Generalized fuzzy filters of <Emphasis Type="Italic">R</Emphasis><Subscript>0</Subscript>-algebras

In this paper, we introduce the notions of interval valued -fuzzy filters and interval valued -fuzzy Boolean (implicative) filters in R ₀-algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters are derived. In particular, we prove that an interval valued fuzzy set F in R ₀-algebras is an interval valued -fuzzy Boolean filter if and only if it is an interval valued -fuzzy implicative filter.     

<Emphasis Type="BoldItalic">H</Emphasis><Subscript>2</Subscript>-Control and the Separation Principle for Discrete-Time Markovian Jump Linear Systems

In this paper we consider the H₂-control problem of discrete-time Markovian jump linear systems. We assume that only an output and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed-loop system is mean square stable and minimizes the H₂-norm of the system. As in the case with no jumps, we show that an optimal controller can be obtained from two sets of coupled algebraic Riccati equations, one associated with the optimal control problem when the state variable is available, and the other associated with the optimal filtering problem. This is the principle of separation for discrete-time Markovian jump linear systems. When there is only one mode of operation our results coincide with the traditional separation principle for the H₂-control of discrete-time linear systems. Date received: June 1, 2001. Date revised: October 13, 2003.     

H∞ State Feedback Delay-dependent Control for Discrete Systems with Multi-time-delay

In this paper, H∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H∞ performance indices is induced, and then a strategy for H1 state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach.     

Three-dimensional analysis of Marangoni flow and radial segregation in Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>1-<Emphasis Type="Italic">x</Emphasis></Subscript> melt with Czochralski configuration

In order to examine the flow field and the radial segregation of silicon (Si) in a Ge _x Si_1-x melt with an idealized Czochralski (Cz) configuration, we conducted a series of unsteady three-dimensional (3-D) numerical simulations under zero-gravity conditions. The effect of convection driven by surface tension on the free surface of the melt was included in the model, by considering thermal, as well as solutal Marangoni convection. The concentration and flow fields at several stages during crystal growth are presented for several temperature differences, driving the Marangoni convection. The simulation results indicate that the flow and concentration fields are axisymmetric for Ma _T < 625 and become oscillatory and 3-D for higher values. It was found that the maximum Si concentration difference at the growth interface decreases as thermal Marangoni number increases due to higher flow velocities in the vicinity of the interface. However, temporal fluctuations of Si concentration at the interface increase at higher thermal Marangoni numbers. The effects of aspect ratio (A _r) were also considered in the model. It was found that the aspect ratio of the melt in the crucible has a prominent influence on the flow pattern in the melt which, in turn, effects the Si concentration at the growth interface.     

Extensions of fuzzy hyperideals in <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">V</Emphasis></Subscript>-semigroups

The object of the present paper is the investigation and study of (fuzzy) hyperideals in H _v - semigroups. Regular equivalence relations play in H _v - semigroup theory a role analogous to congruences in semigroup theory, so we introduce fuzzy regular equivalence relations on H _v -semigroups and then we study fuzzy Rees regular relations on H _v -semigroups. Using this ideas, we establish a relation between fuzzy hyperideal of an H _v -semigroup H and fuzzy hyperideal of a quotient H _v -semigroup of H. Some characterizations of them are then shown.      

Algorithms for P<Subscript>4</Subscript>-Comparability Graph Recognition and Acyclic P<Subscript>4</Subscript>-Transitive Orientation

We consider two problems pertaining to P₄-comparability graphs, namely, the problem of recognizing whether a simple undirected graph is a P₄-comparability graph and the problem of producing an acyclic P₄-transitive orientation of a P₄-comparability graph. These problems have been considered by Hoàng and Reed who described O(n⁴)- and O(n⁵)-time algorithms for their solution, respectively, where n is the number of vertices of the input graph. Faster algorithms have recently been presented by Raschle and Simon, and by Nikolopoulos and Palios; the time complexity of these algorithms for either problem is O(n + m²), where m is the number of edges of the graph. In this paper we describe O(n m)-time and O(n + m)-space algorithms for the recognition and the acyclic P₄-transitive orientation problems on P₄-comparability graphs. The algorithms rely on properties of the P₄-components of a graph, which we establish, and on the efficient construction of the P₄-components by means of the BFS-trees of the complement of the graph rooted at each of its vertices, without however explicitly computing the complement. Both algorithms are simple and use simple data structures.     

