The purpose of this paper is to show that the mathematics quantum mechanics (QM) set partitions (which specify indefiniteness and definiteness) linearized vector spaces, particularly in Hilbert spaces. That is, math QM space version describe objective at level partitions. key analytical concepts are definiteness versus indefiniteness, distinctions indistinctions, distinguishability indistinguis...

This note is a detailed explanation of Shanks–Atkin NUCOMP— composition and reduction carried out “simultaneously”—for all quadratic fields, that is, including real quadratic fields. That explanation incidentally deals with various “exercises” left for confirmation by the reader in standard texts. Extensive testing in both the numerical and function field cases by Michael J Jacobson, Jr, report...

The Sinc quadrature and the Sinc indefinite integration are approximation formulas for definite integration and indefinite integration, respectively, which can be applied on any interval by using an appropriate variable transformation. Their convergence rates have been analyzed for typical cases including finite, semi-infinite, and infinite intervals. In addition, for verified automatic integra...

The purpose of this paper is twofold. The first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems. The schemes are based in the Sobolev space Hl (ii) and require minimal hypotheses. The second is to develop algorithms utilizing a coarse-grid approximation. This leads to iteration matrices whose eigenvalues lie in the right h...

This study investigated the effects of two types of written feedback – direct corrective feedback (DCF) and metalinguistic explanation (ME) - on Iranian EFL learners’ implicit and explicit knowledge of English definite and indefinite articles. Assigned to three groups of DCF, ME, and control groups, the participants took four tests in three testing phases: pretest, posttest, and delayed posttes...

In this paper, a descent line search scheme is proposed to find local minimum point of non-convex optimization problem with simple constraints. The idea ensures that the escapes saddle points and finally settles for problem. A positive definite scaling matrix formed through symmetric indefinite factorization Hessian objective function at each iteration. numerical illustration provided, global c...

This paper mainly studies nonnegativity decision of forms based on variable substitutions. Unlike existing research, the paper regards simplex subdivisions as new perspectives to study variable substitutions, gives some subdivisions of the simplex Tn, introduces the concept of convergence of the subdivision sequence, and presents a sufficient and necessary condition for the convergent self-simi...

In order to extend the ability to handle incomplete information in a definite deductive database, a Horn clause based system representing incomplete information as incomplete constants is proposed. By using the notion of incomplete constants the deductive database system handles incomplete information in the form of sets of possible values, thereby giving more information than null values. The ...

The paper offers a systematic account of four basic types of nouns, of four basic types of nominal determination, and of the interaction of noun type and determination type. The four basic noun types are sortal, individual, relational, and functional; they correspond to the four logical types 〈e,t〉, e, 〈e,〈e,t〉〉, and 〈e,e〉 on the one hand, and to four types of concepts on the other. The four ba...