on equivalence of fis and elm for interpretable rule based knowledge representation this paper presents a fuzzy extreme learning machine f elm that embeds fuzzy membership functions and rules into the hidden layer of extreme learning machine elm similar to the concept of elm that employed the random initialization technique three parameters of f elm are randomly assigned they are the standard deviation of the membership functions matrix c rule combination matrix and matrix d don t care dc matrix fuzzy if then rules are formulated by the rule combination matrix of f elm and a dc approach is adopted to minimize the number of input attributes in the rules furthermore f elm utilizes the output weights of the elm to form the target class and confidence factor for each of the rules this is to indicate that the corresponding consequent parameters are determined analytically the operations of f elm are equivalent to a fuzzy inference system several benchmark data sets and a real world fault detection and diagnosis problem have been used to empirically evaluate the efficacy of the proposed f elm in handling pattern classification tasks the results show that the accuracy rates of f elm are comparable if not superior to elm with distinctive ability of providing explicit knowledge in the form of interpretable rule base

an interpolating memory unit for function evaluation analysis and design a technique for the evaluation of a general continuous function f x is presented and the design of an interpolating memory as an implementation of the technique is described the technique partitions the domain of f x into segments and defines an interpolating or approximating function for each the implementation is a memory subsystem that holds the parameters of the approximating functions and yields an interpolated function value on each read reference polynomial interpolating functions are considered in particular hardware requirements memory and computational logic are analyzed in terms of the required precision it is shown that as long as f x has d 1 derivatives where d is the degree of the interpolating polynomial d 1 additional bits of precision of the computed f x are obtained for each additional address bit used in the interpolating memory this establishes a tradeoff between memory and computational logic which can be exploited in the design of a unit for a specific function for any precision requirement furthermore a single unit can be designed for any class of functions that have the required derivatives two examples of implementations for particular functions are presented

ground state sign changing solutions for asymptotically cubic or super cubic schrodinger poisson systems without compact condition abstract this paper is dedicated to studying the following schrodinger poisson system u v x u u k x f u x r 3 u 2 x r 3 where v k c r 3 r and f c r r under mild assumptions on the decay rate of v x we establish the existence of one ground state sign changing solution with precisely two nodal domains by using a weaker growth condition lim t 0 t f s d s t 3 instead of the usual super cubic condition lim t 0 t f s d s t 4 our result unifies both asymptotically cubic and super cubic cases which generalizes and improves the corresponding ones in the literatures

on the critical schrodinger bopp podolsky system with general nonlinearities abstract this paper deals with the following nonlinear schrodinger bopp podolsky system u v x u u f u u 5 2 a 2 2 4 u 2 in r 3 where a 0 v c r 3 0 with v lim y v y sup x r 3 v x 0 and f c r r satisfying 0 t f s d s t p with p 2 6 for all t 0 by using some new analytic techniques and new inequalities we prove that the above system admits ground state solutions for all 0 if p 4 6 for all 0 if p 2 4 where 0 is a positive constant determined by a v and p our results extend and complement the existence results in d avenia and g siciliano 2019 which only dealt with the subcritical case

semiclassical ground state solutions for critical schrodinger poisson systems with lower perturbations abstract in this paper we study the following singularly perturbed schrodinger poisson system e 2 u v x u u f u u 5 x r 3 e 2 u 2 x r 3 where e is a small positive parameter v c r 3 r and f c r r satisfies neither the usual ambrosetti rabinowitz type condition nor any monotonicity condition on f u u 3 by using some new techniques and subtle analysis we prove that there exists a constant e 0 0 determined by v and f such that for e 0 e 0 the above system admits a semiclassical ground state solution v e with exponential decay at infinity we also study the asymptotic behavior of v e as e 0 in particular our results can be applied to the nonlinearity f u u q 2 u for q 3 4 and extend the previous work that only deals with the case in which f u u q 2 u for q 4 6

