81 research outputs found
Duration, lawful termination and frustration of the Employment Contract
No full textThis chapter emphasises the pivotal role that the common law rules on the implied duration and the termination of the contract of employment play in defining the essence and nature of that institution. The claim is made that the implied common law rule treating the employment contract as indeterminate in duration provides explanatory force for the rules on classification, suspension and termination of the employment contract. Turning to the common law of termination, the chapter explains how key House of Lords and Supreme Court authorities such as Johnson, Eastwood, and Edwards do not preclude the addition of ‘just cause’ requirements to the unrestricted reasonable notice rule as a means of furnishing protection to employees falling outside the coverage of the statutory unfair dismissal regime. The chapter moves on to address other common law rules in play in respect of the termination of the employment contract, e.g. those applying in the context of termination by the employer making a payment in lieu of notice, summary dismissal by the employer, resignation and retirement by the employee and the expiry and non-renewal of a fixed-term employment contract. Reforms of these rules are suggested that pursue an ‘integrationist agenda’, i.e. an approach that is designed to gradually assimilate the common law rules with those applicable for the purposes of the unfair dismissal legislation. Proposals for a similar alignment of the common law rules of frustration with the interpretation of that conception for statutory purposes are also made. The chapter ends by exploring how the suggested reforms can be divided into those which promote substantive fairness on the one hand and those seeking to achieve procedural fairness on the other
A rule-based analysis and comparison of the case Studies
No full textDrawing on data derived from ten hypothetical case studies, we adopt a rule-based comparative evaluation of the company laws of twelve different jurisdictions. The ten case studies examine topics relating to directors’ duties and liabilities generally and in the context of takeovers, the protection of creditors, including the relationship between creditors and a company, and the law governing shares, shareholders’ rights and protection and the flexibility of company law. Each of the corporate law issues raised by the ten case studies are addressed by national reporters appointed in respect of the US (Delaware), UK, Germany, France, the Netherlands, Italy, Spain, Poland, Finland, Latvia, South Africa and Japan. This chapter compares and contrasts the formal company law rules recognised by each of these twelve countries as applicable in respect of the ten case studies, as well as the effects and consequences of the application of those rules. The value in the comparative assessment of the form and function of the relevant company law rules in each of the twelve jurisdictions under review lies in the additional light they can cast on four of the most enduring debates in comparative company law. These concern the propositions that:(i) the pressures exerted by the increased pace of globalisation, international competition, interest groups, and imitation will inevitably lead to the convergence of company law rules (in terms of form or function) across all jurisdictions in the world, and in particular, assimilation to the US model of corporate law and governance (“the convergence proposition”); (ii) the patterns and structures of shareholder ownership (dispersed/outsider v concentrated/insider) of public joint stock companies in a country's main stock exchange will influence the nature and strength of the shareholder protection rules applicable in that country (“the patterns of share ownership proposition”);(iii) countries have a preference for a shareholder primacy model of corporate governance over that of a stakeholder or director primacy framework (“shareholder primacy proposition”); and(iv) the civilian legal origin of a country will influence its company law rules to such an extent that it will be inferior to a country that has its origins in the common law with regard to the level of (a) investor protection, (b) financial development, (c) access to finance, (d) government ownership and regulation, (e) security of property rights and (f) contract enforcement (“the legal origins proposition”)..In this chapter, the authors seek to demonstrate what a careful analysis of the form and function of each of the legal rules operative in the twelve jurisdictions can reveal about the strength of each of these propositions. The conclusions are drawn that there is a lack of evidence for the legal origins, patterns of share ownership, and convergence propositions, but some available for the shareholder primacy one. The broader economic and legal policy implications of these findings are subsequently examined and conclusions drawn.<br/
A rule-based analysis and comparison of the case Studies
