Equality of higher numerical ranges of matrices and a conjecture of Kippenhahn on Hermitian pencils

Let M_n be the algebra of all n × n complex matrices. For 1 k n, the kth numerical range of A M_n is defined by W_k(A) = (1/k)∑_j^k=1x_j^*Ax_j : x₁, …, x_k is an orthonormal set in ⁿ]. It is known that tr A/n = W_n(A) W_n−1(A) W₁(A). We study the condition on A under which W_m(A) = W_k(A) for some given 1 m < k n. It turns out that this study is closely related to a conjecture of Kippenhahn on Hermitian pencils. A new class of counterexamples to the conjecture is constructed, based on the theory of the numerical range.     

Supramolecular assembly of Hoechst-33258 with cucurbit[7]uril macrocycle

Molecular assemblies of potential guest molecules through non-covalent host-guest interactions have found immense use in many applied areas. In this study supramolecular interaction of a biologically important dye Hoechst-33258 (H33258) has been investigated in aqueous solutions at different pHs, in the presence of a macrocyclic host, namely, cucurbit[7]uril (CB7). The pH dependent emission behaviour of H33258 is inherently connected with its protolytic equilibria which allow the dye in different geometrical conformations. This pH dependent structural orientation is greatly affected by the complexation with CB7. The significant structural changes in the monocationic H33258 brought out by CB7 at pH 7 have been documented in the fluorescence emission and lifetime data, which are comparatively less affected in case of the dicationic form, which is prominent in dye solutions at pH 4.5. The strong ion-dipole interactions provided by the carbonyl portals of the CB7 host adequately stabilize the CB7-H33258 complex, both in 1:1 and 2:1 stoichiometries at both the pH conditions. The Job's plot method, fluorescence anisotropy, NMR measurements and geometry optimization calculations confirm the stoichiometric arrangement and are found to be tunable with the addition of metal ions. The non-covalently stabilized assembly brings out large enhancement in the fluorescence emission due to the unique structural orientation attained by H33258, which reduces the non-radiative relaxation pathways. Comparison of the spectral data of the dye at different pH conditions in the absence and presence of CB7 proposes a large upward pK(a) shift due to CB7 encapsulation, thus providing a handy tool to modulate the photophysical characteristics of the guest molecules.     

Structure-based virtual screening,in silico docking,ADME properties prediction and molecular dynamics studies for the identification of potential inhibitors against SARS-CoV-2 Mpro

COVID-19 is a viral pandemic caused by SARS-CoV-2. Due to its highly contagious nature, millions of people are getting affected worldwide knocking down the delicate global socio-economic equilibrium. According to the World Health Organization, COVID-19 has affected over 186 million people with a mortality of around 4 million as of July 09, 2021. Currently, there are few therapeutic options available for COVID-19 control. The rapid mutations in SARS-CoV-2 genome and development of new virulent strains with increased infection and mortality among COVID-19 patients, there is a great need to discover more potential drugs for SARS-CoV-2 on a priority basis. One of the key viral enzymes responsible for the replication and maturation of SARS-CoV-2 is M^pro protein. In the current study, structure-based virtual screening was used to identify four potential ligands against SARS-CoV-2 M^pro from a set of 8,722 ASINEX library compounds. These four compounds were evaluated using ADME filter to check their ADME profile and druggability, and all the four compounds were found to be within the current pharmacological acceptable range. They were individually docked to SARS-CoV-2 M^pro protein to assess their molecular interactions. Further, molecular dynamics (MD) simulations was carried out on protein–ligand complex using Desmond at 100 ns to explore their binding conformational stability. Based on RMSD, RMSF and hydrogen bond interactions, it was found that the stability of protein–ligand complex was maintained throughout the entire 100 ns simulations for all the four compounds. Some of the key ligand amino acid residues participated in stabilizing the protein–ligand interactions includes GLN 189, SER 10, GLU 166, ASN 142 with PHE 66 and TRP 132 of SARS-CoV-2 M^pro. Further optimization of these compounds could lead to promising drug candidates for SARS-CoV-2 M^pro target.

