Block partitions of sequences

Given a sequence A = (a ₁, …, a _n ) of real numbers, a block B of A is either a set B = {a _i , a _i+1, …, a _j } where i ≤ j or the empty set. The size b of a block B is the sum of its elements. We show that when each a _i ∈ [0, 1] and k is a positive integer, there is a partition of A into k blocks B ₁, …, B _k with |b _i ?b _j | ≤ 1 for every i, j. We extend this result in several directions.     

X-ray structural analysis and antitumor activity of new salicylic acid derivatives

Tetrakis-, tris-, bis-, and mono salicylic acid derivatives 1–4 were synthesized by reaction of methyl 2-hydroxy benzoate (methyl salicylate) with 2,2-bis (hydroxymethyl) propane-1,3-diol (pentaerythritol) in the presence of sodium. Yields of different salicyloyloxy derivatives were changed by varying the molar ratios of reactants. For compounds 2 and 3, X-ray structure analysis was performed, as well as molecular energy minimization, to define their conformation in terms of their energy minima. Comparison of crystal and energy minimized structures for these two compounds (2 and 3) revealed that the intramolecular hydrogen bonds play an important role, stabilizing conformation of the most part of the molecule. The antioxidant activity and cytotoxicity of the synthesized derivatives were evaluated in a series of in vitro tests, as well as 17β-hydroxysteroid dehydrogenase type 2 inhibition potency. Tetrakis salicyloyloxy derivative 1 expressed the highest antioxidant potency, tris salicyloyloxy derivative 2 was the best inhibitor of 17βHSD2 enzyme, while bis salicyloyloxy derivative 3 showed strong cytotoxicity against prostate and breast cancer cells with no cytotoxicity against healthy cells.     

Mukaiyama–Michael Reactions with trans‐2,5‐Diarylpyrrolidine Catalysts: Enantioselectivity Arises from Attractive Noncovalent Interactions,Not from Steric Hindrance

The scope of the enantioselective Mukaiyama–Michael reactions catalyzed by trans‐2,5‐diphenylpyrrolidine has been expanded to include both α‐ and β‐substituted enals. However, the rationalization of the observed enantioselectivity is far from obvious since the catalyst is not very sterically hindered. DFT calculations were carried out to rationalize the observed stereoselectivities. Transition states of the C?C bond formation between iminium intermediates and silyloxyfurans were located and their relative energies were used to estimate the stereoselectivity data. We find excellent agreement between the predicted and observed stereoselectivities. The analysis of intermolecular forces reveals that the enantioselectivity is mostly due to stabilizing noncovalent interactions between the reacting partners, not due to steric hindrance. The role of attractive noncovalent interactions in enantioselective catalysis may be underappreciated.     

A New Oxygen Containing Pyclen-Type Ligand as a Manganese(II) Binder for MRI and 52Mn PET Applications: Equilibrium,Kinetic, Relaxometric,Structural and Radiochemical Studies

A new pyclen-3,9-diacetate derivative ligand (H₂3,9-OPC2A) was synthesized possessing an etheric O-atom opposite to the pyridine ring, to improve the dissociation kinetics of its Mn(II) complex (pyclen = 3,6,9,15-tetraazabicyclo(9.3.1)pentadeca-1(15),11,13-triene). The new ligand is less basic than the N-containing analogue (H₂3,9-PC2A) due to the non-protonable O-atom. In spite of its lower basicity, the conditional stability of the [Mn(3,9-OPC2A)] (pMn = −log(Mn(II)), c_L = c_Mn(II) = 0.01 mM. pH = 7.4) remains unaffected (pMn = 8.69), compared to the [Mn(3,9-PC2A)] (pMn = 8.64). The [Mn(3,9-OPC2A)] possesses one water molecule, having a lower exchange rate with bulk solvents (k_ex²⁹⁸ = 5.3 ± 0.4 × 10⁷ s⁻¹) than [Mn(3,9-PC2A)] (k_ex²⁹⁸ = 1.26 × 10⁸ s⁻¹). These mild differences are rationalized by density-functional theory (DFT) calculations. The acid assisted dissociation of [Mn(3,9-OPC2A)] is considerably slower (k₁ = 2.81 ± 0.07 M⁻¹ s⁻¹) than that of the complexes of diacetates or bisamides of various 12-membered macrocycles and the parent H₂3,9-PC2A. The [Mn(3,9-OPC2A)] is inert in rat/human serum as confirmed by ⁵²Mn labeling (nM range), as well as by relaxometry (mM range). However, a 600-fold excess of EDTA (pH = 7.4) or a mixture of essential metal ions, propagated some transchelation/transmetalation in 7 days. The H₂3,9-OPC2A is labeled efficiently with ⁵²Mn at elevated temperatures, yet at 37 °C the parent H₂3,9-PC2A performs slightly better. Ultimately, the H₂3,9-OPC2A shows advantageous features for further ligand designs for bifunctional chelators.     

Demixing in polystyrene/methylcyclohexane solutions

Cloudpoint data for polystyrene/methylcyclohexane solutions extending over moderate ranges of pressure and molecular weight are available in the literature. Those data are supplemented with new results from this laboratory to fill in gaps and extend the MW range (to 761 ≤ MW/amu ≤ 2 × 10⁷). The resulting data net is discussed and reasons to extend studies to higher pressure are presented. © 1996 John Wiley & Sons, Inc.     

Adaptive Neuro-Fuzzy Inference System and a Multilayer Perceptron Model Trained with Grey Wolf Optimizer for Predicting Solar Diffuse Fraction

The accurate prediction of the solar diffuse fraction (DF), sometimes called the diffuse ratio, is an important topic for solar energy research. In the present study, the current state of Diffuse irradiance research is discussed and then three robust, machine learning (ML) models are examined using a large dataset (almost eight years) of hourly readings from Almeria, Spain. The ML models used herein, are a hybrid adaptive network-based fuzzy inference system (ANFIS), a single multi-layer perceptron (MLP) and a hybrid multi-layer perceptron grey wolf optimizer (MLP-GWO). These models were evaluated for their predictive precision, using various solar and DF irradiance data, from Spain. The results were then evaluated using frequently used evaluation criteria, the mean absolute error (MAE), mean error (ME) and the root mean square error (RMSE). The results showed that the MLP-GWO model, followed by the ANFIS model, provided a higher performance in both the training and the testing procedures.     

Role of the C3-substituted derivatives of cinchonidine in the enantioselective hydrogenation of ethyl pyruvate on Pt-alumina catalyst in AcOH

Summary The enantioselective hydrogenation of ethyl pyruvate (EtPy) was studied on Pt-alumina catalysts modified by C3-substituted cinchonidines (NC, A, B, C1, C2in Fig. 1) and for comparison by DHCDand MeO-DHCDin AcOH. The effect of the C3-substituent on the reaction rate and the enantioselectivity were examined. Using the Engelhard 4759 catalyst under mild experimental conditions (room temperature, hydrogen pressure 1 bar) such as DHCDthe (R)-ethyl lactate formed in excess (e.e.max: 79-91%)</o:p>     

A proof of the bounded graph conjecture

Summary An infinite graph is called bounded if for every labelling of its vertices with natural numbers there exists a sequence of natural numbers which eventually exceeds the labelling along any ray in the graph. We prove an old conjecture of Halin, which characterizes the bounded graphs in terms of four forbidden topological subgraphs.Oblatum 17-IV-1991 & 25-X-1991