A system of simultaneous multi-variable nonlinear equations can be solved by the Newton’s method with local q-quadratic convergence if the Jacobian is analytically available. If this is not the case, then quasi-Newton methods with local q-superlinear convergence give solutions by approximating the Jacobian in some way. Unfortunately, the quasi-Newton condition (secant equation) doesn’t completely specify the Jacobian approximate in multi-dimensional case, so its full-rank update is not possible with classic variants of methods. The suggested new iteration strategy (“T-Secant”) allows full-rank update of the Jacobian approximate in each iteration by determining two independent approximates for the solution. They are used to generate a set of new independent trial approximates, then the Jacobian approximate can fully be updated. It is shown, that the T-Secant approximate is in the vicinity of the classic quasi-Newton approximate, providing that the solution is evenly surrounded by the new trial approximates. The suggested procedure increases the super-linear convergence of the secant method (φS = 1.618...) to super-quadratic (φT = φS + 1 = 2.618...) and the quadratic convergence of the Newton-method (φN = 2) to cubic (φT = φN + 1 = 3) in one dimensional case. The Broyden-type efficiency (mean convergence rate) of the suggested method in multi-dimensional case is an order higher than the efficiency of other classic low-rank update quasi-Newton methods as shown by numerical examples on a Rosenbrock-type test-function with up to 1000 variables. The geometrical representation (hyperbolic approximation) in single variable case helps explaining the basic operations and a vector-space description is also given in multi-variable case.

Image stitching is a crucial aspect of image processing. However, factors like perspective and environment often lead to irregular shapes in stitched images. Cropping or completion methods typically result in substantial loss of information. This paper proposes a method for rectifying irregularly images into rectangles using deformable meshes and residual networks. The method utilizes a convolutional neural network to quantify rigid structures of images. Choosing the most suitable mesh structure based on the extraction results, offering options such as triangular, rectangular, and hexagonal. Subsequently, the irregularly image, predefined mesh structure, and predicted mesh structure are input into a wide residual neural network for regression. The loss function comprises local and global, aimed at minimizing the loss of image information within the mesh and global target. This method not only significantly reduces information loss during rectification but also adapting to different images with various rigid structures. Validation on the DIR-D dataset shows this method outperforms state-of-the-art methods in image rectification.

Cable-supported façades represent a novel approach in the design and technology of double skin façades (DSF). This type of systems not only offer flexibility in terms of exterior finishes, but also regulates the access of solar radiation, thereby transforming the appearance of the building in response to varying daylight conditions. However, the structural performance of these façades under wind, impact and seismic loads remains an active area of research. The study is a groundbreaking work that experimentally evaluates the wind and seismic behaviour of these type of façades. The methodology used for the evaluation of flexible masonry facades includes laboratory tests analysing the individual capacity of the connections and materials of the system under standardized and non-standardized procedures. A full-scale experimental sub-assembly specimen of a representative module of the façade is also subjected to uniformly distributed pressures of wind load tests as well as hard body and soft body impact tests. The setup considered the border conditions, tension loads, and actual materials. Furthermore, the earthquake assessment includes tests of full-scale specimens subjected to these demands. Research findings allowed the refinement and redesign of the system's components granting the validation of the DSF used as a case study.

Dynamic optical structural color is always desired in various display applications and usually involves active materials. Full-color generation, especially bi-directional full-color generation in both reflective and transmissive modes, without any active materials included has been rarely investigated. Herein, we demonstrate a scheme of bi-directional full-color generation based on a plasmonic metasurface modulated by rotation of the polarization angle of the incident light without varying the geometry and the optical properties of the materials and the environment where the metasurface resides. The metasurface unit cell consists of plasmonic modules aligning in three directions and is patterned in a square array. The metasurface structural color device generates full colors in both reflection and transmission. Based on the proposed polarization-dependent structural color, information encoding of three multiplexed animal images and quick-responsive (QR) codes is demonstrated to verify the efficient information encoding and decoding of the proposed scheme. The animals can be seen under different polarization incidence and the QR codes can be successfully decoded by the polarization rotation in transmission. The proposed bi-directional full-color generation metasurface has great potential in applications such as kaleidoscope generation, anti-counterfeiting, dynamic color display, and optical information encoding.

