A new sufficient condition for optimal impulsive control problems

In this article we introduce the concept of MP-pseudoinvexity for general nonlinear impulsive optimal control problems whose dynamics are specified by measure driven control equations. This is a general paradigm in that, both the absolutely continuous and singular components of the dynamics depend on both the state and the control variables. The key result consists in showing the sufficiency for optimality of the MP-pseudoinvexity. It is proved that, if this property holds, then every process satisfying the maximum principle is an optimal one. This result is obtained in the context of a proper solution concept that will be presented and discussed. © 2012 IEEE.

Root morphology and phosphorus uptake by potato cultivars grown under deficient and sufficient phosphorus supply

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Arbitrage-Free Conditions and Hedging Strategies for Markets with Penalty Costs on Short Positions

We consider a discrete-time financial model in a general sample space with penalty costs on short positions. We consider a friction market closely related to the standard one except that withdrawals from the portfolio value proportional to short positions are made. We provide necessary and sufficient conditions for the nonexistence of arbitrages in this situation and for a self-financing strategy to replicate a contingent claim. For the finite-sample space case, this result leads to an explicit and constructive procedure for obtaining perfect hedging strategies.

Necessary and Sufficient Condition for Oscillations of Neutral Differential Equation

2000 Mathematics Subject Classification: 34K15, 34C10.

Second Order Optimality Conditions in Nonsmooth Unconstrained Optimization

AMS subject classification: 49J52, 90C30.

New Coefficient Conditions for Functions Starlike with Respect to Symmetric Points

2000 Mathematics Subject Classification: Primary 30C45, secondary 30C80.

Using Ownership to Reason About Inherent Parallelism in Object-Oriented Programs

With the emergence of multi-cores into the mainstream, there is a growing need for systems to allow programmers and automated systems to reason about data dependencies and inherent parallelismin imperative object-oriented languages. In this paper we exploit the structure of object-oriented programs to abstract computational side-effects. We capture and validate these effects using a static type system. We use these as the basis of sufficient conditions for several different data and task parallelism patterns. We compliment our static type system with a lightweight runtime system to allow for parallelization in the presence of complex data flows. We have a functioning compiler and worked examples to demonstrate the practicality of our solution.

Mind change complexity of learning logic programs

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts. Building on Angluin’s notion of finite thickness and Wright’s work on finite elasticity, Shinohara defined the property of bounded finite thickness to give a sufficient condition for learnability of indexed families of computable languages from positive data. This paper shows that an effective version of Shinohara’s notion of bounded finite thickness gives sufficient conditions for learnability with ordinal mind change bound, both in the context of learnability from positive data and for learnability from complete (both positive and negative) data. Let Omega be a notation for the first limit ordinal. Then, it is shown that if a language defining framework yields a uniformly decidable family of languages and has effective bounded finite thickness, then for each natural number m >0, the class of languages defined by formal systems of length <= m: • is identifiable in the limit from positive data with a mind change bound of Omega (power)m; • is identifiable in the limit from both positive and negative data with an ordinal mind change bound of Omega × m. The above sufficient conditions are employed to give an ordinal mind change bound for learnability of minimal models of various classes of length-bounded Prolog programs, including Shapiro’s linear programs, Arimura and Shinohara’s depth-bounded linearly covering programs, and Krishna Rao’s depth-bounded linearly moded programs. It is also noted that the bound for learning from positive data is tight for the example classes considered.

A framework for reasoning about inherent parallelism in modern object-oriented languages

