classical solutions of the chiral model unitons and holomorphic vector bundles this paper deals with classical solutions of thesu 2 chiral model on 2 and of a generalized chiral model on 2 1 such solutions are shown to correspond to certain holomorphic vector bundles over minitwistor space with an appropriate boundary condition the solutions called 1 unitons in 9 correspond to bundles over a compact 2 dimensional complex manifold and the problem becomes one of algebraic geometry

an evidential reasoning based consensus model for multiple attribute group decision analysis problems with interval valued group consensus requirements abstract with the aim of modeling multiple attribute group decision analysis problems with group consensus gc requirements a gc based evidential reasoning approach and further an attribute weight based feedback model are sequentially developed based on an evidential reasoning er approach in real situations however giving precise crisp assessments for alternatives is often too restrictive and difficult for experts due to incompleteness or lack of information experts may also find it difficult to give appropriate assessments on specific attributes due to limitation or lack of knowledge experience and provided data about the problem domain in this paper an er based consensus model ercm is proposed to deal with these situations in which experts assessments are interval valued rather than precise correspondingly predefined interval valued gc igc requirements need to be reached after group analysis and discussion within specified times also the process of reaching igc is accelerated by a feedback mechanism including identification rules at three levels consisting of the attribute alternative and global levels and a suggestion rule particularly recommendations on assessments in the suggestion rule are constructed based on recommendations on their lower and upper bounds detected by the identification rule at a specific level a preferentially developed industry selection problem is solved by the ercm to demonstrate its detailed implementation process validity and applicability

the cauchy problem for space time monopole equations in sobolev spaces we consider the initial value problem of space time monopole equations in one space dimension with initial data in sobolev space hs observing null structures of the system we prove local well posedness in almost critical space unconditional uniqueness and global existence are proved for s 0 moreover we show that the h1 sobolev norm grows at a rate of at most c exp ct2

the evidential reasoning approach for multiple attribute decision analysis using interval belief degrees abstract multiple attribute decision analysis mada problems having both quantitative and qualitative attributes under uncertainty can be modeled using the evidential reasoning er approach several types of uncertainties such as ignorance and fuzziness can be modeled in the er framework in this paper the er approach will be extended to model new types of uncertainties including interval belief degrees and interval data that could be incurred in decision situations such as group decision making the dempster shafer d s theory of evidence is first extended which is one of the bases of the er approach the analytical er algorithm is used to combine all evidence simultaneously two pairs of nonlinear optimization models are constructed to estimate the upper and lower bounds of the combined belief degrees and to compute the maximum and the minimum expected utilities of each alternative respectively interval data are equivalently transformed to interval belief degrees and are incorporated into the nonlinear optimization models a cargo ship selection problem is examined to show the implementation process of the proposed approach

on twistors and conformal field theories from six dimensions we discuss chiral zero rest mass field equations on six dimensional space time from a twistorial point of view specifically we present a detailed cohomological analysis develop both penrose and penrose ward transforms and analyse the corresponding contour integral formulae we also give twistor space action principles we then dimensionally reduce the twistor space of six dimensional space time to obtain twistor formulations of various theories in lower dimensions besides well known twistor spaces we also find a novel twistor space amongst these reductions which turns out to be suitable for a twistorial description of self dual strings for these reduced twistor spaces we explain the penrose and penrose ward transforms as well as contour integral formulae

an adaptive secret image sharing with a new bitwise steganographic property recently numerous studies have been conducted in the area of secret image sharing and steganography the main objective of these schemes is to produce high quality tampering resistant stego images a number of these methods are based on least significant bit embedding and hence the presence of hidden data can be detected by well designed steganalysis algorithms this paper proposes a new sharing scheme for critical images so that stego images are obtained with better visual quality and at the same time the authentication ability can be adjusted to any desired level adaptive in order to achieve these objectives the construction of cellular automata is modified so that visual quality is improved although authentication bits are hidden in cover images furthermore authentication bits are computed in such a way that any tampering with one block affects more than one block for steganographic purposes least significant bit replacement is substituted with a new blockwise xor operation so that the scheme can withstand steganalysis attacks the other interesting property of the proposed method is that the size of blocks is determined dynamically therefore our approach can be adapted with secret cover images of different sizes

backlund transformations and loop group actions we construct a local action of the group of rational maps from 2 to gl n on local solutions of flows of the zs akns sl n hierarchy we show that the actions of simple elements linear fractional transformations give local backlund transformations and we derive a permutability formula from different factorizations of a quadratic element we prove that the action of simple elements on the vacuum may give either global smooth solutions or solutions with singularities however the action of the subgroup of the rational maps that satisfy the u n reality condition on the space of global rapidly decaying solutions of the flows in the u n hierarchy is global and the action of a simple element gives a global backlund transformation the actions of certain elements in the rational loop group on the vacuum give rise to explicit time periodic multisolitons multibreathers we show that this theory generalizes the classical backlund theory of the sine gordon equation the group structures of backlund transformations for various hierarchies are determined by their reality conditions we identify the reality conditions the group structures for the sl n u k n k kdv kupershmidt wilson and gel fand dikii hierarchies the actions of linear fractional transformations that satisfy a reality condition modulo the center of the group of rational maps give backlund and darboux transformations for the hierarchy defined by the reality condition since the factorization cannot always be carried out under this reality condition the action is again local and backlund transformations only generate local solutions for these hierarchies unless singular solutions are allowed 2000 john wiley sons inc

color image encryption based on one time keys and robust chaotic maps we designed a stream cipher algorithm based on one time keys and robust chaotic maps in order to get high security and improve the dynamical degradation we utilized the piecewise linear chaotic map as the generator of a pseudo random key stream sequence the initial conditions were generated by the true random number generators the md5 of the mouse positions we applied the algorithm to encrypt the color image and got the satisfactory level security by two measures npcr and uaci when the collision of md5 had been found we combined the algorithm with the traditional cycle encryption to ensure higher security the ciphered image is robust against noise and makes known attack unfeasible it is suitable for application in color image encryption

the cauchy problem of the ward equation abstract we generalize the results of j villarroel the inverse problem for ward s system stud appl math 83 1990 211 222 a s fokas t a ioannidou the inverse spectral theory for the ward equation and for the 2 1 chiral model comm appl anal 5 2001 235 246 b dai c l terng k uhlenbeck on the space time monopole equation arxiv math dg 0602607 to study the inverse scattering problem of the ward equation with non small data and solve the cauchy problem of the ward equation with a non small purely continuous scattering data

