I consider the direct product algebra formed from two isomorphic Clifford algebras. More specifically, for an element x in each of the two component algebras I consider elements in the direct product space with the form x ⊗ x. I show how this construction can be used to model the algebraic structure of particular vector spaces with metric, to describe the relationship between wavefunction and observable in examples from quantum mechanics, and to express the relationship between the electromagnetic (...) field tensor and the stress-energy tensor in electromagnetism. To enable this analysis I introduce a particular decomposition of the direct product algebra. (shrink)

In this contribution we shall characterize matrix consequence operation determined by a direct product and an ultraproduct of a family of logical matrices. As an application we shall describe finite consequence operations with the help of ultrapowers.

We show that compactness is preserved by arbitrary direct products of lattices of truth values and that the Löwenheim-Skolem property is preserved by finite direct products of lattices of truth values.

We generalize to theories of modules (complete or not) a result of U. Felgner stating that a complete theory of abelian groups is a Horn theory if and only if it is closed under products. To prove this we show that a reduced product of modules $\Pi_F M_i (i \in I)$ is elementarily equivalent to a direct product of ultraproducts of the modules $M_i (i \in I)$.

Natural language involves both speaking and listening. Recent models claim that production and comprehension share aspects of processing and are linked within individuals (Dell & Chang, 2014; MacDonald, 2013; Pickering & Garrod, 2004; 2013a). Evidence for this claim has come from studies of cross-modality structural priming, mainly examining processing in the direction of comprehension to production. The current study replicated these comprehension to production findings and developed a novel cross-modal structural priming paradigm from production to comprehension using a temporally-sensitive online (...) measure of comprehension, Event-Related Potentials. For Comprehension-to-Production priming, participants first listened to active or passive sentences and then described target pictures using either structure. In Production-to-Comprehension priming, participants first described a picture using either structure and then listened to target passive sentences while EEG was recorded. Comprehension-to-Production priming showed the expected passive sentence priming for syntactic choice, but not response time or average syllable duration. In Production-to-Comprehension priming, primed, versus unprimed, passive sentences elicited a reduced N400. These effects support the notion that production and comprehension share aspects of processing and are linked within the individual. Moreover, this paradigm can be used for the exploration priming at different linguistic levels as well as the influence of extra-linguistic factors on natural language use. (shrink)

We characterize the elementary classes generated from a distinguished subclass closing by taking direct products and elementary equivalence. In the second part we give the same characterization in terms of atomic Boolean products. In the last part, we study the cases when the class of Boolean products is elementary but is not given by a discriminator.

Productivity is a central concept in the study of language and language acquisition. As a test case for exploring the notion of productivity, we focus on the noun slots of verb frames, such as __want__, __see__, and __get__. We develop a novel combination of measures designed to assess both the flexibility and creativity of use in these slots. We do so using a rigorously controlled sample of child speech and child directed speech from three English-speaking children between the ages of (...) 2–3 years and their caregivers. We find different levels of creativity and flexibility between the adult and child samples for some measures, for some slots, and for some developmental periods. We discuss these differences in the context of verb frame semantics, conventionality versus creativity and child errors, and draw some tentative conclusions regarding developmental changes in children's early grammatical representations. (shrink)

This is a review of the 2013 film Words and Pictures. Surprisingly, the film is not about justifying a role for the humanities in education but, rather, a battle to determine which is more valuable—literature or art?. At a time when many schools question if these have any value at all, this film uses passionate and afflicted teachers to explore which is most important and finds valuable intersections between the two.

This is a review of the film Big Eyes. Adapted from a true story about artist Margaret Keane, the overarching theme of the movie is plagiarism. While most people think of written works such as books and articles being plagiarized, Big Eyes gives viewers insight into the world of stolen works of visual art, namely paintings. The victim finds moral courage through religion, while the thief lives in denial until death. Anyone with an interest in art, law, or psychiatry will (...) enjoy what Big Eyes has to offer. (shrink)

Last Cab to Darwin is a film about physician-assisted suicide—specifically, a cab driver diagnosed with metastatic cancer and his journey seeking the “machine” that will help him end his life. Along the way, Rex, who has never had a family, creates one, and the result is a reshaping of his values about life, death, and dying.

The product market competition has become a global challenge for business organizations in the challenging and competitive market environment in the influx of the COVID-19 outbreak. The influence of products competition on organizational performance in developed economies has gained scholars’ attention, and numerous studies explored its impacts on business profitability. The existing studies designate mixed findings between the linkage of CSR practices and Chinese business firms’ healthier performance in emerging economies; however, the current global crisis due to the coronavirus (...) has made product market completion fierce, which ultimately affects business firms’ performance. This study focuses on this logical global challenge, investigates the rationale, and examines product-market completion impact on firms’ performance operating in the Chinese markets. The study collected data from the annual reports of Chinese business organizations with A-share listing and registered with the database of China Stock Markets and Accounting Research. The study employed a Generalized Method of Moment technique and investigated the connection between product market competition and Chinese firm performance. The empirical analysis of this study highlights the conclusion that market competition positively and significantly affected business firms’ performance. This study specified that product market competition play a dynamic and indispensable role in achieving healthier firm performance in the Chinese markets. This study provides valuable insights on practical implications and future research directions for the scholars to draw interesting results with new study models. (shrink)

The issue of directed donation of organs from deceased donors for transplantation has recently risen to the fore, given greater significance by the relatively stagnant rate of deceased donor donation in the UK. Although its status and legitimacy is explicitly recognized across the USA, elsewhere a more cautious, if not entirely negative, stance has been taken. In England, Wales and Northern Ireland, the Human Tissue Act 2004, and in Scotland the Human Tissue (Scotland) Act 2006, are both silent in this (...) regard. Although so-called conditional donation, donation to (or perhaps withheld from) a specific class, has been outlawed as a product of guidance issued by the Secretary of State for Health issued in the wake of the controversial incident occurring in the North of England in 1998, its intended application to ‘directed’ donation is less certain. Directed and conditional donations challenge the traditional construct of altruistic donation and impartial (equitable) allocation in a very immediate and striking fashion. They implicitly raise important questions as to whether the body or parts of the body are capable of being owned, and by whom. This paper attempts to explore the notion of donor ownership of body parts and its implications for both directed and conditional donation. (shrink)

The central result of this paper provides a simple equational basis for the join, IRLLG, of the variety LG of lattice-ordered groups (-groups) and the variety IRL of integral residuated lattices. It follows from known facts in universal algebra that IRLLG=IRL×LG. In the process of deriving our result, we will obtain simple axiomatic bases for other products of classes of residuated structures, including the class IRL×s LG, consisting of all semi-direct products of members of IRL by members (...) of LG. We conclude the paper by presenting a general method for constructing such semi-direct products, including wreath products. (shrink)