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1.
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…  相似文献   

2.
As a Rule, when discussing Jewish existence, we use the term survival. Actually, continuity is more accurate. Certainly it is more dynamic. Continuity indicates the state or quality of being continuous. It denotes the fact that Jewish life is an uninterrupted succession of Jewish people and events. Continuity is an absolute condition. Survival, however, indicates an act of surviving or merely lasting longer than others. Survival is something that continues to exist after the cessation of something else. As such, survival is a relative phenomenon. Moreover, continuity implies creative growth; survival connotes bare existence, even decline.  相似文献   

3.
On generalized extending modules   总被引：1，自引：0，他引：1  
A module M is called generalized extending if for any submodule N of M, there is a direct summand K of M such that N≤K and K/N is singular. Any extending module and any singular module are generalized extending. Any homomorphic image of a generalized extending module is generalized extending. Any direct sum of a singular (uniform) module and a semi-simple module is generalized extending. A ring R is a right Co-H-ring if and only if all right R modules are generalized extending modules.  相似文献   

4.
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…  相似文献   

5.
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.  相似文献   

6.
In this paper, it is proved that the radial pth mean body RpK（p 〉 0） is homothetic to the difference body DK when K is a simplex, Furthermore, the equality Rp（Rq） = Rq（Rp） is established when p 〉 0 and q 〉 0. It is also proved the Brunn-Minkowski inequality of radial pth mean body of simplex and uniqueness property.  相似文献   

7.
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.  相似文献   

8.
几乎正则图的全符号控制   总被引：1，自引：2，他引：1  
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…  相似文献   

9.
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.  相似文献   

10.
Consider the mixed-effect coefficient semiparametric regression modelZ=X'α+Y'β+g(T)+e, whereX, Y andT are random vectors onR p×R q×[0, 1], α is a p-dimensional fixed-effect parameter, β is a q-dimensional random-effect parameter (Eβ=b, Cov(β)=Σ),g(.) is an unknown function on [0, 1], e is a random error with mean zero and variance σ2, and (X, Y, T) and (β,e), β ande are mutually independent. We estimate α,b andg(.) by the nearest neighbor and the least square method. In this paper, we prove that estimations of α,b have asymptotic normality and obtain the best convergence raten −1/3 for the estimation ofg(.). Project supported by the NSFC and the Natural Science Foundation of Zhejiang Province.  相似文献   

11.
In this work, we study the Asanov Finsler metric F=α(β2/α2 gβ/α 1)1/2exp{(G/2)arctan[β/(hα) G/2]}, where α=(αijyiyj)1/2 is a Riemannian metric and β=biyj is a 1-form, g∈(-2,2), h=(1-g2/4)1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.  相似文献   

12.
INTRODUCTION In recent years, significant progress has been made in the study of Finsler metris which have straight lines in local coordinates (Hamel, 1903). Finsler metrics with this property are called locally projectively flat metrics. An important fact about these metrics is that locally projectively flat Finsler metrics have scalar flag curvature, a natural extension of the sectional curvature in Riemannian geometry. In general, it also depends on the direction (flag pole) in the se…  相似文献   

13.
Congruences for finite triple harmonic sums   总被引：1，自引：0，他引：1  
Zhao (2003a) first established a congruence for any odd prime p>3, S(1,1,1;p)≡-2Bp-3 (mod p), which holds when p=3 evidently. In this paper, we consider finite triple harmonic sum S(α,β,γ;p) (mod p) is considered for all positive integers α,β,γ. We refer to w=α β γ as the weight of the sum, and show that if w is even, S(α,β,γ;p)≡0 (mod p) for p≥w 3; if w is odd, S(α,β,γ;p)≡rBp≥w (mod p) for p≥w, here r is an explicit rational number independent of p. A congruence of Catalan number is obtained as a special case.  相似文献   

14.
Art's relationship with education is often characterised by paradox. Yet art is often reified within an education system that refuses to see the pedagogical strengths of paradox. This article approaches art education from three positions. The first is that art is a construct that is neither natural nor necessary. The second is that there are no aesthetic or pedagogical imperatives, but that art education is the recognition of groundlessness where paradox facilitates learning. The third approach is to reposition art with regards to its relationship with learning, education and schooling. Here it is argued that art's only choice is to deschool learning. The latter is moved by an underlying dilemma as to whether art, considered as an autonomous human act, could ever engage with systems of learning without being turned into a tool or a thing. Unless art education is deschooled, the teaching and learning of art remains trapped between the assumptions of process and product. So the idea of art and education as shared practices within schooling remains somewhat dubious unless art's practices are recognised in parts perceived as wholes and where conclusions are marked by open‐endedness. No possibilities for art or learning could ever emerge unless a radically different set of conditions give way to a state of affairs where knowledge is a matter to be discovered but never determined, and where a fixed ground is transformed into a wide horizon.  相似文献   

15.
Functions like loge x, e x , e z and loge z are defined and studied systematically. It is observed thate z is the only complex analytic extension of the real analytic functione x . It is also observed that the power (analyticity) of ez is by choice and the beauty (its derivative is itself) of ez is unexpected.  相似文献   

16.
The seed method is used for solving multiple linear systems A^(i) x^(i) = b^(i) for l≤ i≤ s , where the coefficient matrix A^(i) and the right-hand side b^(i) are different in general. It is known that the CG method is an effective method for symmetric coefficient matrices A^(i) . In this paper, the FOM method is employed to solve multiple linear systems when coefficient matrices are non-symmetric matrices. One of the systems is selected as the seed system which generates a Krylov subspace, then the residuals of other systems are projected onto the generated Krylov subspace to get the approximate solutions for the unsolved ones. The whole process is repeated until all the systems are solved.  相似文献   

17.
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;…  相似文献   

18.
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 …  相似文献   

19.
Abstract

There is a legal requirement that schools engage with the spiritual aspects of education, which encompasses pastoral care. This reflects the ethical sensibility that is present in individuals and underlies interactions with Others; and which should be part of the ethos of all educational institutions and especially schools. This is because spirituality is important to leading a moral life and to understanding the Other. The article considers specifically the potential of Jewish spirituality, and uses Martin Buber’s thought, to gain a better understanding of its contribution to education and to pastoral care. In the first part, we comment on the ‘basic words’, I-Thou and I-It, which are connected with Hasidism, the Jewish spiritual movement which had a great influence on Martin Buber. Hasidism understands that it is our duty to find and connect with the ‘divine sparks’, as genuine relations merge with the Divine, and when humans relate genuinely to one another, they relate to God. This is crucial for understanding the superiority of I-Thou relations over I-It relations. In the second and third parts of the article, we consider the implications of this understanding of Jewish spirituality for education and for pastoral care. This is done through highlighting the importance of I-Thou relations if the spiritual aspects of education and of pastoral care are to be encouraged and fulfilled.  相似文献   

20.
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.  相似文献   

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