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We introduce a generalization, called a skew Clifford algebra , of a Clifford algebra, and relate these new algebras to the notion of graded skew Clifford algebra that was defined in 2010. In particular, we examine homogenizations of skew Clifford algebras, and determine which skew Clifford algebras can be homogenized to create Artin-Schelter regular algebras. Just as (classical) Clifford algebras are the Poincaré-Birkhoff-Witt (PBW) deformations of exterior algebras, skew Clifford algebras are the Z 2 -graded PBW deformations of quantum exterior algebras. We also determine the possible dimensions of skew Clifford algebras and provide several examples. [ABSTRACT FROM AUTHOR]

Many competing criteria are under consideration for prioritizing COVID-19 vaccination. Two criteria based on age are demographic: lives saved and years of future life saved. Vaccinating the very old against COVID-19 saves the most lives, but, since older age is accompanied by falling life expectancy, it is widely supposed that these two goals are in conflict. We show this to be mistaken. The age patterns of COVID-19 mortality are such that vaccinating the oldest first saves the most lives and, surprisingly, also maximizes years of remaining life expectancy. We demonstrate this relationship empirically in the United States, Germany, and South Korea and with mathematical analysis of life tables. Our age-risk results, under usual conditions, also apply to health risks. [ABSTRACT FROM AUTHOR]

The notion of a matrix factorization was introduced by Eisenbud in the commutative case in his study of bounded (periodic) free resolutions over complete intersections. Since then, matrix factorizations have appeared in a number of applications. In this work, we extend the notion of (homogeneous) matrix factorizations to regular normal elements of connected graded algebras over a field. Next, we relate the category of twisted matrix factorizations to an element over a ring and certain Zhang twists. We also show that in the setting of a quotient of a ring of finite global dimension by a normal regular element, every sufficiently high syzygy module is the cokernel of some twisted matrix factorization. Furthermore, we show that in the noetherian AS-regular setting, there is an equivalence of categories between the homotopy category of twisted matrix factorizations and the singularity category of the hypersurface, following work of Orlov. [ABSTRACT FROM AUTHOR]

I construct a Koszul algebra A and a finitely generated graded A-module M that together form a counterexample to a recently published claim. M is generated in degree 0 and has a pure resolution, and the graded Jacobson radical of the Yoneda algebra of A does not annihilate the Ext module of M, but nonetheless M is not a Koszul module. [ABSTRACT FROM AUTHOR]

We introduce a new formal model in which demographic behavior such as fertility is postponed by differing amounts depending only on cohort membership. The cohort-based model shows the effects of cohort shifts on period fertility measures and provides an accompanying tempo adjustment to determine the period fertility that would have occurred without postponement. Cohort-based postponement spans multiple periods and produces 'fertility momentum,' with implications for future fertility rates. We illustrate several methods for model estimation and apply the model to fertility in several countries. We also compare the fit of period-based and cohort-based shift models to the recent Dutch fertility surface, showing how cohort- and period-based postponement can occur simultaneously. [ABSTRACT FROM AUTHOR]

A correction is provided for Proposition 3.5 in the above-mentioned article. The correction is: if $S$ is a skew polynomial ring on finitely many generators of degree 1 that are normal elements in $S$, and if $I$ is a homogeneous ideal of $S$ that is generated by a normalizing sequence, then $\dim _{\Bbbk } (S/I)$ is finite if and only if $S/I$ has no point modules and no fat point modules. A similar correction is provided for Corollary 3.6 of the same article. [ABSTRACT FROM PUBLISHER]

Mortality decline has historically been largely a result of reductions in the level of mortality at all ages. A number of leading researchers on ageing, however, suggest that the next revolution of longevity increase will be the result of slowing down the rate of ageing. In this paper, we show mathematically how varying the pace of senescence influences life expectancy. We provide a formula that holds for any baseline hazard function. Our result is analogous to Keyfitz's ‘entropy’ relationship for changing the level of mortality. Interestingly, the influence of the shape of the baseline schedule on the effect of senescence changes is the complement of that found for level changes. We also provide a generalized formulation that mixes level and slope effects. We illustrate the applicability of these models using recent mortality decline in Japan and the problem of period to cohort translation. [ABSTRACT FROM PUBLISHER]

This article introduces the idea of cultural reinvention for cultural textile products. Fundamentally, the term ‘cultural products’ consists of culture and product. Culture means a symbol of a particular time and society. Cultural products can be thought of as artefacts produced by and for a specific cultural group. However, commercial needs and desires may and often do mean that although the form and style of the artefact may remain, it can be produced by other cultural groupings. This article builds an understanding of the term cultural reinvention through the historical and modern consideration of tartan as a case study. It then provides a taxonomy of traditional and cultural Korean textiles and identifies possible strategies for the cultural and commercial reinvention of bojagi textiles. A website has been developed as a design marketing tool to allow consumers to learn about and create their own bojagi designs. This website has been evaluated by five focus groups. [ABSTRACT FROM PUBLISHER]

