balanced projectives and axiom 3 abstract a global definition of k nice subgroup is formulated which generalizes both the notion of a nice subgroup in the context of torsion groups and the notion of a k nice submodule used in a recent study of p local balanced projective groups it is shown analogous to hill s treatment of totally projective p groups that the global balanced projective groups of warfield are precisely those mixed abelian groups that satisfy the third axiom of countability for k nice subgroups a variety of equivalent characterizations of balanced projectives are derived by methods independent of the uniqueness and existence theorems previously established for these groups

inhomogeneous gaussian image models for estimation and restoration two inhomogeneous gaussian image models are presented for estimation and restoration by incorporating the local statistics of an image a homogeneous autoregressive ar random field can be extended to an inhomogeneous ar field this inhomogeneous random field can provide a better description of the image than the homogeneous one as a consequence of this improved modeling a minimum mean square error estimator mmse based on the inhomogeneous gaussian model can produce good results in both subjective and objective criteria two image models are proposed for use in image estimation and restoration a residual image model original image minus the space variant mean and a normalized image model residual image divided by space variant standard variation the novel aspect of these models is the use of an autoregressive dynamical model for residual and normalized images some aspects of parameter estimation are discussed and simulation results are presented

butler groups of infinite rank ii a torsion free abelian group g is called a butler group if bext g t 0 for any torsion group t we show that every butler group g of cardinality ltl is a b2 group i e g is a union of a smooth ascending chain of pure subgroups g0 where g ga b0 b 0 a butler group of finite rank assuming the validity of the continuum hypothesis ch we show that every butler group of cardinality not exceeding n is a b2 group moreover we are able to prove that the derived functor bext2 a t 0 for any torsion group t and any torsion free a with jai this implies that under ch all balanced subgroups of completely decomposable groups of cardinality nt are b2 groups

on the structure of p local abelian groups a uniqueness theorem in terms of numerical invariants is established for certain mixed p local groups called b modules which include both the balanced projective groups and the torsion a groups in general a b module does not contain a decomposition basis and when it does it reduces to a direct sum of an a group and a balanced projective group a special class of b modules the members of which are called s modules constitutes a natural generalization of s groups and the following fact is proved if h is an isotype subgroup of the p local balanced projective group g with gh countable then h is an s module

fuzzy logics with an additional involutive negation this paper surveys the present state of knowledge on propositional fuzzy logics extending sbl with an additional involutive negation the involutive negation is added as a new propositional connective in order to improve the expressive power of the standard mathematical fuzzy logics based on continuous triangular norms

torsion free groups in this paper we introduce the class of torsion free k groups and the notion of a knice subgroup torsion free k groups form a class of groups more extensive than the separable groups of baer but they enjoy many of the same closure properties we establish a role for knice subgroups of torsion free groups analogous to that played by nice subgroups in the study of torsion groups for example among the torsion free groups the balanced projectives are characterized by the fact that they satisfy the third axiom of countability with respect to knice subgroups separable groups are characterized as those torsion free k groups with the property that all finite rank pure knice subgroups are direct summands the introduction of these new classes of groups and subgroups is based on a preliminary study of the interplay between primitive elements and valuated coproducts as a by product of our investigation new proofs are obtained for many classical results on separable groups our techniques lead naturally to the discovery that a balanced subgroup of a completely decomposable group is itself completely decomposable provided the corresponding quotient is a separable group of cardinality not exceeding 81 that is separable groups of cardinality 81 have balanced projective dimension

a note on axiomatizations of pavelka style complete fuzzy logics pavelka style completeness a property relating degrees of provability and truth was previously studied mainly in the context of logics with continuous connectives it is known that in some other logics one can use infinitary deduction rule s to retain this form of completeness the present paper offers a systematic study of this idea for fuzzy logics which expand mtl and are given by a fixed standard algebra we explore the structure of the class of all reasonable expansions of any such logic by rational truth constants and for several prominent cases provide axiomatizations of particular expansions enjoying the pavelka style completeness

perfect pavelka logic zadeh s fuzzy logic was introduced as a mathematical tool for deduction working with different degrees of truth instead of the two truth degrees of classical logic the next step taken by pavelka was to admit assumptions and theorems which are also satisfied only to some truth degree as well as deduction rules transferring these degrees to the deduced formulas in the semantics these possibly but not necessarily correspond to the degrees of satisfaction of formulas a significant consequent progress towards this direction was achieved by hajek s work on rational pavelka logic it forms formulas with graded truth as couples of a formula and a rational truth value the success of the rational pavelka logic follows from the properties of the standard mv algebra i e the real unit interval 0 1 with the ukasiewicz operations which was used as its semantical interpretation the main mathematical result is that the rational pavelka logic is sound and complete in the sense that the syntactical provability degree and the semantical degree of satisfaction coincide in this paper an alternative to pavelka s approach is investigated instead of the standard mv algebra the truth values are taken from a perfect mv algebra in particular chang s mv algebra this is the opposite extreme among mv algebras it admits only infinitesimals besides the two classical truth degrees we argue that such an example also has a motivation in deduction imitating human reasoning as chang s mv algebra is not complete the provability degree need not exist nevertheless as the main result the following weak completeness theorem is proved if the provability degree of a formula exists it coincides with the degree of satisfaction this result is obtained by adding to pavelka s original approach a new rule of inference hajek s book keeping axioms and an axiom valid in chang s mv algebra an example that clarifies the differences between classical logic rational pavelka logic and perfect pavelka logic is given and some new fuzzy rules of inference are introduced

