Compact Definition Research Articles

Design of variable stiffness panels for maximum strength using lamination parameters

Tailoring of laminated composite structures by changing ply angle and thickness locally provides a unique opportunity to take full advantage of anisotropic properties of composite materials. Variable stiffness design has become more attractive with the development of industrial fibre placement machines. Strength design is one of the areas where fibre steering is advantageous. Design methods that consist of directly optimising fibre angles or fibre path coefficients can lead to local optima and/or non-continuous solutions. These problems can be alleviated by using lamination parameters as design variables, which provide a compact definition of laminate stiffness. Additionally these parameters are continuous and the design space has shown to be convex. Dependency of strength failure criteria on ply angles may preclude using lamination parameters as design variables. Here, a recently developed method which incorporates the strength failure criteria in the lamination parameter space by using a conservative failure envelope for all ply angles is utilised. A hybrid approximation for the failure index is developed and is guaranteed to be convex using a convexifying approach. As an example strength maximisation of a panel with a central hole under uniaxial tension is investigated. Numerical results show improvements in strength with respect to the quasi-isotropic design. Although there is a common belief that design for stiffness can be served as a surrogate for strength design, it is shown that considering the strength as a design criteria especially for structures with large stress gradients is very important.

Degrees of fuzzy compactness in L-fuzzy topological spaces

In this paper, we introduce the notion of the degree of fuzzy compactness in L-fuzzy topological spaces by means of an inequality proposed by Shi in 2007. The notion is a generalization of the definition of fuzzy compactness in L-topological spaces. Some properties of this new notion are researched. The Tychonoff theorem is generalized. It is pointed out that our notion is not equivalent to other definition of degree of compactness.

A NEW NOTION OF FUZZY PS-COMPACTNESS

In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity. It is known that compactness and its stronger and weaker forms play very im- portant roles in topology. Based on fuzzy topological spaces introduced by Chang (4), various kinds of fuzzy compactness (2-4,7,11) have been established. However, these concepts of fuzzy compactness rely on the structure of L and L is required to be completely distributive. In (10), for a complete De Morgan algebra L, Shi in- troduced a new definition of fuzzy compactness in L-topological spaces using open L-sets and their inequality. This new definition doesn't depend on the structure of L. In this paper, following the lines of (10), we introduce a new notion of PS- compactness in L-topological spaces by means of pre-semi-open L-sets and their inequality. This notion can also be characterized by pre-semi-closed L-sets and their inequality and is a strong form of semi-compactness(9). This form of PS- compactness is a good generalization and has many characterizations when L is completely distributive De Morgan algebra. 2. Preliminaries

Fuzzy Inverse Compactness

We introduce definitions of fuzzy inverse compactness, fuzzy inverse countable compactness, and fuzzy inverse Lindelöfness on arbitrary -fuzzy sets in -fuzzy topological spaces. We prove that the proposed definitions are good extensions of the corresponding concepts in ordinary topology and obtain different characterizations of fuzzy inverse compactness.

When is a drug-related death not a drug-related death? Implications for current drug-related death policies in the UK and Europe.

BackgroundDrug-related death (DRD) figures, published by the national performance management framework, are used to monitor the performance of Drug (and Alcohol) Action Teams (D[A]ATs) in England and Wales with respect to reducing DRDs among drug abusers. To date, no investigation has been made into the types of death included in these figures, the demographic and drug profile of those who died, nor the likelihood of individuals included in DRD figures interacting with services designed to assist drug abusers. The aim of this work was to examine the characteristics of deaths classified as drug-related and to explore their applicability to performance-monitor drug-related services. Liverpool was chosen because it was reported by the national DRD monitoring system to have the highest number of DRDs in 2004.MethodsInformation was retrieved from the Liverpool coroner's records and established monitoring systems on individuals reported by the national performance monitoring system as a DRD between 1st January 2004 and 30th June 2005 (n = 70). Analyses assessed differences between those categorised by the national performance monitoring system as 'drug abusers/dependents' and 'non-drug abusers/dependents' using χ2, Fisher's exact test and Mann-Whitney U.ResultsNon-drug abusers were significantly older (median age 53.59 vs. 38.23), had no recent contact with drug-related agencies (cv. 31.6% of abusers who had treatment contact) and had different post mortem drug profiles than drug abusers. A significantly greater proportion of non-drug abusers died from drug toxicity – predominantly through anti-depressants, anti-psychotics and analgesics.ConclusionOur findings suggest that the national DRD performance monitoring system includes deaths of people who are not drug abusers – individuals who are not the current focus of drug prevention, treatment or harm minimisation services. This raises concerns regarding the applicability of these figures to performance monitor D(A)ATs. Furthermore, using the more compact definitions used to monitor trends in DRDs across England, Wales and Europe fails to include a proportion of deaths attributable to drug misuse – such as those attributable blood-borne viruses. Current definitions used to monitor DRDs locally, nationally and across Europe fail to capture the true burden of drug-related mortality.

