About the Existence of Integrable Solutions of a Functional-Integral Equation

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Answer to a Question by M. Feder about K(X,Y)

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Remarks on the complementability of spaces of Bochner integrable functions in spaces of vector measures

summary:In the paper [5] L. Drewnowski and the author proved that if $X$ is a Banach space containing a copy of $c_0$ then $L_1({\mu },X)$ is {\it not} complemented in $cabv({\mu },X)$ and conjectured that the same result is true if $X$ is any Banach space without the Radon-Nikodym property. Recently, F. Freniche and L. Rodriguez-Piazza ([7]) disproved this conjecture, by showing that if $\mu$ is a finite measure and $X$ is a Banach lattice not containing copies of $c_0$, then $L_1({\mu },X)$ is complemented in $cabv({\mu },X)$. Here, we show that the complementability of $L_1({\mu },X)$ in $cabv({\mu },X)$ together with that one of $X$ in the bidual $X^{\ast\ast}$ is equivalent to the complementability of $L_1({\mu },X)$ in its bidual, so obtaining that for certain families of Banach spaces not containing $c_0$ complementability occurs (Section 2), thanks to the existence of general results stating that a space in one of those families is complemented in the bidual. We shall also prove that certain quotient spaces inherit that property (Section 3)

The Inferto-Sex Syndrome (ISS): sexual dysfunction in fertility care setting and assisted reproduction

Purpose Infertility represents a peculiar social burden affecting more than 15% of couples, provoking it a real threat to the general quality of life and to the sexual health. The medicalization (diagnosis, therapy and follow up) of the lack of fertility is frequently a challenge in term of personal and couple's involvement. In particular, while the Assisted Reproductive Technology (ART) has allowed many infertile couples to achieve pregnancy, the therapeutic process faced by the couple bears a strong psychological stress that can affect the couple's quality of life, relationship and sexuality. Despite infertility affects both female and male sexual health, only recently the interest in the effects of ART on the couple's sexuality has grown, especially for women. Methods A literature research on the sexual dysfunction in fertility care and particularly in ART setting was performed. Results Literature largely found that intimacy and sexuality appear specifically impaired by intrusiveness of treatments and medical prescriptions. Moreover, there is a close relationship between emotional, psychological and sexual aspects, which can be integrated in the new concept of Inferto-Sex Syndrome (ISS) that can impair the ART treatment outcomes. Evidence demonstrates that the assessment of sexual function is necessary in couples undergoing diagnosis of infertility and ART. Conclusion A close relationship between infertility and sexuality, both in the female and male partners, was detected. ART treatments may heavily impact on the couple's psychosexual health. A couple-centred program for the integrated management of psychological and sexual dysfunction should be considered in the context of ART programs

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical calculation by exploiting the full theory of the quintic equation, i.e., its reduction to Bring-Jerrard form and the resulting expression of roots in terms of generalized hypergeometric functions. By performing the numerical analysis of the exact formulas for the roots, we confirm and slightly improve the theoretical evaluation of quantum corrected coordinates of Lagrangian libration points of stable equilibrium. Second, we prove in detail that also for collinear Lagrangian points the quantum corrections are of the same order of magnitude in the Earth-Moon system. Third, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points, both stable and unstable. The present paper investigates therefore, eventually, a restricted three-body problem involving Earth, Moon and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist

Structurally Dependent Fano Resonances in the Infrared Spectra of Phonons in Few-Layer Graphene

The in-plane optical phonons around 200 meV in few-layer graphene are investigated utilizing infrared absorption spectroscopy. The phonon spectra exhibit unusual asymmetric features characteristic of Fano resonances, which depend critically on the layer thickness and stacking order of the sample. The phonon intensities in samples with rhombohedral (ABC) stacking are significantly higher than those with Bernal (AB) stacking. These observations reflect the strong coupling between phonons and interband electronic transitions in these systems and the distinctive variation in the joint density of electronic states in samples of differing thickness and stacking order.Comment: 20 pages, 7 figures, supplementary material include

Earth-Moon Lagrangian points as a testbed for general relativity and effective field theories of gravity

We first analyse the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L4 or L5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping away. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L4 or L5. It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the long-distance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 meters, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 meters per orbit. The latter is a cumulative effect accurately measured at the centimeter level through the lunar laser ranging positioning technique. Thus, it is possible to study a new laser ranging test of general relativity to measure the 7.61-meter correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. Performing such an experiment requires controlling the propulsion to precisely reach L1, an instrumental accuracy comparable to the measurement of the lunar geodesic precession, understanding systematic effects resulting from thermal radiation and multi-body gravitational perturbations. This will then be the basis to consider a second-generation experiment to study deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system

Multifactorial causes of chronic mortality in juvenile sturgeon (Huso huso)

This investigation focused on an episode of chronic mortality observed in juvenile Huso huso sturgeons. The examined subjects underwent pathological, microbiological, molecular, and chemical investigations. Grossly severe body shape deformities, epaxial muscle softening, and multifocal ulcerative dermatitis were the main observed findings. The more constant histopathologic findings were moderate to severe rarefaction and disorganization of the lymphohematopoietic lymphoid tissues, myofiber degeneration, atrophy and interstitial edema of skeletal epaxial muscles, and degeneration and atrophy of the gangliar neurons close to the myofibers. Chemical investigations showed a lower selenium concentration in affected animals, suggesting nutritional myopathy. Other manifestations were nephrocalcinosis and splenic vessel wall hyalinosis. Septicemia due to bacteria such as Aeromonas veronii, Shewanella putrefaciens, Citrobacter freundii, Chryseobacterium sp., and pigmented hyphae were found. No major sturgeon viral pathogens were detected by classical methods. Next-generation sequencing (NGS) analysis confirmed the absence of viral pathogens, with the exception of herpesvirus, at the order level; also, the presence of Aeromonas veronii and Shewanella putrefaciens was confirmed at the family level by the metagenomic classification of NGS data. In the absence of a primary yet undetected biological cause, it is supposed that environmental stressors, including nutritional imbalances, may have led to immune system impairment, facilitating the entry of opportunistic bacteria and mycotic hyphae