Dual Basis Research Articles

Dilations of (dual) frames for Krein spaces

This paper addresses the dilation problem on (dual) frames for Krein spaces. We characterize Riesz bases for Krein spaces and equivalence ([Formula: see text]-unitary equivalence) between frames for Krein spaces; prove that every frame (dual frame pair) for a Krein space can be dilated to a Riesz basis (dual Riesz basis pair) for a larger Krein space, and that the corresponding [Formula: see text]-orthogonal complementary frame ([Formula: see text]-joint complementary frame) is unique up to equivalence ([Formula: see text]-joint equivalence). Also we illustrate that two equivalent Parseval frames for Krein spaces need not be [Formula: see text]-unitarily equivalent and that not every Parseval frame can be dilated to a [Formula: see text]-orthonormal basis for a larger Krein space, and derive a result on matrices of finite size as application.

Coupled Perturbed Approach to Dual Basis Sets for Molecules and Solids. II: Energy and Band Corrections for Periodic Systems.

When trying to reach convergence of quantum chemical calculations toward the complete basis set limit, crystalline solids generally prove to be more challenging than molecules. This is due both to the closer packing of atoms─hence, to linear dependencies─and to the problematic behavior of Ewald techniques used for dealing with the infinite character of Coulomb sums. Thus, a dual basis set approach is even more desirable for periodic systems than for molecules. In such an approach, the self-consistent procedure is implemented in a small basis set, and the effect of the enlargement of the basis set is estimated a posteriori. In this paper, we extend to crystalline solids our previous coupled perturbed dual basis set approach [J. Chem. Theory Comput. 2020, 16, 1, 340-353] in which the basis set enlargement is treated as a perturbation. Among the notable features of this approach are (i) the possibility of obtaining not only a correction to the energy but also to energy bands and electron density; (ii) the absence of a diagonalization step for the full Fock matrix in the large basis set; and (iii) the possibility of extrapolating low order perturbation energy corrections to infinite order. We also present here the first periodic implementation of the dual basis set method of Liang and Head-Gordon [J. Phys. Chem. A 2004, 108, 3206-3210]. The effectiveness of both approaches is, then, compared on a small, but representative, set of solids.

Some properties of generalized cluster algebras of geometric type

We study the lower bound algebras generated by the generalized projective cluster variables of acyclic generalized cluster algebras of geometric type. We prove that this lower bound algebra coincides with the corresponding generalized cluster algebra under the coprimality condition. As a corollary, we obtain the dual PBW bases of these generalized cluster algebras. Moreover, we show that if the standard monomials of a generalized cluster algebra of geometric type are linearly independent, then the directed graph associated to the initial generalized seed of this algebra does not have 3-cycles.

The Twilight of the Law of the Fairs: Inventing International Cooperation on Bankruptcies in Early Modern Europe (Lyon, 1660–1710)

Abstract Bankruptcy was a key institution in the development of markets in Europe. However, the territoriality of jurisdictions and legal systems made international insolvencies difficult to manage. In the middle of the seventeenth century, cities such as Lyon developed networks of cooperation by granting foreign merchants equal rights to local creditors on a reciprocal basis. However, courts were reluctant to give foreign authorities control over assets and creditors on their territory. The article examines how the Lyon commercial court changed its policy towards international insolvencies during the second half of the seventeenth century. Whereas equal treatment of foreign creditors was conditioned on the recognition of an extraterritorial jurisdiction in the medieval fairs system, it now depended on the reciprocity of the legal status granted to merchants abroad. This system of cooperation between equally sovereign courts prefigured in many ways the current situation of private international law in bankruptcy matters.

Metamorphoses of digital multi-subjectivity: the regulatives of soft governance vs a programmed society

