generalized chirp like polyphase sequences with optimum correlation properties a new general class of polyphase sequences with ideal periodic autocorrelation function is presented the new class of sequences is based on the application of zadoff chu polyphase sequences of length n sm sup 2 where s and m are any positive integers it is shown that the generalized chirp like sequences of odd length have the optimum crosscorrelation function under certain conditions finally recently proposed generalized p4 codes are derived as a special case of the generalized chirp like sequence

a construction of odd length generators for optimal families of perfect sequences in this paper we give a construction of optimal families of n ary perfect sequences of period n 2 where n is a positive odd integer for this we re define perfect generators and optimal generators of any length n which were originally defined only for odd prime lengths by park song kim and golomb in 2016 but investigate the necessary and sufficient condition for these generators for arbitrary length n based on this we propose a construction of odd length optimal generators by using odd prime length optimal generators for a fixed odd integer n and its odd prime factor p the proposed construction guarantees at least n p p 1 phi n p phi p phi p 1 phi n 2 inequivalent optimal generators of length n in the sense of constant multiples cyclic shifts and or decimations here phi cdot is euler s totient function from an optimal generator one can construct lots of different n ary optimal families of period n 2 all of which contain p text min 1 perfect sequences where p text min is the least positive prime factor of n

degree of mapping for nonlinear mappings of monotone type abstract a classical degree function is constructed for pseudomonotone mappings from a reflexive banach space to its dual using galerkin approximations this generalizes the leray schauder degree when the banach space is a hilbert space and yields a flexible analytical tool for the study of nonlinear elliptic problems of higher order in divergence form

a measure theoretic axiomatization of fuzzy sets abstract using measurement theory this paper examines three empirical structures that underlie the representation of fuzzy sets the fuzzy membership structure the fuzzy component structure and the fuzzy system structure these qualitative structures justify the use of the standard min max system to represent fuzzy sets the results of this study facilitate the development of a sound measurement theoretic axiomatization of fuzzy systems

nonresonance conditions for generalised ϕ laplacian problems with jumping nonlinearities abstract we consider the boundary value problem 0 1 x u x u x f x u x u x a e x 0 1 0 2 c 00 u 0 c 01 u 0 c 10 u 1 c 11 u 1 where c j 0 c j 1 0 for each j 0 1 and f 0 1 r 2 r are caratheodory functions with suitable additional properties the differential operator generated by the left hand side of 0 1 together with the boundary conditions 0 2 is a generalisation of the usual p laplacian and also of the so called laplacian which corresponds to x s t t with an odd increasing homeomorphism for the p laplacian problem and more particularly the semilinear case p 2 nonresonance conditions which ensure the solvability of the problem 0 1 0 2 have been obtained in terms of either eigenvalues for non jumping f or the fucik spectrum or half eigenvalues for jumping f of the p laplacian in this paper under suitable growth conditions on and f we extend these conditions to the general problem 0 1 0 2

a browder degree theory from the nagumo degree on the hilbert space of elliptic super regularization abstract let x be a real reflexive separable locally uniformly convex banach space with locally uniformly convex dual space x let q h x be a linear compact injection according to browder and ton such that q h x where h is a real separable hilbert space a degree mapping d on x is constructed from the nagumo degree d n a on h by d t f g 0 lim t 0 d n a i 1 t q t t f q q 1 g 0 where g x is open and bounded t t is the resolvent t 1 t j 1 1 of a strongly quasibounded maximal monotone operator t x d t 2 x with 0 t 0 and f g x is demicontinuous bounded and of type s a range of sums result is also given using the skrypnik degree theory in order to further exhibit the methodology of elliptic super regularization

extension of the leray schauder degree for abstract hammerstein type mappings abstract we introduce a new extension of the classical leray schauder topological degree in a real separable reflexive banach space the new class of mappings for which the degree will be constructed is obtained essentially by replacing the compact perturbation by a composition of mappings of monotone type it turns out that the class contains the leray schauder type maps as a proper subclass the new class is not convex thus preventing the free application of affine homotopies however there exists a large class of admissible homotopies including subclass of affine ones so that the degree can be effectively used we shall construct the degree and prove that it is unique we shall generalize the borsuk theorem of the degree for odd mappings and show that the principle of omitted rays remains valid to illuminate the use of the new degree we shall briefly consider the solvability of abstract hammerstein type equations and variational inequalities

on the degree theory for mappings of monotone type and applications abstract f e browder has recently extended the concept of the classical topological degree for mappings of monotone type we introduce a new construction based on the leray schauder degree we also consider some existence and surjectivity results which illuminate the use of degree theory

