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Abstract Purpose To derive existence and comparison results for extremal solutions of nonlinear singular distributional initial value problems and boundary value problems. Main methods Fixed point results in ordered function spaces and recently introduced concepts of regulated and continuous primitive integrals of distributions. Maple programming is used to determine solutions of examples. Results New existence results are derived for the smallest and greatest solutions of considered problems. Novel results are derived for the dependence of solutions on the data. The obtained results are applied to impulsive differential equations. Concrete examples are presented and solved to illustrate the obtained results. MSC: 26A24, 26A39, 26A48, 34A12, 34A36, 37A37, 39B12, 39B22, 47B38, 47J25, 47H07, 47H10, 58D25

Every countable language which conforms to classical logic is shown to have an extension which conforms to classical logic, and has a definitional theory of truth. That extension has a semantical theory of truth, if every sentence of the object language is valuated by its meaning either as true or as false. These theories contain both a truth predicate and a non-truth predicate. Theories are equivalent when the sentences of the object language are valuated by their meanings. [ABSTRACT FROM AUTHOR]

Every language which conforms to classical logic is shown to have an extension for which a consistent definitional theory of truth is formulated. Also a consistent semantical theory of truth is formulated for that extension if every sentence of the object language is valuated by its meaning either as true or as false. These theories of truth contain both a truth predicate and a non-truth predicate. The case where they compose with predicates having several free variables is also included. Theories are equivalent when sentences of the object language are valuated by their meanings. [ABSTRACT FROM AUTHOR]

Hannes Leitgeb formulated eight norms for theories of truth in his paper: 'What Theories of Truth Should be Like (but Cannot be)'. We shall present in this paper a mathematical theory of truth for suitably constructed languages which contain the first-order language of set theory, and prove that it satisfies all those norms. [ABSTRACT FROM AUTHOR]

The problem with human-robot task communication is that robots cannot understand complex human speech, whereas humans cannot efficiently use the fixed task request utterances required by robots. However, future planetary exploration missions will require astronauts on extravehicular activities to communicate task requests to robot assistants by using speech- and gesture-type user interfaces that can be easily embedded in their space suits. The solution proposed in this paper is indirect task communication based on the humanlike ability to utilize object-action relationships in task communication. A conventional task communication method, in which the astronaut needs to communicate all the task parameters explicitly, is compared with communication methods where affordances, i.e., action possibilities, are used to complete the task communication. This comparison is done with three user experiments: one performed with a fully autonomous centauroid robot in a geological exploration work context and two with a simulated robot in a lander assembly work context. The experiments indicate that affordance-based indirect task communication methods can be used to decrease both the human workload and the task communication times in a planetary exploration type of work context, and that combined direct and indirect task communication methods seem to be preferable from a human point of view. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Existence of the smallest, greatest, minimal, maximal and unique continuous solutions to distributional Cauchy problems, as well as their dependence on the data, are studied. The main tools are a continuous primitive integral and fixed point results in function spaces. [ABSTRACT FROM AUTHOR]

Abstract: We develop a flexible tool in terms of appropriately defined sub- and supersolutions that allows for obtaining existence, bounds, and multiplicity of solutions for quasilinear elliptic inclusions with a discontinuous multi-function that need neither be upper nor lower semicontinuous. The problem under consideration may be used to describe certain free boundary problems in mechanical models involving multi-valued constitutive laws. Our approach is based on a combined use of abstract fixed point results for monotone mappings on partially ordered sets, and on the existence and comparison results for multi-valued quasilinear elliptic problems with Clarke’s generalized gradient. [Copyright &y& Elsevier]

In this article we derive existence and comparison results for discontinuous non-absolute functional integral equations of Volterra type in an ordered Banach space which has a regular order cone. The obtained results are then applied to first-order impulsive differential equations. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the following implicit nonlinear discontinuous functional boundary value problem(IP) L0 u(t)=f(t,u,L0 u) for a.e. t∈I=[a,b],L1(u)=B1(u,L1(u)),0=L2(u(a),u(b)),whereL0 u(t)=−d/dtϕ(t,u(t),u′(t))−g(t,u,u(t),u′(t)),andL1(u)=L1(u(a),u(b),u′(a),u′(b),u).Supposing that there is a lower solution α and an upper solution β, such that α⩽β, the existence of extremal solutions lying between both functions is proved. [Copyright &y& Elsevier]