Local Minimum Point Research Articles

Multi-peak solutions for nonlinear Choquard equation in the plane

In this paper, we consider the nonlinear Choquard equation in the plane with general nonlinearity satisfying Berestycki-Lions condition. By means of global penalization method, we obtain the existence of multi-peak solutions which concentrate near local minimal points of potential.

Existence and concentration of solutions for singularly perturbed doubly nonlocal elliptic equations

We consider the existence and concentration of positive solutions to a singularly perturbed doubly nonlocal elliptic equation [Formula: see text] where [Formula: see text] is a parameter, [Formula: see text] are constants, [Formula: see text] and [Formula: see text] is an external potential, [Formula: see text] and [Formula: see text]. Under some suitable assumptions on [Formula: see text] and [Formula: see text], by using the penalization method, we prove that for [Formula: see text] small enough there exists a family of positive solutions which concentrate on the local minimum points of the potential [Formula: see text] as [Formula: see text].

Dynamically evolving algorithm for minimizing the energy consumption of a manipulator

Global warming and environmental destruction are caused, in part by the mass consumption of energy by industries that use robotic manipulators. Many trajectories planning of the manipulators are determined by giving priority to the operation efficiency such as the operating time and controllability. And it may not be taking the consumption energy into consideration in the trajectory planning. The minimization of the energy under the equation of motion of the manipulator can be reduced to a two-point boundary value problem. This problem can be solved analytically if the equation of motion is linear. However, the equation of motion of a two-links manipulator is non-linear. This paper describes an application of the genetic algorithm based evolution strategy to solve minimizing the consumption energy of a manipulator with non-linear friction at the joints. When applying the genetic algorithm, it is necessary to define the relation between trajectory functions and genes. Fourier cosine series with Mth order are used in this paper. In this minimization problem of the consumption energy, there are many local minimum points due to the non-linearity. A major topic of this paper is to discuss the number of M to increase the accuracy of the solution without falling into the local minimum point. This paper has proposed to change M in the progress of evolution.

Roughly geodesic B - r-preinvex functions on Cartan Hadamard manifolds

In this article, we introduce a new class of functions called roughly geodesic B????r????preinvex on a Hadamard manifold and establish some properties of roughly geodesic B - r-preinvex functions on Hadamard manifolds. It is observed that a local minimum point for a scalar optimization problem is also a global minimum point under roughly geodesic B-r- preinvexity on Hadamard manifolds. The results presented in this paper extend and generalize the results appeared in the literature.

Smile and Laugh Expressions Detection Based on Local Minimum Key Points

In this paper, a smile and laugh facial expression is presented based on dimension reduction and description process of the key points. The paper has two main objectives; the first is to extract the local critical points in terms of their apparent features, and the second is to reduce the system's dependence on training inputs. To achieve these objectives, three different scenarios on extracting the features are proposed. First of all, the discrete parts of a face are detected by local binary pattern method that is used to extract a set of global feature vectors for texture classification considering various regions of an input-image face. Then, in the first scenario and with respect to the correlation changes of adjacent pixels on the texture of a mouth area, a set of local key points are extracted using the Harris corner detector. In the second scenario, the dimension reduction of the extracted points of first scenario provided by principal component analysis algorithm leading to reduction in computational costs and overall complexity without loss of performance and flexibility, etc.

System Constrained Active Power Loss Minimization in Practical Multi-terminal HVDC Systems through GA

In this paper, a novel optimal reactive power flow solution approach in multi-terminal HVDC (High Voltage Direct Current) systems is studied. ULTCs’ (under load tap changer transformers) full equivalent model for the DC converters’ are taken into account in the proposed AC-DC power unlike the similar studies in the literature. Thus, the proposed study provides real accurate results for practical AC-DC applications. Optimal reactive power flow for minimum active power loss is provided by Genetic Algorithm (GA). For the test of the proposed study, the IEEE 14-bus test system modified to AC-DC system is used in the study. The obtained test results prove that the proposed GA based optimization method is effective to reach the global optimum point of minimum active power loss without dropping to local minimum point through satisfying system constraints.

