Dual Theory Research Articles

Charged AdS black holes with higher derivative corrections in the presence of string cloud

We have obtained charged asymptotically anti-de Sitter (AdS) black hole solutions in Einstein–Gauss–Bonnet gravity in the presence of string cloud. It turns out that there exist three black holes in certain range of parameters for small enough chemical potential. However, for large chemical potential, these black holes merge into a single one. The free energy of the black holes is computed from the on-shell Euclidean action by subtracting the contribution of an extremal black hole. We have studied the free energy and specific heat of the solutions, which shows that the medium-sized black hole is unstable. As an application, we have studied the quark–antiquark potential in the dual gauge theory. This study provides necessary ingredients for the study of the dual theories in the context of condensed matter systems.

Localization of the Free Energy in Supergravity.

We derive a general formula for the gravitational free energy of Euclidean supersymmetric solutions to D=4, N=2 gauged supergravity coupled to vector multiplet matter. This allows one to compute the free energy without solving any supergravity equations, just assuming the solutions exist. As well as recovering some known results in the literature with ease, we also present new supergravity results that match with holographically dual field theory computations.

Maximizing virtual power plant profit: A two-level optimization model for energy market participation

Managing dispersed generation via virtual power plants (VPPs) is crucial for maximizing profits in electricity markets. This paper presents a model aimed at maximizing VPP profit through participation in the energy market. The proposed model addresses grid and security constraints of units using deterministic programming, formulated as an equilibrium-constrained, two-level mathematical optimization model. The first level focuses on maximizing VPP profit, while the second optimizes social welfare. Applying duality theory transforms this two-level model into a mixed-integer linear programming model, further refined using Karush–Kuhn–Tucker (KKT) optimality conditions. Given the inherent conflict in these objectives, a novel algorithm employing water flow dynamics is proposed for solving the model. To enhance method performance, the Pareto criterion and fuzzy decision-making are incorporated. Model tests are conducted on a standard 24-bus IEEE grid, demonstrating its efficiency. For the single-objective problem without line congestion, the solving time was 12 s. Introducing line congestion increased the profit by 13.4 %, from $40,413.21 to $45,837.32. In the two-objective problem without congestion, the profit ranged between $36,928.72 and $42,813.28, and emissions ranged from 275.21 to 2,916.32 pounds. With congestion, the profit range increased by a maximum of 8.7 %, and emissions were reduced by up to 4.6 %.

Effect of food stimuli presentation on restrained eater's food choice: An ERP study

Restrained eaters are individuals who consciously follow a limited food intake diet to lose or maintain body weight. With the rising numbers of obesity cases, retrained eating has became more prevalent as more people adopt it to cope with obesity. The dual conflict theory states that restrained eaters often encounter conflicting choices of food pleasure and weight management. The present study investigated the difference in food choice regarding different presentations of the weight management goal. The study hypothesized difference in successful and unsuccessful restrained eaters’ food choice when presented with the conflicting food/weight maintenance stimuli. A total of 49 college students participated in the study and the N2, P3 and LPP event-related potentials (ERPs) were investigated during a food choice task. Results showed that the reaction time in unsuccessful restrained eaters (UREs) were greater than successful restrained eaters (SREs). The ERP results showed that SREs exhibited smaller N2 and greater P3 amplitudes than UREs, however, we did not find a difference in LPP amplitudes between the two groups. The findings suggest that the UREs demonstrated greater sensitivity and smaller inhibition to food cues, while we do not have supports for a difference in motivational and emotional salience. This is the first study that investigated the food choice of SREs and UREs when faced with different presentations of conflicting goals, which enriches the theoretical model and provides neural correlates evidence for future studies.

The dark side of brands: Exploring fear of missing out, obsessive brand passion, and compulsive buying

Understanding the roots of compulsive buying is critical because it often leads to negative outcomes like depression, social anxiety, and debt. The aim of this study is to investigate the influence of the fear of missing out and brand passion on compulsive brand buying. We collect data from 511 consumers and use partial least squares for the data analysis. The study supports the dual theory of passion, which delineates brand passion into harmonious and obsessive forms, with the latter representing a negative aspect. The findings strongly affirm the relationship between the fear of missing out and both types of brand passion. Obsessive passion emerges as a more significant predictor of compulsive buying. Moreover, the study unveils that consumers’ age moderates the relationship between the fear of missing out and obsessive passion. We recommend marketing strategies to facilitate consumers’ passions driven by the fear of missing out, to encourage and nurture harmonious passion, to foster obsessive passion in a more responsible manner, and to focus on brand-passion-driven marketing towards younger consumers.

