Constructive Field Theory and Applications: Perspectives and Open Problems

In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the constructive methods well within the 21st century

On Automated Lemma Generation for Separation Logic with Inductive Definitions

Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas relating the inductive definitions. We propose a novel approach for generating these lemmas automatically which is based on simple syntactic criteria and deterministic strategies for applying them. Our approach focuses on iterative programs, although it can be applied to recursive programs as well, and specifications that describe not only the shape of the data structures, but also their content or their size. Empirically, we find that our approach is powerful enough to deal with sophisticated benchmarks, e.g., iterative procedures for searching, inserting, or deleting elements in sorted lists, binary search tress, red-black trees, and AVL trees, in a very efficient way

The synthesis structure and properties of segmented poly(urethane-urea-siloxanes)

Segmentirani poli(uretan-urea-siloksanski) kopolimeri (PUUS), na bazi 4,4'– metilendifenildiizocijanata (MDI) i etilendiamina (ED) kao komponeti tvrdog segmenta i α,ω–dihidroksipropil-poli(dimetilsiloksana) (PDMS, Мn = 1000 g mol-1) kao mekog segmenta, sintetisani su postupkom dvostepene poliadicije u rastvoru, uz kalaj-oktoat kao katalizator. Eksperimentalni uslovi za sintezu PUUS kopolimera su optimizovani variranjem temperature, odnosa korastvarača, koncentracije katalizatora, početne koncentracije monomera i vremena druge faze reakcije poliadicije. Za sintezu su korišćene dve različite smeše rastvarača: tetrahidrofuran/N,N-dimetilacetamid (THF/DMAc) i tetrahidrofuran/N-metilpirolidon (THF/NMP), pri konstantnom molarnom odnosu monomera (PDMS:MDI:ED=1:2:1). Pokazano je da polarnija THF/NMP smeša predstavlja bolju reakcionu sredinu za sintezu PUUS. Nađeno je da su optimalni reakcioni uslovi sledeći: temperatura 40 °C, koncentracija katalizatora 0,05 mol. % (u odnosu na PDMS), koncentracija monomera u reakcionoj smeši 25 mas. % i vreme druge faze reakcije 3 h, pri zapreminskom odnosu korastvarača THF/NMP=1:9. Serija PUUS kopolimera sa različitim sadržajem tvrdih segmenata sintetisana je pod optimalnim reakcionim uslovima, u THF/NMP smeši sa velikim udelom polarnog NMP rastvarača, što je omogućilo dobru rastvorljivost rastućih polimernih lanaca i dobijanje kopolimera relativno velike molarne mase. Molarni odnos PDMS-a, MDI-a i ED-a je variran od 1:2:1 do 1:6:5, što je odgovaralo promeni masenog udela tvrdih segmenata u kopolimerima od 36 do 64 mas. %. Struktura i sastav PUUS kopolimera su potvrđeni 1H NMR i FTIR spektroskopijom. Prosečna dužina sekvenci mekih i tvrdih segmenata, kao i raspodela sekvenci tvrdih segmenata u seriji PUUS kopolimera, dobijena je korišćenjem 13C NMR i dvodimenzionalne korelacione NMR spektroskopije. Kopolimeri sa manjim sadržajem tvrdih segmenata su imali nasumičnu raspodelu tvrdih i mekih segmenata duž kopolimernih lanaca, dok su se kopolimeri sa udelom tvrdih segmenata većim od 55 mas. % ponašali kao multiblok-kopolimeri. Detaljna analiza strukture je pokazala da se prosečna dužina sekvenci tvrdih urea segmenata povećavala od 2,2 do 4,9 sa povećanjem njihovog masenog udela od 38 do 65 mas. %. Na osnovu rezultata termičke i mehaničke analize, zatim analize rasipanja X-zraka na malim uglovima (SAXS), kao i FTIR analize vodoničnog vezivanja, utvrđeno je da sintetisani PUUS kopolimeri pokazuju mikrofazno razdvojenu strukturu i velike vrednosti zatezne čvrstoće. Globularne superstrukture, zapažene u filmovima uzoraka kopolimera pomoću skenirajuće elektronske mikroskopije (SEM) i mikroskopije atomskih sila (AFM), bile su posledica mikrostrukturne organizacije MDI–ED segmenata, zavisno od njihovog udela i dužine. Velike vrednosti početnih elastičnih modula i zatezne čvrstoće su bile posledica prisustva veoma jakih bidentatnih urea vodoničnih veza. PUUS kopolimeri su pokazali veliku otpornost na vodu, pri čemu se hidrofobnost i hrapavost njihove površine neznatno povećavala sa povećanjem masenog udela PDMS segmenta, što čini ove materijale pogodnim za potencijalnu biomedicinsku primenu...Segmented poly(urethane-urea-siloxane) copolymers (PUUS), based on 4,4′- methylenediphenyl diisocyanate (MDI) and ethylene diamine (ED) аs the hard segment components and α,ω-hydroxypropyl-poly(dimethylsiloxane) (PDMS, Mn= 1000 g mol-1) as the soft segment were prepared by a two-step polyaddition procedure in a solution in the presence of stannous octoate as a catalyst. The experimental conditions for the synthesis of PUUS copolymers were optimized by varying the temperature, the cosolvents ratio, the concentration of the catalyst, the initial monomer concentration and the time of the second step of the polyaddition reaction. Two different solvent mixtures: tetrahydrofuran/N,N-dimethylacetamide (THF/DMAc) and tetrahydrofuran/Nmethylpyrrolidone (THF/NMP) were used for the synthesis, at constant molar ratio of the monomers (PDMS:MDI:ED = 1:2:1). It was demonstrated that the more polar THF/NMP mixture was a better reaction medium for the synthesis of PUUSs. The following conditions were optimal: a temperature of 40 °C, a catalyst concentration of 0.05 mol % (calculated to PDMS), a monomer concentration in the reaction mixture of 25 wt. % and a reaction time for the second step of 3 h, at the co-solvent ratio of THF/NMP = 1:9. A series of PUUS copolymers with different hard segment content was synthesized under optimal reaction conditions, in THF/NMP mixture with a large proportion of polar NMP solvent, which provided good solubility of the growing chains, thus ensuring copolymers of relatively high molecular weight. The molar ratio of PDMS, MDI and ED was varied from 1:2:1 to 1:6:5, which resulted in the predetermined content of the hard segments from 36 to 64 wt. %. The structure and composition of the PUUSs were confirmed by 1H NMR and FTIR spectroscopy. The mean sequence length of the soft and hard segments, as well as the sequence distribution of the hard segments in the PUUS series, were obtained by 13C NMR and two-dimensional correlation spectroscopy. The copolymers with lower hard segment content were random, while the others with the hard segment content higher than ~ 55 wt. % were multi-block copolymers. Detailed structural analysis showed that the mean sequence length of the hard urea segments increased from 2.2 to 4.9 with increasing hard segments content from 38 to 65 wt. %. Thermal, mechanical, small-angle X-ray scattering (SAXS) and hydrogen bonding analyses by FTIR indicated the formation of the microphase-separated copolymers with high tensile strength. Globular superstructures observed in the copolymer films by scanning electron microscopy (SEM) and atomic force microscopy (AFM) were probably arisen from the microstructural organization of the MDI–ED segments, depending on their content and length. The high initial elastic modulus and high values of tensile strength of the PUUSs are the consequences of the presence of a very strong urea bidentate hydrogen bonding. The PUUS copolymers showed high water resistance, their surface became more hydrophobic and the values of the surface roughness slightly increased with increasing the weight fraction of the PDMS segment, which suggested a great promise for the possible use of PUUS copolymers in potential biomedical applications..

