Duality Model Research Articles

Various duality models associated with some constrained robust nonlinear optimal control problems

This paper deals with various duality results for a new class of constrained robust nonlinear control problems. Concretely, we introduce a minimisation problem associated with a vector of functionals of multiple integral type. In addition, the considered multi-objective controlled optimisation problem is governed by several mixed constraints generated by partial derivatives of second order and uncertain data. For this new class of control problems, we establish and characterise Wolfe, Mond-Weir and mixed type robust dual models. To this aim, by using the notion of convex multiple integral functional, generated by a controlled second-order Lagrangian with uncertain data, and the concept of robust weak efficient solution to the problem under study, we build a new mathematical context to state and prove the duality theorems.

On Semi-Infinite Optimization Problems with Vanishing Constraints Involving Interval-Valued Functions

In this paper, we examine a semi-infinite interval-valued optimization problem with vanishing constraints (SIVOPVC) that lacks differentiability and involves constraints that tend to vanish. We give definitions of generalized convex functions along with supportive examples. We investigate duality theorems for the SIVOPVC problem. We establish these theorems by creating duality models, which establish a relationship between SIVOPVC and its corresponding dual models, assuming generalized convexity conditions. Some examples are also given to illustrate the results.

New Class of K-G-Type Symmetric Second Order Vector Optimization Problem

In this paper, we present meanings of K-Gf-bonvexity/K-Gf-pseudobonvexity and their generalization between the above-notice functions. We also construct various concrete non-trivial examples for existing these types of functions. We formulate K-Gf-Wolfe type multiobjective second-order symmetric duality model with cone objective as well as cone constraints and duality theorems have been established under these aforesaid conditions. Further, we have validates the weak duality theorem under those assumptions. Our results are more generalized than previous known results in the literature.

The Development of the Duality Model of Village Government Based on Local Wisdom Tri Hita Karana in Bali Province 1979 to 2019

The Decentralization and Regional Autonomy Policy issued by the Central Government and the Bali Regional Regulation on Pakraman/Indigenous Villages significantly affects the relationship between the two villages, which is currently a concern that leads to dualism and rivalry. In this regard, Balinese local wisdom, Tri Hita Karana, is urgently laying the foundation for harmonious relationship governance for the two village government systems. A descriptive approach is used in this study. The research was carried out in the Province of Bali. This study uses a purposive sampling technique to determine the research subjects. Collecting data using observation methods, document recording methods, and interview methods. The research was carried out using qualitative methods. The first stage consists of gathering primary and secondary data. The second step is to select a theory to study the data. The third stage is to analyze and interpret the selected data. The fourth stage involves writing and constructing research findings. The findings demonstrated the evolution of the duality model of village government from 1979 to 2019. The Duality Model of Village Government Period I. Overall, the Duality Model of Village Government Period I from 1979 to 1998 can be concluded, with the applicable regulations being Law No. 6 of 1986 concerning the Position, Function, and Role of Traditional Villages as Units of Customary Law Communities in Bali. Duality in Functional Relations and leading government administration between the Traditional Village and the Tri Hita Karana Local Wisdom-Based Service Village has been running well. Village Government Duality Model Period II. Overall, it can be concluded that the Village Government Duality Model Period II in the period 1999 to 2013 with the applicable Regional Regulation No. 3 of 2001 concerning Desa Pakraman and Regional Regulation No. 3 of 2003 concerning Amendments to the Regional Regulation of the Province of Bali No. 3 of 2001 concerning Pakraman Village are the regulations. Duality in Functional Relations and leading government administration between the Traditional Village and the Tri Hita Karana Local Wisdom-Based Service Village has been running well. Village Government Duality Model Period III. Overall, it can be concluded that the Village Government Duality Model Period III in the period 2014 to 2019 with the applicable Law No. 23 of 2014 on Regional Government, Law No. 6 of 2014 on Villages, and Regional Regulation No. 4 of 2019 on Traditional Villages in Bali are the regulations. Duality in Functional Relations and leading government administration between Traditional Villages and Tri Hita Karana Local Wisdom-Based Service Villages can still run well. The success of indigenous peoples in overcoming the intervention of various external forces is evident in Bali. The principle of duality, the basis of religious teachings, has succeeded in maintaining the coexistence of the Dinas village and the traditional village/ pekraman that live in harmony. It is recognized that it is in the Customary Village unit or Pekramansocial solidarity and social order can be enforced, two things that the Balinese people need to optimize the benefits of government and development that will be more prosperous.

