Logarithm Research Articles

Analisis Manajemen Laba dengan Adposi IFRS, Ukuran Perusahaan, dan Kepemilikan Blockholder menggunakan modifikasi Model Jones

The aim of this research is to determine the effect of IFRS Adoption, Firm Size, Leverage, and Blockholder Ownership on Earnings Management. The research was conducted on manufacturing companies listed on the Indonesia Stock Exchange (BEI) period of 2012-2015. Sample of this research consist of 64 companies using the purposive sampling method. Earnings Management is proxied with discretionary accruals and measured using a modified jones model. IFRS Adoption measured by Dummy Variables. Firm Size is measured by logarithm base ten. Leverage measured by Debt to Total Asset Ratio (DTA) and Blockholder Ownership measured by Dummy Variables. The results in this study showed that there was a positive and insignificant influence between the adoption of IFRS on earnings management, firm size variable had a negative and insignificant effect on earnings management, leverage variable had a positive and significant effect on earnings management and blockholder ownership had a negative and insignificant effect on earnings management. This research is expected to provide input to users of financial statements as decision-makers and to parties with an interest in financial reports regarding the importance of quality financial report information, especially information regarding earnings management

A novel logarithmic operational law and aggregation operators for trapezoidal neutrosophic number with MCGDM skill to determine most harmful virus.

In the current era, the theory of vagueness and multi-criteria group decision making (MCGDM) techniques are extensively applied by the researchers in disjunctive fields like recruitment policies, financial investment, design of the complex circuit, clinical diagnosis of disease, material management, etc. Recently, trapezoidal neutrosophic number (TNN) draws a major awareness to the researchers as it plays an essential role to grab the vagueness and uncertainty of daily life problems. In this article, we have focused, derived and established new logarithmic operational laws of trapezoidal neutrosophic number (TNN) where the logarithmic base μ is a positive real number. Here, logarithmic trapezoidal neutrosophic weighted arithmetic aggregation (Larm) operator and logarithmic trapezoidal neutrosophic weighted geometric aggregation (Lgeo) operator have been introduced using the logarithmic operational law. Furthermore, a new MCGDM approach is being demonstrated with the help of logarithmic operational law and aggregation operators, which has been successfully deployed to solve numerical problems. We have shown the stability and reliability of the proposed technique through sensitivity analysis. Finally, a comparative analysis has been presented to legitimize the rationality and efficiency of our proposed technique with the existing methods.

Moments of log-tanh integrals

An investigation into families of integrals containing powers of the arctanh and log functions will be undertaken in this paper. It will be shown that Euler sums play an important part in the solution of these integrals. In another special case we prove that the corresponding log-tanh integral can be represented as a linear combination of the product of zeta functions and the Dirichlet eta function.

Manganese accumulation in probiotic Lactobacillus paracasei ATCC 55544 analyzed by synchrotron X-ray fluorescence microscopy and impact of accumulation on the bacterial viability following encapsulation

Lactobacillus spp. are known to accumulate large amounts of inorganic manganese, which protects against oxidative damage by scavenging free radicals. The ability of probiotic L. paracasei ATCC 55544 to maintain viability during long-term ambient storage may be enhanced by this microorganism's ability to accumulate manganese, which may act as a free radical scavenger. To investigate this hypothesis, X-ray fluorescence microscopy (XFM) was employed to determine the changes in the elemental composition of L. paracasei during growth in the MRS medium with or without added manganese. Moreover, manganese uptake by cells as a function of physiological growth state, early log vs. stationary phase was evaluated. The semiquantitative X-ray fluorescence microscopy results revealed that lower levels of manganese accumulation occurred during the early log phase of bacterial growth of L. paracasei cells (0.0064 µg/cm2) compared with the stationary phase cells (0.1355 µg/cm2). L. paracasei cells grown in manganese deficient MRS medium resulted in lower manganese uptake by cells (0.0027 µg/cm2). The L. paracasei cells were further embedded in milk powder matrix using a fluidized-bed drying technique and stored at a water activity (aw) of 0.33 at 25 °C for 15 days. The viability counts of L. paracasei cells grown in MRS medium harvested after 18 h growth and embedded in milk powder matrix retained viability of (9.19 ± 0.12 log CFU/g). No viable L. paracasei cells were observed in the case of embedded L. paracasei cells grown in manganese-deficient MRS medium harvested after 18 h growth or in the case of L. paracasei cells harvested after 4 h when grown in MRS medium. The lower level of manganese accumulation was found to be related to the loss of bacterial viability during storage.