Topology on the set of R 0 semantics for R 0 algebras

This paper introduces the concepts of R ₀ valuation, R ₀ semantic, countable R ₀ category , R ₀ fuzzy topological category , etc. It is established in a natural way that the fuzzy topology δ and its cut topology on the set Ω _M consisting of all R ₀ valuations of an R ₀ algebra M, and some properties of fuzzy topology δ and its cut topology are investigated carefully. Moreover, the representation theorem for R ₀ algebras by means of fuzzy topology is given, that is to say the category is equivalent to the category . By studying the relation between valuations and filters, the Loomis–Sikorski theorem for R ₀ algebras is obtained. As an application, K-compactness of the R ₀ logic is discussed.     

A fast and adaptive method for complex-valued SAR image denoising based on <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">k</Emphasis></Subscript> norm regularization

This paper developed a fast and adaptive method for SAR complex image denoising based on l _k norm regularization, as viewed from parameters estimation. We firstly establish the relationship between denoising model and ill-posed inverse problem via convex half-quadratic regularization, and compare the difference between the estimator variance obtained from the iterative formula and biased Cramer-Rao bound, which proves the theoretic flaw of the existent methods of parameter selection. Then, the analytic expression of the model solution as the function with respect to the regularization parameter is obtained. On this basis, we study the method for selecting the regularization parameter through minimizing mean-square error of estimators and obtain the final analytic expression, which resulted in the direct calculation, high processing speed, and adaptability. Finally, the effect of regularization parameter selection on the resolution of point targets is analyzed. The experiment results of simulation and real complex-valued SAR images illustrate the validity of the proposed method. Supported by the National Natural Science Foundation of China (Grant No. 60572136), the Fundamental Research Fund of NUDT (Grant No. JC0702005)     

An HLLC Scheme to Solve The <Emphasis Type="Italic">M</Emphasis><Subscript>1</Subscript> Model of Radiative Transfer in Two Space Dimensions

The M ₁ radiative transfer model is considered in the present work in order to simulate the radiative fields and their interactions with the matter. The model is governed by an hyperbolic system of conservation laws supplemented by relaxation source terms. Several difficulties arise when approximating the solutions of the model; namely the positiveness of the energy, the flux limitation and and the limit diffusion behavior have to be satisfied. An HLLC scheme is exhibited and it is shown to satisfy all the required properties. A particular attention is payed concerning the approximate extreme waves. These approximations are crucial to obtain an accurate scheme. The extension to the full 2D problem is proposed. It satisfies, once again, all the expected properties. Numerical experiments are proposed. They show that the considered scheme is actually less diffusive than the currently used numerical methods.      

The Zariski topology on the spectrum of prime <Emphasis Type="Italic">L</Emphasis>-submodules

Let R be a commutative ring with identity and let M be an R-module. We topologize L − Spec(M), the collection of all prime L-submodules of M, analogous to that for FSpec(R), the spectrum of fuzzy prime ideals of R, and investigate the properties of this topological space. In particular, we will study the relationship between L − Spec(M) and L − Spec(R/Ann(M)) and obtain some results.     

Fuzzy prime ideals of pseudo-<Emphasis Type="Italic">MV</Emphasis> algebras

The aim of this paper is to introduce the notion of fuzzy prime ideals of pseudo-MV algebras and investigate some of its properties.      

(Weak) Dual hyper <Emphasis Type="Italic">K</Emphasis>-ideals

In this note by considering the notion of (weak) dual hyper K-ideal, we obtain some related results. After that we determine the relationships between (weak) dual hyper K-ideals and (weak) hyper K-ideals. Finally, we give a characterization of hyper K-algebras of order 3 or 4 based on the (weak) dual hyper K-ideals.     