powering by a table look up and a multiplication with operand modification an efficient method for generating a power of an operand i e x sup p for an operand x and a given p is proposed it is applicable to ps in the form of spl plusmn 2 sup k where k is any integer and of spl plusmn 2 k sub 1 spl plusmn 2 k sub 2 where k sub 1 is any integer and k sub 2 is any nonnegative integer the reciprocal the square root the reciprocal square root the reciprocal square the reciprocal cube and so forth are included the method is a modification of the piecewise linear approximation a power of an operand is generated through a table look up and a multiplication with operand modification the same accuracy is achieved as the piecewise linear approximation the multiplication and an addition required for the piecewise linear approximation are replaced by only one double sized multiplication with a slight modification of the operand and hence one clock cycle may be reduced the required table size is reduced because only one coefficient instead of two has to be stored

positive solutions for a schrodinger poisson system involving concave convex nonlinearities abstract in this paper we study the critical growth schrodinger poisson system with a concave term and establish the existence of multiple positive solutions via using the variational method

a geometric approach to maximum speed n dimensional continuous linear interpolation in rectangular grids an algorithm for the linear interpolation of multi input functions sampled on rectangular grids is presented a geometric approach is adopted and the mathematics is thoroughly developed we show that the algorithm is optimum in fact when the number n of inputs grows to infinity its computational requirement is o n log n which is the same as the lower bound on the cost of continuous linear interpolation procedures

schrodinger poisson equations without ambrosetti rabinowitz condition abstract we prove the existence of ground state solutions for a stationary schrodinger poisson equation in r 3 the proof is based on the mountain pass theorem and it does not require the ambrosetti rabinowitz condition

positive solutions for some non autonomous schrodinger poisson systems abstract in this paper we study the schrodinger poisson system sp u u k x x u a x u p 1 u x r 3 k x u 2 x r 3 with p 3 5 assuming that a r 3 r and k r 3 r are nonnegative functions such that lim x a x a 0 lim x k x 0 and satisfying suitable assumptions but not requiring any symmetry property on them we prove the existence of positive solutions

bayesian takagi sugeno kang fuzzy classifier in this paper the takagi sugeno kang tsk fuzzy classifier is casted into the bayesian inference framework and a new fuzzy classifier called bayesian tsk fuzzy classifier b tsk fc is proposed accordingly the proposed classifier can be constructed by learning both the antecedent and consequent parameters of the involved fuzzy rules simultaneously as a result of the introduction of bayesian inference the proposed b tsk fc can be distinguished as follows 1 unlike most existing tsk fuzzy classifiers where the antecedent and consequent parameters of fuzzy rules are learnt in a decoupled manner and the antecedent parameters are learnt only in the input space the antecedent parameters of the fuzzy rules in b tsk fc are learnt by developing a fuzzy clustering method in the input output space and the consequent parameters of fuzzy rules are learnt in accordance with the maximum margin of separation principle thereby resulting to form an intrinsic link between the input and output spaces to achieve improved classification performance and better interpretability 2 with a dirichlet prior assumption about fuzzy memberships in fuzzy clustering a markov chain monte carlo technique is employed to estimate the parameters of the proposed classifier from a sampling perspective 3 rather than being rivals fuzziness and probability in b tsk fc are collaboratively modeled to enhance the performance of tsk fuzzy classifier in terms of classification and interpretability our experimental results in synthetic datasets as well as several real world datasets confirm such merits of the proposed fuzzy classifier

multiplicity of concentrating positive solutions for schrodinger poisson equations with critical growth abstract in this paper we deal with a nonlinear schrodinger poisson equation involving critical sobolev exponent under a local condition imposed on the potential we relate the number of positive solutions with the topology of the set where the potential attains its minimum values in the proofs we apply szulkin and weth s generalized nehari manifold methods penalization techniques and ljusternik schnirelmann theory

positive solutions for schrodinger poisson equations with a critical exponent abstract in this paper we establish the existence of a positive solution of the schrodinger poisson equations with a critical sobolev exponent the methods used here are based on the concentration compactness principle of p l lions and methods of brezis and nirenberg