Ion solubilization in surface soil layers of montane region with heavy snowfall

Although eluvial (E) horizons of podzols typically form on sandy soils, they can also form in acidic clayey soils. Two non-exclusive hypotheses for E-horizon formation in clayey soils are podzolization and the reductive dissolution of iron (Fe). To analyze the effects of redox reactions on Fe solubilization in montane soils in regions with heavy snowfall, we measured the redox potential (Eh), pH, and Fe2+ concentration in soil solutions sampled from the Midagahara peatland of Mt. Tateyama and Mt. Naeba. We also conducted continual in situ Eh monitoring of soils under snow cover in a beech forest on Mt. Naeba. In the Midagahara peatland, Eh decreased with increasing clay content and was lowest in E horizons. A mineral stability diagram of the soil solution data, in which (pH + 3pe) was expressed as a function of log [Fe2+], suggests that ferrihydrite dissolution from the E horizons and precipitation of the other Fe oxides (lepidocrocite or goethite) in the B horizons are ongoing processes. A combination of low pH and reducing conditions in clayey soils can increase the loss of Fe oxides to form impermeable E horizons. Continual monitoring of Eh in the soil of Mt. Naeba revealed a sharp drop in Eh under heavy snow cover during winter. The reducing conditions in winter, along with consistently low pH, are favorable for the formation of E horizons in clayey soils, which lead to poor drainage and summer flooding. The combination of clayey E horizons and flooding with snowmelt are required for peat accumulation in the Midagahara peatland.

A volumetric prediction model for postoperative cyst shrinkage

ObjectivesWith only limited information available on dimensional changes after jaw cyst surgery, postoperative cyst shrinkage remains largely unpredictable. We aimed to propose a model for volumetric shrinkage based on time elapsed since cyst surgery.Material and methodsWe used data from patients that underwent cyst enucleation or decompression between 2007 and 2017 and had at least three computed tomography (CT) scans per patient. We fitted one simple exponential decay model [V(t) = V0 · e−ɑt] and one model with a patient-specific decay rate [Vk(t) = V0 · e−βt + γkt].ResultsBased on 108 CT scans from 36 patients (median age at surgery: 45.5 years, IQR: 32.3–55.3, 44% female), our simple exponential decay model is V(t) = V0· e−0.0035t where V(t) is the residual cyst volume after time t elapsed since surgery, V0 is the initial cyst volume, and e is the base of the natural logarithm. Considering a patient-specific decay rate, the model is Vk(t) = V0· e−0.0049t + γkt where γk is normally distributed, with expectation 0 and standard deviation 0.0041.ConclusionsUsing an exponential regression model, we were able to reliably estimate volumetric shrinkage after jaw cyst surgery. The patient-specific decay rate substantially improved the fit of the model, whereas adding specific covariates as interaction effects to model the decay rate did not provide any significant improvement.Clinical relevanceEstimating postoperative cyst shrinkage is relevant for both treatment planning of jaw cyst surgery as well as evaluating the clinical success of the surgical approach.

Vitamin D and white matter hyperintensities: results of the population-based Heinz Nixdorf Recall Study and 1000BRAINS.

Cross-sectional studies showed an inverse association between serum 25-hydroxyvitamin D (25OHD) and white matter hyperintensities (WMHs) whereas the few longitudinal studies did not. The association between baseline 25OHD and WMHs at 10-year follow-up in the Heinz Nixdorf Recall Study plus 1000BRAINS was investigated. Data of 505 participants (49% women, 56.2±6.6years) with 25OHD at baseline (2000-2003) and WMH volume and grade of WMHs using the Fazekas classification at 10-year follow-up were analysed. The association between deseasonalized 25OHD and the base-10 logarithm of WMH volume was evaluated by multiple linear regression, adjusted for age, sex, education, smoking, alcohol consumption, sports, diabetes mellitus, systolic blood pressure and total cholesterol. β-estimators were transformed back (10β ). Using multiple logistic regression, odds ratios (ORs) and 95% confidence intervals (95% CI) were calculated to evaluate the association between deseasonalized 25OHD and Fazekas grades (0, absence and 1, punctate foci vs. 2, beginning and 3, large confluence). Mean 25OHD was 17.0±8.2ng/ml, and mean deseasonalized 25OHD was 16.9±7.5ng/ml. Mean WMH volume was 16.6±17.4ml, range 1-132ml. Most grade 2-3 WMHs were found to be periventricular (39% of the participants), parietal (32%) and frontal (31%) (temporal 6%, occipital 3%). The linear regression showed an inverse association between 25OHD and WMH volume. On average, a 25OHD increase of 1ng/ml was associated with a reduced WMH volume by a factor of 0.99 (95% CI 0.98; 1.00) (fully adjusted). There was also some indication for an inverse association between 25OHD and extent of periventricular (OR 0.98 [95% CI 0.96; 1.01]), frontal (0.99 [0.97; 1.02]) and parietal (0.98 [0.95; 1.00]) WMHs according to the Fazekas classification. Lower 25OHD may be a risk factor for the occurrence of WMHs.

