Projective Dimension Research Articles

Investigation of the Dimension of the Spectral Projection of a Self-Adjoint Second-Order Quasidifferential Operator

Investigation of the Dimension of the Spectral Projection of a Self-Adjoint Second-Order Quasidifferential Operator

Asymptotic behavior of homological invariants of localizations of modules

Let R be a commutative noetherian ring, I an ideal of R, and M a finitely generated R-module. We consider the asymptotic injective dimensions, projective dimensions, Bass numbers, and Betti numbers of localizations of M/InM at prime ideals of R and prove that these invariants are stable or have polynomial growth for large integers n that do not depend on the prime ideals.

Quasi-pure resolutions and some lower bounds of Hilbert coefficients of Cohen-Macaulay modules

Let (A,m) be a Noetherian local ring and let M be a finitely generated Cohen Macaulay A module. Let G(A)=⨁n≥0mn/mn+1 be the associated graded ring of A and G(M)=⨁n≥0mnM/mn+1M be the associated graded module of M. If A is regular and if G(M) has a quasi-pure resolution then we show that G(M) is Cohen-Macaulay. If A is Gorenstein and G(A) is Cohen-Macaulay and if M has finite projective dimension then we give lower bounds on e0(M) and e1(M). Finally let A=Q/(f1,…,fc) be a strict complete intersection with ord(fi)=s for all i, where Q is a regular local ring. Let M be an Cohen-Macaulay module with complexity cxA(M)=r<c. We give lower bounds on e0(M) and e1(M).

A Novel Unsupervised Domain Adaptation Transformation Reconstructed Gru Framework Considering Prediction Uncertainty for Machinery Prognostics Under Variable Lubrication Conditions

Abstract As critical components in industrial application scenarios, high-precision and high-confidence health assessment of rolling bearings attract more and more attention. Currently, predictive maintenance obtains outstanding achievements under the same object and working conditions. However, evaluation performances under variable working conditions and different specifications still need to be improved. This study zeroes in on the cross-domain prognostics of rotating machinery under oil and grease lubrication conditions. It proposes an unsupervised domain adaptation transform reconstruction GRU (UDATrGRU) prognostics framework, which captures the common degradation characteristics under different lubrication conditions through the designed second-order statistical quantity, facilitating the following high-precision predictions. To be specific, the vibration degradation features are first extracted through signal preprocessing and then input into UDATrGRU. The developed domain adaptation layer calculates high dimensional projections between diverse data sets, and then corresponding degradation features are statistically aligned under the pressure of the designed quantity. Subsequently, time series modeling and Bootstrap-based uncertainty estimations are carried out. Finally, life-cycle accelerated tests of the rolling bearing from PRONOSITA and ABLT-1A cross-validate the feasibility ' effectiveness of the proposed machinery prognostics framework. The results are pretty promising: compared to existing methods, our UDATrGRU framework has achieved an improvement of at least 5.65% in R2 and a reduction of at least 21.5% in RMSE.

Adolescents on the move: the application of an integrated model for documentation and evaluation of “Back Into The Wild” adventure education project aimed at promoting psychophysical and relational well-being

ABSTRACT This paper presents a new integrated model for documentation and evaluation tested in 2021 on Back Into the Wild project, an Adventure Education project by Equilibero Association (Padova-Treviso, Italy). The project proposes educational walks to groups of at-risk adolescents to promote their psychophysical and relational well-being. Due to the paucity of evaluation methods focused on grasping the process dimension of nature-based projects, the research team (CEFEO Research Centre, University of Bologna) chose to construct a new model of documentation and evaluation through a participatory bottom-up process involving practitioners. In addition to outlining the main characteristics of Adventure Education in socio-educational projects in Italy and the peculiarities of BIW project, this paper describes the co-constructed integrated documentation and evaluation model in detail. The first application highlighted the usefulness of the multi-perspective view provided by this tool, allowing for a reflection on how the adventurous project impacted on participants’ psychophysical and relational well-being.