No full textDrawing on data derived from ten hypothetical case studies, we adopt a rule-based comparative evaluation of the company laws of twelve different jurisdictions. The ten case studies examine topics relating to directors’ duties and liabilities generally and in the context of takeovers, the protection of creditors, including the relationship between creditors and a company, and the law governing shares, shareholders’ rights and protection and the flexibility of company law. Each of the corporate law issues raised by the ten case studies are addressed by national reporters appointed in respect of the US (Delaware), UK, Germany, France, the Netherlands, Italy, Spain, Poland, Finland, Latvia, South Africa and Japan. This chapter compares and contrasts the formal company law rules recognised by each of these twelve countries as applicable in respect of the ten case studies, as well as the effects and consequences of the application of those rules. The value in the comparative assessment of the form and function of the relevant company law rules in each of the twelve jurisdictions under review lies in the additional light they can cast on four of the most enduring debates in comparative company law. These concern the propositions that:(i) the pressures exerted by the increased pace of globalisation, international competition, interest groups, and imitation will inevitably lead to the convergence of company law rules (in terms of form or function) across all jurisdictions in the world, and in particular, assimilation to the US model of corporate law and governance (“the convergence proposition”); (ii) the patterns and structures of shareholder ownership (dispersed/outsider v concentrated/insider) of public joint stock companies in a country's main stock exchange will influence the nature and strength of the shareholder protection rules applicable in that country (“the patterns of share ownership proposition”);(iii) countries have a preference for a shareholder primacy model of corporate governance over that of a stakeholder or director primacy framework (“shareholder primacy proposition”); and(iv) the civilian legal origin of a country will influence its company law rules to such an extent that it will be inferior to a country that has its origins in the common law with regard to the level of (a) investor protection, (b) financial development, (c) access to finance, (d) government ownership and regulation, (e) security of property rights and (f) contract enforcement (“the legal origins proposition”)..In this chapter, the authors seek to demonstrate what a careful analysis of the form and function of each of the legal rules operative in the twelve jurisdictions can reveal about the strength of each of these propositions. The conclusions are drawn that there is a lack of evidence for the legal origins, patterns of share ownership, and convergence propositions, but some available for the shareholder primacy one. The broader economic and legal policy implications of these findings are subsequently examined and conclusions drawn.<br/
Duration, lawful termination and frustration of the Employment Contract
No full textThis chapter emphasises the pivotal role that the common law rules on the implied duration and the termination of the contract of employment play in defining the essence and nature of that institution. The claim is made that the implied common law rule treating the employment contract as indeterminate in duration provides explanatory force for the rules on classification, suspension and termination of the employment contract. Turning to the common law of termination, the chapter explains how key House of Lords and Supreme Court authorities such as Johnson, Eastwood, and Edwards do not preclude the addition of ‘just cause’ requirements to the unrestricted reasonable notice rule as a means of furnishing protection to employees falling outside the coverage of the statutory unfair dismissal regime. The chapter moves on to address other common law rules in play in respect of the termination of the employment contract, e.g. those applying in the context of termination by the employer making a payment in lieu of notice, summary dismissal by the employer, resignation and retirement by the employee and the expiry and non-renewal of a fixed-term employment contract. Reforms of these rules are suggested that pursue an ‘integrationist agenda’, i.e. an approach that is designed to gradually assimilate the common law rules with those applicable for the purposes of the unfair dismissal legislation. Proposals for a similar alignment of the common law rules of frustration with the interpretation of that conception for statutory purposes are also made. The chapter ends by exploring how the suggested reforms can be divided into those which promote substantive fairness on the one hand and those seeking to achieve procedural fairness on the other
Limitations on the Shareholder's right to transfer shares
No full textThis work explores in a comparative perspective the validity of restrictions on a shareholder's right to transfer his shares
Subspaces with extra invariance nearest to observed data
