Finite TYCZ expansions and cscK metrics

Let $(M, g)$ be a Kaehler manifold whose associated Kaehler form $\omega$ is integral and let $(L, h)\rightarrow (M, \omega)$ be a quantization hermitian line bundle. In this paper we study those Kaehler manifolds $(M, g)$ admitting a finite TYCZ expansion. We show that if the TYCZ expansion is finite then $T_{mg}$ is indeed a polynomial in $m$ of degree $n$, $n=dim M$, and the log-term of the Szeg\"{o} kernel of the disc bundle $D\subset L^*$ vanishes (where $L^*$ is the dual bundle of $L$). Moreover, we provide a complete classification of the Kaehler manifolds admitting finite TYCZ expansion either when $M$ is a complex curve or when $M$ is a complex surface with a cscK metric which admits a radial Kaehler potential

Symplectic duality between complex domains

In this paper after extending the denition of symplectic duality (given in [3] for bounded symmetric domains ) to arbitrary complex domains of Cn centered at the origin we generalize some of the results proved in [3] and [4] to those domain

Extremal Kähler Metrics Induced by Finite or Infinite-Dimensional Complex Space Forms

In this paper, we address the problem of studying those complex manifolds M equipped with extremal metrics g induced by finite or infinite-dimensional complex space forms. We prove that when g is assumed to be radial and the ambient space is finite-dimensional, then (M, g) is itself a complex space form. We extend this result to the infinite-dimensional setting by imposing the strongest assumption that the metric g has constant scalar curvature and is well behaved (see Definition 1 in the Introduction). Finally, we analyze the radial Kähler–Einstein metrics induced by infinite-dimensional elliptic complex space forms and we show that if such a metric is assumed to satisfy a stability condition then it is forced to have constant nonpositive holomorphic sectional curvature

On the third coefficient of TYZ expansion for radial scalar flat metrics

We classify radial scalar flat metrics with constant third coefficient of its TYZ expansion. As a byproduct of our analysis we provide a characterization of Simanca's scalar flat metric

A characterization of complex space forms via Laplace operators

Inspired by the work of Lu and Tian (Duke Math J 125(2):351–387, 2004), in this paper we address the problem of studying those Kähler manifolds satisfying the Δ -property, i.e. such that on a neighborhood of each of its points the kth power of the Kähler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer k (see below for its definition). We prove two results: (1) if a Kähler manifold satisfies the Δ -property then its curvature tensor is parallel; (2) if an Hermitian symmetric space of classical type satisfies the Δ -property then it is a complex space form (namely it has constant holomorphic sectional curvature). In view of these results we believe that if a Kähler manifold satisfies the Δ -property then it is a complex space form

Kahler–Ricci Solitons Induced by Infinite-Dimensional Complex Space Forms

We exhibit families of nontrivial (i.e., not Kähler–Einstein) radial Kähler– Ricci solitons (KRS), both complete and not complete, which can be Kähler immersed into infinite-dimensional complex space forms. This shows that the triviality of a KRS induced by a finite-dimensional complex space form proved by Loi and Mossa (Proc. Amer. Math. Soc. 149:11 (2020), 4931–4941) does not hold when the ambient space is allowed to be infinite-dimensional. Moreover, we show that the radial potential of a radial KRS induced by a nonelliptic complex space form is necessarily defined at the origin

Bioerosion by microbial euendoliths in benthic foraminifera from heavy metal-polluted coastal environments of Portovesme (South-Western Sardinia, Italy)

A monitoring survey of the coastal area facing the industrial area of Portoscuso-Portovesme (south-western Sardinia, Italy) revealed intense bioerosional processes. Benthic foraminifera collected at the same depth (about 2 m)but at different distances from the pollution source show extensive microbial infestation, anomalous Mg/Ca molar ratios and high levels of heavy metals in the shell associated with a decrease in foraminifera richness, population density and biodiversity with the presence of morphologically abnormal specimens. We found that carbonate dissolution induced by euendoliths is selective, depending on the Mg content and morpho-structural types of foraminiferal taxa. This study provides evidences for a connection between heavy metal dispersion, decrease in pH of the sea-water and bioerosional processes on foraminifera

Symplectic duality between complex domains

In this paper after extending the denition of symplectic duality (given in [3] for bounded symmetric domains ) to arbitrary complex domains of Cn centered at the origin we generalize some of the results proved in [3] and [4] to those domains

Fossichnus solus and Oichnus simplex, two peculiar ichnospecies in modern benthic foraminifera from a polluted area in SW coast of Sardinia, Italy

The modern benthic foraminiferal tests collected from a coastal area of south-western Sardinia (Portoscuso-Portovesme) that is heavily polluted by industrial activity reveal intense and widespread bioerosional structures induced by diversifi ed microborers. A large number of the foraminifera reveals microscopic round holes (1-60 μm in diameter) and roundish concavities (25x40 μm in external diameter) on their surface that belong, respectively, to the ichnospecies Oichnus simplex Bromley, 1981, and Fossichnus solus Nielsen et al., 2003. These traces just occur in the tests of the foraminifera which are heavily infested by microendolithic cyanobacteria, algae and fungi suggests comparable ethological behaviour between the ichnospecies Fossichnus and Oichnus and the microbial euendoliths that are ascribed to individual biological taxa. The greater occurrence of F. solus and O. simplex in the high-Mg foraminiferal porcelanaceous tests than in the low-Mg foraminiferal hyaline tests reveals that the bioerosional processes seem to be related to the Mg/Ca ratio, as well as to morphological structures of the taxa

Clinical characteristics, neuroimaging findings, and neuropsychological functioning in attention-deficit hyperactivity disorder: Sex differences

Recent clinical studies, in both children/adolescents and adults, have shown the extreme neuropsychological heterogeneity of attention-deficit hyperactivity disorder (ADHD): specific neuropsychological deficits have been found only in a minority of individuals, with no direct correlation between discrete cognitive performances and the trajectory of clinical symptoms. Deficits in specific neuropsychological functions may be common in ADHD, but nevertheless no cognitive or neuropsychological profile may fully explain the disorder. Sex differences in the ADHD presentation, both at a neuropsychological and clinical level, also contribute to this clinical and neuropsychological heterogeneity. At a neuropsychological level, females with ADHD may show greater working memory problems, poorer vocabulary skills and worse visual spatial reasoning. Structural and functional imaging study also show discrete differences across sex; however, the great majority of clinical studies mainly or exclusively include male participants with insufficient data to draw firm conclusions on sex differences within the disorder. Here, we report the recent literature data, discussing still open research questions about the clinical presentation, neuroimaging findings, and neuropsychological functioning in ADHD with a focus on the impact of sex differences—a deeper insight in these unresolved issues may have relevant clinical and therapeutic implications for tailored, effective, and long-lasting interventions