Lee–Yang Theorems and the Complexity of Computing Averages

We study the complexity of computing average quantities related to spin systems, such as the mean magnetization and susceptibility in the ferromagnetic Ising model, and the average dimer count (or average size of a matching) in the monomer-dimer model. By establishing connections between the complexity of computing these averages and the location of the complex zeros of the partition function, we show that these averages are #P-hard to compute, and hence, under standard assumptions, computationally intractable. In the case of the Ising model, our approach requires us to prove an extension of the famous Lee–Yang Theorem from the 1950s.     

Porous microsphere of magnesium oxide as an effective sorbent for removal of volatile iodine from off-gas stream

Porous microspheres of magnesium oxide were synthesized by calcination of precursor obtained via hydrothermal method. A sample of microsphere was characterized by transmission electron microscopy, scanning electron microscopy–energy dispersion spectroscopy, X-ray diffraction, thermogravimetric analysis, N₂ adsorption–desorption isotherms, and BET surface area. The average pore size and surface area of the microsphere were found to be 9.0 nm and 83.1 m² g^?1, respectively. The performance of sorbent was investigated in a continuous adsorption system. Iodine adsorption on sorbent was studied by varying temperature of adsorption column, sorbent calcination temperature and initial concentration of iodine. The capacity of sorbent increased by ~25 % when calcination temperature was raised from 350 to 500 °C. The maximum iodine adsorption capacity of sorbent was found to be 196 mg g^?1 using Langmuir isotherm. These results indicate the microspherical form of MgO to be effective sorbent to capture iodine vapor from off-gas stream.     

Three-component reaction involving metal-free heteroannulation of N-Boc-3-amido indole, aryl aldehydes, and aromatic alkynes under microwave conditions: synthesis of highly diversified δ-carbolines

An efficient synthesis toward highly diversified δ-carbolines via one-pot multicomponent reaction using N-Boc-3-amido indoles, aryl aldehydes, and aromatic terminal alkynes under microwave conditions has been described.     

Regioselective intramolecular electrophilic substitution reactions involving π-deficient pyridine substrates: a new entry to pyridoquinazolines and benzo[h][1,6]naphthyridines

Regioselective intramolecular electrophilic substitution reactions have been described in π-deficient pyridine substrates tethered at C-2 to the aryl amine. The presence and nature of ring activating groups at C-6 led to the involvement of either N-1 or C-3 of the pyridine ring in the cyclization thereby leading to the regioselective synthesis of pyridoquinazolines and naphthyridines in excellent yields.     

M theory solution to the hierarchy problem

An old idea for explaining the hierarchy is strong gauge dynamics. We show that such dynamics also stabilizes the moduli in M theory compactifications on manifolds of G2 holonomy without fluxes. This gives stable vacua with softly broken supersymmetry, grand unification, and a distinctive spectrum of TeV and sub-TeV sparticle masses.     

Atomistic simulations to study crack tip behaviour in single crystal of bcc niobium and hcp zirconium

In this article, molecular dynamics based simulations were carried out to study the fracture toughness of single crystals of niobium (Nb) and zirconium (Zr). Separate set of simulations were performed with different orientations of crack plane in Nb and Zr. In each case, efforts were made to align the crack front with principal planes of corresponding crystal structure, that was bcc for Nb and hcp for Zr. Deformation in single crystal of Nb and Zr was governed either by twinning or emergence of dislocations from the crack tip and surfaces. The deformation mechanism in single crystal of Nb and Zr also helps in governing the overall toughness of the material, while deforming via twinning leads to higher change in the crack length, whereas dislocations emerging from the crack tip blunts the opening and improves the toughness.     

Sensitive Determination of Acetaminophen in the Presence of Dopamine and Pyridoxine Facilitated by their Extent of Interaction with Single‐walled Carbon Nanotubes

Single‐walled carbon nanotubes (SWCNTs) were immobilized on glassy carbon (GC) electrode by drop casting The resulting modified electrode (represented as GC/SWCNTs) efficiently oxidizes acetaminophen (AC), dopamine (DA) and pyridoxine (PY) by decreasing the respective oxidation potentials and increasing peak currents in comparison to bare GC electrode. The extent of lowering of overpotentials is in the order of AC>PY>DA, in agreement with the order of decrease in the HOMO‐LUMO energy gap (ΔE) of these analytes, as determined from Density Functional Theory (DFT) calculations. DFT calculations further reveal that due to the interaction of the analytes on the SWCNT(10,10) there is a negative charge density transfer (higher probability of electron transfer, lower ΔE value) to the frontier molecular orbitals of the analytes, which eases their oxidation. Since AC, DA and PY oxidize distinctly at distinct potential values, the present SWCNTs modified electrodes could be used to simultaneously determine them. Cyclic voltammetry, differential pulse voltammetry and amperometry techniques are utilized to understand the electrochemical characteristics of the analytes (AC, DA and PY) and subsequent sensing of them at the GC/SWCNTs electrode. The electrode is then applied to the determination of AC as a case study. Sensitivity, detection limit and linear calibration range for the AC are found to be 7.9 μA μM^?1 cm^?2, 1.1 μM and 2.0–100.0 μM, respectively. The increased electroactive surface area of the GC/SWCNTs increases the oxidation peak currents and hence increases the sensitivity of the determination.     

Synthesis of Novel 4‐Substituted Coumarins,Docking Studies,and DHODH Inhibitory Activity

Coumarins are the important class of naturally occurring heterocyclic compounds. Activities like antioxidant, antibacterial, anti‐inflammatory, and anticancer have been reported for coumarin derivatives. Present work details the synthesis of substituted coumarin‐4‐pyrrolones as well as coumarin‐4‐acetyl amino acids and their DHODH inhibitory activity, which is a dual target for malaria and cancer. Coumarin‐4‐acetic acids ( 2a – c ) were coupled with different methyl esters of α‐amino acids ( 3 ) giving rise to corresponding coumarin‐4‐acetyl amino acid methyl esters ( 4a – o ), which on hydrolysis under basic condition underwent cyclization forming substituted dihydropyrrole‐2‐ones ( 5a – i ), dihydroindolizine‐3‐ones ( 5j – l ), and dihydropyrrolizin‐3‐one ( 5m – o ). Acidic hydrolysis of the compounds ( 4a – o ) yielded corresponding coumarin‐4‐acetyl amino acids ( 6a – f ). The docking study was performed with the protein 4IGH (obtained from PDB) using Surflex–Dock module. The newly synthesized compounds were tested for DHODH inhibitory activity using Brequinar as the standard. Compound 6b showed remarkable inhibition compared with the standard, and the other compounds with terminal COOH showed moderate inhibition.     

Study on linear and nonlinear stability analysis of double diffusive electro-convection in couple stress anisotropic fluid-saturated rotating porous layer

The influence of rotation and electric field on the onset of double-diffusive convection in rotating anisotropic couple stress fluid embedded porous media, which is caused by the combined action of external AC electric field and heating from below, has been investigated in this study. The associated equations were solved using the normal mode technique in conjunction with the modified Brinkman model, with free-free and rigid-rigid boundary conditions. Solute concentration and temperature are treated as independent parameters for the two diffusive components. Finally, neutral stability curves have been sketched to show how various flow parameters affect neutral stability. It is noticed that electric field has destabilizing effect on thermodynamic convection while rotation couple stress parameters have a tendency to stabilize the physical system under consideration. Furthermore, heat and mass transport have been studied using non-linear analysis in unsteady case. It is found that rotation, couple stress, porous parameters has influence of declining heat and mass transport while electric and anisotropic parameters have effect of boosting up heat and mass transport.