Local Lower Norm Estimates for Dyadic Maximal Operators and Related Bellman Functions

We provide lower \(L^{q}\) and weak \(L^{q}\)-bounds for the localized dyadic maximal operator on \(\mathbb {R}^{n}\), when the local \(L^{1}\) and the local \(L^{p}\) norms of the function are given. We actually do that in the more general context of homogeneous trees in probability spaces.     

Sharp Lorentz Estimates for Dyadic-like Maximal Operators and Related Bellman Functions

We precisely evaluate Bellman-type functions for the dyadic maximal operator on \(\mathbb {R}^{n}\) and of maximal operators on martingales related to local Lorentz-type estimates. Using a type of symmetrization principle, introduced for the dyadic maximal operator in earlier works of the authors, we precisely evaluate the supremum of the Lorentz quasinorm of the maximal operator on a function \(\phi \) when the integral of \(\phi \) is fixed and also the same Lorentz quasinorm of \(\phi \) is fixed. Also we find the corresponding supremum when the integral of \(\phi \) is fixed and several weak type conditions are given.     

On the denesting of nested square roots

We present the basic theory of denesting nested square roots, from an elementary point of view, suitable for lower level coursework. Necessary and sufficient conditions are given for direct denesting, where the nested expression is rewritten as a sum of square roots of rational numbers, and for indirect denesting, where the nested expression is rewritten as a sum of fourth-order roots of rational numbers. The theory is illustrated with several solved examples.     

Palmatine,a Bioactive Protoberberine Alkaloid Isolated from Berberis cretica,Inhibits the Growth of Human Estrogen Receptor-Positive Breast Cancer Cells and Acts Synergistically and Additively with Doxorubicin

Palmatine (PLT) is a natural isoquinoline alkaloid that belongs to the class of protoberberines and exhibits a wide spectrum of pharmacological and biological properties, including anti-cancer activity. The aim of our study was to isolate PLT from the roots of Berberis cretica and investigate its cytotoxic and anti-proliferative effects in vitro alone and in combination with doxorubicine (DOX) using human ER⁺/HER2⁻ breast cancer cell lines. The alkaloid was purified by column chromatography filled with silica gel NP and Sephadex LH-20 resin developed in the mixture of methanol: water (50:50 v/v) that provided high-purity alkaloid for bioactivity studies. The purity of the alkaloid was confirmed by high resolution mass measurement and MS/MS fragmentation analysis in the HPLC-ESI-QTOF-MS/MS-based analysis. It was found that PLT treatment inhibited the viability and proliferation of breast cancer cells in a dose-dependent manner as demonstrated by MTT and BrdU assays. PLT showed a quite similar growth inhibition on breast cancer cells with IC₅₀ values ranging from 5.126 to 5.805 µg/mL. In contrast, growth of normal human breast epithelial cells was not affected by PLT. The growth inhibitory activity of PLT was related to the induction of apoptosis, as determined by Annexin V/PI staining. Moreover, PLT sensitized breast cancer cells to DOX. Isobolographic analysis revealed synergistic and additive interactions between studied agents. Our studies suggest that PLT can be a potential candidate agent for preventing and treating breast cancer.     

Compact Metric Spaces and Weak Forms of the Axiom of Choice

It is shown that for compact metric spaces (X, d) the following statements are pairwise equivalent: “X is Loeb”, “X is separable”, “X has a we ordered dense subset”, “X is second countable”, and “X has a dense set G = ∪{G_n : n ∈ ω}, ∣G_n∣ < ω, with lim_n→∞ diam (G _n) = 0”. Further, it is shown that the statement: “Compact metric spaces are weakly Loeb” is not provable in ZF⁰ , the Zermelo‐Fraenkel set theory without the axiom of regularity, and that the countable axiom of choice for families of finite sets CAC_fin does not imply the statement “Compact metric spaces are separable”.     

