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We study the interaction between the block decompositions of reduced enveloping algebras in positive characteristic, the Poincaré-Birkhoff-Witt (PBW) filtration, and the nilpotent cone. We provide two natural versions of the PBW filtration on the block subalgebra A λ of the restricted universal enveloping algebra χ () and show these are dual to each other. We also consider a shifted PBW filtration for which we relate the associated graded algebra to the algebra of functions on the Frobenius neighborhood of 0 in the nilpotent cone and the coinvariants algebra corresponding to λ. In the case of = 2 (k) in characteristic p > 2 we determine the associated graded algebras of these filtrations on block subalgebras of 0 ( 2). We also apply this to determine the structure of the adjoint representation of 0 ( 2). [ABSTRACT FROM AUTHOR]

Abstract We provide a construction of Saito primitive forms for Gepner singularity by studying the relation between Saito primitive forms for Gepner singularities and primitive forms for singularities of the form F k , n = ∑ i = 1 n x i k invariant under the natural S n -action. [ABSTRACT FROM AUTHOR]

ABSTRACT: Borehole guided waves that are excited by explosive sources outside of the borehole are important for interpreting borehole seismic surveys and for rock property inversion workflows. Borehole seismograms are typically modelled using numerical methods of wave propagation. In order to benchmark such numerical algorithms and partially to interpret the results of modelling, an analytical methodology is presented here to compute synthetic seismograms. The specific setup is a wavefield emanating from a monopole point source embedded within a homogeneous elastic medium that interacts with a fluid‐filled borehole and a free surface. The methodology assumes that the wavelength of the seismic signal is much larger than the borehole radius. In this paper, it is supposed that there is no poroelastic coupling between the formation and the borehole. The total wavefield solution consists of P, PP, and PS body waves; the surface Rayleigh wave; and the low‐frequency guided Stoneley wave (often referred as the tube wave) within the borehole. In its turn, the tube wave consists of the partial responses generated by the incident P‐wave and the reflected PP and PS body waves at the borehole mouth and by the Rayleigh wave, as well as the Stoneley wave eigenmode. The Mach tube wave, which is a conic tube wave, additionally appears in the Mach cone in a slow formation with the tube‐wave velocity greater than the shear one. The conditions of appearance of the Mach wave in a slow formation are formulated. It is shown that the amplitude of the Mach tube wave strongly depends on Poisson's ratio of the slow surrounding formation. The amplitude of the Mach tube wave exponentially decreases when the source depth grows for weakly compressible elastic media with Poisson's ratio close to 0.5 (i.e., saturated clays and saturated clay soils). Asymptotic expressions are also provided to compute the wavefield amplitudes for different combinations of source depth and source‐well offset. These expressions allow an approximate solution of the wavefield to be computed much faster (within several seconds) than directly computing the implicit integrals arising from the analytical formulation. [ABSTRACT FROM AUTHOR]

We prove that a pair of singularities related by a transformation arising from the McKay correspondence are orbifold equivalent. From this we deduce a McKay type category equivalence for the matrix factorization categories. [ABSTRACT FROM AUTHOR]

Sb is a three-dimensional Peierls insulator. The Peierls instability gives rise to doubling of the translational period along the [111] direction and alternating van der Waals and covalent bonding between (111) atomic planes. At the (111) surface of Sb, the Peierls condition is violated, which in theory can give rise to properties differing from the bulk. The atomic and electronic structure of the (111) surface of Sb have been simulated by density functional theory calculations. We have considered the two possible (111) surfaces, containing van der Waals dangling bonds or containing covalent dangling bonds. In the models, the surfaces are infinite and the structure is defect free. Structural optimization of the model containing covalent dangling bonds results in strong deformation, which is well described by a topological soliton within the Su–Schrieffer–Heeger model centered about 25 Å below the surface. The electronic states associated with the soliton see an increase in the density of states (DOS) at the Fermi level by around an order of magnitude at the soliton center. Scanning tunneling microscopy and spectroscopy (STM/STS) measurements reveal two distinct surface regions, indicating that there are different surface regions cleaving van der Waals and covalent bonds. The DFT is in good agreement with the STM/STS experiments. [ABSTRACT FROM AUTHOR]

ABSTRACT The dynamic response of a semi-infinite fluid-filled borehole embedded in an elastic half-space under a concentrated normal surface load is analysed in the long-wavelength limit. The solution of the problem is obtained with integral transforms in the form of a double integral with respect to the slowness and frequency. The partial P- and SV -wave responses are further transformed to path integrals along Cagniard paths in the complex slowness plane. Unlike the traditional Cagniard-de Hoop technique based on the Laplace transform of time dependence, this paper is based on the Fourier transform. The tube-wave response is presented as a causal integral over a slowness range. The resultant representation in the time-domain is suitable for the numerical evaluation of the complete response in the fluid-filled borehole, especially at large distances. Asymptotic analysis of seismic phases arising in the borehole is performed on the basis of the obtained solution. The complete asymptotic wavefield consists in P - and SV -waves, the Rayleigh wave and the low-frequency Stoneley (tube) wave. Pressure synthetics obtained by the use of the asymptotic formulas are shown to be in good agreement with straightforward calculations. [ABSTRACT FROM AUTHOR]

For a polynomial f = x 1 n + ... + x N n let G f be the non–abelian maximal group of symmetries of f. This is a group generated by all g ∈ GL (N , C) , rescaling and permuting the variables, so that f (x) = f (g ⋅ x). For any G ⊆ G f we compute explicitly Hochschild cohomology of the category of G –equivariant matrix factorizations of f. We introduce the pairing on it showing that it is a Frobenius algebra. [ABSTRACT FROM AUTHOR]