The article is devoted to an urgent and controversial topic– the spontaneous formation of regulators for managing the behavior of subjects in the virtual world in the context of digital transformation and hybrid social space and the impact of these processes on the social order. The diversity of subjects (multi-subjects) is represented both by traditional subjects of society in the virtual space (representatives of government bodies, citizens and their associations included in digital communications), The diversity of subjects (multi-subjects ) is represented both by traditional subjects of society in the virtual space (representatives of government bodies, citizens and their associations included in digital communications), the transformed form virtual reality, that is the actor of virtual reality with a high level of anonymity; and by techno-subjects (products with built-in artificial intelligence algorithms (chatbots, neural networks, digital twins, etc.) showing some elements of subjectivity (the possibility of influencing the behavior of communication participants, the possession of technosubjects by a social body (according to V.Tikhonov). Soft governance is considered as a democratic style of subject-subject management through influencing culture, con-sciousness, behavior with the transfer of necessary powers to participants and the use of informal communication methods. The regulatives of programmed society have high risks of blatant manipulation by authorities or anonymous power contenders. The regulatives of Soft governance have a dual basis: the establishment of laws, rules and instructions for all types of subjects, regulations for coordinating the interests of partners in participatory interactions, the development of a resistant reaction to manipulative influences, technical and technological services in ecosystems and digital platforms. But soft governance regulatives have signs of a latent and manipulative nature also. It is concluded that it is necessary to include all these aspects in the problems of the scientific discipline "Sociology of Management".

Optimization of battery charging and discharging strategies in substation DC systems using the dual self-attention network-N-BEATS model.

With the rapid pace of urbanization and industrialization, the demand for electricity has surged, placing immense pressure on power management systems. Substation DC systems play a crucial role in managing these fluctuations to ensure a stable and reliable power supply. However, existing battery charging and discharging strategies often suffer from inefficiencies, which can negatively impact overall system performance and sustainability. In this study, we introduce a novel approach that leverages artificial intelligence and time series predictive analytics through the dual self-attention network-neural basis expansion analysis for time series (DSAN-N-BEATS) model. This model integrates the self-attention network with the neural basis expansion analysis for time series (N-BEATS) model to accurately capture time-series data and optimize battery management. Our experimental results demonstrate that the DSAN-N-BEATS model significantly enhances battery state prediction accuracy, achieving a 95.84% accuracy rate, and improves charging and discharging efficiency by 20% compared to traditional methods. These improvements contribute to the overall reliability and sustainability of power systems. This research provides innovative methods for optimizing battery strategies, supporting sustainable development in the power industry, and enhancing system stability and reliability.

Dual space-based fuzzy graphs and orthogonal basis clustering for unsupervised feature selection

Unsupervised feature selection (UFS) takes an important position because gaining the class labels is laborious or even impossible. In the domain of UFS, clustering is a major means to exploit label information. The existing methods either could not model a clear clustering structure or could not utilize the local structure of data. Consequently, a new clustering method in combination with graph learning is proposed in this work. Specifically, for clustering, orthogonal basis clustering is introduced, where orthogonal constraints are imposed on the cluster center matrix and the clustering matrix. The clustering indicator matrix is also imposed by a non-negative constraint. A clearer clustering structure and more independent clustering centers are obtained through these constraints. For local preservation, given that traditional graphs for keeping the local manifold are faced with the problem of imbalanced neighbors, the fuzzy graph is introduced to acquire a robust structure, which is applied to both data space and feature space. The topological structure in these spaces can be well maintained. For the choice of salient features, ℓ2,0-norm regularization is imposed on the projection matrix. The object function is solved alternately. Then, a feature selection algorithm is designed. Experiments are designed and performed on nine real-world data sets. The results attest to the effectiveness of the proposed algorithm compared with other relevant algorithms.

Theoretical study of the methylprolithospermate's pKa in aqueous solution

Protonation and deprotonation reactions play an important role in the biological processes. Such processes are fully thermodynamic and occur in complex media where functional groups are surrounded by other chemicals such as molecules, ions, water, etc. In this paper, the compound of interest is the methylprolithospermate (MPL) molecule, which was recently isolated from salvia yunnanensis CH Wright. The intended functional groups for deprotonation are -OH and -COOH. These are the potential groups depicted at four sites located in MPL. Three thermodynamic cycles were required for the estimation of MPL's pKa by the means of DFT at the levels of B3LYP and PW6B95 with the dual basis set 6–311++G(d,p)//6–31+G(d). Cycle 1 is the direct pKa calculation, Cycle 2 is also the direct pKa calculation with proton hydration, and Cycle 3, the proton exchange process with hydroxyl anion hydration. In these cycles, water molecules as, reagents as well as products, were held as monomers in one hand (monomer cycle approaches), and cluster on the other hand (cluster cycle approaches). The isodesmic scheme was used as benchmark method for pKa calculation and yielded: pKa1 = 3.6 ± 0.3, pKa2 = 6.6 ± 0.2, pKa3 = 9.3 ± 0.2, and pKa4 = 14.4. The inclusion of binding energies of MPL anions in the pKa calculation has improved the results. The best cycles depend on the level of waters and the level of acidity. The more the number of waters clustered to MPL anions, the more the deviation of pKa values.

