Bitcoin has been launched for over a decade and made an increasing impact on the world’s financial order, which attracted extensive attention of researchers. Bitcoin system runs on a dynamic P2P network, containing tens of thousands of nodes including reachable nodes and unreachable nodes. In this article, a detection system BNS (Bitcoin Network Sniffer) was prososed, which could collect as many Bitcoin nodes as possible. For reachable nodes, the authors designed an algorithm BRF (Bitcoin Reachable-nodes Finding) based on node activity evaluation, which reduced the nodes to be detected and greatly shortened the detection time. For unreachable nodes, the authors trained a dicision tree model BUF(Bitcoin Unreachable-nodes Finding) to identify unreachable nodes based on attribute features from massive node addresses. Experiments showed that BNS performed better than the website "Bitnodes" in total number and efficiency. Based on the experimental results, the authors analyzed the real network size, node "churn" and geographical distribution.

Cervical cancer (CC) continues to be a significant global public health concern, even with preventive measures in place. In women with early-stage CC, the status of lymph nodes is of paramount importance, not only for final prognosis but also for determining the best therapeutic strategy. According to main international guidelines, pelvic full lymphadenectomy (PLND) is recommended for lymph node staging. However, in these early stages of CC, Sentinel lymph node biopsy (SLNB) has emerged as a precise technique for evaluating lymph node involvement, improving its morbidity profile. We performed a literature review through PubMed articles about progress on the application of SLNB in women with early-stage CC focusing on the comparison with PET/CT and PLND in terms of oncological outcomes and diagnostic accuracy. While the superiority of SLNB is clear compared to radiologic modalities, it demonstrates no clear oncologic inferiority over PLND, given the higher detection rate of positive lymph nodes and predominance of no lymph node recurrences. However, due to a lack of prospective evidence, particularly concerning long-term oncological safety, SLNB is not the current gold standard. With careful patient selection and adherence to straightforward protocols, a low false negative rate can be ensured. The aim of the ongoing prospective trials is to address these issues.

In the surgical treatment of lung cancer, systemic mediastinal lymph node dissection, as one important routine procedure, has been accepted by most peers in the world. However, due to the special location of some mediastinal lymph nodes, the difficulty of dissection, and the negative preoperative CT results, the specific scope of lymph node dissection is still controversial. Especially the second group, which is located at the top of thorax, is likely to be overlooked for the above reasons. Here, we report a case of lung adenocarcinoma in which the preoperative CT showed no abnormal lymph nodes in the second group and also no enlarged lymph nodes of the second group were found during the surgery, yet lymphadenectomy was still performed according the routine with the lymph node of station 2 being sampled. In the postoperative pathological report, cancer cells were found in the second group, instead of lung adenocarcinoma, these cells come from thyroid and were proved to be papillary thyroid carcinoma, which is unusual because no obvious indication of thyroid carcinoma was found in preoperative color doppler ultrasound of superficial lymph nodes.

The accurate and timely assessment of lymph node involvement is paramount in the management of patients with malignant tumors, owing to its direct correlation with cancer staging, therapeutic strategy formulation, and prognostication. Dual-energy computed tomography (DECT), as a burgeoning imaging modality, has shown promising results in the diagnosis and prediction of preoperative metastatic lymph nodes in recent years. This article aims to explore the application of DECT in identifying metastatic lymph nodes (LNs) across various cancer types, including but not limited to thyroid carcinoma (focusing on papillary thyroid carcinoma), lung cancer, and colorectal cancer. Through this narrative review, we aim to elucidate the clinical relevance and utility of DECT in the detection and predictive assessment of lymph node metastasis in malignant tumors, thereby contributing to the broader academic discourse in oncologic radiology and diagnostic precision.

