The Rees product of posets

We determine how the flag f-vector of any graded poset changes under the Rees product with the chain, and more generally, any t-ary tree. As a corollary, the M\"obius function of the Rees product of any graded poset with the chain, and more generally, the t-ary tree, is exactly the same as the Rees product of its dual with the chain, respectively, t-ary chain. We then study enumerative and homological properties of the Rees product of the cubical lattice with the chain. We give a bijective proof that the M\"obius function of this poset can be expressed as n times a signed derangement number. From this we derive a new bijective proof of Jonsson's result that the M\"obius function of the Rees product of the Boolean algebra with the chain is given by a derangement number. Using poset homology techniques we find an explicit basis for the reduced homology and determine a representation for the reduced homology of the order complex of the Rees product of the cubical lattice with the chain over the symmetric group.Comment: 21 pages, 1 figur

Impact of Personality Type on Marital Satisfaction

Not available

Racial Identification Versus Professional Identification: Can They Be Reconciled

For close to a decade, members of the social work profession, who also were members of a minority race, have been confronting the profession with their perception that social work has not addressed adequately the needs of their racial groups. The fact that members of one group (a minority race) confronted another group (the social work profession) in which they also held membership signaled the strong and serious conflict between a person\u27s identification with two major groups. Whether the two group identifications could find a common ground, became a concern for not only the individual belonging to the two groups, but also for the profession. Members of minority races, specifically the Black race, brought the conflict to the attention of the profession by\u27firstly presenting \u27demands\u27 to national conferences and then organizing formally into all Black professional organizations. The profession has moved quickly to attest to its openness with respect to the minority races. Professional members, who were also members of racial minorities, were seated on many deliberating bodies of the social work profession. Agencies and schools began recruitment of social workers, students, and teachers from minority races. Social work journals began to find room for articles on issues and problems related to the minority races. This flurry of \u27reactivity\u27, however, obscured the need for systematic analysis of how the potential conflict between the two major group identifications suddenly became a reality and what the conflict meant to the professional and to the profession. The purpose of this article is to cast some light on the emergence of the overt struggle between the two identifications and how the conflict has been mitigated by social workers of minority races. Specifically, the subject will be pursued by scrutinizing the concern as it has related to Black social workers

Differential Utilization of the Health Care Delivery System by Members of Ethnic Minorities

Research and statistical reports of the 1960\u27s strongly attested to the underutilization of the health care delivery system by members of ethnic minorities. For example, a 1968 national report on hospital utilization showed that a larger proportion of white persons was hospitalized than were persons of \u27color.\u27I This was found to be true regardless of sex and age; but ... as family income increased, the rate for white persons and those of other races became closer. This fact not withstanding, each income level saw whites using hospitalization more than persons of \u27color.\u27 Reasons for this difference in utilization were offered by the authors of the above report: It is ...not just the orientation of physicians nor the age and sex of a person that dictates whether he will be hospitalized. Of prime consideration is one\u27s realization or knowledge of his own condition and his attitudes toward disease, illness, and the medical profession. Although cultural factors were not offered as reasons for the difference in utilization, Suchman in his 1964 report on the Sociomedical Variations Among Ethnic Groups,4 interpreted his findings of underutilization to be the result of cultural factors that influenced attitudes toward illness and the medical profession. Although statistical reports and research of the 1960\u27s indicated a lesser utilization of the health care system by members of ethnic minorities when compared to members of the compact majority, there was mention in the aforementioned 1968 statistical report of the increase in ethnic minorities utilization of hospitalization over that reported in 1965. This fact of an increase in utilization over a three year span suggested to this writer the possibility that there no longer would be found a significant difference in utilization over a 6 year span. This possibility became the impetus for a library search through research published in the 1970\u27s on ethnic minorities\u27 utilization of the health care delivery system. The initial questions guiding the search were What is the pattern of utilization of the health care delivery system by members of ethnic minorities? Which variables seem to be associated with levels of utilization? The purpose of this paper is to explore answers to the above and related questions as they are found in research of the 1970\u27s

Some Properties Of Polynomials With Matrix Coefficients

In this paper, some properties of polynomials with matrix coefficients will be studied. Matrix theory will be used extensively in developing these properties. There are five chapters in this thesis. The first is devoted to defining and notating terms and/or symbols used; the second to basic arithmetic of polynomials with matrix coefficients the third to a polynomial spectrum; the fourth to a main theorem and the fifth to applications

Can Anyone Be Trusted to Enforce National Treatment Disciplines With Respect to Tax Measures?

