Approximate Criterion Research Articles

Uniform approximation of functions by solutions of strongly elliptic equations of second order on compact subsets of

Criteria for the uniform approximation of functions by solutions of second-order strongly elliptic equations on compact subsets of are obtained using the method of reduction to similar problems in , which were previously investigated by Mazalov. A number of metric properties of the capacities used are established. Bibliography: 16 titles.

Numerical algorithm based on regularized equations for incompressible flow modeling and its implementation in OpenFOAM

Various aspects of incompressible viscous flow modeling using regularized equations are considered: from the formulation of quasi hydrodynamic (QHD) equations for fluid motion to the demonstration of the capabilities of the associated OpenFOAM solver QHDFoam.The numerical algorithm for fluid flow simulations is devised using the QHD approach. Unlike prominent operator splitting techniques (PISO, SIMPLE and their variants), the QHD approach provides an equation for pressure explicitly. Practical issues of QHD approximation and stability criteria for the numerical scheme are presented.Several problems are used to validate the developed solver and to demonstrate its capabilities: backward facing step, skewed cavity flow, natural convection and generation of internal gravity waves attractor. Results of simulations for the last case are obtained using 3 different methods to show peculiarities of the quasi hydrodynamic equations approach in comparison with the standard PISO algorithm and finite-volume method and with the solution based on the spectral element method.The source code of the developed OpenFOAM solver(s) can be downloaded from the GitHub repository: https://github.com/unicfdlab/QGDsolver.

Threats and Trade-Offs in Resource Critical Crowdsourcing Tasks Over Networks

In recent times, crowdsourcing over social networks has emerged as an active tool for complex task execution. In this paper, we address the problem faced by a planner to incentivize agents in the network to execute a task and also help in recruiting other agents for this purpose. We study this mechanism design problem under two natural resource optimization settings: (1) cost critical tasks, where the planner's goal is to minimize the total cost, and (2) time critical tasks, where the goal is to minimize the total time elapsed before the task is executed. We define a set of fairness properties that should be ideally satisfied by a crowdsourcing mechanism. We prove that no mechanism can satisfy all these properties simultaneously. We relax some of these properties and define their approximate counterparts. Under appropriate approximate fairness criteria, we obtain a non-trivial family of payment mechanisms. Moreover, we provide precise characterizations of cost critical and time critical mechanisms.

The temperature-sensitive point screening for spindle thermal error modeling based on IBGOA-feature selection

Thermal error compensation is a simple and efficient method to reduce thermal errors of machine tools, and the compensation effect largely depends on the temperature-sensitive points screened for the thermal error modeling. In this paper, 5 spindle heating experiments are carried out, and a new temperature-sensitive point screening method based on the Improved Binary Grasshopper Optimization Algorithm (IBGOA) feature selection is proposed. Firstly, an optimal approximation criterion is added to the Binary Grasshopper Optimization Algorithm (BGOA) for ensuring the convergence of the algorithm. And the temperature measuring points are regarded as the feature of the thermal error. Then these feature temperature point subsets are generated by IBGOA. Next, the stepwise regression analysis is carried out to remove non-significant temperature points from these subsets. And each subset is evaluated to search the temperature-sensitive points based on the cross-validation result of the multiple linear regression (MLR). Finally, for further testing the applicability of the proposed temperature-sensitive points screening method, 3 common thermal error models are established with MLR, support vector regression, and back propagation neural network respectively. Compared with the traditional fuzzy C-means clustering (FCM) temperature-sensitive points screening method, the RMSE of these models could decrease by 30–50% in the thermal drift error of X-direction, 10%–30% in the thermal tilt error of Y-direction, generally 40%–60% in the thermal elongation of Z-direction and the thermal drift error of Y-direction. The results show the superiority of the proposed IBGOA-feature selection method.

