**Research on Knowledge Transfer/Capture methods on learning Oscillators with or without self-quenching qualities and Oscillators with or without Schmitt effect, using single or multiple Integrals, derivatives or delays.**

Knowledge transfer methods or capturing what depict the deeper working details of all systems, varies with the complexity of the system in question. Oscillators are normally taught to students by first describing a linear undamped second order differential equation whose mathematical model is synthesized through electronic circuits containing two integrals or differentials or delays in conjunction with an amplification and /or inversion operation to ensure correct feedback for maintaining oscillations. The manner in which this is achieved is diverse and theoretically such a second order system need not have a Schmitt trigger effect to assist oscillation, but only a phasing of signals of the required magnitude. Self-starting on such circuits is always questionable.

Other oscillators may operate using a single derivative or a single integral with their magnitude, delayed or advanced through operators, as long as they contain a Schmitt trigger effect through a high gain comparator. The trigger is used to saturate the system until some signal within the system changes sufficiently to trigger a change. The high gain comparator gives a dual threshold and hysteresis and this action, implies that the Schmitt trigger possesses memory, gainfully employed. Oscillators without Schmitt trigger effect do in fact include analogue memories contained in the dual integrators differentiators or delay elements.

Research shows that a generalized system may be used to describe all types of oscillators, those with and those without Schmitt trigger effect, self-quenching and no quenching type, each containing a variation of integrals, differentiators and delays to achieve the requirements using actual components or their electronic digital simulations as in unstable digital filters. The link between those oscillators using and not using the Schmitt effect is identified when the high gain comparator, say in a relaxation oscillator using one integral or a derivative operator, is replaced with a limited gain amplifier, the gain being related to the point at which trigger or comparison occurs.

When a limited gain amplifier is used instead of a high gain comparator in a Schmitt triggered oscillator, the output does not retain its dual high and low only memory values but as the reference point is approached the output changes gradually from being a square wave containing zero rate of changes during the high and low values to one which approaches a sinusoidal wave, where the nature of the waveform depends on the value of the gain used. Not only a sinusoidal waveform may be produced with one integral/derivative but such Schmitt trigger oscillators seem to ensure reliable self-starting characteristics.

Studies of past Knowledge Transfer/Capturing methods to teach various oscillators as individual circuits indicate that the partial of full self-quenching effect of some oscillators using resistors/capacitors/inductors combined with the diode effect of an emitter base junction of a BJT transistor is normally not well covered nor understood in class. The deeper details of a partial or full, self- quenching oscillators are not given enough coverage for full comprehension to flourish.

Knowledge Transfer/Capturing methods are being researched upon to group all oscillators in one field where it is shown that the understanding of Schmitt Trigger application in conjunction with fewer integrals , derivatives and delays, would provide the best path for the student to comprehend all the other conventional oscillatory circuits and the partial and the full self-quenching oscillators.

This research is aimed at assisting students to understand the higher order multiple operations in simple and complex oscillators through the unification of various linear and non-linear electronic effects/logic which are not normally covered in undergraduate courses.

Prof.Carmel Pule'

**Research on Knowledge Transfer/Capture methods on teaching three or more dimensional interpretations of Laplace, Fourier, Convolution Integrals and Correlations methods as applied to Engineering, domestic and social diagnosis.**

The nature of most components and behavior taking place within the various operators used in a signal processing methods as applied to recognize system functions, such as Laplace, Fourier, Convolution and Correlation processes are normally depicted as two dimensional or flat functions drawn and illustrated on flat surfaces during the teaching procedure. The conventional kernels used are normally sinusoidal, cosine with exponential envelopes.

Practical situations other than simple electrical or electronic work indicate that the relations between components and operations found in space/time systems may be interpreted as being of multiple dimensions requiring a multiple dimensional kernel to recognize their hidden nature.

Signals containing, frequency or periodicity, phase, sequence, time allocation segment, space orientations, colour, sounds, form, etc., these need a higher order interpretation of Laplace, Fourier, etc. even to a higher order space than three dimensions. Recognizing a time/space multiplexed, frequency burst signals would need a kernel that fits both the time and frequency allocation, even space allocation to recognize the location and nature of the signal.

Research on a Higher Dimensional form of Laplace, Convolution, Fourier, and Correlation indicates that students are much better equipped to recognize the practical meaning of Laplace function rather than just to solve differential equations using accepted methods.

This research shows that most engineering students are surprised when they are made to realize that the application of a higher order Laplace Function and associated memorized kernels learnt through their social and academic education are even used to recognize a toothbrush in a bathroom and a shooting star in the dark sky, or meeting a person at a particular time or catching the bus at the bus stop, not to mention all our movements are coordinated through a Laplace function whose result enable us to walk through a door. It is interesting that all learnt kernels are modified through tiredness and how much alcohol is consumed, where, in our mind, the result of the Laplace integral is not so high and so recognition fails drastically. Luckily for us the kernels resume their accuracy when we are sober.

One property of a higher dimensional interpretation of Laplace Function would indicate that a rotating action is not recognized by a kernel rotating in the same direction as the function itself but by a kernel with the conjugate kernel rotating in opposite direction where the product of the kernel multiplied by the function eliminates the rotation and hence the sign of the product does not change, resulting in the integral increasing in value where the magnitude of this value describes the relation between the function and the kernel chosen to compare it with .

Such fine detail of these familiar operators taught in Engineering Courses is not normally depicted when flat functions as sine and cosine are used to illustrate these operators. The sine and cosine associated with the j notation raises the dimension of interpretation but one wonders how much the average engineering student comprehend the full scenario while he follows an engineering or any other course including mathematics.

In case of signals depicting the conventional complex frequency plane using the notation s=p+jw, three phase power systems cannot be described but through increasing the dimension of s from a point s=p+jw on a surface, to s=p+jw +kq within a block, then a phase shifts q can be allocated to the kernel used in Laplace operators. The term “Complex frequency can now contain many variables to describe a really complex kernel associated with everything existing in real life”

This research clearly indicates that when mature students are made aware of functions having higher dimensions and the kernels we learn throughout all our life to help us recognize our surroundings, a better formation and understanding is achieved. Most students are surprised to find that all type of Education, perhaps even our intelligence, all boils down to our efforts in learning enough rich kernels in life to be able us to apply Laplace function and recognize and diagnose what is happening around us, only if the product of what we have in mind and the scenario around us produces and integral which grows to a high value!

Prof.Carmel Pule'