On the Dual Basis of Projective Semimodules and Its Applications

On the Dual Basis of Projective Semimodules and Its Applications

Floquet nonadiabatic mixed quantum-classical dynamics in periodically driven solid systems.

In this paper, we introduce the Floquet mean-field dynamics and Floquet surface hopping approaches to study the nonadiabatic dynamics in periodically driven solid systems. We demonstrate that these two approaches can be formulated in both real and reciprocal spaces. Using the two approaches, we are able to simulate the interaction between electronic carriers and phonons under periodic drivings, such as strong light-matter interactions. Employing the Holstein and Peierls models, we show that strong light-matter interactions can effectively modulate the dynamics of electronic population and mobility. Notably, our study demonstrates the feasibility and effectiveness of modeling low-momentum carriers' interactions with phonons using a truncated reciprocal space basis, an approach impractical in real space frameworks. Moreover, we reveal that even with a significant truncation, carrier populations derived from surface hopping maintain greater accuracy compared to those obtained via mean-field dynamics. These results underscore the potential of our proposed methods in advancing the understanding of carrier-phonon interactions in various periodically driven materials.

Nonuniform Sampling in Lp-Subspaces Associated with the Multi-Dimensional Special Affine Fourier Transform

In this paper, the sampling and reconstruction problems in function subspaces of Lp(Rn) associated with the multi-dimensional special affine Fourier transform (SAFT) are discussed. First, we give the definition of the multi-dimensional SAFT and study its properties including the Parseval’s relation, the canonical convolution theorems and the chirp-modulation periodicity. Then, a kind of function spaces are defined by the canonical convolution in the multi-dimensional SAFT domain, the existence and the properties of the dual basis functions are demonstrated, and the Lp-stability of the basis functions is established. Finally, based on the nonuniform samples taken on a dense set, we propose an iterative reconstruction algorithm with exponential convergence to recover the signals in a Lp-subspace associated with the multi-dimensional SAFT, and the validity of the algorithm is demonstrated via simulations.

GREEN EDUCATION IN THE CONTEXT OF ECOSYSTEM SERVICES

Ecosystem services are considered on the basis of reciprocity. On the one hand, nature provides its services to society, on the other hand, society undertakes to mutually take measures to ensure sustainable development. In this regard, the role of green education in the context of providing ecosystem services is highlighted, when the beneficiaries not only seek to effectively use the benefits of nature, but also acquire the ability to prevent damage to ecosystems as much as possible. The article substantiates the expediency of using a transdisciplinary educational aproach in the context of ecosystem services, whereby the end results of green education are not only the ability to apply environmentally friendly behavioral norms, but also the creative skills, that contribute to sustainable development.

Numerical analysis of a history-dependent mixed hemivariational-variational inequality in contact problems

This paper is devoted to a study of a history-dependent mixed hemivariational-variational inequality arising in contact mechanics. The contact problem concerns the deformation of a viscoelastic body with long memory, subject to a general friction law on one part of the boundary and a frictionless Signorini condition on another part of the boundary. The solution existence and uniqueness of the history-dependent mixed hemivariational-variational inequality based on a Lagrange multiplier approach are proved. Then, a fully discrete scheme is introduced and studied. The trapezoidal rule is used to approximate the integral in the history-dependent operator. For the spatial discretization, the linear finite elements are used to discretize the displacement field, and dual basis functions are used in the approximation of the Lagrange multiplier. Optimal order error estimates are derived for the displacement and the Lagrange multiplier under appropriate solution regularity assumptions. Numerical results are presented to illustrate the theoretical prediction of the convergence orders.

The dual-process approach to human sociality: Meta-analytic evidence for a theory of internalized heuristics for self-preservation.

