Summation Method Research Articles

Comparative analysis and prediction of cation exchange capacity via summation: influence of biochar type and nutrient ratios

IntroductionEnhancing soil cation exchange capacity (CEC) is of paramount importance for sustainable agriculture and ecosystem health. This study investigated the pivotal role of biochar in altering soil CEC and challenges conventional assumptions about universal effects of biochar application.MethodsContrasting biochar types, one with a low ash content of 4.4% (switchgrass-derived biochar, SGB) and the other with a high ash content of 45.9% (poultry litter-derived biochar, PLB) were used. Two experiments treated with increasing biochar application rates were conducted: one without plants and the other grown with ryegrass. Effective CEC (summation method) was determined by two extraction methods: Mehlich-3 (M3) and ammonium acetate (AA).Results and discussionThe SGB decreased CEC by 27% on average (from both experiments) from the lowest to the highest rate of biochar application, while the PLB significantly increased CEC by 91%. This highlights the critical role of biochar properties in influencing CEC dynamics. In the second experiment, ryegrass cultivation revealed the greater importance of the calcium and magnesium/potassium ratio ([Ca+Mg]/K) in the soil CEC than CEC only for plant growth in biochar-amended soils. The ratios for optimum ryegrass production ranged from 82‒86 (M3) and 69‒74 (AA), which was translated to 88:11:1 Ca:Mg:K percent base saturation ratios. Moreover, predictive models for estimation of soil CEC after biochar application were successfully developed based on initial soil and biochar CEC. However, M3 was more reliable than AA for such predictions mainly because it was more successful in predicting nutrient availability from biochar. These models offer a promising tool for informed soil management decisions.ConclusionThis research emphasizes the importance of biochar feedstock, elucidates nutrient ratio effects on plant growth, and provides a practical means to anticipate soil CEC changes post-biochar application.

Different methods of 3D QRS area calculation from vectorcardiographic X, Y, and Z Leads.

3DQRSarea is a strong marker for cardiac resynchronization therapy and can be obtained by taking the (i) summation or the (ii) difference of the areas subtended by positive and negative deflections in X, Y, Z vectorcardiographic electrocardiogram (ECG) leads. We correlated both methods with the instantaneous-absolute-3D-voltage-time-integral (VTIQRS-3D). 3DQRSarea consistently underestimated the VTIQRS -3D, but the summation method was a closer and more reliable approximation. The dissimilarity was less apparent in left bundle branch block (r2 summation.996vs. difference.972) and biventricular paced ECGs (r2.996vs..957) but was more apparent in normal ECGs (r2.988vs..653).

Successful robotic kidney transplantation for surgeons with no experience in minimally invasive surgery: a single institution experience.

Robotic kidney transplantation (RKT) is a novel and welcomed innovation yielding good surgical outcomes. However, data on the feasibility and safety of performing RKT by surgeons with a lack of prior minimally invasive surgery (MIS) experience are limited. The authors aimed to evaluate the surgical and functional results of RKT and present the learning curves (LC) of RKT by a single surgeon with no prior experience in MIS. This was a retrospective study of all RKT performed between November 2019 and April 2023 at Severance Hospital in Seoul, South Korea. The authors analyzed surgical and functional outcomes, as well as complication rates of RKT in comparison to open kidney transplantation (OKT). The authors evaluated LCs using the cumulative summation method to describe the number of cases associated with the competency of a single surgeon. A total of 50 patients who underwent RKT and 104 patients who underwent OKT were included in this study. In RKT group, the median surgical console time was 193min (interquartile range, 172-222) and the median vascular anastomoses time was 38min (35-44). Total operation time was 323min (290-371) and rewarming time was 62.5min (56.0-70.0) in RKT group compared to 210min (190-239) and 25min (21-30), respectively, in OKT group. Despite extended surgical durations with a robotic technique, both groups had comparable intraoperative and postoperative outcomes, as well as renal function. Estimated blood loss and post-transplant hospital stays were significantly lower in RKT group than in OKT group. LC analysis of RKT by the single surgeon revealed that surgical competence was achieved after 15 cases. Even if surgeons do not have prior experience with MIS, they can rapidly overcome the LC and safely perform RKT with adequate preparation and acquisition of basic robotic surgical techniques.

Ramanujan Summation for Pascal’s Triangle

The concept of Pascal’s triangle has fascinated not only professional mathematicians but also everyone interested in exploring science. Similarly, the idea of Ramanujan summation has made a revolution in mathematical research after it was introduced by Srinivasa Ramanujan. In this paper, we will provide the Ramanujan summation methods for numbers located in slant diagonals of Pascal’s triangle and derive a generalized formula for such summations.