handling possibilistic labels in pattern classification using evidential reasoning abstract a category of learning problems in which the class membership of training patterns is assessed by an expert and encoded in the form of a possibility distribution is considered each example i thus consists in a feature vector x i and a possibilistic label u 1 i u c i where u k i denotes the possibility of that example belonging to class k this problem is tackled in the framework of evidence theory the evidential distance based classifier previously introduced by one of the authors is extended to handle possibilistic labeling of training data two approaches are proposed based either on the transformation of each possibility distribution into a consonant belief function or on the use of generalized belief structures with fuzzy focal elements in each case a belief function modeling the expert s beliefs concerning the class membership of each new pattern is obtained this information may then be either interpreted by a human operator to support decision making or automatically processed to yield a final class assignment through the computation of pignistic probabilities experiments with synthetic and real data demonstrate the ability of both classification schemes to make effective use of possibilistic labels as training information

reply to the note on article the evidential reasoning approach for multiple attribute decision analysis using interval belief degrees abstract in a very recent note by gao and ni b gao m f ni a note on article the evidential reasoning approach for multiple attribute decision analysis using interval belief degrees european journal of operational research in press doi 10 1016 j ejor 2007 10 0381 they argued that yen s combination rule j yen generalizing the dempster shafer theory to fuzzy sets ieee transactions on systems man and cybernetics 20 1990 559 570 which normalizes the combination of multiple pieces of evidence at the end of the combination process was incorrect if this were the case the nonlinear programming models we proposed in y m wang j b yang d l xu k s chin the evidential reasoning approach for multiple attribute decision analysis using interval belief degrees european journal of operational research 175 2006 35 66 would also be incorrect in this reply to gao and ni we re examine their numerical illustrations and reconsider their analysis of yen s combination rule we conclude that yen s combination rule is correct and our nonlinear programming models are valid

physical space time and nonrealizable text cr structures space time views leading up to einstein s general relativity are described in relation to some of poincare s early ideas on the subject the basic geometry of twistor theory is introduced as it arises both from minkowski space time and the more general curved einstein models it is shown how this provides a cr structure this being in essence another of poincare s poioneering concepts in a natural way nonrealizable cr structure can arise and an example is presented due to c d hill g a j sparling and the author of a complex manifold with boundary which cannot be extended as a complex manifold beyond its c sup infinity boundary

how to select and how to rank projects the promethee method abstract in this paper we present the promethee methods a new class of outranking methods in multicriteria analysis their main features are simplicity clearness and stability the notion of generalized criterion is used to construct a valued outranking relation all the parameters to be defined have an economic signification so that the decision maker can easily fix them two ways of treatment are proposed it is possible to obtain either a partial preorder promethee i or a complete one promethee ii both on a finite set of feasible actions a comparison is made with the electre iii method the stability of the results given by the two methods is analysed numerical applications are given in order to illustrate the properties of the new methods and some further problems are discussed

on the combination and normalization of interval valued belief structures this paper investigates the issues of combination and normalization of interval valued belief structures within the framework of dempster shafer theory dst of evidence existing approaches are reviewed examined and critically analysed they either ignore the normalization or separate it from the combination process leading to irrational or suboptimal interval valued belief structures a new logically correct optimality approach is developed where the combination and the normalization are optimised together rather than separately numerical examples are provided throughout the paper

a family of hyperchaotic multi scroll attractors in rn abstract in this work we present a mechanism how to yield a family of hyperchaotic multi scroll systems in r n based on unstable dissipative systems this class of systems is constructed by a switching control law changing the equilibrium point of an unstable dissipative system for each equilibrium point presented in the system a scroll emerges the switching control law that governs the position of the equilibrium point varies according to the number of scrolls displayed in the attractor thus if two systems display different numbers of scrolls they have different switching control laws this paper also presents a generalized theory that explains different approaches such as hysteresis and step functions from a unified viewpoint extending the concept of chaos in r 3 to hyperchaotic multi scroll systems in r n n 4 an illustrative example of synchronizing a communication system is given based on the developed theory

hyperchaotic encryption based on multi scroll piecewise linear systems a hyperchaotic multi scroll piecewise linear system in r4 is binarized to generate a pseudo random sequence which encrypt a grayscale image via symmetric key algorithm the sequence is analyzed throughout statistical tests according to the national institute of standards and technology nist specifications the scrolls of the system are the result of a switching law that changes between the saddle hyperbolic equilibria of piecewise linear systems with eigenvalues as follows two negative real and one pair of complex conjugate eigenvalues with positive real part thus the encryption quality is evaluated depending on the variation of the number of scrolls

uniqueness of weak solutions of 1 1 dimensional wave maps in this paper we prove that finite energy distributional solutions to the cauchy problem of wave maps from 1 1 dimensional minkowsky space to any complete riemannian manifold are unique

backlund transformations ward solitons and unitons the ward equation also called the modified 2 1 chiral model is obtained by a dimension reduction and a gauge fixing from the self dual yang mills field equation on r it has a lax pair and is an integrable system ward constructed solitons whose extended solutions have distinct simple poles he also used a limiting method to construct 2 solitons whose extended solutions have a double pole ioannidou and zakrzewski and anand constructed more soliton solutions whose extended solutions have a double or triple pole some of the main results of this paper are i we construct algebraic backlund transformations bts that generate new solutions of the ward equation from a given one by an algebraic method ii we use an order k limiting method and algebraic bts to construct explicit ward solitons whose extended solutions have arbitrary poles and multiplicities iii we prove that our construction gives all solitons of the ward equation explicitly and the entries of ward solitons must be rational functions in x y and t iv since stationary ward solitons are unitons our method also gives an explicit construction of all k unitons from finitely many rational maps from c to c

global strong solution to the thirring model in critical space abstract we obtain a strong solution in charge critical space l 2 r of the thirring system and federbusch equations in one space dimension by using solution representation of the models the uniqueness is obtained for the solution l 0 t l 2 r l 4 r a decay of local charge and asymptotic behavior of the field can be shown directly

global solutions to space time monopole equations in one space dimension abstract we prove global existence of solutions to space time monopole equations in one space dimension observing the null structure of the system we first prove local existence in l p by applying a bilinear estimate from a priori l p estimates we can extend the local solution to the global one for the critical case l 1 the concentration of the solution is denied to show the time global solvability

