Gradings on classical Lie algebras via sesquilinear forms over graded-division algebras

Charla sobre graduaciones en álgebras de Lie.En esta charla de aproximadamente una hora el profesor Dr. Mikhail V. Kochetov nos introduce en las últimas técnicas usadas para clasificar graduaciones sobre ciertas álgebras de Lie clásicas. Técnicas usadas en su monografía sobre álgebras de Lie graduadas, trabajo conjunto con el profesor Dr. Alberto Elduque catedrático en la Universidad de Zaragoza.DepartamentoÁlgebra, Geometría y Topología Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

On the extra phase correction to the semiclassical spin coherent-state propagator

The problem of an origin of the Solary-Kochetov extra-phase contribution to the naive semiclassical form of a generalized phase-space propagator is addressed with the special reference to the su(2) spin case which is the most important in applications. While the extra-phase correction to a flat phase-space propagator can straightforwardly be shown to appear as a difference between the principal and the Weyl symbols of a Hamiltonian in the next-to-leading order expansion in the semiclassical parameter, the same statement for the semiclassical spin coherent-state propagator holds provided the Holstein-Primakoff representation of the su(2) algebra generators is employed.Comment: 19 pages, no figures; a more general treatment is presented, some references are added, title is slightly changed; submitted to JM

Coupling electromagnetic pulse-shaped waves into wire-like interconnection structures with a non-linear protection – Time domain calculations by the PEEC method

An interconnection system whose loads protected by a voltage suppressor and a low-pass filter against overvoltages caused by coupling pulse-shaped electromagnetic waves is analyzed. The external wave influencing the system is assumed as a plane wave with HPM form. The computation is provided by a full-wave PEEC model for the interconnection structure incorporated in the SPICE code. Thus, nonlinear elements of the protection circuit can be included in the calculation. The analysis shows intermodulation distortions and penetrations of low frequency interferences caused by intermodulations through the protection circuits. The example examined shows the necessity of using full-wave models for interconnections together with non-linear circuit solvers for simulation of noise immunity in systems protected by nonlinear devices

Clarification Of Aqueous Suspensions With A High Content Of Suspended Solids In Rapid Sand Filters

The presented work is devoted to solving the actual problem of increasing the efficiency of rapid sand filters with granular filling, which operate at a constant filtration rate when cleaning suspensions with a relatively high concentration of contaminants. The proposed mathematical model for clarifying the suspension by filtration consists of three interconnected blocks: clarified, filtration, and hydraulic. Convenient dimensionless mathematical dependencies are obtained for calculating the concentrations of contaminants and sediment from the height of the filter and suspension in the filtrate; head loss in the filter loading; the effective time of the filter (the duration of the filter cycle). The design of the experimental setup and the methodology for conducting experimental studies and mathematical processing of the results are valid. The results of experimental studies of the suspension filtering process through the granular loading are presented, and the obtained data is analyzed. Measurement of pressure losses in the filter loading is performed when a suspension is passed with a relatively high concentration of contaminants at various filtration rates. The nature of the change in the filtration rate with time and height (length) loading at various filtration rates and initial contamination concentrations is determined. Measured variable concentration of suspended matter in filtered water and retained contamination over time. As a result of the experiments, it is confirmed that an increase in the concentration of retained contaminants S leads to an increase in the parameter Δn/n. Upon reaching a certain value of the concentration of the retained sediment S (in our case S=30 g/dm3), an increase in the relative specific volume of the sediment greater than Δn/n0=0.65 is not observed. It is established that an important characteristic of the retained sediment is the ratio of the volume concentration of the sediment to the volume concentration of solid particles in this sediment γ=Csd/Сs. The values of the adhesion and detachment of particles of contaminant in the particles of the material loading =4,9; =0,009. The results of experimental studies in general confirm the correctness and reliability of the obtained analytical dependencies

Electronic properties of disclinated flexible membrane beyond the inextensional limit: Application to graphene

