On the ideal of functions with compact support in pointfree function rings

As usual, let RL\mathcal{R}L denote the ring of real-valued continuous functions on a completely regular frame L. We consider the ideals R_s(L)\mathcal{R}_{s}(L) and R_K(L)\mathcal{R}_{K}(L) consisting, respectively, of functions with small cozero elements and functions with compact support. We show that, as in the classical case of C(X), the first ideal is the intersection of all free maximal ideals, and the second is the intersection of pure parts of all free maximal ideals. A corollary of this latter result is that, in fact, R_K(L)\mathcal{R}_{K}(L) is the intersection of all free ideals. Each of these ideals is pure, free, essential or zero iff the other has the same feature. We observe that these ideals are free iff L is a continuous frame, and essential iff L is almost continuous (meaning that below every nonzero element there is a nonzero element the pseudocomplement of which induces a compact closed quotient). We also show that these ideals are zero iff L is nowhere compact (meaning that non-dense elements induce non-compact closed quotients).     

Novel class of hybrid natural products derived from lupeol as antimalarial agents

Thirty-four novel hybrid lupeol derivatives (4-18) were prepared and evaluated for antimalarial activity in vitro against Plasmodium falciparum. Three compounds (13d, 16a and 17a) have shown antimalarial activity at lower dose (10 microg mL(-1)) than lupeol.     

Photodynamic efficacy of chlorin p6: a pH dependent study in aqueous and lipid environment

Photodynamic efficacy of chlorin p6, a potential candidate of photodynamic therapy (PDT), has been studied at pH 5.0, 6.0 and 7.6 in aqueous and lipid environment. Increased chlorin p6 mediated photodynamic bleaching of N,N-dimethyl-4-nitrosoaniline (RNO), a measure of singlet oxygen yield, was obtained at higher pH. Rate of photodynamic bleaching of RNO was also higher at higher pH and the rate decreased with lowering in pH of irradiated solution. Photodynamic oxidation of tryptophan was also found to be higher at higher pH. Diminished oxidation of RNO was obtained with decrease in pH of irradiated solution. Both, RNO bleaching and tryptophan oxidation was significantly reduced by sodium azide, a known quencher of singlet oxygen. At lower pH, chlorin p6 mediated photodynamic malondialdehyde (MDA) and lipid hydroperoxide formation in egg lecithin liposome was higher. At higher pH chlorin p6 was found to be photodynamically more effective in aqueous environment whereas at lower pH chlorin p6 was photodynamically more effective in hydrophobic environment.     

Pointfree functional compactness

By introducing a conservative notion of functional compactness to frames and using frame-theoretic techniques, we identify two classes of topological spaces that can be densely embedded in functionally compact ones. Since θ-open elements of frames (corresponding in spaces to complements of Veličko’s [15] θ-closed subspaces) play an important role in functional compactness, we also study the concept of co-rigidity in frames and show that it is enjoyed by all θ-open elements of functionally compact frames. Dedicated to the memory of Sergio Salbany     

Validation of primary formaldehyde gas standards prepared by dynamic thermogravimetry through a tri-national comparison of gaseous formaldehyde amount fraction

A validation study for primary formaldehyde gas standards was performed at three National Metrology Institutes: the Korea Research Institute of Standards and Science (KRISS), the National Metrology Institute of Japan (NMIJ) and the National Institute of Metrology of China (NIM). The studied materials had a nominal amount fraction of 2 μmol/mol formaldehyde in nitrogen balance and were prepared in 10-L aluminum cylinders by KRISS. The impurities in the materials were analyzed using a gas chromatograph/atomic emission detector and a Fourier-transform infrared spectrometer (FTIR). The stability of the materials was assessed for 1 year by KRISS using paraformaldehyde as a source for the primary standard gas and a cavity ring-down spectrometer (CRDS) instrument as the measurement method. The amount fraction of formaldehyde in the materials decreased linearly by 0.74 % each month. The studied materials that exhibited similar linear rates of decline were distributed to the participants. After the measurement was completed by the participants, the materials were returned to KRISS and the stability analysis based on the primary standard maintained at KRISS was repeated. NMIJ analyzed the materials using paraformaldehyde as the source of the primary standard of formaldehyde and FTIR analysis, whereas NIM used trioxane as the primary standard gas source and CRDS analysis. The results of the comparison revealed good agreement between the results and were within the expanded uncertainty of 2 % although each of them used different combinations of methods in the generation of primary gas standards and measurements.     

Concerning P-frames, essential P-frames, and strongly zero-dimensional frames

We give characterizations of P-frames, essential P-frames and strongly zero-dimensional frames in terms of ring-theoretic properties of the ring of continuous real-valued functions on a frame. We define the m-topology on the ring RL{\mathcal{R}L} and show that if L belongs to a certain class of frames properly containing the spatial ones, then L is a P-frame iff every idealof RL{\mathcal{R}L} is m-closed. We define essential P-frames (analogously to their spatial antecedents) and show that L is a proper essential P frame iff all the nonmaximal prime ideals of RL{\mathcal{R}L} are contained in one maximal ideal. Further, we show that L is strongly zero-dimensional iff RL{\mathcal{R}L} is a clean ring, iff certain types of ideals of RL{\mathcal{R}L} are generated by idempotents.     

Photoinduced carbene generation from diazirine modified task specific phosphonium salts to prepare robust hydrophobic coatings

3-Aryl-3-(trifluormethyl)diazirine functionalized highly fluorinated phosphonium salts (HFPS) were synthesized, characterized, and utilized as photoinduced carbene precursors for covalent attachment of the HFPS onto cotton/paper to impart hydrophobicity to these surfaces. Irradiation of cotton and paper, as proof of concept substrates, treated with the diazirine-HFPS leads to robust hydrophobic cotton and paper surfaces with antiwetting properties, whereas the corresponding control samples absorb water readily. The contact angles of water were determined to be 139° and 137° for cotton and paper, respectively. In contrast, water placed on the untreated or the control samples (those treated with the diazirine-HFPS but not irradiated) is simply absorbed into the surface. Additionaly, the chemically grafted hydrophobic coating showed high durability toward wash cycles and sonication in organic solvents. Because of the mode of activation to covalently tether the hydrophobic coating, it is amenable to photopatterning, which was demonstrated macroscopically.     

Numerical modelling of storm surges in the Arabian Sea

Using the basic hydrodynamic equations governing motion in the sea, a coastal zone numerical model has been developed for the prediction of storm surges along the west coast of India. Numerical experiments were performed with the help of this model to simulate the surge generated by the devastating 1975 Porbandar cyclone. The results of the experiments were in good agreement with the reported values along the Gujarat coast.