This paper describes several classical constructions of thin bases of finite order in additive number theory, and, in particular, gives a complete presentation of a beautiful construction of J. W. S. Cassels of a class of polynomially asymptotic bases. Some open problems are also discussed. 1. Additive bases of finite order The fundamental object in additive number theory is the sumset. If h ≥ ...

In this paper we present an overview of knowledge-based systems. We begin by discussing the basic characteristics of knowledge base rules and present an example comparing a toy knowledge base to an equivalent procedural version of the same code. We then discuss the applications for which it makes sense to use knowledge-based technology and the advantages offered by reuse of a general-purpose up...

The authors investigated the predictive utility of people's subjective assessments of whether their evaluations are affect- or cognition driven (i.e., meta-cognitive bases) as separate from whether people's attitudes are actually affect- or cognition based (i.e., structural bases). Study 1 demonstrated that meta-bases uniquely predict interest in affective versus cognitive information above and...

The problem of computer assisted literature search is often misstated as the attempt to nd, in a repository of electronic literature, a paper which, according to title and keywords, contains the desired information. This assumes that the original author was correct and complete in assigning keywords, and that the search criteria are free of preconceived expectations on the context in which the ...

Abstract: Mutually unbiased bases generalize the X, Y and Z qubit bases. They possess numerous applications in quantum cryptography and quantum information. It is well-known that in prime power dimensions N = p (with p prime and m a positive integer) there exists a maximal set of N + 1 mutually unbiased bases. In the present paper, we derive a new, simple and compact expression for those bases,...

the crystal structure of the compound c20 h24 n2 o24 was determined by direct methods. thecrystals are monoclinic, space group p21/n, and unit cell parameters are: a= 10.2342 (9), b=4.8763 (5),c=19.3578 (11) a, β =98.9632 (10) o ,v=956.6 (5) a3, z=2, dc=1.239grm-3, dm=1.22grm-3. the final rfactorsare converged to r=0.059 and rw=0.056 for 553 independent observed reflections. themolecules are li...

The hydration of biomolecules is vitally important in molecular biology, so in this paper thesolvation energy and radial distribution function of DNA bases have been calculated by theMonte Carlo simulation.The geometries of isolated Adenine, Guanine, Cytosine, and Thyminehave been optimized using 6-31+G(d,p) basis function sets. These geometries then will be used inthe Monte Carlo calculation o...

The study of ideals in polynomial rings over fields is absolutely central to algebraic geometry. We think of an affine variety (usually called affine algebraic set without an irreducibility hypothesis) in n dimensions as defined to be the common zero set of a collection of polynomials f1(x1, . . . , xn), . . . , fm(x1, . . . , xn) with coefficients in some field k. We see that if a point (c1, ....