Porosity-based representative elementary volume for geomaterials and its fractal theory-based approximate criterion

<p indent=0mm>The representative volume element (RVE) and/or the representative elementary volume (REV) and their existence and determination are a basic scientific issue in the research field of size effect. The similarities and differences between the RVE and REV are analyzed from the fields of composite micromechanics and geotechnical engineering. A three-level classification of the REV research on geomaterials is then proposed based on these fields, especially REV research in geotechnical engineering. The pore size distribution and the corresponding fractal dimension are introduced and selected as the constrained parameters for describing the complex pore structure of geomaterials. Accordingly, an approximate criterion is first presented via theoretical deduction and comparison with previous research results, through which the size of a P-REV of mesoscale porous geomaterials can be determined using their pore size distributions (i.e., the edge length of the cubic P-REV is approximately equal to five times of the maximum pore diameter). Finally, some statistical methods, such as low-order probability functions, are utilized to validate the performance of the proposed criterion. The verification results using two types of geomaterials, namely, sandstone and foamed concrete, reveal that both are in a reasonable agreement, indicating that the P-REV determined according to this approximate criterion can provide representative statistical results and find a balance between characterization accuracy and calculation efficiency.

Application of some special operators on the analysis of a new generalized fractional Navier problem in the context of q-calculus

The key objective of this study is determining several existence criteria for the sequential generalized fractional models of an elastic beam, fourth-order Navier equation in the context of quantum calculus (q-calculus). The required way to accomplish the desired goal is that we first explore an integral equation of fractional order w.r.t. q-RL-integrals. Then, for the existence of solutions, we utilize some fixed point and endpoint conditions with the aid of some new special operators belonging to operator subclasses, orbital α-admissible and α-ψ-contractive operators and multivalued operators involving approximate endpoint criteria, which are constructed by using aforementioned integral equation. Furthermore, we design two examples to numerically analyze our results.

Potential well escape via vortex-induced vibrations: A single-degree-of-freedom analysis

This paper presents approximate criteria that can be used to predict potential-well escape for a body undergoing vortex-induced vibrations. To this end, the method of harmonic balance is used to obtain an approximate analytical solution of the response assuming that the dynamics can be well described by adopting a single-degree-of-freedom reduced-order model. The escape phenomenon is investigated considering two flow conditions that are often encountered in engineering problems. The first occurs when the flow approaches the oscillator instantaneously at a set speed such that the transient dynamics of the oscillator are significant and can play an important role in determining the escape conditions. The second occurs when the speed of the flow approaching the body is quasi-statically increased such that the transient dynamics has a very little influence on the escape trajectories. In both scenarios, the dependence of the flow escape speed on the Strouhal number, the mass ratio between the flow and the oscillating body, and the shape of the potential well is resolved. The approximate analytical escape conditions are shown to be in good agreement with those obtained by numerically integrating the equations of motion.

On the Gaussian Approximation to Bayesian Posterior Distributions

The present article derives the minimal number N of observations needed to approximate a Bayesian posterior distribution by a Gaussian. The derivation is based on an invariance requirement for the likelihood <img src=image/13422860_01.gif>. This requirement is defined by a Lie group that leaves the <img src=image/13422860_01.gif> unchanged, when applied both to the observation(s) <img src=image/13422860_05.gif> and to the parameter <img src=image/13422860_02.gif> to be estimated. It leads, in turn, to a class of specific priors. In general, the criterion for the Gaussian approximation is found to depend on (i) the Fisher information related to the likelihood <img src=image/13422860_01.gif>, and (ii) on the lowest non-vanishing order in the Taylor expansion of the Kullback-Leibler distance between <img src=image/13422860_01.gif> and <img src=image/13422860_03.gif>, where <img src=image/13422860_04.gif> is the maximum-likelihood estimator of <img src=image/13422860_02.gif>, given by the observations <img src=image/13422860_05.gif>. Two examples are presented, widespread in various statistical analyses. In the first one, a chi-squared distribution, both the observations <img src=image/13422860_05.gif> and the parameter <img src=image/13422860_02.gif> are defined all over the real axis. In the other one, the binomial distribution, the observation is a binary number, while the parameter is defined on a finite interval of the real axis. Analytic expressions for the required minimal N are given in both cases. The necessary N is an order of magnitude larger for the chi-squared model (continuous <img src=image/13422860_05.gif>) than for the binomial model (binary <img src=image/13422860_05.gif>). The difference is traced back to symmetry properties of the likelihood function <img src=image/13422860_01.gif>. We see considerable practical interest in our results since the normal distribution is the basis of parametric methods of applied statistics widely used in diverse areas of research (education, medicine, physics, astronomy etc.). To have an analytical criterion whether the normal distribution is applicable or not, appears relevant for practitioners in these fields.

