Some Operations on Quaternion Numbers

In this article, we give some equality and basic theorems about quaternion numbers, and some special operations.Li Bo - Qingdao University of Science and Technology, ChinaLiang Xiquan - Qingdao University of Science and Technology, ChinaWang Pan - Qingdao University of Science and Technology, ChinaZhuang Yanping - Qingdao University of Science and Technology, ChinaGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Fuguo Ge. Inner products, group, ring of quaternion numbers. Formalized Mathematics, 16(2):135-139, 2008, doi:10.2478/v10037-008-0019-x.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Xiquan Liang and Fuguo Ge. The quaternion numbers. Formalized Mathematics, 14(4):161-169, 2006, doi:10.2478/v10037-006-0020-1.Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990

Several Integrability Formulas of Special Functions. Part II

In this article, we give several differentiation and integrability formulas of special and composite functions including the trigonometric function, the hyperbolic function and the polynomial function [3].Bo Li - Qingdao University of Science and Technology, ChinaYanping Zhuang - Qingdao University of Science and Technology, ChinaYanhong Men - Qingdao University of Science and Technology, ChinaXiquan Liang - Qingdao University of Science and Technology, Chin

Folic acid-functionalized drug delivery platform of resveratrol based on Pluronic 127/D-α-tocopheryl polyethylene glycol 1000 succinate mixed micelles

A folic acid (FA)-functionalized drug vehicle platform based on Pluronic 127 (P127)/D-α-tocopheryl polyethylene glycol 1000 succinate (TPGS) mixed micelles was orchestrated for an effective delivery of the model drug resveratrol in order to address the problem of poor water solubility and rapid metabolism of resveratrol and improve its targeted accumulation at tumor site. The FA-decorated mixed micelles were prepared using thin-film hydration method and optimized by central composite design approach. The micelles were also characterized in terms of size and morphology, drug entrapment efficiency and in vitro release profile. In addition, the cytotoxicity and cell uptake of the micelles were evaluated in folate receptor-overexpressing MCF-7 cell line. In vivo pharmacokinetic and biodistribution studies were also performed. The average size of the micelles was ~20 nm with a spherical shape and high encapsulation efficiency (99.67%). The results of fluorescence microscopy confirmed the targeting capability of FA-conjugated micelles in MCF-7 cells. FA-modified micelles exhibited superior pharmacokinetics in comparison with that of solution. Further, the low accumulation of resveratrol-loaded FA micelles formulation in the heart and kidney avoided toxicity of these vital organs. It could be concluded that folate-modified P127/TPGS mixed micelles might serve as a potential delivery platform for resveratrol

Polyhydride CeH9 with an atomic-like hydrogen clathrate structure.

Compression of hydrogen-rich hydrides has been proposed as an alternative way to attain the atomic metallic hydrogen state or high-temperature superconductors. However, it remains a challenge to get access to these states by synthesizing novel polyhydrides with unusually high hydrogen-to-metal ratios. Here we synthesize a series of cerium (Ce) polyhydrides by a direct reaction of Ce and H2 at high pressures. We discover that cerium polyhydride CeH9, formed above 100 GPa, presents a three-dimensional hydrogen network composed of clathrate H29 cages. The electron localization function together with band structure calculations elucidate the weak electron localization between H-H atoms and confirm its metallic character. By means of Ce atom doping, metallic hydrogen structure can be realized via the existence of CeH9. Particularly, Ce atoms play a positive role to stabilize the sublattice of hydrogen cages similar to the recently discovered near-room-temperature lanthanum hydride superconductors

Stability Assessment of Hesigewula Open-pit Coal Mine Based on Geomorphic Information Entropy of Watershed System

