Extremum Values Research Articles

Quantum $$\alpha $$-fidelity of unitary orbits

The extremum values of quantum $$\alpha $$ -fidelity under unitary orbits of quantum states are explicitly derived by applying rearrangement inequalities, matrix trace inequalities, and theory of majorization. Furthermore, the $$\alpha $$ -fidelity is successfully verified to go through the whole closed interval, which works from the minimum value to the maximum value.

Data on the optimization of the formula of Xiaokeyinshui extract combination treating diabetes mellitus using uniform experimental design in mice

This dataset is supplementary to our accepted article in Journal of Ethnopharmacology [1]. Xiaokeyinshui (XKYS) formula, an anti-diabetic formula, was recorded in many ancient Chinese medical books. Xiaokeyinshui extract combination (XEC) originated from this ancient formula, consisting extracts of four herbal drugs, i.e., Coptidis Rhizoma, Liriopes Radix, bitter melon, and Cassiae Semen. In this study, herb extracts were prepared and mixed, producing Xiaokeyinshui extract combination (XEC). The optimized formula of XEC was also investigated via uniform experimental design. Diabetes was induced in Kunming mice, using high-sugar-high-fat diet combined with injection of streptozotocin (STZ) intraperitoneally. Different formulae of XEC were intragastrically administered to diabetic mice for 28 days. Fasting blood glucose (FBG), oral glucose tolerance test (OGTT), hemoglobin A1c (HbA1c), total cholesterol (TC), total triglyceride (TG) were measured to assess the anti-diabetic effects of each formula. Multivariate second degree polynomial model was applied in the fitting of metabolic parameters, and the extremum value of each regression model was calculated using grid algorithm. In addition, an optimized formula of XEC was subjected to validation experiment in mice model. This data could provide basis for a reasonable analysis for the optimization of the formula of XEC.

Analysis of fluid-induced force of centrifugal pump impeller with compound whirl

In order to research the fluid-induced force of centrifugal pump impeller with compound whirling, based on the N-S equations, the RNG k-ε turbulence model is applied to simulate the low specific speed centrifugal pump under eccentric assembly condition. The effects of different flow rates, impeller eccentricities and whirl ratios on the fluid-induced force of impeller were investigated. Finally, the fitting models of fluid-induced force with compound whirl were obtained by least square method (LSM). The results imply that the calculated results considering the impeller eccentricity are closer to the experimental data than those without considering the eccentric whirl. In addition, the extremum value of fluid-induced force of impeller has a significant positive correlation with the impeller eccentricity. With the increase of flow rate, the fluid-induced force is non-monotonic. The whirl ratio can change the numbers of peak and valley of fluid-induced force, and the nonlinear fitting model of fluid-induced force using LSM presents high precision. This study can provide important references for the design and fluid-structure interaction (FSI) vibration of centrifugal pump.

The mean, variance, and bias of the OLS based estimator of the extremum of a quadratic regression model for small samples

Many economic theories suggest that the relation between two variables y and x follow a function forming a convex or concave curve. In the classical linear model (CLM) framework, this function is usually modeled using a quadratic regression model, with the interest being to find the extremum value or turning point of this function. In the CLM framework, this point is estimated from the ratio of ordinary least squares (OLS) estimators of coefficients in the quadratic regression model. We derive an analytical formula for the expected value of this estimator, from which formulas for its variance and bias follow easily. It is shown that the estimator is biased without the assumption of normality of the error term, and if the normality assumption is strictly applied, the bias does not exist. A simulation study of the performance of this estimator for small samples show that the bias decreases as the sample size increases.

Direct control method for improving stability and reliability of nonlinear stochastic dynamical systems

Optimal control for improving the stability and reliability of nonlinear stochastic dynamical systems is of great significance for enhancing system performances. However, it has not been adequately investigated because the evaluation indicators for stability (e.g. maximal Lyapunov exponent) and for reliability (e.g. mean first-passage time) cannot be explicitly expressed as the functions of system states. Here, a unified procedure is established to derive optimal control strategies for improving system stability and reliability, in which a physical intuition-inspired separation technique is adopted to split feedback control forces into conservative components and dissipative components, the stochastic averaging is then utilized to express the evaluation indicators of performances of controlled system, the optimal control strategies are finally derived by minimizing the performance indexes constituted by the sigmoid function of maximal Lyapunov exponent (for stability-based control)/the reciprocal of mean first-passage time (for reliability-based control), and the mean value of quadratic form of control force. The unified procedure converts the original functional extreme problem of optimal control into an extremum value problem of multivariable function which can be solved by optimization algorithms. A numerical example is worked out to illustrate the efficacy of the optimal control strategies for enhancing system performance.