Left atrium stress echocardiography: correlation between left atrial volume, function, and B-lines at rest and during stress

Aim: Left atrial volume index (LAVI), left atrial reservoir function through left atrial reservoir strain (LASr), and B-lines in lung ultrasound serve as supplementary indicators of left ventricular filling pressures. This study analyzes the interrelation between LAVI, LASr, and B-lines in both resting and peak vasodilator stress. Methods: Dipyridamole stress echocardiography (SE) was conducted on 252 individuals (180 males, 71%, age 65 years ± 10 years) with chronic coronary syndromes. LAVI was quantified using the biplane disk summation method; LASr was obtained using 2-dimensional speckle tracking echocardiography; B-lines were evaluated through a simplified 4-site scan in the third intercostal space during lung ultrasound. Results: During SE, a reduction in LAVI (26 ml/m2 ± 14 ml/m2 vs. 24 ml/m2 ± 12 ml/m2, P < 0.001) and an increase in LASr from rest (33% ± 8% vs. 38% ± 10%, P < 0.001) were respectively observed from rest to stress. B-lines were increased significantly during SE, from 19 (7.5%) to 29 (11.5%), P < 0.001. A substantial, inverse linear correlation was identified between LAVI and LASr both at rest (r = –0.301, P < 0.001) and peak stress (r = –0.279, P < 0.001). At group analysis, peak B-lines showed a direct correlation with peak LAVI (r = 0.151, P = 0.017) and an inverse correlation with peak LASr (r = –0.234, P < 0.001). In individual assessments, 9.7% (20/207) of patients displayed stress B-lines with normal LAVI and preserved LASr, while 20% (9/45) exhibited stress B-lines with abnormalities in both LAVI and LASr. Conclusions: Vasodilator SE with combined left atrial and volume assessment, related to pulmonary congestion, is feasible with a high success rate. Pulmonary congestion is more frequent with dilated left atrium with reduced atrial contractile reserve (ClinicalTrials.gov identifier: NCT030.49995; NCT050.81115).

Multi-criteria decision analysis of alternative fuel buses: methodology and case-study

ABSTRACT In this paper, a Multi-Criteria Decision Analysis methodological framework is developed to rank alternative fuel buses. It is applied to the case-study of the public transportation system of the island of Gotland in Sweden. Seven alternative fuel buses are identified: bioethanol, biodiesel, biogas, plug-in hybrid electric biodiesel, plug-in hybrid electric biogas, battery electric and hybrid electric hydrogen fuel cell buses. These alternatives are evaluated under 11 criteria that are categorized under four dimensions and measured under a Life Cycle Sustainability Analysis approach where possible. The ranking is accomplished by means of the weighted summation method; weights are determined through the Analytic Hierarchy Process. Explicit weights on these criteria provided by local experts and stakeholders are used to evaluate the alternatives under various island-specific scenarios. Results show that biogas and plug-in hybrid electric biogas buses are the preferred alternatives as long as biogas is produced from waste residuals; otherwise, the import of biodiesel could be the preferred short-term alternative. Bioethanol appears to be the least suitable fuel. The developed methodological framework proved helpful to the local authorities of Gotland when they sought to identify the best compromise fuel bus solution and has shown that it can be applied in similar case-studies.

Trap induced broadening in a potential hydrogen lattice clock

We consider the potential use of optical traps for precision measurements in atomic hydrogen (H). Using an implicit summation method, we calculate the atomic polarisability, the rates of elastic/inelastic scattering and the ionisation rate in the wavelength range (395–1000) nm. We extend previous work to predict three new magic wavelengths for the 1S–2S transition. At the magic wavelengths, the 1S–2S transition is unavoidably and significantly broadened due to trap-induced ionisation associated with the high intensity required to trap the 1S state. However, we also find that this effect is partially mitigated by the low mass of H, which increases the trap frequency, enabling Lamb–Dicke confinement in shallow lattices. We find that a H optical lattice clock, free from the motional systematics which dominate in beam experiments, could operate with an intrinsic linewidth of the order of 1 kHz. Trap-induced losses are shown not to limit measurements of other transitions.