Crossers in a Segmented Labour Market: Occupational Advancement and Wage Changes from Semi-Skilled and Unskilled Jobs

How the upward mobility chances of workers in unskilled or semi-skilled jobs are shaped by influences at the organisational and sectoral level remains an open question. This article aims to close this research gap by examining the role of internal labour market characteristics in the promotion prospects and wage increases of workers in semi-skilled and unskilled positions. The hypotheses are derived from dual and segmented labour market theory. Regression analyses based on linked-employer-employee-data (LIAB), covering 44,024 workers in semi-skilled and unskilled positions from 2005 to 2010, underline the importance of the internal labour market. A considerable share of workers moved to skilled positions through company change. For the workers who stayed with the company, career advancements were associated with regular training investments and formalised regulations at the company level. Collective agreements, in contrast, were associated with lower chances of upward mobility, but higher wages.

Flat-space limit of holographic pseudoentropy in (A)dS spacetimes

The real part of pseudoentropy in conformal field theories is holographically calculated by the area of some extremal spacelike surfaces in the dual de Sitter (dS) and anti–de Sitter (AdS) spacetimes. We show that the flat-space limit of these curves in three-dimensional (A)dS spacetimes is well defined. We find that, if the length of the curves is calculated from the radial coordinate where the retarded time is extremum, then after taking the flat-space limit, the entanglement entropy of the dual theory of three-dimensional flat spacetime is obtained. For dS spacetime, the radial coordinate corresponding to the extremum of retarded time is located inside the cosmological horizon. Our results suggest that, on the field theory side, the entanglement entropy in the dual theory of flat spacetimes should be obtained from the ultrarelativistic limit of pseudoentropy in the dual conformal field theory to (A)dS spacetimes. Published by the American Physical Society 2024

Stone Pseudovarieties

We extend the theory of profinite algebras, as it is used in the algebraic theory of regular languages, to the more general setting of Stone topological algebras with the ultimate goal of going beyond classes of regular languages. We introduce Stone pseudovarieties, that is, classes of Stone topological algebras of a fixed topological signature that are closed under taking Stone quotients, closed subalgebras and finite direct products. Looking at the dual Stone spaces of Boolean algebras of subsets of a given topological algebra, we find a simple characterization of when the dual space admits a natural structure of topological algebra; the characterization is given in terms of how the Boolean algebra behaves under the inverses of the operation evaluation mappings of each arity. This provides an alternative, which is presented in the form of an equivalence of categories, to the duality theory of M. Gehrke. As an application, a Stone quotient of a Stone topological algebra that is residually in a given Stone pseudovariety is shown to be also residually in it, thereby extending the corresponding result of M. Gehrke for the Stone pseudovariety of all finite algebras over discrete signatures, which was recently extended to topological signatures jointly by the authors and H. Goulet-Ouellet. The residual closure of a Stone pseudovariety is thus a Stone pseudovariety, and these are precisely the Stone analogues of varieties. A Birkhoff type theorem for Stone varieties is also established and it is shown how Reiterman’s theorem can be derived from it.

Regularization method and a posteriori error estimates for the bilateral obstacle problem

In this paper, we present a relatively complete analysis of the regularization method for of the bilateral obstacle problem with a non-homogeneous condition on the boundary. We provide both the convergence result and a priori estimates. Then by the duality theory from the convex analysis, we determine the dual problem associated with the of the bilateral obstacle problem. Based on this dual problem, we provide a posteriori error estimates for the continuous and the discrete problems. The a posteriori error estimates are desired for the practical implementation of the regularized problem.

Note on holographic torus stress tensor correlators in AdS3 gravity

In the AdS3/CFT2 framework, the Euclidean BTZ black hole corresponds to the dominant high-temperature phase of its dual field theory. We initially employ perturbative methods to solve the Einstein equations as boundary value problems, providing correlators for the energy-momentum tensor operator at low points. Utilizing operator equations established in our previous work, we further compute arbitrary high-point correlators for the energy-momentum tensor operator in the high-temperature phase and recursive relations for these high-point functions. Concurrently, we employ the Chern-Simons formalism to derive consistent results. Further, using the cut-off AdS/TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformed CFT duality, we calculate the energy-momentum tensor correlators, contributing to the comprehensive understanding of the system’s dynamics. Finally, stress tensor correlators enable us to ascertain the corresponding KdV operator correlators at low-temperature.