Synthesis and structural characterization of the new Zintl phases Ba3Cd2P4 and Ba2Cd2P3. Rare example of small gap semiconducting behavior with negative thermopower within the range 300 ​K–700 ​K

The new Zintl phases Ba3Cd2P4 and Ba2Cd2P3 have been synthesized using Pb flux, which allowed for the growth of 4–5 ​mm large crystals. The structures were determined utilizing single-crystal X-ray diffraction methods. Both compounds crystalize in the monoclinic crystal system (space group C2/m (No. 12)) and their structures are closely related. The structure of Ba3Cd2P4 can be seen as being comprised of divalent Ba atoms and conjoined CdP4 tetrahedra in the form of [Cd2P4]6– layers. Within the layers, homoatomic P–P bonds are present, which if cleaved, leave two infinite [CdP3]7– chains running along the crystallographic b-axis. The other structure, that of Ba2Cd2P3, can be rationalized as also having divalent Ba atoms and conjoined CdP4 tetrahedra in the form of [Cd2P3]6– layers. These layers, again, can be visualized as chains that run down the crystallographic b-axis, which are further connected by P–P dimers. Electronic band structure calculations show that each structure has an optimal number of valence electrons, and therefore conform to the Zintl-Klemm concept. Accordingly, the two compounds can be considered small band gap semiconductors, with band gaps of ca. 0.1 ​eV and 0.6 ​eV for Ba3Cd2P4 and Ba2Cd2P3, respectively. Electrical resistivity measurements show that Ba3Cd2P4 displays a large resistivity value at room temperature and an experimental band gap of ca. 0.05 ​eV, which fits reasonably well with the theoretical predictions. Thermopower measurements show that throughout the temperature range 300 ​K–700 ​K, Ba3Cd2P4 displays a negative Seebeck coefficient. The extremum value of −84 μV is reached at 630 ​K, suggestive of an n-type semiconductor, a rarity among Zintl phases.

Thermochemistry of Solutions of Alkanes in Binary Mixtures: Azeotropes

This work is devoted to the study of azeotropes by the method of solvation thermodynamics. In the present work the thermochemistry of alkane solutions in binary mixtures was studied. The infinite dilution solution enthalpies of n-hexane, n-octane, and n-dodecane in binary mixtures were measured at 298.15 K. Alkanes were used as solutes since they are not capable of specific interactions with solvents. It should be noted that the differences in the solution of alkanes in a series of solvents are caused by differences in the interactions between the solvent molecules. Binary mixtures (benzene–cyclohexane) and (n-hexane–acetone) at different molar ratios, including the compositions corresponding to azeotropes, were used. The composition of both azeotropes obtained by distillation was determined by means of densimetry, and was found to be in good agreement with published data. The compositions of chosen azeotropes insignificantly change with temperature. The excess solution enthalpies of n-alkanes in binary solvents were calculated. It was found that the extremum value of the excess solution enthalpy corresponds to their azeotrope composition.

Detection of genuine N-Qubit W state, GHZ state and Twin-Fock state via Quantum Fisher information

We study the entanglement detection of three classes of state in the white noise model: N-qubit W state, Greenberger-Horne-Zeilinger state and Twin-Fock state. Taking advantage of Quantum Fisher information, we first present how to witness M-separable W state (M≤N) in the ideal situation, and then derive the criteria for detecting genuine W state, Greenberger-Horne-Zeilinger state and Twin-Fock state in the noisy model. Meanwhile, the bounds for M-separable W state, k-partite entangled GHZ state and k-partite entangled Twin-Fock state are also investigated. The results show that with the increase of the number of particles, the requirement of visibility V for genuine multipartite entanglement becomes more and more stringent, while it is relaxed for partial entanglement. Specially, an extremum value of VWN=1/3 is found in the limit of large N.

A novel angle extremum maximum method for recognition of pulse wave feature points

Background and objectivesPulse wave is one of the biomedical signals that has been studied over the past years. Accurate recognition of feature points is the basis of verifying the connections between pulse waves and certain diseases. Therefore, the aim of the study is to discuss the use of angle mapping on feature points recognition. MethodsThe mathematical method is based on the application of angle curve with parameter " k " on pulse wave. The data used is collected by PVDF sensor. Approximate curve and mathematical model are used for the discussion of the influence of parameter k and pulse wave amplitude by numerical calculation. The conclusion drawn from the numerical solution is that when k changes to maximize the angle extremum value, the corresponding position of angle extremum point is the feature point position. For the sampling rate f = 455Hz in this paper, k can be taken from 5 to 15. ResultsWe present the recognition results of unobvious feature points based on the "angle extremum maximum method" and corresponding angle values. The results are compared with traditional methods and the determination of angle threshold value is discussed. ConclusionsThis method can be used for accurate and efficient feature points identification, and it can be better applied to pulse waves with noise or unobvious feature points.

