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N-rich organic materials bearing polyphenolic moieties in their building networks and nanoscale porosities are very demanding in the context of designing efficient biomaterials or drug carriers for the cancer treatment. Here, we report the synthesis of a new triazine-based secondary-amine- and imine-linked polyphenolic porous organic polymer material TrzTFPPOP and explored its potential for in vitro anticancer activity on the human colorectal carcinoma (HCT 116) cell line. This functionalized (-OH, -NH-, -C=N-) organic material displayed an exceptionally high BET surface area of 2140 m2 g−1 along with hierarchical porosity (micropores and mesopores), and it induced apoptotic changes leading to high efficiency in colon cancer cell destruction via p53-regulated DNA damage pathway. The IC30, IC50, and IC70 values obtained from the MTT assay are 1.24, 3.25, and 5.25 μg/mL, respectively.

Mesoporous tungsten trioxide (WO3) was prepared from tungstic acid (H2WO4) as a tungsten precursor with dodecylamine (DDA) as a template to guide porosity of the nanostructure by a solvothermal technique. The WO3 sample (denoted as WO3-DDA) prepared with DDA was moulded on an electrode to yield efficient performance for visible-light-driven photoelectrochemical (PEC) water oxidation. Powder X-ray diffraction (XRD) data of the WO3-DDA sample calcined at 400°C indicate a crystalline framework of the mesoporous structure with disordered arrangement of pores. N2 physisorption studies show a Brunauer-Emmett-Teller (BET) surface area up to 57 m2 g-1 together with type IV isotherms and uniform distribution of a nanoscale pore size in the mesopore region. Scanning electron microscopy (SEM) images exhibit well-connected tiny spherical WO3 particles with a diameter of ca. 5 to 20 nm composing the mesoporous network. The WO3-DDA electrode generated photoanodic current density of 1.1 mA cm-2 at 1.0 V versus Ag/AgCl under visible light irradiation, which is about three times higher than that of the untemplated WO3. O2 (1.49 μmol; Faraday efficiency, 65.2%) was evolved during the 1-h photoelectrolysis for the WO3-DDA electrode under the conditions employed. The mesoporous electrode turned out to work more efficiently for visible-light-driven water oxidation relative to the untemplated WO3 electrode.

This article is a continuation of study of star-Menger selection properties in line of (Kočinac, 2009, 2015), where we mainly use covers consisting of Gδ sets with certain additional condition. It is observed that star-Mengerness is equivalent to the fact that every such type of cover of a space has a countable subcover. We improve this result by considering ‘subcovers of cardinality less than 𝔟’ instead of ‘countable subcovers’, which is our primary observation. We also show that it is possible to produce non normal spaces using box products and dense star-Menger subspaces.

We intend to localize the selection principles in uniform spaces (Kočinac, 2003) by introducing their local variations, namely locally γ-bounded spaces (where γ is Menger, Hurewicz or Rothberger). It has been observed that the difference between uniform selection principles and the corresponding local correlatives as introduced here is reasonable enough to discuss about these new notions. Certain observations using the critical cardinals (on the uniform selection principles which have not studied before) as well as preservation like properties (on the local versions) are presented. The interrelationships between the notions considered in this paper are outlined into an implication diagram. Certain interactions between these local variations are also investigated. We present several examples to illustrate the distinguishable behaviour of the new notions.

We primarily make a general approach to the study of open covers and related selection principles using the idea of statistical convergence in metric space. In the process we are able to extend some results in (Caserta et al. 2012; Chandra et al. 2020) where bornological covers and related selection principles in metric spaces have been investigated using the idea of strong uniform convergence (Beer and Levi, 2009) on a bornology. We introduce the notion of statistical- γ B s -cover, statistically-strong-𝔅-Hurewicz and statistically-strong-𝔅-groupable cover and study some of its properties mainly related to the selection principles and corresponding games. Also some properties like statistically-strictly Frèchet Urysohn, statistically-Reznichenko property and countable fan tightness have also been investigated in 𝐶(𝑋) with respect to the topology of strong uniform convergence τ B S .