Automatic detection of steel rebar in bridge decks from ground penetrating radar data

This paper develops a fully automatic algorithm to detect steel rebar in concrete bridge decks from ground penetrating radar (GPR) data. The surveyed GPR data from reinforced concrete (RC) structure carries significant amount of information, such as rebar locations, dielectric constant of concrete, corrosion conditions of steel rebars, and etc. However, current methodologies to identify rebar hyperbolas from GPR data are either manual or interactive, which is time-consuming. An unsupervised, efficient, and robust pattern recognition algorithm is proposed. In the algorithm, a template of a rebar hyperbola is selected first from the data, and is updated automatically to achieve better performance of rebar detection during the data processing. A rebar hyperbola in the GPR data is detected from the local minimum points on the map of sum of square difference (SSD) with an adaptive threshold value. An output file is created and saved, containing the amplitudes of rebar reflection and the geometrical locations of the detected rebars. The proposed algorithm is tested with ground-coupled GPR data collected from several decommissioned RC slabs, which are saw cut from a highway bridge. The overall percentage of accurate rebar hyperbola detection is 88.0%. Finally, the reflection amplitudes extracted from the rebar hyperbolas are used to create a corrosion indicator map, which shows good agreement with the results of half-cell potential maps.

Прогнозування тренду світових цін на нафту на базі СМІ-моделі економічних циклів

This paper presents author's method to forecast price trend direction for crude oil based on CMI-model of business cycles. As crude oil is included in CRB-index, which is the average weighted prices for 19 raw materials, the price dynamics for crude oil and the index is mainly unidirectional. Therefore, the method to forecast crude oil price, which is proposed here, can be also used for CRB-index forecasting. The price trend is determined by aggregate demand, which, in turn, depends on economic growth rate, and on the phase of the U.S. business cycle. According to CMI-model, phases of business cycles are determined by the value of cumulative market imperfection for the U.S. economy (∆P). Two rules to forecast the price trend for crude oil or for CRB-index are proposed: 1) yearly price decreases between minimum and maximum values of ∆P; 2) yearly price increases between maximum and minimum values of ∆P. These rules underwent empirical testing for the time period of 1975-2017 using yearly data for the crude oil (at NYMEX, ICE). We also demonstrated empirically that relationship between phases of the U.S. business cycles and turning points for CRB-index dynamics is of critical importance for the accurate forecasting of Ukrainian business cycle. Using the US economy data, it was demonstrated that the effect of the crude oil price rise on economic growth rate depends rather on the phase of business cycle (on its critical points location), than on the absolute value of this price. As long as an economy does not reach the point of ∆P minimum (by CMI-model), crude oil price may reach its historical maximum many times without triggering a recession. At the same time, if an economy passes the point of ∆P minimum, any even comparatively small external shock will trigger a recession (even if crude oil price does not reach its historical maximum). The US economy passed through the point of local maximum starting from the fourth quarter of 2017. It means that an upward price trend for crude oil (CRB-index) has formed and will cause further acceleration of the US economy growth rate (peak of this acceleration will be reached when ∆P=0). One can expect that the upward price trend for main raw materials will last until the next US recession (until the value of ∆P become negative). Herewith, growth rates for the crude oil price are expected 1,5-2 times higher than nowadays just 6-12 months before the recession starting point (i.e. when ∆P→0). According to pessimistic scenario, the US recession may occur as early as in 2020-21. Therefore, Ukrainian economy may be growing with a rate equal to the growth rate of prices for raw materials within at least 2-3 years. However, such favorable external factors for Ukrainian economy cannot last for a long time. If the peak of payments of the national debt coincides with the US recession bottom (local minimum point), some major problems for Ukrainian economy may occur. In this case, prices for raw materials may drop by 50% and more, as a result of another exchange crash all over the world. This crash would increase significantly the probability of a new recession in Ukraine that would shorten substantially budget revenues into the national economy. Therefore, it makes sense nowadays, while monitoring the US economy conditions, to plan certain actions to provide a soft landing for the national economy in case of a global exchange crash.

