Polarisation diversity of conformal arrays based on geometric algebra via convex optimisation

A simple and general design procedure is presented for the polarisation diversity of arbitrary conformal arrays; this procedure is based on the mathematical framework of geometric algebra and can be solved optimally using convex optimisation. Aside from being simpler and more direct than other derivations in the literature, this derivation is also entirely general in that it expresses the transformations in terms of rotors in geometric algebra which can easily be formulated for any arbitrary conformal array geometry. Convex optimisation has a number of advantages; solvers are widespread and freely available, the process generally requires a small number of iterations and a wide variety of constraints can be readily incorporated. The study outlines a two-step approach for addressing polarisation diversity in arbitrary conformal arrays: first, the authors obtain the array polarisation patterns using geometric algebra and secondly use a convex optimisation approach to find the optimal weights for the polarisation diversity problem. The versatility of this approach is illustrated via simulations of a 7×10 cylindrical conformal array. © 2012 The Institution of Engineering and Technology.

Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.

stochastic process algebra based software process simulation modeling

Chinese Acad Sci, ISCAS Lab Internet Software Technologies

Relation algebra operations on formal contexts.

This paper discusses the use of relation algebra operations on formal contexts. These operations are a generalisation of some of the context operations that are described in the standard FCA textbook (Ganter & Wille, 1999). This paper extends previous research in this area with respect to applications and implementations. It also describes a software tool (FcaFlint) which in combination with FcaStone facilitates the application of relation algebra operations to contexts stored in many formats.

Algebra Llinol - Cyflwyniad

Cyfieithiad yw'r llyfr hwn o Linear Algebra - An Introduction a ymddangosodd gyntaf yn 1978 ac a gyhoeddwyd gan y cwmni Van Nostrand Reinhold. Cafwyd Ail Argraffiad yn 1982 a dros y blynyddoedd bu nifer o ail brintiadau. Yn y cyfamser cyfieithwyd y llyfr i'r Groeg a Thwrceg. Er i'r llyfr gael ei ddefnyddio dros y blynyddoedd gan nifer o fyfyrwyr yn Aberystwyth a oedd yn cyflwyno eu gwaith yn Gymraeg, nid oedd ar gael yn y Gymraeg. Dyma, o'r diwedd, ymgais i wneud rhyw fath o iawn am hynny. Er bod y llyfr wedi bod allan o brint yn y Saesneg ers rhai blynyddoedd yn awr, mae'n amlwg ei fod yn dal i gael ei gymeradwyo mewn nifer o brifysgolion. Felly, y gobaith yw y bydd o ddefnydd. Efallai mai'r peth nesaf bydd ei gyfiethu'n ?l i'r Saesneg! Mae nifer o newidiadau yn y fersiwn hwn. Mae'n siwr bod nifer o gamgymeriadau ac efallai gwelliannau posibl i'r cyfieithu - byddwn yn ddiolchgar dderbyn unrhyw awgrymiadau. Gellir eu cyflwyno hefyd drwy Dr Gwion Evans o'r Adran Fathemateg, Prifysgol Aberystwyth.

Adding Polymorphic Abstraction to ML (Detailed Abstract)

The ML programming language restricts type polymorphism to occur only in the "let-in" construct and requires every occurrence of a formal parameter of a function (a lambda abstraction) to have the same type. Milner in 1978 refers to this restriction (which was adopted to help ML achieve automatic type inference) as a serious limitation. We show that this restriction can be relaxed enough to allow universal polymorphic abstraction without losing automatic type inference. This extension is equivalent to the rank-2 fragment of system F. We precisely characterize the additional program phrases (lambda terms) that can be typed with this extension and we describe typing anomalies both before and after the extension. We discuss how macros may be used to gain some of the power of rank-3 types without losing automatic type inference. We also discuss user-interface problems in how to inform the programmer of the possible types a program phrase may have.

A Biomechanical Model of Human Oculomotor Plant Kinematics Based Upon Geometric Algebra

A biomechanical model of the human oculomotor plant kinematics in 3-D as a function of muscle length changes is presented. It can represent a range of alternative interpretations of the data as a function of one parameter. The model is free from such deficits as singularities and the nesting of axes found in alternative formulations such as the spherical wrist (Paul, l98l). The equations of motion are defined on a quaternion based representation of eye rotations and are compact atnd computationally efficient.