On reduced semidefinite programs for second order moment bounds with applications

We show that the complexity of computing the second order moment bound on the expected optimal value of a mixed integer linear program with a random objective coefficient vector is closely related to the complexity of characterizing the convex hull of the points \(\{{1 \atopwithdelims (){\varvec{x}}}{1 \atopwithdelims (){\varvec{x}}}' \ | \ {\varvec{x}} \in {\mathcal {X}}\}\) where \({\mathcal {X}}\) is the feasible region. In fact, we can replace the completely positive programming formulation for the moment bound on \({\mathcal {X}}\), with an associated semidefinite program, provided we have a linear or a semidefinite representation of this convex hull. As an application of the result, we identify a new polynomial time solvable semidefinite relaxation of the distributionally robust multi-item newsvendor problem by exploiting results from the Boolean quadric polytope. For \({\mathcal {X}}\) described explicitly by a finite set of points, our formulation leads to a reduction in the size of the semidefinite program. We illustrate the usefulness of the reduced semidefinite programming bounds in estimating the expected range of random variables with two applications arising in random walks and best–worst choice models.     

An end-point global gradient weighted estimate for quasilinear equations in non-smooth domains

A weighted norm inequality involving A₁ weights is obtained at the natural exponent for gradients of solutions to quasilinear elliptic equations in Reifenberg flat domains. Certain gradient estimates in Lorentz–Morrey spaces below the natural exponent are also obtained as a consequence of our analysis.     

Electrochemically promoted Friedel-Crafts acylation of aromatic compounds

Friedel-Crafts acylation is carried out with several aromatic substrates in the presence of an electrochemically active aluminium anode to minimize the inorganic reagents. Only a catalytic amount of AlCl₃ (5 mol %) is required to enable the anodic polarization of the aluminium electrode to promote continuous acylation. This process typically gave products in good yields (70-96%).     

Amberlyst-15 catalyzed synthesis of novel thiophene–pyrazoline derivatives: spectral and crystallographic characterization and anti-inflammatory and antimicrobial evaluation

Increasing instances of antimicrobial drug resistance and Inflammation-mediated disorders requires the design and synthesis of new small-molecules with higher affinity and specificity for their potential targets to serve as antibiotics or anti-inflammatory drugs, respectively. The current study presents the synthesis of a series of chalcones, 3(a–h) by the reaction of 3-methylthiophene-2-carbaldehyde, 1 and acetophenones, 2(a–h) by Claisen–Schmidt approach. The chalcones were efficiently transformed into thienyl-pyrazolines, 5(a–h) by their reaction with thiosemicarbazide hydrochloride, 4 in the presence of Amberlyst-15 as a catalyst in acetonitrile at room temperature. Alternatively, the compounds 5(a–h) were prepared by conventional method using acetic acid (40%) medium. Structures were characterized by spectral and single crystal X-ray diffraction studies. Preliminary assessment of the anti-inflammatory properties of the compounds showed that, amongst the series, compounds 5b and 5c have excellent anti-inflammatory activities. Further, compound 5c showed excellent activity against Escherichia coli (MIC, 15 µg/mL), Bacillus subtilis (MIC, 20 µg/mL), Aspergillus niger (MIC, 20 µg/mL), and Aspergillus flavus (MIC 15 µg/mL), respectively. Compounds 5a and 5b were also found to be active against the tested microorganisms.     

Novel one pot synthesis of 2-amino-4-chloroquinolines via Smiles rearrangement

We have developed a novel one pot synthesis of 4-chloroquinolin-2-ylamines via Smiles rearrangement under milder condition. The key transformation involves O-alkylation of 4-chloro-1H-quinolin-2-ones with chloroacetamide followed by Smiles rearrangement. The scope of this methodology is further extended to the synthesis of 4-chloroquinolin-2-ylmethylamines and 2-(4-chloroquinolin-2-ylamino)ethanols. This methodology has furnished good yields of 2-amino-4-chloroquinolines.     

Conformational Change from a Twisted Figure‐Eight to an Open‐Extended Structure in Doubly Fused 36π Core‐Modified Octaphyrins Triggered by Protonation: Implication on Photodynamics and Aromaticity

Two examples of core‐modified 36π doubly fused octaphyrins that undergo a conformational change from a twisted figure‐eight to an open‐extended structure induced by protonation are reported. Syntheses of the two octaphyrins (in which Ar=mesityl or tolyl) were achieved by a simple acid‐catalyzed condensation of dipyrrane unit containing an electron‐rich, rigid dithienothiophene (DTT) core with pentafluorobenzaldehyde followed by oxidation with 2,3‐dichloro‐5,6‐dicyano‐1,4‐benzoquinone (DDQ). The single‐crystal X‐ray structure of the octaphyrin (in which Ar=mesityl) shows a figure‐eight twisted conformation of the expanded porphyrin skeleton with two DTT moieties oriented in a staggered conformation with a π‐cloud distance of 3.7 Å. Spectroscopic and quantum mechanical calculations reveal that both octaphyrins conform to a [4n]π nonaromatic electronic structure. Protonation of the pyrrole nitrogen atoms of the octaphyrins results in dramatic structural change, which led to 1) a large redshift and sharpening of absorption bands in electronic absorption spectrum, 2) a large change in chemical shift of pyrrole β‐CH and ? NH protons in the ¹H NMR spectrum, 3) a small increase in singlet lifetimes, and 4) a moderate increase in two‐photon absorption cross‐section values. Furthermore, nucleus‐independent chemical shift (NICS) values calculated at various geometrical positions show positive values and anisotropy‐induced current density (AICD) plots indicate paratropic ring‐currents for the diprotonated form of the octaphyrin (in which Ar=tolyl); the single‐crystal X‐ray structure of the diprotonated form of the octaphyrin shows an extended structure in which one of the pyrrole ring of each dipyrrin subunit undergoes a 180 ° ring‐flip. Four trifluoroacetic acid (TFA) molecules are bound above and below the molecular plane defined by meso‐carbon atoms and are held by N? H ??? O, N? H ??? F, and C? H ??? F intermolecular hydrogen‐bonding interactions. The extended‐open structure upon protonation allows π‐delocalization and the electronic structure conforms to a [4n]π Hückel antiaromatic in the diprotonated state.     

Choosing among heterogeneous server clouds

This paper considers a model of interest in cloud computing applications. We consider a multiserver system consisting of N heterogeneous servers. The servers are categorized into M(\(\ll N\)) different types according to their service capabilities. Jobs having specific resource requirements arrive at the system according to a Poisson process with rate \(N \lambda \). Upon each arrival, a small number of servers are sampled uniformly at random from each server type. The job is then routed to the sampled server with maximum vacancy per server capacity. If a job cannot obtain the required amount of resources from the server to which it is assigned, then the job is discarded. We analyze the system in the limit as \(N \rightarrow \infty \). This gives rise to a mean field, which we show has a unique fixed point and is globally attractive. Furthermore, as \(N\rightarrow \infty \), the servers behave independently. The stationary tail probabilities of server occupancies are obtained from the stationary solution of the mean field. Numerical results suggest that the proposed scheme significantly reduces the average blocking probability compared to static schemes that probabilistically route jobs to servers in proportion to the number of servers of each type. Moreover, the reduction in blocking holds even for systems at high load. For the limiting system in statistical equilibrium, our simulation results indicate that the occupancy distribution is insensitive to the holding time distribution and only depends on its mean.