Poisson trace orders

The two main approaches to the study of irreducible representations of orders (via traces and Poisson orders) have so far been applied in a completely independent fashion. We define and study a natural compatibility relation between the two approaches leading to the notion of Poisson trace orders. It is proved that all regular and reduced traces are always compatible with any Poisson order structure. The modified discriminant ideals of all Poisson trace orders are proved to be Poisson ideals and the zero loci of discriminant ideals are shown to be unions of symplectic cores, under natural assumptions (maximal orders and Cayley--Hamilton algebras). A base change theorem for Poisson trace orders is proved. A broad range of Poisson trace orders are constructed based on the proved theorems: quantized universal enveloping algebras, quantum Schubert cell algebras and quantum function algebras at roots of unity, symplectic reflection algebras, 3 and 4-dimensional Sklyanin algebras, Drinfeld doubles of pre-Nichols algebras of diagonal type, and root of unity quantum cluster algebras.Comment: 24 page

Weak splittings of quotients of Drinfeld and Heisenberg doubles

We investigate the fine structure of the simplectic foliations of Poisson homogeneous spaces. Two general results are proved for weak splittings of surjective Poisson submersions from Heisenberg and Drinfeld doubles. The implications of these results are that the torus orbits of symplectic leaves of the quotients can be explicitly realized as Poisson-Dirac submanifolds of the torus orbits of the doubles. The results have a wide range of applications to many families of real and complex Poisson structures on flag varieties. Their torus orbits of leaves recover important families of varieties such as the open Richardson varieties.Comment: 20 pages, AMS Late

AC Conductance in Dense Array of the Ge0.7_{0.7}Si0.3_{0.3} Quantum Dots in Si

Complex AC-conductance, $\sigma^{AC}$, in the systems with dense Ge$_{0.7}$Si$_{0.3}$ quantum dot (QD) arrays in Si has been determined from simultaneous measurements of attenuation, $\Delta\Gamma=\Gamma(H)-\Gamma(0)$, and velocity, $\Delta V /V=(V(H)-V(0)) / V(0)$, of surface acoustic waves (SAW) with frequencies $f$ = 30-300 MHz as functions of transverse magnetic field $H \leq$ 18 T in the temperature range $T$ = 1-20 K. It has been shown that in the sample with dopant (B) concentration 8.2$\times 10^{11}$ cm$^{-2}$ at temperatures $T \leq$4 K the AC conductivity is dominated by hopping between states localized in different QDs. The observed power-law temperature dependence, $\sigma_1(H=0)\propto T^{2.4}$, and weak frequency dependence, $\sigma_1(H=0)\propto \omega^0$, of the AC conductivity are consistent with predictions of the two-site model for AC hopping conductivity for the case of $\omega \tau_0 \gg$1, where $\omega=2\pi f$ is the SAW angular frequency and $\tau_0$ is the typical population relaxation time. At $T >$ 7 K the AC conductivity is due to thermal activation of the carriers (holes) to the mobility edge. In intermediate temperature region 4$< T<$ 7 K, where AC conductivity is due to a combination of hops between QDs and diffusion on the mobility edge, one succeeded to separate both contributions. Temperature dependence of hopping contribution to the conductivity above $T^*\sim$ 4.5 K saturates, evidencing crossover to the regime where $\omega \tau_0 <$1. From crossover condition, $\omega \tau_0(T^*)$ = 1, the typical value, $\tau_0$, of the relaxation time has been determined.Comment: revtex, 3 pages, 6 figure

Density of States and Conductivity of Granular Metal or Array of Quantum Dots

The conductivity of a granular metal or an array of quantum dots usually has the temperature dependence associated with variable range hopping within the soft Coulomb gap of density of states. This is difficult to explain because neutral dots have a hard charging gap at the Fermi level. We show that uncontrolled or intentional doping of the insulator around dots by donors leads to random charging of dots and finite bare density of states at the Fermi level. Then Coulomb interactions between electrons of distant dots results in the a soft Coulomb gap. We show that in a sparse array of dots the bare density of states oscillates as a function of concentration of donors and causes periodic changes in the temperature dependence of conductivity. In a dense array of dots the bare density of states is totally smeared if there are several donors per dot in the insulator.Comment: 13 pages, 15 figures. Some misprints are fixed. Some figures are dropped. Some small changes are given to improve the organizatio

Ge quantum dot arrays grown by ultrahigh vacuum molecular beam epitaxy on the Si(001) surface: nucleation, morphology and CMOS compatibility

Issues of morphology, nucleation and growth of Ge cluster arrays deposited by ultrahigh vacuum molecular beam epitaxy on the Si(001) surface are considered. Difference in nucleation of quantum dots during Ge deposition at low (<600 deg C) and high (>600 deg. C) temperatures is studied by high resolution scanning tunneling microscopy. The atomic models of growth of both species of Ge huts---pyramids and wedges---are proposed. The growth cycle of Ge QD arrays at low temperatures is explored. A problem of lowering of the array formation temperature is discussed with the focus on CMOS compatibility of the entire process; a special attention is paid upon approaches to reduction of treatment temperature during the Si(001) surface pre-growth cleaning, which is at once a key and the highest-temperature phase of the Ge/Si(001) quantum dot dense array formation process. The temperature of the Si clean surface preparation, the final high-temperature step of which is, as a rule, carried out directly in the MBE chamber just before the structure deposition, determines the compatibility of formation process of Ge-QD-array based devices with the CMOS manufacturing cycle. Silicon surface hydrogenation at the final stage of its wet chemical etching during the preliminary cleaning is proposed as a possible way of efficient reduction of the Si wafer pre-growth annealing temperature.Comment: 30 pages, 11 figure