Gauge-theory approach to describe Dirac fermions on a disclinated flexible membrane beyond the inextensional limit is formulated. The elastic membrane is considered as an embedding of 2D surface into R^3. The disclination is incorporated through an SO(2) gauge vortex located at the origin, which results in a metric with a conical singularity. A smoothing of the conical singularity is accounted for by replacing a disclinated rigid plane membrane with a hyperboloid of near-zero curvature pierced at the tip by the SO(2) vortex. The embedding parameters are chosen to match the solution to the von Karman equations. A homogeneous part of that solution is shown to stabilize the theory. The modification of the Landau states and density of electronic states of the graphene membrane due to elasticity is discussed.Comment: 15 pages, Journal of Physics:Condensed Matter in pres

Doped carrier formulation of the t-J model: the projection constraint and the effective Kondo-Heisenberg lattice representation

We show that the recently proposed doped carrier Hamiltonian formulation of the t-J model should be complemented with the constraint that projects out the unphysical states. With this new important ingredient, the previously used and seemingly different spin-fermion representations of the t-J model are shown to be gauge related to each other. This new constraint can be treated in a controlled way close to half-filling suggesting that the doped carrier representation provides an appropriate theoretical framework to address the t-J model in this region. This constraint also suggests that the t-J model can be mapped onto a Kondo-Heisenberg lattice model. Such a mapping highlights important physical similarities between the quasi two-dimensional heavy fermions and the high-T$_c$ superconductors. Finally we discuss the physical implications of our model representation relating in particular the small versus large Fermi surface crossover to the closure of the lattice spin gap.Comment: corrected and enlarged versio

Transgenic plants as genetic models for studying functions of plant genes

Transgenic plants are widely used for the investigation of functions of particular genes as well as for reconstruction of complex gene networks controlling plant morphology, biochemistry, and physiology during different development stages and in response to various external stimuli. Gene engineering instruments for the design of transgenic plants with either elevated or suppressed expression of target genes are discussed. Genetic constructs for protein synthesis or antisense RNA/self-complementary double-stranded RNA transcription are described. Transgenic plants with elevated or decreased levels of expression of S-like ribonucleases and decreased expression of the proline dehydrogenase gene are considered as examples. It was believed that S-like RNase functions concern mainly phosphate remobilization from senescent organs. However, expression patterns of some genes coding for S-like RNases were similar to some pathogen-responsive genes (both local and systemic induction after wounding or pathogen inoculation). In addition, some pathogenesis-related proteins (PR-4 family) possess RNase activity and can inhibit growth of pathogenic fungi. Investigation of transgenic plants revealed that high ribonuclease activity in apoplast correlated with increased resistance against tobacco mosaic virus. Thus, S-like RNases may have a new function as a part of the plant basal antiviral defense mechanism. Another set of transgenic plants bears an antisense suppressor of the proline dehydrogenase gene (PDH) constructed with an Arabidopsis target gene segment. Tobacco, maize and sunflower plants with this heterologous suppressor were characterized with a moderate decrease in PDH activity and a mild (1.5–3-fold) increase in the proline content under normal conditions. It was also found that these plants were more tolerant to various abiotic stresses (drought, NaCl, cold, toxic heavy metals), which may result from the protective proline effect early in exposure to stress, preventing the cellular gene expression machinery from damage by stress-generated free radicals

Dirac fermions on a disclinated flexible surface

A self-consisting gauge-theory approach to describe Dirac fermions on flexible surfaces with a disclination is formulated. The elastic surfaces are considered as embeddings into R^3 and a disclination is incorporated through a topologically nontrivial gauge field of the local SO(3) group which generates the metric with conical singularity. A smoothing of the conical singularity on flexible surfaces is naturally accounted for by regarding the upper half of two-sheet hyperboloid as an elasticity-induced embedding. The availability of the zero-mode solution to the Dirac equation is analyzed.Comment: 6 page