Coordination Dynamics of Upper Limbs in Swimming: Effects of Speed and Fluid Flow Manipulation

ABSTRACT Purpose: Motor outputs are governed by dynamics organized around stable states and spontaneous transitions: we seek to investigate the swimmers’ motor behavior flexibility as a function of speed and aquatic environment manipulations. Method: Eight elite male swimmers partook an eight-level incremental test (4% increment from 76% to 104% of their mean speed on 200 m front crawl) in a quasi-static aquatic environment (pool). Swimmers then partook another incremental test at similar effort in a dynamic aquatic environment (swimming flume) up to maximal speed. Stroke rate (SR), index of coordination (IdC) and intersegmental coupling of the upper limbs were computed from the inertial sensors located on the upper limbs and the sacrum. Results: With speed increase, SR values presented a steeper linear increase in the pool than in the flume. IdC values increased also in the pool but remained stable in the flume. Individual SR and IdC vs. speed increase displayed second-order polynomial dynamics, indicative of adaptive flexibility with a range of extremum values more restricted in the flume. Finally, a reduction of the in-phase coordination pattern was noted with flume speed increase. Conclusions: Action possibilities were strongly constrained in the flume at the highest speeds as the fluid flow led to discontinuity in the propulsive actions of the upper limbs and lack of in-phase inter-segmental coordination. This highlights that the behavioral flexibility was restricted in the flume in comparison to the pool, in which the exploitation of opportunities for action involved a larger number of degrees of freedom in the movement.

Machine Learning for a Power Consumption and Generation Prediction

The paper is devoted to the preparation and analysis of data sets in order to improve the prediction of the amount of consumed and generated electrical energy volumes using machine learning methods. The importance level and influence on predicting the time of day, month, year, temperature, humidity, atmospheric pressure, and other factors were determined. The dataset used in this article contains the data of smart house equipped by photovoltaic cells for the own generation of electrical energy that covers the part of house’s demand. There are following values in dataset: «time», consumed electrical energy («use [kW]»), generated electrical energy («gen [kW]»), «temperature», «humidity», «visibility», «pressure», «windSpeed», «cloudCover», «windBearing», the temperature as it felt by human «apparentTemperature», precipitation intensity «precipIntensity», «dewPoint», precipitation probability «precipProbability». The data was collected during 11 months with a data fixing period of 1 minute. Before the data analysis and further learning it’s necessary to execute preliminary processing. At first stage, it was investigated how large is the part of missed and zero values in dataset. The second stage includes elimination of outliers that are situated at anomaly distance from other values in random sample. These outliers could be caused by measurement errors, wrong measuring units use. Also, it could be correct but extremum values. The purification procedure includes defining the lower and the upper quartiles of existing data for the distribution of used energy. For effective learning of the model it is necessary to choose the values that are most important and suitable for training. Pearson’s correlation coefficient was used to estimate numerically the level and positivity of linear connections between the pairs of values as well as to estimate their influence to the used and generated energy. Among the values with the high level of correlation only one was chosen that helped increasing adequacy, generalization and results interpretation. As a result of correlation analysis three parameters were selected for the training - «apparentTemperature», «dewPoint» and «precipProbability». Use of proposed preprocessing methods allows increasing the predictions exactness by 25% for the used energy and by 2% for the generated energy. The initial dataset was divided as follows: 70% of values were considered as the training samples and 30% - as testing ones. To compare the training methods three models of machine learning from the library Scikit-learn in programming language Python were considered: «Linear», «Random forest», «k nearest neighbors». The determination coefficient R² was used as a metrics to estimate the exactness. The diagrams of numerical values of R² coefficient for the parameters of generation and consumption of electrical energy and for three considered models of machine learning were built. Among the tested model the best result was demonstrated for the “Random forest” model (84% for the used energy and by 95% for the generated energy). Additional exactness increasing could be reached by use of more amount of testing samples and parameters during the analysis and more time intervals of observation as well as additional methods of data preprocessing.

Cross-Sectional Views of GDP Growth in the Light of Innovations

This paper involves an analysis to investigate the limits to GDP growth in the present economic scenario. One objective of this study is to investigate how innovation alters these limits to economic growth. The present analysis is based on cross-section data. Results show the impact of the size of the economy on GDP growth and the relation between GDP growth and GDP across the world at particular point of time is convex. Growth increases with GDP, reaches its maximum and then begins to decline. There exists some extremum value. This is not exactly middle income trap. It is observed for both developed and developing economies. Actually, countries having this property belong to conventional growth domain. However, the extremum could be extended by technological and policy innovations and some countries move into innovative growth domain with higher limiting values.

