An improved solvent-free synthesis of flunixin and 2-(arylamino) nicotinic acid derivatives using boric acid as catalyst

A simple solvent-free protocol for the preparation of flunixin, a potent non-narcotic, non-steroidal anti-inflammatory drugs is reported using boric acid as catalyst. Its salt, flunixin meglumine are then prepared under reflux in EtOH. This sustainable method are then extended for the synthesis of a series of 2-(arylamino) nicotinic acid derivatives. The present protocol combines non-hazardous neat conditions with associated benefits like excellent yield, straightforward workup, and use of readily available and safe catalyst in the absence of any solvent, which are important factors in the pharmaceutical industry. The pathway for catalytic activation of 2-chloronicotic acid with boric acid was also investigated using Gaussian 03 program package.

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Evaluation of the biosafety of cyanoacrylate adhesive in vitro

This paper considers the evaluation of the biosafety of cyanoacrylate adhesive in vitro on human multipotent mesenchymal stem cells. This adhesive is intended for medical use, in particular, for X-ray and endovascular interventions. A toxicity study was carried out in a culture of multipotent mesenchymal stem cells isolated from human subcutaneous fat. As a result of the work, the concentration of cyanoacrylate adhesive in lipiodol was chosen, which has the lowest toxicity.     

Adaptive symplectic conservative numerical methods for the Kepler problem

We suggest and substantiate a unified form of a family of adaptive conservative numerical methods for the Kepler problem. The family contains methods of the second, fourth, and sixth approximation order as well as an exact method. The methods preserve all the global properties of the exact solution of the problem. The variable time step is chosen automatically depending on the properties of the solution.     

O the volume growth of the hyperbolic regular $$\varvec{}$$-simplex

In this paper we give lower and upper bounds for the volume growth of a regular hyperbolic simplex, namely for the ratio of the n-dimensional volume of a regular simplex and the \((n-1)\)-dimensional volume of its facets. In addition to the methods of U. Haagerup and M. Munkholm we use a third volume form based on the hyperbolic orthogonal coordinates of a body. In the case of the ideal, regular simplex our upper bound gives the best known upper bound. On the other hand, also in the ideal case our general lower bound, improved the best known one for \(n=3\).     

Weighted inequalities for Hardy-type operators on the cone of decreasing functions in an Orlicz space

We establish criteria for the validity of modular inequalities for the Hardy operator on the cone Ω of nonnegative decreasing functions from weighted Orlicz spaces with general weight. The result is based on the theorem on the reduction of modular inequalities for positively homogeneous operators on the cone Ω, which enables passing to modular inequalities for modified operators on the cone of all nonnegative functions from an Orlicz space. It is shown that, for the Hardy operator, the modified operator is a generalized Hardy operator. This enables us to establish explicit criteria for the validity of modular inequalities.     

On weak* convergent sequences in duals of symmetric spaces of <Emphasis Type="Italic">τ</Emphasis>-measurable operators

It is shown that the pre-dual of a σ-finite von Neumann algebra has property (k) in the sense of Figiel, Johnson and Pelczyński [12]. This resolves in the affirmative an open question raised in [12]. It is shown further that a weakly sequentially complete symmetric space E of τ-measurable operators affiliated with a semifinite σ-finite von Neumann algebra has property (k).     

Infinite Horizon Controlled Diffusions with Randomly Varying and State-Dependent Discount Cost Rates

This work focuses on optimal controls of diffusions in an infinite horizon. It has several distinct features in contrast to the existing literature. The discount factor is allowed to be randomly varying and state dependent. The existence and uniqueness of the viscosity solution to the associated Hamilton–Jacobi–Bellman equation are established. The verification theorem is also obtained. Because closed-form solutions are virtually impossible to obtain in most cases, we develop numerical methods. Using the Markov chain approximation methods, numerical schemes are constructed; viscosity solution methods are used to prove the convergence of the algorithm. In addition, examples are given for demonstration purpose.     

Malliavin calculus for regularity structures: The case of gPAM

Malliavin calculus is implemented in the context of Hairer (2014) [16]. This involves some constructions of independent interest, notably an extension of the structure which accommodates a robust, and purely deterministic, translation operator, in $L^2$-directions, between “models”. In the concrete context of the generalized parabolic Anderson model in 2D – one of the singular SPDEs discussed in the afore-mentioned article – we establish existence of a density at positive times.     

Lattices with Defining Relations Close to Distributivity

We consider the 3-generated lattices whose generators enjoy the defining relations of the type a∨(b∧c) = (a∨b)∧(a∨c). Moreover, if the lattice is finite then we obtain its diagram; otherwise, we prove that the corresponding lattice is infinite.