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This article aims to investigate the calculation problem of the fourth-power mean of the specific Kloosterman sums by utilizing analytic methods and the properties of classical Gauss sums. It provides a captivating calculation formula for this purpose. Additionally, an effective method for studying high-power mean of Kloosterman sums is introduced in this research.

Epithelial-mesenchymal transformation (EMT) plays an important role in the progression of diabetic nephropathy. Dexmedetomidine (DEX) has shown renoprotective effects against ischemic reperfusion injury; however, whether and how DEX prevents high glucose-induced EMT in renal tubular epithelial cells is incompletely known. Here, we conduct in vitro experiments using HK-2 cells, a human tubular epithelial cell line. Our results demonstrate that high glucose increases the expressions of EMT-related proteins, including Vimentin, Slug, Snail and Twist, while decreasing the expression of E-cadherin and increasing Cdk5 expression in HK-2 cells. Both Cdk5 knockdown and inhibition by roscovitine increase the expressions of E-cadherin while decreasing the expressions of other EMT-related markers. DEX inhibits Cdk5 expression without affecting cell viability and changes the expressions of EMT-related markers, similar to effects of Cdk5 inhibition. Furthermore, Cdk5 is found to interact with Drp1 at the protein level and mediate the phosphorylation of Drp1. In addition, Drp1 inhibition with mdivi-1 could also restrain the high glucose-induced EMT process in HK-2 cells. Immunofluorescence results show that roscovitine, Mdivi-1 and DEX inhibit high glucose-induced intracellular ROS accumulation, while the oxidant H2O2 eliminates the protective effect of DEX on the EMT process. These results indicate that DEX mitigates high glucose-induced EMT progression in HK-2 cells via inhibition of the Cdk5/Drp1/ROS pathway.

The main purpose of this article is to use elementary methods and properties of classical Gauss sums to determine identities for the number of residue systems of aa mod pp such that aa, a+a¯a+\bar{a}, and a−a¯a-\bar{a} are all quadratic residues, improving on results of Wang and Lv.

This paper investigates and analyzes the dynamic response of asphalt pavement under pavement-unevenness excitation based on an orthogonal vector function system and efficient DVP (dual variable and position) method. Firstly, starting from the pavement unevenness of the vehicle excitation source, the pavement-unevenness excitation is established by using the filtered white-noise method, and the random load of the vehicle model is obtained by simulation. Then, based on the basic governing equation of the road-surface problem under the random load, the analytical solution of the road-surface mechanical response is obtained by using the orthogonal vector function system and DVP method. The effects of pavement-unevenness grade, vehicle speed, vehicle load, interlayer contact condition, and transverse isotropy on the mechanical response of the road surface are analyzed via the analytical results. The results show that DVP can effectively solve the dynamic response of pavements under the excitation of pavement unevenness; in addition, it can also be applied to certain situations, such as transverse isotropy of materials and interface conditions. The results show that the pavement unevenness does not affect the average stress and strain of each layer but has a significant effect on the peak value and dispersion degree. An increase in vehicle speed causes a peak in strain and a larger coefficient of variation. Poor bonding between interfaces can lead to increased stress and strain at the bottom of the surface layer. [ABSTRACT FROM AUTHOR]

Background: Presenilin (PSEN, PS) is essential for γ-secretase function, and mutations can disrupt amyloid-β (Aβ) production in familial Alzheimer's disease. Targeting γ-secretase is complex due to its broad involvement in physiological processes. Objective: Our aim was to create a novel knockin (KI) mouse model expressing PSEN1 D385A mutation and investigate the efficacy of a Geniposide and Ginsenoside Rg1 combination (NeuroProtect modified formula, NP-2) in restoring γ-secretase activity. Methods: Using gene manipulation, we established the PS1 D385A KI mouse model and confirmed the mutation, mRNA, and protein levels using Southern blotting, northern blotting, and western blotting, respectively. In vitro γ-secretase assay was conducted to measure γ-secretase activity, while histological analyses examined neurogenesis effects. NP-2 administration evaluated its impact on γ-secretase activity. Results: The PS1 D385A KI homozygotes displayed severe cerebral hemorrhage, postnatal lethality, developmental disorders, reduced proliferation of neural progenitor cells, and disrupted γ-secretase function. The mutation abolished PS1 protein self-shearing, leading to compromised γ-secretase activity. NP-2 intervention effectively restored γ-secretase activity in the heterozygous mice. Conclusions: PS1 D385A mutant disrupted PS1 protein self-cleaving, impairing γ-secretase activity in KI mice. NP-2 restored γ-secretase function, offering potential for novel AD treatment strategies despite the challenges posed by γ-secretase's complex role in physiological processes. [ABSTRACT FROM AUTHOR]