A Duality Model of Dynamic Capabilities: Combining Routines and Improvisation

Dynamic Capabilities are predominantly conceptualised as being based on routine, stable patterns of behaviour. This is paradoxical with their intended purpose to elicit change in firms’ resource base and operational capabilities that allows them to face highly dynamic environments. I contribute to resolve this paradox by bringing the concept of duality to the Dynamic Capabilities debate. In particular, I argue that the view of Dynamic Capabilities as routines stems from the misconception that reliable outcomes can be attained only through stable mechanisms. Drawing on the literature on routine dynamics and on improvisation, as well as the empirical evidence of previous research, I propose a duality model that conceives Dynamic Capabilities as based both on routines and on improvisation. This duality perspective highlights the interdependence and complementarity between predictable stable routines and extemporaneous improvised actions that are both necessary to reliably achieve the (often radical) change needed to compete in highly dynamic environments. Rather than dealing with stable routines and improvisation as a trade-off, organisations must dynamically strive for the right balance, managing them concurrently and synergistically.

Generalizations of Higher-Order Duality for Multiple Objective Nonlinear Programming under the Generalizations of Type-I Functions

In this study, we introduce new generalizations of higher-order type-I functions and higher-order pseudo-convexity type-I functions. The application of the notion of sublinear functionals to these generalizations of higher-order type-I and higher-order pseudo-convexity type-I functions is crucial to our main findings. Furthermore, under these generalizations of the higher-order type-I and higher-order pseudo-convexity type-I functions, we established and studied six new types of higher-order duality models and programs for multiple objective nonlinear programming problems. In addition, we use these generalizations of higher-order type-I functions and higher-order pseudo-convexity type-I functions, to formulate and prove the theorems of weak duality, strong duality, and strict converse duality for these new six types of higher-order model programs.

Set-valued minimax programming problems under $ \sigma $-arcwisely connectivity

<abstract><p>A set-valued minimax programming problem (in short, SVMP) is taken into consideration in this study. We present the idea of $ \sigma $-arcwisely connectivity of set-valued maps (in short, SVM) in the broader sense of arcwisely connected SVMs. The sufficient criteria for Karush-Kuhn-Tucker (KKT) optimality are constituted for the problem (MP) under contingent epidifferentiation and $ \sigma $-arcwisely connectivity suppositions. In addition, we develop the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) kinds models of duality and verify the associated strong, weak, and converse theorems of duality among the primal (MP) and the associated figures of duals under $ \sigma $-arcwisely connectivity supposition.</p></abstract>

Reconstruct the Teacher-Student Relationship Based on Intersubjectivity Theory

Human beings are a relational existence, and the order of relations between teachers and students is the reflection of subject-object philosophical concepts in educational life, and is the logical premise of "student-centered" education and teaching reform. The first nature of teacher-student relationship is interpersonal relationship, which not only has the commonality of general relationships, but also has its own particularity because of its unique position in the field of education and teaching. The regulations on the order of teacher-student relations directly restrict the effectiveness of educational and teaching activities. The traditional paradigm of teacher-student relationship order highlights "teacher-centeredness" or "child-centeredness", which places teachers and students in a one-way model of duality and opposition, which often breeds disadvantages such as confrontation, conflict, and hegemony. At present, under the background of "student-centered" education and teaching reform, due to the lack of effective balance between students' subjective status and teachers' rational authority, the teacher-student relationship order still has drawbacks such as one-way interaction, behavioral utilitarianism, emotional indifference, and inter-interpersonal antagonism. This study attempts to take the theory of intersubjectivity as the logical starting point and attempts to reconstruct a new paradigm of teacher-student relationship order with equality as the primary premise, understanding as the core connotation, dialogue as the path, respect as the fundamental guarantee, and empathy as the value implication, in order to provide guidance for the "student-centered" education and teaching reform in the new era of China.

