From Plato's Rational Diameter to Proclus' Elegant Theorem

A novel interpretation of a single sentence in Proclus' Commentary to Plato's "Republic" suggests a virtually algebraic rigorous derivation of an infinite sequence of pairs of side and diameter numbers.Comment: 21 pages, 1 figure -- minor changes added 12/30/202

Bessarion on Economics and Geopolitics

This paper deals with those aspects of Byzantine intellectual heritage, which belong to the Bessarion’s thought and writing. Bessarion, Cardinal of the Roman-Catholic Church, proposed specific, systematic and analytical measures for a re-organization and recovery of the Despotate of Mistra, while, as it is known, he lived there from the end of 1431 until the end of 1436. Then Вessarion, in his capacity as cardinal, showed his continual and undiminished interest to the advancement of Greek nation, as proven by three famous memoranda of scholar. These are appeals to Constantine Palaiologos, Despot of Mistra, as well as to the doge of Venice. Dated July 13, 1453 the letter to the doge informed him on the Fall of Constantinople and the sufferings of Greek nation! Especially noteworthy is the third (and only surviving) letter of Вessarion, addressed to his friend, Despot Constantine Palaiologos in the spring of 1444. Here Вessarion proposes a specific, specialized program for the economic restructure, social reorganization and military strengthening of the Despotate. The intellectual associates education with economy. Sharing the economic philosophy of ancient Greeks on self-sufficiency and utilization of local means, Вessarion became a forerunner of mercantilism, while also acknowledging the productive contribution of education. The proposal of Вessarion for the transfer of the Despotate’s capital closer to the Isthmus was of great geopolitical importance since, when the guarding of the Hexamilion Wall would be reconstructed and constant and properly updated. These proposals, having been so important for the evolution of Byzantine economic thought, took an appropriate place in its development

On technological change and stage evolution in the works of Seneca and Adam Smith

The present paper investigates the links that connect Seneca and Adam Smith in relation to the concept of the technological change and the evolution of society. The Roman philosopher and jurist discusses extensively the technical achievements in various factors of production which are an outcome of the division of labour. The main question concerning the fact, if all inventions stem originally from the cogitations of philosophers, or, the common workman is exposed to the manufacturing process in his daily tasks appears also in Adam Smith's thought. The analysis shows Smith's classical roots and the significance of the Roman literature

An entertaining tale of quadrupeds - translation and commentary

A1 - Research Book

Gas-Phase Reactivity Studies of Small Molybdenum Cluster Ions with Dimethyl Disulfide

Molybdenum sulfide is a potent hydrogen evolution catalyst, and is discussed as a replacement of platinum in large-scale electrochemical hydrogen production. To learn more about the elementary steps of MoS2 production by sputtering in the presence of dimethyl disulfide (DMDS), the reactions of Mox+, x=1-3, with DMDS are studied by Fourier transform ion cyclotron resonance mass spectrometry and density functional theory calculations. A rich variety of products composed of molybdenum, sulfur, carbon and hydrogen was observed. MoxSy+ species are formed in the first reaction step, together with products containing carbon and hydrogen. The calculations indicate that the strong Mo-S bonds are formed preferentially, followed by Mo-C bonds. Hydrogen is exclusively bound to carbon atoms, i.e. no insertion of a molybdenum atom into a C-H bond is observed. The reactions are efficient and highly exothermic, explaining the rich chemistry observed in the experiment.(VLID)461980

Structural properties of gas-phase molybdenum oxide clusters [Mo4O13]2-, [HMo4O13]-, and [CH3Mo4O13]- studied by collision-induced dissociation

Molybdenum oxide-based catalysts are widely used for the ammoxidation of toluene, methanation of CO, or hydrodeoxygenation. As a first step towards a gas-phase model system, we investigate here structural properties of mass-selected [Mo4O13]2-, [HMo4O13]-, and [CH3Mo4O13]- by a combination of collision-induced dissociation (CID) experiments and quantum chemical calculations. According to calculations, the common structural motif is an eight-membered ring composed of four MoO2 units and four O atoms. The 13th O atom is located above the center of the ring and connects two to four Mo centers. For [Mo4O13]2- and [HMo4O13]-, dissociation requires opening or rearrangement of the ring structure, which is quite facile for the doubly charged [Mo4O13]2-, but energetically more demanding for [HMo4O13]-. In the latter case, the hydrogen atom is found to stay preferentially with the negatively charged fragments [HMo2O7]- or [HMoO4]-. The doubly charged species [Mo4O13]2- loses one MoO3 unit at low energies while Coulomb explosion into the complementary fragments [Mo2O6]- and [Mo2O7]- dominates at elevated collision energies. [CH3Mo4O13]- affords rearrangements of the methyl group with low barriers, preferentially eliminating formaldehyde, while the ring structure remains intact. [CH3Mo4O13]- also reacts efficiently with water, leading to methanol or formaldehyde elimination.(VLID)4795195Version of recor