Projectively flat exponential Finsler metric

INTRODUCTION One century ago, Hilbert announced his famous 23 problems. The Hilbert’s Fourth Problem is to characterize the (not-necessarily-reversible) distance functions on an open subset in ún such that straight lines are shortest paths. Distance functions induced by a Finsler metric are regarded as smooth ones. Thus Hilbert’s Fourth Problem in the smooth case is to characterize Finsler metric on an open subset in ún whose geodesics are straight lines. Finsler metric on an ope…     

Global dimension of weak smash product

INTRODUCTION In (Auslander, 1995), the author established the relationship of homological dimension between skew group algebra ΛG and Λ. Recall from Corollary 4.7 and Corollary 4.10 in (Auslander, 1995) that gl.dim(ΛG)=gl.dim(Λ) where ΛG is a skew group algebra with the order of G invertible in Λ. Recently, more and more mathematicians have studied homological dimension for Hopf algebra. Yang (2002) gave the relationship of homological dimension between smash product algebra A#H…     

Phenomenology and curriculum implementation: discerning a living curriculum through the analysis of Ted Aoki’s situational praxis

The argumentation in this paper is grounded in a critical and conceptual analysis of Ted Aoki’s phenomenology, wherein curriculum is read as phenomenological text. The problem explored emerges from Aoki’s critique of the Tyler rationale for curriculum design, implementation and evaluation as it is conceived and practised in contemporary standardized education, which is driven by the ideology of social efficiency. Aoki focuses on the way in which the scientific and technical modes of curriculum implementation preclude particular modes of Being-in-the-world because curriculum implementation, as a technical and instrumental process, reduces both educators and students to epistemological subjects, and beyond, objects of knowledge. By focusing on curriculum implementation as a form of ‘situational-praxis’ as opposed to ‘instrumental-action’, this paper concludes, it is possible to put educators and students in touch with the ontological aspects of their Being-in-the-world. Aoki’s practice of phenomenology reveals an understanding of an attuned mode of human transcendence in learning, which opens the possibility for an authentic educational experience where educators and students dwell in the midst of the curriculum’s unfolding as an ontological phenomenon.     

On closed weak supplemented modules

INTRODUCTION In recent years theory of extending modules and rings has come to play an important role in the theory of rings and modules. A module is called an extending module (or CS-module) if every submodule is essen- tial in a direct summand, or equivalently, every closed submodule is a direct summand. Although this gen- eralization of injectivity is extremely useful, it does not satisfy some important properties. For example, direct sums of extending modules need not be ex- tending;…     

Semi On-line Scheduling Problem for Maximizing the Minimum Machine Completion Time on m Identical Machines

In this paper, a semi on-line version on m identical machines M1 , M2, …, Mm ( m ≥ 3 ) was considered, where the processing time of the largest job is known in advance. Our goal is to maximize the minimum machine load, an NPLS algorithm was presented and its worst-case ratio was proved to be equal to m - 1 which is the best possible value. It is concluded that if the total processing time of jobs is also known to be greater than (2 m - 1 )Pmax where pmax is the largest job‘s processing time, then the worstcase ratio is 2 - 1/m.     

有向线图中的(k,l)-核

1 Introduction We consider the finite digraphs that do not havemultiple arcs or loops , but pairs of opposite arcs areallowed.LetD=(V,A) be a digraph , whereVisthe set of vertices andAis the set of arcs .If there isan arc (x,y) fromxtoy,thenthe vertexxis …     

Metaphorical images of schooling: beliefs about teaching and learning among prospective teachers from the United States displaying different motivational profiles

This study focused on investigating the types of schooling beliefs (teaching and learning) expressed through metaphorical images by prospective teachers (PTs) from the United States. Participants (N = 215) rated 10 schooling metaphors illustrating the student–school–teacher relationships (i.e. Passenger–Bus–Driver; Student is a passenger, School is a bus and Teacher is a driver). Two main factors, a student-centred and a teacher-centred approach described the key schooling beliefs of PTs. Additionally, differences in PTs’ schooling beliefs across typologies/clusters of PTs were found. Further, qualitative data from interviews illustrated how each cluster specifically expressed their instructional views.     

The teacher efficacy for inclusive practices (TEIP) scale: dimensionality and factor structure

The Teacher Efficacy for Inclusive Practices (TEIP) scale is designed to measure teacher‐self efficacy to teach in inclusive classrooms. The original study identified three scale factors: efficacy in using inclusive instruction (EII), efficacy in collaboration (EC), and efficacy in managing behavior (EMB) (Sharma et al., 2012). The purpose of our study was to examine the TEIP scale for dimensionality and to cross‐validate its factor structure for pre‐service teachers in the context of early childhood education. A bifactor model fit to the data revealed that the TEIP scale is essentially unidimensional, that is, there is one dominant latent factor and the originally found three scale factors (EII, EC, and EMB) represent specific aspects of the general factor of teacher self‐efficacy to teach in inclusive classrooms. Along with providing validation evidence, these findings have important implications for the scoring on the TEIP scale using classical test analysis or unidimensional item response theory models.     