Sustaining foreign aid initiatives in the field of media and information literacy within the central asian context

In the ever-evolving landscape of global media and information dissemination, the need for literacy and critical understanding has become increasingly paramount. Central Asia, with its unique cultural tapestry and geopolitical challenges, stands as a region ripe for intervention in the realm of media and information literacy (MIL). This research paper examines the endeavours to attain sustainability in international MIL projects within the distinctive context of Central Asia. Through a multi-faceted approach incorporating in-depth interviews with prominent media trainers and MIL experts and research works from Central Asian scholars, the study offers a comprehensive exploration of the sustainability landscape in the region. This study delves into the challenges and strategies associated with sustaining MIL initiatives, shedding light on the intricacies of fostering MIL in Central Asia. Findings highlight the importance of local partnerships, contextualization of interventions, resource allocation, technology integration, and policy advocacy in promoting sustainable MIL practices. Through a comprehensive review of existing literature, policy documents, and empirical data, this paper sheds light on the various dimensions of foreign aid projects in MIL. The paper provides valuable guidance for policymakers, practitioners, and stakeholders involved in advancing MIL efforts in Central Asia and beyond.

The finite type of modules of bounded projective dimension and Serre's conditions

AbstractLet be a commutative Noetherian ring. For a natural number , we prove that the class of modules of projective dimension bounded by is of finite type if and only if satisfies Serre's condition . In particular, this answers positively a question of Bazzoni and Herbera in the specific setting of a Gorenstein ring. Applying similar techniques, we also show that the ‐dimensional version of the Govorov–Lazard theorem holds if and only if satisfies the ‘almost’ Serre condition .

On $G$-$(n,d)$-rings and $n$-coherent rings

Let $n$ and $d$ be non-negative integers. We introduce the concept of $strongly$ $(n,d)$-$injective$ modules to characterize $n$-coherent rings. For a right perfect ring $R$, it is shown that $R$ is right $n$-coherent if and only if every right $R$-module has a strongly $(n,d)$-injective (pre)cover for some non-negative integer $d \leq n$. We also provide equivalent conditions for an $(n,d)$-ring being $n$-coherent. Then we investigate the so-called $right$ $G$-$(n,d)$-$rings$, over which every $n$-presented right module has Gorenstein projective dimension at most $d$. Finally, we prove a Gorenstein analogue of Costa's first conjecture.

Off-diagonal elements of projection matrices and dimension asymptotics

We provide insights on asymptotic behavior of the off-diagonal elements of projection matrices in settings, where the dimension of underlying vectors grows with the sample size. Under designs favorable to application of the random matrix theory, the off-diagonal elements are asymptotically normal with a simple variance expression. We also discuss the robustness of the result to deviations of the design from the ideal setup.

Spaces of Architectural Overcoming

This paper reflects an interest in how interior and landscape sites are connectedin their capacity to exceed or ‘overcome’ architecture and practice conventions of designing, making and use. In professional architectural practice, these conventions are generally treated as distinct and hierarchical steps. This reflects a view of life that is ordered, controlled and deterministic. Referring to ideas that affirm the unpredictable and evolutionary nature of life, I argue for more experimental, improvised spatial practices. I have drawn from Elizabeth Grosz’s writings about space and time to show how we can use change and spontaneous making in everyday life as designing. This has helped me to question how spaces are produced, and the singular design ‘authority’ of the architect or building designer. I have found that working in interior and landscape sites provides more opportunities for unplanned construction connected to the lives of those who inhabit space: opening up architecture and architectural practice to unpredictable forces repressed in professional practice. This paper, part of my doctoral research, explores the conceptual and practical dimensions of experimental interior projects.

Regular variation in Hilbert spaces and principal component analysis for functional extremes

Motivated by the increasing availability of data of functional nature, we develop a general probabilistic and statistical framework for extremes of regularly varying random elements X in L2[0,1]. We place ourselves in a Peaks-Over-Threshold framework where a functional extreme is defined as an observation X whose L2-norm ‖X‖ is comparatively large. Our goal is to propose a dimension reduction framework resulting into finite dimensional projections for such extreme observations. Our contribution is double. First, we investigate the notion of Regular Variation for random quantities valued in a general separable Hilbert space, for which we propose a novel concrete characterization involving solely stochastic convergence of real-valued random variables. Second, we propose a notion of functional Principal Component Analysis (PCA) accounting for the principal ‘directions’ of functional extremes. We investigate the statistical properties of the empirical covariance operator of the angular component of extreme functions, by upper-bounding the Hilbert–Schmidt norm of the estimation error for finite sample sizes. Numerical experiments with simulated and real data illustrate this work.

