Disjoint Domains Research Articles

Eliciação e comunicação de requisitos em domínios disjuntos: estudo de caso para automação na área médica

O final do século passado foi marcado por um crescente intresse nas fases preliminares do processo de design, especificamente na fase de requisitos e definição do problema. Na área de automação, o gerenciamento de requisitos é determinante para o sucesso dos projetos, embora grande parte do esforço no desenvolvimento de técnicas e métodos ter sido direcionado para as fases posteriores: o design e a implementação. Por não serem formais, os processos de eliciação e análise de requisitos são subestimados por profissionais da área de automação, onde o formalismo é fundamental para a validação dos processos de controle, automação e supervisão. Em especial, quando os ambientes de desenvolvimeno e de aplicação são disjuntos, isto é, usuários e stakeholders pertencem a um domínio com pouca ou nenhuma interseção com a área da engenharia, informática e automação, os processos de eliciação e análise se tornam bastante complicados. Neste trabalho é apresentada uma proposta de sistematização do gerenciamento de requisitos para domínios disjuntos, adaptando técnicas já conhecidas ao processo de prototipagem virtual, consolidado após o início deste século. Um estudo de caso é apresentado onde o desenvolvimento se dá na área de Engenharia de Automação para aplicações em processos pertinentes à cirurgia de catarata. Para aproximar os domínios busca-se uma abordagem mais simplificada das técnicas de prototipagem virtual tornando o processo mais prático, sem no entanto abdicar do formalismo dos modelos. Os dados levantados foram obtidos com a colaboração do Hospital Santa Luzia, Salvador, Bahia, e do Instituto da Visão, UNIFESP, em São Paulo.

Restitution of the Temperature Field Inside a Cylinder of Semitransparent Dense Medium From Directional Intensity Data

The purpose of this paper is to obtain the temperature field inside a cylinder filled in with a dense nonscattering semitransparent medium from directional intensity data by solving the inverse radiative transfer equation. This equation is solved in a first approach with the help of a discrete scheme, and the solution is then exactly obtained by separating the physical set on two disjoint domains on which a Laplace transform is applied, followed by the resolution of a first kind Fredholm equation.

Iterative scheduling algorithms based on the subdivision of the solution space into domains

Iterative multiprocessor scheduling algorithms are considered. The iterative algorithms make it possible to solve scheduling problems for a wide class of computer architectures but are very intricate from the computational point of view. To simplify the iterative algorithms, we propose an approach to their construction based on the subdivision of the space of correct schedules into disjoint domains, namely, an algorithm for constructing domains is proposed, the operations of the schedule transformations closed within the domains are introduced, and a technique for cutting off domains is developed. The approach developed also makes it possible to construct parallel algorithms with a low traffic of the exchange between parallel processes.

Inequalities for inner radii of disjoint domains and open sets

In geometric function theory there is a well-known field related to estimates for functionals that depend on the inner radii of nonoverlapping domains. Many authors has contributed to the development of this field. Today, great attention is being paid to the study of extremal problems for nonoverlapping domains with free poles. In this paper, one result of this kind is generalized and strengthened.

Hyperbolic Hubbard–Stratonovich transformation made rigorous

We revisit a long standing issue in the theory of disordered electron systems and their effective description by a nonlinear sigma model: the hyperbolic Hubbard–Stratonovich (HS) transformation in the bosonic sector. For time-reversal invariant systems without spin, this sector is known to have a noncompact orthogonal symmetry Op,q. There exists an old proposal by Pruisken and Schäfer how to perform the HS transformation in an Op,q-invariant way [Nucl. Phys. B. 200, 20 (1982)]. Giving a precise formulation of this proposal, we show that the HS integral is a sign-alternating sum of integrals over disjoint domains.

Shared and Closed-Shell O−O Interactions in Silicates

Bond paths of maximum electron density spanning O-O edges shared between equivalent or quasiequivalent MOn (n > 4) coordination polyhedra are not uncommon electron density features displayed by silicates. On the basis of the positive values for the local electronic energy density, H(rc), at the bond critical points, rc, they qualify as weak "closed-shell" interactions. As observed for M-O bonded interactions (M = first and second row metal atoms), the electron density, rho(rc), and the Laplacian of the electron density increase in a regular way as the separation between the O atoms, R(O-O), decreases. A simple model, based on R(O-O) and the distances of the Si atoms from the midpoint between adjacent pairs of O atoms, partitions the O-O bond paths in the high-pressure silica polymorph coesite into two largely disjoint domains, one with and one without bond paths. The occurrence of O-O bond paths shared in common between equivalent coordination polyhedra suggests that they may be grounded in some cases on factors other than bonded interactions, particularly since they are often displayed by inert procrystal representations of the electron density. In these cases, it can be argued that the accumulation of the electron density along the paths has its origin, at least in part, in the superposition of the peripheral electron density distributions of the metal M atoms occupying the edge-sharing polyhedra. On the other hand, the accumulation of electron density along the paths may stabilize a structure by shielding the adjacent M atoms in the edge-sharing polyhedra. For closed-shell Li-O, Na-O, and Mg-O interactions, H(rc) is positive and increases as the value of rho(rc) increases, unlike the "shared" Be-O, B-O, C-O, Al-O, Si-O, P-O, and S-O interactions, where H(rc) is negative and decreases as rho(rc) increases. The H(rc) values for the weak closed-shell O-O interactions also increase as rho(rc) increases, as observed for the closed-shell M-O interactions. On the basis of the bond critical point properties and the negative H(rc) value, the O-O interaction comprising the O2 molecule in silica III qualifies as a shared interaction.