Effect of pressure on the characteristics of lifted flames

The effects of pressure on the characteristics of lifted flames in a coflow with propane fuel were investigated experimentally in a pressure chamber. Changing the pressure influenced the density, reaction kinetics, and flame propagation speed. The pressure range tested was P = 0.5–5.5 atm. As the fuel jet velocity increased, a nozzle-attached flame transitioned to a lifted flame before blowout occurred. Depending on pressure, the onset conditions of liftoff and blowout occurred in the laminar, transition, or turbulent regimes. When P < 1.6 atm, the flame was lifted and had a tribrachial edge structure in the laminar regime, and the liftoff height (HL) increased with increasing pressure. Both the liftoff and blowout velocities decreased with decreasing pressure, and they merged at 0.5 atm. A correlation was derived in terms of the Schmidt number (Sc) and the Reynolds number (Re): Pn/2(HLPn/2)(Sc−1)/(2Sc−1)∝Re. The reattachment velocity in the laminar and transition regimes linearly decreased with pressure. The liftoff height had two local minimum points at given Reynolds number in the transition regime, and then increased linearly in the turbulent regime.

Improved wavelet cerebellar model articulation controller for precision positioning of piezo-driven stage

This paper proposes an improved wavelet cerebellar model articulation control system (IWCMACS) to control precision positioning of the linear piezoelectric motor (LPM). The proposed system combines the improved wavelet cerebellar articulation model controller (IWCMAC) with the estimated bound compensator controller to obtain high-precision positioning for applications requring accuracy within micrometer or nanometer range. In this research, the momentum and propotional factors are added into learning algorithm to escape from local minima points and speed up convergence of the system. The Lyapunov-Like Lema theory is used to estimate error bound to guarantee the stable of the system. The experimental results for the piezo-priven stage conclude the effectiveness and applicability of the proposed control system for model-free nonlinear.

Existence and Boundedness of Second-order Karush-Kuhn-Tucker Multipliers for Set-valued Optimization with Variable Ordering Structures

In this paper we investigate second-order Karush-Kuhn-Tucker multipliers for both local nondominated and local minimal points of set-valued optimization with variable ordering structures. We prove calculus rules of second-order contingent derivatives of index $\gamma \in \{0,1\}$ and use them to establish improved Karush-Kuhn-Tucker multiplier rules of nonclassical forms which involve separately such derivatives of the objective, constraint and ordering maps. The equivalence between the nonemptiness and boundedness of the multiplier sets in these rules and second-order constraint qualifications of the Kurcyusz-Robinson-Zowe and Mangasarian-Fromovitz types is demonstrated.

A Real-Time QRS Detection System With PR/RT Interval and ST Segment Measurements for Wearable ECG Sensors Using Parallel Delta Modulators.

This paper presents a real-time electrocardiogram (ECG) monitoring system for wearable devices. The system is based on the proposed parallel delta modulator architecture with local maximum point and local minimum point algorithms to detect QRS and PT waves. Therefore, using the proposed system and algorithm, real-time PR and RT intervals, and ST segment measurements can be achieved in long-term wearable ECG recording. The algorithm is tested with the MIT-BIH Arrhythmia Database for QRS complex detection and with the QT Database for the P and T wave detections. The simulation result shows that the algorithm achieves above 99%, 91%, and 98% accuracy in the QRS complex, P wave, and T wave detections, respectively. Experimental results are presented from the system prototype, in which the parallel delta modulator circuits are fabricated in IBM 0.13$\mu \text{m}$ standard CMOS technology and the algorithms are implemented in a Xilinx Spartan-6 field programmable gate array (FPGA). The parallel delta modulators consume 720nW at 1kHz sampling rate with $\pm$0.6V power supply. The proposed system has the potential to be applied in future long-term wearable ECG recording devices.

