One-dimensional models for organic magnetic materials

In the preparation of small organic paramagnets, these structures may conceptually be divided into spin-containing units (SCs) and ferromagnetic coupling units (FCs). The synthesis and direct observation of a series of hydrocarbon tetraradicals designed to test the ferromagnetic coupling ability of m-phenylene, 1,3-cyclobutane, 1,3- cyclopentane, and 2,4-adamantane (a chair 1,3-cyclohexane) using Berson TMMs and cyclobutanediyls as SCs are described. While 1,3-cyclobutane and m-phenylene are good ferromagnetic coupling units under these conditions, the ferromagnetic coupling ability of 1,3-cyclopentane is poor, and 1,3-cyclohexane is apparently an antiferromagnetic coupling unit. In addition, this is the first report of ferromagnetic coupling between the spins of localized biradical SCs.

The poor coupling of 1,3-cyclopentane has enabled a study of the variable temperature behavior of a 1,3-cyclopentane FC-based tetraradical in its triplet state. Through fitting the observed data to the usual Boltzman statistics, we have been able to determine the separation of the ground quintet and excited triplet states. From this data, we have inferred the singlet-triplet gap in 1,3-cyclopentanediyl to be 900 cal/mol, in remarkable agreement with theoretical predictions of this number.

The ability to simulate EPR spectra has been crucial to the assignments made here. A powder EPR simulation package is described that uses the Zeeman and dipolar terms to calculate powder EPR spectra for triplet and quintet states.

Methods for characterizing paramagnetic samples by SQUID magnetometry have been developed, including robust routines for data fitting and analysis. A precursor to a potentially magnetic polymer was prepared by ring-opening metathesis polymerization (ROMP), and doped samples of this polymer were studied by magnetometry. While the present results are not positive, calculations have suggested modifications in this structure which should lead to the desired behavior.

Source listings for all computer programs are given in the appendix.

A computer-aided investigation of motion detection units in the fly

This work deals with two related areas: processing of visual information in the central nervous system, and the application of computer systems to research in neurophysiology.

Certain classes of interneurons in the brain and optic lobes of the blowfly Calliphora phaenicia were previously shown to be sensitive to the direction of motion of visual stimuli. These units were identified by visual field, preferred direction of motion, and anatomical location from which recorded. The present work is addressed to the questions: (1) is there interaction between pairs of these units, and (2) if such relationships can be found, what is their nature. To answer these questions, it is essential to record from two or more units simultaneously, and to use more than a single recording electrode if recording points are to be chosen independently. Accordingly, such techniques were developed and are described.

One must also have practical, convenient means for analyzing the large volumes of data so obtained. It is shown that use of an appropriately designed computer system is a profitable approach to this problem. Both hardware and software requirements for a suitable system are discussed and an approach to computer-aided data analysis developed. A description is given of members of a collection of application programs developed for analysis of neuro-physiological data and operated in the environment of and with support from an appropriate computer system. In particular, techniques developed for classification of multiple units recorded on the same electrode are illustrated as are methods for convenient graphical manipulation of data via a computer-driven display.

By means of multiple electrode techniques and the computer-aided data acquisition and analysis system, the path followed by one of the motion detection units was traced from open optic lobe through the brain and into the opposite lobe. It is further shown that this unit and its mirror image in the opposite lobe have a mutually inhibitory relationship. This relationship is investigated. The existence of interaction between other pairs of units is also shown. For pairs of units responding to motion in the same direction, the relationship is of an excitatory nature; for those responding to motion in opposed directions, it is inhibitory.

Experience gained from use of the computer system is discussed and a critical review of the current system is given. The most useful features of the system were found to be the fast response, the ability to go from one analysis technique to another rapidly and conveniently, and the interactive nature of the display system. The shortcomings of the system were problems in real-time use and the programming barrier—the fact that building new analysis techniques requires a high degree of programming knowledge and skill. It is concluded that computer system of the kind discussed will play an increasingly important role in studies of the central nervous system.

Applications of a nuclear technique for depth-sensitive hydrogen analysis : trapped H in lunar samples and the hydration of terrestrial obsidian

The resonant nuclear reaction ¹⁹F(p,αy)¹⁶O has been used to perform depth-sensitive analyses for both fluorine and hydrogen in solid samples. The resonance at 0.83 MeV (center-of-mass) in this reaction has been applied to the measurement of the distribution of trapped solar protons in lunar samples to depths of ~1/2µm. These results are interpreted in terms of a redistribution of the implanted H which has been influenced by heavy radiation damage in the surface region. Fluorine determinations have been performed in a 1-µm surface layer on lunar and meteoritic samples using the same ¹⁹F(p,αy)¹⁶O resonance. The measurement of H depth distributions has also been used to study the hydration of terrestrial obsidian, a phenomenon of considerable archaeological interest as a means of dating obsidian artifacts. Additional applications of this type of technique are also discussed.

On the distribution of the signs of the conjugates of the cyclotomic units in the maximal real subfield of the qth cyclotomic field, q A prime

Let F = Ǫ(ζ + ζ ^–1) be the maximal real subfield of the cyclotomic field Ǫ(ζ) where ζ is a primitive qth root of unity and q is an odd rational prime. The numbers u₁=-1, u_k=(ζ^k-ζ^-k)/(ζ-ζ^-1), k=2,…,p, p=(q-1)/2, are units in F and are called the cyclotomic units. In this thesis the sign distribution of the conjugates in F of the cyclotomic units is studied.