Minimal graphs in $${M \times \mathbb{R}}$$

We study minimal graphs in \({M \times \mathbb{R}}\) . First, we establish some relations between the geometry of the domain and the existence of certain minimal graphs. We then discuss the problem of finding the maximal number of disjoint domains Ω ⊂ M that admit a minimal graph that vanishes on ∂Ω. When M is two-dimensional and has non-negative sectional curvature, we prove that this number is 3. This was proved by Tkachev in \({\mathbb{R}^3}\) .

Sharp estimates for inner radii of systems of nonoverlapping domains and open sets

We study extremal problems of the geometric theory of functions of a complex variable. Sharp upper estimates are obtained for the product of inner radii of disjoint domains and open sets with respect to equiradial systems of points.

Some extremal problems in the theory of nonoverlapping domains with free poles on rays

We obtain new results on the maximization of the product of powers of the interior radii of pairwise disjoint domains with respect to certain systems of points in the extended complex plane.

Phase Separation in Binary Polymer/Liquid Crystal Mixtures: Network Breaking and Domain Growth by Coalescence-induced Coalescence

A small-angle light scattering (SALS) technique together with optical microscopy observation are used to investigate phase separation kinetics in films of low molecular weight thermotropic liquid crystal (4-cyano-4'-n-octyl-biphenyl, 8CB) with flexible polymer (polystyrene, PS). The growth of domains is studied as a function of time, film thickness, and film composition. The light scattering results are correlated with the images obtained by optical microscopy observation. In this paper, we study the breaking of a bicontinuous network of polymer in liquid crystal into droplets and their further growth via the coalescence-induced coalescence mechanism. The appearance of droplets in the system leads to a strong scattering at small wave vectors, while the bicontinuous network gives a peak at a nonzero wave vector. Superposition of these scattering intensities leads to the appearance of a second peak in the full scattering intensity signal, when the bicontinuous network starts to break up into disjointed elongated domains. Finally, both peaks merge into a single peak, which moves quickly toward zero wave vectors, indicating a complete transformation of elongated domains into spherical droplets of variable size. We found that the separation process does not depend on the size of the system. Irrespective of the sample thickness, the network breaks into fragments always at the same time after temperature quench. On the basis of morphological analysis, we found that the average size of the droplets which formed from the network grows with time, t, as t(alpha), alpha = 0.9 +/- 0.1, in the isotropic phase and in the nematic phase.

Chaotic diffusion of orbits in systems with divided phase space

In this paper we discuss the relevance of diffusive processes in multidimensional Hamiltonian systems. By means of a rather simple model, we present evidence that for moderate-to-strong chaotic systems the stochastic motion remains confined to disjoint domains on the energy surface, at least for mild motion times. We show that only for extremely large timescales and for rather large perturbations, does the chaotic component appear almost fully connected through the relics of the resonance structure. The discussion whether diffusion over the energy surface could actually occur in asteroidal or galaxy dynamics is also included.

Combining Solutions of Semilinear Partial Differential Equations in ℝ n with Critical Sobolev Exponent

We consider a positive C 2-function u in ℝ n which is equal to two different spherical solutions respectively in two disjoint domains. u satisfies the equation in ℝ n . By a result of Gidas, Ni and Nirenberg, K ≢ 1 in ℝ n . In this paper we discuss lower bounds on . The estimates are applied to study blow-up solutions and interaction of bubbles.

State Variables for Coupled Circuit-Field Problems

We study systematical detection of the state variables for a quasi-static coupled circuit-field problem, which may consist of several disjoint domains for both field problems and electric networks. We translate the relevant questions about coupling into linear algebraic problems, i.e., use the homology theory. This enables us to express the state variable detection problem with readily programmable and computable concepts.

