Generation of substituted styrenes via Suzuki cross-coupling of aryl halides with 2,4,6-trivinylcyclotriboroxane

The synthesis of functionalized styrene derivatives can be readily achieved utilizing a Suzuki cross-coupling protocol between aryl halides and 2,4,6-trivinylcyclotriboroxane-pyridine complex. The scope and limitations of the procedure were demonstrated by investigation of an array of ortho-substituted aryl halides.     

Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations

We establish some new criteria for the oscillation of second-order nonlinear dynamic equations on a time scale. We study the case of strongly superlinear and the case of strongly sublinear equations subject to various conditions.     

Optimization of Oligosaccharide Synthesis from Cellobiose by Dextransucrase

There is a growing market for oligosaccharides as sweeteners, prebiotics, anticariogenic compounds, and immunostimulating agents in both food and pharmaceutical industries. Interest in novel carbohydrate-based products has grown because of their reduced toxicity and low immune response. Cellobiose is potentially valuable as a nondigestible sugar. The reaction of cellobiose, as an acceptor with a sucrose as a donor, catalyzed by a dextransucrase from Leuconostoc mesenteroides B-512FMCM, produced a series of cellobio-oligosaccharides. This production system was optimized using a Box–Behnken experimental design for 289 mM of sucrose and 250 mM of cellobiose and 54 U of the enzyme at pH 5.2 and 30 °C, to produce maximum yields of oligosaccharide.     

An upper and lower solution approach for singular boundary value problems with sign changing non‐linearities

We obtain via Schauder's fixed point theorem new results for singular second‐order boundary value problems where our non‐linear term f(t,y,z) is allowed to change sign. In particular, our problem may be singular at y=0, t=0 and/or t=1. Copyright © 2002 John Wiley & Sons, Ltd.     

The generalized Thomas–Fermi singular boundary value problems for neutral atoms

This paper presents an upper and lower solution theory for singular boundary value problems modelling the Thomas–Fermi equation, subject to a boundary condition corresponding to the neutral atom with Bohr radius equal to its existence interval. Furthermore, we derive sufficient conditions for the existence–construction of the above‐mentioned upper–lower solutions. Copyright © 2005 John Wiley & Sons, Ltd.     

Soe fractional integral inequalities involving $$\varvec{}$$-convex functions

In this paper, some fractional integral inequalities involving m-convex functions are established. The presented results are generalizations of the obtained inequalities in Dragomir and Toader (Babe?-Bolyai Math 38:21–28, 1993).     

On the Nagumo uniqueness theorem

By a convenient reparametrization of the integral curves of a nonlinear ordinary differential equation (ODE), we are able to improve the conclusions of a recent generalization of Nagumo’s uniqueness theorem. In this way, we establish a flexible uniqueness criterion for ODEs without Lipschitz-like nonlinearities.     

An inequality concerning the growth bound of an evolution family and the norm of a convolution operator

Let \(\mathcal {U}=\{U(t,s)\}_{t\ge s\ge 0}\) be a strongly continuous and exponentially bounded evolution family acting on a complex Banach space X and let \(\mathcal {X}\) be a certain Banach function space of X-valued functions. We prove that the growth bound of the family \(\mathcal {U}\) is less than or equal to \(-\frac{1}{c(\mathcal {U}, \mathcal {X})}\) provided that the convolution operator \(f\mapsto \mathcal {U}*f\) acts on \(\mathcal {X}.\) It is well known that under the latter assumption, the convolution operator is bounded and then \(c(\mathcal {U}, \mathcal {X})\) denotes (ad-hoc) its norm in \(\mathcal {L}(\mathcal {X}).\) As a consequence, we prove that if \(\sup \nolimits _{s\ge 0}\int \nolimits _{s}^\infty \Vert U(t,s)\Vert dt=u_1(\mathcal {U})<\infty ,\) then \(\omega _0(\mathcal {U})u_1(\mathcal {U})\le -1.\) Finally, we give an example showing that the accuracy of the estimates may be quite accurate.     

Topological structure of solution sets in Fréchet spaces: The projective limit approach

In this paper we show that the solution set of certain Volterra inclusions defined between Fréchet spaces is a continuum. The proof relies on results in Banach spaces and on viewing a Fréchet space as a projective limit of a sequence of Banach spaces.     

Fixed point theory for permissible extension type maps

Several new fixed point results for permissible self extension type maps are presented in this paper.