DETERMINANTS OF THE DIMENSIONS OF FINANCING FOR INVESTMENT PROJECTS TO CREATE JOBS DURING THE PERIOD 2002-2013: A QUANTITATIVE STUDY OF THE NATIONAL AGENCY FOR INVESTMENT DEVELOPMENT IN ALGERIA

The study aims to fix the determinants of the financing dimensions of investment projects completed during the period 2002-2013. The purpose of undertaking these investment projects is to reduce unemployment and create new jobs. The study is purely quantitative after a complete database was obtained for each of the 48 states of Algeria, according to the administrative division in that period, from the National Agency for Investment Development (NAID) in Algeria. The determinants of the dimensions of financing for investment projects were obtained after we used the statistical technique of multiple linear regression analysis. From the perspective of the objective database, the methodology used to analyze the data, and complete transparency in dealing with the research process, we can confirm that the research results are honest and reliable, and the results can be generalized and a strategy for promoting investment in Algeria can be drawn up on a correct basis.

Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one

Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one

Un singe compatissant

&lt;p&gt;Through a cross-reading of the fictional epistle Lettre d’un singe aux êtres de son espèce, and the utopia La Découverte australe par un homme volant, this article aims to highlight the originality of the conception of animality expressed by the polygraph Nicolas-Edme Restif de La Bretonne (1734-1806). Indeed, Restif is able in these writings, thanks to an imaginative representation of animality, to go beyond the simple criticism of anthropocentrism, to insert animal literature at the centre of the process of ‘invention’ of the rights of man and woman typical of the Enlightenment. Restif’s pamphlet is indeed focused – from a philosophical point of view – on the imaginative and projective dimension of compassion, mobilised by fiction, which allows the subject to go beyond his usual picture of life, until authentically sympathising with all possible forms of otherness, embodied by the non-human animal – the monkey – and by the half-breed, i.e. the man-beast.&lt;/p&gt;

Additive and geometric transversality of fractal sets in the integers

AbstractBy juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we introduce and study — in the discrete context of the integers — analogs of some of the notions and results surrounding Furstenberg's work. In particular, we define a new class of fractal sets of integers that parallels the notion of ‐invariant sets on the 1‐torus and investigate the additive and geometric independence between two such fractal sets when they are structured with respect to multiplicatively independent bases. Our main results in this direction parallel the works of Furstenberg, Hochman–Shmerkin, Shmerkin, Wu, and Lindenstrauss–Meiri–Peres and include: a classification of all subsets of the positive integers that are simultaneously ‐ and ‐invariant; integer analogs of two of Furstenberg's transversality conjectures pertaining to the dimensions of the intersection and the sumset of ‐ and ‐invariant sets and when and are multiplicatively independent; and a description of the dimension of iterated sumsets for any ‐invariant set . We achieve these results by combining ideas from fractal geometry and ergodic theory to build a bridge between the continuous and discrete regimes. For the transversality results, we rely heavily on quantitative bounds on the ‐dimensions of projections of restricted digit Cantor measures obtained recently by Shmerkin. We end by outlining a number of open questions and directions regarding fractal subsets of the integers.

The Geopolitics of Global Infrastructure Projects: Challenges and Opportunities for Health and Wellbeing

Abstract Global infrastructure projects have emerged as pivotal instruments in shaping economic growth and geopolitical dynamics in the contemporary world. Infrastructure, traditionally associated with physical structures like roads, bridges and utilities, now extends to include services vital for societal standards and economic progress. This evolution reflects a broader recognition of infrastructure’s role in fostering development, with distinctions drawn between physical infrastructure such as transport and energy networks, and services-oriented infrastructures encompassing health and education. Scholarly discourse on the correlation between infrastructure development and economic growth varies significantly. While some researchers assert a positive relationship, citing infrastructure’s stimulative effects on economies, others argue that this link is not universally conclusive, highlighting nuances in variables and methodologies used in studies. Nevertheless, the consensus underscores the critical role of infrastructure in enhancing economic activities, particularly in developing countries where the infrastructure gap remains stark. Central to contemporary infrastructure dynamics is China’s Belt and Road Initiative (BRI), a global development policy launched in 2013 aimed at enhancing connectivity and economic integration across Asia, Europe and beyond. The USA and its allies have also initiated the Partnership for Global Infrastructure and Investment (PGII), to promote sustainable infrastructure development aligned with Western values and global governance standards. As these global powers focus on infrastructure development, the implications for health and well-being emerge as critical considerations. Infrastructure projects not only promise economic benefits but also present opportunities to address public health challenges, enhance connectivity and promote sustainable development goals. However, they also pose challenges such as environmental impact, debt sustainability and geopolitical tensions, underscoring the complex interplay between infrastructure development, global governance and human welfare. This paper explores the multifaceted dimensions of global infrastructure projects, examining their implications for health and well-being amidst evolving geopolitical competition. By analyzing key initiatives like BRI and PGII, it aims to provide insights into how infrastructure investments can be leveraged to foster equitable socio-economic development while navigating the challenges posed by climate change, governance issues and geopolitical rivalries. Understanding these dynamics is crucial for harnessing the transformative potential of global infrastructure projects to promote health and well-being on a global scale.

