Projective Dimension Research Articles

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

<p>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.</p>

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.

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

AbstractEach connected graded, graded-commutative algebra A of finite type over a field $$\Bbbk $$ k 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 $$A=\Bbbk \langle \Delta \rangle $$ A = k ⟨ Δ ⟩ is the exterior Stanley–Reisner algebra associated to a finite simplicial complex $$\Delta $$ Δ , 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.

Bounds on cohomological support varieties

Over a local ring R R , the theory of cohomological support varieties attaches to any bounded complex M M of finitely generated R R -modules an algebraic variety V R ( M ) {\mathrm {V}}_R(M) that encodes homological properties of M M . We give lower bounds for the dimension of V R ( M ) {\mathrm {V}}_R(M) in terms of classical invariants of R R . In particular, when R R is Cohen–Macaulay and not complete intersection we find that there are always varieties that cannot be realized as the cohomological support of any complex. When M M has finite projective dimension, we also give an upper bound for dim ⁡ V R ( M ) \dim {\mathrm {V}}_R(M) in terms of the dimension of the radical of the homotopy Lie algebra of R R . This leads to an improvement of a bound due to Avramov, Buchweitz, Iyengar, and Miller on the Loewy lengths of finite free complexes, and it recovers a result of Avramov and Halperin on the homotopy Lie algebra of R R . Finally, we completely classify the varieties that can occur as the cohomological support of a complex over a Golod ring.

Analysis of the chemical diffusion master equation for creation and mutual annihilation reactions

We propose an infinite dimensional generating function method for finding the analytical solution of the so-called chemical diffusion master equation (CDME) for creation and mutual annihilation chemical reactions. CDMEs model by means of an infinite system of coupled Fokker–Planck equations the probabilistic evolution of chemical reaction kinetics associated with spatial diffusion of individual particles; here, we focus an creation and mutual annihilation chemical reactions combined with Brownian diffusion of the single particles. Using our method we are able to link certain finite dimensional projections of the solution of the CDME to the solution of a single linear fourth order partial differential equation containing as many variables as the dimension of the aforementioned projection space. Our technique extends the one presented in Lanconelli [J. Math. Anal. Appl. 526, 127352 (2023)] and Lanconelli et al. [arXiv:2302.10700 [math.PR] (2023)] which allowed for an explicit representation for the solution of birth-death type CDMEs.

Seeing Santurbán through ISDS: A sociolegal case study of Eco Oro v. Colombia

Abstract This article aims to enrich the emerging, multi-coloured tapestry of ‘international law in context’ through a study of how international economic law operates in complex investment-related disputes. Focusing on the Eco Oro v. Colombia investor-state arbitration, and drawing on both doctrinal analysis and sociolegal research, the study investigates how different actors make sense of the issues, of the dispute, and of the law. Besides shedding light on the neglected multi-actor, multi-layered dimensions of investment disputes, and on tensions between often incommensurable values, juxtaposing arbitral proceedings and underlying social realities highlights how investor-state arbitration involves a socio-political process of re-presenting actors, territory, the environment, and livelihoods through the prism of international arrangements that are primarily designed to protect foreign investment. The findings provide policy pointers on the need for systemic reform of international investment law, moving away from the predominant emphasis on investment protection and investor-state dispute settlement, towards a governance model that effectively considers the social, political, and environmental dimensions of foreign investment projects.

Barile–Macchia resolutions

We construct cellular resolutions for monomial ideals via discrete Morse theory. In particular, we develop an algorithm to create homogeneous acyclic matchings and we call the cellular resolutions induced from these matchings Barile–Macchia resolutions. These resolutions are minimal for edge ideals of weighted oriented forests and (most) cycles. As a result, we provide recursive formulas for graded Betti numbers and projective dimension. Furthermore, we compare Barile–Macchia resolutions to those created by Batzies and Welker and some well-known simplicial resolutions. Under certain assumptions, whenever the above resolutions are minimal, so are Barile–Macchia resolutions.

Ext modules related to syzygies of the residue field

Let R be a commutative noetherian ring. In this paper, we find out close relationships between the module M being embedded in a module of projective dimension at most n and the (n+1)-torsionfreeness of the nth syzygy of M. As an application, when R is local with residue field k, we compute the dimensions as k-vector spaces of Ext modules related to syzygies of k.

