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.

Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling

Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending, the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length. Based on Rayleigh's quotient, an iterative strategy is developed to find the approximated torsional stiffness coefficients, which allows the reconciliation between the theoretical model results and the experimental ones, obtained through impact tests. The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh's quotient but also on the mode shapes, considering the shape functions defined in branches. Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.

Considerações prévias: distinctions between academic and intellectual goals for young children

Lilian Katz refere-se à crescente tendência nos Estados Unidos de introduzir objetivos de caráter “académico” nos programas destinados a crianças pequenas, em alternativa a programas centrados simplesmente no jogo espontâneo. Katz propõe uma terceira alternativa que desenvolva as competências de caráter intelectual nas crianças, de modo a estimular o desenvolvimento das suas mentes e as suas sensibilidades morais e estéticas. Katz propõe a introdução do trabalho de projeto com crianças desde os primeiros anos.

Modelling a Rotating Shaft as an Elastically Restrained Bernoulli-Euler Beam

Industrial rotating machines may be exposed to severe dynamic excitations due to resonant working regimes. Dealing with the bending vibration, problem of a machine rotor, the shaft - and attached discs - can be simply modelled using the Bernoulli-Euler beam theory, as a continuous beam subjected to a specific set of boundary conditions. In this study, the authors recall Rayleigh's method to propose an iterative strategy, which allows for the determination of natural frequencies and mode shapes of continuous beams taking into account the effect of attached concentrated masses and rotational inertias, including different stiffness coefficients at the right and the left end sides. The algorithm starts with the exact solutions from Bernoulli-Euler's beam theory, which are then updated through Rayleigh's quotient parameters. Several loading cases are examined in comparison with the experimental data and examples are presented to illustrate the validity of the model and the accuracy of the obtained values.

Resting energy expenditure, macronutrient utilization, and body composition in term infants after corrective surgery of major congenital anomalies: a case-study

Introduction - Knowledge on the metabolic changes and nutritional needs during the postsurgical anabolic phase in infants is scarce. This analysis explores the associations of resting energy expenditure (REE) and macronutrient utilization with body composition of full-term infants, during catch-up growth after corrective surgery of major congenital anomalies. Methods - A cohort of full-term appropriate for-gestational-age neonates subjected to corrective surgery of major congenital anomalies were recruited after gaining weight for at least one week. REE and macronutrient utilization, measured by respiratory quotient (RQ), were assessed by indirect calorimetry using the Deltatrac II Metabolic Monitor ®. Body composition, expressed as fat-free mass (FFM), fat mass (FM) and adiposity defined as percentage of FM (% FM), was measured by air displacement plethysmography using the Pea Pod ®. Results - Four infants were included at 3 to 5 postnatal weeks. Recommended energy and macronutrient intakes for healthy term infants were provided. Through the study, the median (min-max) REE (Kcal/Kg FFM/d) was 70.8 (60.6-96.1) and RQ was 0.99 (0.72-1.20). Steady increases in both body weight and FFM were associated with initial decrease in FM and adiposity followed by their increase. Low RQ preceded decrease in adiposity. Conclusion - The marked adiposity depletion, not expected during steady weight gain in the postsurgical period, prompts us to report this finding. The subsequent adiposity catch-up was associated with relatively high REE and RQ, suggesting preferential oxidation of carbohydrates and preservation of lipids for fat storage.