We do fuzzification the concept of domination in crisp graph by using membership values of nodes, $\alpha$-strong arcs and arcs. In this paper, we introduce a new variation on the domination theme which we call vertex domination. We determine the vertex domination number $\gamma_v$ for several classes of fuzzy graphs, specially complete fuzzy graph and complete bipartite fuzzy graphs. The bounds is obtained for the vertex domination number of fuzzy graphs. Also the relationship between $M$-strong arcs and $\alpha$-strong is obtained. In fuzzy graphs, monotone decreasing property and monotone increasing property is introduced. We prove the vizing's conjecture is monotone decreasing fuzzy graph property for vertex domination. we prove also the Grarier-Khelladi's conjecture is monotone decreasing fuzzy graph property for it. We obtain Nordhaus-Gaddum (NG) type results for these parameters. The relationship between several classes of operations on fuzzy graphs with the vertex domination number of them is studied.

The last-mile logistics in cities have become an indispensable part of the urban logistics system. This study aims to explore the effective selection of last-mile logistics nodes to enhance the efficiency of logistics distribution, strengthen the corporate distribution image, and further reduce corporate operating costs and alleviate urban traffic congestion. This paper proposes a clustering-based approach to identify urban logistics nodes from the perspective of geographic information fusion. This method comprehensively considers several key indicators, including the coverage, balance, and urban traffic conditions of logistics distribution. Additionally, we employed a greedy algorithm to identify secondary nodes around primary nodes, thus constructing an effective nodal network. To verify the practicality of this model, we conducted an empirical simulation study using the logistics demand and traffic conditions in the Xianlin District of Nanjing. This research not only identified the locations of primary and secondary logistics nodes but also provided a new perspective for constructing the urban last-mile logistics system, enriching the academic research related to logistics node construction. The results of this study are of significant theoretical and practical importance for optimizing urban logistics networks, enhancing logistics efficiency, and promoting the improvement of urban traffic conditions.

In the modern world where research is taking a huge leap, the collaboration network between authors is also expanding, increasing the probability of different authors coming together to work on the same project, same research paper making them co-authors. In coauthorship, link prediction is used to anticipate new interactions between its members that are likely to occur in the future. Researchers have concentrated their efforts on studying and suggesting methods for providing effective reviews for authors who can collaborate on a scientific endeavor. In order to provide a precise link prediction, a graph database approach is proposed in this paper using nodes to determine most possible co-authors in future. In order to forecast the connections, we preprocessed the data set for the maximum relative contents. A supervised learning approach is used to execute the solution, which includes random forest classifier and logistic regression. The first findings of our technique reveal that the total of two author node’s research collaboration indices has the greatest influence on the performance of supervised link prediction than that of the traditional approach, which stimulates us to conduct further study on employing such a forecast.

Background: Ultrasonography’s usefulness in endometrial cancer (EC) diagnosis consists of its staging and predictive roles. Ultrasound-measured tumor-free distance from the tumor to the uterine serosa (uTFD) is a promising marker for this variable. The aim of the study was to determine the usefulness of this biomarker in locoregional staging, and thus in the prediction of lymph node metastasis (LNM). Methods: We conducted a single-institutional, prospective study on 116 consecutive patients with EC who underwent 2D transvaginal ultrasound examination. The uTFD marker was compared with the depth of ultrasound-measured myometrial invasion (uMI). Univariate and multivariate logit models were evaluated to assess the predictive power of the uTFD and uMI in regard to LNM. The reference standard was a final histopathology result. Survival was assessed by the Kaplan-Meyer method. Results: LNM was found in 17% of the patients (20/116). In the univariate analysis, uMI and uTFD were significant predictors of LNM. Accuracy was 70.7%, and NPV was 92.68% (OR 4.746, 95% CI 1.710-13.174) for uMI (p = 0.002), and 63.8%, and 89.02% (OR 0.842, 95% CI 0.736 – 0.963), respectively, for uTFD (p = 0.01). The cut-off value for uTFD in the prediction of LNM was 5.2 mm. The absence of LNM was associated more with biomarker values uMI <1/2 and uTFD >=5.2 mm than with the presence of metastases with uMI >1/2 and uTFD values <5.2 mm. In the multivariate analysis, the accuracy of the uMI-uTFD model was 74%, and NPV was 90.24% (p = NS). Neither uMI nor uTFD are surrogates for overall and recurrence-free survivals in endometrial cancer. Conclusions: Both uMI and uTFD, either alone or in combination, are valuable tools for gaining additional preoperative information on expected lymph node status. Negative lymph nodes status is better described by ultrasound biomarkers than a positive status. It is easier to use uTFD measurement as a biomarker of EC invasion than uMI, and the former still maintains a similar predictive value for lymph node metastases to the latter at diagnosis.

