Quantum Mechanics without the quantum

Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to study the wave-particle dualism and the energy-time uncertainty relation. Afterwards we look upon the present state of the quantum mechanical formalism. We demonstrate that the two incompatibilities are employed in the same treatment forming a "hybrid" description of the phenomena and leading to a contradiction.Comment: Corrected typos Changed conten

Selective imaging of extended reflectors in a two-dimensional waveguide

We consider the problem of selective imaging extended reflectors in waveguides using the response matrix of the scattered field obtained with an active array. Selective imaging amounts to being able to focus at the edges of a reflector which typically give raise to weaker echoes than those coming from its main body. To this end, we propose a selective imaging method that uses projections on low rank subspaces of a weighted modal projection of the array response matrix, $\widehat{\mathbb{P}}(\omega)$. We analyze theoretically our imaging method for a simplified model problem where the scatterer is a vertical one-dimensional perfect reflector. In this case, we show that the rank of $\widehat{\mathbb{P}}(\omega)$ equals the size of the reflector devided by the cross-range array resolution which is $\lambda/2$ for an array spanning the whole depth of the waveguide. We also derive analytic expressions for the singular vectors of $\widehat{\mathbb{P}}(\omega)$ which allows us to show how selective imaging can be achieved. Our numerical simulations are in very good agreement with the theory and illustrate the robustness of our imaging functional for reflectors of various shapes

Indeterminacy and Creation in the Work of Cornelius Castoriadis

This article explores the notions of indeterminacy and creation in Castoriadis' work. The notions of indeterminacy and creation are initially associated with Castoriadis' conception of Being as Chaos contradicted with what Castoriadis calls "ensemblistic-identitary logic”. The conception of Being as Chaos is then linked with the notion of otherness analyzed as creation ex nihilo. In particular, creation ex nihilo is analyzed in the context of Castoriadis division of Being's multiplicity into difference and otherness. I will argue that Being's multiplicity as difference refers to the "ensemblistic-identitary logic” while otherness comes up with a novel form of Being identified as ex nihilo creation. Finally, otherness is approached through Castoriadis' conception of time whereby otherness and, consequently, time is further associated with Castoriadis' notion of imaginary as the latter deploys in the social-historical field of mankind through the imaginary significations of society

From Socialism to Open Cooperativism: Convergences and Divergences in the Work of Castoriadis, Olin Wright and Bauwens

This article attempts at integrating core socialist elements analyzed through the prism of Castoriadis s and Wright s work into a model of open cooperativism between Commons-based peer production ethical market entities and a partner state introduced by Bauwens and Kostakis It concludes with a critical appraisal of Bauwens and Kostakis s mode

The Commons

"This book explores the potential creation of a broader collaborative economy through commons-based peer production (P2P) and the emergent role of information and communication technologies (ICTs). The book seeks to critically engage in the political discussion of commons-based peer production, which can be classified into three basic arguments: the liberal, the reformist and the anti-capitalist. This book categorises the liberal argument as being in favour of the coexistence of the commons with the market and the state. Reformists, on the other hand, advocate for the gradual adjustment of the state and of capitalism to the commons, while anti-capitalists situate the commons against capitalism and the state. By discussing these three viewpoints, the book contributes to contemporary debates concerning the future of commons-based peer production. Further, the author argues that for the commons to become a fully operational mode of peer production, it needs to reach critical mass arguing that the liberal argument underestimates the reformist insight that technology has the potential to decentralise production, thereby forcing capitalism to transition to post-capitalism. Surveying the three main strands of commons-based peer production, this book makes the case for a post-capitalist commons-orientated transition that moves beyond neoliberalism.

The Commons

"This book explores the potential creation of a broader collaborative economy through commons-based peer production (P2P) and the emergent role of information and communication technologies (ICTs). The book seeks to critically engage in the political discussion of commons-based peer production, which can be classified into three basic arguments: the liberal, the reformist and the anti-capitalist. This book categorises the liberal argument as being in favour of the coexistence of the commons with the market and the state. Reformists, on the other hand, advocate for the gradual adjustment of the state and of capitalism to the commons, while anti-capitalists situate the commons against capitalism and the state. By discussing these three viewpoints, the book contributes to contemporary debates concerning the future of commons-based peer production. Further, the author argues that for the commons to become a fully operational mode of peer production, it needs to reach critical mass arguing that the liberal argument underestimates the reformist insight that technology has the potential to decentralise production, thereby forcing capitalism to transition to post-capitalism. Surveying the three main strands of commons-based peer production, this book makes the case for a post-capitalist commons-orientated transition that moves beyond neoliberalism.

Fourier restriction phenomenon in thin sets

We study the Fourier restriction phenomenon in settings where there is no underlying proper smooth subvariety. We prove an (Lp, L2) restriction theorem in general locally compact abelian groups and apply it in groups such as (Z/pLZ)n, R and locally compact ultrametric fields K. The problem of existence of Salem sets in a locally compact ultrametric field (K, | · |) is also considered. We prove that for every 0 0 there exist a set E ⊂ K and a measure μ supported on E such that the Hausdorff dimension of E equals α and |bμ(x)| ≤ C|x|−α 2 +ǫ. We also establish the optimal extension of the Hausdorff-Young inequality in the compact ring of integers R of a locally compact ultrametric field K. We shall prove the following: For every 1 ≤ p ≤ 2 there is a Banach function space Fp(R) with σ-order continuous norm such that (i) Lp(R) ( Fp(R) ( L1(R) for every 1 < p < 2. (ii) The Fourier transform F maps Fp(R) to ℓp′ continuously. (iii) Lp(R) is continuously included in Fp(R) and Fp(R) is continuously included in L1(R). (iv) If Z is a Banach function space with the same properties as Fp(R) above, then Z is continuously included in Fp(R). (v) F1(R) = L1(R) and F2(R) = L2(R)