The influence of a transverse magnetic field on a subnormal glow discharge in air

In subnormal glow discharge under d.c. excitation at different pressure in a varying transverse magnetic field (0 to 30 G) some measurements have been carried out for various initial average tube currents. The voltage across the discharge increases and average tube current and residual current decreases in the magnetic field. With the help of Beckman’s expression [4] for the axial field and the electron density distribution in a transverse magnetic field the observed variation of current and voltage can be satisfactorily explained. The variation of axial electric field with transverse magnetic field can be represented to a fair degree of accuracy by the derived equation. The behaviour of residual current with magnetic field has been observed in these oscillations.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Structure, interactions, and antibacterial activities of MSI-594 derived mutant peptide MSI-594F5A in lipopolysaccharide micelles: role of the helical hairpin conformation in outer-membrane permeabilization

Lipopolysaccharide (LPS) provides a well-organized permeability barrier at the outer membrane of Gram-negative bacteria. Host defense cationic antimicrobial peptides (AMPs) need to disrupt the outer membrane before gaining access to the inner cytoplasmic membrane or intracellular targets. Several AMPs are largely inactive against Gram-negative pathogens due to the restricted permeation through the LPS layer of the outer membrane. MSI-594 (GIGKFLKKAKKGIGAVLKVLTTG) is a highly active AMP with a broad-spectrum of activities against bacteria, fungi, and virus. In the context of LPS, MSI-594 assumes a hairpin helical structure dictated by packing interactions between two helical segments. Residue Phe5 of MSI-594 has been found to be engaged in important interhelical interactions. In order to understand plausible structural and functional inter-relationship of the helical hairpin structure of MSI-594 with outer membrane permeabilization, a mutant peptide, termed MSI-594F5A, containing a replacement of Phe5 with Ala has been prepared. We have compared antibacterial activities, outer and inner membrane permeabilizations, LPS binding affinity, perturbation of LPS micelles structures by MSI-594 and MSI-594F5A peptides. Our results demonstrated that the MSI-594F5A has lower activities against Gram-negative bacteria, due to limited permeabilization through the LPS layer, however, retains Gram-positive activity, akin to MSI-594. The atomic-resolution structure of MSI-594F5A has been determined in LPS micelles by NMR spectroscopy showing an amphipathic curved helix without any packing interactions. The 3D structures, interactions, and activities of MSI-594 and its mutant MSI-594F5A in LPS provide important mechanistic insights toward the requirements of LPS specific conformations and outer membrane permeabilization by broad-spectrum antimicrobial peptides.     

Finite frames,P-frames and basically disconnected frames

Let \({\mathcal{P}}\) be an ideal of closed quotients of a completely regular frame L and \({\mathcal{R}_{\mathcal{P}}(L)}\) the collection of all functions in the ring \({\mathcal{R}(L)}\) whose support belong to \({\mathcal{P}}\) . We show that \({\mathcal{R}(L)}\) is a Noetherian ring if and only if \({\mathcal{R}(L)}\) is an Artinian ring if and only if L is a finite frame. Using this result, we next show that if \({\mathcal{P}}\) is the ideal of all compact closed quotients of L and L is \({\mathcal{P}}\) -continuous, then \({\mathcal{R}_{\mathcal{P}}(L)}\) is a Noetherian ring if and only if L is finite. Moreover, we show that L is a P-frame if and only if each ideal of \({\mathcal{R}(L)}\) is of the form \({\mathcal{R}_{\mathcal{P}}(L)}\) for some choice of \({\mathcal{P}}\) . We furnish equivalent conditions for \({\mathcal{R}_{\mathcal{P}}(L)}\) to be a prime ideal, a free ideal, and an essential ideal of \({\mathcal{R}(L)}\) separately in terms of the cozero elements of L. Finally, we show that L is basically disconnected if and only if \({\mathcal{R}(L)}\) is a coherent ring.     

Two valued measure and summability of double sequences

In this paper, following the methods of Connor [2], we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely [12]) to μ-statistical convergence and convergence in μ-density using a two valued measure μ. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure μ called the (APO₂) condition, inspired by the (APO) condition of Connor [3]. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure μ has the condition (APO₂).     

Derivatization of Coumarins at the Benzenoid Ring in Aqueous Medium

Some 6‐disubstituted, 8‐disubstituted, and/6,8‐disubstituted compounds have been prepared from coumarin, 7‐methylcoumarin, and 3,4‐benzocoumarin. The Reimer–Tiemann reaction, Lederer–Manasse reaction, bromination using molecular bromine as well as 2,4,4,6‐tetrabromocyclohex‐2,5‐dien‐1‐one, Elbs reaction, and diazocoupling have been carried under controlled conditions to obtain various derivatives. Further, several reactions of aldehyde derivatives of these coumarins have been carried on to prepare important functional compounds including some heterocycles. It is noteworthy that these aldehydes behave as phenolic aldehydes under alkaline conditions to undergo the Dakin reaction. The reactions are mostly carried in aqueous media involving a dianionic intermediate and hence fulfill one important criterion of green chemistry.     

Gold-catalyzed 1,2-difunctionalizations of aminoalkynes using only N- and O-containing oxidants

We report two viable routes for the 1,2-difunctionalization of aminoalkynes using only oxidants. In the presence of a gold catalyst, nitrones enable the oxoamination of aminoalkynes 1 to form 2-aminoamides 2. With a suitable gold catalyst, nitrosobenzenes implement an alkyne/nitroso metathesis of the same substrates to give 2-oxoiminylamides 3. These two novel oxidations also provide 1,2-aminoalcohols with opposite regioselectivity via NaBH(4) reduction in situ.     

Two valued measure and summability of double sequences in asymmetric context

We extend the ideas of convergence and Cauchy condition of double sequences extended by a two valued measure (called ??-statistical convergence/Cauchy condition and convergence/Cauchy condition in ??-density, studied for real numbers in our recent paper [7]) to a very general structure like an asymmetric (quasi) metric space. In this context it should be noted that the above convergence ideas naturally extend the idea of statistical convergence of double sequences studied by Móricz [15] and Mursaleen and Edely [17]. We also apply the same methods to introduce, for the first time, certain ideas of divergence of double sequences in these abstract spaces. The asymmetry (or rather, absence of symmetry) of asymmetric metric spaces not only makes the whole treatment different from the real case [7] but at the same time, like [3], shows that symmetry is not essential for any result of [7] and in certain cases to get the results, we can replace symmetry by a genuinely asymmetric condition called (AMA).     

Inventory of differential items selling at two shops under single management

Inventory of differential (both good and defective) items purchased in a lot for two shops under a single management is considered here. In the primary shop, the lot is received and separated, only good units are sold and shortages are allowed which are backlogged from the good units specially purchased at the beginning of the next cycle. The separated defective units are continuously trasnsferred and sold at a reduced price from the secondary shop. This inventory model is formulated and illustrated numerically for three scenarios depending upon the time periods of the shops.     

Deterministic inventory models for variable production

This paper presents two deterministic inventory models for a single item, where for the first model, the production rate at any instant depends on the on-hand inventory and for the second one, it is demand dependent. However, in both cases, the demand rate at any moment of time is a linear function of time for the scheduling period. Both the models are formulated and solved without allowing shortages. Two numeric examples have been added to illustrate the results.