Modernist planners were given the opportunity to apply the idea of ​​the Modern Movement in the implementation of cities transforming after World War II, which was not possible before in long-term evolving structures. Usually, however, it was impossible to change everything: some urban and even architectural elements were necessary to be preserved. As a result, the elements of the ancient landscapes of these cities - historical objects and spaces - necessary for the continuity of evidence of history and identity have been preserved, sometimes through reconstruction. Finally, in some of these cities, both old and new elements contribute to the contemporary urban landscape. The aim of the research is to examine two key categories of urban structure in this perspective: 1. landmarks 2. urban network nodes. For this purpose: 1. the changes in the number and rank of the space with which the landmarks exhibition was carried out were compared; 2. the changes in the rank of nodes in the urban structure functioning both in the pre-war and in the present structure, as well as changes in their distribution and concentration areas were analyzed. The numbers of individual elements were balanced and the changes in the structure of their arrangement were analyzed with the use of a polygon grid. The analyzes were based on the case of a medium-scale European city (Białystok). Research shows that as a result of post-war reconstruction, the number of elements of the urban grid decreased, especially those of lower rank, the rank of others decreased.

Background: Myometrial invasion (MI) is a parameter currently used in transvaginal ultrasound (TVS) in endometrial cancer (EC) to determine local staging, however, without molecular diagnostics, it is insufficient for selection of high-risk cases, i.e., those with a high risk of lymph node metastases (LNM). Methods: One hundred sixteen consecutive EC patients, who had received 2D transvaginal ultrasound examinations in their preoperative workup and final histopathology results as a reference standard, were included in this prospective study. Univariate and multivariate logistic models of analyzed TVS biomarkers (tumor [T] size, T area [AREA], T volume [SPE-VOL], MI, T-free distance to serosa [TFD], endo-myometrial irregularity, [EMIR], cervical stromal involvement, CSI) were evaluated to assess the relative accuracy of the possible LNM predictors. To avoid a potential bias in assuming linear relations between LNM and continuous predictors, spline functions were applied. Calculations were made in R with the use of libraries splines, glmulti, and pROC. Results: LNM was found in 20 out of 116 (17%) patients. In univariate analysis, only uMI, EMIR, uCSI and uTFD were significant predictors of LNM. Accuracy was 0.707 (AUC 0.684, 95% CI 0.568-0.801) for uMI (p<0.01), 0.672 (AUC 0.664, 95% CI 0.547-0.781) for EMIR (p<0.01), 0.776 (AUC 0.647, 95% CI 0.529-0.765) for uCSI (p<0.01), and 0.638 (AUC 0.683, 95% CI 0.563-0.803) for uTFD (p<0.05). The cut-off value for uTFD was 5.2 mm. However, AREA and VOL revealed significant relation by non-linear analysis as well. Among all possible multivariate models, the one comprising interactions of splines of uTFD with uMI and splines of SPE-VOL with uCSI showed most usefulness. Accuracy was 0.802 (AUC 0.791, 95% CI 0.673-0.91) Conclusions: A combination of uTFD for patients with uMI>50%, and SPE-VOL for patients with uCSI, allows for the most accurate prediction of LNM in EC, rather than uMI alone.