a secret sharing scheme based on cellular automata a new secret sharing scheme based on a particular type of discrete delay dynamical systems memory cellular automata is proposed specifically such scheme consists of a k n threshold scheme where the text to be shared is considered as one of the k initial conditions of the memory cellular automata and the n shares to be distributed are n consecutive configurations of the evolution of such cellular automata it is also proved to be perfect and ideal

measures of uncertainty in expert systems abstract this paper compares four measures that have been advocated as models for uncertainty in expert systems the measures are additive probabilities used in the bayesian theory coherent lower or upper previsions belief functions used in the dempster shafer theory and possibility measures fuzzy logic special emphasis is given to the theory of coherent lower previsions in which upper and lower probabilities expectations and conditional probabilities are constructed from initial assessments through a technique of natural extension mathematically all the measures can be regarded as types of coherent lower or upper previsions and this perspective gives some insight into the properties of belief functions and possibility measures the measures are evaluated according to six criteria clarity of interpretation ability to model partial information and imprecise assessments especially judgements expressed in natural language rules for combining and updating uncertainty and their justification consistency of models and inferences feasibility of assessment and feasibility of computations each of the four measures seems to be useful in special kinds of problems but only lower and upper previsions appear to be sufficiently general to model the most common types of uncertainty

approximate reasoning an evidence theory abstract one approach to approximate reasoning is to make use of results arising from research in evidence theory in this theory evidence is represented by evidential functions and the reasoning is conducted by evidential operations on them our objective in this paper is to contribute to the understanding of these evidential operations we discuss some basic operations on evidential functions the orthogonal sum operation the discount operation the refining operation and the coarsening operation for example we show that coarsening and discount operations are not commutative with the orthogonal sum operation the relationships among the orthogonal sum refining coarsening and discount operations are all investigated a well known case study from the evidential reasoning literature is used to illustrate the interplay between these operations

modeling uncertainty in multi criteria decision analysis abstract his paper provides a review of multiple criteria decision analysis mcda for cases where attribute evaluations are uncertain the main aim is to identify different tools which can be used to represent uncertain evaluations and to broadly survey the available decision models that can be used to support uncertain decision making the review includes models using probabilities or probability like quantities explicit risk measures such as quantiles and variances fuzzy numbers and scenarios the practical assessment of uncertain outcomes and preferences associated with these outcomes is also discussed

dispersionless limit of the noncommutative potential kp hierarchy and solutions of the pseudodual chiral model in 2 1 dimensions the usual dispersionless limit of the kp hierarchy does not work in the case where the dependent variable has values in a noncommutative e g matrix algebra passing over to the potential kp hierarchy there is a corresponding scaling limit in the noncommutative case which turns out to be the hierarchy of a pseudodual chiral model in 2 1 dimensions pseudodual to a hierarchy extending ward s modified integrable chiral model applying the scaling procedure to a method generating exact solutions of a matrix potential kp hierarchy from solutions of a matrix linear heat hierarchy leads to a corresponding method that generates exact solutions of the matrix dispersionless potential kp hierarchy i e the pseudodual chiral model hierarchy we use this result to construct classes of exact solutions of the su m pseudodual chiral model in 2 1 dimensions including various multiple lump configurations

a t n multi secret sharing scheme in the t n multi secret sharing scheme there are n participants in the system at least t or more participants can easily pool their secrets shadows and reconstruct p secrets at the same time chien et al ieice trans fundamentals e83 a 2000 2762 used n p t 1 public values 2 n p t x n p storages and solved n p t simultaneous equations to share p secrets in this article we shall propose an alternative t n multi secret sharing based on shamir s secret sharing we shall use n p t 1 or n 1 public values 2 t 1 or 2 p 1 storages and employ the lagrange interpolation polynomial to share p secrets our scheme will have exactly the same power as chien et al s scheme

minitwistors and 3d yang mills higgs theory we construct a minitwistor action for yang mills higgs ymh theory in three dimensions the feynman diagrams of this action will construct perturbation theory around solutions of the bogomolny equations in much the same way that mhv maximally helicity violating diagrams describe perturbation theory around the self dual yang mills equations in four dimensions we also provide a new formula for all tree amplitudes in ymh theory and its maximally supersymmetric extension in terms of degree d maps to minitwistor space we demonstrate its relationship to the roiban spradlin volovich witten rsvw formula in four dimensions and show that it generates the correct mhv amplitudes at d 1 and factorizes correctly in all channels for all degrees we construct a minitwistor action for yang mills higgs ymh theory in three dimensions the feynman diagrams of this action will construct perturbation theory around solutions of the bogomolny equations in much the same way that mhv maximally helicity violating diagrams describe perturbation theory around the self dual yang mills equations in four dimensions we also provide a new formula for all tree amplitudes in ymh theory and its maximally supersymmetric extension in terms of degree d maps to minitwistor space we demonstrate its relationship to the roiban spradlin volovich witten rsvw formula in four dimensions and show that it generates the correct mhv amplitudes at d 1 and factorizes correctly in all channels for all degrees

time frequency analysis of the dirac equation abstract the purpose of this paper is to investigate several issues concerning the dirac equation from a time frequency analysis perspective more precisely we provide estimates in weighted modulation and wiener amalgam spaces for the solutions of the dirac equation with rough potentials we focus in particular on bounded perturbations arising as the weyl quantization of suitable time dependent symbols as well as on quadratic and sub quadratic non smooth functions hence generalizing the results in 40 we then prove local well posedness on the same function spaces for the nonlinear dirac equation with a general nonlinearity including power type terms and the thirring model for this study we adopt the unifying framework of vector valued time frequency analysis 56 most of the preliminary results are stated under general assumptions and hence they may be of independent interest

harmonic maps into lie groups classical solutions of the chiral model on considere deux aspects de la structure algebrique de 7b m l espace des applications harmoniques d un domaine a 2 dimensions simplement connexe dans un groupe de lie reel g r la forme reelle d un groupe complexe g on construit une representation du groupe boucle 7b a s 1 g r sur 7b m correspondant a l algebre de lie de kacmoody des deformations infinitesimales on decrit l action sur 7b m et l action d un sous groupe sur l espace des applications harmoniques dans des gaussmanniens dans une seconde partie on se restreint a une theorie qui s applique seulement quand est un domaine riemannien a 2 dimensions simplement connexe et le groupe est g r u n

