Exterior Point Research Articles

ELEMENTS OF RETAIL STORE INTERIOR DESIGN : A QUALITATIVE STUDY ON ENHANCING CUSTOMER IN STORE EXPERIENCE

This research aimed to formulate the essential elements in retail store interior design. The retail store landscape is expected to undergo significant changes and trends in 2024. In this context, digitalization is expected to grow directly in proportion to e-commerce. Several AI-related concepts are also becoming increasingly favored. There are opportunities to explore key design elements in adapting to these developments. A good understanding of these elements can enhance the store’s image and create a positive experience. A qualitative method was also used to obtain 10 participants through focus group discussions involving retail store visitors as well as experts and interior product designers. The results showed that there are several important elements in designing retail store interiors, including physical elements such as the exterior area, interior area, display area, interior layout, and point of purchase. These physical elements play a significant role in creating an attractive and functional store appearance. Additionally, social elements are also important, including merchant characteristics, merchant outfits, crowding, customer characteristics, and privacy. These elements help in creating symbols and meanings relevant to visitors. Therefore, retail interior design that considers the store exterior, store interior, interior layout, and store displays can create a pleasant and meaningful shopping experience for customers

Solving Max-cut Problem with a mixed penalization method for Semidefinite Programming

This paper is an attempt to exploit the opportunity of Semi Definite Programming (SDP), which is an area of convex and conic optimization. Indeed, Numerous NP-hard problems can be solveby using this approach. Hence, we intend to investigate the strength of SDP to model and provide tight relaxations of combinatorial and quadratic problems in order to present a new polynomial time algorithm for solving this robust model. This algorithm was firstly use to solve the nonlinear programs, the reason for which we search to extend it to the SDP programs. Actually, this algorithm designs the combination of two penalization methods. The first one is a primal-dual interior point (PDIM) method while the second one is a primal-dual exterior point (PDEM) method. Unlike the first method, which converges globally, the second one, also called the primal dual nonlinear rescaling method, has local super linear/quadratic convergence. Therefore, it seems appropriate to use a mixed algorithm based on the interior-exterior point method (IEPM). In fact, this resolution starts from the interior method, and at a certain level of execution, it proceeds to exterior method. Hence, a convergence evaluation function is use to know the level of permutation. Through evaluation, it has been approve that our approach is use to solve some instances of max-cut problem. This problem is a central graph theory model that occurs in many real problems and it is one of many NP-hard problems, which has attracted many researchers over the years. Then, we have used a semi definite programming solver SDPA (Semi Definite Programming Algorithm) that is modify to include the exterior point method subroutine. From the computational performance, we conclude that as the problem size increases, interior-exterior point algorithm gets relatively faster. The numerical results obtained are promising.

A method for calculating two-phase equilibrium: Constrained gray prediction evolutionary algorithm with a surrogate model based on quadratic interpolation

Traditional methods, including direct solution methods based on Newton's method and indirect solution methods based on thermodynamic principles, are the mainstream methods used to solve the volume-temperature flash calculation (called NVT-flash), even though they suffer from drawbacks such as sensitivity to initial value and complexity of derivative calculations. A constrained backtracking search algorithm (CBSA), proposed in 2024, was the first and only metaheuristic algorithm to successfully tackle the NVT-flash problem, which overcomes shortcomings of traditional methods. Considering the advantages of metaheuristic algorithms, a constrained gray prediction evolutionary algorithm with a surrogate model based on quadratic interpolation (CGPE-QI) is proposed in this paper to deal with the NVT-flash problem. CGPE-QI considers total Helmholtz free energy as the objective function, moles vector, and volume of a single phase as variables. Constraints to solve the NVT-flash problem are addressed by using a direct search method and an exterior point method. Numerical experiments on two-phase equilibrium of pure substance and mixtures are carried out employing CGPE-QI. Experimental results are the same as those obtained by traditional methods, which confirms that CGPE-QI can effectively tackle the NVT-flash problem and possesses energy decay property. In particular, the results demonstrate that CGPE-QI is more competitive than CBSA in terms of convergence speed, stability, and calculation cost. CGPE-QI proposed in this paper is the second metaheuristic algorithm to successfully solve the NVT-flash problem, illustrating that metaheuristic algorithms have great potential in solving phase equilibrium calculation problems.