Strong, Ultra-narrow Peaks of Longitudinal and Hall Resistances in the Regime of Breakdown of the Quantum Hall Effect

With unusually slow and high-resolution sweeps of magnetic field, strong, ultra-narrow (width down to $100 {\rm \mu T}$) resistance peaks are observed in the regime of breakdown of the quantum Hall effect. The peaks are dependent on the directions and even the history of magnetic field sweeps, indicating the involvement of a very slow physical process. Such a process and the sharp peaks are, however, not predicted by existing theories. We also find a clear connection between the resistance peaks and nuclear spin polarization.Comment: 5 pages with 3 figures. To appear in PR

Effects of concomitant benzodiazepines and antidepressants long-term use on social decision-making: results from the ultimatum game

Benzodiazepines and antidepressants have been shown to change responses to unfairness; however, the effects of their combined use on unfairness evaluation are unknown. This study examines the effects of concomitant benzodiazepines and antidepressants long-term use on the evaluation of fair and unfair offers. To analyze behavioral changes on responses to unfairness, we compared the performance of medicated participants and healthy controls in the Ultimatum Game (UG), both in the proposer and in the respondent role. The results showed that long-term psychotropic users had the worse economic strategy by accepting less offers than control subjects. However, in the proposer role, the unfair offers made by participants were similar between groups. The present results suggest that long-term use of psychotropic medication, specifically the combination of benzodiazepines and antidepressants, may increase the sensitivity to unfairness, resulting in higher rejection rates in conditions where this strategy is the most disadvantageous

Frequency Scaling of Microwave Conductivity in the Integer Quantum Hall Effect Minima

We measure the longitudinal conductivity $\sigma_{xx}$ at frequencies $1.246 {\rm GHz} \le f \le 10.05$ GHz over a range of temperatures $235 {\rm mK} \le T \le 4.2$ K with particular emphasis on the Quantum Hall plateaus. We find that $Re(\sigma_{xx})$ scales linearly with frequency for a range of magnetic field around the center of the plateaus, i.e. where $\sigma_{xx}(\omega) \gg \sigma_{xx}^{DC}$. The width of this scaling region decreases with higher temperature and vanishes by 1.2 K altogether. Comparison between localization length determined from $\sigma_{xx}(\omega)$ and DC measurements on the same wafer show good agreement.Comment: latex 4 pages, 4 figure

Absence of Scaling in the Integer Quantum Hall Effect

We have studied the conductivity peak in the transition region between the two lowest integer Quantum Hall states using transmission measurements of edge magnetoplasmons. The width of the transition region is found to increase linearly with frequency but remains finite when extrapolated to zero frequency and temperature. Contrary to prevalent theoretical pictures, our data does not show the scaling characteristics of critical phenomena.These results suggest that a different mechanism governs the transition in our experiment.Comment: Minor changes and new references include

Self-consistent local-equilibrium model for density profile and distribution of dissipative currents in a Hall bar under strong magnetic fields

Recent spatially resolved measurements of the electrostatic-potential variation across a Hall bar in strong magnetic fields, which revealed a clear correlation between current-carrying strips and incompressible strips expected near the edges of the Hall bar, cannot be understood on the basis of existing equilibrium theories. To explain these experiments, we generalize the Thomas-Fermi--Poisson approach for the self-consistent calculation of electrostatic potential and electron density in {\em total} thermal equilibrium to a {\em local equilibrium} theory that allows to treat finite gradients of the electrochemical potential as driving forces of currents in the presence of dissipation. A conventional conductivity model with small values of the longitudinal conductivity for integer values of the (local) Landau-level filling factor shows that, in apparent agreement with experiment, the current density is localized near incompressible strips, whose location and width in turn depend on the applied current.Comment: 9 pages, 7 figure