Unifying local–global type properties in vector optimization

It is well-known that all local minimum points of a semistrictly quasiconvex real-valued function are global minimum points. Also, any local maximum point of an explicitly quasiconvex real-valued function is a global minimum point, provided that it belongs to the intrinsic core of the function’s domain. The aim of this paper is to show that these “local min–global min” and “local max–global min” type properties can be extended and unified by a single general local–global extremality principle for certain generalized convex vector-valued functions with respect to two proper subsets of the outcome space. For particular choices of these two sets, we recover and refine several local–global properties known in the literature, concerning unified vector optimization (where optimality is defined with respect to an arbitrary set, not necessarily a convex cone) and, in particular, classical vector/multicriteria optimization.

A Branch-and-bound algorithm for concave minimization problem with upper bounded variables

This paper presents a branch-and-bound algorithm for solving the concave minimization problems with upper bounded variables. The algorithm uses simplex to construct the branching and the bounding procedure. The linear convex envelope (the objective function of the subproblem) is uniquely determined on the candidate simplex which contains the subset of the local minimal points. The optimal solution of the subproblem is a local optimum of the original concave problem and used in reducing the list of active subproblems. The branching process splits the candidate simplex into two subsimplices by fixing the selected branching variable at value 0 or upper bound. Then the subsimplices are one less dimensional than the candidate. It means that the size of the subproblems gradually decreases. Further research needs to be focused on the efficient determination method of the simplex. The algorithm of this paper can be applied to solving the concave minimization problems under knapsack type constraints.

Shape optimisation problem for stability of Navier–Stokes flow field

ABSTRACTThis paper presents the numerical results of a shape optimisation problem with regard to delaying the transition of a Navier–Stokes flow field from laminar to turbulent by using the theory developed by Nakazawa and Azegami. The theory was reviewed within the framework of functional analysis and updated with another expression of the shape derivative with respect to the objective function. A computer program was developed with the FreeFEM++. Numerical analyses were performed for two types of problems: a two-dimensional Poiseuille flow field with a sudden expansion and a two-dimensional uniform flow field around an isolated body. From the first example, two local minimum points of symmetric and asymmetric flow fields were determined, and the asymmetric flow field was found to be more stable. With regard to the second example, we reached the local minimum point of an elliptical shape, and infrequently determined a solution converging to an elliptical shape with the bluff in the leeward direction. By comparison, the superiority of the elliptical shape was obvious.

An infinite sequence of localized semiclassical bound states for nonlinear Dirac equations

In this paper, we study the following nonlinear Dirac equation $$\begin{aligned} -i\varepsilon \alpha \cdot \nabla u+a\beta u+V(x)u=|u|^{p-2}u,\ x\in \mathbb {R}^3, \ \mathrm{for}\ u\in H^1({{\mathbb {R}}}^3, {{\mathbb {C}}}^4), \end{aligned}$$ where $$p\in (2,3)$$ , $$a > 0$$ is a constant, $$\alpha =(\alpha _1,\alpha _2,\alpha _3)$$ , $$\alpha _1,\alpha _2,\alpha _3$$ and $$\beta $$ are $$4\times 4$$ Pauli–Dirac matrices. Under only a local condition that V has a local trapping potential well, when $$\varepsilon >0$$ is sufficiently small, we construct an infinite sequence of localized bound state solutions concentrating around the local minimum points of V. These solutions are of higher topological type in the sense that they are obtained from a minimax characterization of higher dimensional symmetric linking structure. The existing work in the literature give finitely many such localized solutions depending on both the local behavior of the potential function V near the local minimum points of V and the global behavior of V at infinity.

