discrete and continuous maxima in multicarrier communication the ratio between the discrete and continuous maxima of signals used in multicarrier communications is analyzed an exact expression up to an additive term is obtained for the considered ratio when the number of uniformly distributed samples is equal to the number of carriers a more accurate upper estimate on the continuous maximum from discrete samples of the signal and its derivative is suggested finally a tight upper bound is given for the value of the continuous maximum via discrete values of samples when the number of samples is greater than the number of carriers

a general theory of fuzzy topological spaces abstract this paper presents a unification of different approaches to fuzzy topology originated from the early works of c l chang b hutton u hohle r lowen a sostak and l n stout

a survey of fuzzy set and topos theory abstract this paper is a comparison and contrast of approaches to many valued mathematics offered by fuzzy set theory and topos theory it gives a survey of the categorical foundations of fuzzy set theory and related topoi topoi are not a basis for fuzzy set theory butthey do suggest appropriate directions to go and questions to ask for a synthesis which does provide a foundation one possible structure which has a lopos like internal logic and the rich variety of loggical connectives used in fuzzy sets is included

a balancing method for pmepr reduction in ofdm signals a relation is established between the strength of a binary code over the alphabet 1 1 and its ability to reduce peak to mean envelope power ratio pmepr in n subcarrier ofdm signals based on this relation a method is proposed to deterministically bound pmepr of such signals using coordinate wise multiplication by a balancing vector bv chosen from a code of given strength a practical probabilistic scheme considering a small number of candidate codewords is devised for this scheme estimates on the pmepr reduction achievable with arbitrary high probability are derived in particular the scheme provides for large n pmepr of lnn 2 01lnlnn with ln2 middot log2n 2 1 bits of redundancy the failure probability at most e n and testing n lnlnn candidate bvs finally several practical settings are considered for example for quaternary phase shift keying n 128 the scheme with 36 bits of redundancy 18 redundant subcarriers by testing only 4 bvs provides over 2 db pmepr reduction for any failure rate below 10 2 5

peak value estimation of bandlimited signals from their samples noise enhancement and a local characterization in the neighborhood of an extremum the paper addresses the problem of estimating the peak value of bandlimited signals from their samples with and without oversampling this problem has significant relevance to orthogonal frequency division multiplexing ofdm signal processing and system design in particular an upper bound on the peak value is established given the peak value of the samples and the oversampling rate moreover it is shown that the bounds are sharp for all practical rates by constructing bandlimited signals taking on this bound the proof also provides a local characterization of bandlimited signals in the neighborhood of an extremum a different analysis examines the effect of small errors in the samples it is shown that oversampling can provide robust recovery in the sense that small errors in the samples lead to small errors in the reconstructed signal again an upper bound is derived relating the peak error in the samples and the peak error in the signals furthermore both problems are shown to be coupled and put in a unifying context the bounds are compared and applied to problems concerning ofdm

point set lattice theoretic topology this essay attempts to survey in a coherent way certain aspects of point set lattice theoretic or poslat topology by which we mean fuzzy topology grounded in notions of sets functions powersets and powerset operators the latter two being lattice theoretic in nature and examined from a lattice theoretic point of view using methods of category theory connections with other related issues and developments are frequently given

peak to average power control via tone reservation in general orthonormal transmission systems in this paper we study the tone reservation method for reducing the peak to average power ratio papr in general orthonormal transmission systems we prove that strong solvability where the peak value of the transmit signal has to be bounded by a constant times the energy of the information symbols is equivalent to weak solvability where the peak value of the transmit signal has to be only bounded further we show that in the case where the papr problem is not weakly solvable almost all information sequences lead to an unbounded transmit signal

optimal tone reservation for cdma systems in this paper we analytically analyze the tone reservation method for the reduction of the peak to average power ratio papr in code division multiple access systems that employ the walsh functions we find the best possible reduction of the papr and give one optimal information set that achieves this reduction interestingly when using more than one information carrier the smallest possible extension constant is independent of the size of the information set and has the value sqrt 2 we further show that the minimal extension constant can also be achieved with finite compensation sets and illustrate the findings with a numerical example for certain special cases we are also able to provide results for the system of complex exponentials which is employed in orthogonal frequency division multiplexing