Improved Decomposed-Coordinated Kriging Modeling Strategy for Dynamic Probabilistic Analysis of Multicomponent Structures

The probabilistic design of complex structure usually involves the features of numerous components, multiple disciplines, nonlinearity, and transients and, thus, requires lots of simulations as well. To enhance the modeling efficiency and simulation performance for the dynamic probabilistic analysis of the multicomponent structure, we propose an improved decomposed-coordinated Kriging modeling strategy (IDCKMS), by integrating decomposed-coordinated (DC) strategy, extremum response surface method (ERSM), genetic algorithm (GA), and Kriging surrogate model. The GA is used to resolve the maximum-likelihood equation and achieve the optimal values of the Kriging hyperparameter θ . The ERSM is utilized to resolve the response process of outputs in surrogate modeling by extracting the extremum values. The DC strategy is used to coordinate the output responses of analytical objectives. The probabilistic analysis of an aeroengine high-pressure turbine blisk with blade and disk is conducted to validate the effectiveness and feasibility of this developed method, by considering the fluid–thermal–structural interaction. In respect of this investigation, we see that the reliability of turbine blisk is 0.9976 as the allowable value of radial deformation is 2.319 × 10−3 m. In terms of the sensitivity analysis, the highest impact on turbine blisk radial deformation is of gas temperature, followed by angular speed, inlet velocity, material density, outlet pressure, and inlet pressure. By the comparison of methods, including the DC surrogate modeling method (DCSMM) with quadratic polynomial, the DCSMM with Kriging, and the direct simulation with finite-element model, from the model-fitting features and simulation performance perspectives, we discover that the developed IDCKMS is superior to the other three methods in the precision and efficiency of modeling and simulation. The efforts of this article provide a highly efficient and highly accurate technique for the dynamic probabilistic analysis of complex structure and enrich reliability theory.

Extremal trees for the modified first Zagreb connection index with fixed number of segments or vertices of degree 2

The modified first Zagreb connection index is a graph invariant, initially appeared within a formula of the total electron energy of alternant hydrocarbons in 1972, and revisted in a recent paper [A. Ali, N. Trinajstić. A novel/old modification of the first Zagreb index. Mol Inform. 2018;37(6). Art# 1800008; arXiv:1705.10430 [math.CO]]. In this paper, the graph(s) with the maximum/minimum value is/are characterized from the class of all n-vertex trees with fixed number of segments. As the number of segments in a tree can be determined from the number of vertices of degree 2 (and vice versa), the trees with the extremum values are also determined from the class of all n-vertex trees having a fixed number of vertices of degree 2.

Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell

In this article, wave propagation behavior of a size-dependent spinning graphene nanoplatelet-reinforced composite (GNPRC) cylindrical nanoshell with porosity is presented. The effects of small scale are analyzed based on nonlocal strain gradient theory (NSGT), this accurate theory employs exact length scale parameter and nonlocal constant. The governing equations of GNPRC cylindrical nanoshell coupled with piezoelectric actuator (PIAC) are evolved by minimum potential energy principle and solved by the analytical method. For the first time in the current study, wave propagation-porosity behavior of a GNPRC cylindrical nanoshell coupled with PIAC is examined based on NSGT. The results show that, as the angular velocity increases, the difference between the minimum and maximum values of the phase velocity decreases. Another important result of this paper is that, by increasing the radius, extremum values of phase velocity occur in the lower values of the wave number. Finally, the influences of porosity, angular velocity, wave number and different graphene platelet distribution patterns on the phase velocity are investigated using the mentioned continuum mechanics theory. The outputs of the present work can be used in structural health monitoring and ultrasonic inspection techniques.

