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Extreme learning machine (ELM) as an emerging technology has recently attracted many researchers’ interest due to its fast learning speed and state-of-the-art generalization ability in the implementation. Meanwhile, the incremental extreme learning machine (I-ELM) based on incremental learning algorithm was proposed which outperforms many popular learning algorithms. However, the incremental algorithms with ELM do not recalculate the output weights of all the existing nodes when a new node is added and cannot obtain the least-squares solution of output weight vectors. In this paper, we propose orthogonal convex incremental learning machine (OCI-ELM) with Gram-Schmidt orthogonalization method and Barron’s convex optimization learning method to solve the nonconvex optimization problem and least-squares solution problem, and then we give the rigorous proofs in theory. Moreover, in this paper, we propose a deep architecture based on stacked OCI-ELM autoencoders according to stacked generalization philosophy for solving large and complex data problems. The experimental results verified with both UCI datasets and large datasets demonstrate that the deep network based on stacked OCI-ELM autoencoders (DOC-IELM-AEs) outperforms the other methods mentioned in the paper with better performance on regression and classification problems.

Not only can the icing coat on transmission line cause the electrical fault of gap discharge and icing flashover but also it will lead to the mechanical failure of tower, conductor, insulators, and others. It will bring great harm to the people’s daily life and work. Thus, accurate prediction of ice thickness has important significance for power department to control the ice disaster effectively. Based on the analysis of standard support vector machine, this paper presents a weighted support vector machine regression model based on the similarity (WSVR). According to the different importance of samples, this paper introduces the weighted support vector machine and optimizes its parameters by hybrid swarm intelligence optimization algorithm with the particle swarm and ant colony (PSO-ACO), which improves the generalization ability of the model. In the case study, the actual data of ice thickness and climate in a certain area of Hunan province have been used to predict the icing thickness of the area, which verifies the validity and applicability of this proposed method. The predicted results show that the intelligent model proposed in this paper has higher precision and stronger generalization ability.

Anderson's inequality (Anderson, 1958) as well as its improved version given by Fink (2003) is known to provide interesting examples of integral inequalities. In this paper, we establish local fractional integral analogue of Anderson's inequality on fractal space under some suitable conditions. Moreover, we also show that the local fractional integral inequality on fractal space, which we have proved in this paper, is a new generalization of the classical Anderson's inequality.

This paper deals with a class of algebraic hyperstructures called semihypergroups, which are a generalization of semigroups. In this paper, we introduce pure hyperradical of a hyperideal in a semihypergroup with zero element. For this purpose, we define pure, semipure, and other related types of hyperideals and establish some of their basic properties in semihypergroups.

Es reproducción del documento publicado en http://dx.doi.org/10.1155/2008/592950 This paper is devoted to the study of a generalized modified version of the well-known Beverton-Holt equation in ecology. The proposed model describes the population evolution of some species in a certain habitat driven by six parametrical sequences, namely, the intrinsic growth rate (associated with the reproduction capability), the degree of sympathy of the species with the habitat (described by a so-called environment carrying capacity), a penalty term to deal with overpopulation levels, the harvesting (fishing or hunting) regulatory quota, or related to use of pesticides when fighting damaging plagues, and the independent consumption which basically quantifies predation. The independent consumption is considered as a part of a more general additive disturbance which also potentially includes another extra additive disturbance term which might be attributed to net migration from or to the habitat or modeling measuring errors. Both potential contributions are included for generalization purposes in the proposed modified generalized Beverton-Holt equation. The properties of stability and boundedness of the solution sequences, equilibrium points of the stationary model, and the existence of oscillatory solution sequences are investigated. A numerical example for a population of aphids is investigated with the theoretical tools developed in the paper. Ministerio de Ciencia y Tecnología DPI2006-00714; Gobierno Vasco IT-269-07;SAIOTEK SPE07UN04 y SPED06UN10