Sequential definitions of compactness

A subset F of a topological space is sequentially compact if any sequence x = ( x n ) of points in F has a convergent subsequence whose limit is in F . We say that a subset F of a topological group X is G -sequentially compact if any sequence x = ( x n ) of points in F has a convergent subsequence y such that G ( y ) ∈ F where G is an additive function from a subgroup of the group of all sequences of points in X . We investigate the impact of changing the definition of convergence of sequences on the structure of sequentially compactness of sets in the sense of G -sequential compactness. Sequential compactness is a special case of this generalization when G = lim .

A new definition of fuzzy compactness

In this paper, a new definition of fuzzy compactness is presented in L-topological spaces when L is a complete DeMorgan algebra. This definition does not rely on the structure of the basis lattice L and no distributivity in L is required. The intersection of a fuzzy compact L-set and a closed L-set is fuzzy compact. The continuous image of a fuzzy compact L-set is fuzzy compact. If the set of all prime elements of L is order generating, then the Alexander Subbase Theorem is true. When L is a completely distributive DeMorgan algebra, it is equivalent to Lowen's fuzzy compactness, and in this case, its many characterizations are presented by means of open L-sets and closed L-sets.

On the Convergence of a Class of Multilevel Methods for Large Sparse Markov Chains

This paper investigates the theory behind the steady state analysis of large sparse Markov chains with a recently proposed class of multilevel methods using concepts from algebraic multigrid and iterative aggregation-disaggregation. The motivation is to better understand the convergence characteristics of the class of multilevel methods and to have a clearer formulation that will aid their implementation. In doing this, restriction (or aggregation) and prolongation (or disaggregation) operators of multigrid are used, and the Kronecker-based approach for hierarchical Markovian models is employed, since it suggests a natural and compact definition of grids (or levels). However, the formalism used to describe the class of multilevel methods for large sparse Markov chains has no influence on the theoretical results derived.

Increasing the Efficiency of Graph Colouring Algorithms with a Representation Based on Vector Operations

We introduce a novel representation for the graph colouring problem, called the Integer Merge Model, which aims to reduce the time complexity of graph colouring algorithms. Moreover, this model provides useful information to aid in the creation of heuristics that can make the colouring process even faster. It also serves as a compact definition for the description of graph colouring algorithms. To verify the potential of the model, we use it in the complete algorithm DSATUR, and in two version of an incomplete approximation algorithm; an evolutionary algorithm and the same evolutionary algorithm extended with guiding heuristics. Both theoretical and empirical results are provided investigation is performed to show an increase in the efficiency of solving graph colouring problems. Two problem suites were used for the empirical evidence: a set of practical problem instances and a set of hard problem instances from the phase transition.

Quantifying Urban Form: Compactness versus 'Sprawl'

This paper develops a set of quantitative variables to characterise urban forms at the metropolitan level and, in particular, to distinguish compactness from 'sprawl'. It first reviews and analyses past research on the definitions of urban form, compactness and sprawl, and corresponding quantitative variables. Four quantitative variables are developed to measure four dimensions of urban form at the metropolitan level: metropolitan size, activity intensity, the degree that activities are evenly distributed, and the extent that high-density sub-areas are clustered. Through a series of simulation analyses, the global Moran coefficient, which characterises the fourth dimension, distinguishes compactness from sprawl. It is high, intermediate and close to zero for monocentric, polycentric and decentralised sprawling forms respectively. In addition, the more there is more local sprawl, composed of discontinuity and strip development, the lower is the Moran coefficient.

Catch-up Growth or Regression to the Mean? Recovery from Stunting Revisited

An important question for policy is the extent to which catch-up growth can ease the impact of early stunting. Martorell et al. (1992) showed that stunted Guatemalan infants remain stunted into adulthood, whereas Adair (1999) found appreciable catch-up growth in Filipino children from 2-12 years. Both groups defined catch-up as an inverse correlation between early height and subsequent growth, but Martorell based the correlation on height, whereas Adair used height z scores. The statistical phenomenon of regression to the mean is much like catch-up growth, an inverse correlation between initial height and later height gain. The objective of this study was to reexamine the relationship between stunting and later catch-up growth in the context of regression to the mean. The design was a theoretical analysis showing that catch-up growth is more evident based on height z scores than on height, validated using data on 495 stunted South African children seen at 2 and 5 years of age. The correlation between height at 2 and height change from 2 to 5 was small based on height (-0.11) but large and highly significant based on height z score (-0.58), providing strong evidence of catch-up growth. We argue that catch-up growth should be estimated using height z score not height and that catch-up is present only when the change in z score exceeds that predicted by regression to the mean. This leads to a compact definition of catch-up growth: if z1 and z2 are the initial and final (mean) height z scores, and r is the correlation between them, then catch-up growth for groups or individuals is given by (z2 - rz1).