Because the traditional non-discrimination article of tax treaties seemingly provides protection against only the most blatant discrimination against non-residents and non-nationals of a taxing State, governments may be emboldened to adopt “anti-abuse” rules that are in reality disguised trade barriers. On the other hand, trade disciplines in non-tax agreements may include protections against discriminatory taxes that non-specialist courts interpret in expansive ways, contrary to the wishes of tax authorities. An OECD project in the mid-2000s was an opportunity for governments to re-think the piecemeal nature of the traditional non-discrimination article in tax treaties and develop a coherent national treatment system that takes into account legitimate tax policy concerns. Instead, the project resulted in a mishmash of changes that largely blessed the various discriminatory practices that governments had adopted to that date. If tax authorities want to continue to play a leading role in developing international tax policy, they should consider whether a tax treaty approach that borrows concepts from non-tax agreements would better balance the interests of governments and taxpayers than the current version of Article 24 (and the Commentaries thereon)

A Serendipitous Relationship Between Theory Modification and a Study of Staff Development

There are instances in which the guiding impetus to a study is a very practical problem, the answers to which are expected to have immediate applicability. Although the practical purpose is accomplished, at the study\u27s end comes the recognition that perhaps the most important contribution of the investigation had been the uncovering of theoretical implications. The above serendipitous process is applicable to the following report of a limited study of staff development in a new youth serving agency. The study is presented in detail so that the main elements associated with the validation and elaboration of a conceptualization of organizational behavior can be trace

Developing the evidence and associated service models to support older adults living with frailty to manage their pain and to reduce its impact on their lives: protocol for a mixed-method, co-design study (The POPPY Study)

Introduction The Pain in Older People with Frailty Study is a mixed-method, co-design study, which aims to develop the content, implementation strategies, service and professional guidance to support older adults with frailty to manage their pain. Methods and analysis The study has four phases: Phase 1, research evidence and information synthesis from randomised controlled trials of multicomponent pain management programmes and psychological therapies for community-dwelling older adults. Phase 2, qualitative interviews with 30 community-dwelling older adults (≥75 years) living with frailty and persistent pain, including dyadic interviews with a spouse or unpaid carer. Phase 3, qualitative interviews with healthcare professionals (HCPs) working within various pain service types; 5–8 HCPs per service and up to 12 services including primary care, secondary care, tertiary centres and services with voluntary sector input. Phase 4, co-design workshops with older adults, HCPs and commissioners. Inclusion criteria (Phase 2): community-dwelling older adults (≥75 years) living with frailty and persistent pain. Exclusion criteria (Phase 2): care home residents, a dementia or cancer diagnosis. Cancer survivors, ≥5 years cancer free, and not undergoing active cancer treatment can participate. Analysis for Phase 1 will use narrative synthesis, Phase 2 will use grounded theory analysis and Phase 3 will use thematic analysis. Oversight is provided from a patient and public involvement group and an independent steering committee. Ethics and dissemination The protocol was approved by Leeds-East Research Ethics Committee on 28 April 2022 (22/YH/0080). Consent is sought if an individual is willing to participate (Phases 2–4) and has capacity. Findings will be disseminated at conferences, in newsletters and journals and to local authorities and charities

Teaching Anxieties Revealed: Pre-Service Elementary Teachers’ Reflections on their Mathematics Teaching Experiences

Over the last 50 years, there has been ample research dedicated to mathematics anxiety in contexts of teaching and learning. However, there has been less attention focused on pre-service teachers\u27 anxieties about teaching mathematics in classroom settings. This study analyzed pre-service teachers\u27 reflections at the conclusion of an elementary mathematics field experience in order to determine common themes surrounding anxiety-related events based on mathematics practice-teaching experiences. Through qualitative analysis of pre-service teachers\u27 reflections using open and axial coding, three categories and ten themes surrounding elementary pre-service teachers\u27 anxiety-related events based on mathematics practice-teaching experiences emerged. Some of the themes presented were ones that increased pre-service teachers\u27 anxieties for teaching mathematics, whereas other themes reflected aspects of the field experience that decreased anxiety for teaching mathematics. Based on the themes revealed in this study, suggestions for strategies and materials that could be developed for university mathematics methods courses are discussed. Novel perspectives for considering mathematics teaching anxiety, such as locus of control and future time perspective, are shared. (Contains 1 table and 1 figure.