Development of a genetic algorithm and its application to a bi-level problem of system cost optimal electricity price zone configurations

The topic of alternative price zone configurations is frequently discussed in Central Western Europe where – so far – national borders coincide with borders of price zones. Reconfiguring these price zones is one option in order to improve congestion management, foster trading across borders of price zones and, thus, to increase welfare. In view of the significant increase in redispatch volumes and costs over the last years due to increasing feed-in from renewable energy sources in conjunction with delayed grid expansion, this topic has gained in importance. To determine these improved price zone configurations for a large-scale system like Central Western Europe, often either configurations based on expert guesses are considered or heuristics using approximate criteria like locational marginal prices are used to obtain price zones through clustering. In contrast, the present paper formulates a bi-level optimization problem of how to determine optimal configurations in terms of system costs and – given the size and nature of the problem – solves it with a specially developed genetic algorithm. Resulting price zone configurations are compared to both exogenously given, expert-based price zone configurations from the Entso-E bidding zone study and endogenously assessed configurations from a hierarchical cluster algorithm. Results show that the genetic algorithm achieves best results in terms of system costs. Moreover, the comparison with results from a hierarchical cluster analysis reveals important drawbacks of the latter methodology.

Improving the Development Technology of an Oil and Gas Company Using the Minimax Optimality Criterion

The article deals with the problem of adaptation of the Russian oil and gas company (Novatek, Russia) to the rapidly changing external environment, the avalanche of data from competitors, and the need to filter important information for business development and the prosperity of the industry as a whole. The approach is based on the system of integrated software monitoring of key business processes at the enterprise developed by the authors—from the formation of the idea of a new product to its implementation to paying customers. The scientific novelty lies in the use of an optimization model that allows for minimizing the maximum losses of the investor at all levels of decision-making, from the distribution of capital between companies, to the optimization of internal reserves to increase the competitiveness of the company. The toolkit is a minimax model that allows you to redistribute the shares of investor influence at the portfolio level, and then within the business processes of each company selected by investors, in order to achieve the optimal solution in accordance with the selected estimated indicators. Application of the well-known portfolio investment models of Markowitz, Tobin, Sharp, etc. is not possible due to the lack of necessary data on the basis of which the probabilistic parameters involved in the model are estimated. Even if we get them, it is necessary to take into account the level of correlation influence of the technological process in the composition of each subsystem, which is unacceptable for the data used, as it leads to a strong increase in errors. Using minimax and a systematic approach allows you to minimize such errors by choosing a balanced concentration of distributed assets for both the investor and the buyer. To this end, a three-way analysis of the company’s development was carried out and a technology for comprehensive improvement of the company’s activities was developed in the following areas: the company’s rating in the industry, financial condition, and interaction with counterparties using merchandising technologies. Tools for optimal image zoning at the Novatek site using the minimax approximation criterion have been developed. The technology provides a procedure for creating a comfortable mode of image perception based on high-tech visualization of merchandising, zoning of the screen area, and a mathematical approach that allows you to develop a calculation algorithm.

