On a conjecture of Lapidus and van Frankenhuysen

In this paper it is shown that a conjecture of Lapidus and van Frankenhuysen of 2003 on the existence of a vertical line such that the density of the complex dimensions of nonlattice fractal strings with M scaling ratios off this line vanishes in the limit as M→∞, fails on the class of nonlattice self-similar fractal strings.

On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

Human creation, imagination and autonomy: a brief introduction to Castoriadis’ social and psychoanalytical philosophy

During the last decade Castoriadis’ questioning has become a reference point in contemporary social theory. In this article I examine some of the key notions in Castoriadis’ work and explore how he strives to develop a theory on the irreducible creativity in the radical imagination of the individual and in the institution of the social-historical sphere. Firstly, I briefly discuss his conception of modern capitalism as bureaucratic capitalism, a view initiated by his criticism of the USSR regime. The following break up with Marxist theory and his psychoanalytic interests empowered him to criticize Lacan and read Freud in an imaginative, though unorthodox, fashion. I argue that this critical enterprise assisted greatly Castoriadis in his conception of the radical imaginary and in his unveiling of the political aspects of psychoanalysis. On the issue of the radical imaginary and its methodological repercussions, I’m focusing mainly on the radical imagination of the subject and its importance in the transition from the ‘‘psychic’’ to the ‘‘subject’’. Taking up the notion of “Being” as a starting point, I examine the notion of autonomy, seeking its roots in the ancient Greek world. By looking at notions such as “praxis”, “doing”, “project” and “elucidation”, I show how Castoriadis sought to redefine revolution as a means for social and individual autonomy. Finally I attempt to clarify the meaning of “democracy” and “democratic society” in the context of the social imaginary and its creations, the social imaginary significations.

National Minorities, Nationalizing States, and External National Homelands in the New Europe. Notes toward a Relational Analysis. Institute of Advanced Studies Political Science Series, 11 December 1993

Nationalism remains central to politics in and among the new nation-states. Far from »solving« the region's national question, the most recent reconfiguration of political space – the replacement of the Soviet Union, Yugoslavia, and Czechoslovakia by some twenty would-be nation-states – only recast it in a new form. It is this new phase and form of the national question that I explore in this paper. I begin by outlining a particular relational configuration – the triadic relational nexus between national minorities, nationalizing states, and external national homelands – that is central to the national question in post-Soviet Eurasia. In the second, and most substantial, section of the paper, I argue that each of the »elements« in this relational nexus – minority, nationalizing state, and homeland – should itself be understood in dynamic and relational terms, not as a fixed, given, or analytically irreducible entity but as a field of differentiated positions and an arena of struggles among competing »stances.« In a brief concluding section, I return to the relational nexus as a whole, underscoring the dynamically interactive quality of the triadic interplay.

Chemical composition of plagioclase from DSDP Legs 45 and 46, Atlantic Ocean

Phyric basalts recovered from DSDP Legs 45 and 46 contain abundant plagioclase phenocrysts which occur as either discrete single grains (megacrysts) or aggregates (glomerocrysts) and which are too abundant and too anorthitic to have crystallized from a liquid with the observed bulk rock composition. Almost all the plagioclase crystals are complexly zoned. In most cases two abrupt and relatively large compositional changes associated with continuous internal morphologic boundaries divide the plagioclase crystals into three parts: core, mantle and rim. The cores exhibit two major types of morphology: tabular, with a euhedral to slightly rounded outline; or a skeletal inner core wrapped by a slightly rounded homogeneous outer core. The mantle region is characterized by a zoning pattern composed of one to several spikes/plateaus superimposed on a gently zoned base line, with one large plateau always at the outside of the mantle, and by, in most cases, a rounded internal morphology. The inner rim is typically oscillatory zoned. The width of the outer rim can be correlated with the position of the individual crystal in the basalt pillow. The presence of a skeletal inner core and the concentration of glass inclusions in low-An zones in the mantle region suggest that the liquid in which these parts of the crystals were growing was undercooled some amount. The resorption features at the outer margins of low-An zones indicate superheating of the liquid with respect to the crystal. It is proposed that the plagioclase cores formed during injection of primitive magma into a previously existing magma chamber, that the mantle formed during mixing of a partially mixed magma and the remaining magma already in the chamber, and that the inner rim formed when the mixed magma was in a sheeted dike system. The large plateau at the outside of the mantle may have formed during the injection of the next batch of primitive magma into the main chamber, which may trigger an eruption. This model is consistent with fluid dynamic calculations and geochemically based magma mixing models, and is suggested to be the major mechanism for generating the disequilibrium conditions in the magma.