Let G(F/Ǫ) denote the Galoi's group of F over Ǫ, and let V denote the units in F. For each σϵ G(F/Ǫ) and μϵV define a mapping sgn_σ: V→GF(2) by sgn_σ(μ) = 1 iff σ(μ) ˂ 0 and sgn_σ(μ) = 0 iff σ(μ) ˃ 0. Let {σ₁, ... , σ_p} be a fixed ordering of G(F/Ǫ). The matrix M_q=(sgn_σj(v_i) ) , i, j = 1, ... , p is called the matrix of cyclotomic signatures. The rank of this matrix determines the sign distribution of the conjugates of the cyclotomic units. The matrix of cyclotomic signatures is associated with an ideal in the ring GF(2) [x] / (x^p+ 1) in such a way that the rank of the matrix equals the GF(2)-dimension of the ideal. It is shown that if p = (q-1)/ 2 is a prime and if 2 is a primitive root mod p, then M_q is non-singular. Also let p be arbitrary, let ℓ be a primitive root mod q and let L = {i | 0 ≤ i ≤ p-1, the least positive residue of defined by ℓⁱ mod q is greater than p}. Let H_q(x) ϵ GF(2)[x] be defined by H_q(x) = g. c. d. ((Σ xⁱ/I ϵ L) (x+1) + 1, x^p + 1). It is shown that the rank of M_q equals the difference p - degree H_q(x).

Further results are obtained by using the reciprocity theorem of class field theory. The reciprocity maps for a certain abelian extension of F and for the infinite primes in F are associated with the signs of conjugates. The product formula for the reciprocity maps is used to associate the signs of conjugates with the reciprocity maps at the primes which lie above (2). The case when (2) is a prime in F is studied in detail. Let T denote the group of totally positive units in F. Let U be the group generated by the cyclotomic units. Assume that (2) is a prime in F and that p is odd. Let F₍₂₎ denote the completion of F at (2) and let V₍₂₎ denote the units in F₍₂₎. The following statements are shown to be equivalent. 1) The matrix of cyclotomic signatures is non-singular. 2) U∩T = U². 3) U∩F²₍₂₎ = U². 4) V₍₂₎/ V₍₂₎² = ˂v₁ V₍₂₎²˃ ʘ…ʘ˂v_p V₍₂₎²˃ ʘ ˂3V₍₂₎²˃.

The rank of M_q was computed for 5≤q≤929 and the results appear in tables. On the basis of these results and additional calculations the following conjecture is made: If q and p = (q -1)/ 2 are both primes, then M_q is non-singular.

The geochronology of the plutonic and metamorphic rocks of New Zealand

Extensive Rubidium-Strontium age determinations on both mineral and total rock samples of the crystalline rocks of New Zealand, which almost solely crop out in the South Island, indicate widespread plutonic and metamorphic activity occurred during two periods, one about 100-118 million years ago and the other about 340-370 million years ago. The former results date the Rangitata Orogeny as Cretaceous. They associate extensive plutonic activity with this orogeny which uplifted and metamorphosed the rocks of the New Zealand Geosyncline, although no field association between the metamorphosed geosynclinal rocks and plutonic rocks has been found. The Cretaceous plutonic rocks occur to the west in the Foreland Province in Fiordland, Nelson, and Westland, geographically separated from the Geosynclinal Province. Because of this synchronous timing of plutonic and high pressure metamorphic activity in spatially separated belts, the Rangitata Orogeny in New Zealand is very similar to late Mesozoic orogenic activity in many other areas of the circum-Pacific margin (Miyashiro, 1961).

The 340-370 million year rocks, both plutonic and metamorphic, have been found only in that part of the Foreland Province north of the Alpine Fault. There, they are concentrated along the west coast over a distance of 500 km, and appear scattered inland from the coast. Probably this activity marks the outstanding Phanerozoic stratigraphic gap in New Zealand which occurred after the Lower Devonian.

A few crystalline rocks in the Foreland Province north of the Alpine Fault with measured ages intermediate between 340 and 120 million years have been found. Of these, those with more than one mineral examined give discordant results. All of these rocks are tentatively regarded as 340-370 million year old rocks that have been variously disturbed during the Rangitata Orogeny, 100-120 million years ago.

In addition to these two periods, plutonic activity, dominantly basic and ultrabasic, but including the development of some rocks of intermediate and acidic composition, occurred along the margin of the Geosynclinal Province at its border with the Foreland Province during Permian times about 245 million years ago, and this activity possibly extended into the Mesozoic.

Evidence from rubidium-strontium analyses of minerals and a total rock, and from uranium, thorium, and lead analyses of uniform euhedral zircons from a meta-igneous portion of the Charleston Gneiss, previously mapped as Precambrian, indicate that this rock is a 350-370 million year old plutonic rock metamorphosed 100 million yea rs ago during the Rangitata Orogeny. No crystalline rocks with primary Precambrian ages have been found in New Zealand. However, Pb²⁰⁷/Pb₂₀₆ ages of 1360 million years and 1370 million years have been determined for rounded detrital zircons separated from each of two hornfels samples of one of New Zealand's olde st sedimentary units, the Greenland Series. These two samples were metamorphosed 345- 370 million years ago. They occur along the west coast, north of the Alpine Fault, at Waitaha River and Moeraki River, separated by 135 km. The Precambrian measured ages are most likely minimum ages for the oldest source area which provided the detrital zircons because the uranium, thorium and lead data are highly discordant. These results are of fundamental importance for the tectonic picture of the Southwest Pacific margin and demonstrate the existence of relatively old continental crust of some lateral extent in the neighborhood of New Zealand.