Holographic RG flows in a 3D gauged supergravity at finite temperature

In this paper, we consider finite-temperature holographic renormalization group (RG) flows in D=3 N=(2,0) gauged truncated supergravity coupled to a sigma model with a hyperbolic target space. In the context of the holographic duality, fixed points (CFTs) at finite temperature are described by anti–de Sitter (AdS) black holes. We come from the gravity equations of motion to a 3D autonomous dynamical system, which critical points can be related to fixed points of dual field theories. Near-horizon black hole solutions correspond to infinite points of this system. We use Poincaré transformations to project the system on R3 into the 3D unit cylinder such that the infinite points are mapped onto the boundary of the cylinder. We explore numerically the space of solutions. We show that the exact RG flow at zero temperature is the separatrix for asymptotically AdS black hole solutions if the potential has one extremum, while for the potential with three extrema the separatrices are RG flows between AdS fixed points. We find near-horizon analytical solutions for asymptotically AdS black holes using the dynamical equations. We also present a method for constructing full analytical solutions. Published by the American Physical Society 2024

Optimal economic configuration by sharing hydrogen storage while considering distributed demand response in hydrogen-based renewable microgrid

With the issues of the greenhouse effect and environmental pollution globally, a high proportion of renewable energy has been integrated into microgrids. Its interconnection brings many challenges to the electric power industry. This paper proposes a new distributed response strategy through sharing hydrogen storage resources, aiming to solve the supply-demand imbalance in microgrids. First, the uneven power distribution from shared energy storage stations necessitates ensuring a fair power dispatch among users. Next, a microgrid demand response model with multi-constraint conditions and high penetration of wind and solar power is established, incorporating constraints like user power consumption, energy storage capacity, and charging/discharging power while considering differences in user electricity behaviors. Finally, the optimal economic configuration uses Lagrange duality theory to process the integrated models, including the demand response, hydrogen sharing, and power generation models, to make the optimization goals fairer. Results demonstrate that our strategy can adjust user electricity usage according to real-time supply-demand conditions, reducing users' total costs by 39.4 %. Compared with the existing configurations of sharing hydrogen storage configurations, our model uses more accurate utility functions, demonstrating better economic advantages, with users' total costs reduced by 4.89 % and revenue of the shared storage station increased by 4.02 %.

Pre-disaster allocation and post-disaster dispatch strategies of power emergency resources for resilience enhancement of distribution networks

With the frequent occurrence of large-scale power outages caused by extreme disasters, coordinated dispatch of power emergency resources (PERs) and repair crews (RCs) has gradually become an essential method to enhance the resilience of distribution networks (DNs). Previous works solve this coordinated dispatch problem in a risk-neutral approach with the assumption that the supply of power repair materials (PRMs) is still fully available after the disaster. However, growing evidence indicates that certain extreme disasters may lead to limited availability of PERs in the DN, rendering risk-neutral decision making impractical. To fill this gap, this paper proposes a resilience-oriented PERs pre-disaster allocation and post-disaster dispatch strategy in a risk-averse manner. In the pre-disaster prevention process, a two-stage distributionally robust optimization (DRO) model based on mean-CVaR is developed, considering the uncertainties of both system damage and PERs demands, along with the decision maker's preference for risk. In the post-disaster restoration process, a collaborative spatio-temporal dispatching model for PERs and RCs with the goal of minimizing outage losses is established. To tackle the computational challenges associated with PRMs allocation based on DRO, robust counterpart transformation and dual theory are utilized. Case studies are conducted using a real world modified 118-bus distribution network. In comparative analysis, five control groups are established to validate the necessity to consider the limited supply of PRMs and the risk-averse attitude of decision makers in enhancing DNs resilience.

Constructive holography

We consider the collective field theory description of the singlet sector of a free and massless matrix field in d dimensions. The k-local collective fields are functions of (d − 1)k + 1 coordinates. We provide a map between the collective fields and fields in the dual gravitational theory defined on AdSd+1 spacetime. The coordinates of the collective field have a natural interpretation: the k-local collective field is a field defined on an AdSd+1×Sk−1×S(d−2)(k−2)×Sd−3 spacetime. The modes of a harmonic expansion on the Sk−1×S(d−2)(k−2)×Sd−3 portion of the spacetime leads to the spinning bulk fields of the dual gravity theory.

Open AdS/CFT via a double-trace deformation

A concrete model of extracting the physics from the bulk of a gravitational universe is important to the study of quantum gravity and its possible relationship with experiments. Such a model can be constructed in the AdS/CFT correspondence by gluing a bath on the asymptotic boundary of the bulk anti-de Sitter (AdS) spacetime. This bath models a laboratory and is described by a quantum field theory. In the dual conformal field theory (CFT) description this coupling is achieved by a double-trace deformation that couples the CFT with the bath. This suggests that the physics observed by the laboratory is fully unitary. In this paper, we analyze the quantum aspects of this model in detail which conveys new lessons about the AdS/CFT correspondence, and we discuss the potential usefulness of this model in understanding subregion physics in a gravitational universe.