a new fuzzy compactness defined by fuzzy nets compactness is one of the most important notions in topology and is thoroughly investigated in general topology but it seems that the research about this notion in the area of fuzzy topology is not so effective as in general topology in fact it would seem that there was not even a good definition of compactness in this area until recently indeed soon after the famous article written by zadeh 8 was published chang 1 introduced the notion of fuzzy topological spaces and at the same time a certain fuzzy compactness was given from then on a series of different notions of fuzzy compactness have been discussed 2 3 71 and in 5 they were compared in detail but it seems unsatisfactory that all these fuzzy compactness ideas are defined for the whole fuzzy topological space but not for an arbitrary fuzzy subset therefore they are far from the crisp compactness for example it is impossible to discuss the hereditary property with respect to closed subsets of fuzzy compactness in 1977 pu and liu introduced the notion of fuzzy nets and a new concept of so called q neighborhood was given which could reflect the features of neighborhood structure in fuzzy topological spaces and by this new neighborhood structure the moore smith convergence theory was established spendidly 6 it furnishes us a basic tool to investigate the fuzzy compactness in a more general way to investigate the compactness of arbitrary fuzzy subsets in this paper a new fuzzy compactness defined by fuzzy nets we shall call it n compactness is given but we introduce the notion of r neighborhood see section 2 instead of qneighborhood to establish the moore smith convergence theory for it is perhaps more convennient to use n compactness possesses the following properties 1 n compactness is defined for arbitrary fuzzy subsets 2 for n compactness the hereditary property with respect to closed subsets holds 3 n compactness is a good extension 5 4 the continuous images of ncompact sets are n compact 5 for n compactness the tychonoff product theorem holds 6 if an n compact fuzzy topological space is t2 6 then it will satisfy a stronger separation axiom which will be called t4 in this paper 1 0022 247x 83 3 00

compact g fuzzy topological spaces abstract considering complete boolean algebras g as sets of truth values a new concept of compactness so called probabilistic compactness is introduced to g fuzzy topological spaces the aim of this paper is to show that the most important theorems of the theory of ordinary compact spaces remain true e g probabilistic compactness is preserved under projective limits every probabilistic compact space has an unique g fuzzy uniformity being compatible with the underlying g fuzzy topology etc finally using the selection theorem due to kuratowski and ryll nardzewski a non trivial example of a probabilistic compact space is given

peak power reduction of ofdm signals with sign adjustment it has recently been shown that significant reduction in the peak to mean envelope power pmepr can be obtained by altering the sign of each subcarrier in a multicarrier system with n subcarriers however finding the best sign not only requires a search over 2n possible signs but also may lead to a substantial rate loss for small size constellations in this paper we first propose a greedy algorithm to choose the signs based on p norm minimization and prove that the resulting pmepr is guaranteed to be less than c log n where c is a constant independent of n for any n this approach has lower complexity in each iteration compared to the derandomization approach of while achieving similar pmepr reduction we further improve the performance of the proposed algorithm by enlarging the search space using pruning simulation results show that pmepr of a multicarrier signal with 128 subcarriers can be reduced to within 1 6 db of the pmepr of a single carrier system in the second part of the paper we address the rate loss by proposing a block coding scheme in which only one sign vector is chosen for k different modulating vectors the sign vector can be computed using the greedy algorithm in n iterations we show that the multi symbol encoding approach can reduce the rate loss by a factor of k while achieving the pmepr of c logkn i e only logarithmic growth in k simulation results show that the rate loss can be made smaller than 10 at the cost of only 1 db increase in the resulting pmepr for a system with 128 subcarriers

novel low complexity slm schemes for papr reduction in ofdm systems selected mapping slm schemes are commonly employed to reduce the peak to average power ratio papr in orthogonal frequency division multiplexing ofdm systems it has been shown that the computational complexity of the traditional slm scheme can be substantially reduced by adopting conversion vectors obtained by using the inverse fast fourier transform ifft of the phase rotation vectors in place of the conventional ifft operations c l wang and y ouyang low complexity selected mapping schemes for peak to average power ratio reduction in ofdm systems ieee trans signal process vol 53 no 12 pp 4652 4660 dec 2005 to ensure that the elements of these phase rotation vectors have an equal magnitude conversion vectors should have the form of a perfect sequence this paper presents three novel classes of perfect sequence each of which comprises certain base vectors and their cyclically shifted versions three novel low complexity slm schemes are then proposed based upon the unique structures of these perfect sequences it is shown that while the papr reduction performances of the proposed schemes are marginally poorer than that of the traditional slm scheme the three schemes achieve a substantially lower computational complexity

errata complete fuzzy topological hyperfields and fuzzy multiplication in the fuzzy real lines abstract we construct a fuzzy multiplication for the case l a chain in the l fuzzy real line r l which is jointly fuzzy continuous and which is the unique piecewise consistent extension of ordinary multiplication to r l distributing over the fuzzy addition constructed by the author in 47 we also specify the fuzzy integers and give an extensive analysis of fuzzy contractions and expansions these results the constructions of this paper and the results of 47 are used to prove r l and the stratified r c l are nontopologically isomorphic complete fuzzy topological hyperfields if l is a chain with l 3 we can now completely answer for l a chain the following question of 27 in the affirmative can a set of fuzzy numbers its fuzzy topology and its fuzzy addition and multiplication be defined such that these operations are jointly fuzzy continuous extensions of the usual addition and multiplication of r and can we specify the fuzzy integers these results in combination with recent papers of several authors would seem to answer in the affirmative the following philosophical question cf 34 does fuzzy topology have deep specific canonical examples