Violations of quark-hadron duality in low-energy determinations of αs

Using the spectral functions measured in τ decays, we investigate the actual numerical impact of duality violations on the extraction of the strong coupling. These effects are tiny in the standard αs( {m}_{tau}^2 ) determinations from integrated distributions of the hadronic spectrum with pinched weights, or from the total τ hadronic width. The pinched-weight factors suppress very efficiently the violations of duality, making their numerical effects negligible in comparison with the larger perturbative uncertainties. However, combined fits of αs and duality-violation parameters, performed with non-protected weights, are subject to large systematic errors associated with the assumed modelling of duality-violation effects. These uncertainties have not been taken into account in the published analyses, based on specific models of quark-hadron duality.

Using ρ-cone arcwise connectedness on parametric set-valued optimization problems

Within the inquiry about work, we explore a parametric set-valued optimization problem, where the objective as well as constraint maps are set-valued. A generalization of cone arcwise associated set-valued maps is presented named ρ-cone arcwise connectedness of set-valued maps. We set up adequate Karush–Kuhn–Tucker optimality conditions for the problem beneath contingent epiderivative and ρ-cone arcwise connectedness presumptions. Assist, Mond–Weir, Wolfe, and blended sorts duality models are examined. We demonstrate the related theorems between the primal and the comparing dual problems beneath the presumption.

Set-valued minimax fractional programming problems under ρ-cone arcwise connectedness

Abstract In this paper, we consider a set-valued minimax fractional programming problem (MFP), where the objective as well as constraint maps are set-valued. We introduce the notion of ρ-cone arcwise connectedness of set-valued maps as a generalization of cone arcwise connected set-valued maps. We establish the sufficient Karush-Kuhn-Tucker (KKT) conditions for the existence of minimizers of the problem (MFP) under ρ-cone arcwise connectedness assumption. Further, we study the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types of duality models and prove the corresponding weak, strong, and converse duality theorems between the primal (MFP) and the corresponding dual problems under ρ-cone arcwise connectedness assumption.

Hidden Information in Uniform Design for Visual and Near-Infrared Spectrum and for Inkjet Printing of Clothing on Canvas to Enhance Urban Security

In this paper, we publish the algorithm to create a dual image manifested in the infrared and visible spectrum. To distinguish the information in the two light spectra, twin dyes are introduced for the inkjet plotter and printing realization for garment and canvas items. The graphics, invisible to the naked eye, are designed for the near infrared (NIR) spectrum and are suitable for urban security where surveillance cameras with IR detectors are installed. The duality of dyes is presented in tables, and the analysis is a basis for programming and developing new algorithms for the application of “Infrared Dyeing” on different materials and printing technologies. Through spectroscopy, this innovative solution demonstrates twin colorants by printing in one pass through the plotter such that one image remains visible, while the other one is hidden to the bare eye. The uniform and the school bag cover presented in this paper are kept simple in design because they incorporate information hidden to the naked eye but visible with surveillance cameras and all the other infrared detectors. The article provides mathematical models of duality coloring as a basis for programming the graphic prepress that merges both of the images, the visual one and the infrared one. A topic is the fusion of two images with colors that represent two graphs, with independent contents for the visual and near-infrared spectrum.

Programmable interactions and emergent geometry in an arrayof atom clouds.

Interactions govern the flow of information and the formation of correlations between constituents of many-body quantum systems, dictating phases of matter found in nature and forms of entanglement generated in the laboratory. Typical interactions decay with distance and thus produce a network of connectivity governed by geometry-such as the crystalline structure of a material or the trapping sites of atoms in a quantum simulator1,2. However, many envisioned applications in quantum simulation and computation require more complex coupling graphs including non-local interactions, which feature in models of information scrambling in black holes3-6 and mappings of hard optimization problems onto frustrated classical magnets7-11. Here we describe the realization of programmable non-local interactions in an array of atomic ensembles within an optical cavity, in which photons carry information between atomic spins12-19. By programming the distance dependence of the interactions, we access effective geometries for which the dimensionality, topology and metric are entirely distinct from the physical geometry of the array. As examples, we engineer an antiferromagnetic triangular ladder, a Möbius strip with sign-changing interactions and a treelike geometry inspired by concepts of quantum gravity5,20-22. The tree graph constitutes a toy model of holographic duality21,22, in which the quantum system lies on the boundary of a higher-dimensional geometry that emerges from measured correlations23. Our work provides broader prospects for simulating frustrated magnets and topological phases24, investigating quantum optimization paradigms10,11,25,26 and engineering entangled resource states for sensing and computation27,28.