Improved defogging algorithm for sea surface images based on dark channel prior theory

To improve the quality of the sea surface image under foggy weather, we propose an innovative single-image defogging algorithm based on the dark channel prior principle. The median filter is combined with the minimum filter for the purpose of obtaining accurate dark channel values in areas where the depth of field changes sharply. Then, the algorithm constructs a fog density detection model to obtain the atmospheric light value from the dense fog area and effectively eliminate the interference of bright spots. Subsequently, the atmospheric scattering model is applied to obtain a preliminary fog-free image. Finally, an adaptive logarithmic mapping algorithm is introduced to enhance the visual effect of the defogged image. Experimental results show that the proposed algorithm can effectively improve image quality degradation and avoid halos in the intersection region of sky and sea, Moreover, the method does not require guided filtering for transmittance refinement, which greatly improves the execution speed of the algorithm.

Bottleneck analysis: Simple prediction of the precision of a planned case-control or cohort study based on healthcare registers.

In pharmacoepidemiological studies, the precision of effect estimates usually depends on the lowest number in the underlying two by two table. We denote this the "bottleneck count" (BNC). We describe how to translate the BNC into an achievable precision and provide empirical examples. First, we derive a theoretical prediction of the precision in a study where only the BNC determines precision. As an illustration, we calculated the expected precision of a null-effect study on retinoids and peptic ulcer bleeding, expressed as the upper/lower confidence limit ratio (ULCLR). Finally, we reviewed 126 effect estimates from the literature, analyzing the relationship between the predicted and achieved precision. The log-log transformed ULCLR was shown to be a simple linear function of log(BNC). The expected annual number of retinoid-users experiencing a peptic ulcer bleeding was 9.8, yielding an estimated ULCLR for a 1-year study of 3.84. The literature review showed an inverse linear relationship between the logarithmic BNC and the log-log transformed ULCLR, which was largely independent of study design, effect measure and category of BNC. Achieved precision deviated little from predictions but was usually lower than predicted, particularly with low BNC. The precision of a study can be predicted simply and with good accuracy from the BNC, which is useful for determining whether a study is worth pursuing or not.

Using Software Containers for Privileged Access Management in Cloud Environments: A Novel Approach to Handle Access Management for Cloud-based Networks

This paper presents a novel approach for privileged access and session management using containers. Current solutions are built using proxies, proxy suites or jump servers, but they do not cater for third party remote access security requirements, have additional vulnerabilities and have scalabilty limitations.
 The novelty of the solution proposed in this paper is a global orchestrator that instantiates a purpose-built container adapted to the virtual network functions’ system. Every container has a logging function, a pre-defined time-to-live and one-time-credentials. This approach is secure because the containers isolate different connections, privileges are restricted, permissions are always time-limited and the provider has full control over the sessions. The solution brings several other security enhancements, discussed in this paper.

Exposure of street sweepers to cadmium, lead, and arsenic in dust based on variable exposure duration in zinc smelting district, Northeast China

Street dust is an important contributor to heavy metal exposure in street sweepers. In this work, the levels of cadmium (Cd), lead (Pb), and arsenic (As) in street dust were evaluated, and the corresponding health implications for street sweepers in the smelting district of Huludao city northeast China were assessed. The contributions of dietary sources and dust to total metal exposure in street sweepers were compared. Because street sweepers are exposed to street dust both during work and nonwork hours, the health risks faced by street sweepers are uncertain. Therefore, variable exposure duration was considered using a deterministic model. A probabilistic risk assessment model was developed to explore the health effects of street dust on street sweepers via Monte Carlo simulation. The various exposure parameters that affect risk were analyzed using sensitivity analysis. The average Cd, Pb, and As levels in the hair of street sweepers were 2.04, 20.12, and 0.52 mg·kg-1, respectively. These values were higher than those for residents (i.e., not street sweepers) of Huludao. Strong correlations were found between the logarithms (base 10) of the Cd, Pb, and As contents in dust and hair (rCd = 0.581, p < 0.01; rPb = 0.428, p < 0.01; rAs = 0.378, p < 0.01; n = 62). Based on analysis using deterministic models, the maximum exposures to Cd and Pb via dust through the alimentary canal were nearly three and six times higher than the dietary exposures, respectively. Sensitivity analysis indicated that exposure duration is an important parameter.

