze two important classes of x t with locally stationary structure and with varying variances of the coordinates and calculate exact asymptotics of simultaneous ruin probability and ruin time in a gaussian risk model

fluids with highly directional attractive forces i statistical thermodynamics a new formulation of statistical thermodynamics is derived for classical fluids of molecules that tend to associate into dimers and possibly highers mers due to highly directional attraction a breakup of the pair potential into repulsive and highly directionally attractive parts is introduced into the expansion of the logarithm of the grand partition function in fugacity graphs the bonding by the directional attraction is used to classify the graphs and to introduce a topological reduction which results in the replacement of the fugacity by two variables singlet density and monomer density 0 results for the thermodynamic functions as functionals of and 0 are given in the form of graph sums pair correlations are analyzed in terms of a new matrix analog of the direct correlation function it is shown that the low density limit is treated exactly while major difficulties arise when the mayer expansion which employs onlyp is used the intricate resummations required for the mayer expansion are illustrated for the case where dimers are the only association products

a functional approach to efficient fault detection in iterative logic arrays we consider the problem of fault detection in iterative logic arrays ila s this problem has been studied by numerous researchers for many years the results can be succinctly summarized by stating that one dimensional arrays can be effectively analyzed and significant results obtained while the problems associated with arrays of dimension two or greater appear to be intractable i e np complete for general arbitrary ila s however as is the case for many other switching theory problems general case problems that are intractable can be readily handled for the special cases defined by functions commonly encountered in practice we show that arrays of dimension two or greater can be effectively tested for the case when the functions defined by the arrays have inverses many specific arithmetic functions satisfy this property we also show that even for functions which do not satisfy this property the functional approach simplifies testing problems considerably

on the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids it is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density we derive the explicit form that the functional takes for a system of hard rods and propose an approximate one for hard spheres attractive interactions are also considered in mean field approximation in all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated

adsorption of dimerizing fluids in disordered porous networks abstract we consider the application of the integral equation theory to the study of associative fluids in disordered porous networks the theory also takes into account associative fluid network interactions the calculations reported here illustrate the effect of associative forces on the fluid fluid and fluid network correlation functions we find that an associative interaction gives rise to a strong intracore peak in the correlation functions but dampens the peaks outside the core

the kirkwood salsburg equations for random continuum percolation we develop two different hierarchies of kirkwood salsburg equations for the connectedness functions of random continuum percolation these equations are derived by writing the kirkwood salsburg equations for the distribution functions of thes state continuum potts model cpm taking thes 1 limit and forming appropriate linear combinations the first hierarchy is satisfied by a subset of the connectedness functions used in previous studies it gives rigorous low order bounds for the mean number of clusters n c and the two point connectedness function the second hierarchy is a closed set of equations satisfied by the generalized blocking functions each of which is defined by the probability that a given set of connections between particles is absent these auxiliary functions are shown to be a natural basis for calculating the properties of continuum percolation models they are the objects naturally occurring in integral equations for percolation theory also the standard connectedness functions can be written as linear combinations of them using our second kirkwood salsburg hierarchy we show the existence of an infinite sequence of rigorous upper and lower bounds for all the quantities describing random percolation including the mean cluster size and mean number of clusters these equations also provide a rigorous lower bound for the radius of convergence of the virial series for the mean number of clusters most of the results obtained here can be readily extended to percolation models on lattices and to models with positive repulsive pair potentials

interacting squares in arbitrary external field a model of a many body system composed of squares with contact pair interactions in an arbitrary external field is presented the formulation uses a mapping of the system onto polydisperse hard core mixtures on the polydisperse level then a simplified hamiltonian function is specified this assumption together with a further one about the global free energy functional for the pure hard core part of the idealized mixture make the model solvable it is expected to hold for high temperatures low densities or low temperatures the validity of the method of construction in the latter case is illustrated by a further application to a corresponding lattice system for which exact results to compare with are readily available when the temperature is sufficiently low

new microscopic approach to the statistical mechanics of chemical association we consider a new approach to the statistical mechanics of chemical association a b ab in principle it is exact and its thermodynamic basis goes back to gibbs but its statistical mechanical implementation in terms of molecular models does not appear to have been given before for practical computations the success of the method hinges on our ability to calculate the free energy for a mixture of a b and ab species where the species concentrations are regarded as independent we illustrate the method by analysis of some simple limiting cases

the design of easily testable vlsi array multipliers array multipliers are well suited for vlsi implementation because of the regularity in their iterative structure however most vlsi circuits are difficult to test this correspondence shows that with appropriate cell design array multipliers can be designed to be very easily testable an array multiplier is called c testable if all its adder cells can be exhaustively tested while requiring only a constant number of test patterns the testability of two well known array multiplier structures is studied in detail the conventional design of the carry save array multiplier is modified the modified design is shown to be c testable and requires only 16 test patterns similar results are obtained for the baugh wooley two s complement array multiplier a modified design of the baugh wooley array multiplier is shown to be c testable and requires 55 test patterns the c testability of two other array multipliers namely the carry propagate and the trw designs is also presented

testability conditions for bilateral arrays of combinational cells two sets of conditions are derived that make one dimensional bilateral arrays of combinational cells testable for single faulty cells the test sequences are preset and in the worst case grow quadratically with the size of the array conditions for testability in linear time are also derived the basic cell can operate at the bit or at the word level an implementation of fir filters using systolic one dimensional bilateral arrays of cells which can be considered combinational at the word level is presented as an example a straightforward generalization for the two dimensional case is made a systolic array used for matrix multiplication is presented as an example for this case

detection of multiple faults in two dimensional ilas we provide test sets proportional to the sum of the two dimensions of the array for a large class of cells which allow us to test rows or columns of cells of the array independently constant length test sets for array multipliers have been found under the single faulty cell model if the array is modified and otherwise test sets are proportional to the number of cells we can verify the full adder array of a combinational n spl times m multiplier in o n m tests under the multiple faulty cell mfc model the entire multiplier including the and gates which generate the summands can be verified after applying the same modifications which make the multiplier c testable under the single faulty cell model

testing schemes for fir filter structures this paper presents a new pseudoexhaustive test methodology for digital finite impulse response fir filters the proposed scheme can be employed to detect any combinational faults within the basic cell of the functional units occurring in linear phase comb filters trees of sign extended adders and phase shift multipliers it uses additive generators as a source of pseudoexhaustive patterns to systematically test all fir filter building blocks