Investigation of the Interaction of Students’ Mental Models with Peer Instructional Elements in an Undergraduate Physics Course

Peer Instruction (PI) involves interaction between students and provides opportunities for students to reveal their own ideas, articulate their thinking, and facilitate construction of their knowledge with social interaction. Since the classroom environment of PI provides a rich information for students to discuss scientific phenomena, this research examined how students’ mental models interacted with Peer Instructional elements in an undergraduate level physics course. After the identification of students’ mental models of wave-particle duality in the first step of the project, the analyses of several data sources showed that some group-related issues, such as the explanatory based annotations before classes, good performance answering conceptual questions and discussion of additional concepts during classes, were important for scientific understanding. When students have similar group environments (i.e., peers in the same group), then individual pre-class preparation had a positive influence on students' scientific mental models of wave-particle duality. In addition, students having scientific models indicated that the satisfaction with their knowledge and the importance of conflict with their peers for their learning. All students in the classroom stated they benefited from peer discussions in different ways such as by recalling and reinforcing their knowledge, by getting feedback, and by reconstructing their knowledge. Both pre-class preparation and discussion of additional concepts and conflicting ideas in peer groups should be promoted in physics classes for facilitation of construction of scientific mental models.

SET-VALUED OPTIMIZATION PROBLEMS WITH (p, r)-ρ -CONE ARCWISE CONNECTEDNESS

In this paper, we introduce a new type of generalized arcwise connectedness, namely (p,r)-ρ-cone arcwise connectedness, for set-valued optimization problems. We establish the sufficient Karush-Kuhn-Tucker (KKT) optimality conditions under contingent epiderivative and (p,r)-ρ-cone arcwise connectedness assumptions. Further, we study Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types duality models and prove the corresponding weak, strong, and converse duality theorems between the primal (P) and the corresponding dual problems under (p,r)-ρ-cone arcwise connectedness assumption. We also construct an example to ensure that (p,r)-ρ-cone arcwise connectedness is more general than cone arcwise connectedness.

The stability and duality of dynamic Cournot and Bertrand duopoly model with comprehensive preference

In this paper, a Cournot model and its dual Bertrand model where firms have comprehensive preferences are developed. The preference was proposed by Bowles (2004) based on the results of Rabin (1993) and Lebine (1998). Comparable static method is used to illustrate the impact of parameters on equilibrium. Three scenarios are classified by preference parameter: completely cooperative, hostile to each other and general Cournot or Bertrand model. In each situation, Cournot model and its dual model present different chaos phenomenon which have various and abundant strange attractors, while the shapes of the stability regions are similar in the same situation. In the static setting, the local stability analysis of equilibrium gives the bounded region of quantity or price. The one-dimensional Logistic mapping is applied to studying the dynamics of the models on invariant axes. The critical curves classify different regions according to the number of preimages (q1, q2) or (p1, p2). Besides, simulations give more intuitive results: the cycle attractor, chaotic attractor and the basin of attraction with “holes” are presented. The article also provides new findings that under the assumption of comprehensive preference, the Cournot model with substitutes (complements) and the Bertrand model with complements (substitutes) are still duality models in the dynamic settings.

