Formulation Of Theory Research Articles

Equilibrium analysis in game theory using nonlinear functional analysis techniques

Game theory provides a mathematical framework for analyzing the tactical choices of rational decision makers. The idea of equilibrium, which states that no player has a motivation to change their existing approach given the strategies of other players, is one of the core ideas of game theory. This study examines a type of undirected graph-based distributed quadratic game. The problem of communication topology constraints is presented and nonlinear dynamics with uncertain time-dependent perturbations are present in the participant's dynamics. Based on a high-gain observer approach, a distributed Nash equilibrium (NE) finding technique is given, and the Lyapunov stability theory is used to study the convergence. It represents that every player approximates the positions of their rival players and that there are differences between the NE and the placements of the minor limitation that finally restricts the players. In addition, chattering problems are eliminated since the offered theory's formulation employs the hyperbolic tangent function to control the perturbation rather than the signum function. In an imitation of the oligopoly match, five enterprises manufacture identical materials in a duopoly market framework; this is done to confirm the effectiveness of the recommended strategy. Our results provide novel perspectives and methods for understanding complicated strategic situations, helping to close the gap between mathematical theory and real-world applications.

On the boundary conditions for a thin circular plate conjugated to a massive body

The problem of deformation under the action of uniform pressure of a circular plate coupled with a massive base is considered, while the condition for the coupling of the plate with the base is modeled using boundary conditions of the generalized elastic embedding type, i.e. the relationship between the bending moment and forces at the edge of the plate with displacements and rotation angles through the compliance matrix. The main goal of the work is to study the influence of the elasticity of the embedding on the elastic response of the plate. The solution to the problem was obtained in the formulation of the linear theory of plates, the theory of membranes in the approximation of homogeneity of longitudinal forces, and the Foppl — von Karman theory, also in the approximation of the assumption of homogeneity of longitudinal forces. The values of the coefficients of the compliance matrix were obtained using the finite element method for the auxiliary problem and compared with the values of the coefficients obtained for related problems by analytical methods. Numerical results were obtained for an aluminum wafer on a silicon base. The obtained solution was compared with the solution obtained for the rigid embedment condition for all three models used. It is shown that in the case of large deflections (several plate thicknesses), taking into account the compliance of the embedment becomes essential.

Logical-semantic models and methods of knowledge representation: cases for energy management systems and SMR digital infrastructures

The subject of this article is the development of information technologies at the end of the 20th and the beginning of the 21st century for the Fourth Industrial Revolution in the form of Industry 4.0, i.e., Internet of Things (IoT) technologies. Successes in the implementation of this technology have led to the development of new applications in the energy sector, such as energy management systems, small modular reactor (SMR) management systems, and alternative power supply systems based on renewable energy sources. The digital infrastructure of these management systems is characterized by a high "density of knowledge", which requires clarification of fundamental concepts in information theory, namely the content of the concepts "data", "information", "knowledge" and "meaning of knowledge". Special attention was given to defining the role of knowledge. The aim of this study is to further develop methods and models of semiotic theory by determining the role and place of logical as well as eight- and four-factor logical-semantic models of knowledge bases in semiotic space. The tasks: comparing existing knowledge representation methods and models. Research results: We found that the logical models used in the development of knowledge bases are based on the principles of artificial intelligence theory, which relies on sign system hypotheses and formal logic theory. The main drawback is the complexity of practical implementation in the form of expert systems. For logical-semantic models in the form of eight-vector graphic models, it was found that there is currently no theoretical justification for defining the vectors that form the coordinate axes, making these models unique to specific subject areas. It was determined that the advantage of using these methods is that an expert can independently form such a knowledge model. For logical-semantic models in the form of four-factor graphic models, there is a theoretical justification for defining the factors of the model that form the coordinate axes, making these models universal for specific subject areas. It was established that the advantage of these models is that they can be developed by experts without the involvement of a knowledge engineer. Therefore, it is proposed to use four-factor logical-semantic knowledge representation models for further application. It is also proposed to split the element "logical-semantic models" into two elements in the semiotic spatial model in vector K8 "Knowledge Representation Models", namely: "logical-semantic eight-vector models" and "logical-semantic four-factor models". Additionally, it is proposed to add the element "post-Cartesian representation of meta-knowledge" to the element "geometric" in vector K5 "Ideal Models". Conclusions: The theoretical basis for developing eight-factor logical-semantic knowledge representation models is the form of connections between adjacent vectors in the form of Cartesian products on elements of the corresponding inter-coordinate matrices. The theoretical basis for the methodology of developing four-factor logical-semantic knowledge representation models is the form of connections between adjacent vectors in the form of Cartesian products for elements of the corresponding inter-coordinate matrices, as well as for diametrically opposite pairs of factors in the form of dialectical unity of the concepts "general" and "particular." The application of logical-semantic knowledge representation models for alternative energy-source management systems will ensure increased energy efficiency. Other cases related to the development of databases for SMR digital infrastructure are discussed.

