Function Spaces, Approximation Theory, and Their Applications

The purpose of this special issue was to present new developments in the theory of function spaces, along with the deep interconnections with approximation theory and the applications in various fields of pure and applied mathematics. The reaction of the mathematical community was very satisfactory. We collected thirty-five submissions, covering a wide range of mathematical topics, ten of which were found to be suitable for publications in this issue. The major part of the accepted papers treats function spaces and their applications. In this respect, in the article by X Yang et al. a new class of function spaces, named "multi-βnormed spaces", is introduced, in connection with stability properties of certain type of functional equations, while, in the paper by A. A. Bakery, sequential spaces of Orlicz type are studied and connected with the theory of summability. In the review paper by L. Angeloni and G. Vinti, the approximation theory in the space of functions with bounded variation is developed, in view of applications to signal processing. Different notions of variation are considered and several approximation theorems for families of integral or discrete type operators are given. In the more theoretical article by S. Wulede et al., a new class of Banach spaces which generalizes the class of uniformly extremely convex Banach spaces is introduced, and some characterizations of these spaces are given. Another paper by N. Khan treats the convergence of new type of double sequences, here introduced, in n-normed spaces. An interesting abstract approach to the theory of filter convergence is given in the article by A. Boccuto and X. Dimitriou, in which the links with function spaces and approximation theory are also dealt with. Other aspects of the theory of function spaces and their interconnections with calculus of variations, numerical analysis, complex variables, and stochastic processes are discussed, respectively, in the articles by T. Ma and Y. Feng, H. Wang et al., S. Wang and T. Zhan, and finally P. Duan.These four papers point out how certain methods of general approximation theory in function spaces can be employed in order to solve problems coming from a large variety of mathematical fields. We think that these contributions may represent starting points for new researches in the field of function spaces and approximation theory

Multivariate approximation: Theory and applications 2020

A summary of the main facts about the Conference ‘Multivariate Approximation: Theory and Applications’ (MATA 2020) held at the Department of Mathematics and Computer Science of the University of Perugia (Italy), on January 16-18, 2020 and the contents of the associated Special Issue appearing on Dolomites Research Notes on Approximation, are here reported

Block Spin Effective Action for 4d SU(2) Finite Temperature Lattice Gauge Theory

The Svetitsky-Yaffe conjecture for finite temperature 4d SU(2) lattice gauge theory is confirmed by observing matching of block spin effective actions of the gauge model with those of the 3d Ising model. The effective action for the gauge model is defined by blocking the signs of the Polyakov loops with the majority rule. To compute it numerically, we apply a variant of the IMCRG method of Gupta and Cordery.Comment: LaTeX2e, 22 pages, 8 Figure

High frequency of ribosomal protein gene deletions in Italian Diamond-Blackfan anemia patients detected by multiplex ligation-dependent probe amplification assay

Diamond-Blackfan anemia is an autosomal dominant disease due to mutations in nine ribosomal protein encoding genes. Because most mutations are loss of function and detected by direct sequencing of coding exons, we reasoned that part of the approximately 50% mutation negative patients may have carried a copy number variant of ribosomal protein genes. As a proof of concept, we designed a multiplex ligation-dependent probe amplification assay targeted to screen the six genes that are most frequently mutated in Diamond-Blackfan anemia patients: RPS17, RPS19, RPS26, RPL5, RPL11, and RPL35A. Using this assay we showed that deletions represent approximately 20% of all mutations. The combination of sequencing and multiplex ligation-dependent probe amplification analysis of these six genes allows the genetic characterization of approximately 65% of patients, showing that Diamond-Blackfan anemia is indisputably a ribosomopathy

Bone marrow failure may be caused by chromosome anomalies exerting effects on RUNX1T1 gene

Background: The majority of the cases of bone marrow failure syndromes/aplastic anaemias (BMFS/AA) are non-hereditary and considered idiopathic (80-85%). The peripheral blood picture is variable, with anaemia, neutropenia and/or thrombocytopenia, and the patients with idiopathic BMFS/AA may have a risk of transformation into a myelodysplastic syndrome (MDS) and/or an acute myeloid leukaemia (AML), as ascertained for all inherited BMFS. We already reported four patients with different forms of BMFS/AA with chromosome anomalies as primary etiologic event: the chromosome changes exerted an effect on specific genes, namely RUNX1, MPL, and FLI1, leading to the disease. Results: We report two further patients with non-hereditary BM failure, with diagnosis of severe aplastic anaemia and pancytopenia caused by two different constitutional structural anomalies involving chromosome 8, and possibly leading to the disorder due to effects on the RUNX1T1 gene, which was hypo-expressed and hyper-expressed, respectively, in the two patients. The chromosome change was unbalanced in one patient, and balanced in the other one. Conclusions: We analyzed the sequence of events in the pathogenesis of the disease in the two patients, including a number of non-haematological signs present in the one with the unbalanced anomaly. We demonstrated that in these two patients the primary event causing BMFS/AA was the constitutional chromosome anomaly. If we take into account the cohort of 219 patients with a similar diagnosis in whom we made cytogenetic studies in the years 2003-2017, we conclude that cytogenetic investigations were instrumental to reach a diagnosis in 52 of them. We postulate that a chromosome change is the primary cause of BMFS/AA in a not negligible proportion of cases, as it was ascertained in 6 of these patients