Emergence of anti-<Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity in type-IV bouncing cosmology as due to <Emphasis Type="Italic">M</Emphasis><Subscript>0</Subscript>-brane

Recently, some authors considered the origin of a type-IV singular bounce in modified gravity and obtained the explicit form of F(R) which can produce this type of cosmology. In this paper, we show that during the contracting branch of type-IV bouncing cosmology, the sign of gravity changes, and antigravity emerges. In our model, M0 branes get together and shape a universe, an anti-universe, and a wormhole which connects them. As time passes, this wormhole is dissolved in the universes, F(R) gravity emerges, and the universe expands. When the brane universes become close to each other, the squared energy of their system becomes negative, and some tachyonic states are produced. To remove these states, universes are assumed to be compact, the sign of compacted gravity changes, and anti-F(R) gravity arises, which causes getting away of the universes from each other. In this theory, a Type-IV singularity occurs at t = t _s , which is the time of producing tachyons between expansion and contraction branches.     

On BCK algebras: Part II: New algebras. The ordinal sum (product) of two bounded BCK algebras

Since all the algebras connected to logic have, more or less explicitly, an associated order relation, it follows, by duality principle, that they have two presentations, dual to each other. We classify these dual presentations in “left” and “right” ones and we consider that, when dealing with several algebras in the same research, it is useful to present them unitarily, either as “left” algebras or as “right” algebras. In some circumstances, this choice is essential, for instance if we want to build the ordinal sum (product) between a BL algebra and an MV algebra. We have chosen the “left” presentation and several algebras of logic have been redefined as particular cases of BCK algebras. We introduce several new properties of algebras of logic, besides those usually existing in the literature, which generate a more refined classification, depending on the properties satisfied. In this work (Parts I–V) we make an exhaustive study of these algebras—with two bounds and with one bound—and we present classes of finite examples, in bounded case. In Part II, we continue to present new properties, and consequently new algebras; among them, bounded α γ algebra is a common generalization of MTL algebra and divisible bounded residuated lattice (bounded commutative Rl-monoid). We introduce and study the ordinal sum (product) of two bounded BCK algebras. Dedicated to Grigore C. Moisil (1906–1973).     

Electrical properties and crystallization behavior of Sb<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Se<Subscript>100−<Emphasis Type="Italic">x</Emphasis></Subscript> thin films

The structural transformation and transformation kinetics of Sb _x Se_100−x films (60 ≤ x ≤ 70) were studied to investigate the feasibility of applying Sb _x Se_100−x alloys in phase-change nonvolatile memories. The temperature-dependent van der Pauw measurements, Hall measurements, X-ray diffraction and a static tester were used to investigate the electrical properties and crystallization behavior of the Sb _x Se_100−x films. The sheet resistance difference between amorphous and crystalline state was higher than 10⁴ Ω per square According to Hall measurement, Sb _x Se_100−x films have p-type conduction and the Hall mobility and carrier concentration increases with the increase in Sb content. The crystalline structure of the metastable phase of Sb _x Se_100−x alloys, which plays a major roll in fast crystallization, is similar to that of Sb₂Te (rhombohedral structure). The transition temperature, sheet resistance and activation energy for transformation decrease as the amount of Sb increases in the Sb _x Se_100−x film. Applying the Kissinger method, the activation energies for crystallization were in the range from 1.90 ± 0.15 to 4.16 ± 0.28 eV. The desired crystallization speed can be obtained by a systematic change of the composition owing to the variation of the activation barrier with stoichiometry.     