With software’s increasing scale and complexity, software failure is inevitable. To date, although many kinds of software fault localization methods have been proposed and have had respective achievements, they also have limitations. In particular, for fault localization techniques based on machine learning, the models available in literatures are all shallow architecture algorithms. Having shortcomings like the restricted ability to express complex functions under limited amount of sample data and restricted generalization ability for intricate problems, the faults cannot be analyzed accurately via those methods. To that end, we propose a fault localization method based on deep neural network (DNN). This approach is capable of achieving the complex function approximation and attaining distributed representation for input data by learning a deep nonlinear network structure. It also shows a strong capability of learning representation from a small sized training dataset. Our DNN-based model is trained utilizing the coverage data and the results of test cases as input and we further locate the faults by testing the trained model using the virtual test suite. This paper conducts experiments on the Siemens suite and Space program. The results demonstrate that our DNN-based fault localization technique outperforms other fault localization methods like BPNN, Tarantula, and so forth.

Neutrosophic set (NS) is a generalization of fuzzy set (FS) that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function, and falsity membership function. In this paper, we study the multiattribute group decision making (MAGDM) problems under neutrosophic environment with the incompletely known or completely unknown attribute weight. We first define the single-valued neutrosophic ideal solution (SVNIS) and the weighted distance measure and establish the program models to derive the attribute weights. Then, we give a practical application in the framework of SVNS; the result shows that our method is reasonable and effective in dealing with decision making (DM) problems. Furthermore, we extend the method to interval-valued neutrosophic set (IVNS).

Real hypersurfaces satisfying the conditionϕl=lϕ(l=R(·,ξ)ξ)have been studied by many authors under at least one more condition, since the class of these hypersurfaces is quite tough to be classified. The aim of the present paper is the classification of real hypersurfaces in complex projective planeCP2satisfying a generalization ofϕl=lϕunder an additional restriction on a specific function.

In many practical engineering applications, data are usually collected in online pattern. However, if the classes of these data are severely imbalanced, the classification performance will be restricted. In this paper, a novel classification approach is proposed to solve the online data imbalance problem by integrating a fast and efficient learning algorithm, that is, Extreme Learning Machine (ELM), and a typical sampling strategy, that is, the synthetic minority oversampling technique (SMOTE). To reduce the severe imbalance, the granulation division for major-class samples is made according to the samples’ distribution characteristic, and the original samples are replaced by the obtained granule core to prepare a balanced sample set. In online stage, we firstly make granulation division for minor-class and then conduct oversampling using SMOTE in the region around granule core and granule border. Therefore, the training sample set is gradually balanced and the online ELM model is dynamically updated. We also theoretically introduce fuzzy information entropy to prove that the proposed approach has the lower bound of model reliability after undersampling. Numerical experiments are conducted on two different kinds of datasets, and the results demonstrate that the proposed approach outperforms some state-of-the-art methods in terms of the generalization performance and numerical stability.

The Cattaneo-Vernotte equation is a generalization of the heat and particle diffusion equations; this mathematical model combines waves and diffusion with a finite velocity of propagation. In disordered systems the diffusion can be anomalous. In these kinds of systems, the mean-square displacement is proportional to a fractional power of time not equal to one. The anomalous diffusion concept is naturally obtained from diffusion equations using the fractional calculus approach. In this paper we present an alternative representation of the Cattaneo-Vernotte equation using the fractional calculus approach; the spatial-time derivatives of fractional order are approximated using the Caputo-type derivative in the range(0,2]. In this alternative representation we introduce the appropriate fractional dimensional parameters which characterize consistently the existence of the fractional space-time derivatives into the fractional Cattaneo-Vernotte equation. Finally, consider the Dirichlet conditions, the Fourier method was used to find the full solution of the fractional Cattaneo-Vernotte equation in analytic way, and Caputo and Riesz fractional derivatives are considered. The advantage of our representation appears according to the comparison between our model and models presented in the literature, which are not acceptable physically due to the dimensional incompatibility of the solutions. The classical cases are recovered when the fractional derivative exponents are equal to1.