The purpose of this review is to present the current knowledge about the diagnostic and treatment options in bladder cancer (BCa) patients with clinically positive lymph nodes (cN+). In this review compaction of CT and MRI performance in preoperative prediction of lymph node invasion (LNI) in BCa patients was presented, along with other diagnostic methods. Most scientific societies do not distinguish cN+ patients in their guidelines, recommendations concern muscle-invasive bladder cancer (MIBC) and differ between associations. Currently, the standard treatment of patients with MIBC is radical cystectomy (RC) with bilateral pelvic lymph node dis-section (PLND). The template of PLND and its therapeutic value remain debatable. Moreover, most guidelines recommend neoadjuvant chemotherapy (NAC). However, there is still lack of definitive evidence of the superiority of neoadjuvant chemotherapy over adjuvant chemotherapy. Nevertheless, the curative treatment that provides the best long-term survival in cN+ patients is a multimodal approach with a combination of chemotherapy and RC. Recent studies demonstrate the growing importance of immunotherapy. Special attention should be paid to cN+ BCa patients as the oncological outcomes are significantly worse for this group.

In rice, symbiotic N fixation via nodule bacteroids does not take place naturally. Although N fixation by endophytic and associative diazotrophs has been reported in rice, main organs and seasonal regulation for the N fixation have not been elucidated. In this study, therefore, seasonal changes of nitrogenase (acetylene reduction) activity and carbohydrate contents in culm internode (IN), basal nodes (BN), and crown root (CR) were investigated in manure compost (MC)- and chemical fertilizer-applied rice. Nitrogenase activity increased after rooting, and reached the highest activity in BN of MC-applied rice at panicle initiation. In BN of MC-applied rice, the sucrose content was low whereas the higher glucose content was detected at panicle initiation. Although bacterial and diazotrophic bacterial populations were most abundant in CR, the nitrogenase activity seemed to be restricted by its trace sucrose and glucose contents. In addition, alpha-Proteobacteria and Clostridia phyla were abundant in BN-specific bacterial microbiota at panicle initiation. These results suggest that the increased N fixation in BN at panicle initiation might be sustained both by the non-structural carbohydrate supply from photosynthetic apparatus and BN-specific bacterial microbiota including diazotrophs.

The reliability of Underwater Wireless Sensor Networks (UWSNs) is measured in terms of energy consumption (EC), end-to-end delay(E2E) and packet delivery ratio (PDR). The adverse effects of channel may cause data loss. Reducing delay up to possible extend improves the reliability of the network, also increasing the number of nodes in a particular network increase reliability. Besides, increasing the number of nodes improve reliability but also increase power consumption. In order to overcome these shortcomings, the two routing protocols are proposed in this paper, namely Delay and Reliability Aware Routing (DRAR) protocol and Cooperative Delay and Reliability Aware Routing (Co-DRAR) protocol for UWSNs. In DRAR protocol, network is divided into two equal regions where two sink nodes(SNs) are positioned at upper region of the network and two SNs are placed at the mid region of the network. The protocol choose the relay node based on residual energy (RE), distance and Bit Error Rate (BER). These parameters protect the data packets from corruption and also provide stable path (where nodes remain active for longer period and do not die quickly). The protocol uses single link and may get worse sometimes while changing channel circumstances. To address this problem, cooperative routing scheme is added to DRAR protocol in order to developed its enhanced version known as Co-DRAR protocol. The protocol works by allowing the destination to receive multiple copies of data packets in order to decide the quality of packets. The proposed protocols DRAR and Co-DRAR perform routing irrespective to geographical position of sensors nodes conversely to the some of conventional routing protocols that's way our propose protocol better perform than the well-known protocol i.e. Depth base routing (DBR) in terms of EC, E2E, PDR, dead nodes, packet drop ratio and number of alive nodes (ANs).

Keywords: Energy harvesting, Hybrid, Medical Wearable Sensor Nodes, Health Monitoring, Power Management

Influence of reaction time on silver nanoparticles-catalyzed oxidation of 3,3’,5,5’-tetramethylbenzidine (TMB) was evaluated via probing the oxidation process by recording the UV-Visible absorbance of the resulting colored products of TMB oxidation by hydrogen peroxide in the presence of silver nanoparticles as peroxides mimics. The time curve of the oxidation process was constructed, revealed that the concentration of the oxidation product was increased by increasing the reaction time and then levled off because the nanozyme active nodes were saturated after a certain reaction time and consequently the steady-state condition can be observed. The maximal activity of the silver nanozymes was achieved after a very short reaction time as short as 3.0 min and after this time, the color intensity of the oxidation products remained constant, revealing saturation of active nodes of nanoparticles with nanozyme-substrate.