     

Modeling of misalignment effects in microfluidic interconnects for modular bio‐analytical chip applications

Minimizing misalignments during the interconnection of microfluidic modules is extremely critical to develop a fully integrated microfluidic device. Misalignments arising during chip‐to‐chip or world‐to‐chip interconnections can be greatly detrimental to efficient functioning of microfluidic devices. To address this problem, we have performed numerical simulations to investigate the effect of misalignments arising in three types of interconnection methods: (i) end‐to‐end interconnection (ii) channel overlap when chips are stacked on top of each other, and (iii) tube‐in‐reservoir misalignment occurring due to the offset between the external tubing and the reservoir. For the case of end‐to‐end interconnection, the effect of misalignment was investigated for 0, 13, 50, 58, and 75% reduction in the available flow area at the location of geometrical misalignment. In the channel overlap interconnection method, various possible misalignment configurations were simulated by maintaining the same amount of misalignment (75% flow area reduction). The effect of misalignment in a tube‐in‐reservoir interconnection was investigated by positioning the tube at an offset of 164 μm from the reservoir center. All the results were evaluated in terms of the equivalent length of a straight pipe. The effect of Reynolds number (Re) was also taken into account by performing additional simulations of aforementioned cases at Re ranging between 0.075 ≤ Re ≤ 75. Correlations were developed and the results were interpreted in terms of equivalent length (L_e). Equivalent length calculations revealed that the effect of misalignment in tube‐in‐reservoir interconnection method was the least significant when compared to the other two methods of interconnection.     

Application of Response Surface Method for Studying the Role of Dissolved Oxygen and Agitation Speed on Gamma-Linolenic Acid Production

To study the effect of agitation speed (rpm) and dissolved oxygen concentration (DO) on the production of gamma linolenic acid by Mucor sp. RRL001, a central composite design experiment was performed in a 5-L stirred tank bioreactor. The design consisted of a total of 10 runs consisting of runs at five levels for each factor and was divided in two blocks. The ANOVA analysis and Pareto chart of effects suggested agitation speed (p = 0.0142) linear effect and DO concentration (p = 0.0342) quadratic effects were significant factors with significant contribution to the response. The validation run based on the optimum production zone in response surface plot resulted in the maximum 350.3 mg l⁻¹ GLA yield as compared with model predicted value of 340.7 mg l⁻¹. The study suggests that agitation rate is having more pronounced effect on GLA yield than dissolved oxygen concentration by ensuring enhanced mass transfer and by preventing wall growth at elevated agitation speed. Also, it shows that higher GLA yields can be obtained in a simple medium at moderate oxygen saturation and that the Mucor sp. RRL001 is resistant to high agitation linked shear stress and suitable for GLA production at higher scale.     

Hybrid synchronization of hyperchaotic Lu system

In this paper, we study the hybrid synchronization between two identical hyperchaotic Lu systems. Hybrid synchronization of hyperchaotic Lu system is achieved through synchronization of two pairs of states and anti-synchronization of the other two pairs of states. Active controls are designed to achieve hybrid synchronization between drive and response systems using the sum and difference of relevant variables of the chaotic systems. Numerical simulations are presented to evaluate the analysis and effectiveness of the controllers.     

Regio- and diastereoselective reduction of nonenolizable alpha-diketones to acyloins mediated by indium metal

[reaction: see text] Alpha-diketones are efficiently reduced with indium metal in methanol-water in the presence of NH(4)Cl, LiCl, or NaCl to give regio- and diastereoselectively the corresponding acyloins in good to excellent yield. The cleavage of the acyloins under Pb(OAc)(4)/MeOH-PhH condition provides a convenient and regioselective access to highly functionalized cyclopentane carboxaldehydes, potential building blocks in organic syntheses.     

A rapid and stereoselective route to the trans-hydrindane ring system

A short and stereoselective route to the trans-hydrindane derivative, a potential building block for the synthesis of steroidal and related molecules, was achieved by the operation of indium, tin, and ruthenium based reagents, starting from a tetrabromo norbornyl derivative.