The virial theorem for non-relativistic complex fields in $D$ spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in low-dimensional systems. The potential appearance of a Jacobian $J$ due to a change of variables in the path-integral expression for the partition function of the system is pointed out, although in order to make contact with the literature most of the analysis deals with the $J=1$ case. The virial theorem is recast into a form that displays the effect of microscopic scales on the thermodynamics of the system. From the point of view of this paper the case usually considered, $J=1$, is not natural, and the generalization to the case $J\neq 1$ is briefly presented., Comment: 6 pages (this version is the published version)

Currently, the research for reversible watermarking focuses on the decreasing of image distortion. Aiming at this issue, this paper presents an improvement method to lower the embedding distortion based on the prediction-error expansion (PE) technique. Firstly, the extreme learning machine (ELM) with good generalization ability is utilized to enhance the prediction accuracy for image pixel value during the watermarking embedding, and the lower prediction error results in the reduction of image distortion. Moreover, an optimization operation for strengthening the performance of ELM is taken to further lessen the embedding distortion. With two popular predictors, that is, median edge detector (MED) predictor and gradient-adjusted predictor (GAP), the experimental results for the classical images and Kodak image set indicate that the proposed scheme achieves improvement for the lowering of image distortion compared with the classical PE scheme proposed by Thodi et al. and outperforms the improvement method presented by Coltuc and other existing approaches.

By using Frobenius’ idea together with integral bifurcation method, we study a third order nonlinear equation of generalization form of the modified KdV equation, which is an important water wave model. Some exact traveling wave solutions such as smooth solitary wave solutions, nonsmooth peakon solutions, kink and antikink wave solutions, periodic wave solutions of Jacobian elliptic function type, and rational function solution are obtained. And we show their profiles and discuss their dynamic properties aim at some typical solutions. Though the types of these solutions obtained in this work are not new and they are familiar types, they did not appear in any existing literatures because the equationut+ux+νuxxt+βuxxx+αuux+1/3να(uuxxx+2uxuxx)+3μα2u2ux+νμα2(u2uxxx+ux3+4uuxuxx)+ν2μα2(ux2uxxx+2uxuxx2)=0is very complex. Particularly, compared with the cited references, all results obtained in this paper are new.

Here we construct different approximate solutions of the plane inverse boundary value problem of aerohydrodynamics. In order to do this we solve some conditional optimization problems in the norms∥·∥2,∥·∥∞, and ∥·∥1and some of their generalizations. We present the example clarifying the mathematical constructions and show that the supremum norm generalization seems to be the optimal one of all the functionals considered in the paper.

Some generalized forms of the hyperideals of a hyperring in the paper of Zhan et al. (2008) will be given. As a generalization of the interval valued(α,β)-fuzzy hyperideals of a hyperring withα,β∈{∈,q,∈∧q,∈∨q}andα≠∈∧q, the notion of generalized interval valued(α,β)-fuzzy hyperideals of a hyperring is also introduced. Special attention is concentrated on the interval valued(∈γ~,∈γ~∨qδ~)-fuzzy hyperideals. As a consequence, some characterizations theorems of interval valued(∈γ~,∈γ~∨qδ~)-fuzzy hyperideals will be provided.

Çalışıcı and Türkmen called a module M generalized ⊕-supplemented if every submodule has a generalized supplement that is a direct summand of M. Motivated by this, it is natural to introduce another notion that we called generalized ⊕-radical supplemented modules as a proper generalization of generalized ⊕-supplemented modules. In this paper, we obtain various properties of generalized ⊕-radical supplemented modules. We show that the class of generalized ⊕-radical supplemented modules is closed under finite direct sums. We attain that over a Dedekind domain a module M is generalized ⊕-radical supplemented if and only if M/P(M) is generalized ⊕-radical supplemented. We completely determine the structure of these modules over left V-rings. Moreover, we characterize semiperfect rings via generalized ⊕-radical supplemented modules.

In the last one decade, neural networks-based modeling has been used for computing different performance parameters of microstrip antennas because of learning and generalization features. Most of the created neural models are based on software simulation. As the neural networks show massive parallelism inherently, a parallel hardware needs to be created for creating faster computing machine by taking the advantages of the parallelism of the neural networks. This paper demonstrates a generalized neural networks model created on field programmable gate array- (FPGA-) based reconfigurable hardware platform for computing different performance parameters of microstrip antennas. Thus, the proposed approach provides a platform for developing low-cost neural network-based FPGA simulators for microwave applications. Also, the results obtained by this approach are in very good agreement with the measured results available in the literature.

