A subset family structure is a topological structure. LetM be a subset family structure and let A be a subset ofM . We introduce A is independent as a synonym of A is open. We introduce A is dependent as an antonym of A is open. Let M be a subset family structure. The family of M yielding a family of subsets of M is defined as follows: (Def. 1) The family of M = the topology of M . Let M be a s...

PP-Def is the problem which takes as input a relation r and a finite set Γ of relations on the same finite domain A, and asks whether r is definable by a conjunctive query over (A,Γ), i.e., by a formula of the form ∃~yφ(~x, ~y) where φ(~x, ~y) is a conjunction of atomic formulas built using the relations in Γ∪ {=}, and where the variables range over A. (Such formulas ∃~yφ(~x, ~y) are called pri...

The synthesis of Mg3(NDC)3(DEF)4 (NDC = 2,6-naphthalenedicarboxylate, DEF = N,N-diethylformamide, 1), the first porous metal-organic framework solid incorporating Mg2+ ions, is reported. Its structure consists of linear Mg3 units linked via NDC bridges to form a three-dimensional framework, featuring one-dimensional channels filled with DEF molecules. Significantly, its framework is fully analo...

Resumo: O objetivo deste estudo foi estimar a prevalência de uso dispositivos eletrônicos para fumar (DEF) e explorar o fluxo lógico esperado do potencial impacto dos DEF na iniciação cigarro convencional. Foram utilizados dados da Vigilância Fatores Risco Proteção Doenças Crônicas por Inquérito Telefônico (Vigitel) 2019, que entrevistou 52.443 indivíduos 18 anos ou mais das 26 capitais brasile...

class Out[-A] { def send(msg: A): Unit

In this paper, it is proved that any algehraicgeometr ic code can be expressed as a cross section of an extended multidimensional cyclic code. Both algebraic-geometric codes and multidimensional cyclic codes are descr ibed by a unified theory of l inear block codes def ined over point sets: algebraic-geometric codes are def ined over the points of an algebraic curve, and an m-dimensional cyclic...

Predicate Transformer (Sketchy) ̧P ‹ post[[X:=E]] ‹ ‚P(fq1; : : : ; qng) where fq1; : : : ; qng „ fp1; : : : ; pkg = ̧P ‹ post[[X:=E]]( n \ i=1 I[[qi]]) def. ‚P = ̧P(f[X=[[E]]] j  2 n \ i=1 I[[qi]]g) def. post[[X:=E]] = ̧P( n \ i=1 f[X=[[E]]] j  2 I[[qi]]g) def. \ = ̧P( n \ i=1 I[[qi[X=E]]]) def. substitution = fpj j I[[qi[X=E]) pj]]g def. ̧P ) fpj j theorem_prover[[qi[X=E]) pj]]g since th...

In the title compound, C(15)H(8)O, the asymmetric unit contains four independent mol-ecules and crystallizes with aromatic π-π stacking inter-actions[centroid-centroid distances = 3.5326 (18) Å].