Natural numbers

Mathematical modeling is one of the competencies that have been focused in the curriculum of many countries in the world such as Australia, Germany, Singapore and USA. In Vietnam, the Mathematics curriculum promulgated in 12/2018 clarified that modeling competency would be one of the domainspecific competencies that contribute to the formation and development of the mathematical competency in particular, and numeracy in general.
9p nguathienthan6 06072020 3 0 Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Stapled Sequences and Stapling Coverings of Natural Numbers...
20p thulanh3 10092011 44 3 Download

Lecture 1  Addition and subtraction of natural numbers. In this lecture student teachers will be able to: Increase their mathematical content knowledge for numbers and operations, algebra and algebraic thinking, geometry and geometric measurement, and Information handling for teaching in elementary grades; increase their confidence, competence, interest, and enthusiasm for mathematics by exploring and doing mathematics; deepen an understanding of how children learn mathematics;…
44p larachdumlanat122 26112020 5 0 Download

The rapidly increasing global population has dramatically increased the demands for natural resources and has caused signiﬁcant changes in quantity and quality of natural resources.To achieve sustainable resource management, it is essential to obtain insight ful guidance from emerging disciplines such as landscape ecology.This text addresses the links between landscape ecology and natural resource management.These links are discussed in the context of various landscape types,a diverse set of resources,and a wide range ofmanagement issues.
518p huetay_1 28022013 80 26 Download

Let b ≥ 2 be an integer. We prove that the bary expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms. In particular, irrational automatic numbers are transcendental. Our main tool is a new, combinatorial transcendence criterion. 1. Introduction Let b ≥ 2 be an integer. The bary expansion of every rational number is eventually periodic, but what can be said about the bary expansion of an irrational algebraic number? ...
20p noel_noel 17012013 33 6 Download

The kissing number problem asks for the maximal number k(n) of equal size nonoverlapping spheres in ndimensional space that can touch another sphere of the same size. This problem in dimension three was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. In three dimensions the problem was ﬁnally solved only in 1953 by Sch¨tte and van der u Waerden. In this paper we present a solution of a longstanding problem about the kissing number in four dimensions. Namely, the equality k(4) = 24 is proved. The proof is based on a modiﬁcation of...
33p dontetvui 17012013 35 6 Download

Asperger Syndrome (AS) has, as Dr. Suzanne Lawton so correctly reminds the reader, baffled Dr. Hans Asperger and baffles parents, children, physicians, and other health care practitioners, researchers, and others to this day. We cannot seem to agree on the cause or even, universally, on the diagnosis, much less the treatment. Auditoriums full of angry, impassioned, sometimes desperate, parents have gathered to berate the apparent lack of concern on the part of governmental institutions regarding mercuryladen vaccine preservatives.
201p cronus75 18012013 35 6 Download

We give a new construction of the moonshine module vertex operator algebra V , which was originally constructed in [FLM2]. We construct it as a framed VOA over the real number ﬁeld R. We also oﬀer ways to transform a structure of framed VOA into another framed VOA. As applications, we study the ﬁve framed VOA structures on VE8 and construct many framed VOAs including V from a small VOA. One of the advantages of our construction is that we are able to construct V as a framed VOA with a positive deﬁnite invariant bilinear form and we...
63p tuanloccuoi 04012013 38 5 Download

We show that a tensor product of irreducible, ﬁnite dimensional representations of a simple Lie algebra over a ﬁeld of characteristic zero determines the individual constituents uniquely. This is analogous to the uniqueness of prime factorisation of natural numbers. 1. Introduction 1.1. Let g be a simple Lie algebra over C. The main aim of this paper is to prove the following unique factorisation of tensor products of irreducible, ﬁnite dimensional representations of g:
23p tuanloccuoi 04012013 37 5 Download

We give an upper bound on the number of extensions of a ﬁxed number ﬁeld of prescribed degree and discriminant ≤ X; these bounds improve on work of Schmidt. We also prove various related results, such as lower bounds for the number of extensions and upper bounds for Galois extensions.
20p noel_noel 17012013 46 5 Download