The purpose of this paper is to give a foundation for providing a new soft algebraic tool in considering many problems containing uncertainties. In order to provide these new soft algebraic structures, we discuss a new soft set-(M, N)-soft intersection set, which is a generalization of soft intersection sets. We introduce the concepts of (M, N)-SI filters of BL-algebras and establish some characterizations. Especially, (M, N)-soft congruences in BL-algebras are concerned.

The tripled fixed point is a generalization of the well-known concept of “coupled fixed point.” In this paper, tripled coincidence and common fixed point results for two hybrid pairs consisting of multivalued and single valued mappings on a metric space are proved. We give examples to illustrate our results. In the process, several comparable coincidence and fixed point results in the existing literature are improved, unified, and generalized.

Now, it is known that the split common fixed point problem is a generalization of the split feasibility problem and of the convex feasibility problem. In this paper, the split common fixed point problem associated with the pseudocontractions is studied. An iterative algorithm has been presented for solving the split common fixed point problem. Strong convergence result is obtained.

The aim of this paper is to characterize the exponential stability of linear systems of difference equations with slowly varying coefficients. Our approach is based on the generalization of the freezing method for difference equations combined with new estimates for the norm of bounded linear operators. The main novelty of this work is that we use estimates for the absolute values of entries of a matrix-valued function, instead of bounds on its eigenvalues. By this method, new explicit stability criteria for linear nonautonomous systems are derived.

Many studies have investigated the management of data delivered over sensor networks and attempted to standardize their relations. Sensor data come from numerous tangible and intangible sources, and existing work has focused on the integration and management of the sensor data itself. The data should be interpreted according to the sensor environment and related objects, even though the data type, and even the value, is exactly the same. This means that the sensor data should have semantic connections with all objects, and so a knowledge base that covers all domains should be constructed. In this paper, we suggest a method of domain terminology collection based on Wikipedia category information in order to prepare seed data for such knowledge bases. However, Wikipedia has two weaknesses, namely, loops and unreasonable generalizations in the category structure. To overcome these weaknesses, we utilize a horizontal bootstrapping method for category searches and domain-term collection. Both the category-article and article-link relations defined in Wikipedia are employed as terminology indicators, and we use a new measure to calculate the similarity between categories. By evaluating various aspects of the proposed approach, we show that it outperforms the baseline method, having wider coverage and higher precision. The collected domain terminologies can assist the construction of domain knowledge bases for the semantic interpretation of sensor data.

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number. However, there are fewer reliable operations for INSs, as well as the INS aggregation operators and decision making method. For this purpose, the operations for INSs are defined and a comparison approach is put forward based on the related research of interval valued intuitionistic fuzzy sets (IVIFSs) in this paper. On the basis of the operations and comparison approach, two interval neutrosophic number aggregation operators are developed. Then, a method for multicriteria decision making problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.

We propose a refined gradient ascent method including heuristic parameters for solving the dual problem of nonlinear SVM. Aiming to get better tuning to the particular training sequence, the proposed refinement consists of the use of heuristically established weights in correcting the search direction at each step of the learning algorithm that evolves in the feature space. We propose three variants for computing the correcting weights, their effectiveness being analyzed on experimental basis in the final part of the paper. The tests pointed out good convergence properties, and moreover, the proposed modified variants proved higher convergence rates as compared to Platt’s SMO algorithm. The experimental analysis aimed to derive conclusions on the recognition rate as well as on the generalization capacities. The learning phase of the SVM involved linearly separable samples randomly generated from Gaussian repartitions and the WINE and WDBC datasets. The generalization capacities in case of artificial data were evaluated by several tests performed on new linearly/nonlinearly separable data coming from the same classes. The tests pointed out high recognition rates (about 97%) on artificial datasets and even higher recognition rates in case of the WDBC dataset.