A Family of Potent Ru(II) Photosensitizers with Enhanced DNA Intercalation: Bimodal Photokillers

A new family of Ru(II)‐based photosensitizers was synthesized and systematically characterized. The ligands employed to coordinate the ruthenium metal center were the commercially available 2,2′‐bipyridine and a pyridine‐quinoline hybrid bearing an anthracene moiety. The complexes obtained carry either or Cl^? counterions. These counterions determine the complexes' hydrophobic or hydrophilic character, respectively, therefore dictating their solubility in biologically related media. All photosensitizers exhibit characteristic, relatively strong and wide UV–Vis absorption spectral profiles. Their high efficiency in generating cytotoxic singlet oxygen was established (up to Φ_Δ ~0.8). Moreover, the interaction of these photosensitizers with double‐stranded DNA was studied fluoro‐ and photospectroscopically and their binding affinities were found to be of the order of 3 × 10⁷ M^?1. All complexes are photocytotoxic to DU145 human prostate cancer cells. The highest light‐induced toxicity was conferred by the photosensitizers bearing Cl^? counterions, probably due to the looser ionic “chaperoning” of Cl^?, in comparison to , leading to higher cell internalization.     

Comparison of PD BLADE with fat saturation (FS), PD FS and T2 3D DESS with water excitation (WE) in detecting articular knee cartilage defects

The purpose of this study, is to compare the sequences: 1) proton density (PD) BLADE (BLADE is a PROPELLER-equivalent implementation of the Siemens Medical System) with fat saturation (FS) coronal (COR), 2) PD FS COR, 3) multi-planar reconstruction (MPR) with 3 mm slice thickness and 4) multi-planar reconstruction (MPR) with 1.5 mm slice thickness, both from the T2 3D-double-echo steady state (DESS) with water excitation (WE) sagittal (SAG), regarding their abilities to identify changes in the femorotibial condyle cartilage in knee MRI examinations. Thirty three consecutive patients with osteoarthritis (18 females, 15 males; mean age 56 years, range 37–71 years), who had been routinely scanned for knee examination using the previously mentioned image acquisition techniques, participated in the study. A quantitative analysis was performed based on the relative contrast (ReCON) measurements, which were taken both on normal tissues as well as on pathologies. Additionally, a qualitative analysis was performed by two radiologists. Motion and pulsatile flow artifacts were evaluated. The PD BLADE FS COR sequence produced images of higher contrast between Menisci and Cartilage, Fluid and Cartilage, Pathologies and Cartilage as well as of the Conspicuousness Superficial Cartilage and it was found to be superior to the other sequences (p < 0.001). The sequences T2 3D DESS 1.5 mm and T2 3D DESS 3 mm were significantly superior to the PD BLADE FS COR and the PD FS COR sequences in the visualization of Bone and Cartilage and the Conspicuousness Deep Surface Cartilage. This pattern of results is also confirmed by the quantitative analysis. PD FS BLADE sequences are ideal for the depiction of the cartilage pathologies compared to the conventional PD FS and T2 3D DESS sequences.     

Elimination of motion,pulsatile flow and cross-talk artifacts using blade sequences in lumbar spine MR imaging

The purpose of this study is to evaluate the ability of T2 turbo spin echo (TSE) axial and sagittal BLADE sequences in reducing or even eliminating motion, pulsatile flow and cross-talk artifacts in lumbar spine MRI examinations. Forty four patients, who had routinely undergone a lumbar spine examination, participated in the study. The following pairs of sequences with and without BLADE were compared: a) T2 TSE Sagittal (SAG) in thirty two cases, and b) T2 TSE Axial (AX) also in thirty two cases. Both quantitative and qualitative analyses were performed based on measurements in different normal anatomical structures and examination of seven characteristics, respectively. The qualitative analysis was performed by experienced radiologists. Also, the presence of image motion, pulsatile flow and cross-talk artifacts was evaluated. Based on the results of the qualitative analysis for the different sequences and anatomical structures, the BLADE sequences were found to be significantly superior to the conventional ones in all the cases. The BLADE sequences eliminated the motion artifacts in all the cases. In our results, it was found that in the examined sequences (sagittal and axial) the differences between the BLADE and conventional sequences regarding the elimination of motion, pulsatile flow and cross-talk artifacts were statistically significant. In all the comparisons, the T2 TSE BLADE sequences were significantly superior to the corresponding conventional sequences regarding the classification of their image quality. In conclusion, this technique appears to be capable of potentially eliminating motion, pulsatile flow and cross-talk artifacts in lumbar spine MR images and producing high quality images in collaborative and non-collaborative patients.