Polymorphism in the neurofibromin gene, Nf1, is associated with antagonistic selection on wing size and development time in Drosophila melanogaster

In many invertebrates, body size shows genetically based clines, with size increasing in colder climates. Large body size is typically associated with prolonged development times. We consider variation in the CNS-specific gene neurofibromin 1 (Nf1) and its association with body size and development time. We identified two major Nf1 haplotypes in natural populations, Nf1-insertion-A and Nf1-deletion-G. These haplotypes are characterized by a 45-base insertion/deletion (INDEL) in Nf1 intron 2 and an A/G synonymous substitution (locus L17277). Linkage disequilibrium (LD) between the INDEL and adjacent sites is high but appears to be restricted within the Nf1 gene interval. In Australia, the frequency of the Nf1-insertion-A haplotype increases with latitude where wing size is larger, independent of the chromosomal inversion In(3R)Payne. Unexpectedly, the Nf1-insertion-A haplotype is negatively associated with wing size. We found that the Nf1-insertion-A haplotype is enriched in females with shorter development time. This suggests that the Nf1 haplotype cline may be driven by selection for development time rather than size; females from southern (higher latitude) D. melanogaster populations maintain a rapid development time despite being relatively larger, and the higher incidence of Nf1-insertion-A in Southern Australia may contribute to this pattern, whereas the effects of the Nf1 haplotypes on size may be countered by other loci with antagonistic effects on size and development time. Our results point to the potential complexity involved in identifying selection on genetic variants exhibiting pleiotropic effects when studies are based on spatial patterns or association studies

Critical Exponents of the 3D Ising Universality Class From Finite Size Scaling With Standard and Improved Actions

We propose a method to obtain an improved Hamiltonian (action) for the Ising universality class in three dimensions. The improved Hamiltonian has suppressed leading corrections to scaling. It is obtained by tuning models with two coupling constants. We studied three different models: the +1,-1 Ising model with nearest neighbour and body diagonal interaction, the spin-1 model with states 0,+1,-1, and nearest neighbour interaction, and phi**4-theory on the lattice (Landau-Ginzburg Hamiltonian). The remarkable finite size scaling properties of the suitably tuned spin-1 model are compared in detail with those of the standard Ising model. Great care is taken to estimate the systematic errors from residual corrections to scaling. Our best estimates for the critical exponents are nu= 0.6298(5) and eta= 0.0366(8), where the given error estimates take into account the statistical and systematic uncertainties.Comment: 55 pages, 12 figure

On the Possibility of Measuring the Gravitomagnetic Clock Effect in an Earth Space-Based Experiment

In this paper the effect of the post-Newtonian gravitomagnetic force on the mean longitudes $l$ of a pair of counter-rotating Earth artificial satellites following almost identical circular equatorial orbits is investigated. The possibility of measuring it is examined. The observable is the difference of the times required to $l$ in passing from 0 to 2$\pi$ for both senses of motion. Such gravitomagnetic time shift, which is independent of the orbital parameters of the satellites, amounts to 5$\times 10^{-7}$ s for Earth; it is cumulative and should be measured after a sufficiently high number of revolutions. The major limiting factors are the unavoidable imperfect cancellation of the Keplerian periods, which yields a constraint of 10$^{-2}$ cm in knowing the difference between the semimajor axes $a$ of the satellites, and the difference $I$ of the inclinations $i$ of the orbital planes which, for $i\sim 0.01^\circ$, should be less than $0.006^\circ$. A pair of spacecrafts endowed with a sophisticated intersatellite tracking apparatus and drag-free control down to 10$^{-9}$ cm s$^{-2}$ Hz$^{-{1/2}}$ level might allow to meet the stringent requirements posed by such a mission.Comment: LaTex2e, 22 pages, no tables, 1 figure, 38 references. Final version accepted for publication in Classical and Quantum Gravit

Infrared thermography to estimate vine water status: optimizing canopy measurements and thermal indices for the varieties Merlot and Moscato in northern Italy

This study investigated the effectiveness of infrared thermography to estimate water status in Merlot and Moscato grown in northeast Italy by comparing the crop water stress index (CWSI) and the stomatal conductance index (IG). The influence of the portion of the canopy in which the thermal images were captured (sunlit or shaded) was also investigated. During the 2018 growing season, potted vines were subjected to three irrigation treatments: T0 = 100% of daily water usage restored; T1 = 50% of daily water usage restored; and T2 = 30% of daily water usage restored. Measurements included stomatal conductance (gs), stem water potential (SWP), and thermal imagery. Results showed that both the CWSI and IG indices were effective in discriminating the irrigation treatments in Moscato and Merlot. CWSI showed higher correlations with gs and SWP compared to IG, especially in Moscato. CWSI was less influenced by the portion of the canopy the image was taken on. In general, Moscato showed greater differences in gs, SWP, and the thermal indices between the three irrigation treatments. This study suggests that the efficacy of thermography in estimating vine water status depends on the variety and its stomatal control physiology.Nicola Belfiore, Rosanna Vinti, Lorenzo Lovat, Walter Chitarra, Diego Tomasi, Roberta de Bei, Franco Meggio, and Federica Gaiott