A lower bound in Nehari's theorem on the polydisc

By theorems of Ferguson and Lacey (d=2) and Lacey and Terwilleger (d>2), Nehari's theorem is known to hold on the polydisc D^d for d>1, i.e., if H_\psi is a bounded Hankel form on H^2(D^d) with analytic symbol \psi, then there is a function \phi in L^\infty(\T^d) such that \psi is the Riesz projection of \phi. A method proposed in Helson's last paper is used to show that the constant C_d in the estimate \|\phi\|_\infty\le C_d \|H_\psi\| grows at least exponentially with d; it follows that there is no analogue of Nehari's theorem on the infinite-dimensional polydisc

Some results on the lattice parameters of quaternionic Gabor frames

Gabor frames play a vital role not only modern harmonic analysis but also in several fields of applied mathematics, for instances, detection of chirps, or image processing. In this work we present a non-trivial generalization of Gabor frames to the quaternionic case and give new density results. The key tool is the two-sided windowed quaternionic Fourier transform (WQFT). As in the complex case, we want to write the WQFT as an inner product between a quaternion-valued signal and shifts and modulates of a real-valued window function. We demonstrate a Heisenberg uncertainty principle and for the results regarding the density, we employ the quaternionic Zak transform to obtain necessary and sufficient conditions to ensure that a quaternionic Gabor system is a quaternionic Gabor frame. We conclude with a proof that the Gabor conjecture do not hold true in the quaternionic case

Characterization of individual airborne particles in Taiyuan City, China

Taiyuan, the capital of Shanxi province, China, is one of the most polluted cities in the world. To characterize the ambient particulate pollution, samples of particulates with aerodynamic diameter less than 10 µm (PM(10)) were collected during a 6-day campaign. Individual particles were analyzed by Scanning Electron Microscope with Energy-Dispersive Spectrometer (SEM-EDS) to determine their chemical composition. Meanwhile, photomicrographs were obtained from SEM to aid in particles’ source identification. The lumped data from SEM-EDS were subjected to hierarchical cluster analysis (HCA) to sort out particle types chemically. HCA combined with SEM photomicrographs allowed us to identify 20 different particle types, namely (in order of particle frequency), soil/fly ash particles, coal-burning, sulfur-rich, and iron-rich particles, gypsum, syngenite, quartz, cement, silicon sulfide, siliconferro alloy, calcium-rich particles, ferrochromium alloy, ammonium sulfate and chloride, iron-zinc, ammonium chloride, molybdenum-rich, potassium sulfate, dolomite, lead sulfate, and copper-rich particles. Their possible origins and pathways are suggested. The majority of the particles seem to originate from coal combustion, which conforms to Taiyuan’s industrial structure

Studies of acid deposition and its effects in two small catchments in Hunan, China

International audienceAcid deposition and its effects were studied by analysing the chemistry in precipitation, stream water, soil water and soils in two catchments in Hunan. One site, Linkesuo (denoted LKS), is on the outskirts of Changsha, the provincial capital of Hunan, the other (Bailutang, denoted BLT) on the outskirts of Chenzhou in southern Hunan. Volume-weighted average pH values and sulphate concentrations in wet deposition were 4.58 (BLT) and 4.90 (LKS) and 174 ?molc L-1 and 152 ?molc L-1, respectively. Wet deposition of sulphate has been estimated as 4.3 gS m-2yr-1 and 3.4 gS m-2yr-1 at BLT and LKS, respectively. Estimates of the corresponding total depositions (dry + wet) are 6.1 gS m-2yr-1 and 5.3 gS m-2yr-1. In precipitation and throughfall, sulphate was the major anion and calcium the major cation. In stream and soil water, nitrate was slightly higher than sulphate on an equivalent basis and magnesium (Mg) not much lower than calcium (Ca). Important soil properties, such as soil pH, soil organic matter (SOM) content, exchangeable acidic cations, exchangeable base cations, effective cation exchange capacity (CECe), base saturation (BS), and aluminium (Al) and iron (Fe) pools, were determined for five forest soil profiles (consisting of four horizons) in each of the two catchments. The soils in BLT are generally more acid, have lower BS and higher Al and Fe pools than the LKS soils. The Al- and Fe-pools were generally higher in the topsoils (i.e. the O and A horizons) than in deeper soils (i.e. E and B horizons) especially at the most acidic site (BLT). There are significant correlations between Fe-pools and the corresponding Al-pools in both catchments except between the amorphous Feox and Alox. Considering the long-term high deposition of sulphate, there is a risk of future ecological damage due to acidification, especially in the BLT catchment, although vegetation damage has yet to be observed in the catchments. This condition appears to be representative of a large part of Hunan. Keyword: acid deposition, soil acidification, catchment, Al-pools, Fe-pools, Hunan</p