We study the 2016 January 21 (⁠|${{{M}}}_{\rm{w}}$|  5.9) and 2022 January 8 (⁠|${{{M}}}_{\rm{w}}$|  6.7) earthquake sequence that struck the Menyuan region in northwest China's Qinghai province. These two earthquakes are destructive events that occurred around/on the Lenglongling fault (LLLF). Here, we derive the line-of-sight displacement fields of the two earthquakes using Interferometric Synthetic Aperture Radar (InSAR) measurements of Sentinel-1 SAR data, and map the range and horizontal offset fields of the 2022 event using Sentinel-1 amplitude images and Planet-Lab optical images. Based on the offset maps, we determine the detailed surface rupture trace of the 2022 event. We perform slip inversions for the two earthquakes on triangle fault patches whose size increases with depth. Results show that the western branch segment of the 2022 event has a ∼0.5-m normal dip-slip motion. This result contradicts previous inferences on dip-slip sense of this branch segment. We identify a left-stepping fault structure with a ∼5-km step width in the transition zone between the Tuolaishan fault (TLSF) and LLLF, which may serve as a kinematic barrier to prevent further propagation of seismic rupture along the TLSF. Stress calculation shows that a stress drop of ∼0.4 bar produced by the 2016 event on a ∼5-km long LLLF segment may act as a negative stress barrier to suppress rupture propagation of the 2022 event toward the southeast of the LLLF. [ABSTRACT FROM AUTHOR]

Recent studies have shown that MRI demonstrates promising results for evaluating the chemotherapy efficacy in bone sarcomas. This article reviews current methods for evaluating the efficacy of malignant bone tumors and the application of MRI in this area, and emphasizes the advantages and limitations of each modality. Level of Evidence: 5 Technical Efficacy: Stage 2 [ABSTRACT FROM AUTHOR]

We derive the ALOS‐2 coseismic interferograms, pixel‐offsets and Sentinel‐2 sub‐pixel offsets of the 2023 Mw7.8 and Mw7.7 Kahramanmaras, Turkey earthquake sequence. Offset maps show that the sequence ruptured ∼300 km along the East Anatolian Fault (EAF) and ∼180 km along the secondary Cardak and Dogansehir faults. We infer the coseismic slip distribution and interseismic fault motion by inverting the co‐ and inter‐seismic observations. Inversion results show that the coseismic slip (∼8.0 m) and interseismic strike‐slip rate (∼4.6 mm/yr) on the main rupture of the Mw7.8 event are basically consistent with the ∼8.4 m and ∼3.9 mm/yr of the Mw7.7 event. Most coseismic slips of the Mw7.8 and Mw7.7 events occur within 10 and 12 km at depth, respectively, in keeping with the interseismic locking depth of 10.4 ± 3.3 km and 11.1 ± 3.1 km. This implies that the coseismic rupture kinematics correlate with the interseismic strain accumulation. Moreover, static stress changes show that the Mw7.7 event is likely promoted by ∼2 bar stress increase from the Mw7.8 event on the central section of its main rupture. Plain Language Summary: The middle and northern sections of the East Anatolian Fault (EAF) have experienced seven major earthquakes (M > 6.0) since the twentieth century, in accordance with the fast slip rate (∼10.5 mm/yr) and shallow locking depth (∼5 km) (Bletery et al., 2020, https://doi.org/10.1029/2020gl087775), leaving a well‐known seismic gap, the Pazarcık segment in the southern section of the EAF. Stress analysis by Nalbant et al. (2002, https://doi.org/10.1016/s0012-821x(01)00592-1) suggested that this seismic gap has potential to produce an Mw ≥ 7.3 earthquake. The 2023 Mw7.8 and Mw7.7 Kahramanmaras, Turkey earthquake sequence ruptured the Pazarcık segment. This earthquake sequence offers a valuable opportunity to explore the critical stage of the seismic cycle from interseismic strain accumulation to coseismic rupture. We extract the surface fault traces from the deformation maps derived from the ALOS‐2 interferometric synthetic aperture radar (InSAR), pixel offset and Sentinel‐2 sub‐pixel offset measurements, and then construct a seven‐segment fault geometric model according to the fault segmentation based on Duman and Emre (2013, https://doi.org/10.1144/SP372.14). By inverting the coseismic interferograms and pixel offsets and the interseismic LOS velocities from Weiss et al. (2020, https://doi.org/10.1029/2020GL087376), we determine the coseismic slip model of Mw7.8 and Mw7.7 earthquakes, and relate it to the interseismic kinematics. Key Points: We drive a complete series of coseismic deformation maps and detailed slip distribution of the 2023 Kahramanmaras earthquakesThe Mw7.7 event produced normal dip‐slip (∼6 m) near the Goksun releasing bend and thrust dip‐slip (∼2 m) on the Dogansehir faultThe coseismic slip behaviors on the Cardak and Pazarcık faults correlate with the interseismic kinematics [ABSTRACT FROM AUTHOR]