stationary solutions of non autonomous maxwell dirac systems abstract the maxwell dirac system describes the interaction of a particle with its self generated electromagnetic field in this paper we study the existence of least energy stationary solutions for non autonomous maxwell dirac system with a nonlinear term in 3 1 minkowski space time via variational methods this problem is strongly indefinite and presents a lack of compactness to overcome these difficulties we will use the linking and concentration compactness arguments

a hybrid number system processor with geometric and complex arithmetic capabilities the architecture design and performance of a hybrid number system processor are described the processor performs multiplication division square root and square in the logarithmic number system lns domain however the input output addition and subtraction are all executed in the 32 b ieee standard floating point number system with the lns multiplier and pipelined architecture the processor is able to perform the geometric and complex arithmetic very effectively the processor is also shown to compare well to an existing 32 b floating point dsp digital signal processor chip for the same level of cmos technology the performance ratios between the hybrid number system and the floating point processor are shown to be 6 4 1 and 8 1 for division and square root respectively for the complex fft fast fourier transform algorithm the ratio is around 2 1

existence of ground state solutions of nehari pohozaev type for fractional schrodinger poisson systems with a general potential abstract in this paper we consider the following fractional schrodinger poissonproblem s u v x u u f u in r 3 t u 2 in r 3 where 0 s t 1 and 2 s 2 t 3 the potential v x is weakly differentiable and f c r r by introducing some new tricks we prove that the problem admits a ground state solution of nehari pohozaev type under mild assumptions on v and f the results here extend the existing study

on the planar schrodinger poisson system with the axially symmetric potential abstract in this paper we develop some new variational and analytic techniques to prove that the following planar schrodinger poisson system u v x u u f u x r 2 u 2 x r 2 admits a nontrivial solution and a ground state solution possessing the least energy in the axially symmetric functions space where v x is axially symmetric our results improve and extend the ones in the case v 1 and f u u p 2 u with 2 p 6 in particular we use the assumption that 2 v x v x x is bounded from below instead of the usually one that lim x v x 1 moreover v x is even admitted to be unbounded

high speed vlsi multiplication algorithm with a redundant binary addition tree a high speed vlsi multiplication algorithm internally using redundant binary representation is proposed in n bit binary integer multiplication n partial products are first generated and then added up pairwise by means of a binary tree of redundant binary adders since parallel addition of two n digit redundant binary numbers can be performed in a constant time independent of n without carry propagation n bit multiplication can be performed in a time proportional to log2 n the computation time is almost the same as that by a multiplier with a wallace tree in which three partial products will be converted into two in contrast to our two to one conversion and is much shorter than that by an array multiplier for longer operands the number of computation elements of an n bit multiplier based on the algorithm is proportional to n2 it is almost the same as those of conventional ones furthermore since the multiplier has a regular cellular array structure similar to an array multiplier it is suitable for vlsi implementation thus the multiplier is excellent in both computation speed and regularity in layout it can be implemented on a vlsi chip with an area proportional to n2 log2 n the algorithm can be directly applied to both unsigned and 2 s complement binary integer multiplication

positive solutions for a schrodinger poisson system with singularity and critical exponent abstract we study multiplicity of positive solutions for a class of schrodinger poisson system with singularity and critical exponent and obtain two positive solutions via the variational and perturbation methods

on ground state solutions for some non autonomous schrodinger poisson systems abstract in this paper we study the schrodinger poisson system sp u u k x x u a x f u in r 3 k x u 2 in r 3 and prove the existence of ground state solutions for system sp under certain assumptions on the linear and nonlinear terms some recent results from different authors are extended

existence of infinitely many large solutions for the nonlinear schrodinger maxwell equations abstract in this paper we study the nonlinear stationary schrodinger maxwell equations u v x u u f x u in r 3 u 2 in r 3 using the variant fountain theorem introduced by zou w zou variant fountain theorems and their applications manuscripta math 104 2001 343 358 under certain assumptions on v and f we get infinitely many large solutions for