Printability Study of Bioprinted Tubular Structures Using Liquid Hydrogel Precursors in a Support Bath

Microextrusion-based bioprinting within a support bath material is an emerging additive manufacturing paradigm for complex three-dimensional (3D) tissue construct fabrication. Although a support bath medium enables arbitrary in-process geometries to be printed, a significant challenge lies in preserving the shape fidelity upon the extraction of the support bath material. Based on the bioprinting in a support bath paradigm, this paper advances quantitative analyses to systematically determine the printability of cell-laden liquid hydrogel precursors towards filament-based tissue constructs. First, a yield stress nanoclay material is judiciously selected as the support bath medium owing to its insensitivity to temperature and ionic variations that are considered in the context of the current gelatin-alginate bio-ink material formulation. Furthermore, phenomenological observations for the rheology-mediated print outcomes enable the compositions for the bio-ink material (10% gelatin, 3% alginate), in tandem with the support bath medium (4% nanoclay, 0.5% CaCl2), to be identified. To systematically evaluate the performance outcomes for bioprinting within a support bath, this paper advances an experimental parametric study to optimize the 3D structural shape fidelity by varying parameters such as the layer height, extrusion flowrate, printing temperature, and printhead speed, towards fabricating complex 3D structures with the stabilization of the desired shape outcome. Specifically, it is found that the layer height and printhead speed are determinant parameters for the extent of successive layer fusion. Moreover, maintenance of an optimal bath temperature is identified as a key parameter for establishing the printability for the hydrogel bio-ink. Studying this effect is enabled by the custom design of a PID temperature control system with integration with the bioprinter for real-time precision control of the support bath temperature. In order to qualify the printed construct, a surface irregularity metric, defined as the average height difference between consecutive local maximum and minimum points of the binary image contour for the printed structure, is advanced to evaluate the quality of the printed constructs. Complex one-to-four bifurcating tubular structure prints demonstrate the applicability of the optimized bioprinting parameter space to create exemplar 3D human vessel-like structures. Finally, a cell viability assay and perfusion test for a printed cell-laden tubular element demonstrates high cell survival rates and leakage-free flow, respectively.

Application of Neural Network Optimized by Mind Evolutionary Computation in Building Energy Prediction

Building Energy forecasting plays an important role in energy management and plan. Using mind evolutionary algorithm to find the optimal network weights and threshold, to optimize the BP neural network, can overcome the problem of the BP neural network into a local minimum point. The optimized network is used for time series prediction, and the same month forecast, to get two predictive values. Then two kinds of predictive values are put into neural network, to get the final forecast value. The effectiveness of the method was verified by experiment with the energy value of three buildings in Hefei.

Optimization of cluster resource indexing of Internet of Things based on improved ant colony algorithm

In Internet of Things, the resource distribution is random in space, which leads to the poor precision ratio of the cluster resource indexing of Internet of Things, so in order to improve the information fusion and dispatching ability of Internet of Things, it is necessary to optimize the resource indexing of Internet of Things. Therefore, an algorithm for cluster resource indexing of Internet of Things based on improved ant colony algorithm is proposed in this paper. Directed graph models are used to construct a distribution structure model of cluster resource indexing nodes of Internet of Things, carry out semantic association feature extraction in the cluster resource storage information flow of Internet of Things. And the improved ant colony algorithm is used to crawl and capture cluster information in Internet of Things. According to the ant colony trajectory information, the velocity and position of the cluster resource indexing of Internet of Things are updated, and the balanced ant colony algorithm is used to carry out the global search and local search to resources and initialize the clustering center, and the target function of the cluster resource indexing of Internet of Things is constructed and the optimization parameter is solved with the constraint condition of the minimum variance of the whole fitness. The strong ability of global optimization of the ant colony algorithm is used to realize resource indexing optimization. Simulation results show that the improved algorithm can quickly realize resource index convergence, effectively escape local minimum points, and has strong global search ability and relatively high resource indexing precision ratio.

Multiplicity and concentration of positive solutions for fractional [formula omitted]-Laplacian problem involving concave–convex nonlinearity

In this paper, we discuss a fractional p-Laplacian problem. Under suitable assumptions on nonlinearity and weight, the existence and multiplicity of positive solutions are obtained via variational method. Moreover, the global maximum point of the solution concentrates at a local minimum point of the weight function.