A constrained differential evolution algorithm for calculation of two-phase equilibria at given volume, temperature and moles

A variety of strategies including two types of direct solution methods based on Newton's method and indirect solution methods based on thermodynamic principles have been developed, which can find satisfactory solutions for the phase equilibrium calculation problem at given volume, temperature and moles (NVT-flash). However, these methods are sensitive to the initial values and depend on the objective function's derivative during calculation. To resolve these deficiencies, a constrained differential evolution algorithm (abbreviated as CDE) for calculating two-phase equilibria at given volume, temperature, and moles is presented in this paper. The total Helmholtz free energy is regarded as the objective function, and the moles vector and volume of a certain phase are taken as the decision variables. This paper deals with the constraints of the NVT-flash problem by using direct search method and exterior point method. The results of the investigations on pure substance, binary and ternary mixtures are in agreement with the published data, which proves the effectiveness in solving the NVT-flash problem and the energy attenuation characteristic of the algorithm. The proposed algorithm represents the first successful attempt to apply the meta-heuristic optimization algorithm to solve the phase equilibrium computation under NVT-flash, and it shows the promising application prospect of meta-heuristic optimization algorithms for solving the phase equilibrium calculation problems.

Semi-delta-open sets in topological space

This purpose of this paper is to introduce a new class of open sets namely semi-delta-open sets . Further, some basic topological concepts such as neighbourhood axioms, border point, exterior point, frontier point of a set are defined and their properties have been investigated. In addition, in terms of these open sets, semi-delta-closed functions and semi-delta-continuous functions are also defined and their properties have been discussed

On Crofton’s type formulas and the solid angle of convex sets

AbstractHere we analyze three dimensional analogues of the classic Crofton formula for planar compact convex sets. In this formula a fundamental role is played by the visual angle of the convex set from an exterior point. A generalization of the visual angle to convex sets in the Euclidean space is the visual solid angle. This solid angle, being an spherically convex set in the unit sphere, has perimeter, area and other geometric quantities to be considered. The main goal of this note is to express invariant quantities of the original convex set depending on volume, surface area and mean curvature integral by means of integrals of functions related to the solid angle.

Actor-critic objective penalty function method: an adaptive strategy for trajectory tracking in autonomous driving

Trajectory tracking is a key technology for controlling the autonomous vehicles effectively and stably to track the reference trajectory. How to handle the various constraints in trajectory tracking is very challenging. The recently proposed generalized exterior point method (GEP) shows high computational efficiency and closed-loop performance in solving the constrained trajectory tracking problem. However, the neural networks used in the GEP may suffer from the ill-conditioning issue during model training, which result in a slow or even non-converging training convergence process and the control output of the policy network being suboptimal or even severely constraint-violating. To effectively deal with the large-scale nonlinear state-wise constraints and avoid the ill-conditioning issue, we propose a model-based reinforcement learning (RL) method called the actor-critic objective penalty function method (ACOPFM) for trajectory tracking in autonomous driving. We adopt an integrated decision and control (IDC)-based planning and control scheme to transform the trajectory tracking problem into MPC-based nonlinear programming problems and embed the objective penalty function method into an actor-critic solution framework. The nonlinear programming problem is transformed into an unconstrained optimization problem and employed as a loss function for model updating of the policy network, and the ill-conditioning issue is avoided by alternately performing gradient descent and adaptively adjusting the penalty parameter. The convergence of ACOPFM is proved. The simulation results demonstrate that the ACOPFM converges to the optimal control strategy fast and steadily, and perform well under the multi-lane test scenario.

Pengaruh Store Atmosphere terhadap Minat Beli Konsumen pada Rumah Makan Hawaii, Sanggau Kalimantan Barat