Asymptotic analysis of the eigenstructure of the two-layer model and a new family of criteria for evaluating the model hyperbolicity

Two-layer and multi-layer depth-averaged models have become popular for simulating exchange flows, seawater currents and geophysical flows. The partial differential equation systems associated with these models are similar to the single-layer shallow-water model. Yet, their eigenstructures are more complex owing to the pressure coupling between the layers. Such models occasionally lose their hyperbolic character, which may lead to numerical issues. A physical explanation is that Kelvin-Helmholtz type instabilities arise at the layers' interface, if the velocity difference between the layers becomes sufficiently large. A way to avoid the hyperbolicity loss is to locally introduce an extra momentum exchange between the layers, assessable from the system eigenstructure and aimed at roughly mimicking the dynamical effects of such instabilities. To better understand the hyperbolicity conditions, the eigenstructure of the two-layer model is methodically studied by an asymptotic analysis. The analysis for the limiting cases, where the layers' thicknesses are either comparable or very different from each other, reveals new stability criteria. These analytical criteria are, then, exploited to design a new family of approximate criteria, valid for any flow condition. Numerical investigations demonstrate the reliability of this approach, which can be easily implemented in numerical schemes for preserving the hyperbolicity.

A Novel Flux State-based Control Method for Improved Dynamic Performance of Induction Motor

ABSTRACT Induction machine (IM) is widely used in industries because of certain advantages. In previous research studies, investigations were completed to analyze the machine flux behavior in different reference frames such as Stationary and Park’s, however, the analysis and comparison for the wide-ranging machine flux behavior, in synchronously rotating stator field-oriented, and rotor-oriented reference frames, is not offered particularly during transients. In addition, the dynamically accurate torque and flux control is an essential requirement for high-performance induction motor drive. A number of techniques, including direct and indirect field-oriented control, direct torque and direct power control techniques, have been developed; however, most of them apply certain approximation criteria to optimize the linear system. It results in inaccurate tuning of respective current, torque and flux controllers, which deteriorates the dynamic performance. In this paper, a novel flux state-based nonlinear control method is presented which results in improved dynamic performance of induction motor drive. The proposed control method is simulated in the MATLAB/Simulink environment and experimentally validated on a 0.75 kW IM. The obtained results show the effectiveness of the proposed flux state-based control method for improved dynamic performance of induction motor drive.

Statistical approaches to identifying lapses in psychometric response data.

Psychometric curve fits relate physical stimuli to an observer's performance. In experiments an observer may "lapse" and respond with a random guess, which may negatively impact (e.g., bias) the psychometric fit parameters. A lapse-rate model has been popularized by Wichmann and Hill, which reduces the impact of lapses on other estimated parameters by adding a parameter to model the lapse rate. Since lapses are discrete events, we developed a discrete lapse theory and tested a "lapse identification" algorithm to identify individual outlier trials (i.e., potential lapses) based upon an approximate statistical criterion and discard these trials. Specifically, we focused on stimuli sampled using an adaptive staircase for a one-interval, direction-recognition task (i.e., psychometric function ranging from 0 to 1 and the spread of the curve corresponds to the threshold, which is often a parameter of interest for many fitted psychometric functions). Through simulations, we found that as the lapse rate increased the threshold became substantially overestimated, consistent with earlier analyses. While the lapse-rate model reduced the overestimation of threshold with many lapses, with lower lapse rates it yielded substantial threshold underestimation, though less so when fitting many (e.g., 1,000) trials. In comparison, the lapse-identification algorithm yielded accurate threshold estimates across a wide range of lapse rates (from 0 to 5%), which is critical since the lapse rate is seldom known. We further demonstrate the performance of the lapse-identification algorithm to be suitable for a variety of experimental conditions and conclude with some considerations of its use. In particular, we suggest using the lapse-identification algorithm unless the experiment has many trials (e.g., >500) or if somehow the lapse rate is known to be high (e.g., ≥5%), for which the lapse-rate model approaches remain preferred.