State Dependent Delay Maps: Numerical Algorithms and Dynamics of Projections

This work concerns the dynamics of a certain class of delay differential equations (DDEs) which we refer to as state dependent delay maps. These maps are generated by delay differential equations where the derivative of the current state depends only on delayed variables, and not on the un-delayed state. However, we allow that the delay is itself a function of the state variable. A delay map with constant delays can be rewritten explicitly as a discrete time dynamical system on an appropriate function space, and a delay map with small state dependent terms can be viewed as a “non-autonomous” perturbation. We develop a fixed point formulation for the Cauchy problem of such perturbations, and under appropriate assumptions obtain the existence of forward iterates of the map. The proof is constructive and leads to numerical procedures which we implement for illustrative examples, including the cubic Ikeda and Mackey-Glass systems with constant and state-dependent delays. After proving a local convergence result for the method, we study more qualitative/global convergence issues using data analytic tools for time series analysis (dimension and topological measures derived from persistent homology). Using these tools we quantify the convergence of the dynamics in the finite dimensional projections to the dynamics of the infinite dimensional system.

INTEGRATION OF AN URBAN TRANSPORTATION SYSTEM AS AN ELEMENT OF MOBILITY PLANS

In today’s urban mobility scene, the increasing number of private cars trying to travel through the city centers is one of the most onerous problems facing urban transport. Knowing about the impact that different transport demand management models can have on the efficiency of the urban transport system may be of key importance for developing solutions in this area. This knowledge is the main goal of the considerations undertaken. The observations presented in this article took place during the formation of a Sustainable Urban Mobility Plan (SUMP) for the Bielsko-Biała agglomeration. The author of the article is a member of the working group that prepared the SUMP project for the city. The study examined the effectiveness of mobility planning activities. The scope of these activities included collecting the data necessary to create a mobility plan, analyzing this data, building scenarios in the area of transport demand management, and designing the assessment of the adopted solutions. The article shows the procedure for creating a model of a SUMP for urban areas, which may be a prerequisite for municipal governments for effective applications for funding projects related to transport. The most important part of the analysis is the evaluation using integration indicators of selected key elements of the urban transport system of the Bielsko-Biała agglomeration in the area of transfer accessibility. Such research allows us to answer the question of whether the locations of new railway stops proposed under the agglomeration SUMP contribute to increasing the integration of the urban transport system. The current research implements one of the dimensions of mobility management projects. Related goals are, among other things, to achieve more effective integration of the urban transport system. The analyses were carried out by measuring selected properties of the transport network and a survey questionnaire.

Finite dimensional approximation to fractional stochastic integro-differential equations with non-instantaneous impulses

This manuscript proposes a class of fractional stochastic integro-differential equations (FSIDEs) with non-instantaneous impulses in an arbitrary separable Hilbert space. We use a projection scheme of increasing sequence of finite dimensional subspaces and projection operators to define approximations. In order to demonstrate the existence and convergence of approximate solutions, we utilize stochastic analysis theory, fractional calculus, theory of fractional cosine family of linear operators, and fixed point approach. Furthermore, we examine the convergence of the Faedo–Galerkin (F–G) approximate solutions to the mild solution of our given problem. Finally, a concrete example involving a partial differential equation is provided to validate the main abstract results.

Higher resonance schemes and Koszul modules of simplicial complexes

Each connected graded, graded-commutative algebra A of finite type over a field k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Bbbk $$\\end{document} of characteristic zero defines a complex of finitely generated, graded modules over a symmetric algebra, whose homology graded modules are called the (higher) Koszul modules of A. In this note, we investigate the geometry of the support loci of these modules, called the resonance schemes of the algebra. When A=k⟨Δ⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A=\\Bbbk \\langle \\Delta \\rangle $$\\end{document} is the exterior Stanley–Reisner algebra associated to a finite simplicial complex Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta $$\\end{document}, we show that the resonance schemes are reduced. We also compute the Hilbert series of the Koszul modules and give bounds on the regularity and projective dimension of these graded modules. This leads to a relationship between resonance and Hilbert series that generalizes a known formula for the Chen ranks of a right-angled Artin group.