Innovative player evaluation: Dual-possibility Pythagorean fuzzy hypersoft sets for accurate international football rankings

This study introduces an advanced approach for ranking international football players, addressing the inherent uncertainties in performance evaluations. By integrating dual possibility theory and Pythagorean fuzzy sets, the model accommodates varying degrees of ambiguity and imprecision in player attributes. Additionally, the use of hypersoft set theory enriches the analysis by capturing the multifaceted nature of player evaluations. The proposed aggregation operators refine the synthesis of diverse information sources, leading to a comprehensive and nuanced assessment. This research significantly enhances player evaluation methodologies, providing a more adaptable framework for a fair assessment of international football talent. A practical example illustrates the application of dual-possibility Pythagorean fuzzy hypersoft sets (DP-PFHSS). A numerical technique is proposed for solving multi-criteria decision-making (MCDM) challenges with known dual possibility information using the proposed aggregation operators. This decision-making algorithm effectively determines a football player's worth, contributing to the overall ranking and evaluation process. The approach aids in scouting and recruitment by facilitating talent identification and informed player signings. Graphical analysis, comparing existing and proposed methods using average and geometric operators, demonstrates the superiority of the proposed approach in the players evaluation, indicating that F1 is in the top ranking.

Type II string theory on AdS3×S3×T4 and symmetric orbifolds

We discuss in detail the 1+1-dimensional superconformal field theory dual to type II string theory on AdS3×S3×T4, emphasizing the string theoretic aspects of this duality. For one unit of Neveu-Schwarz (NS-NS) 5-brane flux (Q5=1), this string theory has been suggested to be dual to a grand-canonical ensemble of T4N/SN free symmetric orbifold conformal field theories (CFTs). We show how the string genus expansion emerges to all orders for the free orbifold grand-canonical correlation functions. We also discuss how the strong coupling limit of the NS-NS string theory arises (even at large N) in the free orbifold description, and argue why this limit does not have a weakly coupled RR description. The dual conformal field theory (CFT) includes (for all values of Q5) an extra T4 factor that is decoupled from perturbative string theory. We discuss the exactly marginal deformations that relate the different values of Q5, including the precise JJ¯ deformations mixing this extra T4 with the symmetric orbifold. Published by the American Physical Society 2024

A carbon integrated energy pricing strategy based on non-cooperative game for energy hub in seaport energy system

Seaports are significant energy consumers and sources of carbon emissions within the maritime industry. To address this problem, an energy hub (EH) can be established as an intensive energy interconnection center. This paper proposes a carbon emission flow (CEF) model based on the energy hub in seaport, which monitors the carbon emissions generated by the internal energy conversion unit operating within the hub. Additionally, a carbon integrated energy pricing strategy based on non-cooperative game theory is proposed. Based on duality theory and gradient descent method, an iterative algorithm is designed to seek the global optimal solution satisfying the Nash equilibrium point. The aim of the strategy is to encourage seaport energy consumers to adjust their energy consumption strategy according to the optimal benefits and reduce carbon emissions. A comparative study of three different strategy cases are conducted to evaluate the effectiveness of the proposed strategy. Numerical simulation results show the reduction of the total energy consumption and carbon emissions of the system, which is conducive to realizing the low-carbon operation of the seaport energy system.

Solving the QLY Least Squares Problem of Dual Quaternion Matrix Equation Based on STP of Dual Quaternion Matrices

Dual algebra plays an important role in kinematic synthesis and dynamic analysis, but there are still few studies on dual quaternion matrix theory. This paper provides an efficient method for solving the QLY least squares problem of the dual quaternion matrix equation AXB+CYD≈E, where X, Y are unknown dual quaternion matrices with special structures. First, we define a semi-tensor product of dual quaternion matrices and study its properties, which can be used to achieve the equivalent form of the dual quaternion matrix equation. Then, by using the dual representation of dual quaternion and the GH-representation of special dual quaternion matrices, we study the expression of QLY least squares Hermitian solution of the dual quaternion matrix equation AXB+CYD≈E. The algorithm is given and the numerical examples are provided to illustrate the efficiency of the method.

Impact of Immigration Policies on Economic Growth in Germany

Purpose: To aim of the study was to analyze the impact of immigration policies on economic growth in Germany. Methodology: This study adopted a desk methodology. A desk study research design is commonly known as secondary data collection. This is basically collecting data from existing resources preferably because of its low cost advantage as compared to a field research. Our current study looked into already published studies and reports as the data was easily accessed through online journals and libraries. Findings: Germany's immigration policies have had a significant impact on its economic growth. These policies have facilitated the influx of skilled labor, which has helped to address the country's demographic challenges, particularly the aging population and labor shortages in key sectors. Immigrants have contributed to the labor market by filling both high-skilled and low-skilled jobs, boosting productivity and innovation. Additionally, immigration has increased consumer demand, further stimulating economic growth. Unique Contribution to Theory, Practice and Policy: Human capital theory, dual labor market theory & endogenous growth theory may be used to anchor future studies on the impact of immigration policies on economic growth in Germany. Implement comprehensive language and vocational training programs for refugees and low-skilled immigrants to facilitate their economic integration and productivity. Formulate balanced immigration policies that address sector-specific labor demands without disadvantaging native workers.