Othermotherwork: testimonio and the refusal of historical trauma

Abstract

This paper is an ofrenda (offering), a testimonio (testimony) of the healing power of reconstituting severed relationships and reconstructing agentic creation stories in the pathology of soul-wounds where pictures and cuentos serve to mend genealogical traumas. This paper is a refusal of neglecting traumas, it is othermotherwork as an invitation of kin towards the healing soul-wounds by engaging my ageing father (apá), who has been battling a debilitating disease for over 30 years. In choosing to erase his memory and refusing well-being, I engage my apá by remembering and restoring cuentos (stories) retrieved from pictures in my abuela’s archival orange box. I retell the cuentos as told by my apá of his mother, father, great-grandmother and great-grandfather, while he offers an unexpected remedy for both our soul-wounds. In this exchange of ancestral herstories, it is an important move towards an Indigenous Else, transits beyond borders and separation, towards the restorative act of forging unity, love and compassion amongst my father, my ancestors and myself.     

The role of spatial ability in mixed reality learning with the HoloLens

The use of mixed reality in science education has been increasing and as such it has become more important to understand how information is learned in these virtual environments. Spatial ability is important in many learning contexts, but especially in neuroanatomy education where learning the locations and spatial relationships between brain regions is paramount. It is currently unclear what role spatial ability plays in mixed reality learning environments, and whether it is different compared to traditional physical environments. To test this, a learning experiment was conducted where students learned neuroanatomy using both mixed reality and a physical plastic model of a brain (N = 27). Spatial ability was assessed and analyzed to determine its effect on performance across the two learning modalities. The results showed that spatial ability facilitated learning in mixed reality (β = 0.21, P = 0.003), but not when using a plastic model (β = 0.08, P = 0.318). A non-significant difference was observed between the modalities in terms of knowledge test performance (d = 0.39, P = 0.052); however, mixed reality was more engaging (d = 0.59, P = 0.005) and learners were more confident in the information they learned compared to using a physical model (d = 0.56, P = 0.007). Overall, these findings suggest that spatial ability is more relevant in virtual learning environments, where the ability to manipulate and interact with an object is diminished or abstracted through a virtual user interface.     

Deterministic and randomized scheduling problems under the 1p norm on two identical machines

Parallel machine scheduling problems, which are important discrete optimization problems, may occur in many applications. For example, load balancing in network communication channel assignment, parallel processing in large-size computing, task arrangement in flexible manufacturing systems, etc., are multiprocessor scheduling problem. In the traditional parallel machine scheduling problems, it is assumed that the problems are considered in offline or online environment. But in practice, problems are often not really offline or online but somehow in-between. This means that, with respect to the online problem, some further information about the tasks is available, which allows the improvement of the performance of the best possible algorithms. Problems of this class are called semi-online ones. In this paper, the semi-online problemP2|decr|l _p (p>1) is considered where jobs come in non-increasing order of their processing times and the objective is to minimize the sum of thel _p norm of every machine's load. It is shown thatLS algorithm is optimal for anyl _p norm, which extends the results known in the literature. Furthermore, randomized lower bounds for the problemsP2|online|l _p andP2|decr|l _p are presented. Project supported by the National Natural Science Foundation of China (Nos. 10271110, 10301028) and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, China     

Aesthetic Learning About,In, With and Through the Arts: A Curriculum Study

Aesthetic learning is a major issue in arts education. The ‘method of art’ is often expected to facilitate in‐depth learning not only in the arts but across the curriculum. This article defines aesthetic learning in terms of a conceptual framework based on two dimensions, one representing the goal and the other the means of aesthetic learning. The goal is described as convergent or divergent. Convergent learning is goal‐directed, focused and rational, while divergent learning is explorative, open‐ended and intuitive. The means are described as medium‐specific or medium‐neutral. Medium‐specific learning emphasises the forms of representation, for example words, pictures, algebra, dance. Medium‐neutral learning emphasises instrumental aspects of learning, such as academic achievement or personal development. Combining these dimensions two‐by‐two, the author arrives at a suggested definition of what is meant by learning about, learning in, learning with and learning through the arts. The rest of the article investigates the potential utility of this framework in various contexts and for different purposes. First, the author presents two temporary ‘Culture‐in‐School’ projects. Secondly, the framework is used to study aesthetic learning processes in sloyd (art & craft), based on student teachers’ portfolios in metalwork. Thirdly, the four modes of learning are compared to equivalent modes of teaching: the instructor, the facilitator, the advisor and the educator. Fourthly, there is a discussion on the role of aesthetics in a ‘balanced’ curriculum. Finally, there is an argument on the need for a variety of assessment tools based on the four modes of learning and teaching, such as copying, portfolios, projects and the repertory grid technique.     

