Optimally ending an epidemic

A stochastic and controlled version of the classic three-dimensional Kermack–McKendrick model for the spread of epidemics is considered. The aim is to end the epidemic as soon as possible, taking the quadratic control costs into account. An exact and explicit solution is found in a particular case by making use of the method of similarity solutions to solve the partial differential equation satisfied by the value function, subject to the appropriate conditions.     

VT-NMR and cytotoxic evaluation of some new ortho-(alkylchalcogen)acetanilides

Several novel atropisomeric N-alkyl-N-[(2-alkylchalcogen)phenyl)]acetamides have been synthesized and fully characterized by ¹H and ¹³C NMR, FTIR, and HRMS (FAB). The barriers of the restricted rotation about the N-aryl bond between the two atropisomeric forms were measured by accurate lineshape simulation of variable temperature NMR (VT-NMR) spectra obtained in DMSO-d₆ solution and ranged from 17.0 to 20.5 kcal/mol. The relationship between the structure of the different acetanilide moieties and both coalescence temperature and energy of rotation are herein discussed. Taking in mind the acetamide structural resemblances with nimesulide related compounds known by their anticancer activity, the in vitro cytotoxicity of 20 representative acetanilides, against human breast (MCF-7) and prostate (LNCaP) cancer cell lines as well as normal human dermal fibroblasts (NHDF) was also preliminary evaluated. Interestingly a selective antiproliferative activity was observed for cancerous cells with prominence to LNCaP within the most potent O- and/or N-benzylic and -hexyl acetanilides.     

Oscillation for nonlinear second order dynamic equations on a time scale

We obtain some oscillation criteria for solutions to the nonlinear dynamic equation

xΔΔ+q(t)xΔσ+p(t)(f○xσ)=0,     

Determination of glyphosate and AMPA in surface and waste water using high-performance ion chromatography coupled to inductively coupled plasma dynamic reaction cell mass spectrometry (HPIC–ICP–DRC–MS)

A novel method employing high-performance cation chromatography in combination with inductively coupled plasma dynamic reaction cell mass spectrometry (ICP–DRC–MS) for the simultaneous determination of the herbicide glyphosate (N-phosphonomethylglycine) and its main metabolite aminomethyl phosphonic acid (AMPA) is presented. P was measured as ³¹P¹⁶O⁺ using oxygen as reaction gas. For monitoring the stringent target value of 0.1 μg L⁻¹ for glyphosate, applicable for drinking and surface water within the EU, a two-step enrichment procedure employing Chelex 100 and AG1-X8 resins was applied prior to HPIC–ICP–MS analysis. The presented approach was validated for surface water, revealing concentrations of 0.67 μg L⁻¹ glyphosate and 2.8 μg L⁻¹ AMPA in selected Austrian river water samples. Moreover, investigations at three waste water-treatment plants showed that elimination of the compounds at the present concentration levels was not straightforward. On the contrary, all investigated plant effluents showed significant amounts of both compounds. Concentration levels ranged from 0.5–2 μg L⁻¹ and 4–14 μg L⁻¹ for glyphosate and AMPA, respectively.     

Finite and infinite-horizon single vehicle routing problems with a predefined customer sequence and pickup and delivery

We consider the problem of finding the optimal routing of a single vehicle that starts its route from a depot and picks up from and delivers K different products to N customers that are served according to a predefined customer sequence. The vehicle is allowed during its route to return to the depot to unload returned products and restock with new products. The items of all products are of the same size. For each customer the demands for the products that are delivered by the vehicle and the quantity of the products that is returned to the vehicle are discrete random variables with known joint distribution. Under a suitable cost structure, it is shown that the optimal policy that serves all customers has a specific threshold-type structure. We also study a corresponding infinite-time horizon problem in which the service of the customers is not completed when the last customer has been serviced but it continues indefinitely with the same customer order. For each customer, the joint distribution of the quantities that are delivered and the quantity that is picked up is the same at each cycle. The discounted-cost optimal policy and the average-cost optimal policy have the same structure as the optimal policy in the finite-horizon problem. Numerical results are given that illustrate the structural results.     

Regulation of d-Band Centers in Localized CdS Homojunctions through Facet Control for Improved Photocatalytic Water Splitting

The accelerated kinetic behaviour of charge carrier transfer and its unhindered surface reaction dynamic process involving oxygenated-intermediate activation and conversion are urgently required in photocatalytic water (H₂O) overall splitting, which has not been nevertheless resolved yet. Herein, localized CdS homojunctions with optimal collocation of high and low index facets to regulate d-band center for chemically adsorbing and activating key intermediates (*-OH and *-O) have been achieved in H₂O overall splitting into hydrogen. Density functional theory, hall effect, and in situ diffuse reflectance infrared Fourier transform spectroscopy confirm that, electrons and holes are kinetically transferred to reductive high index facet (002) and oxidative low index facet (110) of the localized CdS homojunction induced by facet Fermi level difference to dehydrogenate *-OH and couple *-O for hydrogen and oxygen evolution, respectively, along with a solar conversion into hydrogen (STH) of 2.20 % by Air Mass 1.5 Global filter irradiation. These findings contribute to solving the kinetic bottleneck issues of photocatalytic H₂O splitting, which will further enhance STH.     

Palladium-Catalyzed Enantioselective C−H Olefination to Access Planar-Chiral Cyclophanes by Dynamic Kinetic Resolution

Planar-chiral cyclophanes have received increasing attention for drug discovery and catalyst design. However, the catalytically asymmetric synthesis of planar-chiral cyclophanes has been a longstanding challenge. We describe the first Pd(II)-catalyzed enantioselective C−H olefination of prochiral cyclophanes. The low rotational barrier of less hindered benzene ring in the substrates allows the reaction to proceed through a dynamic kinetic resolution. This approach exhibits broad substrate scope, providing the planar-chiral cyclophanes in high yields (up to 99 %) with excellent enantioselectivities (up to >99 % ee). The ansa chain length scope studies reveal that the chirality of the cyclophanes arises from the bond rotation constraint of the benzene ring around the macrocycle plane, rather than the C−N axis. The C−H activation approach is also applicable to the late-stage modification of bioactive molecules and pharmaceuticals.     

Finding common RNA pseudoknot structures in polynomial time

This paper presents the first polynomial time algorithm for finding common RNA substructures that include pseudoknots and similar structures. While a more general problem is known to be NP-hard, this algorithm exploits special features of RNA structures to match RNA bonds correctly in polynomial time. Although the theoretical upper bound on the algorithm?s time and space usage is high, the data-driven nature of its computation enables it to avoid computing unnecessary cases, dramatically reducing the actual running time. The algorithm works well in practice, and has been tested on sample RNA structures that include pseudoknots and pseudoknot-like tertiary structures.     

A branch and bound algorithm for dynamic resource allocation in population disease management

We embed an approximate dynamic program into a branch-and-bound framework to solve sequential resource allocation problems in population disease management. The proposed algorithm is capable of providing an optimality guarantee and getting bounds on the optimality gap of healthcare interventions. A numerical study on screening and treatment policy implementation for chronic hepatitis C virus (HCV) infection provides useful insights regarding HCV elimination for baby boomers.