Store Atmosphere plays a highly persuasive role in attracting customers and creating a comfortable ambiance within restaurants. The store atmosphere encompasses various elements, including the exterior, general interior, store layout, and interior point of purchase display. The primary objective of this research is to explore the impact of store atmosphere on consumer purchasing interest at Hawaii restaurants, while also reinforcing existing theories. To conduct this study, a sample of 100 responses was collected, and data was gathered using questionnaires and the Likert scale. Several statistical tests, such as validity, reliability, normality, and heteroscedasticity, were employed for data analysis. The information verification approach involved utilizing the basic straight relapse check technique, followed by hypothesis testing using specific t-tests, f-tests, the coefficient of determination (R2) test, and correlation coefficient analysis. Based on the t-test results, it was found that the exterior, general interior, and store layout significantly influence consumer buying interest in Hawaii restaurants. However, the t-test indicated that the interior point of purchase display does not have a significant effect on consumer buying interest in Hawaii restaurants, specifically in Sanggau, West Kalimantan. Additionally, the f-test revealed that both store atmosphere variables and indicators collectively impact consumer buying interest. Furthermore, the coefficient of determination test demonstrated that the R square value is 92.5%. This implies a strong relationship between Store Atmosphere and buyers' purchasing interest, accounting for 92.5% of the variation in the dependent variable. The remaining 7.5% is influenced by various factors not explored in this study.
 Keywords: Store Atmosphere, Hawaii restaurants, Consumer Buying Interest.

Safe Deep Reinforcement Learning-Based Constrained Optimal Control Scheme for HEV Energy Management

Considering physical constraints in online optimization and training safety is a challenge for implementation of deep reinforcement learning (DRL) algorithm. Especially for the non-linear system, the mapping relationship between output action of the agent and the control signals is difficult to obtain. This paper proposes a novel DRL framework for online optimization in energy management of a power-split hybrid electric vehicle (HEV) which combines a neural-network (NN)-based multi-constraints optimal strategy and a rule-based-restraints system (RBRS). The proposed method named Reward Directed Policy Optimization (RDPO) adopts exterior point method (EPM) and curriculum learning (CL) to direct the agent to recognize and avoid irrational control signals and optimize the fuel economy. The EMS considering fuel consumption minimization and irrational control signals avoidance is optimized by training the agent through WLTC. A competitive fuel economy, 4.495L/100km, is achieved with no irrational control signals. Based on the online adaptability evaluation conducted, the fuel consumption of the vehicle under NEDC and CTUDC has been reduced to 4.113L/100km and 3.221L/100km, respectively, with no irrational control signals. The superiority in optimization, calculation efficiency and safety is verified through the comparisons with various DRL agents.

Equal Strength Optimal Design of Planetary Gear Transmission

In the design of planetary gear transmission, some gears are damaged during early use because of low strength, yet some are big structure sizes with high strength. In the paper, gears’ equal strength and minimum volume of the gearbox is regarded as optimization objective, and the exterior point penalty function method is used to solve them. Last, we obtain the design parameters under the condition of equal strength of the planetary transmission. Compared to the conventional design method, the weak strength of some gears is enhanced, the whole life is increased, and the overall volume is decreased. It shows we can get ideal results by equal strength optimization in the planetary transmission design.

The impact of load-PV profile resolution on distribution system risk assessment

Risk assessment is utilized to evaluate the risk level of the system and guide further operation and planning of utilities. However, to lower the cost of communication and storing, only a coarse resolution profile of load and PV can be collected and used to evaluate the risk level of the system, which may lead to inaccurate assessment. To this end, this paper investigates the impact of load-PV profile resolution on distribution system risk assessment. A super-resolution Generative Adversarial Network with pre- and post-processing processes is proposed to restore the high-frequency component of the load-PV profile. Then, with the generated high-resolution profile, a risk assessment model based on the exterior point method is proposed to evaluate the risk level of the distribution system. Case studies in a modified 33-bus system showed that the proposed super-resolution method could achieve the best performance to restore the peak values and high-frequency component of the load-PV profile compared to the other four methods. In addition, compared to super-resolution Generative Adversarial Networks without the post-processing process, the accuracy of risk assessment can be significantly improved using the proposed super-resolution method, which proves that the post-processing process is necessary.