Who ought to look towards the horizon? A qualitative study on the collective social responsibility of scientific research

There is a growing concern for the proper role of science within democratic societies, which has led to the development of new science policies for the implementation of social responsibility in research. Although the very expression ‘social responsibility of science’ may be interpreted in different ways, many of these emerging policy frameworks define it, at least in part, as a form of anticipative reflection about the potential impacts of research in society. What remains a rather under-discussed issue is the definition of the bearer of the social responsibility of science. In other words, it is not clear who is supposed to engage in such an anticipative reflection, whether individual researchers or research groups. In the past few years, philosophers of science have begun to use qualitative research methods to fill the gaps between normative models of the organisation of ideal scientific communities and the reality of actual scientific practices. In this article, I follow this approach to discuss the issue of the collective dimension of the social responsibility of science. I rely on a qualitative study conducted on an interdisciplinary research group and I describe how group dynamics position individuals and distribute duties and roles, including social responsibility. Qualitative descriptions of the distribution of duties within actual research groups should inform the formulation of general prescriptive theories on the collective responsibility of science.

Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions

The non-Hermitian skin effect dramatically reshapes the energy bands of non-Hermitian systems, meaning that the usual Bloch band theory is fundamentally inadequate as their characterization. The non-Bloch band theory, in which the concept of Brillouin zone is generalized, has been widely applied to investigate non-Hermitian systems in one spatial dimension. However, its generalization to higher dimensions has been challenging. Here, we develop a formulation of the non-Hermitian skin effect and non-Bloch band theory in arbitrary spatial dimensions, which is based on a natural geometrical object known as the amoeba. Our theory provides a general framework for studying non-Hermitian bands beyond one dimension. Key quantities of non-Hermitian bands, including the energy spectrum, eigenstates profiles, and the generalized Brillouin zone, can be efficiently obtained from this approach. Published by the American Physical Society 2024

Defining metrics of visual acuity from theoretical models of observers.

Many experimental studies show that metrics of visual image quality can predict changes in visual acuity due to optical aberrations. Here we use statistical decision theory and Fourier optics formalism to demonstrate that two metrics known in the field of vision sciences are approximations of two different theoretical models of linear observers. The theory defines metrics of visual acuity to potentially predict changes in visual acuity due to optical aberrations, without needing a posteriori scale or offset. We illustrate our approach with experiments, using combinations of defocus and spherical aberration, and pure coma.