Backround Cochlear implant is the first approved cranial nerve stimulator that works by directly stimulating the cochlear nerve. Various attempts have been made to evaluate the dimensions of the cochlea related to cochlear implantationThe preoperative computed tomographic examination is essential in assessing the anatomical aspect of the cochlea, but also in determining its dimensions, in order to choose an appropriate electrode, in order to obtain the best possible audiological performance. Method In the present paper, we aimed to carry out an observational study, regarding the role of cochlear measurements in the preoperative evaluation of patients proposed for cochlear implant. The purpose of the study was to measure the cochlea and to establish the existence of a correlation between the size of the cochlea and the age and gender of the patients. Results From the group of 35 examined patients, 54% (n= 19) were male and 46% (n=16) female. The average length of the cochlea in the age group 0-4 years is 7.82 mm in the left ear and 7.86 in the right ear, in the age group 4-7 years it is 7.82 mm and 7.94 mm respectively, for the age group 7-14 years the dimensions increase to 8.48 and 8.77 mm respectively, and after 14 years these dimensions reach 9.12, respectively 9.18 mm. Comparative measurements of the length of the cochlea by age groups show an increase in length with the patient's age, but this increase does not exceed 1.5 mm for both the right and left ears. The measurements of the width of the cochlea, by age group, start from 6.84 mm left ear and 6.81 mm right ear at 0-4 years, 6.94 mm and respective 6.97 mm at the group 4-7 years, 7.71 mm and respective 7.55 mm at 7-14 years , and reaching 8.19 mmm and 8.12 mm at the age of over 14 years. Conclusions From the study carried out it can be concluded that the evaluation of the dimensions of the cochlea is important for cochlear implantation, the size variables, although small, are still an element to be considered in correlation with the age of the patient and the implanted ear. This increase is statistically insignificant, but it still exists, even if from a theoretical point of view, it is considered that the dimensions of the cochlea remain constant.

The concept of graphs with clique-width at most was first introduced by Courcelle et al.to be the graphs that can be characterized using -expressions derived from graph operations that use labels of vertices. If the clique-width for some graph is bounded then a grand number of algorithmic problems, in general NP-hard, can be solved in polynomial time when restricted to this graph. This important fact motivated the researchers to prove that the clique-width of certain graphs is bounded. Following this research direction, we prove in this paper that the clique-width of series-parallel digraphs is at most 6 and we present an time algorithm to construct a 6-expression for this class of digraphs. In another part, we present a linear time recognition algorithm for a similar class of series-parallel digraphs and prove that the clique-width of this class is at most 3.

Based on the high-precision quantitative measurement ability, the S-band subsystem of China's high- resolution aviation system carried out the agricultural application test for the first time in Jilin elm, China. The experiment is mainly carried out in combination with vegetation growth, soil moisture content inversion, wheat straw returning and ground feature classification. Through the design of quantitative measurement scheme, the results of different straw coverage and observation at different times are compared, which shows the prospect of S-band full polarization synthetic aperture radar system in the field of agricultural application.