a combined transform coding ctc scheme for medical images a combined transform coding ctc scheme is proposed to reduce the blocking artifact of conventional block transform coding and hence to improve the subjective performance the proposed ctc scheme is described and its information theoretic properties are investigated computer simulation results for a class of chest x ray images are presented a comparison between the ctc scheme and the conventional discrete cosine transform dct and discrete walsh hadamard transform dwht demonstrates the performance improvement of the proposed scheme in addition combined coding can also be used in noiseless coding yielding a slight improvement in the compression performance if it is used properly

a methodology for modeling the distributions of medical images and their stochastic properties the probabilistic distribution properties of a set of medical images are studied it is shown that the generalized gaussian function provides a good approximation to the distribution of ap chest radiographs based on this result and a goodness of fit test a generalized gaussian autoregressive model ggar is proposed its properties and limitations are also discussed it is expected that the ggar model will be useful in describing the stochastic characteristics of some classes of medical images and in image data compression and other applications

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

adding truth constants to logics of continuous t norms axiomatization and completeness results in this paper we study generic expansions of logics of continuous t norms with truth constants taking advantage of previous results for lukasiewicz logic and more recent results for godel and product logics indeed we consider algebraic semantics for expansions of logics of continuous t norms with a set of truth constants r r c for a suitable countable c 0 1 and provide a full description of completeness results when i the t norm is a finite ordinal sum of lukasiewicz godel and product components ii the set of truth constants covers all the unit interval in the sense that each component of the t norm contains at least one value of c different from the bounds of the component and iii the truth constants in lukasiewicz components behave as rational numbers

statistical distributions of dct coefficients and their application to an interframe compression algorithm for 3 d medical images displacement estimated interframe dei coding a coding scheme for 3 d medical image data sets such as x ray computed tomography ct or magnetic resonance mr images is presented to take advantage of the correlation between contiguous slices a displacement compensated difference image based on the previous image is encoded the best fitting distribution functions for the discrete cosine transform dct coefficients obtained from displacement compensated difference images are determined and used in allocating bits and optimizing quantizers for the coefficients the dei scheme is compared with 2 d block discrete cosine transform dct as well as a full frame dct using the bit allocation technique of s lo and h k huang 1985 for x ray ct head images the present bit allocation and quantizer design using an appropriate distribution model resulted in a 13 db improvement in the snr compared to the full frame dct using the bit allocation technique for an image set with 5 mm slice thickness the dei method gave about 5 improvement in the compression ratio on average and less blockiness at the same distortion the performance gain increases to about 10 when the slice thickness decreases to 3 mm

isotype submodules of p local balanced projective groups by giving necessary and sufficient conditions for two isotype submodules of a p local balanced projective group to be equivalent we are able to introduce a general theory of isotype submodules of p local balanced projective groups or ib modules numerous applications of the above result are available particularly for the special class of ib modules introduced by wick known as skt modules we first show that the class of skt modules is closed under direct summands and then we are able to show that if h appears as an isotype submodule of the p local balanced projective group g such that g h is the coproduct of countably generated torsion groups then h is an skt module finally we show that ib modules satisfy general structural properties such as transitivity full transitivity and the equivalence of p high

the balanced projective dimension of p local abelian groups abstract by generalizing hill s theorem giving a necessary and sufficient condition for an isotype subgroup of a totally projective p group to be itself totally projective we are able to give a condition which will determine the balanced projective dimension of an arbitrary p local abelian group when that dimension is finite we rely on our recent third axiom of countability characterization for p local balanced projectives and are able to carry over almost routinely the arguments given recently by fuchs and hill which were used to determine the balanced projective dimension of an arbitrary abelian p group we are then able to prove that the balanced projective dimension of any countable p local abelian group and of any p local warfieid group is less than or equal to 1

