Multivariate Bernoulli and Euler polynomials via L\'evy processes

By a symbolic method, we introduce multivariate Bernoulli and Euler polynomials as powers of polynomials whose coefficients involve multivariate L\'evy processes. Many properties of these polynomials are stated straightforwardly thanks to this representation, which could be easily implemented in any symbolic manipulation system. A very simple relation between these two families of multivariate polynomials is provided

Macro- and Microplastics in the Antarctic Environment: Ongoing Assessment and Perspectives

The number of scientists and tourists visiting Antarctica is on the rise and, despite the management framework for environmental protection, some coastal areas, particularly in the Antarctic Peninsula region, are affected by plastic contamination. The few data available on the occurrence of microplastics (<5 mm) are difficult to compare, due to the different methodologies used in monitoring studies. However, indications are emerging to guide future research and to implement environmental protocols. In the surface and subsurface waters of the Southern Ocean, plastic debris >300 p.m appears to be scarce and far less abundant than paint chips released from research vessels. Yet, near some coastal scientific stations, the fragmentation and degradation of larger plastic items, as well as microbeads and microfibers released into wastewater from personal care products and laundry, could potentially affect marine organisms. Some studies indicate that, through long-range atmospheric transport, plastic fibers produced on other continents can be deposited in Antarctica. Drifting plastic debris can also cross the Polar Front, with the potential to carry alien fouling organisms into the Southern Ocean. Sea ice dynamics appear to favor the uptake of microplastics by ice algae and Antarctic krill, the key species in the Antarctic marine food web. Euphausia superba apparently has the ability to fragment and expel ingested plastic particles at the nanoscale. However, most Antarctic organisms are endemic species, with unique ecophysiological adaptations to extreme environmental conditions and are likely highly sensitive to cumulative stresses caused by climate change, microplastics and other anthropogenic disturbances. Although there is limited evidence to date that micro- and nanoplastics have direct biological effects, our review aims at raising awareness of the problem and, in order to assess the real potential impact of microplastics in Antarctica, underlines the urgency to fill the methodological gaps for their detection in all environmental matrices, and to equip scientific stations and ships with adequate wastewater treatment plants to reduce the release of microfibers

The tailor-made treatment in a particular case of pulmonary hypertension in thalassaemia intermedia: A case report

Background: Pulmonary hypertension (PH) is a haemodynamic condition, secondary to different causes. Thalassaemia may lead to PH of different origin and needs a comprehensive analysis to be correctly characterized and possibly treated. Case summary: We present a case study of a patient with a non-transfusion-dependent thalassaemia and a previous diagnosis of group 5 PH. A complete diagnostic assessment led to a specific diagnosis of chronic thromboembolic PH. Thus, we were able to start a specific therapy with riociguat that provided an improvement in terms of haemodynamic, imaging, and functional status. Discussion: A correct characterization and treatment of PH are essential in order to change the patient's prognosis. Chronic thromboembolic PH is a treatable cause of PH in thalassemic patients and should be investigated

Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a lattice. Related ideas appeared in recent publications and we show that the examples treated there are special cases of umbral calculus. This observation then suggests various generalizations of these examples. A special umbral representation of the canonical commutation relations given in terms of the position and momentum operator on a lattice is investigated in detail.Comment: 19 pages, Late

The diverse Grania fauna (Clitellata : Enchytraeidae) of the Esperance area, Western Australia, with descriptions of two new species