학생 주도성이 발현되는 맥락과 수준에 대한 중학교 교사의 인식

Objectives This study was conducted to discover substantive and formal theories about the contexts and levels at which student agency, which has recently been recognized as a future educational competency, is manifested.
 Methods In order to uncover and reproduce the concept of student agency as a social and contextual product through teachers' perspectives and voices, the data from in-depth interviews with five middle school teachers about student agency were analyzed in the order of initial coding, focused coding, and theoretical coding according to constructivist grounded theory.
 Results The findings revealed that teachers categorized student agency as agency in learning and life and agency in the individual and community, with differing perceptions of the orientation, noting the timing specificity of middle school students undergoing major transitions in learning and life, and that personal and external factors contribute to the gap in agency among middle school students. They emphasized the need for teachers to take agency, such as running phased and customized lessons through cross-curricular activities and connecting life and learning. In particular, students who have experienced agency have the power to extend their personal agency to other contexts, accumulate opportunities for continuous growth, spread agency to others, and empower communities. Most importantly, we captured a shared perspective that the transfer and expansion of student agency, when supported by committed guidance and support from teachers, can be aggregated and amplified at the individual and community levels.
 Conclusions The findings suggest that the realization of student agency requires the convergence of a variety of factors, including personal, home environmental, and socio-contextual aspects, and recommend further research on teacher agency to bring student agency to the forefront.

Spin and Susceptibility Effects of Electromagnetic Self-Force in Effective Field Theory.

The classic Abraham-Lorentz-Dirac self-force of pointlike particles is generalized within an effective field theory setup to include linear spin and susceptibility effects described perturbatively, in that setup, by effective couplings in the action. Electromagnetic self-interactions of the pointlike particle are integrated out using the in-in supersymmetric worldline quantum field theory formalism. Divergences are regularized with dimensional regularization, and the resulting equations of motion are in terms only of an external electromagnetic field and the particle degrees of freedom.

O(D,D) -covariant formulation of perfect and imperfect fluids in the double geometry

We study generic matter coupled to a D-dimensional supergravity using a formulation of double field theory (DFT), where all the fields are encoded in O(D,D) multiplets. We study both the case when the matter comes from a variational principle, as well as the case where the matter comes from a statistical or thermodynamic approach. For the latter, we construct the distribution function for the perfect fluid and its entropy current, which is a conserved quantity. We then include general viscous and elastic terms in the generalized energy-momentum tensor which, in the general case, lead to entropy production. We consistently deform the conservation law of the generalized entropy current and identify a particular nondissipative deformation. Using the generalized fluid model, we revisit the issue of noncovariance of perfect fluids under T-dualities and we show how to resolve it in our DFT model with matter. Published by the American Physical Society 2024

Realization of IR Photodetector based on AGNRs operating in the Atmospheric Windows

Nowadays, the importance of Atmospheric windows in optoelectronic industries is not hidden from anyone. On the other hand, using graphene nanoribbons widely has been applied in optical devices. So, armchair graphene nanoribbons (AGNRs) from three different families as IR photodetectors are proposed and modeled, in this work. Our results show that the energy gap of AGNRs has been in the 1–3 μm and 8–14 μm atmospheric windows in the pure state and with nitrogen (N)/boron (B) substitutional doping. Also, responsivity and specific detectivity (D*) have been calculated, by introducing a simple structure as an IR photodetector. The energy gap and dark current (Jdark) calculations have been done by density functional theory (DFT) and non-equilibrium Green's function (NEGF) formalism, respectively. The specific detectivity peaks on the order of 109 cmHz1/2/W for 9-AGNR and 10-AGNR at 1–3 μm atmospheric window have been concluded. Furthermore, our results show that 11-AGNR with B dopants can be used to design dual-band detectors in the 1–3 μm and 8–14 μm atmospheric windows.