Exploring Knowing/Being Through Discordant Professional Practice

Despite an increasing array of ‘quality indicators’ and substantial investments in educating professionals, there continues to be clear evidence of discordant, or even negligent, practice by accredited professionals. We refer to discordant professional practice as being ‘out of tune’ with what is accepted as good practice. In a conceptual/theoretical analysis, we use discordant practice as a backdrop to exploring ways of being professionals. Our analysis is grounded in Heidegger’s notion of being-in-the-world. We explore how being-in-the-world can be uncanny and discordant, while at the same time, dwelling in the world implies familiarity and a sense of being ‘at home’. We also draw upon Merleau-Ponty’s arguments that know-how is performed, settling in the body to become habitual, while also incorporating others and things in the accomplishment of practice. We argue that conceiving know-how as knowing/being provides insights into what is entailed in learning to be professionals.     

Unit ball in high dimensions

In this article, we compute the volume V _n of the unit ball in an n-dimensional space. For n = 1, 2, 3, the volumes are respectively 2, π 4π /3, which are the length of interval [−1,1], area of a unit circle and volume of the unit sphere. The numbers V _n ‘appear’ to increase. But in fact this not so. In fact V _n tends to zero as n tends to infinity! K B Athreya is a Visiting Professor at IMI, Mathematics Department, IISc, Bangalore. He is a professor in the Mathematics Department of the Iowa State University, USA. His research interests include mathematical analysis, probability theory and its applications and statistics. His spare time is spent listening to Indian classical music.     

The Fiscal Impacts of College Attainment

This study quantifies one part of the return to U.S. public investment in college education, namely, the fiscal benefits associated with greater college attainment. College graduates pay much more taxes than those not going to college. Government expenditures are also much less for college graduates than for those without a college education. Indeed, over an average lifetime, total government spending per college degree is negative. That is, direct savings in post-college government expenditures (conservatively, about 85,000 per four-year-equivalent degree over an average lifetime) are greater than government expenditures on higher education (generously, about85,000 per four-year-equivalent degree over an average lifetime) are greater than government expenditures on higher education (generously, about 74,500 per degree). Plus, the direct extra tax revenues from college graduates alone (roughly $471,000 per degree over a lifetime) are more than six times the gross government cost per college degree. The average real fiscal internal rate of return on government investment in college students is conservatively estimated to be 10.3%.     

Deaf children's use of cognitive strategies in simple arithmetic problems

Research shows that deaf children have inferior achievement in simple arithmetic compared to their hearing agemates. The reported study investigates whether the reasons for deaf children's poor achievement can be sought in their strategy development. As this is a central issue, the strategies used by deaf children when solving symbolic addition and subtraction problems are identified, classified and compared to findings from earlier research, involving both deaf and hearing children. The effect of Sign Language in strategy invention and use is the main concern in this study. One result from the present study is that structural aspects of Sign Language counting may influence deaf children's thinking in a way that does not lead to a developed conceptual knowledge base, but instead to refined procedural competence. This is a development in simple arithmetic that is compatible with that of less able hearing children. The counting procedures used by the deaf children involve both oral counting and Sign Language counting. Due to the small sample size, and the shortcomings of the research design, the results are more suggestive than conclusive. Thus, further studies are needed in this area.This revised version was published online in September 2005 with corrections to the Cover Date.     

Species-specific SCAR markers for authentication of Sinocalycanthus chinensis

Sinocalycanthus chmensis, an endangered species endemic to China, is cultivated as an omamental landscape tree in China. However, S. chinensis, Chimonanthus species and Calycanthusfloridus are difficult to be distinguished in seedling market because of their similar morphological characters. In this study, ISSR （inter-simple sequence repeats） were applied to detect S. chinensis from its closely related species. A unique 748-bp band was found in all accessions of S. chinensis. SCAR （sequence characterized amplified regions） markers were created by cloning and sequencing the specific band, and designing a pair of primers to amplify the band of 748 bp. Diagnostic PCRs were performed using the primer pair with the total DNAs ofS. chinensis, Chimonanthus species and C. floridus as templates, with only S. chinensis being able to be amplified. This amplification is not only rapid （results can be obtained in less than 3 h）, but is also easy to perform. Hence it is a feasible method for identifying S. chmensis in seedling market.     

几乎正则图的全符号控制

1IntroductionFor notation and graph theory terminology we ingeneral follow[1].LetG=(V,E)be a graph with thevertex setVand the edge setE,andletvbe a vertexinV.The open neighborhood ofvisN(v)={u∈V|uv∈E}and the closed neighborhood ofvisN[v]={v}∪N(v).The d…