modeling vague beliefs using fuzzy valued belief structures abstract this paper presents a rational approach to the representation and manipulation of imprecise degrees of belief in the framework of evidence theory we adopt as a starting point the non probabilistic interpretation of belief functions provided by smets transferable belief model as well as previous generalizations of evidence theory allowing to deal with fuzzy propositions we then introduce the concepts of interval valued and fuzzy valued belief structures defined respectively as crisp and fuzzy sets of belief structures verifying hard or elastic constraints we then proceed with a generalization of various concepts of dempster shafer theory including those of belief and plausibility functions combination rules and normalization procedures most calculations implied by the manipulation of these concepts are based on simple forms of linear programming problems for which analytical solutions exist making the whole scheme computationally tractable we discuss the application of this framework in the areas of decision making under uncertainty and classification of fuzzy data

note a preference ranking organisation method the promethee method for multiple criteria decision making principles for a new family of outranking methods are given the main aim of the proposed promethee approach is to be as easily understood as possible by the decision maker it is based on extensions of the notion of criterion six possible extensions are considered these extensions can easily be identified by the decision maker because the parameters to be defined at most 2 have an economic significance a valued outranking graph is constructed by using a preference index two possibilities are considered to solve the ranking problem by using this valued graph promethee i provides a partial preorder and promethee ii a total preorder on the set of the possible actions

belief functions and default reasoning abstract we present a new approach to deal with default information based on the theory of belief functions our semantic structures inspired by adams epsilon semantics are epsilon belief assignments where mass values are either close to 0 or close to 1 in the first part of this paper we show that these structures can be used to give a uniform semantics to several popular non monotonic systems including kraus lehmann and magidor s system p pearl s system z brewka s preferred subtheories geffner s conditional entailment pinkas penalty logic possibilistic logic and the lexicographic approach in the second part we use epsilon belief assignments to build a new system called lcd and show that this system correctly addresses the well known problems of specificity irrelevance blocking of inheritance ambiguity and redundancy

an interval dempster shafer approach abstract in the dempster shafer theory basic probability assignment plays a key role all other measures can be defined in terms of basic probability assignment which can only take point values in 0 1 in practical situations the basic probability assignment is usually provided by experts subjectively because of which an interval value instead of a point value is frequently provided the original theory does not provide any means to handle interval values in this work the definitions of all basic measures in dempsters shafer s theory were extended so that the theory can also be applied to interval valued situations it is shown that the original theory is a special case of the proposed one to illustrate the approach a numerical example is given

an extended rule based inference for general decision making problems complex decision making problems are usually modeled in terms of a number of decisive variables that are related hierarchically pieces of evidence are aggregated in a bottom up way to determine the final decision goal for dealing with such problems ishizuka et al 5 6 developed a rule based inference procedure by using fuzzy sets to represent imprecise data and employed the dempster shafer theory to aggregate evidence for structural damage assessment this paper highlights the necessity of applying the rules with all possible consequent clauses in the procedure with the considerations of information quality and quantity when applying the procedure to more general decision making problems the use of such rules can provide high quality information which contains much less ignorance in the resultant information also it can afford more information due to the decrease in total ignorance a simple example with two cases is used to compare the results based on the two different presentations of rules in the inference procedure for illustrating the importance of considering the rules proposed in this paper

environmental impact assessment using the evidential reasoning approach environmental impact assessment eia problems are often characterised by a large number of identified environmental factors that are qualitative in nature and can only be assessed on the basis of human judgments which inevitably involve various types of uncertainties such as ignorance and fuzziness so eia problems need to be modelled and analysed using methods that can handle uncertainties the evidential reasoning er approach provides such a modelling framework and analysis method in this paper the er approach will be applied to conduct eia analysis for the first time the environmental impact consequences are characterized by a set of assessment grades that are assumed to be collectively exhaustive and mutually exclusive all assessment information quantitative or qualitative complete or incomplete and precise or imprecise is modelled using a unified framework of a belief structure the original er approach with a recursive er algorithm will be introduced and a new analytical er algorithm will be investigated which provides a means for using the er approach in decision situations where an explicit er aggregation function is needed such as in optimisation problems the er approach will be used to aggregate multiple environmental factors resulting in an aggregated distributed assessment for each alternative policy a numerical example and its modified version are studied to illustrate the detailed implementation process of the er approach and demonstrate its potential applications in eia

global strong solution to a nonlinear dirac type equation in one dimension abstract this paper studies a class of nonlinear massless dirac equations in one dimension which include the equations for the massless thirring model and the massless gross neveu model under the assumptions of the initial data having small charge and being bounded the global existence of the strong solution is established the decay of the local charge is also proved

maximal confidence intervals of the interval valued belief structure and applications an unsolved problem in the interval valued belief structure is the existence of maximal confidence intervals referring to the credible and maximal interval valued beliefs assigned to focal elements in which every point can be reached by a combination rule in this study the existence of maximal confidence intervals of the interval valued belief structure was investigated and validated in addition some applications of the maximal confidence interval in constructing valid and normalized interval valued belief structures are discussed a numerical experiment was conducted to illustrate the existence of maximal confidence intervals several propositions and a theorem were further proposed to demonstrate the validity of the maximal confidence interval by using the concept of the maximal confidence interval a procedure was proposed to construct valid and normalized interval valued belief structures and some meaningful guidance for assigning interval valued beliefs was also suggested to the experts finally a series of well designed examples was presented as applications of the maximal confidence interval the proposed procedure and the suggestions they indicated that valid and normalized interval valued belief structures can be achieved accurately and efficiently in practical applications with the proposed procedure and guidance on the basis of the concept of the maximal confidence interval

a novel lossless color image encryption scheme using 2d dwt and 6d hyperchaotic system this paper proposes a new lossless encryption algorithm for color images based on a six dimensional 6d hyperchaotic system and the two dimensional 2d discrete wavelet transform dwt different from the current image encryption methods our image encryption scheme is constructed using the 2d dwt and 6d hyperchaotic system in both the frequency domain and the spatial domain where the key streams depend on not only the hyperchaotic system but the plain image in the presented algorithm the plain image is firstly divided into four image sub bands by means of the 2d dwt secondly the sub bands are permutated by a key stream and then the size of them is decreased by a constant factor thirdly the 2d inverse dwt is employed to reconstruct an intermediate image by the four encrypted image sub bands finally to further enhance the security the pixel values of the intermediate image are modified by using another key stream experimental results and security analysis demonstrate that the proposed algorithm has a high security fast speed and can resist various attacks