No full textGiven an arbitrary finite set of data F = {f1, ..., fm} ⊂ L2(Rd) we prove the existence and show how to construct a “small shift invariant space” that is “closest” to the data F over certain class of closed subspaces of L2(Rd). The approximating subspace is required to have extra-invariance properties, that is to be invariant under translations by a prefixed additive subgroup of Rd containing Zd. This is important for example in situations where we need to deal with jitter error of the data. Here small means that our solution subspace should be generated by the integer translates of a small number of generators. An expression for the error in terms of the data is provided and we construct a Parseval frame for the optimal space. We also consider the problem of approximating F from generalized Paley–Wiener spaces of Rd that are generated by the integer translates of a finite number of functions. That is finitely generated shift invariant spaces that are translation invariant. We characterize these spaces in terms of multi-tile sets of Rd, and show the connections with recent results on Riesz basis of exponentials on bounded sets of Rd. Finally we study the discrete case for our approximation problem.Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaFil: Mosquera, Carolina Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentin
An approximation problem in multiplicatively invariant spaces
No full textLet H be Hilbert space and (Ω, m) a σ-finite measure space. Multiplicatively invariant(MI) spaces are closed subspaces of L2(Ω, H) that are invariant under point-wise multiplication byfunctions from a fixed subset of L∞(Ω). Given a finite set of data F ⊆ L2(Ω, H), in this paper weprove the existence and construct an MI space M that best fits F, in the least squares sense. MIspaces are related to shift-invariant (SI) spaces via a fiberization map, which allows us to solve anapproximation problem for SI spaces in the context of locally compact abelian groups. On the otherhand, we introduce the notion of decomposable MI spaces (MI spaces that can be decomposed into anorthogonal sum of MI subspaces) and solve the approximation problem for the class of these spaces.Since SI spaces having extra invariance are in one-to-one relation to decomposable MI spaces, we alsosolve our approximation problem for this class of SI spaces. Finally we prove that translation-invariantspaces are in correspondence with totally decomposable MI spaces.Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Mosquera, Carolina Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Paternostro, Victoria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentin
Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
No full textIn this article we construct affine systems that provide a simultaneous atomic decomposition for a wide class of functional spaces including the Lebesgue spaces Lp(Rd) 1 < p < +∞. The novelty and difficulty of this construction is that we allow for non-lattice translations. We prove that for an arbitrary expansive matrix A and any set Λ - satisfying a certain spreadness condition but otherwise irregular- there exists a smooth window whose translations along the elements of Λ and dilations by powers of A provide an atomic decomposition for the whole range of the anisotropic Triebel-Lizorkin spaces. The generating window can be either chosen to be bandlimited or to have compact support. To derive these results we start with a known general “painless” construction that has recently appeared in the literature. We show that this construction extends to Besov and Triebel-Lizorkin spaces by providing adequate dual systems.Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Romero, Jose Luis Fernando. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentin
Frames by orbits of two operators that commute
No full textFrames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded operators acting on some separable Hilbert space H. We completely characterize operators T and L with TL=LT and sets Φ⊂H such that the collection {TkLjϕ:k∈Z,j∈J,ϕ∈Φ} forms a frame of H. This is done in terms of model subspaces of the space of square integrable functions defined on the torus and having values in some Hardy space with multiplicity. The operators acting on these models are the bilateral shift and the compression of the unilateral shift (acting pointwisely). This context includes the case when the Hilbert space H is a subspace of L2(R), invariant under translations along the integers, where the operator T is the translation by one and L is a shift-preserving operator.Fil: Aguilera Aguilera, Alejandra Patricia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Carbajal, Diana Agustina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Paternostro, Victoria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin
Learning optimal smooth invariant subspaces for data approximation
No full textIn this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated by a small set of smooth functions. The invariance is either by translations under a full-rank lattice or through the action of crystallographic groups. Smoothness is ensured by stipulating that the generators belong to a Paley-Wiener space, which is selected in an optimal way based on the characteristics of the given data. To complete our investigation, we analyze the fundamental role played by the lattice in the process of approximationThis project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No 777822. In addition, D. Barbieri and E. Hernández were supported by Grants PID2019-105599GB-I00, PID2022-142202NB-I00 / AEI / 10.13039/501100011033. The research of C. Cabrelli and U. Molter is partially supported by Grants PICT 2018-003399 and 2022-4875 (ANPCyT), PIP 11220150100355 and 202287/22 (CONICET), UBACyT 20020170100430BA and 20020220300154BA (UBA
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