Local-global compatibility of mod pp Langlands program for certain Shimura varieties

We generalize the local-global compatibility result in arXiv:1506.04022 to higher dimensional cases, by examining the relation between Scholze's functor and cohomology of Kottwitz-Harris-Taylor type Shimura varieties. Along the way we prove a cuspidality criterion from type theory. We also deal with compatibility for torsion classes in the case of semisimple mod $p$ Galois representations with distinct irreducible components under certain flatness hypotheses.Comment: 21 pages, comments welcom

Experimental investigation on shock mechanical properties of red sandstone under preloaded 3D static stresses

Triaxial impact mechanical performance experiment was performed to study the mechanical properties of red sandstone subjected to three-dimensional (3D) coupled static and dynamic loads, i.e., three confining pressures (0, 5, and 10 MPa) and three axial pressures (11, 27, and 43 MPa). A modified 3D split Hopkinson pressure bar testing system was used. The change trend in the deformation of red sandstone and the strength and failure modes under axial pressures and confining pressures were analyzed. Results show that, when the confining pressure is constant, the compressive strength, secant modulus, and energy absorbed per unit volume of red sandstone initially increases and subsequently decreases, whereas the average strain rate exhibits an opposite trend. When the axial pressure is constant, both the compressive strength and secant modulus of red sandstone are enhanced, but the average strain rate is decreased with increasing confining pressure. The energy absorbed per unit volume is initially increased and subsequently decreased as the confining pressure increases. Red sandstone exhibits a cone-shaped compression–shear failure mode under the 3D coupled static and dynamic loads. The conclusions serve as theoretical basis on the mechanical properties of deep medium-strength rock under a high ground stress and external load disturbance condition

Measurement method of torsional vibration signal to extract gear meshing characteristics

A technique in measuring torsional vibration signal based on an optical encoder and a discrete wavelet transform is proposed for the extraction of gear meshing characteristics. The method measures the rotation angles of the input and output shafts of a gear pair by using two optical encoders and obtains the time interval sequences of the two shafts. By spline interpolation, the time interval sequences based on uniform angle sampling can be converted into angle interval sequences on the basis of uniform time sampling. The curve of the relative displacement of the gear pair on the meshing line (initial torsional vibration signal) can then be obtained by comparing the rotation angles of the input and output shafts at the interpolated time series. The initial torsional vibration signal is often disturbed by noise. Therefore, a discrete wavelet transform is used to decompose the signal at certain scales; the torsional vibration signal of the gear can then be obtained after filtering. The proposed method was verified by simulation and experimentation, and the results showed that the method could successfully obtain the torsional vibration signal of the gear at a high frequency. The waveforms of the torsional vibration could reflect the meshing characteristics of the teeth. These findings could provide a basis for fault diagnosis of gears

Investigation of Properties Alternation during Super-Critical CO2 Injection in Shale

The low recovery of oil from tight liquid-rich formations is still a major challenge for a tight reservoir. Thus, supercritical CO2 flooding was proposed as an immense potential recovery method for production improvement. While up to date, there have been few studies to account for the formation properties\u27 variation during the CO2 Enhanced Oil Recovery (EOR) process, especially investigation at the micro-scale. This work conducted a series of measurements to evaluate the rock mechanical change, mineral alteration and the pore structure properties\u27 variation through the supercritical CO2 (Sc-CO2) injection process. Corresponding to the time variation (0 days, 10 days, 20 days, 30 days and 40 days), the rock mechanical properties were analyzed properly through the nano-indentation test, and the mineralogical alterations were quantified through X-ray diffraction (XRD). In addition, pore structures of the samples were measured through the low-temperature N2 adsorption tests. The results showed that, after Sc-CO2 injection, Young\u27s modulus of the samples decreases. The nitrogen adsorption results demonstrated that, after the CO2 injection, the mesopore volume of the sample would change as well as the specific Brunauer-Emmett-Teller (BET) surface area which could be aroused from the chemical reactions between the CO2 and some authigenic minerals. XRD analysis results also indicated that mesopore were altered due to the chemical reaction between the injected Sc-CO2 and the minerals

Simulation and experimental research on dynamic characteristics of overrunning clutch