ordinal decomposability and fuzzy connectives the benefit of computing with linguistic terms is now generally accepted fuzzy set theory provides us the conceptual tool for the interpretation and evaluation of linguistic concepts and expressions it constitutes a quantification of the compatibility degree of objects with the associated linguistic concept through a membership function when we make computation using fuzzy membership values such as in the evaluation of fuzzy rules confidence the implicit assumptions are that the membership values have quantitative semantics the extensive scale assumption and that the numeric values are commensurate among the different fuzzy sets generated by the different concepts involved the common scale assumption in most situations these assumptions are difficult to justify and may lead to various anomalies the membership values are more suitably interpreted only as ordinal scales where the numeric representations reflect compatibility orderings in this paper we examine the concept of fuzzy intersection and union from the perspective of decomposability and ordinal conjoint structure in measurement theory we determine conditions under which a weak order induced by a fuzzy set or otherwise can be decomposed into other weak orders we show particular cases of ordinal decomposability which correspond naturally to our concept of fuzzy intersection and union this perspective of fuzzy connectives help us resolve some of the difficulties related to the above assumptions

fixed point theory and nonlinear problems introduction among the most original and far reaching of the contributions made by henri poincare to mathematics was his introduction of the use of topological or qualitative methods in the study of nonlinear problems in analysis his starting point was the study of the differential equations of celestial mechanics and in particular of their periodic solutions his work on this topic began with his thesis in 1879 and was developed in detail in his great three volume work methodes nouvelles de la mechanique celeste which appeared in the early 1890s and summarized his many memoirs of the intervening period it continued until his memoir shortly before his death in 1912 in which he put forward the unproved fixed point result usually referred to as poincare s last geometric theorem the ideas introduced by poincare include the use of fixed point theorems the continuation method and the general concept of global analysis the writer s acquaintance with poincare s influence came through contact with solomon lefschetz and marston morse both of whom were very explicit as to the role of poincare as an initiator in this direction of mathematical development in 1934 in the foreword to his colloquium volume on the calculus of variations in the large morse had put this forward very forcefully in the first paragraph

on the decimations of frank sequences sets of decimated frank 1962 sequences with optimal correlation properties were first considered by alltop 1984 by regarding decimated frank sequences as special cases of the generalized frank sequences proposed by suehiro and hatori 1988 the set size of decimated frank sequences can be doubled without sacrificing the optimality of the correlation properties besides the proposed sequences form representatives of generalized frank sequences of different classes they thus provide an efficient way to generate signature sequences for spread spectrum multiple access systems with dynamic signature assignments

modulatable orthogonal sequences and their application to ssma systems a set of n 1 orthogonal sequences of period n sup 2 is proposed where n is a natural number each orthogonal sequence proposed can be modulated by n complex numbers of absolute value 1 so the modulated sequence is also orthogonal when n is an odd prime number the absolute value of the cross correlation function between any two of the n 1 orthogonal sequences is constant and satisfies the mathematical lower bound this property of the cross correlation function is not changed when each of the two orthogonal sequences is modulated by n complex numbers of absolute value 1 two spread spectrum multiple access ssma systems using these sequences are proposed one system is an asynchronous ssma system using the proposed sequences unmodulated the cochannel interference peak between any two channels in this system realizes the mathematical lower bound for an asynchronous ssma system using a set of orthogonal sequences the other system is a synchronous ssma system without cochannel interference which uses the modulated form of the proposed sequences

prime phase sequences with periodic correlation properties better than binary sequences for the case where p is an odd prime n or 2 is an integer and omega is a complex primitive pth root of unity a construction is presented for a family of p sup n p phase sequences symbols of the form omega sup i where each sequence has length p sup n 1 and where the maximum nontrivial correlation value c sub max does not exceed 1 square root p sup n a complete distribution of correlation values is provided as a special case of this construction a previous construction due to sidelnikov 1971 is obtained the family of sequences is asymptotically optimum with respect to its correlation properties and in comparison with many previous nonbinary designs the present design has the additional advantage of not requiring an alphabet of size larger than three the new sequences are suitable for achieving code division multiple access and are easily implemented using shift registers they wee discovered through an application of deligne s bound 1974 on exponential sums of the weil type in several variables the sequences are also shown to have strong identification with certain bent functions

on the homotopy property of topological degree for maximal monotone mappings abstract let e be a real reflexive banach space e the dual space of e and e an open bounded subset and let t i d t i 2 e i 1 2 be two maximal monotone mappings such that d t 1 d t 2 and 0 t 0 1 tt 1 1 t t 2 d t 1 d t 2 under some additional assumptions we prove that deg t 1 d t 1 0 deg t 2 d t 2 0

