Nonreductive deiodination of ortho-iodo-hydroxylated arenes using tertiary amines

A convenient and nonreductive deiodination is reported for the ortho-iodo-hydroxylated arenes including derivatives of quinolinol, phenol, and naphthol. Tertiary amines pyridine, triethylamine, and N-methylmorpholine in the presence of water initiated deiodination of ortho-iodo-hydroxylated arenes without affecting para-iodine and other reduction-susceptible groups. This reported method also works efficiently for polyiodinated systems. Simplicity, short reaction times, and absence of reducing catalyst are features of this method.     

Optimal design of rotating disk for given radial displacement of edge

Minimum-weight design of axially-symmetric, rotating, elastic disks is usually discussed in terms of uniform strength. In this paper, an alternative constraint is used: under the combined influence of centrifugal forces and a uniform radial traction along the circular edge, the radial displacement at this edge is to have a prescribed value. A necessary and sufficient optimality condition is derived, and its use in the determination of optimal disk profiles is illustrated by examples. It is shown that the resulting disks are far from satisfying the condition of uniform strength although their weights are only very slightly smaller than those of the corresponding disks of uniform strength.This research was sponsored by the Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio, under Contract No. F33615-C-1826.     

Some congruences modulo 5 and 25 for overpartitions

We present two new Ramanujan-type congruences modulo 5 for overpartitions. We also give an affirmative answer to a conjecture of Dou and Lin, which includes four congruences modulo 25 for overpartition.     

An inventory model for increasing demand under two levels of trade credit linked to order quantity

During the growth stage of a product life cycle especially for high-tech products, the demand function increases with time. In this paper, we extend the constant demand to a linear non-decreasing demand function of time and incorporate a permissible delay in payment under two levels of trade credit into the model. The supplier offers a permissible delay linked to order quantity, and the retailer also provides a downstream trade credit period to its customers. The objective is to find the optimal replenishment cycle that minimizes the retailer’s annual total relevant cost per unit time. The condition for an optimal solution to the generalized model is presented and some fundamental theoretical results are established. Finally, numerical examples to illustrate the proposed model are provided. Sensitivity analysis is performed and some relevant managerial insights are obtained.     

Vanishing coefficients and identities concerning Ramanujan’s parameters

The Ramanujan Journal - In this paper we investigate several infinite products with vanishing Taylor coefficients in arithmetic progressions. These infinite products are closely related to...     

Synthesis of 2‐[4‐(Imidazolin‐2‐Ylideneamino)Benzyl]‐Indan‐1‐Ones as Novel Potent Prostacyclin Antagonists

Prostacyclin is involved in many pathological conditions, such as sensitization of inflammation induced pain and isovolumetic distention. Therefore, antagonism of prostacyclin action may be useful in the alleviation of these conditions. In this study, novel potent prostacyclin antagonists, 2‐[4‐(imidazolin‐2‐ylideneamino)benzyl]‐indan‐1‐ones were synthesized from their respective substituted indanones in three steps. The construction of the amino‐imidazole moiety of these derivatives is achieved by using in situ generation of chloro‐imidazole and reaction with their respective anilines. Thus, these N‐substituted 2‐imidazolines can be prepared safely and efficiently. Moreover, these compounds show potent prostacyclin antagonistic activity by inhibition of prostacyclin agonist induced ERK_1/2 phosphorylation in human erythroleukemia cells. Moreover, we observed an increase in activity with the increase in electro‐donating property of the substitution on the indanone aromatic ring. Prostacyclin antagonists with increased potency may be designed based on these findings. These compounds may also be invaluable tools for the study of the physiological functions of prostacyclin.