Power corrections to the modified QCD perturbative series based on conformal mapping of the Borel plane

Modifications of the QCD perturbative expansions by the subtraction of the dominant infrared renormalon have been proposed recently as attempts to solve the longstanding discrepancy between fixed-order and contour-improved perturbation theory for the hadronic τ decays. In this approach, the modified perturbative series is supplemented by a modified gluon condensate in the operator product expansion of the Adler function. Motivated by these works, we revisited recently a formulation of the QCD perturbation theory, proposed some time ago, which takes into account the renormalons by means of the conformal mapping of the Borel plane. One expects that the modified perturbative series obtained in this framework should be accompanied by modified power-suppressed nonperturbative corrections. However, in the previous studies the focus was on the perturbative series and the question of the possible power corrections has not been considered. In the present paper, we investigate for the first time this problem. Using techniques from the mathematical resurgence theory, we derive the expression of the dominant power correction to the perturbative series obtained by conformal mapping of the Borel plane, and discuss its implications for phenomenological applications. Published by the American Physical Society 2024

New basis for Hamiltonian SU(2) simulations

Due to rapidly improving quantum computing hardware, Hamiltonian simulations of relativistic lattice field theories have seen a resurgence of attention. This computational tool requires turning the formally infinite-dimensional Hilbert space of the full theory into a finite-dimensional one. For gauge theories, a widely used basis for the Hilbert space relies on the representations induced by the underlying gauge group, with a truncation that keeps only a set of the lowest dimensional representations. This works well at large bare gauge coupling, but becomes less efficient at small coupling, which is required for the continuum limit of the lattice theory. In this work, we develop a new basis suitable for the simulation of an SU(2) lattice gauge theory in the maximal tree gauge. In particular, we show how to perform a Hamiltonian truncation so that the eigenvalues of both the magnetic and electric gauge-fixed Hamiltonian are mostly preserved, which allows for this basis to be used at all values of the coupling. Little prior knowledge is assumed, so this may also be used as an introduction to the subject of Hamiltonian formulations of lattice gauge theories. Published by the American Physical Society 2024

The formal theory of relative monads

We develop the theory of relative monads and relative adjunctions in a virtual equipment, extending the theory of monads and adjunctions in a 2-category. The theory of relative comonads and relative coadjunctions follows by duality. While some aspects of the theory behave analogously to the non-relative setting, others require new insights. In particular, the universal properties that define the algebra object and the opalgebra object for a monad in a virtual equipment are stronger than the classical notions of algebra object and opalgebra object for a monad in a 2-category. Inter alia, we prove a number of representation theorems for relative monads, establishing the unity of several concepts in the literature, including the devices of Walters, the j-monads of Diers, and the relative monads of Altenkirch, Chapman, and Uustalu. A motivating setting is the virtual equipment ▪ of categories enriched in a monoidal category ▪, though many of our results are new even for ▪.

Mechanisms of Change in School Counseling Intervention Studies: A Content Analysis

The purpose of this content analysis was to examine the use of theory in school-counselor-led interventions. Specifically, we examined intervention characteristics, evaluation design, and use of theory in school-counselor-led intervention studies that were published by the American Counseling Association, the American School Counselor Association (ASCA), and in other school-counseling-related journals from 2003 to 2022. Drawing from 45 published articles, results indicated that few school counseling articles explicitly included ASCA Mindsets & Behaviors (ASCA, 2021) or integrated formal counseling theory to inform student outcomes.

A proof of conjectured partition identities of Nandi

abstract: We generalize the theory of linked partition ideals due to Andrews using finite automata in formal language theory and apply it to prove three Rogers--Ramanujan type identities for modulus 14 that were posed by Nandi through a vertex operator theoretic construction of the level 4 standard modules of the affine Lie algebra $A^{(2)}_{2}$.

Decoherence and entropy generation at one loop in the inflationary de Sitter spacetime for Yukawa interaction