Asymptotic estimates for deviations of Fejér means on Poisson integrals

The work is devoted to the investigation of problem of approximation of continuous periodic functions of a real variable by trigonometric polynomials generated by linear methods of summation of Fourier series. The simplest example of the process of linear approximation of periodic functions is approximation of functions by partial sums of their Fourier series. However, sequences of partial Fourier sums are not uniformly convergent on the whole class of continuous periodic functions. Therefore, numerous studies are devoted to the study of approximation properties of approximating methods, which are generated by different transformations of sequences of partial sums of the Fourier series and allow obtaining sequences of trigonometric polynomials that are uniformly convergent for the entire class of continuous functions. In particular, Fejér means have been intensively studied in recent decades. One of the important tasks in this direction is study of the asymptotic behavior of the upper bounds of the deviations of trigonometric polynomials for a fixed class of periodic functions. The aim of the work is to systematize the known results concerning the approximation of classes of periodic functions of high smoothness by arithmetic means of Fourier sums, and to present new facts obtained for a more general case. In paper we investigate the asymptotic behavior of upper bounds on classes of Poisson integrals of periodic functions of real variable of deviations of linear means of Fourier series, which are constructed using the Fejér summation method. We study the classes consist of analytic functions of a real variable, which can be regularly extended into the corresponding strip of the complex plane. In the work, asymptotic inequalities for the upper bounds of the deviations of the Fejér means on the class of Poisson integrals were found. In certain case of parameters defining the class, the obtained formulas coincide with previously known asymptotic equalities.

Response of soil nutrients and erodibility to slope aspect in the northern agro-pastoral ecotone, China

Abstract. Soil erosion, considered a major environmental and social problem, leads to the loss of soil nutrients and the degradation of soil structure and impacts plant growth. However, data on the effects of land use changes caused by vegetation restoration on soil nutrients and erodibility for different slope aspects are limited. This study was conducted to detect the response of soil nutrients and erodibility to slope aspect in a typical watershed in the northern agro-pastoral ecotone in China. The following indexes were used to determine the improvement in soil nutrients and erodibility through a weighted summation method: the comprehensive soil nutrient index and the comprehensive soil erodibility index. The results showed that the vegetation types with the highest comprehensive soil quality index (CSQI) values on western, northern, southern, and eastern slopes were Pinus sylvestris and Astragalus melilotoides (1.45), Caragana korshinskii and Capillipedium parviflorum (2.35), Astragalus melilotoides (4.78), and Caragana korshinskii and Lespedeza bicolor (5.00), respectively. Slope aspect had a significant effect on understory vegetation characteristics, soil nutrients, and soil erodibility. Understory vegetation and soil characteristics explained 50.86 %–74.56 % of the total variance in soil nutrients and the erodibility. Mean weight diameter and total phosphorus were the main factors that affected the CSQI for different slope aspects. Our study suggests that the combinations of species, such as C. korshinskii and L. bicolor, were the optimal selection to improve soil nutrients and soil erodibility for any slope aspect.

What is Islamic Hotel? A Simple Additive Weighting Method

Halal tourism or halal industry is a tourism concept that focuses on the maqosid sharia values in it which are usually divided into: Hifdz Addin (religion), Hifdz nafs (soul), Hifdz aql (reason), Hifdz nasl (offspring), and hifdz Bi'ah (environment).Indonesia was awarded the first rank in the field of the best halal tourist destinations in the world according to the Global Muslim Travel Index (GMTI) 2023 report. The method used in this research uses qualitative methods. In this qualitative method will use the SAW (Simple Additive Weighting) method commonly known as the weighted summation method. This method is carried out with the type of data here carried out qualitatively which makes two research objects namely Noor In and Harris Hotel lodging. In interviews and recording methods through the web, newspapers, and journals, the results of the above research are data on the assessment of maqasid sharia indicators in sentul area hotels. Of these two hotels consist of harris hotel and Noor In inn. We get a reverse comparison of various aspects of maqasid sharia indicators in the fields of hifdz maal and hidz nashl. The first object is the Noor-In inn which has a value of 0.8333 and explains that this value gets the highest accreditation, namely A because it has a value between 0.75 - 1. While the second object is the Harris Sentul hotel which has a value of 0.3889 and states that this value has a maqaosid sharia accreditation of C or Fair maqosid sharia because it has between 0.25 - 0.49.

Additively Manufactured Flexible Liquid Metal-Coated Self-Powered Magnetoelectric Sensors with High Design Freedom.

