There is a quite natural way in which the safe/normal variable discipline of Bellantoni-Cook recursion (1992) can be imposed on arithmetical theories like PA: quantify over safes and induct on normals. This weakens the theory severely, so that the provably recursive functions become more realistically computable (slow growing rather than fast growing). Earlier results of Leivant (1995) are re-w...

This small book has been written to meet the requirements of matriculation students in the Punjab and other parts of India, where the subject of elementary hygiene is studied along with a course of physiology. From a perusal of the book, we can say that the authors have carried out their object well. Facts are clearly stated and in the recommendations and advice given, full cognisance of Indian...

Factors Affecting Public-Private Sector's Support for the Elementary Schools M.H. Hassani Shalmaani, Ph.D. Factors affecting the public-private sector's support for elementary education were identified perusing related legislations, documents, and programs. To validate these factors a sample of 432 elementary school principals was given the list of factors of which 8 were confirme...

background: students’ health and future health of the community are related to providing health care in schools and since in every society, different contextual factors affect this matter, the present study aims to recognize the factors influencing the health care elementary students are provided with. methods: this qualitative content analysis was performed in 2014 in isfahan. this study was c...

We give a proof of Connes’ trace formula for a function field for a function of support in the norm-one ideles. The proof only uses elementary properties of the adeles.

Any nonempty, compact, semi-algebraic set in [0, 1]n is the projection of the set of mixed equilibria of a finite game with 2 actions per player on its first n coordinates. A similar result follows for sets of equilibrium payoffs. The proofs are constructive and elementary.

An elementary approach to the construction of Coxeter group representations is presented.

In this paper we discuss general tridiagonal matrix models which are natural extensions of the ones given in [3] and [4]. We prove here the convergence of the distribution of the eigenvalues and compute the limiting distributions in some particular cases. We also discuss the limit of fluctuations, which, in a general context, turn out to be Gaussian. For the case of several random matrices, we ...

This paper answers some questions of D. Ross in [R]. In x1, we show that some consequences of the @0 or @1{special model axiom in [R] can not be proved by the {isomorphism property for any cardinal . In x2, we show that with one exception, the @0{isomorphism property does imply the remaining consequences of the special model axiom in [R]. In x3, we improve a result in [R] by showing that the {s...

Graph searching encompasses a wide variety of combinatorial problems related to the problem of capturing a fugitive residing in a graph using the minimum number of searchers. In this annotated bibliography, we give an elementary classification of problems and results related to graph searching and provide a source of bibliographical references on this field.