Objectives (Purpose) This study aims to evaluate the outcomes of the Subcrestally Placed Implant (SPI) technique in single molar cases, focusing on biological stability and aesthetics. It proposes a schematic model to elucidate the interplay between the biological stability of soft tissues and bone around the SPI and the morphological requisites that Implant Abutment Prostheses (IAP) must fulfill to effectively replace natural teeth. Materials and methods I examined 20 cases using the SPI technique with Internal Platform Switching (IPS) design implants for single molar replacements to assess their stability. Routine check-ups utilized plain panoramic X-rays to measure changes in crestal bone on the mesial and distal sides. Additionally, 10 cases with CBCT X-rays taken more than one year after the initial surgery underwent a novel 3-dimensional soft tissue analysis (3DSTA). Measurements included placement depths (PD), soft tissue thickness (STT) at central (cPD, cSTT) and peripheral areas (pPD, pSTT), the length of the Transitional Zone (TZ) on mesial, distal, facial, and lingual aspects, and crestal bone thickness (CBT) at buccal and lingual sites. Results Panoramic analyses showed minimal changes in crestal bone (mean changes of pPD were less than 0.1 mm) over an average period of 3.3 years. Average measurements were as follows: cPD was 1.7 mm, pPD was 2.7 mm, cSTT was 0.2 mm, pSTT was 0.6 mm, TZ length was 3.8 mm, buccal CBT was 3.0 mm, and lingual CBT was 3.7 mm. Conclusions CBCT analyses of the topographical relationships between soft tissue and crestal bone with IAP for SPIs demonstrated stable results over an average 3-year period. The consistency in the relationship between crestal bone and surrounding soft tissue can be ascribed to biological structural integrity. The study classified peri-implant soft tissues into subcrestal and supracrestal (transitional zone – TZ) segments, exploring their characteristics through dimensional measurements and assessing mechanical resistance. Further histological study is needed to identify specific features of each segment.

In this compact and focused paper, we revisit the interplay between Bramble and Filter through the lens of a submodular partition function.

The medium-voltage DC (MVDC) technology has gained increasing interests in recent years. Power electronics devices dominate those grids. Accurate simulation of such a grid, with detailed models of switching semiconductors, can quickly became very time-consuming, according to the number of connected devices to be simulated. A simulation approach based on interactions on a continuous time model can be very interesting, especially for developing a system level control model of such a modern MVDC distribution grid. Aim of this paper is to present all the steps required for obtaining a continuous time modelling of a +/- 10 kV MVDC grid case study, including Solid State Transformer (SST) and Modular Multilevel Converter (MMC) based Active Front End (AFE). Additional aim of this paper is to supply an educational content about the use of the continuous time simulation approach, thanks to a detailed description of the various devices modelled into the presented MVDC grid. The results of a certain number of simulation scenarios are eventually presented.

In an effort to enhance the efficiency and safety of open-pit mines, this study explores the optimization of end slope road parameters and slope structures, specifically focusing on unmanned driving lanes.A significant aspect of the study is the development of a truck trajectory offset model, which considers the different reaction times between automated sensors and human drivers in adapting to environmental changes. To test these concepts, the study uses numerical simulations to confirm the stability of the proposed end slope designs. Using Victory West Mine No. 1 as a case study, the research determines the optimized width for unmanned driving lanes and the maximum angle for safe steepening of end slopes. The findings indicate that the optimized unmanned lane width for NTE240 mining dump trucks is 1743 mm, allowing for a 2-degree increase in the slope angle at the south end slope. This optimization leads to a steep mining stripping volume of 3.2735 million m³ and a coal output of 2.49628 million tons, maintaining a stripping ratio of 1.31m³/t. These results demonstrate that the unmanned driving road width optimization not only ensures slope safety but also significantly boosts the economic benefits of steep mining in open-pit mines.

The aging of the population in developing and developed countries has lead to a significant increase in health burden of spinal diseases. These elderly patients often have a number of medical co-morbidities due to aging. The need for minimally invasive techniques to address spinal disorders in this elderly population group cannot be stressed enough. Minimally invasive spine surgery (MISS) has several proven benefits such as minimal muscle trauma, minimal bony resection, lesser post-operative pain, decreased infection rate and shorter hospital stay. Over the last 40 years, constant efforts are being made to develop newer techniques of spine surgery. Endoscopic spine surgery is one such subset of MISS which has all the benefits of modern MISS. Endoscopic spine surgery initially was limited only to treatment of lumbar disc herniations. With improvement in optics, endoscopes, endoscopic drills and shavers, irrigation pumps, there has been a paradigm shift. Endoscopic spine surgery can now be performed with high magnification thus allowing its application not only to lumbar spinal stenosis, but also to spinal fusion surgeries, cervical and thoracic pathology as well. There has been increasing evidence in support of these newer techniques of spine surgery. For the purpose of this review, we studied current available literature and outlined the historical evolution of endoscopic spine surgery, the various different endoscopic systems, and techniques available and the current applications of endoscopic techniques as an alternative to traditional spinal surgery.