Distributed Denial of Service Attacks Detection System by Machine Learning Based on Dimensionality Reduction

Data mining algorithms have essential methods and rules that can contribute in detecting and preventing various types of network attacks. These methods are utilized with the intrusion detection systems that can be designed and developed preserve the information in organizations from damage. Specifically, the data mining technique allows users to effectively distinguish between normal and malicious traffic with good accuracy. In this paper, a methodology for revealing and detecting (DDOS) network attack was suggested using DM algorithms. The utilized methodology is divided especially into four parts, each part has its own rules, as the following: First one is the pre-processing which consists of three sub-steps: (i) encoding, (ii) log2, and (iii) PCA. Encoding is used by converting the original nominal packets into numeric features. Standardization of data was performed using logarithmic algorithm. Finally the PCA technique is applied eight times for several different features to reduce the dimensions of the dataset. The second stage is an anomaly detection model, (RF) algorithm is implemented for the extraction of data patterns while classification the types of the given features in training step, (NB) algorithm was also used in classifying the data to compare the results of its classification with the results of using the classifier (RF). In the third stage, the outcomes were tested by implementing the already trained datasets. In the fourth stage, the proposed system performance evaluation metrics were collected such as the rates of accuracy, false alarm, detection, precision, and F.measure.MIX dataset were utilized to train and test the proposed model which resulted from merging two datasets (PORTMAP+LDAP), which are used from the CICDDOS2019 datasets, each consisting of several types of attack packets, and benign packets.Several metrics were utilized in the evaluation of the proposed system. The best outcomes were obtained for detection by using the log2 algorithm and PCA technique in the preprocessing step and using (RF)classifier to classify the dataset. the accuracy when using MIX dataset was 99.9764%, the detection rate was 100%, false alarm rate ≍ 0, and the F.measure was 99.9% when PCA = 25.

The power-law component of the X-ray emissions from pulsar-wind nebulae and their pulsars

ABSTRACT To look for possible phenomenological connections between pulsar timing properties and emissions from pulsar-wind nebulae and their pulsars, we studied the power-law component of the X-ray emissions from 35 pulsar-wind nebulae that have a detected pulsar in X-rays. Our major results are as follows. (1) The power-law components of the X-ray luminosities, in the energy range from 0.5–8 keV, of the nebulae and of the pulsar both show a strong correlation with the pulsar spin-down power ($\dot{E}$), consistent with earlier studies. However, equally significant correlations with the magnetic field strength at the light cylinder (Blc) are also found. The similar significance level of the correlations with $\dot{E}$ and with Blc suggests that not only $\dot{E}$ but also Blc plays an important role in understanding these power-law emissions. (2) Thermal X-ray emissions are detected in 12 pulsars among the 35 samples. With derived temperature as one additional variable, we found that the photon indices of a pulsar’s non-thermal X-ray power-law spectra can be well described by a linear function of log P, $\log \dot{P}$, and temperature logarithm log T. This indicates that the surface temperature of neutron stars plays an important role in determining the energy distribution of the radiating pair plasma in pulsar magnetospheres.

Nutritional status of vitamin B_(12) and its influence factors in Chinese lactating women in 2013

