THE ROLE OF REASON IN PLATO’S PHILOSOPHY

The world of the Platonic teaching is a realm of changelessness for a heart saddened by the spectacle of inevitable change. It is order for a mind perturbed by a nightmare of endless chaos. It is the cosmos of reason, of which one may have a glimpse in anything of beauty ... It is the pattern which the mind of man may come to know ... (Edman 1927: xxxviii

Remnant superfluid collective phase oscillations in the normal state of systems with resonant pairing

The signature of superfluidity in bosonic systems is a sound wave-like spectrum of the single particle excitations which in the case of strong interactions is roughly temperature independent. In fermionic systems, where fermion pairing arises as a resonance phenomenon between free fermions and paired fermionic states (examples are: the atomic gases of lithium or potassium controlled by a Feshbach resonance, polaronic systems in the intermediary coupling regime, d-wave hole pairing in the strongly correlated Hubbard system), remnants of such superfluid characteristics are expected to be visible in the normal state. The single particle excitations maintain there a sound wave like structure for wave vectors above a certain q_{min}(T) where they practically coincide there with the spectrum of the superfluid phase for T<T_{c}. Upon approaching the transition from above this region in q-space extends down to small momenta, except for a narrow region around q=0 where such modes change into damped free particleComment: 5 pages, 3 figures; to appear in Phys Rev

Interplay between pairing and correlations in spin-polarized bound states

We investigate the single and multiple defects embedded in a superconducting host, studying interplay between the proximity induced pairing and interactions. We explore influence of the spin-orbit coupling on energies, polarization and spatial patterns of the bound (Yu-Shiba-Rusinov) states of magnetic impurities in 2-dimensional square lattice. We also address the peculiar bound states in the proximitized Rashba chain, resembling the Majorana quasiparticles, focusing on their magnetic polarization which has been recently reported by S. Jeon et al., [Science 358, 772 (2017)]. Finally, we study leakage of these polarized Majorana quasiparticles on the side-attached nanoscopic regions and confront them with the subgap Kondo effect near to the singlet-doublet phase transition.Comment: 10 pages, 9 figure

Extension and splitting theorems for Fréchet spaces of type 2

Sin resume

WHY OUGHT WE TO OBEY THE LAW? PLATO'S STARTLING ANSWER

Picture this scenario. Criminal charges have been brought against you. You are tried, convicted, and sentenced to death. (Mercifully, this could not happen in present-day South Africa.) While you have been given a procedurally fair trial, the charges brought against you and your conviction are substantively unjust. You are now in prison. Two days hence you are to die. What is your state of mind? Calm? Agitated? Depressed? Now suppose a friend arrives to visit you. He tells you that plans have been made for your escape, that your warder can easily be bribed, and that a car is waiting outside to whisk you away to a safe and secret destination. How do you react? Rejoice and run? Stay put and face the prospect of death? Most people in such a situation, we may agree, would escape without hesitation

Rating of Mixed Split Residential Air Conditioners

A methodology is presented for rating the performance of mixed, split residential air conditioners. The method accounts for the impact on system performance of the indoor evaporator, expansion device and fan; three major components that are likely to be substituted for the matched components in a mixed system. The method allows calculation of capacity at 95°F rating point and seasonal energy efficiency ratio, SEER, without performing laboratory test of the complete system. Limitations of the procedure, present work, and anticipated improvements are also discussed

Simple theory of extremely overdoped HTS

We demonstrate the existence of a simple physical picture of superconductivity for extremely overdoped CuO2 planes. It possesses all characteristic features of HTS, such as a high superconducting transition temperature, the $d_{x^2 - y^2}$ symmetry of order parameter, and the coexistence of a single electron Fermi surface and a pseudogap in the normal state. Values of pseudogap are calculated for different doping levels. An orbital paramagnetism of preformed pairs is predicted.Comment: 7 pages, 1 figur