induction of fuzzy decision trees abstract most decision tree induction methods used for extracting knowledge in classification problems do not deal with cognitive uncertainties such as vagueness and ambiguity associated with human thinking and perception in this paper cognitive uncertainties involved in classification problems are explicitly represented measured and incorporated into the knowledge induction process a fuzzy decision tree induction method which is based on the reduction of classification ambiguity with fuzzy evidence is developed fuzzy decision trees represent classification knowledge more naturally to the way of human thinking and are more robust in tolerating imprecise conflict and missing information

degree of mapping for nonlinear mappings of monotone type densely defined mapping abstract the classical degree function constructed earlier for pseudomonotone mappings has been used to develop a broader degree theory of classical type for the sum of a maximal monotone map from a reflexive banach space to its dual together with a bounded pseudomonotone map the proof uses the generalized yosida approximation of the maximal monotone mapping

ordinal fuzzy sets fuzzy set theory has been used as a framework for interpreting imprecise linguistic expressions in general a linguistic term is described by the compatibility ordering induced in some universe of discourse uod a membership function in fuzzy set theory serves to reflect this ordering by assignment of values in 0 1 for objects in uod when we compute the meaning of a linguistic expression such as young and tall using fuzzy membership functions two implicit assumptions are made first we assume the membership values have quantitative meaning so that they can be quantitatively manipulated for example by adding or subtracting the extensive scale assumption second we assume that the scales of the membership values used in describing the different linguistic terms are comparable and the same the common scale assumption in many cases these assumptions cannot be justified some proposals have been made to address the first issue by using ordinal scale in defining fuzzy membership functions however the second issue has not been properly investigated in this paper we propose a framework that does not depend on both of these assumptions such framework will facilitate our understanding and investigation of qualitative reasoning without the extensive scale and common scale assumptions

n shift cross orthogonal sequences n shift cross orthogonal sequences and a complete complementary code derived from them are defined and discussed a general method for generating this code is also discussed a synchronous multiple user spread spectrum multiple system is proposed that uses n shift cross orthogonal sequences

on the normalized eigenvalue problems for nonlinear elliptic operators abstract this paper solves the following form of normalized eigenvalue problem a u c u 0 0 and u d where d is a bounded open set in a real infinite dimensional banach space x and both x and its dual x are locally uniformly convex a is an unbounded maximal monotone operator on x the operators c is defined and continuous only on r d such that zero is not in the weak closure of a subset of c u c u this research reveals the fact that such eigenvalue problems do not depend on any properties of c located in r d this remarkable discovery extends theorem 4 in a g kartsatos i v skrypnik normalized eigenvalues for nonlinear abstract and elliptic operators j differential equations 155 1999 443 475 and is applied to the nonlinear elliptic operators under degenerate and singular conditions

a new topological degree theory for pseudomonotone perturbations of the sum of two maximal monotone operators and applications abstract let x be a real reflexive locally uniformly convex banach space with locally uniformly convex dual space x and g be a nonempty bounded and open subset of x let t x d t 2 x and a x d a 2 x be maximal monotone operators assume further that for each y x there exists a real number y and there exists a strictly increasing function 0 0 with 0 0 t as t satisfying w x y x x y for all x d a w a x and s x 2 x is bounded of type s or bounded pseudomonotone such that 0 t a s d t d a g or 0 t a s d t d a g respectively new degree theory is developed for operators of the type t a s with degree mapping d t a s g 0 the degree is shown to be unique invariant under suitable homotopies the theory developed herein generalizes the asfaw and kartsatos degree theory for operators of the type t s new results on surjectivity and solvability of variational inequality problems are obtained the mapping theorems extend the corresponding results for operators of type t s the degree theory developed herein is used to show existence of weak solution of nonlinear parabolic problem in appropriate sobolev spaces

soft sets an ordinal formulation of vagueness with some applications to the theory of choice abstract in the theory of fuzzy sets it is usual to represent the degree of belongingness by a number lying between 0 and 1 this paper develops an alternative framework which dispenses with such cardinal numerical representations of the degree of belongingness and relies instead on an ordinal formulation the ordinal notion of a vague set is called a soft set soft sets are shown to have a tight logical relation with the concept of l sets introduced earlier by goguen the paper also discusses applications of the framework of soft sets to several problems in the theory of choice

decimations of the frank heimiller sequences the frank heimiller sequence of period n2with n phases is constructed by writing the n by n discrete fourier transform matrix by rows the periodic autocorrelation sidelobes for such a sequence are all zero small families of n phase sequences with optimal periodic cross correlations can be formed by judicious selection of decimations of the frank heimiller sequence

degree of mapping for nonlinear mappings of monotone type strongly nonlinear mapping abstract the classical degree function developed earlier for pseudomonotone operators from a reflexive banach space to its dual is extended for the special case of sobolev spaces to the sum of a pseudomonotone mapping representing a nonlinear elliptic operator and a strongly nonlinear lower order term