To examine the vitamin B_(12) status of lactating women in China and to analyze the factors affecting the level of serum vitamin B_(12) in these subjects. Participants were from the Chinese National Nutrition and Health Surveillance in 2013. By multi-stage stratified cluster randomly sampling method, 10 331 lactating women were selected from 55 counties of 30 provinces in China. Questionnaire was conducted to collect the basic information of lactating women and the dietary intake of them in the past one month was collected by food frequency questionnaire. A total of 20% of the total number of lactating women(a total of 1976) were randomly selected to analyze serum vitamin B_(12) by electro-chemiluminescence immunoassay method. Serum vitamin B_(12) deficiency was defined as a serum vitamin B_(12) level&lt;200 pg/mL. The distribution of serum vitamin B_(12 )was lognormal, a generalized linear model was used to analyze the factors affecting the serum vitamin B_(12) level after logarithm transformation of it. The median of serum vitamin B_(12)(P25, P75) in lactating women was 469. 0(349. 0, 633. 5)pg/mL, the prevalence of vitaminB_(12) deficiency was 2. 7%(53/1976)and marginal deficiency rate was 12. 8%. With the increase of the education level of the lactating women the rate of vitamin B_(12) deficiency decreased gradually. The rate of vitamin B_(12 )deficiency of the lactating women presented regional differences and varied significantly among different regionals, education levels and the mothers who were breastfeeding or not. The value of serum vitamin B_(12 )was analyzed by generalized linear regression model showed that the levels of serum vitamin B_(12) in general rural counties and medium-sized or small cities were 1. 07 and 1. 13 times higher than those in poor rural areas, respectively. The serum vitamin B_(12) level of non-lactating women was 1. 08 times higher than that of lactating women. The serum vitamin B_(12 )level of the lactating women with junior high school level or below was significantly lower than that of the lactating women with college education and university education level, 88. 3% and 85. 0% of the lactating women with college education and university education, respectively. Serum vitamin B_(12) levels were positively correlated with intake of livestock meat, fish and seafood. The status of vitamin B_(12) in lactating women in China is good. Our findings suggest that some regionals, education levels, breastfeeding or not and livestock meat, fish meat and seafood supplement may be associated with serum vitamin B_(12 )in lactating women.

Harmonic Progression in Bioinformatics and Recurrent Series in Inherited Biostructures

The article is devoted to the study of new approaches to the development of mathematical models in genetic biomechanics, which studies the structural relationships of the genetic coding system with genetically inherited biological forms. More specifically, we are talking about models based on the recurrent harmonic progression whose connection with the information sequences of DNA molecules in the genomes of higher and lower organisms was recently revealed. In particular, the article describes previously unknown connections of the function of natural logarithms with the structures of the molecular genetic system, which allow modelling the main psychophysical logarithmic law by Weber-Fechner and also many other logarithmic structures in genetically inherited biological systems. In physics, the harmonic progression is traditionally considered, first of all, as related to standing waves in resonators. Our results are correlated with Frohlich’s vibration-resonant theory about collective quantum effects and long-range communication in biological systems.

Approximation algorithms for profit maximisation in multicast D2D networks

As the demand for mobile data services increases, telecom companies need to develop wise strategies to retain existing customers. For instance, in a multicast scenario, satisfying individual user's quality of service (QoS), data demand at varying rates, etc. are complicated tasks. Earlier works on device-to-device (D2D) multicast have majorly discussed the cases of throughput maximisation without considering the individual user's data request rates. In this paper, we propose two algorithms to maximise the telecom operator's profit collected from the users in a two-hop D2D multicast network, when users have different channel qualities and data request rates while receiving multicast data through a single transmission session. First, we model our multicast scheme for the proposed scenario as a budgeted maximum coverage problem. Later, we propose two approximation algorithms that guarantee approximation ratios of 1−1/ √e and 1 − 1 / e, respectively, where e denotes the base of the natural logarithm. Numerical results show that the proposed algorithms perform better than the other candidate algorithms and nearly approximates the optimal solution.

Determination of Conducted EMI in SiC Based Dual Active Bridge Converter

Power converters are required to work faster and with higher power density with the developing technology. Therefore, the converter is expected to work in more than one direction. Usage of Dual Active Bridge DC-DC Converter is an example. To increase the power density of the converters, it is necessary to increase the switching frequency. In conventional Si MOSFET based converters, power losses are very high and cause high electromagnetic interferences at high frequencies. These disadvantages lead developers to the use of wide-band gap semiconductor based converters such as SiC However, SiC MOSFETs will also emit electromagnetic interference (EMI) above a certain frequency. In this study, the EMI, emitted at certain frequencies by the Dual Active Bridge (DAB) DC-DC Converter, is simulated by the LTspice. It was observed that the Si-based inverter parts of the DAB converter generate 10 V EMI on the linear base, that means 140 dBµV EMI on the logarithmic base, at 20 kHz. The SiC-based converter does not emit any noise at the same frequency. However, when the frequency was increased to 250 kHz, it was determined that the SiC based converter emitted 2.3 V noise on the linear base, thus 123 dBµV noise on the logarithmic base. This study shows that not only Si MOSFET’s but only SiC MOSFET’s emit EMI over a certain frequency.