Metastable tert-butylcalix[6]arene with unusually large tunable free volume for non-threshold enclathration of volatiles

A metastable material with tunable free volume of molecular size, vapor sorption properties of a porous sorbent and variable thermal stability was prepared from tert-butylcalix[6]arene. © 2008 The Royal Society of Chemistry

Syntopy of Pulmonary Vein Orifices in the Left Atrium of the Human Heart

INTRODUCTION: The syntopy of the left atrial (LA) structures is the least studied aspect of the normal heart anatomy. The morphometric data on the position of orifices of the pulmonary veins in the LA walls relative to the adjacent heart structures and heart vessels are important as reference parameters of heart morphology and are needed in the endovascular treatment of atrial fibrillations. AIM: To establish the general patterns and topospecific peculiarities of the location of the pulmonary vein orifices relative to the oval fossa and orifices of the venae cavae using morphometric methods of anatomical preparations of conventionally normal adult human heart. MATERIALS AND METHODS: Fifty–four wet anatomical preparations of the heart without macroscopic signs of hemodynamically significant cardiac pathology were studied. The preparations were obtained from patients aged 35–89 years who died from diseases not related to heart pathology. LA diastole was modeled by filling its cavity with silicone; after it hardened, the distances from the oval fossa and orifices of the venae cavae to the orifices of the pulmonary veins were measured using sliding calipers. RESULTS: The article presents variation, medians, and extreme values of distances from the oval fossa and orifices of the venae cavae to the orifices of the pulmonary veins at the site of their opening to LA. The significance of differences of morphometric parameters of the topography was evaluated, and their correlation and one–way regression analyses were implemented. The strongest regression dependence was found for LA width and distance from the orifice of the superior vena cava to the orifice of the left inferior pulmonary vein (Y) r2 = 0.45; Х = 19.94 + 0.545Y). The heart dimensions and LA length were not significant predictors for the studied parameters. CONCLUSION: The right pulmonary veins were located expectedly closer to the orifices of the venae cavae and the oval fossa than the left pulmonary veins. The narrowest was the space between the orifices of the superior vena cava and the right superior pulmonary vein. The farthest from the orifices of both venae cavae was the orifice of the left inferior pulmonary artery. The strongest correlation relationships were characteristic of the distances from the orifices of both venae cavae to the orifices of the homolateral pulmonary veins, which we propose to consider as one of the criteria of the harmoniousness of the structure of the atrial complex. © Authors, 2022

Organization of Repair of Locomotives on the Data of Moni-toring Their Technical Condition

The article discusses the structure of the organization of current repairs of modern locomotives equipped with microprocessor control and diagnostic systems. Based on these sys-tems, remote monitoring of the technical condition of locomotive units has been implemented. The block diagram of the recommendatory nature of the organization of current repairs using diagnostic information is presented. The above algorithm allows predicting the residual life by any of the studied parameters, thereby determining the mileage at the moment of which a fail-ure occurs on some parameter. This gives a huge advantage in preventing incidents, as well as in the long-term planning of repair work on wheel turning and rolling, based on the remaining life. Thus, the well-coordinated organization of current repairs using diagnostic information, allows operational methods to eliminate the faults of the nodes. A recommender structure in the form of a single integrated system for organizing repair cycles will allow establishing links between the involved repair personnel in the form of electronic terminals for notification of the actual technical condition of the locomotive. A program has been developed for calculating the residual mileage of wheel sets for the corresponding types of defects, which also allows long-term planning for turning and rolling of wheel-motor blocks wheelsets, as well as to regulate the overhaul runs of a locomotive. © Published under licence by IOP Publishing Ltd

Effect of the size of calixarene macrocycle on the thermodynamic parameters of formation of inclusion compounds in guest vapor - Solid host systems

The influence of the calixarene macrocycle size on the thermodynamic parameters of inclusion formation in organic guest vapor - solid host systems was studied in the series of tert-butylcalix[4]arene (1), tert-butylcalix[6] arene (2), and tert-butylcalix[8]arene (3). For this purpose, sorption isotherms of a guest vapor by a solid host were determined using the static method of headspace GC analysis for the systems involving calixarenes 2 and 3 in addition to the earlier obtained data for calixarene 1. Besides, the stoichiometry and decomposition temperatures of saturated clathrates formed in these systems were determined using thermogravimetry. The compositions of some of these clathrates differ substantially from those of clathrates crystallized from a host solution in a liquid guest. For the most guests studied with the thermodynamic activity below 0.6, their uptake by calixarenes 1 - 3 changes in the series 2 < 1 < 3. As a whole, the trend for each particular parameter of clathrates of hosts 1 - 3 (stoichiometry, guest activity at 50% saturation of the host) with increasing the size of the calixarene macrocycle is specific for each guest studied. The results obtained are useful for the estimation of receptor properties of calixarenes in quartz microbalance sensors

Cluster structures on quantum coordinate rings

We show that the quantum coordinate ring of the unipotent subgroup N(w) of a symmetric Kac-Moody group G associated with a Weyl group element w has the structure of a quantum cluster algebra. This quantum cluster structure arises naturally from a subcategory C_w of the module category of the corresponding preprojective algebra. An important ingredient of the proof is a system of quantum determinantal identities which can be viewed as a q-analogue of a T-system. In case G is a simple algebraic group of type A, D, E, we deduce from these results that the quantum coordinate ring of an open cell of a partial flag variety attached to G also has a cluster structure.Comment: v2: minor corrections. v3: references updated, final version to appear in Selecta Mathematic