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As the demand for spatial positioning continues to grow, positioning methods based on inertial measurement units (IMUs) are emerging as a promising research topic due to their low cost and robustness against environmental interference. These methods are particularly well suited for global navigation satellite system (GNSS)-denied environments and challenging visual scenarios. While existing algorithms for position estimation using IMUs have demonstrated some effectiveness, there is still significant room for improvement in terms of estimation accuracy. Current approaches primarily treat IMU data as simple time series, neglecting the frequency-domain characteristics of IMU signals. This paper emphasizes the importance of frequency-domain information in IMU signals and proposes a novel neural network, WINNet (Wavelet Inertial Neural Network), which integrates time- and frequency-domain signals using a wavelet transform for spatial positioning with inertial sensors. Additionally, we collected ground-truth data using a LiDAR setup and combined it with the TLIO dataset to form a new IMU spatial positioning dataset. The experimental results demonstrate that our proposed method outperforms the current state-of-the-art inertial neural network algorithms in terms of the ATE, RTE, and drift error metrics overall. [ABSTRACT FROM AUTHOR]

One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic functions. We derive various properties of the new class of normalized analytic functions X defined in the new domain, including the sharp estimates for the coefficients a 2 , a 3 , and a 4 , and for three second-order and third-order Hankel determinants, H 2 , 1 X , H 2 , 2 X , and H 3 , 1 X . The optimality of each obtained estimate is given as well. [ABSTRACT FROM AUTHOR]

This paper presents a geometric approach to the problems in differential subordination theory. The necessary conditions for a function to be in various subfamilies of the class of starlike functions and the class of Carathéodory functions are studied, respectively. Further, several consequences of the findings are derived. [ABSTRACT FROM AUTHOR]

Introduction: The heterocyclic compound 4‐hydroxy‐(2,2,6,6‐Tetramethylpiperidin‐1‐yl)oxyl (TEMPOL) has a protective effect on neurological function in brain tissues damaged by ischemia and hypoxia. This study explored the effects of TEMPOL pretreatment on postoperative cognitive function in aged rats under sevoflurane anesthesia, focusing on inflammatory response and oxidative stress. Methods: Sixty male rats were divided into normal control (C), sevoflurane anesthesia (S), TEMPOL pretreatment (T), and sevoflurane anesthesia + TEMPOL pretreatment (ST) groups (15 per group). Groups T and ST rats received continuous intraperitoneal TEMPOL (100 mg/kg) for 3 days, while groups C and S rats were injected with 0.9% saline. After pretreatment, groups S and ST received 3% sevoflurane anesthesia. Results: Rats in group S exhibited a longer swimming distance, longer escape latency, lower frequency of platform crossing, and shorter dwell time in the targeted quadrant than those in groups C and T. Rats in group ST exhibited a shorter swimming distance, shorter escape latency, higher frequency of platform crossing, and longer dwell time in the targeted quadrant than those in group S. The expressions of interleukin‐6, tumor necrosis factor‐α, inducible nitric oxide synthase, and Ym1/2 messenger ribonucleic acid were higher in groups S and ST rats than in groups C and T rats and lower in group ST rats than in group S rat (p <.05). Superoxide dismutase (SOD), total antioxidant capacity (T‐AOC), and glutathione peroxidase (GSH‐Px) were lower, while malondialdehyde (MDA) was higher in groups S and ST rats than in groups C and T rats (p <.05). Group ST showed higher SOD, T‐AOC, and GSH‐Px, and lower MDA than group S (p <.05). Conclusions: TEMPOL pretreatment attenuated postoperative cognitive impairment induced by sevoflurane anesthesia in aged rats. This may be attributed to the downregulation of NR2B‐CREB‐BDNF pathway, reducing the inflammatory response and oxidative stress damage in hippocampal tissue. [ABSTRACT FROM AUTHOR]

Oceanic transform faults connect spreading centers and are imprinted with previous tectonic events. However, their tectonic interactions are not well understood due to limited observations. The Discovery transform fault system at 4°S, East Pacific Rise (EPR), represents a young transform system, offering a unique opportunity to study the interplay between faulting and other tectonic events at an early phases of an oceanic transform system. Discovery regularly hosts M5–6 characteristic earthquakes, and the seafloor north of Discovery includes a 35 km‐long rift zone that records a complex history of rifting, faulting and volcanism, suggesting that the transform faults likely interact with regional tectonic activity. We apply a machine‐learning enabled workflow to locate 21,391 earthquakes recorded during a 1‐year ocean bottom seismometer experiment in 2008. Our results indicate that seismicity on the western Discovery fault is separated into seven patches with distinct aseismic and seismic slip modes. Additionally, we observe a patch of off‐fault seismicity near where seafloor abyssal hills intersect the rift zone. This seismicity may have been caused by varying opening rates as spreading rate decreases from north to south in the rift zone. Our findings suggest that the Discovery system is still evolving, and that system equilibrium has not been reached between rifting and faulting. These results reflect the complex yet rarely observed interactions between fault slip, plate rotation, and rifting which are likely ubiquitous at oceanic transform systems. Plain Language Summary: Oceanic transform faults are major plate boundaries connecting mid‐ocean ridges. Despite their important role in plate tectonics, their interactions with adjacent mid‐ocean ridges and surrounding oceanic plates are not well understood. The Discovery transform fault system at 4°S, East Pacific Rise, is a young oceanic transform system formed approximately 1 My ago, offering a unique opportunity to study the interplay between faulting and other tectonic events at an early phase of an OTF. Discovery faults have quasi‐periodical magnitude (M) 5–6 earthquakes. Using ocean bottom seismometer data recorded over 1 year, we find that seismicity of the western Discovery fault can be grouped into seven patches, indicating division of alternating slip modes that either releases tectonic strain by M > 5 earthquakes or creep steadily. North of the western Discovery fault, a ∼10 km wide rift zone, abundant seamounts, and abyssal hills form an interactive tectonic complex. We observe a patch of off‐fault seismicity coinciding with seafloor abyssal hills near their intersection with the rift zone. This off‐fault seismicity indicates ongoing deformation within the oceanic plate and possible spatial variations in rifting rates. Our results suggest that the Discovery system is still evolving with rifting and faulting accommodating plate spreading simultaneously. Key Points: The western Discovery transform fault has seven patches that are likely dominated by alternating seismic and aseismic slip modesMachine‐learning method helps to identify off‐fault seismicity along abyssal hills, indicating ongoing deformation within the oceanic plateThe Discovery transform system is young and still evolving, forming an interactive system with faulting, rifting, and plate rotation [ABSTRACT FROM AUTHOR]