In flotation processes, concentrate grade is the key production index but is difficult to be measured online. The mechanism models reflect the basic tendency of concentrate grade changes but cannot provide adequate prediction precision. The data-driven models based on froth image features provide accurate prediction within well-sampled space but rely heavily on sample data with less generalization capability. So, a hybrid intelligent model combining the two kinds of model is proposed in this paper. Since the information of image features is enormous, and the relationship between image features and concentrate grade is nonlinear, a B-spline partial least squares (BS-PLS) method is adopted to construct the data-driven model for concentrate grade prediction. In order to gain better generalization capability and prediction accuracy, information entropy is introduced to integrate the mechanism model and the BS-PLS model together and modify the model output online through an output deviation compensation strategy. Moreover, a slide window scheme is employed to update the hybrid model in order to improve its adaptability. The industrial practical data testing results show that the performance of the hybrid model is better than either of the two single models and it satisfies the accuracy and stability requirements in industrial applications.

Recently, a worst-case $O(1/t)$ convergence rate was established for the Douglas-Rachford alternating direction method of multipliers (ADMM) in an ergodic sense. The relaxed proximal point algorithm (PPA) is a generalization of the original PPA which includes the Douglas-Rachford ADMM as a special case. In this paper, we provide a simple proof for the same convergence rate of the relaxed PPA in both ergodic and nonergodic senses.

Recently, in 2013, we proved that certain presentations present the Dunwoody3-manifold groups. Since the Dunwoody3-manifolds do not have a unique Heegaard diagram, we cannot determine a unique group presentation for the Dunwoody3-manifolds. It is well known that every(1,1)-knots in a lens space can be represented by the set𝒟of the 4-tuples(a,b,c,r)(Cattabriga and Mulazzani (2004); S. H. Kim and Y. Kim (2012, 2013)). In particular, to determine a unique Heegaard diagram of the Dunwoody3-manifolds, we proved the fact that the certain subset of𝒟representing all2-bridge knots of(1,1)-knots is determined completely by using the dual and mirror(1,1)-decompositions (S. H. Kim and Y. Kim (2011)). In this paper, we show how to obtain the dual and mirror images of all elements in𝒟as the generalization of some results by Grasselli and Mulazzani (2001); S. H. Kim and Y. Kim (2011).

This paper considers the oscillation on meromorphic solutions of the second-order linear differential equations with the formf′′+A(z)f=0,whereA(z)is a meromorphic function with[p,q]-order. We obtain some theorems which are the improvement and generalization of the results given by Bank and Laine, Cao and Li, Kinnunen, and others.

The solution of a Least Squares Support Vector Machine (LS-SVM) suffers from the problem of nonsparseness. The Forward Least Squares Approximation (FLSA) is a greedy approximation algorithm with a least-squares loss function. This paper proposes a new Support Vector Machine for which the FLSA is the training algorithm—the Forward Least Squares Approximation SVM (FLSA-SVM). A major novelty of this new FLSA-SVM is that the number of support vectors is the regularization parameter for tuning the tradeoff between the generalization ability and the training cost. The FLSA-SVMs can also detect the linear dependencies in vectors of the input Gramian matrix. These attributes together contribute to its extreme sparseness. Experiments on benchmark datasets are presented which show that, compared to various SVM algorithms, the FLSA-SVM is extremely compact, while maintaining a competitive generalization ability.

This paper deals with the algebraic hypersystems. The notion of regularity of different type of algebraic systems has been introduced and characterized by different authors such as Iseki, Kovacs, and Lajos. We generalize this notion to algebraic hypersystems giving a unified generalization of the characterizations of Kovacs, Iseki, and Lajos. We generalize also the concept of ideal introducing the notion of j-hyperideal and hyperideal of an algebraic hypersystem. It turns out that the description of regularity in terms of hyperideals is intrinsic to associative hyperoperations in general. The main theorem generalizes to algebraic hypersystems some results on regular semigroups and regular rings and expresses a necessary and sufficient condition by means of principal hyperideals. Furthermore, two more theorems are obtained: one is concerned with a necessary and sufficient condition for an associative, commutative algebraic hypersystem to be regular and the other is concerned with nilpotent elements in the algebraic hypersystem.

This paper is concerned with partial regularity to nonlinear subelliptic systems with Dini continuous coefficients under quadratic controllable growth conditions in the Heisenberg groupℍn. Based on a generalization of the technique of𝒜-harmonic approximation introduced by Duzaar and Steffen, partial regularity to the sub-elliptic system is established in the Heisenberg group. Our result is optimal in the sense that in the case of Hölder continuous coefficients we establish the optimal Hölder exponent for the horizontal gradients of the weak solution on its regular set.

The notion of (co)derivations of ranked bigroupoids is discussed by Alshehri et al. (in press), and their generalized version is studied by Jun et al. (under review press). In particular, Jun et al. (under review press) studied coderivations of ranked bigroupoids. In this paper, the generalization of coderivations of ranked bigroupoids is discussed. The notion of generalized coderivations in ranked bigroupoids is introduced, and new generalized coderivations of ranked bigroupoids are obtained by combining a generalized self-coderivation with a rankomorphism. From the notion of (X,∗,&)-derivation, the existence of a rankomorphism of ranked bigroupoids is established.

This paper is concerned with a class of fractional differential inclusions whose multivalued term depends on lower-order fractional derivative with fractional (non)separated boundary conditions. The cases of convex-valued and non-convex-valued right-hand sides are considered. Some existence results are obtained by using standard fixed point theorems. A possible generalization for the inclusion problem with integral boundary conditions is also discussed. Examples are given to illustrate the results.

In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Alkhazaleh et al. in 2011 introduced the definition of a soft multiset as a generalization of Molodtsov's soft set. In this paper we give the definition of fuzzy soft multiset as a combination of soft multiset and fuzzy set and study its properties and operations. We give examples for these concepts. Basic properties of the operations are also given. An application of this theory in decision-making problems is shown.

Very recently, Ahmad and Yao (2009) introduced and considered a system of generalized resolvent equations with corresponding system of variational inclusions in uniformly smooth Banach spaces. In this paper we introduce and study a general system of generalized resolvent equations with corresponding general system of variational inclusions in uniformly smooth Banach spaces. We establish an equivalence relation between general system of generalized resolvent equations and general system of variational inclusions. The iterative algorithms for finding the approximate solutions of general system of generalized resolvent equations are proposed. The convergence criteria of approximate solutions of general system of generalized resolvent equations obtained by the proposed iterative algorithm are also presented. Our results represent the generalization, improvement, supplement, and development of Ahmad and Yao corresponding ones.

The purpose of this paper is to introduce new types of asymptotically (g,φ)-contractions which generalize the Binayak S. Choudhury type contraction on fuzzy metric spaces and prove some fixed-point theorems for single- and multivalued mappings on fuzzy metric spaces. Hence, our results can be viewed as a generalization and improvement of many recent results.

The aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of weak reciprocal continuity. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. We demonstrate that weak reciprocal continuity ensures the existence of common fixed points under contractive conditions, which otherwise do not ensure the existence of fixed points. Our results generalize and extend Banach contraction principle and Meir-Keeler-type fixed point theorem.

The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely, average path length, degree distribution, and clustering coefficient. Although the degree distribution and the average path length admit straightforward generalizations, for the clustering coefficient several different definitions have been proposed in the literature. We examined the different definitions and identified the similarities and differences between them. In order to elucidate the significance of different definitions of the weighted clustering coefficient, we studied their dependence on the weights of the connections. For this purpose, we introduce the relative perturbation norm of the weights as an index to assess the weight distribution. This study revealed new interesting statistical regularities in terms of the relative perturbation norm useful for the statistical characterization of weighted graphs.

