Rounding Procedures for the Discrete Version of the Capacitated Economic Order Quantity Problem

The capacitated Economic Order Quantity problem (capacitated EOQ) is a well-known problem where products have to be shipped between two points with a vehicle of given capacity. Each shipment has a fixed cost, independent of the shipped quantity, and an inventory cost is generated in the two points. The problem consists in finding the optimal time between consecutive shipments, which minimizes the total cost. The problem is a capacitated variant of the EOQ problem and has a closed form solution. Since such solution is often irrational, it is often rounded to an integer value. In this paper we investigate the errors which are generated by rounding procedures to integer and powers-of-two values. We show that, although in the worst case a tight general relative error of 2 is generated by all the considered rounding procedures, the procedure which rounds to the best between the lower and upper values (integer or powers-of-two) has a performance of $\frac{1}{2}$ ( $\sqrt 2 + 1/\sqrt 2 $ )≈1.06 on classes of instances of high practical relevance.     

Electron delocalization in linearly pi-conjugated systems: a concept for quantitative analysis

Donor- and/or acceptor-substituted pi-conjugated systems represent an important class of compounds in organic chemistry. However, up to now, a general method to quantitatively address the efficiency of a conjugated path is still missing. In this work, a novel computational approach based on deletion energies and on second-order orbital interaction energies in a natural bond orbital (NBO) scheme is employed to quantitatively assess ("measure") delocalization energies. Moreover, the purpose of this work is to assess the efficiency of distinct pi-conjugated paths, that is, geminal, cis, and trans, as well as to predict the impact of substituents on a given backbone. This study is focused on various mono-, di-, tri-, and tetrasubstituted tetraethynylethenes (TEEs). These model systems are suitable for our analysis, because they offer distinct conjugation paths within the same molecule, and can also be substituted in multiple ways. Differences between conjugation paths, the effect of neighbor paths, and the impact of donor and acceptor substituents on the various paths are discussed.     

Synthesis and lectin binding ability of glycosamino acid-calixarenes exposing GlcNAc clusters

Novel calix[4 or 8]arene-based glycoconjugates exposing terminal N-acetyl-D-glucosamine clusters have been synthesized using amino acid-calixarenes as building blocks. The obtained glycosamino acid-calixarenes 9b-14b have lectin-binding ability and amplified inhibitory effects on erythrocyte agglutination induced by wheat germ (Triticum vulgaris) agglutinin (WGA). The inhibitory ability is dependent on the presence of the spacer and on the shape and rigidity of the calixarene skeleton.     

Novel rearrangements of 4-silyl-3-buten-2-ones

Two 4-silyl-3-buten-2-ones, 2a and 2c, underwent an interesting rearrangement involving migration of the allyl or phenyl group on the silicon atom to the adjacent enone carbon when treated with various bases.     

Nonmonotone Algorithms for Pattern Search Methods

This work deals with the solution of ill-conditioned unconstrained minimization problems by means of pattern search methods. To this end, the usual requirement of monotonic reduction of the objective function is relaxed and nonmonotone pattern search methods are proposed, which maintain the convergence properties of their monotone counterparts. Numerical experimentation on several well-known ill-conditioned functions is reported. The results highlight a class of pattern search methods which benefit very much by the introduction of nonmonotone strategies.     

Pyrrolo[3,4‐e][1,2,3]triazolo[1,5‐a]pyrimidine and pyrrolo[3,4‐d] [1,2,3]triazolo[1,5‐a]pyrimidine. New tricyclic ring systems of biological interest

Derivatives of the new ring system pyrrolo[3,4‐e][1,2,3] triazolo[1,5‐a]pyrimidine 6 were prepared in high yields in one step by reaction of 3‐azidopyrrole 3 and substituted acetonitriles. Compound 6b rearranged, upon heating in dimethyl sulfoxide in the presence of water, to pyrrolo[3,4‐d][1,2,3]triazolo‐[1,5‐a]pyrimidine 7.     

Kluyveromyces marxianus CBS 6556 growing cells as a new biocatalyst in the asymmetric reduction of substituted acetophenones

The use of microorganism growing cells is a well recognized methodology in biocatalyzed organic reactions. A non-conventional thermotolerant Kluyveromyces marxianus yeast strain was used for the bio-reduction of different arylketones. Differently substituted ketones were converted into the corresponding (S)-alcohols with up to 96% enantiomeric excess under very mild reaction conditions. Kluyveromyces marxianus represents a promising biocatalyst for the production of optically active 1-arylethanols.     

Incorporation of Ce3+ in crystalline Gd-silicate nanoclusters formed in silica

Structural and optical properties of sol–gel silica based glassceramics doped with 0.1 mol% Ce and codoped with Gd at high concentrations, from 5 mol% up to 40 mol%, are investigated and compared to those of analogous samples doped only with Ce. Raman scattering, transmission electron microscopy, and x-ray diffraction reveal the formation of Gd apatite-like silicate (Gd_4.67O(SiO₄)₃) and of Gd pyrosilicate (Gd₂Si₂O₇) nanophases whose morphology and crystallinity depend on the Gd concentration and thermal treatments. Optical absorption measurements demonstrate the role of the densification atmosphere in modifying the charge state of Ce ions. The incorporation of Ce³⁺ ions in the nanophases is put in evidence by photo- and radio-luminescence results.