Bipolar Soft Limit Points in Bipolar Soft Generalized Topological Spaces

The concept of soft set theory can be used as a mathematical tool for dealing with problems that contain uncertainty. Then, a new mixed mathematical model called the bipolar soft set is created by merging soft sets and bipolarity, which gave the concept of a binary model of grading. Bipolar soft set is characterized by two soft sets, one of which provides positive information and the other negative. Bipolar soft generalized topology is a generalization of bipolar soft topology. The importance of limit points in all branches of mathematics cannot be ignored. It forms one of the most significant and fundamental concepts in topology. On this basis, the derived set concept is required in the establishment and continuation of some properties. Accordingly, the limit point in bipolar soft generalized theory is defined. In this paper, we present the notion of bipolar soft generalized limit points. We explained the relation between the bipolar soft generalized derived and the bipolar soft generalized closure set. Added to that, we discussed some structures of a bipolar soft generalized topological space such as: <img src=image/13428354_01.gif>-interior point, <img src=image/13428354_01.gif>-exterior point, <img src=image/13428354_01.gif>-boundary point, <img src=image/13428354_01.gif>-neighborhood point and basis on <img src=image/13428354_02.gif>. Finally, we give comparisons among these concepts of bipolar soft generalized topological spaces (<img src=image/13428354_02.gif>) by using bipolar soft point (<img src=image/13428354_03.gif>). Each concept introduced in this paper is explained with clear examples.

Illuminating spiky balls and cap bodies

The convex hull of a ball with an exterior point is called a spike (or cap). A union of finitely many spikes of a ball is called a spiky ball. If a spiky ball is convex, then we call it a cap body. In this note we upper bound the illumination numbers of 2-illuminable spiky balls as well as centrally symmetric cap bodies. In particular, we prove the Illumination Conjecture for centrally symmetric cap bodies in sufficiently large dimensions. In fact, we do a bit more by showing that any d-dimensional centrally symmetric cap body can be illuminated by <2d directions in Euclidean d-space for d=3,4,9 and d≥19. Furthermore, we strengthen the latter result for 1-unconditionally symmetric cap bodies.

Impact of a Mobile Void within a Charge Distribution on the Electric Field

The electric field of a 3D spherical uniform charge distribution embodying a spherical mobile void at an exterior point is calculated. The size of the void and its path is arbitrary. Specifically, three different trajectories are analyzed. The movement of the void impacts the electric field so that the field becomes time-dependent. In terms of the chosen path and the size of the bubble, we evaluate the time-dependent electric field. The time profile of the field is calculated. Because of the computational challenges, the most of calculation is carried out utilizing a Computer Algebra System (CAS), specifically Mathematica [1]. This project makes the CAS an essential tool not only for calculating the field but for animating the features of the mobile void. An atlas of the study cases is included.

Images of point charges in conducting ellipses and prolate spheroids

This is an investigation into the exact forms of images of point charges in 2D conducting ellipses and 3D prolate spheroids. For an ellipse with an exterior point source, we compare two previous expressions for the analytic continuation inside the ellipse down to the focal line, the location of the image charge. For an interior source, we discover a sequence of image charges lying outside. For a point source close to the surface of a spheroid, series solutions for the potential diverge in a region that encompasses the singularities of the continuation of the reflected potential inside the spheroid. We uncover an image system for a point charge on the axis of a prolate spheroid that extends from the focal segment somewhat further up the axis. For an off-axis charge, we find a new approximate image charge. For a point charge at the center of the spheroid, the image singularity is found to lie on an infinitely wide, flat sheet with a hole around the spheroid. For a point charge located anywhere inside the spheroid, we find two new approximate image charge solutions: a point charge in real space, which applies when the source lies near the surface, or a point charge in complex space that projects as a ring in the real space which applies when the source lies near the rotation axis. When the point charge lies exactly on a focal point, a multipole of order 1/2 is an ideal image approximation.

Closure System and Its Semantics

It is well known that topological spaces are axiomatically characterized by the topological closure operator satisfying the Kuratowski Closure Axioms. Equivalently, they can be axiomatized by other set operators encoding primitive semantics of topology, such as interior operator, exterior operator, boundary operator, or derived-set operator (or dually, co-derived-set operator). It is also known that a topological closure operator (and dually, a topological interior operator) can be weakened into generalized closure (interior) systems. What about boundary operator, exterior operator, and derived-set (and co-derived-set) operator in the weakened systems? Our paper completely answers this question by showing that the above six set operators can all be weakened (from their topological counterparts) in an appropriate way such that their inter-relationships remain essentially the same as in topological systems. Moreover, we show that the semantics of an interior point, an exterior point, a boundary point, an accumulation point, a co-accumulation point, an isolated point, a repelling point, etc. with respect to a given set, can be extended to an arbitrary subset system simply by treating the subset system as a base of a generalized interior system (and hence its dual, a generalized closure system). This allows us to extend topological semantics, namely the characterization of points with respect to an arbitrary set, in terms of both its spatial relations (interior, exterior, or boundary) and its dynamic convergence of any sequence (accumulation, co-accumulation, and isolation), to much weakened systems and hence with wider applicability. Examples from the theory of matroid and of Knowledge/Learning Spaces are used as an illustration.