This article summarises the findings of a study about the angle from which consumers view displays in fashion stores, as they walk past the store windows. Two experiments were carried out, and the results were used to propose a change in the angle at which window displays are arranged, and where the focus or centre piece of a display should be placed. This would enable more consumers to comprehend the contents of the window display with the possible consequence that they will enter the store and make purchases. [ABSTRACT FROM AUTHOR]

Associated to any uniform finite layered graph Γ there is a noncommutative graded quadratic algebra A(Γ) given by a construction due to Gelfand, Retakh, Serconek and Wilson. It is natural to ask when these algebras are Koszul. Unfortunately, a mistake in the literature states that all such algebras are Koszul. That is not the case and the theorem was recently retracted. We analyze the Koszul property of these algebras for two large classes of graphs associated to finite regular CW-complexes, X. Our methods are primarily topological. We solve the Koszul problem by introducing new cohomology groups HX( n, k), generalizing the usual cohomology groups Hn( X). Along with several other results, our methods give a new and primarily topological proof of the main result of [Serconek and Wilson, J. Algebra 278: 473–493, 2004] and [Piontkovski, J. Alg. Comput. 15, 643–648, 2005]. [ABSTRACT FROM AUTHOR]

Abstract: Green and Marcos (2005) call a graded -algebra -Koszul if the corresponding Yoneda algebra is finitely generated and there exists a function such that is zero if . For any integer we exhibit a noncommutative quadratic -Koszul algebra for which the Yoneda algebra is generated in degrees and . These examples answer a question of Green and Marcos. These algebras are not Koszul but -Koszul (in the sense of Backelin). [Copyright &y& Elsevier]

For decades, the study of graded Clifford algebras has provided a theory where commutative algebraic geometry has dictated the algebraic and homological behavior of a noncommutative algebra. In particular, it is well known that a graded Clifford algebra, C, is quadratic and regular if and only if a certain quadric system associated to C is base point free. In this article, we introduce a generalization of a graded Clifford algebra, namely a graded skew Clifford algebra, and to such an algebra we associate a notion of quadric system in the spirit of the noncommutative algebraic geometry of Artin, Tate and Van den Bergh. We prove that a graded skew Clifford algebra is quadratic and regular if and only if its associated quadric system is normalizing and base point free. To prove our results, we extend the notions of complete intersection, base point free, quadratic form and symmetric matrix to the noncommutative setting. We use our results to produce several families of quadratic regular skew Clifford algebras of global dimension four that are not twists of graded Clifford algebras. Many of our examples have a 1-dimensional line scheme and a point scheme that consists of exactly twenty distinct points, and thus are candidates for generic regular algebras of global dimension four. [ABSTRACT FROM PUBLISHER]

Although team leadership and its relationship with creative performance has attracted significant attention recently from academia and practicing managers, its implications on the creativity of industrial design teams have not been explored systematically. To avoid unfounded generalisations, this paper is aimed at identifying the main factors which may influence creative enhancement specifically in the context of industrial design leadership in Taiwan, a research tool suitable for this, and for similar investigations under different cultural conditions, is presented. [Copyright &y& Elsevier]

Abstract: Given a ring R, we introduce the notion of a generalized Laurent polynomial ring over R. This class includes the generalized Weyl algebras. We show that these rings inherit many properties from the ground ring R. This construction is then used to create two new families of quadratic global dimension four Artin–Schelter regular algebras. We show that in most cases the second family has a finite point scheme and a defining automorphism of finite order. Nonetheless, a generic algebra in this family is not finite over its center. [Copyright &y& Elsevier]

We introduce a large class of infinite dimensional associative algebras which generalize down–up algebras. Let K be a field and fix f∈K[x] and r,s,γ∈K. Define L=L(f,r,s,γ) to be the algebra generated by d,u and h with defining relations: Included in this family are Smith''s class of algebras similar to U(sl2), Le Bruyn''s conformal sl2 enveloping algebras and the algebras studied by Rueda. The algebras L have Gelfand–Kirillov dimension 3 and are Noetherian domains if and only if rs≠0. We calculate the global dimension of L and, for rs≠0, classify the simple weight modules for L, including all finite dimensional simple modules. Simple weight modules need not be classical highest weight modules. [Copyright &y& Elsevier]

This paper studies two homogenizations of the down-up algebras introduced in Benkart and Roby (Benkart, G., Roby, T. (1998). Down-up Algebras. J. Algebra 209:305–344). We show that in all cases the homogenizing variable is not a zero-divisor, and that when the parameter β is non-zero, the homogenized down-up algebra is a Noetherian domain and a maximal order, and also Artin-Schelter regular, Auslander regular, and Cohen-Macaulay. We show that all homogenized down-up algebras have global dimension 4 and Gelfand-Kirillov dimension 4, and with one exception all homogenized down-up algebras are prime rings. We also exhibit a basis for homogenized down-up algebras and provide a necessary condition for a Noetherian homogenized down-up algebra to be a Hopf algebra. [ABSTRACT FROM AUTHOR]