The aim of this paper is the generalization of the notion of fuzzy vector spaces to fuzzy hypervector spaces. In this regard, by considering the notion of fuzzy hypervector spaces, we characterized a fuzzy hypervector space based on its level sub-hyperspace. The algebraic nature of fuzzy hypervector space under transformations is studied. Certain conditions are obtained under which a given fuzzy hypervector space can or cannot be realized as a union of two fuzzy hypervector spaces such that none is contained in the other. The construction of a fuzzy hypervector space generated by a given fuzzy subset of a hypervector space is given. The set of all fuzzy cosets of a fuzzy hypervector space is shown to be a hypervector space. Finally, a fuzzy quotient hypervector space is defined and an analogue of a consequence of the “fundamental theorem of homomorphisms” is obtained.

The convolution summability method is introduced as a generalization of the random-walk method. In this paper, two well-known summability analogs concerning the strong law of large numbers (SLLN) and the law of the single logarithm (LSL), that gives the rate of convergence in SLLN for the random-walk method, are extended to this generalized method.

This paper describes two families of canonical Reed-Muller forms, called inclusive forms (IFs) and their generalization, the generalized inclusive forms (GIFs), which include minimum ESOPs for any Boolean function. We outline the hierarchy of known canonical forms, in particular, pseudo-generalized Kronecker forms (PGKs), which led us to the discovery of the new families. Next, we introduce special binary trees, called the S/D trees, which underlie IFs and permit their enumeration. We show how to generate IFs and GIFs and prove that GIFs include minimum ESOPs. Finally, we present the results of computer experiments, which show that GIFs reduce the search space for minimum ESOP by several orders of magnitude, and this reduction grows exponentially with the number of variables.

1. Introduction. In this paper, we study the existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for impulsive functionaldifferential evolution equation. Such problems arise in some physical applications as a natural generalization of the classical initial value problems. The results for semilinear functional-differential evolution nonlocal problem [2] are extended for the case of impulse effect. We consider the nonlocal Cauchy problem in the form

Weak laws of large numbers for arrays of rowwise negatively dependent random variables are obtained in this paper. The more general hypothesis of negative dependence relaxes the usual assumption of independence. The moment conditions are similar to previous results, and the stochastic bounded condition also provides a generalization of the usual distributional assumptions.

In 1995, Faith and Menal have established theV-ring theorem which gives a characterization of aV-ring. In this paper, we generalize this theorem toV-modules and consider some applications for Noetherian self-cogenerators.

Clifford and Preston (1961) showed several important characterizations of right groups. It was shown in Roy and So (1998) that, among topological semigroups, compact right simple or left cancellative semigroups are in fact right groups, and the closure of a right simple subsemigroup of a compact semigroup is always a right subgroup. In this paper, it is shown that such results can be generalized in convergence semigroups. In the discussion of maximal right simple subsemigroups and maximal right subgroups of semigroups, generalization of the results that no two maximal right simple subsemigroups and maximal right subgroups of a convergence semigroup intersect, is also established.

In this paper, we propose a generalization of continuous-time processed defined by Xt=∫f(t−s)dWs, to the case of f being a distribution. We give a necessary and sufficient condition for f, such that the obtained process is a second order distribution process. We study the moments and the regularity of these processes. In addition, we investigate a generalization to processes with stationary increments.

In this paper we study the fixed points of the Log-linear discrete dynamics. We show that almost all Log-linear dynamics have at most two fixed points which is a generalization of Soni's result.

This paper deals with a generalization of Browder fixed point theorems and variational inequalities by relaxing the assumptions of compactness and continuity

Research on Wiener type spaces was initiated by N.Wiener in [15]. A number of authors worked on these spaces or some special cases of these spaces. A kind of generalization of the Wiener's definition was given by H.Feichtinger in [2] as a Banach spaces of functions (or measures, distributions) on locally compact groups that are defined by means of the global behaviour of certain local properties of their elements. In the present paper we discussed Wiener type spaces using the spacesAw,ωp,q(G)andFw,ωp,q(G)(c. f. [8]) as a local component, andLνr(G)as a global component, wherewandνare Beurling weights onGandωis a Beurling weight onGˆ(c. f. [13]).

In this paper, a generalization of a theorem of Mishra and Srivastava [4] on|C,1|ksummability factors has been proved.