An Online Energy-Saving Driving Strategy for Metro Train Operation Based on the Model Predictive Control of Switched-Mode Dynamical Systems

With the rapid development of urban rail transit systems and the consequent sharp increase of energy consumption, the energy-saving train operation problem has been attracting much attention. Extensive studies have been devoted to optimal control of a single metro train in an inter-station run to minimize the energy consumption. However, most of the existing work focuses on offline optimization of the energy-saving driving strategy, which still needs to be tracked in real train operation. In order to attain better performance in the presence of disturbances, this paper studies the online optimization problem of the energy-saving driving strategy for a single metro train, by employing the model predictive control (MPC) approach. Firstly, a switched-mode dynamical system model is introduced to describe the dynamics of a metro train. Based on this model, an MPC-based online optimization problem is formulated for obtaining the optimal mode switching times with minimal energy consumption for a single train in an inter-station run. Then we propose an algorithm to solve the constrained optimization problem at each time step by utilizing the exterior point penalty function method. The proposed online optimal train control algorithm which determines the mode switching times can not only improve the computational efficiency but also enhances the robustness to disturbances in real scenarios. Finally, the effectiveness and advantages of this online optimal train control algorithm are illustrated through case studies of a single train in an inter-station run.

Collision-free and crossing-free trajectory design for second-order agents persistent monitoring

In this paper, we utilize second-order agents to address a one-dimensional persistent monitoring problem with potential agent collision and boundary-crossing problems. The objective is to minimize a sum of accumulated performance metric associated with targets over a finite time horizon by controlling the movements of agents. Different from the existing work where a collision avoidance algorithm is designed for avoiding collisions and boundary crossings, we consider these problems at the beginning of the problem formulation and further utilize Exterior Point Method (EPM) to propose a novel combinatorial objective function which guarantees a collision-free and crossing-free solution by penalizing all possible agents collisions and boundary crossings. According to Pontryagin Minimum Principle (PMP), we show that the optimal agent trajectories can be fully described by some parameters. Based on Infinitesimal Perturbation Analysis (IPA), a standard gradient descent method is proposed to obtain the optimal parameters. Our collision-free and crossing-free approach is computationally efficient as compared to the existing algorithm. Numerical examples are included to demonstrate the effectiveness of the proposed methods.

Clustering of subsample means based on pairwise L1 regularized empirical likelihood

To classify a vast amount of strata or subsamples with unknown families of distributions according to their strata-means, a clustering approach is developed based on pairwise $$L_1$$ regularized empirical likelihood. Under such a clustering approach, all possible contradictory conclusions are ruled out automatically. On the contrary, the decision rules based on many existing pairwise comparison procedures can generate contradictory results. Moreover, under certain mild conditions, the proposed clustering method enjoys the consistency property that with probability going to one, all strata are classified correctly. An exterior point algorithm is presented for the clustering. The applications of the proposed methods are demonstrated using stock market data and microarray data of breast cancer patients.

Decay rates for 1-d mixed type II and type III thermoelastic system with localized viscous damping

This work is devoted to discussing that how the locations of the thermal and viscous damping affect the stability of the 1-d elastic systems. The spatial domain of the 1-d thermoelastic system under consideration can be divided into three sub-intervals, that is, the thermoelastic region of type II, the one of type II with viscous damping, and the one of type III. The following two kinds of energy decay rates for the system are obtained:1.If the thermoelastic region of type III includes one exterior point of the spatial domain of the system, the energy of the system decays exponentially;2.If not, that is the thermoelastic region of type III is strictly inside the spatial domain, the system always lacks of exponential decay. However, the optimal polynomial decay rate is further estimated for this system with smooth initial states. Finally, some numerical simulations are presented to verify the stability results obtained in this work.