infinitely many positive solutions for a schrodinger poisson system abstract we are interested in the existence of infinitely many positive solutions of the schrodinger poisson system u u v x u u p 1 u x r 3 v x u 2 x r 3 where v x is a positive bounded function 1 p 5 and v r r x has the following decay property v r a r m o 1 r m with a 0 m 3 2 0 the solutions obtained are non radial

hardware implementation trade offs of polynomial approximations and interpolations this paper examines the hardware implementation trade offs when evaluating functions via piecewise polynomial approximations and interpolations for precisions of up to 24 bits in polynomial approximations polynomials are evaluated using stored coefficients polynomial interpolations however require the coefficients to be computed on the fly by using stored function values although it is known that interpolations require less memory than approximations but at the expense of additional computations the trade offs in memory area delay and power consumption between the two approaches have not been examined in detail this work quantitatively analyzes these trade offs for optimized approximations and interpolations across different functions and target precisions hardware architectures for degree 1 and degree 2 approximations and interpolations are described the results show that the extent of memory savings realized by using interpolation is significantly lower than what is commonly believed furthermore experimental results on a field programmable gate array fpga show that for high output precision degree 1 interpolations offer considerable area and power savings over degree 1 approximations but similar savings are not realized when degree 2 interpolations and approximations are compared the availability of both interpolation based and approximation based designs offers a richer set of design trade offs than what is available using either interpolation or approximation alone

positive solutions for a nonlocal schrodinger newton system involving critical nonlinearity abstract in this paper we study the critical schrodinger newton system with a nonlocal term and establish the existence of multiple positive solutions via using variational method

existence and multiplicity of non trivial solutions for a class of modified schrodinger poisson systems abstract in the present paper we study the following modified schrodinger poisson system p u v x u u 1 2 u u 2 u p 1 u h x in r 3 u 2 in r 3 where 4 p 1 12 h l 2 r 3 and h 0 this model describes the interaction of a charge particle with an electro magnetic field under some hypotheses on v x we prove the existence of a non trivial ground state solution and two non trivial ground state solutions for the system p

infinitely many solutions for a class of sublinear schrodinger maxwell equations abstract in this paper we study the existence of infinitely many solutions for a class of sublinear schrodinger maxwell equations the proof is based on the variant fountain theorem established by zou recent results from the literature are extended

multiple solutions for a nonlinear schrodinger poisson system with sign changing potential this paper deals with the existence and multiplicity of nontrivial solutions for a nonlinear schrodinger poisson system under some suitable conditions some criteria on the existence of nontrivial solutions including a ground state solution two solutions and a sequence of nontrivial solutions u k with u k 0 as k is established by applying the morse theory and variational methods some known results in the literatures are extended and improved

multiplicity of positive solutions for some quasilinear elliptic equation in rnwith critical sobolev exponent consider the equation pu g x u p 2u f x u p 2u 1 in rn where 1 0 be the principal eigenvalue of pu g x u p 2uinrn rng x u p 0 2 withu 1 0 the associated eigenfunction we prove i equation 1 has at least one positive solution if 0 1 ii suppose rn f x u 1 p 1such that 1 has at least one positive solution for 1 0 moreover ifp 2 there exists 0 1such that 1 has at least two positive solutions for 1 0

high energy solutions for the superlinear schrodinger maxwell equations abstract in this paper we study the existence of infinitely many large energy solutions for the superlinear schrodinger maxwell equations u v x u u f x u in r 3 u 2 in r 3 via the fountain theorem in critical point theory

on ground state solutions for the schrodinger poisson equations with critical growth abstract in this paper we study the existence of ground state solutions for the following schrodinger poisson equation u v x u u u q 1 u u 4 u in r 3 u 2 in r 3 where is a positive parameter under some certain assumptions on v we prove that for every 0 and q 2 5 such a class of schrodinger poisson equation with critical growth has at least a positive ground state solution via variational methods some recent results from the literature are extended