[Correction Notice: An Erratum for this article was reported in Vol 126(5) of Journal of Personality and Social Psychology (see record 2025-05381-001). The last entry in the Roch et al. (2000) row in Table 3 should appear instead as load decreases taking. All versions of this article have been corrected.] Which social decisions are influenced by intuitive processes? Which by deliberative processes? The dual-process approach to human sociality has emerged in the last decades as a vibrant and exciting area of research. Yet a perspective that integrates empirical and theoretical work is lacking. This review and meta-analysis synthesizes the existing literature on the cognitive basis of cooperation, altruism, truth telling, positive and negative reciprocity, and deontology and develops a framework that organizes the experimental regularities. The meta-analytic results suggest that intuition favors a set of heuristics that are related to the instinct for self-preservation: people avoid being harmed, avoid harming others (especially when there is a risk of harm to themselves), and are averse to disadvantageous inequalities. Finally, this article highlights some key research questions to further advance our understanding of the cognitive foundations of human sociality. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Ethnoecological perspectives on environmental stewardship: Tenets and basis of reciprocity in Gitxsan and nłeʔkepmx (Nlaka'pamux) Territories

Abstract Local and Indigenous Peoples steward and protect a significant proportion of biologically diverse ecosystems globally. This fact is increasingly acknowledged by researchers and international organizations, offering both opportunities and challenges at the intersection of Indigenous and western knowledge production in the context of environmental management research and policy. Drawing on half a century of ethnoecological research and personal experiences in Gitxsan and nłeʔkepmx Territories in the Pacific Northwest of North America, this research considers the role of reciprocity as an inherent philosophy and tenet for successful environmental stewardship. Reciprocity is a legal responsibility and moral perspective that foregrounds many Indigenous worldviews. Such cultural drivers and obligations towards lands and biota appear to be unknown, marginalized or instrumentalized in mainstream and western science and policy. We conclude that fundamental elements of reciprocity may not be adequately blended or braided into western environmental management frameworks. As such, alternatives to blending include acknowledging sole proprietary and self‐determining rights for Indigenous Peoples to govern and steward lands outside of western infrastructures and value systems. This study raises critical questions about the feasibility of reconciling reciprocity with western environmental management practices and regulations. It explores the implications for Indigenous rights and sovereignty, and climate change mitigation. By addressing these complex issues, we contribute to ongoing discourse on the integration of Indigenous and western knowledge in environmental stewardship research, and the ethical, historical and cultural challenges that come with it. Read the free Plain Language Summary for this article on the Journal blog.

외국 소재의 전자적 증거 수집 방식과 증거능력 부여 방안에 관한 연구

In order for investigative agencies to acquire electronic evidence located in a foreign country, mutual legal assistance based on the International Criminal Justice Mutual Aid Act and Interpol Collaboration are used. In some investigations, legally obtained user account information is used to access overseas servers. The international community has already implemented the European Convention on Cybercrimey, which enables prompt preservation, provision, and submission of digital information for ISPs located in each jurisdiction through cooperation between the central authorities, so orders are also issued to ISPs under direct foreign jurisdiction. The system is being improved in such a way that this way is possible, and the same procedure is reflected in the administrative agreement based on the CLOUD Act and the European Electronic Evidence Regulation. However, Korea has not signed such a treaty or agreement.
 For foreign electronic evidence collected using these means, there is a possibility that the collection procedure of the requested country may violate the domestic law of the requesting country due to the different procedural laws between each country. In such a case, whether the content or degree of the violation violated the actual content of due process and whether the exclusion of evidence is in accordance with the constitutional idea and the criminal procedure law procedure for the realization of criminal justice can be judged individually. However, it is not reasonable to deny the admissibility of evidence based on a simple violation of the procedure on the basis of trust or reciprocity among judicial institutions in the international community.
 On the other hand, non-statement digital evidence is not the truth of the content, but the existence of textual information of the same content itself as evidence. Therefore, it is reasonable to regard such evidence as evidence and not to apply the hearsay rule. Even declarative digital evidence can correspond to business records, and it is possible to confirm and verify the circumstantial guarantee of trustworthiness from foreign institutions in the future. In the end, even for electronic evidence collected in foreign countries through cooperation or cooperation in investigations, it seems necessary to establish a separate exception to the recognition of Probative Force.

Poincaré duality for smooth Poisson algebras and BV structure on Poisson cohomology

Similar to the modular vector fields in Poisson geometry, modular derivations are defined for smooth Poisson algebras with trivial canonical bundle. By twisting Poisson module with the modular derivation, the Poisson cochain complex with values in any Poisson module is proved to be isomorphic to the Poisson chain complex with values in the corresponding twisted Poisson module. Then a version of twisted Poincaré duality is proved between the Poisson homologies and cohomologies. Furthermore, a notion of pseudo-unimodular Poisson structure is defined. It is proved that the Poisson cohomology as a Gerstenhaber algebra admits a Batalin-Vilkovisky operator inherited from some one of its Poisson cochain complex if and only if the Poisson structure is pseudo-unimodular. This generalizes the geometric version due to P. Xu. The modular derivation and Batalin-Vilkovisky operator are also described by using the dual basis of the Kähler differential module.