Seven species of the marine enchytraeid genus Grania Southern, 1913 are described from sediments sampled during the 2003 International Workshop on the Marine Flora and Fauna of Esperance Bay and the Recherche Archipelago, on the southern coast of Western Australia. Two species are new to science, the euryhaline Tasmanian G. dolichura Rota and Erseus, 2000 represents a new record for the state, and the remaining four species were known from other parts of Western Australia. Grania quaerens sp. n. is recognized by having a high chaetal index (= 5 short chaetal foot), small coelomocytes, penial apparati with long whip-like terminal stylets, conspicuous spermathecae with ectally bulbous ducts, and ectally granulated ampullae housing sperm rings in their ental region. Grania sperantia sp. n. is readily distinguishable by the complete lack of lateral chaetae, a multiple-banded pattern of the clitellum, extremely long sperm funnels, and the intrasegmental location of the spermathecal pores. The latter new species and four others in the collection (G. bykane Coates, 1990, G. crassiducta Coates, 1990, G. dolichura, and G. ersei Coates, 1990) are remarkable in possessing the head organ, a sensory structure unique to Grania that was not noted previously in Western Australian species. When considering the whole genus, the geographic pattern of the head organ appears southern-centred: of the 17 species of Grania reported to possess it, as many as 13 inhabit the southern latitudes. The seventh species of the Esperance collection, G. vacivasa Coates and Stacey, 1993, is notable for the kind of items found in its gut and the unusual appearance of its pygidium.Seven species of the marine enchytraeid genus Grania Southern, 1913 are described from sediments sampled during the 2003 International Workshop on the Marine Flora and Fauna of Esperance Bay and the Recherche Archipelago, on the southern coast of Western Australia. Two species are new to science, the euryhaline Tasmanian G. dolichura Rota and Erseus, 2000 represents a new record for the state, and the remaining four species were known from other parts of Western Australia. Grania quaerens sp. n. is recognized by having a high chaetal index (= 5 short chaetal foot), small coelomocytes, penial apparati with long whip-like terminal stylets, conspicuous spermathecae with ectally bulbous ducts, and ectally granulated ampullae housing sperm rings in their ental region. Grania sperantia sp. n. is readily distinguishable by the complete lack of lateral chaetae, a multiple-banded pattern of the clitellum, extremely long sperm funnels, and the intrasegmental location of the spermathecal pores. The latter new species and four others in the collection (G. bykane Coates, 1990, G. crassiducta Coates, 1990, G. dolichura, and G. ersei Coates, 1990) are remarkable in possessing the head organ, a sensory structure unique to Grania that was not noted previously in Western Australian species. When considering the whole genus, the geographic pattern of the head organ appears southern-centred: of the 17 species of Grania reported to possess it, as many as 13 inhabit the southern latitudes. The seventh species of the Esperance collection, G. vacivasa Coates and Stacey, 1993, is notable for the kind of items found in its gut and the unusual appearance of its pygidium

Composition-Diamond lemma for λ\lambda-differential associative algebras with multiple operators

In this paper, we establish the Composition-Diamond lemma for $\lambda$-differential associative algebras over a field $K$ with multiple operators. As applications, we obtain Gr\"{o}bner-Shirshov bases of free $\lambda$-differential Rota-Baxter algebras. In particular, linear bases of free $\lambda$-differential Rota-Baxter algebras are obtained and consequently, the free $\lambda$-differential Rota-Baxter algebras are constructed by words

Dynamic Regulation of Vascular Myosin Light Chain (MYL9) with Injury and Aging

Aging-associated changes in the cardiovascular system increase the risk for disease development and lead to profound alterations in vascular reactivity and stiffness. Elucidating the molecular response of arteries to injury and age will help understand the exaggerated remodeling of aging vessels.We studied the gene expression profile in a model of mechanical vascular injury in the iliac artery of aging (22 months old) and young rats (4 months old). We investigated aging-related variations in gene expression at 30 min, 3 d and 7 d post injury. We found that the Myosin Light Chain gene (MYL9) was the only gene differentially expressed in the aged versus young injured arteries at all time points studied, peaking at day 3 after injury (4.6 fold upregulation (p<0.05) in the smooth muscle cell layers. We confirmed this finding on an aging aortic microarray experiment available through NCBI's GEO database. We found that Myl9 was consistently upregulated with age in healthy rat aortas. To determine the arterial localization of Myl9 with age and injury, we performed immunohistochemistry for Myl9 in rat iliac arteries and found that in healthy and injured (30 days post injury) arteries, Myl9 expression increased with age in the endothelial layers.The consistent upregulation of the myosin light chain protein (Myl9) with age and injury in arterial tissue draws attention to the increased vascular permeability and to the age-caused predisposition to arterial constriction after balloon angioplasty