НАБЛИЖЕНИЙ МЕТОД ЕКСПРЕС-ОЦІНКИ ЕФЕКТИВ-НОСТІ АВІАПЕРЕВЕЗЕНЬ ЗА СОБІВАРТІСТЮ РЕЙСУ ПО-ВІТРЯНОГО СУДНА

It is known that the main goal of passenger and cargo airlines is the most stable profitability with a positive gradient of its growth. This goal is provided by a number of factors, among which the prime cost of operating aircraft (AC) on the routes of passenger and cargo transportation lines plays an important role. Based on the analysis of the world and domestic air transportation market, the article highlights the main factors that determine the level of the cost of flights. The analysis of these factors showed that the cost of flights is a complex multifactorial problem that is solved by air carrier companies sequentially at a number of stages as a large amount of information accumulates.At the same time, an air carrier needs a very approximate, but prompt method of assessing this cost, especially at the stage of its entry into the air transportation business.A detailed analysis of the dependence of the cost of air transportation on the length of the runway, proposed by the General Designer O.K. Antonov for an express assessment of this complex parameter in relation to cargo aircraft, which we have expanded for the type of passenger aircraft. The analysis showed the admissibility of considering the curve Scost=f(LRS) as a function of the mathematical expectation of the cost of air transportation, and the points lying outside this curve as the variance of the cost, i.e. as the risk of choosing an alternative aircraft option.The main factors that predetermine the level of the cost of air transportation have been synthesized, among which the factor of non-stop flight is of particular importance, i.e. range. This made it possible to develop the idea of O.K. Antonov to present as an approximate criterion of efficiency the dependence of the cost of air transportation on the range of the aircraft in the form of a hyperbolic dependence of a similar type.The analysis of the efficiency of the proposed method for assessing the effectiveness of the criterion of the cost of air transportation from the flight range of the aircraft showed the validity of its application for the express assessment of the preliminary choice by the aircraft operator at the initial stage of his development of the air transportation business.

Condensing Functions and Approximate Endpoint Criterion for the Existence Analysis of Quantum Integro-Difference FBVPs

A nonlinear quantum boundary value problem (q-FBVP) formulated in the sense of quantum Caputo derivative, with fractional q-integro-difference conditions along with its fractional quantum-difference inclusion q-BVP are investigated in this research. To prove the solutions’ existence for these quantum systems, we rely on the notions such as the condensing functions and approximate endpoint criterion (AEPC). Two numerical examples are provided to apply and validate our main results in this research work.

Power Exponent Based Weighting Criterion for DNN-Based Mask Approximation in Speech Enhancement

In this letter, a novel weighted mean square error (WMSE) is proposed to improve the DNN-based mask approximation method for speech enhancement, in which the weighting is closely related to the power exponent about noisy spectrum amplitude (NSA) base. The power exponents 0 and 2 separately reflect ideal amplitude masking (IAM) without any clippings and the indirect mapping (IM) on short-time spectral amplitude (STSA), and it is highly related to the enhanced spectrum and the performance of the enhanced signal based on the tests. Also, the experimental results show that the outstanding weighting is the noisy spectrum base with the power exponent 1 for the phase-unaware masking and results in better harmonic structure restoration. The objective function with the WMSE on the NSA (WMSE-NSA) can averagely improve 0.1 on the test of perceptual evaluation of speech quality (PESQ) and 1.7% on the test of short-time objective intelligibility (STOI) compared with the MSE-based mask approximation methods.

Stochastic Modelling of Claim Frequency in the Ethiopian Motor Insurance Corporation: A Case Study of Hawassa District in Ethiopia

The objective of this study is to model seasonal variations in claim intensities and to evaluate the dependency of covariates on claim rates. The data for this study are obtained from claimants registered during September 2009 to August 2011, both inclusive at the Ethiopian Insurance Corporation in Hawassa. We present a procedure for consistent estimation of the claim frequency for motor vehicles in the Ethiopian Insurance Corporation, Hawassa District. The seasonal variation is modeled with a non-homogeneous Poisson process with a time varying intensity function. Covariates of the policy holders, like gender and age, is corrected for in the average claim rate by Poisson regression in a GLM setting. An approximate maximum likelihood criterion is used when estimating the model parameters. Numerical simulations are carried out applying the numerical software Matlab. These simulations show the reliability of the estimator. The seasonal parameters are found to be ±25% and to be statistically significant. February has highest while August has lowest claim rate. Only age group 36 - 45 has significantly lower claim rate than age group 20 - 25. The rate is about one third. Lastly female is not found to have significantly lower claim rates than males, however, there are indications that might be slightly so.