We prove that a type II1 factor M can have at most one Cartan subalgebra A satisfying a combination of rigidity and compact approximation properties. We use this result to show that within the class HT of factors M having such Cartan subalgebras A ⊂ M , the Betti numbers of the standard equivalence relation associated with A ⊂ M ([G2]), are in fact isomorphism invariants for HT the factors M , βn (M ), n ≥ 0. The class HT is closed under ampliﬁcations HT HT and tensor products,
92p noel_noel 17012013 29 5 Download

For diﬀeomorphisms of smooth compact ﬁnitedimensional manifolds, we consider the problem of how fast the number of periodic points with period n grows as a function of n. In many familiar cases (e.g., Anosov systems) the growth is exponential, but arbitrarily fast growth is possible; in fact, the ﬁrst author has shown that arbitrarily fast growth is topologically (Baire) generic for C 2 or smoother diﬀeomorphisms.
83p noel_noel 17012013 37 5 Download

We prove two results. (1) There is an absolute constant D such that for any ﬁnite quasisimple group S, given 2D arbitrary automorphisms of S, every element of S is equal to a product of D ‘twisted commutators’ deﬁned by the given automorphisms. (2) Given a natural number q, there exist C = C(q) and M = M (q) such that: if S is a ﬁnite quasisimple group with S/Z(S) C, βj (j = 1, . . . , M ) are any automorphisms of S, and qj (j = 1, . . . , M ) are...
36p noel_noel 17012013 30 5 Download

In this paper, we study the growth of sX(L), the number of simple closed geodesics of length ≤ L on a complete hyperbolic surface X of finite area. We also study the frequencies of different types of simple closed geodesics on X and their relationship with the WeilPetersson volumes of moduli spaces of bordered Riemann surfaces.
30p dontetvui 17012013 41 5 Download

The annual labour of every nation is the fund which originally supplies it with all the necessaries and conveniencies of life which it annually consumes, and which consist always either in the immediate produce of that labour, or in what is purchased with that produce from other nations. According, therefore, as this produce, or what is purchased with it, bears a greater or smaller proportion to the number of those who are to consume it, the nation will be better or worse supplied with all the necessaries and conveniencies for which it has occasion. But this proportion must in...
930p nguyenhuucanh1212 23012013 44 5 Download

This paper describes an unsupervised knowledge–lean methodology for automatically determining the number of senses in which an ambiguous word is used in a large corpus. It is based on the use of global criterion functions that assess the quality of a clustering solution.
4p bunthai_1 06052013 41 3 Download

In this report we present some noncommutative weak and strong laws of large numbers. Two case are considered: a von Neumann algebra with a normal faithful state on it and the algebra of measurable operators with normal faithful trace. 1. Introduction and notations One of the problems occurring in noncommutative probability theory concerns the extension of various results centered around limit theorems to the noncommutative context.
9p tuanlocmuido 19122012 41 2 Download

Based on experience with INTELLECT in the areas of quality assurance and customer support, a number of issues in evaluating a natural language database query system, particularly the INTELLECT system, will be discussed. A, I. Corporation offers licenses for customers t o use the INTELLECT software on their computers, to access their databases. We now have a number of customer installations, plus reports from companies that are marketing INTELLECT under agreements with us, so that we can begin to discuss user reactions as possible criteria for evaluating our system. ...
2p bungio_1 03052013 32 2 Download

( 'What you see is what you meant') is a userinterface technique which uses natural language generation (NLG) technology to provide feedback for user interactions. To date, the technology has been applied in a number of demonstrator applications, using customised, nonportable implementations. In this demonstration, we introduce a WYSIWYM library package, designed to be used as a modular component of a larger JAVAbased application.
4p bunthai_1 06052013 40 2 Download

The notion of mild contextsensitivity was formulated in an attempt to express the formal power which is both necessary and sufficient to define the syntax of natural languages. However, some linguistic phenomena such as Chinese numbers and German word scrambling lie beyond the realm of mildly contextsensitive formalisms. On the other hand, the class of range concatenation grammars provides added power w.r.t, mildly contextsensitive grammars while keeping a polynomial parse time behavior.
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