Crazy Children, Fantastical Theories, and the Many Uses of Metaphysics

Woolley rightly challenges the incredible idea, held by some adults, that it is children who are peculiarly "fantastical" in their thinking. However, Woolley expresses little appreciation for "fantastical thinking" as it underlies the capacity for both grand delusions and amazing insights. In reducing "fantastical thinking" to conceptual error, she overlooks the mythical underpinning of her own theorizing and neglects the many constructive roles of "fantastical thinking" in development.     

A theory for decoupling lossless coupled tapered lines with applications to directional couplers

A simple theory is presented for decoupling a pair of lossless coupled nonuniform transmission lines (CNUTL), with a common return and supporting TEM waves, into two lossless nonuniform transmission lines (NUTL). This theory is independent of the port terminations, symmetry conditions, etc. The method directly relates the line parameters of the lossless CNUTL's to those of the decoupled lines and vice versa; further, the matrix parameters of the CNUTL's as a four-port are explicitly expressed in terms of those of the decoupled lines as two-ports. This theory is then utilized to study the applications of CNUTL's as directional couplers.It is shown that for CNUTL's to behave as a codirectional coupler, each of the decoupled lines should be a proportional line, while for contradirectional coupler action, the two decoupled lines have to be duals of each other. The coupling response of the codirectional coupler is found to be periodic, while the phase shift between coupled and transmitted signals varies linearly with frequency. The coupling response of various contradirectional couplers with smooth transition at one of the ends, for which the decoupled lines are “basic NUTL's with hyperbolic solutions”, are studied in detail. It is shown that all these couplers have a high-pass response and that the CNUTL's with “hyperbolic cosine squared lines” as decoupled lines have the best response of all the CNUTL's considered.     

Sum and product separabilities of multivariable functions and applications

Necessary and sufficient conditions for reducibility of certain classes of multivariable polynomials are considered. The special case when a polynomial in that class can be factored into a finite product of single variable polynomials is investigated. A set of necessary and sufficient conditions for decomposing a multivariable p.r.f. into a sum of single variable p.r.f.'s is given. Examples to illustrate applications of sum and product separabilities of functions are given.     

Feedback factorizing control of 3-D transfer functions via a canonical state-space model

The problem factorizing (separating) the transfer function of a given SISO 3-D discrete system, ie of a system depending on three independent variables, is considered. The 3-D system is assumed to be available in its transfer function representation, which is converted to a canonical state-space model by a simple inspection procedure. Then applying state-feedback to this canonical model we choose the feedback matrix gain (under certain conditions) such that the transfer function of the closed-loop system has the desireed factorized form, ie a product of three 1-D transfer functions each one being dependent on a single variable. The method is illustrated by a nontrivial numerical example.     

Assessment of oxidative stress and effect of antioxidant supplementation during radiotherapy in carcinoma of upper digestive tract

Oxidative stress was studied by estimating plasma levels of malondialdehyde (MDA), beta carotene, vitamin E and erythrocytic superoxide dismutase(E-SOD) activity in 50 cases of carcinoma of upper digestive tract which included carcinoma of oral cavity, pharynx and oesophagus. While plasma MDA level was found to be increased (3.5±1.0 nmole/ml), a significant decrease in beta carotene (81.2±14.5mg%), vitamin E (8.5±1.1 mg/L) level and E-SOD activity (657.0±80.6 U/G Hb) were observed in carcinoma of upper digestive tract. Patients were treated with radiotherapy which itself was toxic enough and produced its deleterious effects by generation of reactive oxygen species (ROS). As antioxdiants can detoxify ROS, beneficial effect if any, of antioxidant administration during radiotherapy was studied in two groups of patients, group A (n=5, supplemented with antioxidants) and group B (n=5, without antioxidant supplementation). Plasma MDA level was found to be elevated in both the groups but the increase in group B was significant, compared to pretreatment level. Further, body weight was found to be significantly decreased in group B patients, which was maintained in group A patients. Moreover, group A patients showed significant elevation in beta carotene concentration, thus showing beneficial effect of administration of antioxidants during radiotherapy without disturbing the desirable therapeutic effect of radiotherapy.