Maximum <Emphasis Type="Italic">k</Emphasis>-Splittable <Emphasis Type="Italic">s</Emphasis>,<Emphasis Type="Italic">t</Emphasis>-Flows

Given a graph with a source and a sink node, the NP-hard maximum k-splittable s,t-flow (M k SF) problem is to find a flow of maximum value from s to t with a flow decomposition using at most k paths. The multicommodity variant of this problem is a natural generalization of disjoint paths and unsplittable flow problems. Constructing a k-splittable flow requires two interdepending decisions. One has to decide on k paths (routing) and on the flow values for the paths (packing). We give efficient algorithms for computing exact and approximate solutions by decoupling the two decisions into a first packing step and a second routing step. Usually the routing is considered before the packing. Our main contributions are as follows: (i) We show that for constant k a polynomial number of packing alternatives containing at least one packing used by an optimal M k SF solution can be constructed in polynomial time. If k is part of the input, we obtain a slightly weaker result. In this case we can guarantee that, for any fixed ε>0, the computed set of alternatives contains a packing used by a (1−ε)-approximate solution. The latter result is based on the observation that (1−ε)-approximate flows only require constantly many different flow values. We believe that this observation is of interest in its own right. (ii) Based on (i), we prove that, for constant k, the M k SF problem can be solved in polynomial time on graphs of bounded treewidth. If k is part of the input, this problem is still NP-hard and we present a polynomial time approximation scheme for it.     

Notes on wormhole existence in scalar-tensor and <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

Some recent papers have claimed the existence of static, spherically symmetric wormhole solutions to gravitational field equations in the absence of ghost (or phantom) degrees of freedom. We show that in some such cases the solutions in question are actually not of wormhole nature while in cases where a wormhole is obtained, the effective gravitational constant G _eff is negative in some region of space, i.e., the graviton becomes a ghost. In particular, it is confirmed that there are no vacuum wormhole solutions of the Brans-Dicke theory with zero potential and the coupling constant ω > −3/2, except for the case ω = 0; in the latter case, G _eff < 0 in the region beyond the throat. The same is true for wormhole solutions of F(R) gravity: special wormhole solutions are only possible if F(R) contains an extremum at which G _eff changes its sign.     

Fuzzy <Emphasis Type="Italic">R</Emphasis>-subgroups with thresholds of near-rings and implication operators

Using the belongs to relation (∈) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (α, β)-fuzzy R-subgroup of a near-ring where α , β are any two of {∈, q, ∈∨q , ∈∧q} with α ≠ ∈∧q is introduced and related properties are investigated. We also introduce the notion of a fuzzy R-subgroup with thresholds which is a generalization of an ordinary fuzzy R-subgroup and an (∈, ∈∨q)-fuzzy R-subgroup. Finally, we give the definition of an implication-based fuzzy R-subgroup.     

Using B<Superscript>+</Superscript>-trees for processing of line segments in large spatial databases

Points, lines, and regions are the three basic entities for constituting vector-based objects in spatial databases. Many indexing methods (G-tree, K-D-B tree, Quad-tree, PMR-tree, Grid-file, R-tree, and so on) have been widely discussed for handling point or region data. These traditional methods can efficiently organize point or region objects in a space into a hashing or hierarchical directory. They provide efficient access methods to meet the requirement of accurate retrievals. However, two problems are encountered when their techniques are applied to deal with line segments. The first is that representing line segments by means of point or region objects cannot exactly and properly preserve the spatial information about the proximities of line segments. The second problem is derived from the large dead space and overlapping areas in external and internal nodes of the hierarchical directory caused by the use of rectangles to enclose line objects. In this paper, we propose an indexing structure for line segments based on B ⁺ -tree to remedy these two problems. Through the experimental results, we demonstrate that our approach has significant improvement over the storage efficiency. In addition, the retrieval efficiency has also been significantly prompted as compared to the method using R-tree index scheme. These improvements derive mainly from the proposed data processing techniques and the new indexing method.     

Panconnectivity and edge-pancyclicity of 3-ary <Emphasis Type="Italic">N</Emphasis>-cubes

We study two topological properties of the 3-ary n-cube Q _n ³. Given two arbitrary distinct nodes x and y in Q _n ³, we prove that there exists an x–y path of every length ranging from d(x,y) to 3 ⁿ −1, where d(x,y) is the length of a shortest path between x and y. Based on this result, we prove that Q _n ³ is edge-pancyclic by showing that every edge in Q _n ³ lies on a cycle of every length ranging from 3 to 3 ⁿ .