Modern Narcissus: the lingering reflections of myth in modern art

Why has myth continued to fascinate modern artists, and why the myth of Narcissus, with its modern association with narcissism? This article considers the relationship between the Narcissus myth and the lineage of modern art that runs from Symbolism to surrealism through the polymorphous prism of the Greco-Roman Pantheon to which Narcissus belongs. The article offers an interpretation of the role of mythology in modern art that moves beyond psychoanalysis to incorporate the longer span of the art-historical tradition. Addressing issues of aesthetics, gender and sexuality, the following account highlights Narcissus‟s double nature as an erotic myth that comprises both identity formation and intersubjectivity, as enacted in the field of representation. The myths associated with Narcissus in the history of Western art will help us reconsider his role as a powerful figure capable to activate that slippage between word and image, identity and sociability, representation and reality which was celebrated by the Symbolists and formed the centre of the surrealists‟ social-aesthetic project

Inverse observability inequalities for integrodifferential equations in square domains

In this paper we will consider oscillations of square viscoelastic membranes by adding to the wave equation another term, which takes into account the memory. To this end, we will study a class of integrodifferential equations in square domains. By using accurate estimates of the spectral properties of the integrodifferential operator, we will prove an inverse observability inequality

A Mathematical Model for Signal's Energy at the Output of an Ideal DAC

The presented research work considers a mathematical model for energy of the signal at the output of an ideal DAC, in presence of sampling clock jitter. When sampling clock jitter occurs, the energy of the signal at the output of ideal DAC does not satisfies a Parseval identity. Nevertheless, an estimation of the signal energy is here shown by a direct method involving sinc functions

Reachability problems for a wave-wave system with a memory term

We solve the reachability problem for a coupled wave-wave system with an integro-differential term. The control functions act on one side of the boundary. The estimates on the time is given in terms of the parameters of the problem and they are explicitly computed thanks to Ingham type results. Nevertheless some restrictions appear in our main results. The Hilbert Uniqueness Method is briefly recalled. Our findings can be applied to concrete examples in viscoelasticity theor

Observability of rectangular membranes and plates on small sets

Since the works of Haraux and Jaffard we know that rectangular plates may be observed by subregions not satisfying the geometrical control condition. We improve these results by observing only on an arbitrarily short segment inside the domain. The estimates may be strengthened by observing on several well-chosen segments. In the second part of the paper we establish various observability theorems for rectangular membranes by applying Mehrenberger's recent generalization of Ingham's theorem.Comment: 22 pages, 8 figure

Solutions of fractional logistic equations by Euler's numbers

In this paper, we solve in the convergence set, the fractional logistic equation making use of Euler's numbers. To our knowledge, the answer is still an open question. The key point is that the coefficients can be connected with Euler's numbers, and then they can be explicitly given. The constrained of our approach is that the formula is not valid outside the convergence set, The idea of the proof consists to explore some analogies with logistic function and Euler's numbers, and then to generalize them in the fractional case.Comment: Euler's numbers, Biological Application, Fractional logistic equatio

Control problems for weakly coupled systems with memory

We investigate control problems for wave-Petrovsky coupled systems in the presence of memory terms. By writing the solutions as Fourier series, we are able to prove Ingham type estimates, and hence reachability results. Our findings have applications in viscoelasticity theory and linear acoustic theory