extended wave solutions in an integrable chiral model in 2 1 dimensions there is a modification of the su 2 chiral model which is integrable in 2 1 dimensions j math phys 29 386 1988 in addition to localized lumps it admits extended wave solutions which move at constant velocity the interaction of two waves causes each to experience a phase shift in the interaction between a wave and a lump the wave suffers no phase shift but the lump changes shape

weak solutions of the massless field equations we consider weak solutions of the zero rest mass z r m equations described in eastwood et al 1981 the space of hyperfunctions which contains the space of distributions is defined and we consider hyper function solutions of the equations on real minkowski space m i and its conformal compactification m we define a hyperfunction z r m field to be future or past analytic if it is the boundary value of a holomorphic z r m field on the future or past tube of complex minkowski space respectively and we demonstrate that any field on m i that is the sum of future and past analytic fields extends as a hyperfunction z r m field to all of m it is shown that any distribution solution on m i splits as required and hence extends as a hyperfunction solution to m twistor methods are then used to show that the same applies in the more general case of hyperfunction solutions on m i this leads to an alternative proof of the main result of wells 1981 a hyperfunction z r m field on compactified real minkowski space is a unique sum of future and past analytic solutions

the group consensus based evidential reasoning approach for multiple attributive group decision analysis abstract many multiple attribute decision analysis problems include both quantitative and qualitative attributes with various kinds of uncertainties such as ignorance fuzziness interval data and interval belief degrees an evidential reasoning er approach developed in the 1990s and in recent years can be used to model these problems in this paper the er approach is extended to group consensus gc situations for multiple attributive group decision analysis problems in order to construct and check the gc a compatibility measure between two belief structures is developed first considering two experts utilities the compatibility between their assessments is naturally constructed using the compatibility measure based on the compatibility between two experts assessments the gc at a specific level that may be the attribute level the alternative level or the global level can be constructed and reached after the group analysis and discussion within specified times under the condition of gc we conduct a study on the forming of group assessments for alternatives the achievement of the aggregated utilities of assessment grades and the properties and procedure of the extended er approach an engineering project management software selection problem is solved by the extended er approach to demonstrate its detailed implementation process and its validity and applicability

interval efficiency assessment using data envelopment analysis this paper studies how to conduct efficiency assessment using data envelopment analysis dea in interval and or fuzzy input output environments a new pair of interval dea models is constructed on the basis of interval arithmetic which differs from the existing dea models handling interval data in that the former is a linear ccr model without the need of extra variable alternations and uses a fixed and unified production frontier i e the same constraint set to measure the efficiencies of decision making units dmus with interval input and output data while the latter is usually a nonlinear optimization problem with the need of extra variable alternations or scale transformations and utilizes variable production frontiers i e different constraint sets to measure interval efficiencies ordinal preference information and fuzzy data are converted into interval data through the estimation of permissible intervals and a level sets respectively and are incorporated into the interval dea models the proposed interval dea models are developed for measuring the lower and upper bounds of the best relative efficiency of each dmu with interval input and output data which are different from the interval formed by the worst and the best relative efficiencies of each dmu a minimax regret based approach mra is introduced to compare and rank the efficiency intervals of dmus two numerical examples are provided to show the applications of the proposed interval dea models and the preference ranking approach

fingerprint images encryption via multi scroll chaotic attractors this paper proposes a chaotic fingerprint images encryption approach an image of a fingerprint is encrypted via a two dimensional 2d chaotic sequence obtained from multi scroll chaotic attractors initial values of the chaotic attractors are served as the private key which can be generated from the pixel distribution of the binary images of the captured fingerprints due to the dynamic uncertainties in the acquisition process of fingerprint images the keys generated from the pixel value distribution are virtually random with the elaborately designed 2d chaotic sequence the encrypted fingerprint images have balanced 0 1 ratio and ideal nonlinearity only with the valid private key can the images of fingerprint be recovered simulation results and 2d dft validate this chaotic encryption approach

global solution to nonlinear dirac equation for gross neveu model in 1 1 dimensions abstract this paper studies a class of nonlinear dirac equations with cubic terms in r 1 1 which include the equations for the massive thirring model and the massive gross neveu model under the assumption that the initial data has bounded l 2 norm the global existence and the uniqueness of the strong solution in c 0 l 2 r 1 are proved

on the normalization of interval and fuzzy weights the normalization of interval and fuzzy weights is often necessary in multiple criteria decision analysis mcda under uncertainty especially in analytic hierarchy process ahp with interval or fuzzy judgements the existing normalization methods based on interval arithmetic and fuzzy arithmetic are found flawed and need to be revised this paper presents the correct normalization methods for interval and fuzzy weights and offers relevant theorems in support of them numerical examples are examined to show the correctness of the proposed normalization methods and their differences from those existing normalization methods

a dempster shafer approach for recognizing machine features from cad models abstract this paper introduces an evidential reasoning based approach for recognizing and extracting manufacturing features from solid model description of objects a major difficulty faced by previously proposed methods for feature extraction has been the interaction between features due to non uniqueness and ambiguousness in feature representation to overcome this difficulty we introduce a dempster shafer approach for generating and combining geometric and topologic evidences to identify and extract interacting features the main contributions of this research include introducing different classes of evidences based on the geometric and topologic relationships at different abstraction levels for effective evidential reasoning and developing the principle of association to overcome the mutual exclusiveness assumption of the dempster shafer theory experiments demonstrate the effectiveness of the proposed approach in extracting interacting machine features

a twistor inspired darboux transform for the sine gordon equation the solutions to the sine gordon equation which are derived from an ansatz based on the methods of twistor theory are shown to correspond to darboux transformations for a certain linear equation the linear problem is shown to arise in several different ways and a relationship between the darboux transformation for linear equations of this type and the backlund transformation is examined a possible extension to well known monopole ansatze is briefly considered