Because of the self-locking part inertia, deformation factors, and interspace between the driving and driven sides of the overrunning clutch, the existing dynamic models, which consider the rotational speed discrepancy or angle discrepancy as the only determinant to recognize the engaging state, have some difficulty in accurately describing and studying the dynamic characteristics of the overrunning clutch and its transmission system. In order to solve these problems, this paper proposed a modified method considering the influence of the dynamic characteristics of self-locking components through angle compensation. Four models were established on a MATLAB/Simulink platform, and an experiment was carried out on a transmission experimental platform under a stable driving torque and varying driving torque. Then, the comparison of the dynamic characteristic between the simulation and the experiment showed that under non-stationary excitation, taking the influence of the dynamic characteristic of the self-locking components into account through angle compensation can help to more accurately describe the dynamic characteristics of a transmission system with an overrunning clutch

A Cooperative Mobile Satellite Communication System with the Dynamic Space-Time Coding

Channels of mobile satellite communications are affected by multipath fading and shadowing attenuation. At the same time, diversity gains are believed to improve the transmission reliability in fading channels. Considering that the traditional Space-Time Coding (STC) is not suitable for the cooperative mobile satellite communication, in this paper, a new cooperative mobile satellite communication system is proposed based on the Dynamic Space-Time Coding (D-STC). The transmitting energy of the proposed scheme is saved by avoiding forwarding erroneous signals in cooperative users. Meanwhile, this system benefits from diversity gains and the transmission is robust. Additionally, a closed-form expression of the outage probability for the proposed scheme is derived, and then it is demonstrated that this scheme is much better than the existing noncooperative scheme and schemes with traditional STCs in the outage performance. Finally, the analytical result is supported and validated by numerical simulations

Compatibilité locale-globale du programme de Langlands modulo p pour certaines variétés de Shimura

We generalize the local-global compatibility result in [Sch18] to higher dimensional cases, by examining the relation between Scholze's functor and cohomology of Kottwitz-Harris-Taylor type Shimura varieties. Along the way we prove a cuspidality criterion from type theory. We also deal with compatibility for torsion classes in the case of semisimple mod p Galois representations which are multiplicity free, under certain flatness hypotheses. Finally, we remove the semisimple condition and replace it by the much weaker condition of being multiplicity free. This last result is obtained in joint work with Z. QianNous généralisons le résultat de compatibilité local-global dans [Sch18] aux cas de dimension supérieure, en examinant la relation entre le foncteur de Scholze et la cohomologie des variétés de Shimura de type Kottwitz-Harris-Taylor. En chemin, nous prouvons un critère de cuspidalité de la théorie des types. Nous traitons également de la compatibilité des classes de torsion dans le cas des représentations semi-simples mod p Galois sans multiplicité, sous certaines hypothèses de platitude. Enfin, nous enlevons la condition sur semisimplicité et la remplaçons par la condition beaucoup plus faible d'être sans multiplicité. Ce dernier résultat est obtenu en collaboration avec Z. Qian

Compatibilité locale-globale du programme de Langlands modulo p pour certaines variétés de Shimura

We generalize the local-global compatibility result in [Sch18]to higher dimensional cases, by examining the relation between Scholze's functor and cohomology of Kottwitz-Harris-Taylor type Shimura varieties. Along the way we prove a cuspidality criterion from type theory. We also deal with compatibility for torsion classes in the case of semisimple mod $p$ Galois representations which are multiplicity free, under certain flatness hypotheses. Finally, we remove the semisimple condition and replace it by the much weaker condition of being multiplicity free. This last result is obtained in joint work with Z. QianNous généralisons le résultat de compatibilité local-global dans [Sch18] aux cas de dimension supérieure, en examinant la relation entre le foncteur de Scholze et la cohomologie des variétés de Shimura de type Kottwitz-Harris-Taylor. En chemin, nous prouvons un critère de cuspidalité de la théorie des types. Nous traitons également de la compatibilité des classes de torsion dans le cas des représentations semi-simples mod p Galois sans multiplicité, sous certaines hypothèses de platitude. Enfin, nous enlevons la condition sur semisimplicité et la remplaçons par la condition beaucoup plus faible d'être sans multiplicité. Ce dernier résultat est obtenu en collaboration avec Z. Qian

Recent biomimetic and organocatalytic syntheses of α-tocopherol

We report here on our efforts to develop new strategies for the synthesis of α-tocopherol, the biologically most significant member of the vitamin E family. This review comprises five new methods to generate the chiral chromane of α-tocopherol with overall up to 29% yield from commercially available material and up to 94% de