Abstract: NFinFET transistors with fin channel length 90nm and a planar MOSFET transistor with channel length 180nm and 90nm are presented with characteristic curves at various gate biases. A finalized algorithm with kink effects is effectively responsible for addressing the field effect transistors. The algorithm includes the modified conventional current-voltage formula and a nonlinear heat-associated kink solution which is simplified as a Gaussian form. Three parameters in modified model includes kN (related with channel width, channel length, and gate oxide capacitor, and proportional to the mobility of carriers)Vth(Threshold Voltage), and (the inverse of Early Voltage). Those parameters are determined to minimize the discrepancies between the measured data and the fitting values, but leave kinks located at around (VGS－Vth), which are deliberately eliminated by the Gaussian form because of the agitation of thermal kink effects. The whole fitting is made to be as close as the as-measured IDS-VDS. In the mean time, those determined parameters are physically meaningful after the analysis has been done.

The platelet count, a component of the full blood count, has been identified as a useful diagnostic marker for cancer in primary care. The reference range for the platelet count is 150 to 400 or 450 × 109/l; this range does not account for natural variation in platelet count by age and sex. This study used three primary care cohorts from England Canada, and Australia. Patients aged 40 years and over with a full blood count were included and stratified by age (in 10-year bands), sex, (male/female), and platelet count group. Cancer incidence within one year of test date was estimated from linked registry data. In all three countries there was a clear upwards trend in cancer incidence with increasing platelet count, for both sexes and at all age groups. Lung and colorectal were the most common sites. These results have important implications for the international application of this work; analysis of local health datasets will be crucial to determine appropriate thresholds. Appropriate upper thresholds will depend on local populations, healthcare needs, and priorities. Further research is needed to assess the likely impact of new recommendations on the healthcare system, on cancer outcomes, and patient benefit.

Purpose: To examine the effectiveness of patterned laser trabeculoplasty (PSLT) as an additional treatment for patients of open-angle glaucoma (OAG) receiving maximized ocular hypotensive medications (OHM). Methods: Forty eyes of 33 patients (average age 72.7±10.7 years) who had not previously undergone open glaucoma surgery or laser trabeculoplasty and were treated with maximized OHM between June 2018 and March 2022 were included. A 360-degree PSLT was conducted and postoperative intraocular pressure (IOP) and survival curves at 1, 3, 6, 9, and 12 months were evaluated. Results: According to the Kaplan-Meier survival analysis, the average survival time was 8.1 months with death defined as postoperative IOP reduction of less than 10% or requiring additional treatment. The average survival time was 4.9 months with death defined as postoperative IOP reduction of less than 20% or requiring additional treatment. In the 31 eyes which received no additional treatment after PSLT, the mean preoperative IOP was 18.5±3.9 mmHg, which reduced to 15.3±4.1 mmHg (p=1.62 x 10-6)), 15.5±3.4 mmHg (p=1.51 x 10-5), 15.7±4.0 mmHg (p=1.75 x 10-5), 14.7±4.38 (p=2.89 x 10-6), and 15.0±4.0 mmHg (p=5.74 x 10-9) at 1, 3, 6, 9 and 12 months after PSLT, respectively. The IOP reduction rate one year after PSLT was 18.7%. Thirteen of the 31 eyes (42%) achieved a 20% reduction in IOP compared to the baseline. Conclusion: Adjunctive treatment with PSLT in OAG patients receiving maximized OHM may be effective over 12-months of follow-up.