This paper considers the principles of building a circuit model of film resistor cutting. The conductive resistive medium is defined with the component equations and the topology of the circuit model. A method of estimating the electric parameters of a resistor operating in the system with a measuring voltage source is shown. An equation system for the node voltages is defined, and the resistive layer parameters are analyzed as the circuit model structure changes during the cutting process.

Nodes in wireless sensor networks (WSN) are characterized particularly by their limited power and memory capabilities. Limited memory is an important parameter as it defines the size of the operating system and the processing code. As established previously, energy and memory efficiency is the most important evaluation factors of WSNs as they are directly related to data loss and network lifetime. However, based on our simulation results, memory efficiency determines the selection or abandon of nodes by the botmaster for the propagation of bots in an IoT infrastructure. Consequently, the node’s memory efficiency determined the spread of bots in the network and provides defense actors with an insight of the botmaster behavior for mitigation of the attack. Conventional botnet propagation and mitigation models did not consider the impact of node’s memory efficiency in the IoT platform. To address this gap, we build IoT-SIEF, a novel propagation model with forensic capability that will analyze command and control propagation behavior based on the perspective of the node’s memory efficiency. IoT-SIEF model used to explore the dynamics of propagation using numerical simulation with more than 50% outperform other models in mitigating the number of secondary bots. Consequently, it can serve as a basis for assisting the planning, design, and defense of such networks from the investigator's point of view.

Background and purpose: Dynamic 18F-FDG PET-CT scanning can accurately quantify 18F-FDG uptake and has been successfully applied in diagnosing and evaluating therapeutic effects in various malignant tumors. There is no conclusion as to whether it can accurately distinguish benign and malignant lymph nodes in nasopharyngeal cancer. The main purpose of this study is to reveal the diagnostic value of dynamic PET-CT in cervical lymph node metastasis of nasopharyngeal cancer through analysis. Method: We first searched for cervical lymph nodes interested in static PET-CT, measured their SUV-Max values, and found the corresponding lymph nodes in magnetic resonance images before and after treatment. The valid or invalid groups were included according to the changes in lymph node size before and after treatment. Their Ki values were measured on dynamic PET-CT and compared under different conditions. Then, we conducted a correlation analysis between different factors and Ki values. Finally, diagnostic tests were conducted to compare the sensitivity and specificity of Ki and SUV-Max. Result: We included 67 cervical lymph nodes from different regions of 51 nasopharyngeal cancer patients and divided them into valid and invalid groups based on changes before treatment. The valid group includes 50 lymph nodes, while the invalid group includes 17. Significant differences (P<0.001) between the two groups in SUV-Max, Ki-Mean, and Ki-Max values. When the SUV-Max≤4.5, there was no significant difference in the Ki-Mean and Ki-Max between the two groups (P>0.05). When SUV-Max≤4.5 and pre-treatment lymph nodes<1.0cm, the valid group had significantly higher Ki-Mean (0.00910) and Ki-Maximum (0.01004) values than the invalid group (Ki-Mean=0.00716, Ki -Max=0.00767) (P<0.05). When SUV-Max≤4.5, pre-treatment lymph nodes<1.0cm, and EBV DNA replication was normal, Ki-Mean (0.01060) and Ki-Max (0.01149) in the valid group were still significantly higher than the invalid group (Ki-Mean=0.00670, Ki-Max=0.00719) (P<0.05). The correlation analysis between different factors (SUV-Max, T-stage, normal EB virus DNA replication, age, pre-treatment lymph node<1.0cm) and Ki value showed that SUV-Max and pre-treatment lymph node<1.0cm were related to Ki-Mean and Ki-Max. Diagnostic testing was conducted, the AUC value of the SUV-Max value was 0.8259 (95% confidence interval: 0.7296-0.9222), the AUC value of the Ki-Mean was 0.8759 (95% confidence interval: 0.7950-0.9567), and the AUC value of the Ki-Max was 0.8859 (95% confidence interval: 0.8089-0.9629). It was found that the sensitivity of SUV-Max was 88%, the specificity was 76%, the sensitivity of Ki-Mean was 88%, the specificity was 80%, the sensitivity of Ki-Max was 94%, the specificity was 76%, the specificity of Ki-Mean was better than SUV-Max, the sensitivity of Ki-Max was better than SUV-Max. Conclusion: Dynamic PET-CT has shown significant diagnostic value in diagnosing cervical lymph node metastasis of nasopharyngeal cancer, especially for the small SUV value, and lymph nodes do not meet the metastasis criteria before treatment, and EBV DNA replication is normal. Moreover, its sensitivity and accuracy are superior to static PET-CT.