Entropy evolution characteristics during an intense tropical cyclone

Entropy characteristics are investigated during the tropical cyclone Haiyan (TCH) using the weather research and forecasting (WRF) model in a downscaling experiment with two nests, 18- and 6-km grid spacing. This TC was stronger than most Saffir–Simpson category 5 typhoons. In this research, entropy, air–sea thermodynamic disequilibrium (ASTD) and entropy fluxes (including surface, convective and lateral entropy fluxes) have been analyzed. Scale analysis of these parameters has been done using integrated values over two types of areas including fixed square-ring areas and circular structural-based areas, all surrounding TCH center. The considered parameters (using downscaled data with 6-km grid spacing) integrated over the various areas showed the maximum or minimum value with various lag or lead times, comparing with TCH peak intensity (at 18:00 UTC 07 November, when TCH made landfall in the Philippine Islands). In addition, the multiscale analysis emphasized that entropy transport between different parts of TCH could not be ignored. Most of the considered parameters integrated over the larger areas reached the extremum values before TCH maximum intensity. Integrating over the fixed square areas led to that more parameters got the extremum value before TCH greatest intensity comparing with those integrated over the circular structural-based areas. This indicates that it is unnecessary to focus only on the circular structural-based areas. Conclusively, hierarchy of derived extremum values of entropy and its derivations over the various scales (especially those integrated over the fixed square areas) showed that this parameter could be served as a relevant proxy parameter and its evolution is worthwhile to be considered in TC investigation.

Role of quantum phase transition in spontaneous fission

A systematic study of quantum phase (i.e., nuclear shape) transition has been carried out from the standpoint of spontaneous fission. The quantum phase transition is defined by the ratio of relative excitation energies of IΠ=4+ to IΠ=2+ states between heavier and lighter fission fragments and its extremum value fixes the most probable pair of fission fragments. This ratio provides an effective order parameter which is not only easy to measure, but also distinguishes between first and second order phase transitions and takes on a special value in the critical region. Its (i.e., the energy ratio) variation is mainly controlled by the relative inertia tensors of the correlated pair of fission fragment and is fully supported by our cranking mass parameter calculations based on the asymmetric two center shell model bases.Once the fission fragment pair is governed by the quantum phase transition, its validity is tested by F-spin selection rule that is based on valence nucleons which are responsible for determining the nuclear shape transition. It implies that if a pair of conjugate fission fragments together with appropriate neutron emission have total F-spin equal to 12 with projections F0=±12 then and only then the fission proceeds, provided both the valence shell nucleons in either of the fission fragments are treated as particles like and is valid for the even-even decay modes. The goodness of F-spin selection rule extends further to extract all the allowed pairs of neutron-rich fission fragments. The validity of F-spin selection rule has been tested in various decay modes of spontaneous fission and seems to be a milestone in deciding the appropriate decay channels. These findings have important consequences in the formation and discovery of drip-line exotic nuclei.

The deformation of the Rock wool board external thermal insulation system based on coupled temperature and relative humidity

A coupled heat and humidity transfer model of external thermal insulation wall is established. The effects of different climatic conditions (winter and summer) on the deformation of the rock wool board external insulation system were simulated and analyzed by the meteorological database from Shanghai. The results show that the changes of strain and stress are fluctuated because of the variation of temperature and relative humidity, and their extremum values appear with the extreme value of temperature and relative humidity difference. The coating mortar has the highest stress and strain, and the rock wool board has the lowest stress and strain. The maximum stress can reach 1.97×10-3MPa and the maximum strain can reach 1.36×10-4 of the rock wool thermal insulation system during the periodic changes in temperature and relative humidity within 72 hours in winter and summer.

Approximations wander model for the Lommel Gaussian-Schell beam through unstable stratification and weak ocean-turbulence

By analyzing the construction features of a Lommel Gaussian-Schell beam and the beam wander for Gaussian beams, we derive the closed-from approximations expression for the wander of Lommel Gaussian-Schell beam through unstable stratification and weak ocean-turbulence. Turbulence conditions with a smaller outer- and inner-scale of turbulence usually cause smaller beam wander. There is a extremum value βex of the beam paraxial coefficient corresponding to the maximum beam wander for given parameters of turbulence and beam. We can utilize larger beam waist, longer wavelength, higher quantum number of orbital angular momentum and larger asymmetry factor, meanwhile, avoid extremum value βex to reduce the beam wander. The influence of salinity fluctuations of turbulent ocean on beam wander is greater than temperature fluctuations. Under the assumption of unit diffusivity ratio, the beam wander is either underestimated or overestimated.

Application of the Artificial Fish Swarm Algorithm to Well Trajectory Optimization

Drilling applications involve a number of global optimization problems that require finding the best extremum value of a nonlinear function of many variables. One of such problems is the choice of the optimal well drilling trajectory. Various trajectory optimization algorithms have been previously proposed, but they all suffer from some shortcomings. In the present paper, the shortest well length is used as the objective function, and optimization is performed by the artificial fish swarm algorithm (AFSA). The calculations have been carried out in the Matlab environment. Comparison of our calculations with previously published data suggests that AFSA optimization produces the best numerical results and the shortest trajectory, while in addition ensuring high stability and reliability. The algorithm has a simple structure and fast convergence, quickly producing a global optimum. AFSA thus may be used to calculate the optimal drilling trajectory.