Compactness under constructive scrutiny

AbstractHow are the various classically equivalent definitions of compactness for metric spaces constructively interrelated? This question is addressed with Bishop‐style constructive mathematics as the basic system – that is, the underlying logic is the intuitionistic one enriched with the principle of dependent choices. Besides surveying today's knowledge, the consequences and equivalents of several sequential notions of compactness are investigated. For instance, we establish the perhaps unexpected constructive implication that every sequentially compact separable metric space is totally bounded. As a by‐product, the fan theorem for detachable bars of the complete binary fan proves to be necessary for the unit interval possessing the Heine‐Borel property for coverings by countably many possibly empty open balls. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A CAD assisted design and optimisation methodology for over-voltage ESD protection circuits

To reduce the cycle time and the cost of the design of ESD tolerant over-voltage I/O cells, a methodology for pre-silicon ESD protection optimisation is described, based on Technology Computer Aided Design (TCAD) (device level) and compact (circuit level) simulation studies. Using this methodology, first time right ESD tolerant over-voltage I/O cells were designed in a silicided 0.25 μm CMOS dual gate-oxide process. The methodology consists in a precise TCAD process calibration, a cascoded snapback NMOS compact model definition valid under ESD conditions, a model parameter extraction based on TCAD data and, finally, circuit level optimisation of the I/O protection circuits. Very good agreement was achieved between the simulated pre-silicon characteristics and the experimental behaviour of the I/O protection circuits.

Relative form boundedness and compactness for a second-order differential operator

If A and L are self-adjoint operators on a Hilbert space H such that A is nonnegative and L⩾ εI for some ε>0 we study conditions under which A is form bounded or form compact with respect to L and contrast these concepts with the stronger properties that A be relatively operator bounded or compact with respect to L. In particular several definitions of form compactness are shown to be equivalent. The principal application of the theory is to self-adjoint second order operators. In this case conditions that A be form bounded or form compact with respect to L are shown in some cases to be necessary and sufficient. Examples include the energy operator of the hydrogen atom.

Some good extensions of compactness

The aim of this paper is to introduce good definitions of compactness, almost compactness, near compactness, weak compactness, and S-closedness in fuzzy topological spaces in Sostak s sense. These compactness related concepts are defined for arbitrary fuzzy sets and some of their properties studied.

Products of compact spaces and the axiom of choice II

AbstractThis is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces (first and second countable spaces, Hausdorff spaces, and subspaces of ℝK). We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products.

Definitions of compactness and the axiom of choice

AbstractWe study the relationships between definitions of compactness in topological spaces and the roll the axiom of choice plays in these relationships.

Positivity and conservation of superenergy tensors

Two essential properties of energy–momentum tensors Tμν are their positivity and conservation. This is mathematically formalized by, respectively, an energy condition, as the dominant energy condition, and the vanishing of their divergence ∇μTμν = 0. The classical Bel and Bel–Robinson superenergy tensors, generated from the Riemann and Weyl tensors, respectively, are rank-4 tensors. But they share these two properties with energy–momentum tensors: the dominant property (DP) and the divergence-free property in the absence of sources (vacuum). Senovilla [2, 3] defined a universal algebraic construction which generates a basic superenergy tensor T{A} from any arbitrary tensor A. In this construction, the seed tensor A is structured as an r-fold multivector, which can always be done. The most important feature of the basic superenergy tensors is that they satisfy automatically the DP, independently of the generating tensor A. In [8], we presented a more compact definition of T{A} using the r-direct Clifford algebra ⊗r \U0001d49eℓp,q. This form for the superenergy tensors allowed us to obtain an easy proof of the DP valid for any dimension. In this paper we include this proof. We explain which new elements appear when we consider the tensor T{A} generated by a non-degree-defined r-fold multivector A and how orthogonal Lorentz transformations and bilinear observables of spinor fields are included as particular cases of superenergy tensors. We find some sufficient conditions for the seed tensor A, which guarantee that the generated tensor T{A} is divergence-free. These sufficient conditions are satisfied by some physical fields, which are presented as examples.

On Pseudocompact, Countably Compact, Locally Bicompact Mappings, and k-Mappings

We consider various definitions of a pseudocompact mapping and the basic properties of pseudocompact mappings. Moreover, we consider the definition of countable compactness of a continuous mapping and study the properties of a countably compact mapping similar to the corresponding properties for countably compact spaces and also the interrelation between countable compactness and pseudocompactness of mappings. We also extend the notions of local bicompactness and k-space to continuous mappings.

On the equivalence of four definitions of compactness of LF subsets

In this paper, the equivalence of four definitions of fuzzy compactness, strong fuzzy compactness, N-compactness and ultra-fuzzy compactness of L-fuzzy subsets is discussed systematically. A series of good results is obtained.