linguistic computational model based on 2 tuples and intervals herrera and martinez initiated a 2 tuple fuzzy linguistic representation model for computing with words moreover wang and hao further developed a new 2 tuple fuzzy linguistic representation model to deal with the linguistic term sets that are not uniformly and symmetrically distributed this study proposes another linguistic computational model based on 2 tuples and intervals which we call an interval version of the 2 tuple fuzzy linguistic representation model the proposed model possesses three steps 1 interval numerical scale 2 computation based on interval numbers and 3 a generalized inverse operation of the interval numerical scale the first step transforms linguistic terms into interval numbers based on which the second step is executed with output as an interval number finally this number is then mapped into the interval of the linguistic 2 tuples by the generalized inverse operation this study also generalizes the numerical scale approach presented in the wang and hao model to set the interval numerical scale by considering the context where semantics of linguistic terms are defined by interval type 2 fuzzy sets it2 fss in order to compare the proposed model with the existing linguistic computational model based on it2 fss we have conducted extensive simulations the simulations demonstrate that the results obtained by our proposal are consistent with the results of the linguistic computational model based on it2 fss in some sense in a vast majority of cases

evidential reasoning based preference programming for multiple attribute decision analysis under uncertainty multiple attribute decision analysis mada problems having both quantitative and qualitative attributes under uncertainty can be modelled and analysed using the evidential reasoning er approach several types of uncertainty such as ignorance and fuzziness can be consistently modelled in the er framework in this paper both interval weight assignments and interval belief degrees are considered which could be incurred in many decision situations such as group decision making based on the existing er algorithm several pairs of preference programming models are constructed to support global sensitivity analysis based on the interval values and to generate the upper and lower bounds of the combined belief degrees for distributed assessment and also the expected values for ranking of alternatives a post optimisation procedure is developed to identify non dominated solutions examine the robustness of the partial ranking orders generated and provide guidance for the elicitation of additional information for generating more desirable assessment results a car evaluation problem is examined to show the implementation process of the proposed approach

parameter estimation based on interval valued belief structures abstract parameter estimation based on uncertain data represented as belief structures is one of the latest problems in the dempster shafer theory in this paper a novel method is proposed for the parameter estimation in the case where belief structures are uncertain and represented as interval valued belief structures within our proposed method the maximization of likelihood criterion and minimization of estimated parameter s uncertainty are taken into consideration simultaneously as an illustration the proposed method is employed to estimate parameters for deterministic and uncertain belief structures which demonstrates its effectiveness and versatility

weighted cautious conjunctive rule for belief functions combination denoeux proposed an operator called the cautious conjunctive rule ccr to combine non dogmatic belief functions i e the frame is considered a focal element from reliable dependent sources which can occur in practice however in cases such as uncertain multiple attribute and group decision analyses belief functions may denote data that vary in importance this paper extends ccr as a weighted ccr wccr to combine belief functions in consideration of their relative weights in such situations properties of wccr are analyzed proven and demonstrated using numerical examples in particular the consideration of relative weights enables wccr to combine dogmatic belief functions the normalized wccr is further constructed and used to assess the trustworthiness of a hospital information system employed in many hospitals in anhui province china

ds ahp method a mathematical analysis including an understanding of uncertainty abstract the analytic hierarchy process ahp was developed to aid decision makers to rank or sort information based on a number of criteria a recent advance is the ds ahp method which incorporates the dempster shafer theory of evidence with ahp this method allows judgements on groups of decision alternatives da to be made it also offers a measure of uncertainty in the final results in this paper a mathematical analysis of ds ahp is included constructing the functional form of the preference weightings given to groups of da these functions allow an understanding of the appropriateness of the rating scale values used in the ds ahp method through evaluating the range of uncertainty able to be expressed by the decision maker

theory and applications of cellular automata in cryptography this paper deals with the theory and application of cellular automata ca for a class of block ciphers and stream ciphers based on ca state transitions certain fundamental transformations are defined which are block ciphering functions of the proposed enciphering scheme these fundamental transformations are found to generate the simple alternating group of even permutations which in turn is a subgroup of the permutation group these functions are implemented with a class of programmable cellular automata pca built around rules 51 153 and 195 further high quality pseudorandom pattern generators built around rule 90 and 150 programmable cellular automata with a rule selector i e combining function has been proposed as running key generators in stream ciphers both the schemes provide better security against different types of attacks with a simple regular modular and cascadable structure of ca hardware implementation of such schemes idealy suit vlsi implementation

on the combination of self organized systems to generate pseudo random numbers cellular automata ca is a self organizing structure with complex behavior which can be used to generating pseudo random numbers pure ca has a simple structure and has no ability to produce long sequences of random numbers but in order to resolve this problem a programmable controllable ca pcca using actuating factor or combination of different self organizing criticality phenomena can be used the purpose of the aforementioned methods is the use of the ca speed while preventing the automata self organizing factor for specific use in generating random numbers in this paper a pcca by using sandpile model is proposed the sandpile model is a complex system that operates at a critical state between chaos and order this state is known as self organized criticality soc and is characterized by displaying invariant scale behavior in the precise case of the sandpile model by randomly and continuously dropping sand grains on top of a two dimensional grid lattice a power law relationship between the frequency and size of sand avalanches is observed the avalanche behavior and the pure ca behavior are combined in a novel method which can be used as the pseudo random number generator prng experimental results show that this generator is able to reach a random behavior from a pseudo chaotic one by combining two self organized systems in addition to independency of the initial state it has been also indicated that the generated numbers are independent and its probability distribution is likely to be uniform accordingly some tests of prngs such as entropy chi square diehard and several basic statistical tests have been performed and all of them have been successfully passed

secret image sharing based on cellular automata and steganography recently lin and tsai secret image sharing with steganography and authentication the journal of systems and software 73 2004 405 414 and yang et al improvements of image sharing with steganography and authentication the journal of systems and software 80 2007 1070 1076 proposed secret image sharing schemes combining steganography and authentication based on shamir s polynomials the schemes divide a secret image into some shadows which are then embedded in cover images in order to produce stego images for distributing among participants to achieve better authentication ability chang et al sharing secrets in stego images with authentication pattern recognition 41 2008 3130 3137 proposed in 2008 an improved scheme which enhances the visual quality of the stego images as well and the probability of successful verification for a fake stego block is 1 16 in this paper we employ linear cellular automata digital signatures and hash functions to propose a novel t n threshold image sharing scheme with steganographic properties in which a double authentication mechanism is introduced which can detect tampering with probability 255 256 employing cellular automata instead of shamir s polynomials not only improves computational complexity from o nlog 2n to o n but obviates the need to modify pixels of cover images unnecessarily compared to previous methods c lin w tsai secret image sharing with steganography and authentication the journal of systems and software 73 2004 405 414 c yang t chen k yu c wang improvements of image sharing with steganography and authentication the journal of systems and software 80 2007 1070 1076 c chang y hsieh c lin sharing secrets in stego images with authentication pattern recognition 41 2008 3130 3137 we use fewer number of bits in each pixel of cover images for embedding data so that a better visual quality is guaranteed we further present some experimental results

