Comments and remarks over classic linear loop-gain method for oscillator design and analysis. New proposed method based on NDF/RRT

Abstract. This paper describes a new and original method for designing oscillators based on the Normalized Determinant Function (NDF) and Return Relations (RRT)- Firstly, a review of the loop-gain method will be performed. The loop-gain method pros, cons and some examples for exploring wrong solutions provided by this method will be shown. This method produces in some cases wrong solutions because some necessary conditions have not been fulfilled. The required necessary conditions to assure a right solution will be described. The necessity of using the NDF or the Transpose Return Relations (RRT), which are related with the True Loop-Gain, to test the additional conditions will be demonstrated. To conclude this paper, the steps for oscillator design and analysis, using the proposed NDF/RRj method, will be presented. The loop-gain wrong solutions will be compared with the NDF/RRj and the accuracy of this method to estimate the oscillation frequency and QL will be demonstrated. Some additional examples of plane reference oscillators (Z/Y/T), will be added and they will be analyzed with the new NDF/RRj proposed method, even these oscillators cannot be analyzed using the classic loop gain method.

Influence of origin of the beans on protein quality and nutritive value of commercial soybean meals.

Chemical composition and correlations between chemical analyses and protein quality of 454 batches of SBM of 3 different origins (USA, n=168; Brazil (BRA), n=139, and Argentine (ARG), n=147) were studied. Samples were collected during a 6-yr period. SBM from USA had more CP, sucrose and stachyose and less NDF (P<0.001) than SBM from ARG and BRA. CP content was negatively related (P<0.001) with sucrose for USA meals and with NDF for ARG and BRA meals. Also, P content was positively related (P<0.01) with CP content of the meals. PDI and KOH solubility were higher (P<0.001) for USA than for ARG or BRA SBM, values that were positively related (P<0.001) with trypsin inhibitor activity of the meals. In addition, USA meals had more lys, met+cys, thr, and trp than BRA and ARG meals (P < 0.001). Per unit of CP, lys content was negatively related (P<0.001) with CP content for USA, positively for BRA, and no relations was found for ARG meals. It is concluded that nutritive values and protein quality of the meals varied widely among soybean origins. Consequently, the origin of the beans should be considered in the evaluation of the nutritive value of commercial SBM for non-ruminant animals.

Offsets, Conchoids and Pedal Surfaces

We discuss three geometric constructions and their relations, namely the offset, the conchoid and the pedal construction. The offset surface F d of a given surface F is the set of points at fixed normal distance d of F. The conchoid surface G d of a given surface G is obtained by increasing the radius function by d with respect to a given reference point O. There is a nice relation between offsets and conchoids: The pedal surfaces of a family of offset surfaces are a family of conchoid surfaces. Since this relation is birational, a family of rational offset surfaces corresponds to a family of rational conchoid surfaces and vice versa. We present theoretical principles of this mapping and apply it to ruled surfaces and quadrics. Since these surfaces have rational offsets and conchoids, their pedal and inverse pedal surfaces are new classes of rational conchoid surfaces and rational offset surfaces.