Non-Orthogonal Multiple Access (NOMA) is the key technology promised to be applied in next-generation networks in the near future. In this study, we propose a multi-points cooperative relaying (MPCR) NOMA model instead of just using a relay as the previous studies. Based on the channel state information (CSI), the base station (BS) selects a closest user equipment (UE) and sends a superposed signal to this UE as a first relay node. We have assumed that there are N UEs in the network and Nth UE, which is farthest from BS, has the poorest quality signal transmitted from the BS compared other UEs. Nth UE received the forwarded signal from N-1 relaying nodes that are UEs with better signal quality. At the ith relaying node, it detect its own symbol by using successive interference cancellation (SIC) and will forward the composite signal to the next closest user, namely i+1th UE, and include an excess power which will use for energy harvesting (EH) intention at the next UE. By these, the farthest UE in network can be significantly improved. In addition, closed-form expressions of outage probability for users over both the Rayleigh and Nakagami-m fading channels are also presented. Analysis and simulation results performed by Matlab software which are presented accurately and clearly show that the effectiveness of our proposed model and this model consistents with the multi-access wireless network in future.

Blockchain technology has been gaining great interest from a variety of sectors including healthcare, supply chain, and cryptocurrencies. However, Blockchain suffers from its limited ability to scale (i.e. low throughput and high latency). Several solutions have been proposed to tackle this. In particular, sharding proved that it is one of the most promising solutions to Blockchain’s scalability issue. Sharding can be divided into two major categories: (1) Sharding-based Proof-of-Work (PoW) Blockchain protocols, and (2) Sharding-based Proof-of-Stake (PoS) Blockchain protocols. The two categories achieve good performances (i.e. good throughput with a reasonable latency), but raise security issues. This article focuses on the second category. In this paper, we start by introducing the key components of sharding-based PoS Blockchain protocols. Then, we briefly introduce two consensus mechanisms, namely PoS and practical Byzantine Fault Tolerance (pBFT), and discuss their use and limitations in the context of sharding-based Blockchain protocols. Next, we provide a probabilistic model to analyze the security of these protocols. More specifically, we compute the probability of committing a faulty block and measure the security by computing the number of years to fail. Finally, we evaluate the effectiveness of the proposed model via numerical analysis.

Applications for Wireless Sensor Networks (WSNs) range from monitoring the environment to automating factories. However, sustained and effective functioning is made more difficult by Sensor Nodes (SNs) limited energy supplies in which optimization is the main issue. So with the aim of increasing the lifespan by decreasing the energy consumption of WSN, Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol with Deep Learning (DL) algorithm is analyzed in this paper. LEACH is a hierarchical mechanism that elects Cluster Heads (CHs) and regularly rotates their positions in order to allocate energy use effectively by using the same amount of energy. However, Deep Learning (DL) method is used to further improve energy optimization. In many applications, the types of Deep Learning methods like Artificial Neural Networks (ANNs) have shown to be very useful. Using this method, WSNs may make more efficient decisions that reduce energy consumption. Data aggregation, duty cycling, and transmission protocols may all be optimized by Deep Learning model's ability to recognize patterns and forecast network behavior. This results in lower energy consumption, a longer lifespan for the network, and better overall performance.