This study investigates the generation of the low-frequency borehole Stoneley wave (tube wave) by a plane P-wave propagating through the surrounding elastic formation, which is intersected by a fluid-filled fracture. A model is constructed taking into account the dynamic fluid coupling between the borehole interior and the fluid-filled fracture of infinite extent with parallel walls. The basic mechanism of such coupling is due to the contraction of the fracture walls by the incident P-wave, leading to seismic radiation into the fracture. The dynamic fluid flux from the fracture into the borehole interior, and vice versa, is the source of the low-frequency Stoneley wave. An expression for the monopole pressure source, exciting the tube wave, is obtained. The tube-wave equation in the long-wave approximation is derived in the presence of a fluid-filled fracture of infinite extent. Amplitudes and waveforms of Stoneley waves are analysed in the seismic wavelength range for P-wave pulses of various shapes. It is shown that the amplitude and waveform of the Stoneley wave depends significantly on the two dimensionless parameters of the problem: (1) the ratio of the borehole radius to the dominant wavelength of the incident pulse; (2) the ratio of the fracture width to the borehole radius. It is found that the amplitude of the generated Stoneley wave can be of the order of the P-wave amplitude in the borehole fluid. Stoneley waveforms are found to be completely different from those of the incident pulse. [ABSTRACT FROM AUTHOR]

• Fracture of W[100] micro constriction occurs at 10 GPa close to theoretical strength. • Deformation of etched micro constriction is realized by non-dislocation mechanism. • Deformation of the constriction occurs in accordance with Nabarro-Herring mechanism. • Fracture of a perfect constriction resulted in formation of a flat area at a tip apex. • This W tip was used as a base for creation of a spin-sensitive Fe 3 O 4 -W(100) STM probe. Fracturing microscale constrictions in metallic wires, such as tungsten, platinum, or platinum-iridium, is a common fabrication method used to produce atomically sharp tips for scanning tunneling microscopy (STM), field-emission microscopy and field ion microscopy. Typically, a commercial polycrystalline drawn wire is locally thinned and then fractured by means of a dislocation slip inside the constriction. We examine a special case where a dislocation-free microscale constriction is created and fractured in a single crystal tungsten rod with a long side parallel to the [100] direction. In the absence of dislocations, vacancies become the main defects in the constriction which breaks under the tensile stress of approximately 10 GPa, which is close to the theoretical fracture strength for an ideal monocrystalline tungsten. We propose that the vacancies are removed early in the tensile test by means of deformation annealing, creating a defect-free tungsten constriction which cleaves along the W(100) plane. This approach enables fabrication of new composite STM probes which demonstrate excellent stability, atomic resolution and magnetic contrast that cannot be attained using conventional methods. [ABSTRACT FROM AUTHOR]

Diammonium series of Cu hybrid perovskites of the formula [(NH)(CH)(NH)]CuCl, n = 6-9 are prepared from an ethanolic solution in stoichiometric ratio 1:1 (organic/inorganic). Formation of the desired material was confirmed and characterizes by microchemical analysis, FTIR, XRD and XPS spectra. The structure consists of corner-shared octahedron [CuCl] anion alternative by organic [(NH)(CH)(NH)] cations. The organic and inorganic layers form infinite 2D sheet that are connected via NH···Cl hydrogen bond. The calculated lattice potential energy U (kJ/mol) and lattice enthalpy Δ H (kJ/mol) are inversely proportional to the molecular volume V (nm) and organic chain length. Optical properties show strong absorption peak at UV-visible range. The band gap energy calculated using Kubelka-Munk equation shows the decrease of the energy gap as organic chain length increases. The introduction of bromide ion to [(NH)(CH)(NH)]CuClBr denoted 2C7CuCB hybrid has shifted the energy gap to lower values from 2.6 to 2.18 eV for 2C7CuCl (yellow) and 2C7CuCB (brown), respectively, at the same organic chain length. All elements of [(NH)(CH)(NH)]CuCl and [(NH)(CH)(NH)]CuClBr were found in XPS spectra, as well as valence band spectra. [ABSTRACT FROM AUTHOR]

We study the natural Gieseker and Uhlenbeck compactifications of the rational Calogero-Moser phase space. The Gieseker compactification is smooth and provides a small resolution of the Uhlenbeck compactification. We use the resolution to compute the stalks of the IC-sheaf of the Uhlenbeck compactification. [ABSTRACT FROM AUTHOR]

The strongly correlated electron material, vanadium dioxide (VO 2 ), has seen considerable attention and research application in metal-oxide electronics due to its metal-to-insulator transition close to room temperature. Vacuum annealing a V 2 O 5 (010) single crystal results in Wadsley phases (V n O 2 n + 1 , n > 1) and VO 2 . The resistance changes by a factor of 20 at 342 K, corresponding to the metal-to-insulator phase transition of VO 2 . Macroscopic voltage-current measurements with a probe separation on the millimetre scale result in Joule heating-induced resistive switching at extremely low voltages of under a volt. This can reduce the hysteresis and facilitate low temperature operation of VO 2 devices, of potential benefit for switching speed and device stability. This is correlated to the low resistance of the system at temperatures below the transition. High-resolution transmission electron microscopy measurements reveal a complex structural relationship between V 2 O 5 , VO 2 and V 6 O 13 crystallites. Percolation paths incorporating both VO 2 and metallic V 6 O 13 are revealed, which can reduce the resistance below the transition and result in exceptionally low voltage resistive switching. [ABSTRACT FROM AUTHOR]