nontrivial soliton scattering in an integrable chiral model in 2 1 dimensions soliton solutions of an integrable chiral model in 2 1 dimensions are studied through the solution of a riemann problem with zeros solitons of this model have already been found r s ward j math phys 29 386 1988 which scatter in a trivial manner by exploiting a connection with the o 3 model it is shown that the model also has solitons that are not contained in the above construction and whose scattering properties are highly nontrivial soliton scattering is also discussed for a model which interpolates between this integrable model and the su 2 chiral model

permutation and sampling with maximum length ca or pseudorandom number generation abstract in this paper we study the effect of dynamic permutation and sampling on the randomness quality of sequences generated by cellular automata ca dynamic permutation and sampling have not been explored in previous ca work and a suitable implementation is shown using a two ca model three different schemes that incorporate these two operations are suggested weighted permutation vector sampling with controlled multiplexing weighted permutation vector sampling with irregular decimation and permutation programmed ca sampling the experiment results show that the resulting sequences have varying degrees of improvement in diehard results and linear complexity compared to the ca

evidential reasoning rule for evidence combination this paper aims to establish a unique evidential reasoning er rule to combine multiple pieces of independent evidence conjunctively with weights and reliabilities the novel concept of weighted belief distribution wbd is proposed and extended to wbd with reliability wbdr to characterise evidence in complement of belief distribution bd introduced in dempster shafer d s theory of evidence the implementation of the orthogonal sum operation on wbds and wbdrs leads to the establishment of the new er rule the most important property of the new er rule is that it constitutes a generic conjunctive probabilistic reasoning process or a generalised bayesian inference process it is shown that the original er algorithm is a special case of the er rule when the reliability of evidence is equal to its weight and the weights of all pieces of evidence are normalised it is proven that email protected s rule is also a special case of the er rule when each piece of evidence is fully reliable the er rule completes and enhances email protected s rule by identifying how to combine pieces of fully reliable evidence that are highly or completely conflicting through a new reliability perturbation analysis the main properties of the er rule are explored to facilitate its applications several existing rules are discussed and compared with the er rule numerical and simulation studies are conducted to show the features of the er rule

twistors in 2 1 dimensions the geometry of twistors for 2 1 dimensional flat space time is described functions on twistor space generate solutions of various field equations in space time as an illustrative example it is shown what a sine gordon soliton looks like in this twistor description

numerical twistor procedure for solving a nonlinear field equation this paper concentrates on an integrable su 2 chiral equation in two space and one time dimensions admitting soliton solutions it is in effect a reduction of the self dual yang mills equations in 2 2 dimensions and can therefore be solved by twistor methods however only some solutions can be constructed explicitly and to solve a general initial value problem requires some kind of numerical computation the paper describes a way of implementing the twistor solution procedure numerically in order to do this

chaos and ergodicity are decidable for linear cellular automata over z mz n abstract we prove that important properties describing complex behaviours as ergodicity chaos topological transitivity and topological mixing are decidable for one dimensional linear cellular automata lca over z m z n theorem 6 and corollary 7 a large and important class of cellular automata ca which are able to exhibit the complex behaviours of general ca and are used in applications in particular we provide a decidable characterization of ergodicity which is known to be equivalent to all the above mentioned properties in terms of the characteristic polynomial of the matrix associated with lca we stress that the setting of lca over z m z n with n 1 is more expressive gives rise to much more complex dynamics and is more difficult to deal with than the already investigated case n 1 the proof techniques from 23 25 used when n 1 for obtaining decidable characterizations of dynamical and ergodic properties can no longer be exploited when n 1 for achieving the same goal indeed in order to get the decision algorithm algorithm 1 we need to prove a non trivial result of abstract algebra theorem 5 which is also of interest in its own we also illustrate the impact of our results in real world applications concerning the important and growing domain of cryptosystems which are often based on one dimensional lca over z m z n with n 1 as a matter of facts since cryptosystems have to satisfy the so called confusion and diffusion properties ensured by ergodicity and chaos respectively of the involved lca algorithm 1 turns out to be an important tool for building chaotic ergodic one dimensional linear ca over z m z n and hence for improving the existing methods based on them

extensions of the topsis for group decision making under fuzzy environment the aim of this paper is to extend the topsis to the fuzzy environment owing to vague concepts frequently represented in decision data the crisp value are inadequate to model real life situations in this paper the rating of each alternative and the weight of each criterion are described by linguistic terms which can be expressed in triangular fuzzy numbers then a vertex method is proposed to calculate the distance between two triangular fuzzy numbers according to the concept of the topsis a closeness coefficient is defined to determine the ranking order of all alternatives by calculating the distances to both the fuzzy positive ideal solution fpis and fuzzy negative ideal solution fnis simultaneously finally an example is shown to highlight the procedure of the proposed method at the end of this paper

twistor theory at fifty from contour integrals to twistor strings we review aspects of twistor theory its aims and achievements spanning the last five decades in the twistor approach space time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold the twistor space after giving an elementary construction of this space we demonstrate how solutions to linear and nonlinear equations of mathematical physics anti self duality equations on yang mills or conformal curvature can be encoded into twistor cohomology these twistor correspondences yield explicit examples of yang mills and gravitational instantons which we review they also underlie the twistor approach to integrability the solitonic systems arise as symmetry reductions of anti self dual asd yang mills equations and einstein weyl dispersionless systems are reductions of asd conformal equations we then review the holomorphic string theories in twistor and ambitwistor spaces and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes finally we discuss the newtonian limit of twistor theory and its possible role in penrose s proposal for a role of gravity in quantum collapse of a wave function

monopoles and geodesics using the holomorphic geometry of the space of straight lines in euclidean 3 space it is shown that every static monopole of chargek may be constructed canonically from an algebraic curve by means of the atiyah ward ansatz a k

