Bilateral semidirect product decompositions of transformation monoids

In this paper we consider the monoid OR(n) of all full transformations on a chain with n elements that preserve or reverse the orientation, as well as its submonoids OD(n) of all order-preserving or order-reversing elements, OP(n) of all orientation-preserving elements and O(n) of all order-preserving elements. By making use of some well known presentations, we show that each of these four monoids is a quotient of a bilateral semidirectproduct of two of its remarkable submonoids.

A perceção do dador de sangue face à dádiva de sangue e ao estatuto do dador de sangue

Mestrado em Gestão e Avaliação de Tecnologias da Saúde

New RuII(arene) complexes with halogen-substituted bis- and tris(pyrazol-1-YL)borate ligands

[RuCl(arene)(-Cl)](2) dimers were treated in a 1:2 molar ratio with sodium or thallium salts of bis- and tris(pyrazolyl)borate ligands [Na(BpBr3)], [Tl(TpBr3)], and [Tl(Tp(iPr,4Br))]. Mononuclear neutral complexes [RuCl(arene)((2)-BpBr3)] (1: arene=p-cymene (cym); 2: arene=hexamethylbenzene (hmb); 3: arene=benzene (bz)), [RuCl(arene)((2)-TpBr3)] (4: arene=cym; 6: arene=bz), and [RuCl(arene)((2)-Tp(iPr,4Br))] (7: arene=cym, 8: arene=hmb, 9: arene=bz) have been always obtained with the exception of the ionic [Ru-2(hmb)(2)(-Cl)(3)][TpBr3] (5), which formed independently of the ratio of reactants and reaction conditions employed. The ionic [Ru(CH3OH)(cym)((2)-BpBr3)][X] (10: X=PF6, 12: X=O3SCF3) and the neutral [Ru(O2CCF3)(cym)((2)-BpBr3)] (11) have been obtained by a metathesis reaction with corresponding silver salts. All complexes 1-12 have been characterized by analytical and spectroscopic data (IR, ESI-MS, H-1 and (CNMR)-C-13 spectroscopy). The structures of the thallium and calcium derivatives of ligand TpBr3, [Tl(TpBr3)] and [Ca(dmso)(6)][TpBr3](2)2DMSO, of the complexes 1, 4, 5, 6, 11, and of the decomposition product [RuCl(cym)(Hpz(iPr,4Br))(2)][Cl] (7) have been confirmed by using single-crystal X-ray diffraction. Electrochemical studies showed that 1-9 and 11 undergo a single-electron (RuRuIII)-Ru-II oxidation at a potential, measured by cyclic voltammetry, which allows comparison of the electron-donor characters of the bis- and tris(pyrazol-1-yl)borate and arene ligands, and to estimate, for the first time, the values of the Lever E-L ligand parameter for BpBr3, TpBr3, and Tp(iPr,4Br). Theoretical calculations at the DFT level indicated that both oxidation and reduction of the Ru complexes under study are mostly metal-centered with some involvement of the chloride ligand in the former case, and also demonstrated that the experimental isolation of the (3)-binuclear complex 5 (instead of the mononuclear 5) is accounted for by the low thermodynamic stability of the latter species due to steric reasons.

The effects of parental sensitivity and involvement in caregiving on mother–infant and father–infant attachment in a portuguese sample

In the present longitudinal study, we investigated attachment quality in Portuguese mother–infant and in father–infant dyads, and evaluated whether attachment quality was related to parental sensitivity during parent–infant social interaction or to the amount of time each parent spent with the infant during play and in routine caregiving activities (e.g., feeding, bathing, play). The sample consisted of 82 healthy full-term infants (30 girls, 53 boys, 48 first born), and their mothers and fathers from mostly middle-class households. To assess parental sensitivity, mothers and fathers were independently observed during free play interactions with their infants when infants were 9 and 15 months old. The videotaped interactions were scored by masked coders using the Crittenden’s CARE-Index. When infants were 12 and 18 months old, mother–infant and father–infant dyads were videotaped during an adaptation of Ainsworth’s Strange Situation. Parents also described their level of involvement in infant caregiving activities using a Portuguese version of the McBride and Mills Parent Responsibility Scale. Mothers were rated as being more sensitive than fathers during parent–infant free play at both 9 and 15 months. There also was a higher prevalence of secure attachment in mother–infant versus father–infant dyads at both 12 and 18 months. Attachment security was predicted by the amount of time mothers and fathers were involved in caregiving and play with the infant, and with parents’ behavior during parent–infant free play.

Spectral and weak polynomial completeness for the product of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).