Many researchers have defined the q-analogous of differential and integral operators for analytic functions using the concept of quantum calculus in the geometric function theory. In this study, we conduct a comprehensive investigation to identify the uses of the Sălăgean q-differential operator for meromorphic multivalent functions. Many features of functions that belong to geometrically defined classes have been extensively studied using differential operators based on q-calculus operator theory. In this research, we extended the idea of the q-analogous of the Sălăgean differential operator for meromorphic multivalent functions using the fundamental ideas of q-calculus. With the help of this operator, we extend the family of Janowski functions by adding two new subclasses of meromorphic q-starlike and meromorphic multivalent q-starlike functions. We discover significant findings for these new classes, including the radius of starlikeness, partial sums, distortion theorems, and coefficient estimates. [ABSTRACT FROM AUTHOR]

The principal character of a representation of the free group of rank two into PSL (2 , ℂ) is a triple of complex numbers that determines an irreducible representation uniquely up to conjugacy. It is a central problem in the geometry of discrete groups and low dimensional topology to determine when such a triple represents a discrete group which is not virtually abelian, that is, a Kleinian group. A classical necessary condition is Jørgensen's inequality. Here, we use certain shifted Chebyshev polynomials and trace identities to determine new families of such inequalities, some of which are best possible. The use of these polynomials also shows how we can identify the principal character of some important subgroups from that of the group itself. [ABSTRACT FROM AUTHOR]

Ocean transform faults often generate characteristic earthquakes that repeatedly rupture the same fault patches. The westernmost Gofar transform fault quasi‐periodically hosts ∼M6 earthquakes every ∼5 years, and microseismicity suggests that the fault is segmented into five distinct zones, including a rupture barrier zone that may have modulated the rupture of adjacent M6 earthquakes. However, the relationship between the systematic slip behavior of the Gofar fault and the fault material properties is still poorly known. Specifically, the role of pore fluids in regulating the slip of the Gofar fault is unclear. Here, we use differential travel times between nearby earthquakes to estimate the in‐situ Vp/Vs of the fault‐zone materials. We apply this technique to the dataset collected by an ocean‐bottom‐seismometer network deployed around the Gofar fault in 2008, which recorded abundant microearthquakes, and find a moderate Vp/Vs of 1.75–1.80 in the rupture barrier zone and a low Vp/Vs of 1.61–1.69 in the down‐dip edge of the 2008 M6 rupture zone. This lateral variation in Vp/Vs may be caused by both pore fluids and chemical alteration. We also find a 5%–10% increase in Vp/Vs in the barrier zone during the 9 months before the mainshock. This increase may have been caused by fluid migrations or slip transients in the barrier zone. Plain Language Summary: Oceanic transform faults are ideal natural laboratories for studying earthquake physics due to their regular behaviors. The westernmost Gofar transform fault near the East Pacific Rise generates magnitude six earthquakes every 5–6 years on two rupture zones, respectively, which are separated by a barrier zone repeatedly stopping ruptures on the adjacent segments. The distinct behavior of the barrier zone might be due to differences in material properties from the rupture zones. To explore this hypothesis, we analyze thousands of small earthquakes in 2008 and find that the barrier zone has a higher ratio between P and S velocities than the rupture zone. This difference indicates that the barrier and rupture zones differ in their fluid content and chemical composition, which may have regulated their distinct slip behaviors. We also find an increase in the ratio between P and S velocities in the barrier zone during the 9 months before the magnitude six earthquake in 2008, which may reflect fluid flows or aseismic fault slips. Our findings suggest that pore fluids and the chemical composition of fault‐zone materials likely play a crucial role in regulating the slip behaviors of oceanic transform faults. Key Points: Rupture barrier zone has a moderate Vp/Vs of 1.75–1.80Down‐dip edge of the 2008 M6 mainshock has a low Vp/Vs of 1.61–1.69Vp/Vs in the rupture barrier zone increased in the 9 months before the mainshock [ABSTRACT FROM AUTHOR]

This article defines a new operator called the q-Babalola convolution operator by using quantum calculus and the convolution of normalized analytic functions in the open unit disk. We then study a new class of analytic and bi-univalent functions defined in the open unit disk associated with the q-Babalola convolution operator. The main results of the investigation include some upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szego inequalities for the functions in the new class. Many applications of the finds are highlighted in the corollaries based on the various unique choices of the parameters, improving the existing results in Geometric Function Theory. [ABSTRACT FROM AUTHOR]