Auto-Trending daily quality assurance program for a pencil beam scanning proton system aligned with TG 224.

The Daily Quality Assurance (DQA) for a proton modality is not standardized. The modern pencil beam scanning proton system is becoming a trend and an increasing number of proton centers with PBS are either under construction or in planning. The American Association of Physicists in Medicine has a Task Group 224 report published in 2019 for proton modality routine QA. Therefore, there is a clinical need to explore a DQA procedure to meet the TG 224 guideline. The MatriXX PT and a customized phantom were used for the dosimetry constancy checking. An OBI box was used for imaging QA. The MyQA(TM) software was used for logging the dosimetry results. An in‐house developed application was applied to log and auto analyze the DQA results. Another in‐house developed program "DailyQATrend" was used to create DQA databases for further analysis. All the functional and easy determined tasks passed. For dosimetry constancy checking, the outputs for four gantry rooms were within ±3% with room to room baseline differences within ±1%. The energy checking was within ±1%. The spot location checking from the baseline was within 0.63 mm and the spot size checking from the baseline was within −1.41 ± 1.27 mm (left–right) and −0.24 ± 1.27 mm (in–out) by averaging all the energies. We have found that there was also a trend for the beam energies of two treatment rooms slowly going down (0.76% per month and 0.48 per month) after analyzing the whole data trend with linear regression. A DQA program for a PBS proton system has been developed and fully implemented into the clinic. The DQA program meets the TG 224 guideline and has web‐based logging and auto treading functions. The clinical data show the DQA program is efficient and has the potential to identify the PBS proton system potential issue.

When are randomized trials unnecessary? A signal detection theory approach to approving new treatments based on non-randomized studies.

New therapies are increasingly approved by regulatory agencies such as the Food and Drug Administration (FDA) and the European Medicines Agency (EMA) based on testing in non-randomized clinical trials. These treatments have typically displayed "dramatic effects" (ie, effects that are considered large enough to obviate the combined effects of biases and random errors that may affect the study results). The agencies, however, have not identified how large these effects should be to avoid the need for further testing in randomized controlled trials (RCTs). We investigated the effect size that would circumvent the need for further RCTs testing by the regulatory agencies. We hypothesized that the approval of therapeutic interventions by regulators is based on heuristic decision making whose accuracy can be best characterized by the application of signal detection theory (SDT). We merged the EMA and FDA database of approvals based on non-RCT comparisons. We excluded duplicate entries between the two databases. We included a total of 134 approvals of drugs and devices based on non-RCTs. We integrated Weber-Fechner law of psychophysics and recognition heuristics within SDT to provide descriptive explanations of the decisions made by the FDA and EMA to approve new treatments based on non-randomized studies without requiring further testing in RCTs. Our findings suggest that when the difference between novel treatments and the historical control is at least one logarithm (base 10) of magnitude, the veracity of testing in non-RCTs seems to be established. Drug developers and practitioners alike can use the change in one logarithm of effect size as a benchmark to decide if further testing in RCTs should be pursued, or as a guide to interpreting the results reported in non-randomized studies. However, further research would be useful to better characterize the threshold of effect size above which testing in RCTs is not needed.

Approximation Algorithms for the Generalized Team Orienteering Problem and its Applications

In this article we study a generalized team orienteering problem (GTOP), which is to find service paths for multiple homogeneous vehicles in a network such that the profit sum of serving the nodes in the paths is maximized, subject to the cost budget of each vehicle. This problem has many potential applications in IoTs and smart cities, such as dispatching energy-constrained mobile chargers to charge as many energy-critical sensors as possible to prolong the network lifetime. In this article, we first formulate the GTOP problem, where each node can be served by different vehicles, and the profit of serving the node is a submodular function of the number of vehicles serving it. We then propose a novel (1 - (1/e) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2+e</sup> )-approximation algorithm for the problem, where ε is a given constant with 0 <; ε ≤ 1 and e is the base of the natural logarithm. In particular, the approximation ratio is about 0.33 when ε = 0.5. In addition, we devise an improved approximation algorithm for a special case of the problem where the profit is the same by serving a node once and multiple times. We finally evaluate the proposed algorithms with simulation experiments, and the results of which are very promising. Especially, the profit sums delivered by the proposed algorithms are up to 14% higher than those by existing algorithms, and about 93.6% of the optimal solutions.