Data compilation of marine pelagic organism biomasses, swimming velocities, clearance and respiration rates

Jellyfishes have functionally replaced several overexploited commercial stocks of planktivorous fishes. This is paradoxical, because they use a primitive prey capture mechanism requiring direct contact with the prey, whereas fishes use more efficient visual detection. We have compiled published data to show that, in spite of their primitive life-style, jellyfishes exhibit similar instantaneous prey clearance and respiration rates as their fish competitors and similar potential for growth and reproduction. To achieve this production, they have evolved large, water-laden bodies that increase prey contact rates. Although larger bodies are less efficient for swimming, optimization analysis reveals that large collectors are advantageous if they move through the water sufficiently slowly.

Major and trace element concentration of melt inclusions from Zhupanovsky volcano, Kamchatka

The paper presents data on naturally quenched melt inclusions in olivine (Fo 69-84) from Late Pleistocene pyroclastic rocks of Zhupanovsky volcano in the frontal zone of the Eastern Volcanic Belt of Kamchatka. The composition of the melt inclusions provides insight into the latest crystallization stages (~70% crystallization) of the parental melt (~46.4 wt % SiO2, ~2.5 wt % H2O, ~0.3 wt % S), which proceeded at decompression and started at a depth of approximately 10 km from the surface. The crystallization temperature was estimated at 1100 ± 20°C at an oxygen fugacity of deltaFMQ = 0.9-1.7. The melts evolved due to the simultaneous crystallization of olivine, plagioclase, pyroxene, chromite, and magnetite (Ol: Pl: Cpx : (Crt-Mt) ~ 13 : 54 : 24 : 4) along the tholeiite evolutionary trend and became progressively enriched in FeO, SiO2, Na2O, and K2O and depleted in MgO, CaO, and Al2O3. Melt crystallization was associated with the segregation of fluid rich in S-bearing compounds and, to a lesser extent, in H2O and Cl. The primary melt of Zhupanovsky volcano (whose composition was estimated from data on the most primitive melt inclusions) had a composition of low-Si (~45 wt % SiO2) picrobasalt (~14 wt % MgO), as is typical of parental melts in Kamchatka and other island arcs, and was different from MORB. This primary melt could be derived by ~8% melting of mantle peridotite of composition close to the MORB source, under pressures of 1.5 ± 0.2 GPa and temperatures 20-30°C lower than the solidus temperature of 'dry' peridotite (1230-1240°C). Melting was induced by the interaction of the hot peridotite with a hydrous component that was brought to the mantle from the subducted slab and was also responsible for the enrichment of the Zhupanovsky magmas in LREE, LILE, B, Cl, Th, U, and Pb. The hydrous component in the magma source of Zhupanovsky volcano was produced by the partial slab melting under water-saturated conditions at temperatures of 760-810°C and pressures of ~3.5 GPa. As the depth of the subducted slab beneath Kamchatkan volcanoes varies from 100 to 125 km, the composition of the hydrous component drastically changes from relatively low-temperature H2O-rich fluid to higher temperature H2O-bearing melt. The geothermal gradient at the surface of the slab within the depth range of 100-125 km beneath Kamchatka was estimated at 4°C/km.

Orthogonality relations for Chebyshev polynomials,

"C00-1469-0154."

The use of Chebyshev matrix polynomials in the iterative solution of linear equations compared to the method of successive overrelaxtion /

"(This is being submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, June 1959.)"

Old-time primitive Methodism in Canada, 1829-1884

Mode of access: Internet.

Primitive man in Michigan /

Descriptive letterpress on versos facing the plates.

India in primitive Christianity /

Rev. ed. of: The influence of Buddhism on primitive Christianity.

The Abelian equations of the tenth degree irreducible in a given domain of rationality,

Thesis (Ph. D.)--University of California, 1912.

The primitive inhabitants of Scandinavia...

Mode of access: Internet.

Histoire primitive des euskariens basques : langue, poésie, moeurs et caractère de ce peuple introduction a son histoire ancienne et moderne /

Mode of access: Internet.