An expansion for the number of partitions of an integer

The Ramanujan Journal - We consider p(n) the number of partitions of a natural number n, starting from an expression derived by Báez-Duarte in (Adv Math 125(1):114–120, 1997) by relating...     

Synthesis of novel nocathiacin-class antibiotics. Condensation of glycolaldehyde with primary amides and tandem reductive amination of amadori-rearranged 2-oxoethyl intermediates

Nocathiacin I (1) and nocathiacin IV (2) are novel indole-containing thiazolyl peptide antibiotics, which exhibit potent activity against key Gram-positive bacterial pathogens, including multi drug-resistant Staphylococcus aureus, Streptococcus pneumoniae, and Enterococcus faecium. New nocathiacins 7-12 were prepared from 2 by a condensation with glycolaldehyde followed by tandem reductive amination of the 2-oxoethyl intermediate 4. The latter was formed via Amadori rearrangement from initial 2-hydroxyethylideneamide 3. This transformation readily tolerates the complex architecture of nocathiacins and allows selective incorporation of water solubilizing groups to the primary amide in 2 without protecting group manipulation.     

Urinary phenylacetic acid determination by HPLC

Summary A high-performance liquid chromatographic method for urinary total phenylacetic acid (PAA) determination is reported for clinical diagnostic purpose in depressed patients.The urine samples are hydrolized in 6N HCl at 100°C. The hydrolized samples are then adsorbed on a C₈ reversed-phase extraction cartridge and eluted with 0.05 N NaOH. This solution is extracted on an anionexchange extraction cartridge and eluted with 0.1 M phosforic acid; the eluate is injected into HPLC and separated by reversed-phase liquid chromatography with ultraviolet detection at 225 nm. The extraction recovery is 93±2.8%, the retention time is 3.7 min and the PAA minimum detectable level is 4 mg/l.The normal value determined on 10 healthy subjects was 151.3±19.1 mg/day. Ten depressed subjects were investigated, and no difference in PAA excretion between normal and depressed subjects was observed. Also, the expected PAA enhancement in depressed subjects after treatment did not occur.     

An iterative scheme for variational inequalities

In this paper we introduce and study a general iterative scheme for the numerical solution of finite dimensional variational inequalities. This iterative scheme not only contains, as special cases the projection, linear approximation and relaxation methods but also induces new algorithms. Then, we show that under appropriate assumptions the proposed iterative scheme converges by establishing contraction estimates involving a sequence of norms in Eⁿ induced by symmetric positive definite matrices G_m. Thus, in contrast to the above mentioned methods, this technique allows the possibility of adjusting the norm at each step of the algorithm. This flexibility will generally yield convergence under weaker assumptions.     

A multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR

We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with Adaptive Mesh Refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate “level-solve” packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation (Ψtc). We analyze the magnitude of the Ψtc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichlet boundary data at the coarse–fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the “partial temperature” scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of Ψtc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory and demonstrates the inadequacy of gray diffusion.     

A novel and easy two-step,microwave-assisted method for the synthesis of halophenyl pyrrolo[2,3-b]quinoxalines via their pyrrolo precursors. Evaluation of their bioactivity

A novel, two-step, facile route for the synthesis of pyrrolo[2,3-b]quinoxalines via 2,3-dioxopyrroles, enhanced by microwave irradiation, is presented. The newly synthesized 2,3-dioxo-5-halophenyl pyrrolo precursors 4a–c as well as the non-aromatized ethyl 2-(4-halophenyl)-1-methyl-2,4-dihydro-1H-pyrrolo[2,3-b]quinoxaline-3-carboxylates 6a–c and the aromatized ethyl 2-(4-halophenyl)-1-methyl-1H-pyrrolo[2,3-b]quinoxaline-3-carboxylates 7a–c were evaluated for their antioxidant, cytostatic, and antiviral properties. Most of them proved to be potent hydroxyl radical scavengers and inhibited in vitro lipid peroxidation. The compounds showed moderate antiproliferative activity, while 6a inhibited vaccinia virus at an EC₅₀ value of 2 μM, and 4c and 6c inhibited Sindbis virus at EC₅₀ values of 4 μM.     

Functionalization and Dissolution of Single-Walled Carbon Nanotubes by Chemical-Physical and Electrochemical Treatments

Single-Walled Carbon Nanotubes (SWCNTs) possess a wealth of exceptional structural, mechanical and electronic properties. These have made them potentially useful for applications in nanotube-reinforced materials, nanoelectronic devices, field emitters, probe tips for SPM, as well as for sensors, biosensors, and actuators. However, manipulation and processing of SWCNTs has been limited by their insolubility in most common solvents, although some dissolution has recently been obtained. Their chemical modification might pave the way to many useful applications, including the preparation of composite materials or the immobilization of biological molecules as enzymes (i.e., for biosensors and electrochemical sensors). Attachment of oxygen-containing functional groups (i.e., carboxy groups, carbonyl groups, hydroxy groups, etc.) on the surface of the carbon nanotubes could be achieved using different pretreatments of the nanostructured material. These involved (a) chemical and physical procedures; and (b) electrochemical functionalization. Different attempts at sidewall modification have been hampered by the presence of significant contaminants as graphitic and amorphous carbon or have required solubilization via chemical reactions on the ends of cut nanotubes. A more accommodating and direct approach to functionalize nanotubes is therefore required. We report here the sidewall functionalization of purified SWCNTs, obtained by different approaches and finally, we can discuss possible applications of functionalized SWCNTs in the sensing area.     

Comprehensive two-dimensional liquid chromatography: Ion chromatography × reversed-phase liquid chromatography for separation of low-molar-mass organic acids

In the work presented here a novel approach to comprehensive two-dimensional liquid chromatography is evaluated. Ion chromatography is chosen for the first-dimension separation and reversed-phase liquid chromatography is chosen for the second-dimension separation mode. The coupling of these modes is made possible by neutralising the first-dimension effluent, containing KOH, prior to transfer to the second-dimension reversed-phase column. A test mixture of 24 low-molar-mass organic acids is used for optimisation of the system. Three food and beverage samples were analysed in order to evaluate the developed methodology, the resulting two-dimensional separation is near-orthogonal, the set-up is simple and all instrumental components are available commercially. The method proved to be robust and suitable for the analysis of wine, orange juice and yogurt.