Ordered, naturally

Alkaloids of the Anonace. This botanical family belongs to the natural order Anonales, which is nearly related to the Laurales, in which are included the families Lauraeeas and Monimiaeeas. It is not surprising, therefore, that the characteristic alkaloids found in these families are of one type, namely derivatives of aporphine. 

The author baa also det< Qced traces of it in natural order Viotaw. ... 

Physical constants reflect nature s algorithms. They reflect an ordering of physical systems or events. The human perception of that natural order is reflected in how much constants are expressed mathematically. 

An investigation into claims that Bach employed the natural-order number alphabet in his works. Includes a thorough survey of different number alphabets and their uses in seventeenth- and eighteenth-century Germany. Many references to the Cabala and some to Rosicrucianism. A revised version of her thesis... 

Of course, the natural order need not be maintained and thus we have to sum over all the particle labellings. Because of the integrals over the impulsions, this gives rise simply to combinatorial factors. 

In marked contrast to Dumas s philosophical chemistry is the mode of presentation and the tradition of Lavoisier s Traite elementaire de chimie (1789). Lavoisier self-consciously began his text with observations, not first principles, stating that "chemistry is an incomplete science, not like geometry." The new nomenclature that he and his colleagues had developed is claimed to be based in a "natural order of ideas," not in metaphysics.23... 

The discrete factor number of recrystallizations is naturally ordered (see Figure 2.9). It obviously makes sense to plot yield against the number of recrystallizations in the order 1, 2, 3, 4, 5, 6, 7, 8, 9 it would not make sense to plot the yield against a different ordering of the number of recrystallizations, say 3, 7, 5, 8, 2, 1, 4, 9, 6. Other discrete factors are not always as meaningfully ordered, especially if they are... 

It was Mendeleev who discovered the periodic law, a principle that describes the periodicities that are observed in the properties of the chemical elements. This enabled him to predict the existence of as-yet-undiscovered elements, to predict their atomic weights, and to describe their chemical and physical properties as well. It was Mendeleev who found the natural order in the elements that his predecessors Newlands, Chancourtis, and Odling had been seeking. Mendeleev couldn t explain why there were so many elements he didn t even try to do that. But he did discover the existence of striking patterns. 

The situation is completely different with counterion condensation, considered in this section. A natural order parameter here would be... 

In AT the rows of A appear as columns, and the columns of A as rows in their natural order. 

We are assuming that there exists a positive integer n with dn = 1. Thus, the set of all sums dz +d z with integral exponent z is finite. Let m be an integer such that tf" + d, m is maximal (with respect to the natural ordering of Z). 

This purpose the present author has thought to achieve by a preliminary survey of the historical background of medical herbalism, followed by an explanation and discussion of the philosophy upon which the herbal practitioner of to-day bases his work. The greater part of the book is devoted to the cyclopaedic dictionary of medicinal and other herbs, with their natural order, botanical and common names and synonyms, their habitats, distinctive features, the parts employed and the therapeutic properties, with uses and dosage. 

In this case there is no sense of measuring a characteristic. With this data we use a system of classifications, with no natural ordering. For example, one of the factors that might influence the effectiveness of treatment could be the specific manufacturer of a medical device. Therefore, all patients would be classified as users of Smith , Jones or Williams equipment. There is no natural sequence to these they are just three different makes. 

Fe3+ cation positions over distances of tens of angstroms, although a high level of local ordering was detected [65]. In LiAl-LDHs, in which the Li cations fill octahedral vacancies in a gibbsite-like structure and thus are naturally ordered, the existence of a superlattice is regularly detected (Fig. 9.4) [16, 67,68]. 

The hybrid orbital type d2sp3 refers to a case in which the d orbitals have a smaller principal quantum number than that of the s and p orbitals (e.g., 3d combined with 4s and 4p orbitals). The sp3d2 hybrid orbital type indicates a case where the s, p, and d orbitals all have the same principal quantum number (e.g., 4s, 4p, and 4d orbitals) in accord with the natural order of filling atomic orbitals having a given principle quantum number. Some of the possible hybrid orbital combinations will now be illustrated for complexes of first-row transition metals. 

---