Market microstructure and the historical relationship between the US farm credit system, farm service agency and commercial bank lending

PurposeThe purpose of this paper is to investigate the market microstructure related to the Farm Credit System (FCS), Commercial Banks (CB) and Farm Services Administration (FSA). The commercial banks frequently call out the FCS as having an unfair advantage in the agricultural finance market place due to tax exempt bonds, and an implied guarantee of those bonds. This paper addresses the issue by examining the interrelationships since 1939, while addressing the historically distinctive roles that the FCS, CB and FSA have played in the US agricultural credit market.Design/methodology/approachThere are two components to our model. The first is the estimation of short and long run credit demand elasticities, as well as land elasticities. These are estimated from a dynamic duality model using seemingly unrelated regression. The point elasticity measures are then used as independent variables in least square regressions, combined with farm specific and related macro variables, for the Cornbelt states. The dependent variable is the year-over-year changes in paired FCS, CB and FSA loans.FindingsThe genesis of the FCS was to provide credit to farmers in good and bad years. Therefore, we expected to see a countercyclical relationship between FCS and CB. This is found for the farm crisis years in the 1980s but is not a continuous characteristic of FCS lending. In good times the FCS and CB appear to compete, albeit with differentiated market segmentation into short- and long-term credit. The FSA, which was established to provide tertiary support to both the FCS and CB, appears to be responding as designed, with greater activity in bad years. The authors find the elasticity measures to be economically significant.Research limitations/implicationsThe authors conclude that the market microstructure of the agricultural credit market in the US is important. Our analysis applies a broader definition of market microstructure for institutions and intermediaries and reveals that further research examining the economic frictions caused by comparative bond vs deposit funding of agricultural credit is important.Originality/valueThe authors believe that this is the first paper to examine agricultural finance through the market microstructure lens. In addition our long-term data measures allow us to examine the economics through various sub-periods. Finally, we believe that our introduction of credit and land demand elasticities into a comparative credit model is also a first.

Wave-particle duality: tribute to the memory of Yves Couder

The story of wave-particle duality in quantum mechanics has been told a thousand times. This modest contribution is to get back to a few points, including memories of a discussion we had on a possible experimental evidence of quantum effects at macroscopic scale, but in a way totally unrelated to the experiments he and his group made quite later to exhibit a model of wave-particle duality. The more general question of interpreting/understanding quantum mechanics will be also scrutinized once more.

ПОЭТИКА ДВОЙНИЧЕСТВА В ТЕТРАЛОГИИ Ф. АБРАМОВА «БРАТЬЯ И СЕСТРЫ»

The work is devoted to the poetics of duality in F. Abramov’s tetralogy Brothers and Sisters. The analysis of the duality models allows to imagine historical, social, political reality, the minimal structure of the human community: one and the other. At the center of the study are the key characters of the tetralogy, namely, Mikhail Pryaslin and Yegorshi Stavrov, who embody the eschatological Russian model of duality. The analysis of these characters is carried out against the background of the character structure as a whole. Within a Christian context, the Mikhail — Yegorsha twin pair is included in a broad semantic field. Yegorsha compares his sworn brother with Christ. According to the legend, the latter’s twin was apostle Thomas, whose name coincidentally means ‘a twin.’ If Mikhail is firmly associated with Christ, then Egorsha can be semantically identified with both Judas and Thomas (in all connotations). The destruction of the “country model,” the Russian schism also actualizes another version of duality: George the Victory-bearer and Yegoriy the troublebearer, which is already reflected at the level of character naming. The struggle of the “twin” heroes over a woman, ancestral land and the house, which is interpreted as a confrontation between Christ and the Antichrist, St. George and the “bad Yegorka” (changeling), is also implemented as the “Russian” version — Foma and Erema, in which the doubles lose to the circumstances. Peasant Russia is in captivity of civilization, and no one is able to protect it: the warriors die, the saints abandon the icons. This leads to the general sense of anxiety, of a life “between homes,” when the “prodigal son,” who has nowhere to go back to, becomes the modern hero.

Fluctuation and dissipation from a deformed string/gauge duality model

Using a Lorentz invariant deformed string/gauge duality model at finite temperature we calculate the thermal fluctuation and the corresponding linear response, verifying the fluctuation-dissipation theorem. The deformed AdS$_5$ is constructed by the insertion of an exponential factor $\exp(k/r^2)$ in the metric. We also compute the string energy and the mean square displacement in order to investigate the ballistic and diffusive regimes. Furthermore we have studied the dissipation and the linear response in the zero temperature scenario.