zappa szep products of garside monoids a monoid k is the internal zappa szep product of two submonoids if every element of k admits a unique factorisation as the product of one element of each of the submonoids in a given order this definition yields actions of the submonoids on each other which we show to be structure preserving we prove that k is a garside monoid if and only if both of the submonoids are garside monoids in this case these factors are parabolic submonoids of k and the garside structure of k can be described in terms of the garside structures of the factors we give explicit isomorphisms between the lattice structures of k and the product of the lattice structures on the factors that respect the garside normal forms in particular we obtain explicit natural bijections between the normal form language of k and the product of the normal form languages of its factors

fuzzy topologies and topological space objects in a topos abstract the purpose of this paper is to point out the link between lowen s fuzzy topologies and topological space objects in the topos l set as the main result we obtain the following theorem lowen s fuzzy topologies are the external version of the internal topologies in l set

large families of asymptotically optimal two dimensional optical orthogonal codes nine new two dimensional optical orthogonal codes 2 d oocs are presented here all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature each of these constructions is either optimal or asymptotically optimal with respect to either the original johnson bound or else a nonbinary version of the johnson bound introduced in this paper the first five codes are constructed using polynomials over finite fields the first construction is optimal while the remaining four are asymptotically optimal the next two codes are constructed using rational functions in place of polynomials and these are asymptotically optimal the last two codes also asymptotically optimal are constructed by composing two of the above codes with a constant weight binary code also presented is a three dimensional optical orthogonal code 3 d ooc that exploits the polarization dimension finally phase encoded optical cdma is considered and construction of two efficient codes are provided

separation axioms and the fuzzy real lines we show that for each lattice l which is completely distributive and equipped with an order reversing involution the canonical topology of the fuzzy real line l is uniformizable in the sense of hutton furthermore this uniformity induces a pseudometric which induces the canonical topology consequently l satisfies the higher order separation axioms of hutton and sarkar more generally we answer most of the open questions concerning l and its subspaces with respect to each of the separation axiom schemes of hutton and sarkar answer some of these same questions for the stratified fuzzy real line c l and its subspaces and analyze c l and its subspaces with respect to the separation axioms of rodabaugh

new polyphase sequence families with low correlation derived from the weil bound of exponential sums in this paper the sequence families of which maximum correlation is determined by the weil bound of exponential sums are revisited using the same approach two new constructions with large family sizes and low maximum correlation are given the first construction is an analog of one recent result derived from the interleaved structure of sidel nikov sequences for a prime p and an integer m p 1 the new m ary sequence families of period p are obtained from irreducible quadratic polynomials and known power residue based sequence families the new sequence families increase family sizes of the known power residue based sequence families but keep the maximum correlation unchanged in the second construction the sequences derived from the weil representation are generalized where each new sequence is the elementwise product of a modulated sidel nikov sequence and a modulated trace sequence for positive integers d p and m pn 1 the new family consists of m 1 pnd sequences with period pn 1 alphabet size mp and the maximum correlation bounded by d 1 pn 3

foundations of fuzzy sets abstract this paper gives an overview of the origins of fuzzy set theory and the problems for the foundations of fuzzy sets arising from those origins and current practice it then gives detailed accounts of categorical approaches using a closed structure to capture the fuzzy and connective within these categories weak forms of subobject representations provide an internal second order logic an approach to fuzzy real numbers and fuzzy topology is included to illustrate the use of this internal second order theory

fuzzy addition in the l fuzzy real line abstract under the hypothesis l is a chain we construct a binary operation on the l fuzzy real line r l which reduces to the usual addition on r if is restricted to the embedded image of r in r l which yields a partially ordered abelian cancellation semigroup with identity and which is jointly fuzzy continuous on r l we show is unique i e it is the only extension of addition to r l which is consistent we study the relationship between and other fuzzy continuous extensions of the usual addition we also show that fuzzy translation is a weak fuzzy homeomorphism and under certain conditions a fuzzy homeomorphism

topoi and categories of fuzzy sets abstract let h be a completely distributive lattice and hence a heyting algebra goguen s category of fuzzy sets set h eytan s logos fuz h and the topos of sheaves on h sh h are interconnected by pairs of adjoint functors between them each of the categories has a predicate calculus these predicate calculi are related through the functors between the categories change of base lattice gives rise to several functors which preserve or reflect specific kinds of statements in the predicate calculi this paper gives details of the categories the predicate calculi attached to them the functors between the categories and the preservation properties of those functors