Analytic Representation of Finite Quantum Systems

A transform between functions in R and functions in Zd is used to define the analogue of number and coherent states in the context of finite d-dimensional quantum systems. The coherent states are used to define an analytic representation in terms of theta functions. All states are represented by entire functions with growth of order 2, which have exactly d zeros in each cell. The analytic function of a state is constructed from its zeros. Results about the completeness of finite sets of coherent states within a cell are derived

Analysis of iron-containing compounds in different compartments of the rat liver after iron loading

The livers of iron-loaded rats were fractionated and a cytosolic fraction, a lysosomal fraction, a siderosomal fraction and haemosiderin were obtained. All iron-containing compounds from these fractions were isolated and their morphology, Fe/P ratios, iron core diameter and peptide content were compared. The cytosolic fraction contained ferritin (CF) and a slower sedimenting, light ferritin (CLF). The lysosomal fraction also contained ferritin (LF) and a slower sedimenting light ferritin (LLF). The siderosomal fraction contained ferritin (SF), a faster sedimenting non-ferritin iron compound (SIC) and haemosiderin (HS). SIC and HS did not resemble ferritin as much as the other products did, but were found to be water-insoluble aggregates. The Fe/P ratios of CF and CLF were lower than the Fe/P ratios of LF and LLF and these in turn had lower Fe/P ratios than SF, SIC and HS. The iron core diameter of the cytosolic ferritin was increased after lysosomal uptake. The iron core diameters of the siderosomal products were smaller. CLF, CF, LF, LLF and SF contained one kind of subunit of approximately 20.5 kDa. SIC and HS contained other peptides in addition to the 20.5-kDa subunit. The results indicate that storage of ferritin molecules is not limited to the cytosolic compartment, but is also the case in the lysosomes. Extensive degradation of the ferritin molecule seems to be confined to the siderosomes

Quantum theta functions and Gabor frames for modulation spaces

Representations of the celebrated Heisenberg commutation relations in quantum mechanics and their exponentiated versions form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric quantization, quantum tori, classical and quantum theta functions) and signal analysis (Gabor analysis). In this paper we try to bridge the two communities, represented by the two co--authors: that of noncommutative geometry and that of signal analysis. After providing a brief comparative dictionary of the two languages, we will show e.g. that the Janssen representation of Gabor frames with generalized Gaussians as Gabor atoms yields in a natural way quantum theta functions, and that the Rieffel scalar product and associativity relations underlie both the functional equations for quantum thetas and the Fundamental Identity of Gabor analysis.Comment: 38 pages, typos corrected, MSC class change

Acid rain in Europe and the United States: an update.

Abstract This paper discusses the evolution of science and policies to control acid rain in Europe and the United States over the past several decades. Acid rain gained prominence in the late 1960s because of its perceived effects on ecosystem integrity. Extensive research efforts in both Europe and the United States, however, have concluded that the effects of acid rain-at least those on terrestrial ecosystems-were less serious than originally believed. More recently, interest in controlling acid rain precursors stems primarily from health concerns, particularly their effects in the form of fine particulate matter. The paper discusses the emergence of acid rain as an environmental concern, scientific evidence about the effects of acidic deposition on natural ecosystems, US and European acid rain control policies, studies of the costs and benefits of reducing acid rain, and different policy contexts in Europe and the United States

Inhibition of O-GlcNAc transferase activates tumor-suppressor gene expression in tamoxifen-resistant breast cancer cells

In this study, we probed the importance of O-GlcNAc transferase (OGT) activity for the survival of tamoxifen-sensitive (TamS) and tamoxifen-resistant (TamR) breast cancer cells. Tamoxifen is an antagonist of estrogen receptor (ERa), a transcription factor expressed in over 50% of breast cancers. ERa-positive breast cancers are successfully treated with tamoxifen; however, a significant number of patients develop tamoxifen-resistant disease. We show that in vitro development of tamoxifenresistance is associated with increased sensitivity to the OGT small molecule inhibitor OSMI-1. Global transcriptome profiling revealed that TamS cells adapt to OSMI-1 treatment by increasing the expression of histone genes. This is known to mediate chromatin compaction. In contrast, TamR cells respond to OGT inhibition by activating the unfolded protein response and by significantly increasing ERRFI1 expression. ERRFI1 is an endogenous inhibitor of ERBB-signaling, which is a known driver of tamoxifen-resistance. We show that ERRFI1 is selectively downregulated in ERa-positive breast cancers and breast cancers driven by ERBB2. This likely occurs via promoter methylation. Finally, we show that increased ERRFI1 expression is associated with extended survival in patients with ERa-positive tumors (p = 9.2e-8). In summary, we show that tamoxifen-resistance is associated with sensitivity to OSMI-1, and propose that this is explained in part through an epigenetic activation of the tumor-suppressor ERRFI1 in response to OSMI-1 treatment.Peer reviewe