With the emergence of multi-core processors into the mainstream, parallel programming is no longer the specialized domain it once was. There is a growing need for systems to allow programmers to more easily reason about data dependencies and inherent parallelism in general purpose programs. Many of these programs are written in popular imperative programming languages like Java and C]. In this thesis I present a system for reasoning about side-effects of evaluation in an abstract and composable manner that is suitable for use by both programmers and automated tools such as compilers. The goal of developing such a system is to both facilitate the automatic exploitation of the inherent parallelism present in imperative programs and to allow programmers to reason about dependencies which may be limiting the parallelism available for exploitation in their applications. Previous work on languages and type systems for parallel computing has tended to focus on providing the programmer with tools to facilitate the manual parallelization of programs; programmers must decide when and where it is safe to employ parallelism without the assistance of the compiler or other automated tools. None of the existing systems combine abstraction and composition with parallelization and correctness checking to produce a framework which helps both programmers and automated tools to reason about inherent parallelism. In this work I present a system for abstractly reasoning about side-effects and data dependencies in modern, imperative, object-oriented languages using a type and effect system based on ideas from Ownership Types. I have developed sufficient conditions for the safe, automated detection and exploitation of a number task, data and loop parallelism patterns in terms of ownership relationships. To validate my work, I have applied my ideas to the C] version 3.0 language to produce a language extension called Zal. I have implemented a compiler for the Zal language as an extension of the GPC] research compiler as a proof of concept of my system. I have used it to parallelize a number of real-world applications to demonstrate the feasibility of my proposed approach. In addition to this empirical validation, I present an argument for the correctness of the type system and language semantics I have proposed as well as sketches of proofs for the correctness of the sufficient conditions for parallelization proposed.

Sufficiently informative measurements for stability of approximate conditional mean estimates

This paper establishes sufficient conditions to bound the error in perturbed conditional mean estimates derived from a perturbed model (only the scalar case is shown in this paper but a similar result is expected to hold for the vector case). The results established here extend recent stability results on approximating information state filter recursions to stability results on the approximate conditional mean estimates. The presented filter stability results provide bounds for a wide variety of model error situations.

Translating vision research into policy and practice to improve the visibility, and hence safety, or road workers at night

The process of translating research into policy and practice is not well understood. This paper uses a case study approach to interpret an example of translation with respect to theoretical approaches identified in the literature. The case study concerns research into “biological motion” or “biomotion”: when lights are placed on the moveable joints of the body and the person moves in a dark setting, there is immediate and accurate recognition of the human form although only the lights can be seen. QUT was successful in gaining Australian Research Council funding with the support of the predecessors of the Queensland Department of Transport and Main Roads (TMR) to research the biomotion effect in road worker clothing using reflective tape rather than lights, and this resulted in the incorporation of biomotion marking into AS/NZS 4602.1 2011. The most promising approach to understanding the success of this translation, SWOV’s “knowledge utilisation approach” provided some insights but was more descriptive than predictive and provided “necessary but not sufficient” conditions for translation. In particular, the supportive efforts of TMR staff engaged in the review and promulgation of national standards were critical in this case. A model of the conclusions is presented. The experiences gained in this case should provide insights into the processes involved in effectively translating research into practice.

Generalized azimuthal shear deformations in compressible isotropic elastic materials

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.

On helical shear of a compressible elastic circular cylindrical tube

In this paper we examine the combined azimuthal and axial shear of a compressible isotropic elastic circular cylindrical tube of finite extent, otherwise referred to as helical shear (which is an isochoric deformation). The equilibrium equations are formulated in terms of the principal stretches, and explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation are obtained and compared with those obtained previously for this problem. Several classes of strain-energy functions are derived and in some general cases complete solutions of the equilibrium equations are obtained. Existing results are recovered as special cases and some new results for the strain-energy functions derived are determined and discussed.

On extension and torsion of a compressible elastic circular cylinder

In this paper we examine the combined extension and torsion of a compressible isotropic elastic cylinder of finite extent. The equilibrium equations are formulated in terms of the principal stretches and then applied to the special case of pure torsion superimposed on a uniform extension (an isochoric deformation). Explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation with vanishing traction on the lateral surfaces of the cylinder are obtained. Some strain-energy functions satisfying these conditions are considered, existing results are recovered as special cases and new results are obtained. We also point out how the strain-energy functions generated from the considered isochoric deformation considered (of a compressible material) can be used to generate energy functions and corresponding solutions for the incompressible theory.

Approximate Controllability Of Semilinear Systems Using Integral Contractors

In this article, a non-autonomous (time-varying) semilinear system is considered and its approximate controllability is investigated. The notion of 'bounded integral contractor', introduced by Altman, has been exploited to obtain sufficient conditions for approximate controllability. This condition is weaker than Lipschitz condition. The main theorems of Naito [11, 12] are obtained as corollaries of our main results. An example is also given to show how our results weaken the conditions assumed by Sukavanam[17].