Journey of medical device development from the bench to the bedside—four real-life examples of commercial biomaterials development

Translating biomaterials research into clinical products is a multidisciplinary yet rewarding journey. It should primarily aim to improve patient treatment and clinical outcomes by addressing unmet clinical needs. Four examples of commercial development of biomaterial implants illustrate the diversity of paths, starting from academic research work (AlchiMedics, TISSIUM, Cousin Surgery) or corporate initiatives to develop new products (Medtronic-Sofradim Production). They have been selected from the Translational Research session of the 2022 Conference of the European Society for Biomaterials (ESB) in Bordeaux (France). Commitment, agility, and perseverance were among the key common skills to successfully meet challenges, especially the most unexpected ones. All dimensions of translation projects must be integrated from the start, including the regulatory strategy.

Dilemmas of recognition and redistribution: Constituting intersectional subjects of inclusion in migrant support work

AbstractIn this study, I explore how the subject of inclusion is constituted as intersectional in the organizational discursive practices of a civil society organization promoting migrant and refugee inclusion. Drawing on Crenshaw's notion of political intersectionality and Fraser's politics of recognition and redistribution, I analyze the political dimension of an inclusion project by showing how intersectional categories are connected to differentiated struggles and strategies of inclusion. The ethnographic study illustrates how two subject positions are constituted as being underpinned by either the logic of recognition or redistribution. Moreover, the findings show how the two strategies interact, revealing the dynamics of privilege and disadvantage at play in the inclusion project. The paper contributes to critical studies on inclusion and intersectionality in organizational contexts by extending our understanding of power dynamics and tensions as integral parts of the intersectional approach.

Development of the Cost and Time Estimation Factors of the Project Dimension in the Agile Software

Development of the Cost and Time Estimation Factors of the Project Dimension in the Agile Software

Sincere silting modules and vanishing conditions

We study characterizations of sincere modules, sincere silting modules and tilting modules in terms of various vanishing conditions. Let R be a perfect ring and T be an R-module. It is proved that T is sincere silting if and only if T is presilting satisfing the vanishing condition KerExt R 0 ≤ i ≤ 1 ( T , − ) = 0 , and that T is tilting if and only if KerExt R 0 ⩽ i ⩽ 1 ( T , − ) = 0 and Gen T ⊆ KerExt R 1 ⩽ i ⩽ 2 ( T , − ) . As an application, we prove that a sincere silting R-module T of finite projective dimension is tilting if and only if Ext R i ( T , T ( J ) ) = 0 for all sets J and all integer i ≥ 1 . This not only extends a main result of Zhang’s paper [Self-orthogonal τ-tilting modules and tilting modules, J Pure Appl Algebra, 2022, 226: 106860] from finitely generated modules over Artin algebras to infinitely generated modules over more general rings, but also gives it a different proof without using Auslander-Reiten translations.

Die Bauaussteckung als landestypische Eigenheit

The use of construction scopes in building permit procedures is a Swiss peculiarity and serves both as a means of publicity and to illustrate the dimensions of a construction project. However, whether or not construction scopes can also be useful in other countries depends on the legal system and a cost-benefit analysis.

On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane

On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane

Dual Discriminative Low-Rank Projection Learning for Robust Image Classification

Numerous methods have exploited projection learning to extract low-dimensional features for image classification. Some projection learning methods integrate low-rank matrix recovery into classification models to equip the projection subspace with discrimination and robustness against corruption. However, these methods cannot directly recover “clean” components from the new datum in a low-dimensional subspace. Additionally, they are sensitive to the selection of projection dimensions. To overcome these shortcomings, we propose a dual discriminative low-rank projection learning framework for robust image classification. Specifically, the proposed method learns a low-rank projection and a semi-orthogonal projection to recover “clean” components from the original data and simultaneously obtain a low-dimensional subspace. Thereafter, to preserve discriminative information in the low-dimensional subspace, an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> -norm term is constructed by concentrating the projected intra-class samples around their adaptive class centroids. Regression-based terms are appended using the low-dimensional features extracted from the recovered clean data and the class centroids for more accurate classification. Experiments on five public databases with various corruptions demonstrate that the proposed method can robustly classify image data despite a small training sample sizes and gross corruption. The superiority of the proposed method is further verified on the large-scale PubFig83 database, on which it achieves an 87.58% classification accuracy.