This paper presents an approach to the elastic analysis of beams subjected to Saint-Venant torsion using Green’s theorem and the finite difference method (FDM). The Saint-Venant torsion of beams, also called free torsion or unrestrained torsion, is characterized by the absence of axial stresses due to torsion; only shear stresses are developed. A solution to this torsion problem consists of finding a stress function that satisfies the governing equation and the boundary conditions. The FDM is an approximate method for solving problems described with differential equations; it does not involve solving differential equations, equations are formulated with values at selected nodes of the structure. In this paper, the beam’s cross-section was discretized using a two-dimensional grid and additional nodes were introduced on the boundaries. The introduction of additional nodes allowed us to apply the governing equations at boundary nodes and satisfy the boundary conditions. Beams with solid sections as well as multiply connected cross-sections were analyzed using this model; shear stresses and localized stresses at reentrant corners, torsion constant, and warping displacements were determined. Furthermore, beams with thin-walled closed sections, single-cell or multiple-cell, were analyzed using the Prandtl stress function whereby a linear distribution of the shear stresses over the thickness was considered; closed-form solutions for shear stresses and torsion constant were derived. The results obtained in this study showed good agreement with the exact results for rectangular cross-sections, and the accuracy was increased through a grid refinement. For thin-walled closed sections, the shear stresses obtained at the centerline using the closed-form solutions were in agreement with the values using Bredt’s analysis but the maximal values in the cross-section, which did not necessarily occur at the position with the smallest thickness, were higher; in addition, the results using the closed-form solutions were in good agreement with those using FDM.

In this paper, using the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the balance between the Lorentz force and electrical force, we succeed in deriving the fractional quantum Hall effect and the integer quantum Hall effect; we find that the latter exists as a special case of the former. Moreover, using the derived expression describing the fractional quantum Hall effect, a relationship between the plateau in the resistivity of the sample and the applied magnetic field is obtained. The findings of this model agree well with experimental measurements. Because the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the force balance have concrete physical meanings in this work, we could provide a clear picture of the origin of both the integer quantum Hall effect and the fractional quantum Hall effect.

This paper presents an approach to the two-dimensional analysis of elastic isotropic deep beams using the finite difference method (FDM). Deep beams are subjected to in-plane loading and present a shear span to height ratio of less than 2.50; consequently, Euler-Bernoulli beam theory and Timoshenko beam theory do not apply. Deep beams analysis is generally conducted using numerical methods such as the finite element method and to a lesser extent the FDM; the strut-and-tie model and the stress field method are also widely utilized. Analytical approaches usually make use of the Airy stress function, where stresses are formulated in terms of the stress function; however, the exact solution of this function satisfying all of the boundary conditions can hardly be found, even for simple cases. In this paper, deep beams were analyzed using the FDM. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected nodes of the structure. Therefore, the deep beam was discretized with a two-dimensional grid, and additional nodes were introduced at the boundaries and at positions of discontinuity (openings, brutal change of material properties, non-uniform grid spacing), the number of additional nodes corresponding to the number of boundary conditions at the node of interest. The introduction of additional nodes allowed us to apply the governing equations at boundary nodes and satisfy the boundary and continuity conditions. An Airy stress function approach and a displacement potential function approach were considered in this study whereby strong formulations of equations (equilibrium, kinematic, and constitutive) were set. Stress and stability analyses were carried out with this model; furthermore, deep beams of varying stiffness, layered beams, and beams having openings were analyzed. For slender beams, the results obtained with the Airy stress function approach showed good agreement with those of the Euler-Bernoulli beam theory, and for deep beams, the shapes of stress distributions were in good agreement with a proper understanding of the behavior of structures. On the other hand, the displacement potential function approach delivered unsatisfactory results, probably due to the use of an inefficient equation solver; a more powerful tool will be needed in future research for this purpose.