Primitive root

A right triangle whose sides are relatively prime integers, primitive root of unity... 

A generator is also called a primitive root modulo p . The total number of generators is this is easy to see from the above-mentioned isomorphism to... 

In the special case where p is an integer (and therefore v = 2p an even integer), the infinite sum can be expressed in terms of a finite sum of exponential functions. To this end, let 6 be a primitive root of the equation... 

The existence and use of batteries is thought to have roots in prehistoric times, whereby, through archeological discoveries, it was discovered that prehistoric people had created an electrochemical cell that would qualify, under today s definition, as a battery. A curiosity found in Baghdad in 1932 was probably representative of battery technology dating as far back as 2500 years.1 Such a primitive... 

This was only a first primitive step towards the phenomenon of life. In the last 20 years or so, due to the enormous developments in computers and computer science, it has become possible to work seriously on AL, the roots of which lie in computer simulation. Three factors are required in order to study the phenomenon of artificial life ... 

This simplistic picture, of course, was insufficient to explain even the behaviour of creatures like worms with primitive nervous systems, and in recent years this approach has largely been abandoned as it is becoming recognised that these events on the membranes of nerve cells are often triggered by shifts in the energy levels of sub-atomic particles such as electrons. In fact, at the root of such interactions lie quantum events, and the activity of the brain must now be seen as reflecting these quantum events. 

The atropine series contains a number of very closely allied alkaloids of which the chief are atropine, hyoscyamine, and hyoscine (also called scopolamine). They are found in the roots and leaves of many plants of the Solanaceae, notably belladonna (Atropa belladonna), henbane (Hyoscyamus niger), the thorn apple or jimson weed (Datura stramonium), and some members of the Duboisia and Scopolia genera. These plants were used during the Middle Ages as sorcerer s drugs and have been smoked, chewed, or imbibed in the form of decoctions by primitive people for the hallucinations and frenzy they produce (Figure 14.1). 

The roots of pharmacology extend backward in time to our earliest Pleistocene hominid ancestors on the African savanna, approximately five to ten million years ago. These primitive forebearers grubbed for existence in the brush, where berries, shoots, leaves, tubers, flowers, seeds, nuts, and roots were plentiful. Our predecessors became specialized vegetarians who only later acquired an appetite for meat. It was their vegetarian diet that served to join gastronomic needs with pharmacological discovery. 

For the sake of simplicity, we will put E = a>2/2 or co = -JlE, where we will choose co positive for positive E and otherwise use the same square root convention as in Appendix A. For the primitive function associated with the first term in Eq. (B.17), one obtains... 

It is amazing that alchemy, once called the Divine Art or Sacred Science, has fallen into such obscurity that it is now only remembered as the primitive beginnings of modern chemistry. And yet, alchemy lies at the root of every Western Esoteric tradition as well as many of the arts and sciences, including medicine and pharmacology. Alchemy has been called "The Mother of all Science and Wisdom."... 

The complex number z is a primitive nth root of unity if zn=l but zk is not equal to 1 for any positive integer k less than n. probability... 

As the tree shows, the true relatives of the archaea are not the bacteria but the eukaryotes. However, because the archaea branch-off closest to the root of the tree, the suggestion is that they are the most primitive of the three kingdoms of organisms whereas the eukaryotes are the least primitive (or the most derived). Placement of the archaea closest to the universal ancestor is supported by the fact that many archaea inhabit extreme environments involving high temperature, low pH, high salinity, and so on. Thus, archaea may well be evolutionary relics of the Earth s earliest forms of life. 

Studies on the pathways of central metabolism of the archaebacteria take on special significance when it is realised that, from the universal phylogenetic tree in rooted form, Woese et al. [66] have proposed that the domain of the archaebacteria be known as archaea to denote their apparently primitive nature, especially with respect to the eukaryotes. Furthermore, within the archaea, thermophily is regarded as the ancestral phenotype. 

Mature enamel is a cell-free tissue while cementum though minerahzed is avascular, similar to some bone tissues, and may have developed to serve the local needs, not a primitive, but a derived and modulated tissue system (Poole, 1967). The bulk of the mineralized tooth is dentine, also a vital tissue that contains passageways known as tubules that are intermineralized with apatite. The tubules reach from the pulp cavity with its supply of nerves and blood vessels that enter at the base of the root(s) and extend to the enamel. Dentine has the possibility to repair itself. 

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