a general evidential reasoning algorithm for multi attribute decision analysis under interval uncertainty abstract evidential reasoning er is one of the important approaches used to solve multi attribute decision analysis mada problems under uncertainty involving both quantitative and qualitative attributes the er approach provides a distributed modeling framework fusing several types of uncertain and incomplete information including ignorance and vagueness to work out the optimum alternative rationally in this paper we review the original er algorithm and recursive interval evidential reasoning ier algorithm and derive a general analytical algorithm for ier thus enabling an aggregation of attributes assessments in an explicit manner then a more complicated uncertain occasion is investigated where it is possible to conduct evaluation assessments including quantitative data belief degrees grades and weights in the form of an interval a pair of nonlinear optimization models based on the new algorithm is established to solve this problem under interval uncertainty and the maximum and minimum expected utilities of each alternative are calculated and ranked accordingly additionally we prove that the original er and recursive ier algorithms are special cases of the new algorithm finally a numerical example is used to demonstrate the steps involved in the proposed approach

solutions of the modified chiral model in 2 1 dimensions in this paper we deal with classical solutions of the modified chiral model on r2 1 such solutions are shown to correspond to products of various factors which we call time dependent unitons then the problem of solving the system of second order partial differential equations for the chiral field is reduced to solving a sequence of systems of first order partial differential equations for the unitons

generalization of the dempster shafer theory a fuzzy valued measure the dempster shafer theory dst may be considered as a generalization of the probability theory which assigns mass values to the subsets of the referential set and suggests an interval valued probability measure there have been several attempts for fuzzy generalization of the dst by assigning mass probability values to the fuzzy subsets of the referential set the interval valued probability measures thus obtained are not equivalent to the original fuzzy body of evidence in this paper a new generalization of the dst is put forward that gives a fuzzy valued definition for the belief plausibility and probability functions over a finite referential set these functions are all equivalent to one another and to the original fuzzy body of evidence the advantage of the proposed model is shown in three application examples it can be seen that the proposed generalization is capable of modeling the uncertainties in the real world and eliminate the need for extra preassumptions and preprocessing

an extension of the promethee method for decision making in fuzzy environment ranking of alternative energy exploitation projects abstract in the decision making process for the development of local resources a number of factors sometimes conflicting have to be considered multicriteria decision making procedures are widely applied today to ensure a rigorous analysis in this presentation a multicriteria method of ranking alternative projects promethee is extended to deal with fuzzy input data the method is applied for the evaluation and ranking of alternative energy exploitation schemes of a low temperature geothermal field it is demonstrated that this approach is more realistic and produces a more reliable ranking for problems such as the evaluation of alternative energy exploitation scenarios where the input data are not well defined

the cauchy problem of the ward equation with mixed scattering data we solve the cauchy problem of the ward equation with both continuous and discrete scattering data

a verifiable multi secret sharing scheme based on cellular automata in this paper we propose a verifiable t n threshold multi secret sharing scheme based on one dimensional cellular automata where the number of secrets is not restricted by n or t we show that our scheme can be used to solve an open problem proposed recently in alvarez et al 2008 g alvarez l hernandez encinas a martin del rey a multisecret sharing scheme for color images based on cellular automata information sciences 178 2008 4382 4395

the evidential reasoning approach for mada under both probabilistic and fuzzy uncertainties abstract many multiple attribute decision analysis mada problems are characterised by both quantitative and qualitative attributes with various types of uncertainties incompleteness or ignorance and vagueness or fuzziness are among the most common uncertainties in decision analysis the evidential reasoning er approach has been developed in the 1990s and in the recent years to support the solution of mada problems with ignorance a kind of probabilistic uncertainty in this paper the er approach is further developed to deal with mada problems with both probabilistic and fuzzy uncertainties in this newly developed er approach precise data ignorance and fuzziness are all modelled under the unified framework of a distributed fuzzy belief structure leading to a fuzzy belief decision matrix a utility based grade match method is proposed to transform both numerical data and qualitative fuzzy assessment information of various formats into the fuzzy belief structure a new fuzzy er algorithm is developed to aggregate multiple attributes using the information contained in the fuzzy belief matrix resulting in an aggregated fuzzy distributed assessment for each alternative different from the existing er algorithm that is of a recursive nature the new fuzzy er algorithm provides an analytical means for combining all attributes without iteration thus providing scope and flexibility for sensitivity analysis and optimisation a numerical example is provided to illustrate the detailed implementation process of the new er approach and its validity and wide applicability

a note on article the evidential reasoning approach for multiple attribute decision analysis using interval belief degrees abstract wang et al use an evidential reasoning approach for solving multiple attribute decision analysis mada problems under interval belief degrees y m wang j b yang d l xu k s chin the evidential reasoning approach for multiple attribute decision analysis using interval belief degrees european journal of operational research 175 2006 35 66 in this note it is shown some nonlinear optimization models in that paper are incorrect the necessary corrections are proposed

on the generation of high quality random numbers by two dimensional cellular automata finding good random number generators rngs is a hard problem that is of crucial import in several fields ranging from large scale statistical physics simulations to hardware self test in this paper we employ the cellular programming evolutionary algorithm to automatically generate two dimensional cellular automata ca rngs applying an extensive suite of randomness tests to the evolved cas we demonstrate that they rapidly produce high quality random number sequences moreover based on observations of the evolved cas we are able to handcraft even better rngs which not only outperform previously demonstrated high quality rngs but can be potentially tailored to satisfy given hardware constraints

an attribute weight based feedback model for multiple attributive group decision analysis problems with group consensus requirements in evidential reasoning context abstract in an evidential reasoning context a group consensus gc based approach can model multiple attributive group decision analysis problems with gc requirements the predefined gc is reached through several rounds of group analysis and discussion gad in the approach however the gad with no guidance may not be the most appropriate way to reach the predefined gc because several rounds of gad will spend a lot of time of all experts and yet cannot help them to effectively emphasize on the assessments which primarily damage the gc in this paper an attribute weight based feedback model is constructed to effectively identify the assessments primarily damaging the gc and accelerate the gc convergence considering important attributes with the weights more than or at least equal to the mean of the weights of all attributes the feedback model constructs identification rules to identify the assessments damaging the gc for the experts to renew in addition a suggestion rule is introduced to generate appropriate recommendations for the experts to renew their identified assessments the identification rules are constructed at three levels including the attribute alternative and global levels the feedback model is used to solve an engineering project management software selection problem to demonstrate its detailed implementation process its validity and applicability and its advantages compared with the gc based approach