regularizing effect for some p laplacian systems abstract we study existence and regularity of weak solutions for the following p laplacian system p u a 1 u r 2 u f u w 0 1 p p u r w 0 1 p where is an open bounded subset of r n n 2 p v div v p 2 v is the p laplacian operator for 1 p n a 0 r 1 0 p 1 and f belongs to a suitable lebesgue space in particular we show how the coupling between the equations in the system gives rise to a regularizing effect producing the existence of finite energy solutions

generation of a precise binary logarithm with difference grouping programmable logic array the design algorithm of a differential group programmable logic array dgpla to generate the precise binary logarithm function is suggested it can reach an optimal condition such that the number of bits in a pla is minimized while the error is still kept as small as possible thus the space in the pla is saved estimated at only 15 94 percent of the space for a readonly memory rom counterpart

ground state solutions for quasilinear schrodinger equations via pohožaev manifold in orlicz space abstract this paper is concerned with the following quasilinear schrodinger equations u v x u u 2 u u p 1 u in r n u 0 u h 1 r n where 0 1 p 22 1 2 2 n n 2 and n 3 under some suitable assumptions on v x we prove the existence of ground state solutions via poho aev manifold method the novelty of this works with respect to some recent results is that we treat the existence by using poho aev manifold method in an orlicz space and this enables us to handle the nonlinearity in a uniform way as its supplementary results we also prove the nonexistence of least energy solutions for 1 p 22 1

hardware designs for exactly rounded elementary functions this paper presents hardware designs that produce exactly rounded results for the functions of reciprocal square root 2 sup x and log sub 2 x these designs use polynomial approximation in which the terms in the approximation are generated in parallel and then summed by using a multi operand adder to reduce the number of terms in the approximation the input interval is partitioned into subintervals of equal size and different coefficients are used for each subinterval the coefficients used in the approximation are initially determined based on the chebyshev series approximation they are then adjusted to obtain exactly rounded results for all inputs hardware designs are presented and delay and area comparisons are made based on the degree of the approximating polynomial and the accuracy of the final result for single precision floating point numbers a design that produces exactly rounded results for all four functions has an estimated delay of 80 ns and a total chip area of 98 mm sup 2 in a 1 0 micron cmos technology allowing the results to have a maximum error of one unit in the last place reduces the computational delay by 5 to 30 and the area requirements by 33 to 77

the existence and concentration of positive solutions for a nonlinear schrodinger poisson system with critical growth we consider the schrodinger poisson system e2 u v x u x u f u u2 in r3 where the nonlinear term f is of critical growth in this paper we construct a solution u of the above elliptic system which concentrates at an isolated component of positive locally minimum points of v as 0 under certain conditions on f in particular the monotonicity of f s s3 and the so called ambrosetti rabinowitz condition are not required

the thomas fermi von weizsacker theory of atoms and molecules we place the thomas fermi von weizsacker model of atoms on a firm mathematical footing we prove existence and uniqueness of solutions of the thomas fermi von weizsacker equation as well as the fact that they minimize the thomas fermi von weizsacker energy functional moreover we prove the existence of binding for two very dissimilar atoms in the frame of this model

existence of ground state solutions for the nonlinear fractional schrodinger poisson system with critical sobolev exponent abstract in this paper we study the existence of ground state solutions for the nonlinear fractional schrodinger poisson system with critical sobolev exponent s u v x u u u q 1 u u 2 s 2 u in r 3 t u 2 in r 3 where r is a parameter 1 q 2 s 1 3 2 s 3 2 s s t 0 1 and 2 s 2 t 3 under certain assumptions on v x using the method of pohozaev nehari manifold and the arguments of brezis nirenberg the monotonic trick and global compactness lemma we prove the existence of a nontrivial ground state solution

functional equivalence between radial basis function networks and fuzzy inference systems it is shown that under some minor restrictions the functional behavior of radial basis function networks rbfns and that of fuzzy inference systems are actually equivalent this functional equivalence makes it possible to apply what has been discovered learning rule representational power etc for one of the models to the other and vice versa it is of interest to observe that two models stemming from different origins turn out to be functionally equivalent