A multi-location peak parking approach for calculation of second dimensional retention indices for improved volatile compound identification with cryogen-free comprehensive heart-cut two-dimensional gas chromatography.

Comprehensive heart-cut multidimensional gas chromatography (CH/C MDGC) without a cryogenic trapping device was developed with an established approach for calculation of first and second dimensional retention indices (1I and 2I) for improved compound identification. A first dimensional (1D) DB-1MS column (60 m) and a second dimensional (2D) DB-WAX column (60 m) were applied with a Deans switch (DS) using a constant H/C window of 0.2 min and a periodic multiple heartcut strategy comprising 225H/C throughout the CH/C. 1I was calculated based on comparison of the middle of the heartcut time with the alkane retention times on the 1D column. A multi-location peak parking approach using sixteen sets of automated injections of alkane references was also established with the least square curve fitting method for construction of the alkane isovolatility curves which were applied for 2I calculation. The untargeted compound analysis of a perfume sample was then performed according to comparison with the libraries of mass spectra, 1I and 2I. The CH/C MDGC system with a 25 h analysis time showed a peak capacity (nc) of 9198 and 128 separated peaks with 71 compounds successfully identified according to MS, 1I and 2I library match under the established error approximation criteria. Furthermore, relationship between the analysis time and number of separated peaks was proposed based on the set of 84 identifiable compounds. With the compensation of lower separation performance and greater I errors, the analysis time could be reduced by applying a 2.5 min H/C window with a total analysis time of 2 h and nc of 1134.

Assignment of a Claim Under an Obligation in Which the Identity of the Obligee Is Essential for the Obligor

The Plenum of the Supreme Court of the Russian Federation adopted a resolution of December 21, 2017 No. 54 “On some issues of application of the provisions of Chapter 24 of the Civil Code of the Russian Federation on the change of persons in an obligation on the basis of a transaction", which sets out important clarifications regarding the application standards contained in this chapter. At the same time, not all issues related to the assignment of the claim were resolved by the above resolution. One of these issues is the definition of the term “essential value of the identity of the creditor” or approximate criteria for such a value in the context of the need to obtain the latter’s consent to the assignment of rights. The presence of this problem is rightly indicated in the scientific literature [3, p. 549–655, 688–713]. The Author examines the Model Rules of European Private Law and the UNIDROIT principles in order to find a solution to the problem. Attention is drawn to the problem of determining the essential value of the creditor for the debtor in the case of assignment of the right of claim, as well as to the consequences of making the assignment without the consent of the debtor under an obligation in which the identity of the creditor was essential.In the Author's opinion, the identity of the creditor is recognized as essential for the debtor when the connection between the debtor and the creditor arose as a result of the conclusion of a transaction that has a personallyconfidential nature, or if the connection arose during the conclusion of other transactions in the case when the connection was broken during the execution assignment of rights entails or may entail a significant deprivation for the debtor of what he had the right to count on when concluding a transaction with the creditor.In addition, situations are considered that are an exception to the presumption of the absence of a significant value of the creditor's personality for the assignment of claims for monetary obligations. The author also points out that the consequence of the transaction on the assignment of rights without the consent of the debtor in the context of paragraph 2 of Art. 388 of the Civil Code of the Russian Federation is the nullity of the transaction on the basis of paragraph 2 of Art. 168 of the Civil Code of the Russian Federation.

A sub-linear time algorithm for approximating k-nearest-neighbor with full quality guarantee

In this paper we propose an algorithm for the approximate k-Nearest-Neighbors problem. According to the existing researches, there are two kinds of approximation criteria. One is the distance criterion, and the other is the recall criterion. All former algorithms suffer the problem that there are no theoretical guarantees for the two approximation criteria. The algorithm proposed in this paper unifies the two kinds of approximation criteria, and has full theoretical guarantees. Furthermore, the query time of the algorithm is sub-linear. As far as we know, it is the first algorithm that achieves both sub-linear query time and full theoretical approximation guarantee.