New Tractable Classes From Old

The constraint satisfaction problem is known to be NP-hard in general, but a number of restrictions of the problem have been identified over the years which ensure tractability. This paper introduces two simple methods of combining two or more tractable classes over disjoint domains, in order to synthesise larger, more expressive tractable classes. We demonstrate that the classes so obtained are genuinely novel, and have not been previously identified. In addition, we use algebraic techniques to extend the tractable classes which we identify, and to show that the algorithms for solving these extended classes can be less than obvious.

TWO-DIMENSIONAL MINIMAL GRAPHS OVER UNBOUNDED DOMAINS

In this paper we will study solution pairs $(u,D)$ of the minimal surface equation defined over an unbounded domain $D$ in $R^2$, with $u=0$ on $\partial D$. It is well known that there are severe limitations on the geometry of $D$; for example $D$ cannot be contained in any proper wedge (angle less than $\pi$). Under the assumption of sublinear growth in a suitably strong sense, we show that if $u$ has order of growth $\alpha$ in the sense of complex variables, then the ‘asymptototic angle’ of $D$ must be at least $\pi/\alpha$. In particular, there are at most two such solution pairs defined over disjoint domains. If $\alpha<1$ then $u$ cannot change sign and there is no other disjoint solution pair. This result is sharp as can be seen by a suitable piece of Enneper’s surface which has order $\alpha=\tfrac{2}{3}$ and asymptotic angle $\tfrac{3}{2}\pi$.AMS 2000 Mathematics subject classification: Primary 35J60; 53A10

Duality for some categories of coalgebras

A contravariant duality is constructed between the category of coalgebras of a given signature, and a category of Boolean algebras with operators, including modal operators corresponding to state transitions in coalgebras, and distinguished elements abstracting the sets of states defined by observable equations.¶This duality is used to give a new proof that a class of coalgebras is definable by Boolean combinations of observable equations if it is closed under disjoint unions, domains and images of coalgebraic morphisms, and ultrafilter enlargements. The proof reduces the problem to a direct application of Birkhoff's variety theorem characterising equational classes of algebras.

Spectrum of the Ruelle operator and exponential decay of correlations for open billiard flows

The paper deals with the billiard flow in the exterior of several strictly convex disjoint domains in the plane with smooth boundaries satisfying an additional (visibility) condition. Using a modification of the technique of Dolgopyat, we get spectral estimates for the Ruelle operator related to a Markov family for the nonwandering (trapping) set of the flow similar to those of Dolgopyat in the case of transitive Anosov flows on compact manifolds with smooth jointly non-integrable horocycle foliations. As a consequence, we get exponential decay of correlation for Hölder continuous potentials on the nonwandering set. Combining the spectral estimate for the Ruelle operator with an argument of Pollicott and Sharp, we also derive the existence of a meromorphic continuation of the dynamical zeta function of the billiard flow to a half-plane Re( s ) < h T - ε, where h T is the topological entropy of the billiard flow, and an asymptotic formula with an error term for the number π(λ) of closed orbits of least period λ > 0.

A simple numerical approach for assessing coupled transport processes in partitioning systems

Recent concepts in the solution of multidomain equation systems are applied to the problem of distinct transport processes coupled over geometrically disjoint domains. The (time dependent) transport equations for the composite system are solved using a simple domain decomposition approach, with parallel implementations of detailed Schwarz balances for the system subdomain interfaces. An existing numerical partial differential equation (PDE) solver is coupled with the interface algorithms to provide a code capable of handling a wide range of dynamical equations within the subdomains. Interface partitioning conditions corresponding to sharply discontinuous Dirichlet constraints, and to (discontinuous) rate-limited Neumann constraints are also incorporated into the code. A variety of transport operators can be handled simply by altering the equation system code block. The code is validated against analytical solutions for representative parabolic transport equations including recent solutions for diffusive transport in partitioning laminates, useful for describing the movement of chemical species in composite materials. The code is then applied to an example problem of coupled multiphase chemical transport in a variably saturated soil column with a low-permeability capping.

Fitting hidden semi-Markov models to breakpoint rainfall data

The paper proposes a hidden semi-Markov model for breakpoint rainfall data that consist of both the times at which rain-rate changes and the steady rates between such changes. The model builds on and extends the seminal work of Ferguson (1980) on variable duration models for speech. For the rainfall data the observations are modelled as mixtures of log-normal distributions within unobserved states where the states evolve in time according to a semi-Markov process. For the latter, parametric forms need to be specified for the state transition probabilities and dwell-time distributions.Recursions for constructing the likelihood are developed and the EM algorithm used to fit the parameters of the model. The choice of dwell-time distribution is discussed with a mixture of distributions over disjoint domains providing a flexible alternative. The methods are also extended to deal with censored data. An application of the model to a large-scale bivariate dataset of breakpoint rainfall measurements at Wellington, New Zealand, is discussed.

Privacy risks in recommender systems

Recommender system users who rate items across disjoint domains face a privacy risk analogous to the one that occurs with statistical database queries.