Although additive manufacturing enables controllable structural design and customized performance for magnetoelectric sensors, their design and fabrication still require careful matching of the size and modulus between the magnetic and conductive components. Achieving magnetoelectric integration remains challenging, and the rigid coils limit the flexibility of the sensors. To overcome these obstacles, this study proposes a composite process combining selective laser sintering (SLS) and 3D transfer printing for fabricating flexible liquid metal-coated magnetoelectric sensors. The liquid metal forms a conformal conductive network on the SLS-printed magnetic lattice structure. Deformation of the structure alters the magnetic flux passing through it, thereby generating voltage. A reverse model segmentation and summation method is established to calculate the theoretical magnetic flux. The impact of the volume fraction, unit size, and height of the sensors on the voltage is studied, and optimization of these factors yields a maximum voltage of 45.6 µV. The sensor has excellent sensing performance with a sensitivity of 10.9kPa-1 and a minimum detection pressure of 0.1kPa. The voltage can be generated through various external forces. This work presents a significant advancement in fabricating liquid metal-based magnetoelectric sensors by improving their structural flexibility, magnetoelectric integration, and design freedom.

An Assessment of the Environmental Sensitivity of the Coastal Zone of Negombo, Sri Lanka

The coastal area of Sri Lanka provides various ecosystem services amidst various challenges. For instance, coastal erosion is an ongoing problem caused by human activities. Sensitivity assessment one of the measures which helps planning coastal areas to ensure better urban development and environmental protection. This study developed a framework for the assessment of the environmental sensitivity of coastal zones. The framework primarily considered sensitive biological factors and external disturbances, demonstrated in the Negombo coastal zone. 16 indicators were selected, considering the area with AHP technique, and the weighted summation method was used to assess the sensitivity. The assessment enables the study region of an area of around 38km2 to be divided into zones of very high, high, moderate, low, and very low sensitivity. The maps generated out of this assessment can be used to identify areas that require prioritized management. The very highly sensitive areas need priority in management as the sensitive biological aspects and external disturbances were both high in them. In the other areas, either the external disturbance or the sensitive biological aspects are high. Having identified the level of sensitivity, appropriate actions could be taken to either maintain the status of the biological aspect or to regulate the external disturbance in that area. Some areas were identified as very low to low sensitivity indicating their potential for development. This study provides a model framework to assess the sensitivity of coastal zones as a measure towards planning for sustainable developments in them.

Best approximation by «angle» and the absolute Cesàro summability of double Fourier series

This article is devoted to the topic of absolute summation of series or Cesaro summation. The relevance of this article lies in the fact that a type of absolute summation with vector index which has not been previously studied is considered. In this article, a sufficient condition for the vector index absolute summation method was obtained in terms of the best approximation by «angle» of the functions from Lebesgue space. The theorem that gives a sufficient condition proves the conditions that are sufficient in different cases, which may depend on the parameters. From this proved theorem, a sufficient condition on the term mixed smoothness modulus of the function from Lebesgue space, which is easily obtained by a well-known inequality, is also presented.

The thermodynamic properties of diatomic gases. A rigorous analytical approach

The paper reports a closed-form analytical representation of the thermodynamic functions of diatomic molecules in the ground electronic state. For this purpose, analytical formulas for vibrational and rotational partition functions are derived. A rigorous method is proposed for factorizing the vibrational and rotational contributions to the ro-vibrational partition function using an average vibrational quantum number. The behavior of thermodynamic functions as a function of temperature is discussed for carbon monoxide as a test system. The reliability of the analytical method is verified by comparison with experimental data and with the direct summation method, which uses theoretical values of energy levels.

On the paradoxical behavior of divergent series

This paper presents some considerations on summation method on infinite divergent series. Irrefutably divergent series don’t have a sum in the traditional logic of the term. However there are extensions, where transformed definitions apportion changed values to the same divergent series and they rarely have agreeable properties. Particularly, at beginning and manipulating these instinctively, it easily comes across nasty paradoxes. In this article for any odd prime p, the divergent series and on using this representation for further leads to a paradoxical bewildering novel formula which evidently contradicts the basic principles of arithmetic and the definition of a divergent series identical to Ramanujan paradox. Illustrations to support this illogicality result are discussed analytically and demonstrated graphically.

Spatiotemporal variations and spillover effects of regional water resources metabolism efficiency with heterogeneous resource endowments

Abstract Scientific evaluation of water resources metabolism efficiency (WME) has essential theoretical and practical value for regional water resources security and sustainable utilization. Based on the framework of the water resources metabolism process and construction of the indicator system of WME, the spatiotemporal variations of WME were analyzed using the weighted summation method in the Eastern, Central, and Western regions of China during the period from 1990 to 2020 with heterogeneous resource endowments. The exploratory spatial data analysis (ESDA) and spatial Durbin model were applied to analyze the spatial autocorrelation patterns and reveal spillovers of the WME. The results show that (1) The WME increased at different speeds in the Eastern, Central, and Western regions from 1990 to 2020 with heterogeneous resource endowment, and the spatial variation of WME in the Eastern and Central regions was significantly higher than in the Western regions. (2) The WME had significant spatial autocorrelation except in 2015, indicating obvious spatial agglomeration characteristics and spatial heterogeneity simultaneously. (3) The spatial spillover effects analysis indicated that the waste virtual recycling use ratio, the ratio of output virtual water and input virtual water, and industrial water ratio were the primary factors influencing WME.

The summation method and application of power series

The summation method and application of power series

Efficacy of Marker-Based Motion Capture for Respiratory Cycle Measurement: A Comparison with Spirometry.

Respiratory rate monitoring is fundamental in clinical settings, and the accuracy of measurement methods is critical. This study aimed to develop and validate methods for assessing respiratory rate and the duration leof respiratory cycle phases in different body positions using optoelectronic plethysmography (OEP) based on a motion capture video system. Two analysis methods, the summation method and the triangle method were developed. The study focused on determining the optimal number of markers while achieving accuracy in respiratory parameter measurements. The results showed that most analysis methods showed a difference of ≤0.5 breaths per minute, with R2 ≥ 0.94 (p < 0.001) compared to spirometry. The best OEP methods for respiratory rate were the abdominal triangles and the sum of abdominal markers in all body positions. The study explored inspiratory and expiratory durations. The research found that 5-9 markers were sufficient to accurately determine respiratory time components in all body positions, reducing the marker requirements compared to previous studies. This interchangeability of OEP methods with standard spirometry demonstrates the potential of non-invasive methods for the simultaneous assessment of body segment movements, center of pressure dynamics, and respiratory movements. Future research is required to improve the clinical applicability of these methods.

Field validation of post-mortem interval estimation based on insect development. Part 1: Accuracy gains from the laboratory rearing of insect evidence

There is a consensus that forensic methods must be valid. The high quality of the method may be fully demonstrated only through validation. Unfortunately, there are very few experimental or casework validations of entomological methods for estimating post-mortem interval (PMI). Here, we present the first part of the results from the field validation of minimum PMI (PMImin) estimates based on insect development. From eight pig carcasses (24–46.4 kg) exposed in a forest habitat of Western Poland, one every one or two months, we collected insect evidence with standard entomological techniques. Using weather station temperatures and the thermal summation method, PMImin was estimated based on insect life stages that were reared under controlled laboratory conditions. Through rearing an insect until the next developmental landmark (or until eclosion), its age at the time of collection (and eventually PMImin) may be estimated by subtracting thermal accumulation in the laboratory from the corresponding thermal constant. We hypothesized that rearing insect evidence significantly improves the accuracy of PMImin compared to the estimation based on non-reared insect evidence. The results clearly supported this hypothesis. However, the accuracy significantly increased only in the case of these insects that developed normally during rearing. When their development in the laboratory was prolonged, PMImin was significantly less accurate. For the normal development sample the accuracy improved in all species and life stages. The largest accuracy gains from rearing were recorded for Calliphora vomitoria (Diptera: Calliphoridae) and Stearibia nigriceps (Diptera: Piophilidae). Moreover, when puparia or third instar larvae were reared, gains were larger than in the case of earlier life stages. In conclusion, this study demonstrated that the method of rearing insect evidence to improve the accuracy of PMImin is valid. However, it needs to be used with caution, since substantial part of the evidence may die or slow down their development in the laboratory, which violates assumptions of the method.

An asymptotic development of the Poisson integral for Laguerre polynomial expansions

The purpose of this paper is the study of the rate of convergence of Poisson integrals for Laguerre expansions. The convergence of partial sums of Fourier series of functions in Lp spaces was studied, for several classes of orthogonal polynomials. In the Laguerre case Askey and Waigner proved convergence for functions f∈Lp0,+∞ with 4/3<p<4. In this paper we deal with the Poisson integral Arf0<r<1 which arises by applying Abel’s summation method to the Laguerre expansion of the function f. About 50 years ago, Muckenhoupt intensively studied the Poisson integral for the Laguerre and Hermite polynomials. Among other things he proved pointwise convergence, the convergence by norm, and that the Poisson integral is a contraction mapping in Lp0,∞. Toczek and Wachnicki gave a Voronovskaja-type theorem by calculating the limit 1−r−1Arfx−fx as r→1−, provided that f′′x exists. We generalize this formula by deriving a complete asymptotic development. All its coefficients are explicitly given in a concise form. As an application we apply extrapolation methods in order to improve the rate of convergence of Arfx as r→1−.