on a system involving a critically growing nonlinearity abstract this paper deals with the system u u q u 3 u in b r q u 5 in b r u 0 on b r we prove existence and nonexistence results depending on the value of

existence result for fractional schrodinger poisson systems involving a bessel operator without ambrosetti rabinowitz condition abstract the present study is concerned with the nontrivial solutions for fractional schrodinger poisson system with the bessel operator under certain assumptions on the nonlinearity f a nontrivial nonnegative solution is obtained by perturbation method for the given problem in particular the ambrosetti rabinowitz type condition or the monotone assumption on the nonlinearity is unnecessary

multiplicity of small negative energy solutions for a class of nonlinear schrodinger poisson systems this paper deals with the following nonlinear schrodinger poisson email protected v x u k x f x u h x f x u inr 3 email protected f k x u 2 inr 3 where v x k x and h x are nonnegative continuous functions under appropriate assumptions on v x k x h x and f x u we prove the existence of infinitely many small negative energy solutions by using the variant fountain theorem established by zou recent results from the literature are extended

two positive solutions of a class of schrodinger poisson system with indefinite nonlinearity abstract we study the existence and multiplicity of positive solutions of a class of schrodinger poisson system u u l x u k x u p 2 u h x u in r 3 l x u 2 in r 3 where 4 p 6 k c r 3 k changes sign in r 3 and lim x k x k 0 we mainly prove the existence of at least two positive solutions in the case that 1 and near 1 where 1 is the first eigenvalue of i d in h 1 r 3 with weight function h whose corresponding eigenfunction is denoted by e 1 an interesting phenomenon is that we do not need the condition r 3 k x e 1 p d x 0 which has been shown to be a necessary condition to the existence of positive solutions for semilinear elliptic equations with indefinite nonlinearity see e g s alama g tarantello on semilinear elliptic equations with indefinite nonlinearities calc var partial differential equations 1 1993 439 475

a hardwired generalized algorithm for generating the logarithm base k by iteration a number of previous works of computing the binary logarithm have been developed by a series of line approximations with moderate errors 1 3 in this paper a generalized iterative method for the logarithm of base k evalution is proposed we suggest that an integral constant k is used as a comparative index in each iteration no table lookup is required it can yield a more accurate and rapidly convergent value and can be easily implemented either by software or a hardwired device a numerical example is illustrated for the process of calculation the accuracy is analyzed and plotted by using two schemes in which eight iteration cycle and 16 iteration cycle length are used respectively

on nonlinear schrodinger poisson equations with general potentials abstract we study the existence of infinitely many finite energy radial solutions to the nonlinear schrodinger poisson equations u u x u f u 0 in r 3 u 2 0 lim x x 0 in r 3 nspe for short under some structure conditions on the nonlinearity function f as consequences of the main result we can provide examples of f which guarantee the existence of infinitely many finite energy solutions but i f t grows faster than t 2 and slower than t p for all p 2 or ii f t is the same as t t when t t 0 for arbitrarily given t 0 0 if f t t p 1 t it is known that nspe admits no finite energy nontrivial solutions when p 1 2 and admits infinitely many finite energy solutions when p 2 5 so examples i and ii show some interesting features of nspe

multiple positive solutions for a schrodinger newton system with sign changing potential abstract in this paper we study the schrodinger newton systems with sign changing potential in a bounded domain by using the variational method and analytic techniques the existence and multiplicity of positive solutions are established

concentration and compactness in nonlinear schrodinger poisson system with a general nonlinearity in this paper we use a concentration and compactness argument to prove the existence of a nontrivial non radial solution to the nonlinear schrodinger poisson equations in r3 assuming on the nonlinearity the general hypotheses introduced by berestycki and lions

an asymptotically linear schrodinger poisson system on r3 abstract in this paper we are concerned with the following nonlinear schrodinger poisson equation u u u f x u u x r 3 u 2 lim x x 0 where u r 3 r are positive functions the parameters 0 f x s tend to p x and q x l r 3 respectively as s 0 and s under some simple assumptions on f x s we give existence and nonexistence results depending on the parameters and

