Abstract. Some elementary methods are described which may be used to calculate tangent numbers, Euler numbers, and Bernoulli numbers much more easily and rapidly on electronic computers than the traditional recurrence relations which have been used for over a century. These methods have been used to prepare an accompanying table which extends the existing tables of these numbers. Some theorems about the periodicity of the tangent numbers, which were suggested by the tables, are also proved.
Abstract. Some elementary methods are described which may be used to calculate tangent numbers, Euler numbers, and Bernoulli numbers much more easily and rapidly on electronic computers than the traditional recurrence relations which have been used for over a century. These methods have been used to prepare an accompanying table which extends the existing tables of these numbers. Some theorems about the periodicity of the tangent numbers, which were suggested by the tables, are also proved.
The purpose of our paper is to apply the state progress checklist from direct outcomes theory to a new domain of the university-to-work transition to mediate a dyadic win-win relationship between university careers advisors and graduate recruiters. The state progress checklist incorporates three endeavour elements - (i) potential, (ii) agendas, and (iii) effects; and nine themes - (i) resources, (ii) motivations, (iii) interactions, (iv) assumptions, (v) scenarios, (vi) plans, (vii) actions, (viii) outcomes, and (ix) reuses. The endeavour elements and themes are systematically applied to help envision, pursue, and achieve mutually beneficial relationships between both parties. The application of direct outcomes theory as a mediator of the relationship between university careers services and graduate recruiters offers synergy effects for both parties and helps overcome pre-existing barriers to collaboration and communication. Our paper applies the state progress checklist from direct outcomes theory to a new domain of the university-to-work transition to bridge research agendas across the education, vocational behaviour, and human resource management literature. We identify opportunities for university careers services and graduate recruiters to foster a win-win relationship by aligning their objectives and through the provision and receiving of support. These benefits subsequently transcend additional stakeholders, including university students, universities, and organisations. Moreover, Appendix 1 provides a summary sheet offering some potential questions for each of the nine themes across the three endeavour elements. These example questions are not meant to be an exhaustive list. Their purpose is to act as a starting point for discussion and action. The university careers advisors and graduate recruiters could initially work through this sheet separately before working through the sheet a second time collaboratively.
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