The slipper lobster, Scyllarides latus, uses apatite and fluorapatite to protect its sensory organules

The cuticle of arthropods has been intensely studied not only to better understand the properties of a natural composite material, but also to understand how structural properties and mineral contributions to this composite offer a durable protective covering from predator and microbial attack. Thus far, most marine cuticular studies have focused on the American lobster, Homarus americanus, or several crab species, but have largely ignored other types of lobsters, such as spiny or slipper lobsters that have exoskeletons differing in both structural properties (i.e., amount of trabeculae present in pits and spines) and resistance to structural failure. Using an electron microprobe, we analyzed various segments of the exoskeleton of the Mediterranean slipper lobster, Scyllarides latus, to determine the mineral content in discrete domains of cuticle. EMP analysis determined that the cuticle of S. latus is similar to that of H. americanus in that it contains carbonate apatite in canal linings and in the areas surrounding sensory organules (setae). The slipper lobster also uses a fluorapatite mineral that further adds strength to the shell. Results will be discussed in the context of what this means for defense against attack and differences in environmental water chemistry and resilience to climate change

On the homology of the Harmonic Archipelago

We calculate the singular homology and \v{C}ech cohomology groups of the Harmonic archipelago. As a corollary, we prove that this space is not homotopy equivalent to the Griffiths space. This is interesting in view of Eda's proof that the first singular homology groups of these spaces are isomorphic

Scyllarid Lobster Biology and Ecology

The family Scyllaridae is the most speciose and diverse of all families of marine lobsters. Slipper lobsters are found in both tropical and temperate habitats with hard or soft substrates and at different depths, and exhibit a wide array of morphological, anatomical, and physiological adaptations. Among the 20 genera and at least 89 species constituting 4 subfamilies, only some members of 4 genera, Thenus (Theninae), Scyllarides (Arctidinae), Ibacus and Parribacus (Ibacinae), form significant fisheries because of their large size. While scientific information on these lobsters has increased considerably in recent decades, it is still limited compared with commercially valuable spiny and clawed lobsters, and is confined to a few key species. The present chapter presents the current available knowledge on the biology of scyllarids and attempts to point out where questions remain to help focus further studies in this important group

Transform of Riccati equation of constant coefficients through fractional procedure

We use a particular fractional generalization of the ordinary differential equations that we apply to the Riccati equation of constant coefficients. By this means the latter is transformed into a modified Riccati equation with the free term expressed as a power of the independent variable which is of the same order as the order of the applied fractional derivative. We provide the solutions of the modified equation and employ the results for the case of the cosmological Riccati equation of FRW barotropic cosmologies that has been recently introduced by FaraoniComment: 7 pages, 2 figure

Cauchy's formulas for random walks in bounded domains

Cauchy's formula was originally established for random straight paths crossing a body $B \subset \mathbb{R}^{n}$ and basically relates the average chord length through $B$ to the ratio between the volume and the surface of the body itself. The original statement was later extended in the context of transport theory so as to cover the stochastic paths of Pearson random walks with exponentially distributed flight lengths traversing a bounded domain. Some heuristic arguments suggest that Cauchy's formula may also hold true for Pearson random walks with arbitrarily distributed flight lengths. For such a broad class of stochastic processes, we rigorously derive a generalized Cauchy's formula for the average length travelled by the walkers in the body, and show that this quantity depends indeed only on the ratio between the volume and the surface, provided that some constraints are imposed on the entrance step of the walker in $B$. Similar results are obtained also for the average number of collisions performed by the walker in $B$, and an extension to absorbing media is discussed.Comment: 12 pages, 6 figure

Quantum tomography, phase space observables, and generalized Markov kernels

We construct a generalized Markov kernel which transforms the observable associated with the homodyne tomography into a covariant phase space observable with a regular kernel state. Illustrative examples are given in the cases of a 'Schrodinger cat' kernel state and the Cahill-Glauber s-parametrized distributions. Also we consider an example of a kernel state when the generalized Markov kernel cannot be constructed.Comment: 20 pages, 3 figure

The Non-Trapping Degree of Scattering

We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explicitly and be used for symbolic dynamics of multi-obstacle scattering. If the potential is bounded, then in the non-trapping case the boundary of Hill's Region is empty or homeomorphic to a sphere. We consider classical potential scattering. If at energy E no orbit is trapped, the Hamiltonian dynamics defines an integer-valued topological degree deg(E) < 2. This is calculated explicitly for all potentials, and exactly the integers < 2 are shown to occur for suitable potentials. The non-trapping condition is restrictive in the sense that for a bounded potential it is shown to imply that the boundary of Hill's Region in configuration space is either empty or homeomorphic to a sphere. However, in many situations one can decompose a potential into a sum of non-trapping potentials with non-trivial degree and embed symbolic dynamics of multi-obstacle scattering. This comprises a large number of earlier results, obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more detailed proofs and remark

The Quantum Mellin transform

We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum $p_\eta$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_\eta$. We utilise this new transform to find quantum wavefunctions whose Hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann Zeta function. We finally give possible physical realisations to perform an indirect measurement of the Hyperbolic momentum of a quantum system on the half-line.Comment: 23 pages, 6 Figure

Residence time and collision statistics for exponential flights: the rod problem revisited

Many random transport phenomena, such as radiation propagation, chemical/biological species migration, or electron motion, can be described in terms of particles performing {\em exponential flights}. For such processes, we sketch a general approach (based on the Feynman-Kac formalism) that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution. We then illustrate the proposed method in the case of the so-called {\em rod problem} (a 1d system), and discuss the relevance of the obtained results in the context of Monte Carlo estimators.Comment: 9 pages, 8 figure