infinitely many solutions for schrodinger maxwell equations with indefinite sign subquadratic potentials in this paper we deal with multiplicity of solutions of a class of sublinear schrodinger maxwell equations du v x u fu f x u inr 3 d f u 2 lim x f x 0 inr 3 under more relaxed assumptions on v and f we establish some existence criteria to guarantee that the above problem has at least one or infinitely many nontrivial solutions by using the genus properties in critical theory

neuro fuzzy rule generation survey in soft computing framework the present article is a novel attempt in providing an exhaustive survey of neuro fuzzy rule generation algorithms rule generation from artificial neural networks is gaining in popularity in recent times due to its capability of providing some insight to the user about the symbolic knowledge embedded within the network fuzzy sets are an aid in providing this information in a more human comprehensible or natural form and can handle uncertainties at various levels the neuro fuzzy approach symbiotically combining the merits of connectionist and fuzzy approaches constitutes a key component of soft computing at this stage to date there has been no detailed and integrated categorization of the various neuro fuzzy models used for rule generation we propose to bring these together under a unified soft computing framework moreover we include both rule extraction and rule refinement in the broader perspective of rule generation rules learned and generated for fuzzy reasoning and fuzzy control are also considered from this wider viewpoint models are grouped on the basis of their level of neuro fuzzy synthesis use of other soft computing tools like genetic algorithms and rough sets are emphasized rule generation from fuzzy knowledge based networks which initially encode some crude domain knowledge are found to result in more refined rules finally real life application to medical diagnosis is provided

interleaved memory function interpolators with application to an accurate lns arithmetic unit this paper describes a new method for polynomial interpolation in hardware with advantages demonstrated by its application to an accurate logarithmic number system lns arithmetic unit the use of an interleaved memory reduces storage requirements by allowing each stored function value to be used in interpolation across several segments this strategy can be shown to always use fewer words of memory than an optimized polynomial with stored polynomial coefficients interleaved memory function interpolators are then applied to the specific goal of an accurate logarithmic number system arithmetic unit many accuracy requirements for the lns arithmetic unit are possible although a round to nearest would be desirable it cannot be easily achieved the goal suggested is to insure that the worst case lns relative error is smaller than the worst case floating point fp relative error using the interleaved memory interpolator the detailed design of an lns arithmetic unit is performed using a second order polynomial interpolator including approximately 91k bits of rom this arithmetic unit has better accuracy and less complexity than previous lns units

multi bump solutions for the nonlinear schrodinger poisson system in this paper we study a kind of nonlinear schrodinger poisson system with a parameter e for any positive integer m we prove that there exists e m 0 such that for 0 e e m the equation has an m bump positive solution under some suitable conditions as a consequence the equation has more and more multi bump positive solutions as e 0

localized nodal solutions of higher topological type for nonlinear schrodinger poisson system abstract in this paper we focus our attention on following schrodinger poisson system e 2 u v x u u u p 2 u x r 3 e 2 u 2 u h 1 r 3 where 4 p 6 and e 0 are small positive parameters under a local condition imposed on the potential v we study above system and obtain an infinite sequence of localized sign changing solutions by applying the symmetric mountain pass theorem precisely these solutions are constructed as higher topological type critical points of the energy functional and concentrated at a local minimum set of the potential v our method follows the same spirit of chen and wang s method chen and wang 2017 which does not need any non degeneracy condition of the limiting equations but we cannot use it directly due to the presence of nonlocal term x 1 4 r 3 u 2 y x y d y we employ some new analytical skills to overcome the obstacles caused by the nonlocal term our results improve and extend some related ones in the literature

multiple solutions for a class of schrodinger poisson system with indefinite nonlinearity in this article we investigate the existence and multiplicity of solutions of schrodinger poisson system u u l x u k x u 2u h x u x r3 l x u2 x r3 where the potential k x allows sign changing we obtain the existence and multiplicity of solutions for the system which can be regarded as complementary work of huang et al 2013 12