[Objective] The stability evaluation of an open-pit mining area was carried out in order to provide technical support for landform remodeling, ecological environment restoration, and soil erosion monitoring in a mining area. [Methods] The ArcHydro hydrological model and watershed self-similarity principle were used in this study. The stability of geomorphic forms in an open-pit mining area and in the surrounding undisturbed area was evaluated using the geomorphic information entropy evaluation index. The risk of soil erosion and erosion intensity in the mine area were also determined. [Results] The geomorphic information entropy of the Hesigewula open-pit coal mine area in Inner Mongolia was affected by a series of processes such as stripping, mining, transportation, and disposal, and was mostly concentrated in the index value range of 0.105—0.145. The geomorphic system development of the watershed in the mining area was mostly in the juvenile stage or middle-aged to juvenile stage. The risk of watershed erosion was high. Most of the information entropy of the original landform and undisturbed area was greater than 0.40, where the watershed geomorphic system was stable and strong, with flat terrain and small soil erosion modulus. [Conclusion] The risk of soil erosion gradually increased from south to north at the Hesigewula open-pit mine due to the original landform of the mining area, the mining sequence, and the location of the dump site. The results of this study can be used as the basis for landform reconstruction and ecological environment restoration of similar open-pit coal mines

Advanced lung cancer inflammation index is associated with prognosis in skin cancer patients: a retrospective cohort study

BackgroundSkin cancer ranks as one of the most prevalent malignant tumors affecting humans. This study was designed to explore the correlation between the advanced lung cancer inflammation index (ALI), a metric that gauged both nutrition and inflammation statuses, in skin cancer patients and their subsequent prognosis.MethodsData from the National Health and Nutrition Examination Survey (NHANES) spanning 1999-2018 were scrutinized, along with mortality tracking extending to December 31, 2019. Kaplan-Meier survival curves and COX regression analysis, utilizing NHANES-recommended weights, delineated the association between ALI levels and skin cancer prognosis. To decipher the potential non-linear relationship, a restricted cubic spline analysis was applied. Additionally, stratified analysis was conducted to affirm the robustness of our findings.ResultsThe 1,149 patients participating in NHANES 1999-2018 were enrolled. We observed a reverse J-shaped non-linear relationship between ALI and both skin cancer all-cause mortality and cancer mortality, with inflection points at 81.13 and 77.50, respectively.ConclusionsThe ALI served as a comprehensive indicator of a patient’s nutrition and inflammation status and was demonstrably linked to the prognosis in skin cancer cases. The meticulous evaluation and continuous monitoring of these parameters in skin cancer patients bear clinical importance

Reconstruction of primary vertices at the ATLAS experiment in Run 1 proton–proton collisions at the LHC

This paper presents the method and performance of primary vertex reconstruction in proton–proton collision data recorded by the ATLAS experiment during Run 1 of the LHC. The studies presented focus on data taken during 2012 at a centre-of-mass energy of √s=8 TeV. The performance has been measured as a function of the number of interactions per bunch crossing over a wide range, from one to seventy. The measurement of the position and size of the luminous region and its use as a constraint to improve the primary vertex resolution are discussed. A longitudinal vertex position resolution of about 30μm is achieved for events with high multiplicity of reconstructed tracks. The transverse position resolution is better than 20μm and is dominated by the precision on the size of the luminous region. An analytical model is proposed to describe the primary vertex reconstruction efficiency as a function of the number of interactions per bunch crossing and of the longitudinal size of the luminous region. Agreement between the data and the predictions of this model is better than 3% up to seventy interactions per bunch crossing

Soft Micromanipulation Robot for Real‐Time Adaptive Multimodal Operation

Micromanipulation robots hold immense promise for biomedical applications, yet they remain fundamentally limited by three persistent challenges: cross-scale target heterogeneity, spatially constrained workspaces, and integrated multimodal operation requirements. Here, a soft micromanipulation robot (SMR) capable of omnidirectional, micrometer-precision manipulation via a hollow multi-notch agonist-antagonist mechanism is presented. Combining ± 180° bending and 360° rotation for full-angle operation, this bio-inspired design achieves 14 µm positioning accuracy, enabling reliable handling of single-cell-sized objects. The SMR adapts in situ to sensitive biosamples and limited workspaces, supporting diverse manipulation modes including aspiration, transfer, programmable assembly, targeted microinjection, and localized cutting of biospecimens. To evaluate biomedical applicability, an assembly experiment with human kidney cell spheres, which is essential for establishing co-culture models in new drug development is designed. The SMR successfully aspirated, transferred, and precisely positioned multiple assembloids onto ring-shaped biochips, achieving programmable assembly within limited workspaces. The SMR has the potential to be a flexible and adaptable platform for performing delicate operations in various biomedical scenarios, such as in vitro modeling, drug testing, and microscale surgery

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements