Point-wise Method Research Articles

Theory and Method of Power System Integrated Security Region Irrelevant to Operation States: An Introduction

Abstract How to comprehensively consider the power flow constraints and various stability constraints in a series of power system optimization problems without affecting the calculation speed is always a problem. The computational burden of probabilistic security assessment is even more unimaginable. In order to solve such problems, a security region (SR) methodology is proposed, which is a brand-new methodology developed on the basis of the classical point-wise method. Tianjin University has been studying the SR methodology since the 1980s, and has achieved a series of original breakthroughs that are described in this paper. The integrated SR introduced in this paper is mainly defined in the power injection space, and includes SRs to ensure steady-state security, transient stability, static voltage stability, and small-disturbance stability. These SRs are uniquely determined for a given network topology (as well as location and clearing process for transient faults) and given system component parameters, and are irrelevant to operation states. This paper presents 11 facts and related remarks to introduce the basic concepts, composition, dynamics nature, and topological and geometric characteristics of SRs. It also provides a practical mathematical description of SR boundaries and fast calculation methods to determine them in a concise and systematic way. Thus, this article provides support for the systematic understanding, future research, and applications of SRs. The most critical finding on the topological and geometric characteristics of SRs is that, within the scope of engineering concern, the practical boundaries of SRs in the power injection space can be approximated by one or a few hyperplanes. Based on this finding, the calculation time for power system probabilistic security assessment (i.e., risk analysis) and power system optimization with security constraints can be decreased by orders of magnitude.

Pointwise Methods to Measure Long-term Visual Field Progression in Glaucoma

Rates of visual field (VF) progression vary among patients with glaucoma. Knowing the rate of progression of individual patients would allow appropriately aggressive therapy for patients with high rates of visual loss and protect those with low rates from unnecessary therapy. To compare 3 pointwise methods of estimating the rate of VF progression in glaucoma. This retrospective, observational cohort study included 729 eyes of 567 consecutive patients with primary open-angle glaucoma who had at least 6 reliable VFs and at least 3 years of follow-up. One hundred seventy-six patients (257 eyes) were treated at a tertiary glaucoma center; in addition, data were collected from 391 participants (472 eyes) in the Advanced Glaucoma Intervention Study. Data were collected from May 1988 to November 2004 and analyzed from October 2018 to February 2019. Estimates of VF progression were measured with guided progression analysis (GPA), pointwise linear regression (PLR), and the glaucoma rate index (GRI). A subgroup analysis was performed in a subset of patients with likely VF progression and likely VF stability. Proportion of VF series detected as progressing, estimates of false-positive proportions, time to detect progression, and agreement among measures. Among the 567 patients included in the analysis, mean (SD) age was 65.6 (9.7) years, 300 (52.9%) were female, and 295 (52.0%) were white. The median baseline mean deviation was -6.7 (interquartile range [IQR], -11.6 to -3.5) dB; the median follow-up time, 8.9 (IQR, 7.3-10.4) years. The proportion of eyes labeled as progressing was 27.7% according to the GPA, 33.5% according to the PLR, and 52.9% according to the GRI; pairwise differences for GRI vs PLR were 20% (95% CI, 17%-23%); for GRI vs GPA, 25% (95% CI, 22%-29%); and for PLR vs GPA, 6% (95% CI, 3%-9%; P < .001 for all comparisons, McNemar test). The shortest median time to progression was with the GRI (8.8 [IQR, 2.4-10.5 years), compared with the GPA and PLR (both >16 years). The hazard ratio of VF progression for GRI vs PLR (reference) was 11.3 (95% CI, 9.2-13.7); for GRI vs GPA (reference), 18.1 (95% CI, 14.5-22.6); and for PLR vs GPA (reference), 1.5 (95% CI, 1.3-1.9; P < .001 for all comparisons, Cox proportional hazards regression). These results held in the subgroup with likely progression; the proportions of progressing eyes were 73.7% (115 of 156) for GPA, 81.4% (127 of 156) for PLR, and 92.9% (145 of 156) for GRI. Pairwise difference for GRI vs PLR was 11.5% (95% CI, 7.4%-17.6%; P < .001, McNemar test); for GRI vs GPA, 19.2% (95% CI, 12.6%-26.4%; P < .001, McNemar test); and for PLR vs GPA, 7.7% (95% CI, 0.3%-15.7%; P = .08, McNemar test). These results suggest GRI can detect long-term VF progression in glaucoma earlier than PLR or GPA. Validation with prospective designs may strengthen the generalizability and value of this method.

Efficient Wrench-Closure and Interference-Free Conditions Verification for Cable-Driven Parallel Robot Trajectories Using a Ray-Based Method

This letter introduces a novel approach to verify the feasibility of curved trajectories under both the interference-free (IFC) and wrench-closure (WCC) conditions for spatial cable-driven parallel robots (CDPRs). Existing ray-based methods can only be used either for translation or single degree-of-freedom (DoF) motion, limiting its use to verify the motion of practical trajectories. In this work, the trajectory representation proposed allows the IFC and WFC for the entire trajectory to be verified by simply solving a set of univariate polynomial equations. The translation motion is expressed as polynomial time parametric functions and the orientation motion is defined using a spherical linear interpolation (SLERP) in the quaternion representation for a desired start and end orientation. It is then shown that for the proposed trajectory representation, the IFC and WFC can be verified by solving a set of univariate polynomial equations. Moreover, the exact degree of the resulting polynomial equations are derived for a 6-DoF spatial CDPR. Simulation on a range of different trajectory forms, from linear, quadratic and cubic paths to higher degree functions, show the effectiveness of the method. Finally, comparison with the well-accepted point-wise method shows that the proposed method is more efficient, accurate and ensures the solution continuity.

Autoregressive wild bootstrap inference for nonparametric trends

In this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend. The bootstrap method is easy to implement and does not require any adjustments in the presence of missing data, which makes it particularly suitable for climatological applications. We establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions, allowing for general patterns of missing data, serial dependence and heteroskedasticity. The finite sample properties of the method are studied in a simulation study. We use the method to study the evolution of trends in daily measurements of atmospheric ethane obtained from a weather station in the Swiss Alps, where the method can easily deal with the many missing observations due to adverse weather conditions.

Sentiment disagreement and bitcoin price fluctuations: a psycholinguistic approach

ABSTRACTWe investigate the extent to which Bitcoin price fluctuations are associated with investors’ sentiment disagreement. We employ three textual sentiment analysis techniques: 1) a Python library offered by the Computational Linguistics and Psycholinguistics Research Center; 2) Loughran and McDonald’s (2011) dictionary; and 3) semantic orientation by the point-wise mutual information method. The results show that investors’ attention and sentiment disagreement induce extremely high volatility and jumps in Bitcoin prices. These findings complement existing studies on how investors’ sentiment manifests in asset prices.

Characterization of white matter changes along fibers by automated fiber quantification in the early stages of Alzheimer's disease.

Brain white matter fiber bundles in patients with mild cognitive impairment (MCI) and Alzheimer's disease (AD) have abnormalities not usually seen in unaffected subjects. Ideal algorithm of the localization-specific properties in white matter integrity might reveal the changes of tissue properties varying along each tract, while previous studies only detected the mean DTI parameters of each fiber. The aim of this study was to investigate whether these abnormalities of nerve fiber tracts are localized to specific regions of the tracts or spread throughout and to analyze which of the examined fiber tracts are involved in the early stages of Alzheimer's disease. In this study, we utilized VBA, TBSS as well as AFQ together to comprehensively investigate the white matter fiber impairment on 25 CE patients, 29 MCI patients and 34 normal control (NC) subjects. Two tract profiles, fractional anisotropy (FA) and mean diffusivity (MD), were extracted to evaluate the white matter integrity at 100 locations along each of 20 fiber tracts and then we validated the results with 27 CE patients, 21 MCI patients and 22 NC from the ADNI cohort. Also, we compare the AFQ with VBA and TBSS in our cohort. In comparison with NC, AD patients showed widespread FA reduction in 25% (5 /20) and MD increase in 65%(13/20) of the examined fiber tracts. The MCI patients showed a regional FA reduction in 5% (1/20) of the examined fiber tracts (right cingulum cingulate) and MD increase in 5%(1/20) of the examined fiber tracts (left arcuate fasciculus). Among these changed tracts, only the right cingulum cingulate showed widespread disruption of myelin or/and fiber axons in MCI and aggravated deterioration in AD, findings supported by FA/MD changes both by the mean and FA changes by point wise methods and TBSS. And the AFQ findings from ADNI cohort showed some similarity with our cohort, especially in the pointwise comparison of MD profiles between AD vs NC. Furthermore, the pattern of white matter abnormalities was different across neuronal fiber tracts; for example, the MCI and AD patients showed similar FA reduction in the middle part of the right cingulum cingulate, and the anterior part were not damaged. However, the left arcuate fasciculus showed MD elevation located at the temporal part of the fibers in the MCI patients and expanding to the temporal and middle part of the fibers in AD patients. So, the AFQ may be an alternative complementary method of VBA and TBSS, and may provide new insights into white matter degeneration in MCI and its association with AD.

Distributed Temperature Sensing Monitoring of Well Completion Processes in a CO₂ Geological Storage Demonstration Site.

The Distributed Temperature Sensing (DTS) profiles obtained during well completion of a CO2 monitoring well were analyzed to characterize each well completion process in terms of temperature anomalies. Before analysis, we corrected the depth by redistributing the discrepancy, and then explored three temperature calibration methods. Consequently, we confirmed the depth discrepancy could be well corrected with conventional error redistribution techniques. Among three temperature calibration methods, the conventional method shows the best results. However, pointwise methods using heat coil or in-well divers also showed reliable accuracy, which allows them to be alternatives when the conventional method is not affordable. The DTS data revealed that each well completion processes can be characterized by their own distinctive temperature anomaly patterns. During gravel packing, the sand progression was monitorable with clear step-like temperature change due to the thermal bridge effect of sand. The DTS data during the cementing operation, also, clearly showed the progression up of the cement slurry and the exothermic reaction associated with curing of cement. During gas lift operations, we could observe the effect of casing transition as well as typical highly oscillating thermal response to gas lifting.

Exploit latent Dirichlet allocation for collaborative filtering

Previous work on the one-class collaborative filtering (OCCF) problem can be roughly categorized into pointwise methods, pairwise methods, and content-based methods. A fundamental assumption of these approaches is that all missing values in the user-item rating matrix are considered negative. However, this assumption may not hold because the missing values may contain negative and positive examples. For example, a user who fails to give positive feedback about an item may not necessarily dislike it; he may simply be unfamiliar with it. Meanwhile, content-based methods, e.g. collaborative topic regression (CTR), usually require textual content information of the items, and thus their applicability is largely limited when the text information is not available. In this paper, we propose to apply the latent Dirichlet allocation (LDA) model on OCCF to address the above-mentioned problems. The basic idea of this approach is that items are regarded as words, users are considered as documents, and the user-item feedback matrix constitutes the corpus. Our model drops the strong assumption that missing values are all negative and only utilizes the observed data to predict a user’s interest. Additionally, the proposed model does not need content information of the items. Experimental results indicate that the proposed method outperforms previous methods on various ranking-oriented evaluation metrics. We further combine this method with a matrix factorization-based method to tackle the multi-class collaborative filtering (MCCF) problem, which also achieves better performance on predicting user ratings.

A global envelope test to detect non‐random bursts of trait evolution

AbstractThe joint analysis of species’ evolutionary relatedness and their morphological evolution has offered much promise in understanding the processes that underpin the generation of biological diversity.Disparity through time (DTT) is a popular method that estimates the relative trait disparity within and between subclades, and compares this to the null hypothesis that trait values follow Brownian evolution along the time‐calibrated phylogenetic tree. To visualise the differences a confidence envelope is normally created by calculating, at every time point, the 97.5% minimum and 97.5% maximum disparity values from multiple simulations of the null model. The null hypothesis is rejected whenever the empirical DTT curve falls outside of this envelope, and these time periods may then be linked to events that may have sparked non‐random trait evolution.Here, simulated data are used to show this pointwise (ranking at each time point) method of envelope construction suffers from multiple testing and a poor, uncontrolled, false‐positive rate. As a consequence it cannot be recommended. Instead, each DTT curve can be given a single rank based upon their most extreme disparity value, relative to all other curves, and across all time points. Ordering curves this way leads to a test that avoids multiple testing, but still allows construction of a confidence envelope. The null hypothesis is rejected if the empirical DTT curve is ranked within the most extreme 5% ranked curves from the null model. Comparison of the rank envelope curve to the Morphological Disparity Index and Node Height tests shows it to have generally higher power to detect non‐Brownian trait evolution. An extension to allow simultaneous testing over multiple traits is also detailed.Overall the results suggest the new rank envelope test should be used in null model testing for DTT analyses. The rank envelope method can easily be adapted into recently developed posterior predictive simulation methods used in model selection analyses. More generally, the rank envelope test should be adopted whenever a null model produces a vector of correlated values and the user wants to determine where the empirical data are different to the null model.

Reservoir lithology classification based on seismic inversion results by Hidden Markov Models: Applying prior geological information

Abstract Hidden Markov Models (HMMs) have been applied to predict reservoir lithologies using seismic inversion results as inputs. This approach takes into account the conditional probabilities between different lithologies, i.e. the vertical transitions in sedimentary sequences. These properties are used as prior geological information. In order to relate the seismic inversion results to the true well-log data, HMMs need to be trained based on the Expectation-Maximization theory. Application of the resulting model on a synthetic example from the Book Cliffs (Utah, USA) showed that most lithologies are classified correctly, even for some thin layers. A comparison with point-wise methods in which data samples are treated independently from each other, such as k-means and fuzzy logic classifiers, leads to the conclusion that the spatial correlation in HMMs allows better lithological predictions because the prior information accounts for the geological depositional processes. A real case study with data from the Vienna Basin (Austria) is performed, in which lithologies in a 3D cube are obtained based on properties from seismic inversions, via trained HMMs. While the vertical sequences are shown to be reasonably well predicted, the horizontal continuities are not. This indicates that the future research should focus on the lateral geological relationships.

Incorporating temporal dynamics into LDA for one-class collaborative filtering

In the one-class collaborative filtering (OCCF) scenario, the elements of the user-item rating matrix consist each take one of only two values: either “like” or unknown. Previous methods for solving the OCCF problem can be roughly categorized into content-based methods, pointwise methods, and pairwise methods. A fundamental assumption of these approaches is that all missing values in a rating matrix can be treated as “dislike”. However, this assumption may not hold because the missing values are not always negative. Sometimes users do not give positive feedback on an item simply because they are not familiar with it rather than because they dislike it. In addition, content-based methods usually require textual information on the items. In many cases, however, sufficient textual information is not available; therefore, content-based methods are not applicable. Moreover, a user’s preference for items usually drifts over time, but the previous methods cannot capture the temporal dynamics of this drift. In this paper, we propose to modify the latent Dirichlet allocation (LDA) model to address the above-mentioned problems. Our method uses only observed rating data to predict users’ interests and effectively avoids the issue of data skew. Furthermore, to address the issue that users’ preferences for items usually drift over time, we assign a different weight to each rating according to its timestamp when using Gibbs sampling to estimate the parameters of the LDA model. In this way, the temporal dynamics of the user preferences can be captured. We report experiments conducted to evaluate our model. The results show that the proposed model outperforms state-of-the-art approaches for the OCCF problem.

Analysis of the stress field in a wedge using the fast expansions with pointwise determined coefficients

The stress problem for the elastic wedge-shaped cutter of finite dimensions with mixed boundary conditions is considered. The differential problem is reduced to the system of linear algebraic equations by applying twice the fast expansions with respect to the angular and radial coordinate. In order to determine the unknown coefficients of fast expansions, the pointwise method is utilized. The problem solution derived has explicit analytical form and it’s valid for the entire domain including its boundary. The computed profiles of the displacements and stresses in a cross-section of the cutter are provided. The stress field is investigated for various values of opening angle and cusp’s radius.

Performance monitoring of a wind turbine using extreme function theory

A power curve relates the power produced by a wind turbine to the wind speed. Usually, such curves are unique to the various types of wind turbines, so that by monitoring the power curves, one may monitor the performance of the turbine itself. Most approaches to monitoring a system or a structure at a basic level, generally aim at differentiating between a normal and an abnormal state. Typically, the normal state is represented by a model, and then abnormal, or extreme data points are identified when they are compared to that model. This comparison is very often done pointwise on scalars in the univariate case, or on vectors, if multivariate features are available. Depending on the actual application, the pointwise approach may be limited, or highly prone to false identifications. This paper presents the use of extreme functions for the performance monitoring of wind turbines. Power curves from an actual wind turbine, are assessed as whole functions, and not individual datapoints, with the help of Gaussian process regression and extreme value distributions, with the ultimate aim of the performance monitoring of the wind turbine at a weekly resolution. The approach is compared to the more conventional pointwise method, and approaches which make use of multivariate features, and is shown to be superior in terms of the number of false identifications, with a significantly lower number of false-positives without sacrificing the sensitivity of the approach.

Automatic recognition of symptom severity from psychiatric evaluation records

This paper presents a novel method for automatically recognizing symptom severity by using natural language processing of psychiatric evaluation records to extract features that are processed by machine learning techniques to assign a severity score to each record evaluated in the 2016 RDoC for Psychiatry Challenge from CEGS/N-GRID. The natural language processing techniques focused on (a) discerning the discourse information expressed in questions and answers; (b) identifying medical concepts that relate to mental disorders; and (c) accounting for the role of negation. The machine learning techniques rely on the assumptions that (1) the severity of a patient’s positive valence symptoms exists on a latent continuous spectrum and (2) all the patient’s answers and narratives documented in the psychological evaluation records are informed by the patient’s latent severity score along this spectrum. These assumptions motivated our two-step machine learning framework for automatically recognizing psychological symptom severity. In the first step, the latent continuous severity score is inferred from each record; in the second step, the severity score is mapped to one of the four discrete severity levels used in the CEGS/N-GRID challenge. We evaluated three methods for inferring the latent severity score associated with each record: (i) pointwise ridge regression; (ii) pairwise comparison-based classification; and (iii) a hybrid approach combining pointwise regression and the pairwise classifier. The second step was implemented using a tree of cascading support vector machine (SVM) classifiers. While the official evaluation results indicate that all three methods are promising, the hybrid approach not only outperformed the pairwise and pointwise methods, but also produced the second highest performance of all submissions to the CEGS/N-GRID challenge with a normalized MAE score of 84.093% (where higher numbers indicate better performance). These evaluation results enabled us to observe that, for this task, considering pairwise information can produce more accurate severity scores than pointwise regression – an approach widely used in other systems for assigning severity scores. Moreover, our analysis indicates that using a cascading SVM tree outperforms traditional SVM classification methods for the purpose of determining discrete severity levels.

A Pointwise Method for Identifying Biomechanical Heterogeneity of the Human Gallbladder.

Identifying the heterogeneous biomechanical property of human gallbladder (GB) walls from non-invasive measurements can have clinical significance in patient-specific modeling and acalculous biliary pain diagnosis. In this article, a pointwise method was proposed to measure the heterogeneity of ten samples of human GB during refilling. Three different points, two on the equator of GB body 90° apart and one on the apex of GB fundus, were chosen to represent the typical regions of interest. The stretches at these points were estimated from ultrasound images of the GB during the bile emptying phase based on an analytical model. The model was validated against the experimental data of a lamb GB. The material parameters at the different points were determined inversely by making use of a structure-based anisotropic constitutive model. This anisotropic model yielded much better accuracy when compared to a number of phenomenologically-based constitutive laws, as demonstrated by its significantly reduced least-square errors in stress curve fitting. The results confirmed that the human GB wall material was heterogeneous, particularly toward the apex region. Our study also suggested that non-uniform wall thickness of the GB was important in determining the material parameters, in particular, on the parameters associated with the properties of the matrix and the longitudinal fibers—the difference could be as large as 20–30% compared to that of the uniform thickness model.

A globally linearly convergent method for pointwise quadratically supportable convex–concave saddle point problems

We study the Proximal Alternating Predictor–Corrector (PAPC) algorithm introduced recently by Drori, Sabach and Teboulle [8] to solve nonsmooth structured convex–concave saddle point problems consisting of the sum of a smooth convex function, a finite collection of nonsmooth convex functions and bilinear terms. We introduce the notion of pointwise quadratic supportability, which is a relaxation of a standard strong convexity assumption and allows us to show that the primal sequence is R-linearly convergent to an optimal solution and the primal-dual sequence is globally Q-linearly convergent. We illustrate the proposed method on total variation denoising problems and on locally adaptive estimation in signal/image deconvolution and denoising with multiresolution statistical constraints.

Progress of point-wise scanning superresolution methods

Optical microscope has been giving impetus to the development of modern technology. As the advancement of these techniques, high resolution microscopy becomes crucial in biological and material researches. However, the diffraction limit restricts the resolution of conventional microscopy. In 1968, confocal microscopy, the first pointwise scanning superresolution method, appeared. It improves the imaging resolution, enhances the contrast, and thus breaks through the diffraction limit. Since then many superresolution methods have come into being, among which the pointwise scanning superresolution method earns reputation for its high imaging resolution and contrast. The stimulated emission depletion microscopy becomes the most prominent method with an achievable resolution of about 2.4 nm and then widely used. Besides, the newly developed fluorescence emission difference microscopy (FED) and the saturated absorption competition microscopy (SAC) have their advantages of non-constraint on fluorescent dyes, low saturated beam power, simplified optical setups, while they achieve a resolution of lower than /6. Further explorations of FED will be keen on vivo biological observations by using it, while that of SAC can concentrate on enhancing the resolution on a nanoscale and reducing the signal-to-noise ratio. In addition, the Airyscan technique in which a detector array is used for image acquisition, can serve as a complementary tool to further enhance the imaging quality of pointwise scanning superresolution method. The detector-array enables both the narrowed size of pinhole and the increasing of the acquired signal intensity by 1.84 folds. The other methods, e.g. superoscillation lens and high-index resolution enhancement by scattering, have the potentialities to obtain superresolved image in material science or deep tissues. After being developed in the past three decades, the superresolution methods now encounter a new bottleneck. Further improvement of the current methods is aimed at imaging depth, and being used more practically and diversely. In this review, we detailedly describe the above pointwise scanning superresolution methods, and explain their principles and techniques. In addition, the deficiencies and potentialities of these methods are presented in this review. Finally, we compare the existing methods and envision the next generation of the pointwise scanning superresolution methods.

Large-scale stabilization control of input-constrained quadrotor

The quadrotor has been the most popular aircraft in the last decade due to its excellent dynamics and continues to attract ever-increasing research interest. Delivering a quadrotor from a large fixed-wing aircraft is a promising application of quadrotors. In such an application, the quadrotor needs to switch from a highly unstable status, featured as large initial states, to a safe and stable flight status. This is the so-called large-scale stability control problem. In such an extreme scenario, the quadrotor is at risk of actuator saturation. This can cause the controller to update incorrectly and lead the quadrotor to spiral and crash. In this article, to safely control the quadrotor in such scenarios, the control input constraint is analyzed. The key states of a quadrotor dynamic model are selected, and a two-dimensional dynamic model is extracted based on a symmetrical body configuration. A generalized point-wise min-norm nonlinear control method is proposed based on the Lyapunov function, and large-scale stability control is hence achieved. An enhanced point-wise, min-norm control is further provided to improve the attitude control performance, with altitude performance degenerating slightly. Simulation results showed that the proposed control methods can stabilize the input-constrained quadrotor and the enhanced method can improve the performance of the quadrotor in critical states.

Stability constants and stoichiometries of chromium and zirconium carboxylates complexes calculated by four comparative methods

Four comparative methods for determination of stoichiometries and stability constants of chromium and zirconium complexes with citric and propanoic acids were studies, in purpose to select the most accurate and sensitive method, and to compare the formation of complexes of these two transition metals. (Cr 1st transition series group 6B, Zr 2nd transition series group 4B)Metal-ligand stability constants and stoichiometries of the above systems were determined by Calvin &amp; Bjerrum pH-metric titration technique as adopted by Irving &amp; Rossotti.Four methods employed were point-wise calculation method, half integral method, linear plot method and least squares method. The result seems in a good agreement with each other and any method can represents the other.

Studies of Binary Complexes of Metal Ions with 2, 2-Bipyridyl by Potentiometry

In biological systems transition metal ions exists in the form of different metal ligand complexes therefore investigations on the stability of metal complexes in relation with various structural features are important. Such type of study will help for understanding the driving forces leading to the formation of such complexes in the biological systems. Here we have reported systematic potentiometric studies on the formation of metal ligand complexes of transition metal ions with 2, 2- bipyridyl ligand in aqueous solution at 27 0 C temperature in the presence of electrolyte 1N NaNO3. The protonation constant and metal ligand stability constants were determined using Irving Rossotti titration technique. Data obtained from titrations were analysed by SCOGS computer programs. The protonation constant values obtained by half integral method and point wise method are in agreement.