Fair Division

Wills and inheritances have traditionally been a cause of much discord in families. Which is why, when Mr. Jagirdar drew up his will, he invited his friend, the mathematician Mr. Z to meet him at a popular coffee shop and sought his help! You see, the problem was that he wanted to bequeath his triangular plot of land (shown in Fig. 1), bordered on three sides by roads, to his sons, and he wanted to divide the property so that both sons received equal land area and equal access to the road

APC-AREA, perimeter and congruency

We continue our Low Floor High Ceiling series in which an activity is chosen – it starts by assigning simple age-appropriate tasks which can be attempted by all the students in the classroom. The complexity of the tasks builds up as the activity proceeds so that students are pushed to their limits as they attempt their work. There is enough work for all, but as the level gets higher, fewer students are able to complete the tasks. The point, however, is that all students are engaged and all of them are able to accomplish at least a part of the whole task

Investigating the reliability and validity of the Dutch versions of the illness management and recovery scales among clients with mental disorders

Background: The Illness Management and Recovery scales (IMRS) can measure the progress of clients’ illness self-management and recovery. Previous studies have examined the psychometric properties of the IMRS. Aims: This study examined the reliability and validity of the Dutch version of the IMRS. Method: Clients (n = 111) and clinicians (n = 40) completed the client and clinician versions of the IMRS, respectively. The scales were administered again 2 weeks later to assess stability over time. Validity was assessed with the Utrecht Coping List (UCL), Dutch Empowerment Scale (DES), and Brief Symptom Inventory (BSI). Results: The client and clinician versions of the IMRS had moderate internal reliability, with α = 0.69 and 0.71, respectively. The scales showed strong test–retest reliability, r = 0.79, for the client version and r = 0.86 for the clinician version. Correlations between client and clinician versions ranged from r = 0.37 to 0.69 for the total and subscales. We also found relationships in expected directions between the client IMRS and UCL, DES and BSI, which supports validity of the Dutch version of the IMRS. Conclusions: The Dutch version of the IMRS demonstrated good reliability and validity. The IMRS could be useful for Dutch-speaking programs interested in evaluating client progress on illness self-management and recovery

Limiting Molecular Twisting:Upgrading a Donor–Acceptor Dye to Drive H₂ Evolution

The donor–acceptor (D–A) dye 4-(bis-4-(5-(2,2-dicyano-vinyl)-thiophene-2-yl)-phenyl-amino)-benzoic acid (P1) has been frequently used to functionalize NiO photocathodes and induce photoelectrochemical reduction of protons when coupled to a suitable catalyst. Photoinduced twisting of the P1 dye is steered on NiO by co-adsorption of tetradecanoic acid (C14, myristic acid (MA)). Density Functional Theory and time-resolved photoluminescence studies confirm that twisting lowers the energy levels of the photoexcited D–A dye. The apolar environment provided by the MA suppresses photoinduced D–A twisting, retards charge recombination following photoinduced charge separation between P1 and NiO, and provides a larger electrochemical potential increasing the photocurrent. Very interestingly, co-adsorption of MA induces H2 evolution upon photoexcitation without the presence of an H2 evolution catalyst. Based on prior art, the formation of H2 is assigned to the dissolution of Ni2+, followed by reduction and re-deposition of Ni nanoparticles acting as the catalytically active site. It propose that only excited P1 with suppressed twisting provides the sufficient electrochemical potential to induce deposition of Ni nanoparticles. The work illustrates the importance of understanding the effects of photoinduced intramolecular twisting and highlights the promise of designing twisting-limited D–A dyes to create efficient solar fuel devices.</p

High‐Load Core@Shell Nanocarriers with Irinotecan and 5‐Fluorouracil for Combination Chemotherapy in Colorectal Cancer

Colorectal cancer (CRC) is the third most common cancer type and second leading cause of cancer-related deaths worldwide, requiring novel drug-delivery concepts. ITC@ZrO(TocP)/ZrO(FdUMP) core@shell nanocarriers (designated ITC-FdUMP-NC) with the clinically relevant chemotherapeutics irinotecan (ITC) and fluoro-2 0-deoxyuridine-5 0-phosphate (FdUMP) (active derivative of 5 0-fluorouracil/5-FU) are a new type of nanocarrier with high drug payload (22 wt% of lipophilic ITC: particle core; 10 wt% of hydrophilic FdUMP: particle shell). The nanocarriers are tested in different CRC cell lines, a normal cell line, and rectal cancer patient-derived organoids (PDOs). Fluorescence-labeled nanocarriers show efficient uptake by all CRC cells and allow to distinctly track the intracellular trafficking toward endolysosomal ompartments. Although free chemotherapeutic drugs exhibit a greater potency in 2D cell cultures, ITC-FdUMP-NC demonstrate equivalent cytotoxic efficacies as the freely dissolved drugs in the more complex 3D rectal cancer PDOs. The sustained drug-release profile of the nanocarriers contrasts favorably with conventional free drugs, potentially enhancing the therapeutic outcome in vivo. With a chemotherapeutic cocktail comparable to the clinically applied FOLFIRI (ITC þ 5-FU), the ITC-FdUMP-NC represent a novel type of nanocarrier with high anti-tumor effect and high drug payload, offering a promising strategy to circumvent chemoresistance and to improve therapy efficacy in vivo with less side effects

Myosin-I nomenclature.

We suggest that the vertebrate myosin-I field adopt a common nomenclature system based on the names adopted by the Human Genome Organization (HUGO). At present, the myosin-I nomenclature is very confusing; not only are several systems in use, but several different genes have been given the same name. Despite their faults, we believe that the names adopted by the HUGO nomenclature group for genome annotation are the best compromise, and we recommend universal adoption