We propose a full binary directed tree to represent the set of natural numbers and further divide the set into three sets: pure odd, pure even, and mixed numbers. We utilize a binary string to represent a natural number and demonstrate the composite procedure of odd-number and even-number functions. We analyze the sequence of iteration (or composite) of the Collatz function and reduced Collatz function analog to the inverse function in order to test the Collatz conjecture. We do this by using the parity of a natural number. In order to prove the conjecture, we provide tabular and binary strings to the algebraic formula that states the Collatz sequence. Ultimately, we can convert discrete powers of 2 into continuous powers of 2, ultimately arrive at the smallest natural, 1. If any natural number is the beginning value, the sequence produced by the infinite iterations of the Collatz function becomes the eventually periodic sequence, proving an 87-year-old conjecture.

We use binary string to represent a natural number and show the composite procedure of odd-number and even-number functions, thus we propose full binary directed tree to represent the set of natural numbers and give another partition the natural number set to three sets: pure odd, pure even and mixed number. For the Collatz conjecture we make use of the parity of a natural number to analyse the sequence of iteration (or composite) of Collatz function and reduced Collatz function analog to the inverse function. We give tabular and binary strings to the algebra expression to state the sequence of Collatz, this is the key topic to proof the conjecture: the discrete powers of 2 can be changed to ultimately continuous powers of 2, finally get to pure even number and to the smallest number 1. The sequence created by the infinite iterations of the Collatz function becomes the ultimately periodic sequence if any natural number is the beginning value, proving the conjecture that has been held for 87 years.

During an interdisciplinary study of the mire “Pod Małym Śnieżnikiem”, a very old specimen of the Norway spruce (Picea abies L.) was encountered. The aim of the present work was to perform a detailed examination of this tree, to compare it to other spruce trees on the mire, and to provide support for establishing protection for this tree stand. Tree-ring cores were sampled at 1.3 m above ground using Pressler borer, in two field campaigns: in June and July 2023, the latter campaign aiming to find the oldest trees. A total of 46 trees were sampled, yielding 84 measuring radii. Tree ring widths were measured down to 0.01 mm under a stereomicroscope. The oldest sampled tree yielded a total of 370 tree rings in the two radii, representing the period 1653–2022. The average tree ring width for TM15 equals 0.33 mm/year, and shows low values (on average 0.19 mm/year) for the period 1742–1943, i.e., during the Little Ice Age cooling. TM15 does not stand out from other trees from the population with respect to height or trunk diameter. A comparison of the age of this tree to the oldest spruce trees in Poland indicates that it is one of the longest living specimens of this species. Considering the natural character of the stand, the remaining flora and the peat-forming processes taking place within the mire “Pod Małym Śnieżnikiem”, we argue that the mire should become protected by the law as soon as possible in order to preserve this valuable high-mountain habitat.

Nonlinear loads, a crucial component of power systems grids, pose a challenge due to harmonics injection. Our research tackles this issue with a novel approach - a modified green plug / switched filter compensation scheme using fuzzy logic controllers. This innovative scheme, presented in the paper, utilizes dual action pulse width modulation to ensure switching functions from harmonic reduction and capacitive compensation for inrush nonlinear type AC loads.  The scheme's multi-loop regulations and online switching effectively handle dynamic type slow acting inrush, motorized and other rectifier type-nonlinear loads, enhancing power factor, power quality at source and load buses, and reducing total harmonic distortion at key source and sensitive nonlinear load buses. A simulation model in the MATLAB/SIMULINK software environment demonstrates the efficiency of the proposed FACTS technique. The results show that voltage, current, active power, reactive power, power factor regulation, and effective energy utilization are achievable with the designed FACTS-MFCC-SFC. The switched modulated AC green plug filter significantly improves power quality and enhances power factor in the case of inrush and nonlinear loads.