This paper completes the classification of central extensions of three dimensional Artin-Schelter regular algebras to four dimensional Artin-Schelter regular algebras. Let A be an AS regular algebra of global dimension three and let D be an extension of A by a central graded element z, i.e., D/ = A. If A is generated by elements of degree one, those algebras D which are again AS regular have been classified in Le Bruyn et al. (Le Bruyn L., Smith, S. P., Van den Bergh, M. (1996). Central extensions of three dimensional Artin-Schelter regular algebras. Math. Zeitschrift 222:171–212.) and Cassidy (Cassidy, T. (1999). Global dimension 4 extensions of Artin-Schelter regular algebras. J. Algebra 220:225–254.). If A is not generated by elements of degree one, then A falls under a classification due to Stephenson (Stephenson, D. R. (1996). Artin-Schelter regular algebras of global dimension three. J. Algebra 183(1):55–73 and Stephenson, D. R. (1997). Algebras associated to elliptic curves. Trans. Amer. Math. Soc. 349(6):2317–2340.). We classify the AS regular central extensions of Stephenson's algebras by proving that the regularity of D and z is equivalent to the regularity of z in low degree and this is equivalent to easily verifiable conditions on the defining relations for D. [ABSTRACT FROM AUTHOR]

Evaluates the novel "Contending Forces," by Pauline Hopkins. Work of activist literature; Racial issues discussed in the novel; Discussion on the nineteenth-century lynching and raping of Afro-Americans; Political aspects of the harassment of black Americans.

Domestic information processing appliances include embedded digital technologies with which users interact. The designs of such appliances tend to be technology oriented and not well-suited to the needs of older adults. This is problematic because these appliances are essential in many activities of daily living and so affect the ability of people to live independently. This paper introduces a coding scheme for the analysis of users' interactions with such appliances and uses it to inform recommendations for the design of operational interfaces and associated instructional materials. The efficacy of the coding scheme as a design evaluation tool is illustrated by its application in a microwave oven case study. The coding scheme considers four aspects of users' interactions with this type of device: information processing activities, including the gathering and interpretation of information from the appliance, its user manual and cooking instructions from food packaging; interactions with the device's user interface; concurrent verbalisation supporting problem-solving; and impediments to the user's workflow. [Display omitted] • Coding scheme for analysing user interactions with consumer appliances. • Method for using the coding scheme as a human-centred design evaluation tool. • Microwave oven design case study. • Recommendations for the design of operational interfaces and instructional materials. [ABSTRACT FROM AUTHOR]

Objectives: The aim of this study is to establish useful design strategies for health Information designers when planning and designing healthcare media for new immigrants. Methods: The study is implemented in six stages, namely, a focus group interview, the development of testing media, reliability and validity tests, a questionnaire survey, pre-post knowledge tests, and a usability survey. Results: The results suggest that the key challenges for immigrant mothers when caring for their children's health relate to six factors, namely language, confidence, knowledge, culture, how to take care, and the use of healthcare media. The findings indicate that both leaflet intervention and website intervention are effective and there is no significant difference between them; furthermore, the criteria new immigrants use to evaluate healthcare media can be analysed in terms of the quality of the content, appearance, and process. Conclusions: The study concludes that efforts to assist new immigrants to take care of their children's health by applying healthcare media are still at an early stage of development. Further study is needed to identify which of the characteristics of immigrant users impact their ability to learn about health information in order to incorporate these into an effective health intervention medium that optimises information systems. [ABSTRACT FROM AUTHOR]

Drug-food interactions are a significant problem in clinical practice. Foods may alter the effects of drugs by interfering with pharmacokinetic processes, such as absorption and elimination. For example, absorption of tetracyclines is decreased when taken with milk or other dairy products. Pharmacologic and pharmacodynamic mechanisms also play an important role in drug-food interactions by altering drug effects. An example is the interaction of warfarin sodium with leafy green vegetables, whereby the hypoprothrombinemic effect of warfarin may be decreased and thromboembolic complications may develop. Similarly, certain drugs may have an effect on food intake, absorption, metabolism, and utilization. Numerous drugs, such as antineoplastic agents, have been shown to suppress appetite, resulting in decreased food intake and nutritional deficiency. It is important that health care providers, such as physicians, pharmacists, and dietitians, recognize and work as a team to prevent significant drug-food interactions. Minimizing adverse drug-food interactions would improve patient care by optimizing therapeutic effects and maintaining proper nutritional status. [ABSTRACT FROM AUTHOR]