The polarized Ramsey’s theorem

We study the effective and proof-theoretic content of the polarized Ramsey’s theorem, a variant of Ramsey’s theorem obtained by relaxing the definition of homogeneous set. Our investigation yields a new characterization of Ramsey’s theorem in all exponents, and produces several combinatorial principles which, modulo bounding for formulas, lie (possibly not strictly) between Ramsey’s theorem for pairs and the stable Ramsey’s theorem for pairs. We are grateful to D. Hirschfeldt, A. Montalbán, and R. Soare for making our collaboration possible and for helpful comments and suggestions. We thank J. Schmerl for first bringing the subject of polarized partitions to our attention and J. Mileti for his generous insights. We also thank one anonymous referee for valuable observations and corrections. The first author was partially supported by an NSF Graduate Research Fellowship.     

Multimodal investigations of trans-endothelial cell trafficking under condition of disrupted blood-brain barrier integrity

Background  

Stem cells or immune cells targeting the central nervous system (CNS) bear significant promises for patients affected by CNS disorders. Brain or spinal cord delivery of therapeutic cells is limited by the blood-brain barrier (BBB) which remains one of the recognized rate-limiting steps. Osmotic BBB disruption (BBBD) has been shown to improve small molecule chemotherapy for brain tumors, but successful delivery of cells in conjunction with BBBD has never been reported.     

Next Generation Access Network Deployment in Croatia: Optical Access Networks and Current IoT/5G Status

This paper gives an overview and background of optical access network deployment in Croatia. Optical access network development in Croatia has been put into a global as well as in the European Union context. All the challenges and the driving factors for optical access networks deployment are considered. Optical access network architectures that have been deployed by most of the investors in Croatian telecommunication market are presented, as well as the architectures that are in early phase of deployment. Finally, an overview on current status of mobile networks of the fifth generation and Internet of Things is given.     

J-inner matrix functions, interpolation and inverse problems for canonical systems, IV: Direct and inverse bitangential input scattering problems

Bitangential input scattering problems are formulated and analyzed for canonical integral systems. Special attention is paid to the case when the input scattering matrix is ap×q matrix valued function of Wiener class. Formulas for the solution of the inverse input scattering problem are obtained by reproducing kernel Hilbert space methods. A number of illustrative examples are presented. Additional examples for the case when the input scattering matrix is of Wiener class/rational will be presented in a future publication.     

Dissolution assay of theophylline, diprophylline and proxyphylline from a sustained release dosage form by high performance thin layer chromatography.

The content and dissolution rate of theophylline, diprophylline and proxyphylline from a sustained release formulation were determined by UV in situ densitometry. After separation the chromatographic zones corresponding to the spots of theophylline, diprophylline and proxyphylline on the high performance thin layer chromatographic plates were scanned in reflectance/absorbance mode at 275 nm. Quantification was performed with a second degree polynomial function over the range 40-200 ng for theophylline and 60-300 ng for diprophylline and proxyphylline. Percentages of dissolved theophylline, diprophylline and proxyphylline were monitored over 1, 3 and 6 h. The method was found to be simple, accurate, reliable, time-saving (up to 18 samples can be determined simultaneously) and low-cost.     

On three Krein extension problems and some generalizations

Three basic extension problems which were initiated by M. G. Krein are discussed and further developed. Connections with interpolation problems in the Carathéodory class are explained. Some tangential and bitangential versions are considered. Full characterizations of the classes of resolvent matrices for these problems are given and formulas for the resolvent matrices of left tangential problems are obtained using reproducing kernel Hilbert space methods.Dedicated to the memory of M. G. Krein, a beacon for us both.The authors wish to acknowledge the partial support of the Israel-Ukraine Exchange Program. D. Z. Arov also wishes to thank the Weizmann Institute of Science for partial support and hospitality; H. Dym wishes to thank Renee and Jay Weiss for endowing the chair which supports his research.     

New 3,4-Annelated Coumarin Derivatives: Synthesis, Antimicrobial Activity, Antioxidant Capacity, and Molecular Modeling

Summary.  The one pot reaction preparation, spectral analysis, and molecular modeling experiments on the new 3,4-annelated coumarin systems with bioactivity associated structural features are described. These provided the insight into the equilibrium of the respective tautomeric forms making possible the reconciliation of previously published spectral data with the structure assignments as well as the correction of erroneously established structures. The synthesized compounds were tested in a standard disk diffusion assay and displayed strong to moderate antimicrobial activity, with a promising new lead prototype compound (7-amino-9-hydroxy-5-oxa-7a,8,11-triazacyclopenta[b]phenanthren-6-one (5)) possessing greater activity that the antibiotics Ampicillin and Nystatin. Antioxidant capacities of the compounds, determined spectrophotometrically using a phosphomolybdenum method, were greater, and in the case of compound 5 four times the activity of α-tocopherol acetate.     

Determination of autoprotolysis constants of some non-aqueous solvents using coulometric titration

Autoprotolysis constants of acetonitrile, propionitrile, nitromethane, ethylene carbonate and dimethyl sulphoxide were determined using a coulometric — potentiometric method with a hydrogen/palladium electrode as generator. The method is based on the titration of a strong base, tetrabutylammonium hydroxide, with H⁺ ions generated by anodic oxidation of hydrogen dissolved in palladium. The titration was carried out in a galvanic cell with glass and calomel electrodes at 25°C. The pK_s values for the investigated solvents are: acetonitrile, 28.8; propionitrile, 24.6; nitromethane, 23.7; ethylene carbonate. 21.5; and dimethyl sulphoxide 29.1. These data are in accordance with those reported in the literature.     

Molecular structures and ab initio molecular orbital calculations of the optically active derivatives of 1-aminocyclopropane-1-carboxylic acid

The novel optically active derivatives of 2,2′-disubstituted-1-aminocyclopropane-1-carboxylic acid (−)-2 and (+)-3 were synthesised from the spiro-azlactone (+)-1. Oxidation of the diol moiety of (+)-3 gave by ring enlargement the racemic mixture of 2,3-dihydrofuran derivative (±)-6. This conversion is explained by stepwise rearrangement of the initially formed tetrasubstituted cyclopropanecarbaldehyde 4 through zwitterionic's reactive intermediate 5. The formation of (±)-6 is preferred energetically as established by ab initio calculations of the ground states and possible intermediates for that rearrangement. The crystal structure and absolute configuration of the compounds (+)-1, (−)-2, (+)-3 and (−)-7 were determined by single-crystal X-ray diffraction method. All four compounds possess Z-configuration of the cyclopropane ring. The dioxolane ring in the structures (+)-1 and (−)-2 adopts half-chair conformation, while the cyclopropane ring and geminally substituted groups in the structures (−)-2, (+)-3 and (−)-7 possess the anticlinal conformation. The molecules of the compound (+)-1 are connected by very weak intermolecular hydrogen bond of C-H?O type. In the compounds (−)-2, (+)-3 and (−)-7inter- and intramolecular hydrogen bonds of N-H?O type were observed. The spiro-compound (+)-1 exhibited a more pronounced inhibitory activity against the proliferation of murine leukemia and human T-lymphocytes cells than other type of tumor cell lines and normal human fibroblast cells.     

Genericity for Mathias forcing over general Turing ideals

We construct a homogeneous subspace of 2^ω whose complement is dense in 2^ω and rigid. Using the same method, assuming Martin’s Axiom, we also construct a countable dense homogeneous subspace of 2^ω whose complement is dense in 2^ω and rigid.