Polychromium‐oxo‐deposited TiO2 (CrIIIxOy/TiO2) electrodes were fabricated by a simple electrochemical technique by using different TiO2 basal electrodes (anatase, rutile, and mixed polymorphic phases P25) as earth‐abundant photoanodes for visible‐light‐driven water oxidation. The high‐resolution transmission electron microscopy (HR‐TEM) observation illustrated that an CrIIIxOy layer with approximately 2–3 nm thickness was formed on the surface of the crystalline TiO2 particles. Upon visible‐light irradiation of the electrodes, the photoanodic current based on water oxidation was generated at the CrIIIxOy/TiO2 electrodes. However, the wavelength (below 620 nm) for photocurrent generation at CrIIIxOy/TiO2‐rutile was longer than that (below 560 nm) at CrIIIxOy/TiO2‐P25 by 60 nm, which is in agreement with the difference (0.2 eV) in the conduction band (CB) edge energy between rutile and anatase TiO2. This gives a quantitative account for the photocurrent generation based on interfacial charge transfer (IFCT) from Cr 3d of the deposited CrIIIxOy layer to the TiO2 CB. The photocurrent generated for CrIIIxOy/TiO2‐rutile was higher than that for CrIIIxOy/TiO2‐anatase, which is ascribed to 1) more effective CrIIIxOy deposition on the rutile particles, 2) a larger electrolyte/CrIIIxOy interface for water oxidation as a result of smaller rutile particles (ca. 30–40 nm) compared with larger P25 particles (ca. 40–80 nm), and 3) more effective use of visible light owing to the low energy IFCT transition of rutile. Earth‐abundant photoanode for water splitting: Polychromium‐oxo‐deposited TiO2 (CrIIIxOy/TiO2) electrodes were fabricated by a simple electrochemical technique by using different TiO2 basal electrodes (anatase, rutile, and mixed polymorphic phases P25) as earth‐abundant photoanodes. Visible‐light‐driven water oxidation was achieved based on interfacial charge transfer (IFCT) from Cr 3d of the CrIIIxOy layer to the TiO2 conduction band.

We study selection principles related to bornological covers using the notion of ideals. We consider ideals I and J on ω and standard ideal orderings 1 - 1 , KB and K . Relations between cardinality of a base of a bornology with certain selection principles related to bornological covers are established using cardinal invariants such as the modified pseudointersection number, the unbounding number and slaloms numbers. When I ≤ □ J for ideals I , J and □ ∈ { 1 - 1 , K B , K } , implications among various selection principles related to bornological covers are established. Under the assumption that ideal I has a pseudounion we show equivalences among certain selection principles related to bornological covers. Finally, the I - B s -Hurewicz property of X is investigated. We prove that I - B s -Hurewicz property of X coincides with the B s -Hurewicz property of X if I has a pseudounion. Implications or equivalences among selection principles, games and the I - B s -Hurewicz property which are obtained from our investigation are described in diagrams.

This article is a continuation of our investigations in the function space C ( X ) with respect to the topology τ B s of strong uniform convergence on B in line of (Chandra et al. in Indag Math 31:43-63, 2020; Das et al. in Topol Appl 310:108005, 2022) using the idea of strong uniform convergence (Beer and Levi in J Math Anal Appl 350:568-589, 2009) on a bornology. First we focus on the notion of the tightness property of ( C ( X ) , τ B s ) and some of its variations such as the supertightness, the Id-fan tightness and the T -tightness. Certain situations are discussed when C ( X ) is a k-space with respect to the topology τ B s . Next the notions of strong B -open game and γ B s -open game on X are introduced and some of its consequences are investigated. Finally, we consider discretely selective property and related games. On ( C ( X ) , τ B s ) several interactions between topological games related to discretely selective property, the Gruenhage game on ( C ( X ) , τ B s ) and certain games on X are presented.

We consider certain star versions of the Menger, Hurewicz and Rothberger properties. Few important observations concerning these properties are presented, which have not been investigated in earlier works. A variety of investigations is performed using Alster covers and critical cardinalities \\(\\mathfrak{d}\\), \\(\\mathfrak{b}\\) and \\({\\sf cov}(\\mathcal{M})\\). Our study explores further ramifications on the extent and Alexandroff duplicate. In the process we present investigations on the star versions of the Rothberger property and compare with similar prior observations of the star versions of the Menger and Hurewicz properties. We sketch few tables that interpret (mainly preservation-kind of) properties of the star selection principles obtained so far. We also present implication diagrams to explicate the interplay between the star selection principles.