Abstract The decoherence mechanism is believed to be possibly connected to the quantum to classical transition of the primordial cosmological perturbations in the early universe. In this paper, we extend our previous analysis on decoherence in a fermion and scalar quantum field theory coupled via the Yukawa interaction in the Minkowski spacetime, to the inflationary de Sitter background. We treat the scalar field as the system and the fermions as the environment, and both the fields are taken to be massless. We utilise a non-equilibrium effective field theory formalism, suitable for open quantum systems such as this. We assume that an observer measures only the Gaussian 2-point correlator for the scalar field, as the simplest realistic scenario. In order to compute the von Neumann entropy generated at late times as a measure of the decoherence, we construct the one loop renormalised Kadanoff-Baym equation, which is the equation of motion satisfied by the 2-point correlators in the closed time path Schwinger-Keldysh formalism. These equations account to the self energy corrections. Using this, we next construct the one loop corrected statistical propagator for the scalar, which is related to its phase space area, to compute the von Neumann entropy. We also compute the variation of the von Neumann entropy with respect to relevant parameters. We note the qualitative similarity between our findings and the scenario where both the system and the environment are scalars. Our result is also qualitatively similar to an earlier one found by using the influence functional technique for a massive Yukawa theory.

Euler fluid in 2+1 dimensions as a gauge theory and an action for the Euler fluid in any dimension

In this paper we parallel the construction of Tong of a gauge theory for shallow water, by writing a gauge theory for the Euler fluid in 2+1 dimensions. We then extend it to a Euler fluid coupled to an electromagnetic background. We argue that the gauge theory formulation provides a topological argument for the quantization of 2+1 dimensional Euler Hopfion solution. In the process, we find a (nongauge) action for the Euler fluid that can be extended to any dimension, including the physical 3+1 dimensions. We also discuss several aspects of the Arnold-Beltrami-Childress flow. Published by the American Physical Society 2024

The Effect of Global and Local Chemical Reactivity Descriptors in the Determination of Properties of Transition Metal Clusters

Recently, research on material properties has got lots of attention because of their promising technological applications. In this paper, the author’s focus is on the global and local chemical reactivity descriptors of some transition metal clusters. In addition, the author also include findings of chemical properties with reactivity descriptors. Furthermore, according to Thomas–Fermi approximation and from the exact formulation of Density Functional Theory by Hohenberg and Kohn’s theorem, the author introduce electronegativity and the theory of hardness and softness for further investigation of chemical properties of the clusters. As a part of investigations, the author also introduce the Fukui functions with an emphasis for the determinations of chemical reactivity descriptors. All the results are obtained by theoretical investigation of electronegativity), Chemical potential (), chemical hardness (), and polarizability () of the given transition metal clusters (Cr and Mn). From the results, the author observed that the ionization potential of the clusters increases with decreasing cluster size as the clusters become more stable and tend towards chemical inertness. In conclusion, determination of the reactivity descriptors of the transition metal clusters show results that are in line with previous experimental and theoretical findings.

On the (non-) reliance on algorithms—A decision-theoretic account

A wealth of empirical evidence shows that people display opposite behaviors when deciding whether to rely on an algorithm, even if it is inexpensive to do so and using the algorithm should enhance their own performance. This paper develops a formal theory to explain some of these conflicting facts and submit new testable predictions. Drawing from decision analysis, I invoke two key notions: the ‘value of information’ and the ‘value of control’. The value of information matters to users of algorithms like recommender systems and prediction machines, which essentially provide information. I find that ambiguity aversion or a subjective cost of employing an algorithm will tend to decrease the value of algorithmic information, while repeated exposure to an algorithm might not always increase this value. The value of control matters to users who may delegate decision making to an algorithm. I model how, under partial delegation, imperfect understanding of what the algorithm actually does (so the algorithm is in fact a black box) can cause algorithm aversion. Some possible remedies are formulated and discussed.

Market Freezes

AbstractMarket freezes are an interesting and theoretically challenging phenomenon —they are observed empirically, but cannot occur in standard models. This paper develops a formal theory of recurrent freezes emphasizing liquidity and self‐fulfilling prophecies. While it is well understood how to get hot and cold spells, where prices and quantities fluctuate, we get asset market freezes and thaws where trade completely stops and starts. The simplest specification gets this using negative asset returns. Other specifications use information frictions or fixed costs. We also consider credit freezes, analyze the extent to which the decentralized nature of trade matters, and discuss policy implications.