The Zonotopal Algebra of the Broken Wheel Graph and its Generalization

The machinery of zonotopal algebra is linked with two particular polytopes: the Stanley-Pitman polytope and the regular simplex $\mathfrak{Sim}_n(t_1,...,t_n)$ with parameters $t_1,...,t_n\in \mathbb{R}_+^n$, defined by the inequalities $\sum_{i=1}^n r_i\leq \sum_{i=1}^n t_i, \mbox{ } r_i\in \mathbb{R}_+^n,$ where the $(r_i)_{i\in [n]}$ are variables. Specifically, we will discuss the central Dahmen-Micchelli space of the broken wheel graph $BW_n$ and its dual, the $\mathcal{P}$-central space. We will observe that the $\mathcal{P}$-central space of $BW_n$ is monomial, with a basis given by the $BW_n$-parking functions. We will show that the volume polynomial of the the Stanley-Pitman polytope lies in the central Dahmen-Micchelli space of $BW_n$ and is precisely the polynomial in a particular basis of the central Dahmen-Micchelli space which corresponds to the monomial $t_1t_2\cdots t_n$ in the dual monomial basis of the $\mathcal{P}$-central space. We will then define the generalized broken wheel graph $GBW_n(T)$ for a given rooted tree $T$ on $n$ vertices. For every such tree, we can construct $2^{n-1}$ directed graphs, which we will refer to as generalized broken wheel graphs. Each generalized broken wheel graph constructed from $T$ will give us a polytope, its volume polynomial, and a reference monomial. The $2^{n-1}$ polytopes together give a polyhedral subdivision of $\mathfrak{Sim}_n(t_1,...,t_n)$, their volume polynomials together give a basis for the subspace of homogeneous polynomials of degree $n$ of the corresponding central Dahmen-Micchelli space, and their reference monomials together give a basis for its dual.

Service contract type and consumer choice behavior: the contributory roles of perceived value, brand reputation and consumer incentives

PurposeTo minimize customer churn, many service providers offer consumers the option of automatic contract renewal at the end of a contract period. Such agreements are known as rollover service contracts (RSCs). This research quantifies the effect of RSCs and other related factors, such as incentives, on consumers' service choice decisions.Design/methodology/approachThe study adopts choice-based conjoint analysis to assess the effect of RSCs on consumers' choices and to determine whether effect size varies when selecting a cell phone network or gym/leisure club provider, which represent lower-priced utilitarian and higher-priced hedonic services.FindingsIt was found that RSCs produce negative perceptions and intended behaviors for the majority of consumers across different product types. Nevertheless, as explained by social exchange theory, many individuals may be persuaded to enter into a RSC on the basis of reciprocity if they are offered an incentive such as a price discount or free product add-on.Originality/valueIn the marketing domain, this is the first comprehensive study to quantify the role of contract type among a range of other factors in consumers' decision-making when selecting a service. The authors' results offer context-specific implications for service marketers. First, RSCs are perceived more negatively in high-priced hedonistic categories, especially among those with lower incomes. Second, price discounts are more effective than product add-ons for motivating hedonic purchases, while product add-ons work better with utilitarian services.

Jakutijos medžiotojų bei elnių augintojų ir plėšrūnų keršto santykiai taigoje

This article considers the notion of revenge as an agency of wolves, bears and the master-spirits in the animistic worldview of indigenous Eveny and Sakha hunters and the reindeer herders of the Eveno-Bytantaiskii and Tomponskii ulusy (districts) of North Yakutia. Predators are perceived by hunters and herders as conscious non-human beings that can enter into relations with humans on a reciprocal basis. The possibility that predators may carry out revenge on people can be perceived as showing that there are similarities between humans and non-human predators. This article shows how the notions of reciprocity, similarity and relational symmetry between people and predators are reflected in the narratives and hunting rituals of indigenous hunters and herders. As comparative examples, the blood feud customs that earlier existed among the Tungus, Sakha people and Chukchee clans are also considered here. Although these customs no longer exist in the contemporary societies of the indigenous people of Yakutia, the notions underlying them very much reflect the human-predator relations on the taiga today.