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

axiom 3 modules by introducing the concept of a knice submodule a refinement of the notion of nice subgroup we are able to formulate a version of the third axiom of countability appropriate to the study of plocal mixed groups in the spirit of the well known characterization of totally projective pgroups our axiom 3 modules in fact form a class of zp modules encompassing the totally projectives in the torsion case for which we prove a uniqueness theorem and establish closure under direct summands indeed axiom 3 modules turn out to be precisely the previously classified warfield modules but with the added power of the third axiom of countability characterization we derive numerous new results including the resolution of a long standing problem of warfield and theorems in the vein of familiar criteria due to kulikov and pontryagin

pure subgroups of torsion free groups in this paper we show that certain new notions of purity stronger than the classical concept are relevant to the study of torsion free abelian groups in particular implications of purity a concept introduced in one of our recent papers are investigated we settle an open question posed by nongxa by proving that the union of an ascending countable sequence of pure subgroups is completely decomposable provided the subgroups are this result is false for ordinary purity the principal result of the paper however deals with e purity a concept stronger than purity but weaker than the usual notion of strong purity our main theorem which has a number of corollaries including the recent result of nongxa that strongly pure subgroups of separable groups are again separable states that a e pure subgroup of a k group is itself a k group among other results is the negative resolution of the conjecture valid in the countable case that a strongly pure subgroup of a completely decomposable group is again completely decomposable

the balanced projective dimension of abelian p groups the balanced projective dimension of every abelian p group is de termined by means of a structural property that generalizes the third axiom of countability as a corollary to our general structure theorem we show for a wn that every pa high subgroup of a p group g has balanced projective dimension exactly n whenever g has cardinality nn but pag o our characterization of balanced projective dimension also leads to new classes of groups where different infinite dimensions are distinguished

on endomorphism rings of non separable abelian p groups there have been spectacular advances in recent years in the so called realization problem for certain classes of abelian groups and modules the advances have derived mainly from powerful combinatorial set theoretic tools pioneered by shelah in the case of separable abelian p groups these results appear e g in 1 4 51 for non separable abelian p groups the most significant contribution has been 2 our objective in this paper is to extend the results in 2 and derive analogous results to those obtained in 4 51 it is perhaps worth pointing out that our methods are entirely algebraic the necessary set theoretical work has been carried out in the separable case and no further set theoretical arguments are needed in this the work is reminiscent of s all our set theory with one exception is in zfc and this is not acknowledged in the statement of individual results in the exceptional case where we work in godel s constructible universe v l this is acknowledged by appending v l after the statement number the principal realization result can be stated as

compression of two dimensional data distortion free compressibility of individual pictures i e two dimensional arrays of data by finite state encoders is investigated for every individual infinite picture i a quantity rho i is defined called the compressibility of i which is shown to be the asymptotically attainable lower bound on the compression ratio that can be achieved for i by any finite state information lossless encoder this is demonstrated by means of a constructive coding theorem and its converse that apart from their asymptotic significance might also provide useful criteria for finite and practical data compression tasks the proposed picture compressibility is also shown to possess the properties that one would expect and require of a suitably defined concept of two dimensional entropy for arbitrary probabilistic ensembles of infinite pictures while the definition of rho i allows the use of different machines for different pictures the constructive coding theorem leads to a universal compression scheme that is asymptotically optimal for every picture the results are readily extendable to data arrays of any finite dimension

rate distortion bound for a class of non gaussian sources with memory the rate distortion performance of a class of non gaussian source with memory is studied the source model is generated from a correlated gaussian source through a memoryless transform which actually constitutes a special class of the frequently used gibbs model in speech and image processing applications its entropy and a rate distortion bound are evaluated to obtain further insights into this class of source models several examples are also given to illustrate the usefulness and tightness of the rate distortion bound

characterizations of warfield groups abstract warfield groups are defined to be direct summands of simply presented abelian groups by introducing a global definition of quasi sequentially nice subgroups we prove some characterizations of warfield groups involving these groups knice subgroups and valuated coproducts furthermore we exhibit a new proof of a characterization of warfield groups in terms of nice subgroups and valuated coproducts

a new approach to reduce the blocking effect of transform coding image coding a combined transform coding ctc scheme to reduce the blocking effect of conventional block transform coding and hence to improve the subjective performance is presented the scheme is described and its information theoretic properties are discussed computer simulation results for a chest x ray image are presented the ctc scheme the jpeg baseline scheme and the conventional discrete walsh hadamard transform dwht are compared to demonstrate the performance improvement for the ctc scheme the advantages of the ctc scheme include no ringing effect as there is no error propagation across the boundary no additional computation and distortion always held within a certain level

the transitivity of local warfield groups abstract for a fixed prime p let g denote a module over the integers localized at p such a module is often referred to as a p local abelian group following established precedent we say that g is transitive provided that there exists an automorphism of g that maps a onto b whenever a and b are elements of g having the same height sequence however relatively few nontorsion g meet this criterion of transitivity indeed as we show there are four different classes of simply presented p local groups of torsion free rank 3 that are nontransitive in this article we introduce a weaker version of transitivity that allows all local warfield groups summands of simply presented p local groups to qualify as being transitive in this connection we associate with each element of a local warfield group g a new invariant called a type vector and we prove that there is an automorphism of g that maps a onto b if and only if a and b have the same height sequence and the same type vector as an application of this result we are able to determine exactly which local warfield groups are transitive in the classical sense also our results yield an alternate proof of a recent result of files regarding the equivalence of transitivity and full transitivity for local warfield groups finally we give a complete survey of transitivity for local warfield groups of torsion free rank 3