Abstract Hopf bifurcation theorem and further extensions via second variation

Sufficient conditions of bifurcation stated in Arutyunov et al. (2009) [5] are investigated in order to reconsider celebrated Hopf bifurcation as the simplest bifurcation of Fredholm operators of zero index. In several examples abstract result is applied to both finite and infinite dynamical systems exhibiting classical Hopf bifurcation as well as double Hopf bifurcation.     

A Novel Synthetic Approach to Phosphorylated Peptidomimetics

It has been shown that the derivatives of diethyl 5‐amino‐2‐phthalimidoalkyl‐1,3‐oxazol‐4‐ylphosphonates can be employed in the synthesis of phosphorylated peptidomimetics containing the phosphonoglycine residue. The reaction of diethyl 5‐alkylamino‐2‐aminoalkyl‐1,3‐oxazol‐4‐ylphosphonates with unsaturated azlactones was utilized to obtain phosphorylated peptidomimetics with dehydroamino acid moieties. The double bond in the latter was reduced with zinc in acetic acid to provide the corresponding saturated peptidomimetics containing a diethoxyphosphoryl group in the side chain.     

Structure,Theoretical Studies,and Coupling Reactions of Some New Cyclic Boronic Esters

The present report describes the X‐ray structural and theoretical studies of some new pinacolboronate esters, and it also outlines the use of the target structures in Suzuki coupling reactions to produce new aromatic or heteroaromatic esters and amides. X‐ray structural analysis of the studied compounds revealed that the pinacolborane ring's position with respect to the benzene ring varies, depending on the particular environment. An ortho‐positioned carboxylic ester (methyl ester) causes a nearly perpendicular orientation of the pinacolborane unit with respect to the benzene ring, whereas an ortho‐positioned amide (N,N‐dimethylamide) causes the pinacolborane unit to orient itself nearly coplanar. A plausible explanation has been provided, based on both steric and electronic factors.     

The Kabachnik–Fields and Pudovik Reactions on the Basis of E,Z‐Citral and Its Imines and (R,S)‐Citronellal

The Kabachnik–Fields reaction of E,Z‐citral with diethyl phosphite in the presence of isobutylamine has been found to form α‐aminophosphonates. The Pudovik reactions of diethyl phosphite with prenyl imines prepared on the basis of E,Z‐citral with isobutylamine also allowed us to obtain the same α‐aminophosphonates. We have managed to synthesize α‐aminophosphonates by the reaction of O,O‐dialkyl trimethylsilyl phosphites with prenyl imines in the presence of water or diethylamine. α‐Aminophosphonates were also synthesized by the reaction of diethyl phosphite with (R,S)‐citronellal in the presence of alkylamines. α‐Aminophosphonates obtained showed bacteriostatic activity against Staphylococcus aureus and Bacillus cereus. © 2012 Wiley Periodicals, Inc. Heteroatom Chem 24:36–42, 2013; View this article online at wileyonlinelibrary.com . DOI 10.1002/hc.21060     

Rheological Behavior of Poly(vinylpyrrolidone)/Fullerene C60 Complexes in Aqueous Medium

Aqueous solutions of complexes formed between poly(vinylpyrrolidone) (PVP), as a matrix polymer, and fullerene C₆₀ were investigated. The effect of the external hydrodynamic field on the supermolecular assemblies formed by the complexes was analyzed. Despite the low content in the complexes (1.5 mass%), fullerene significantly modified the viscosity of aqueous PVP. Thus, the dynamic viscosity of the PVP/C₆₀ complexes grew faster than that of the pure PVP upon increasing the PVP/C₆₀ concentration. The difference in viscosities is especially pronounced for semidilute solutions. As a possible explanation, it is assumed that fullerenes act as crosslinks, in addition to the physical entanglements of the PVP macromolecules, which appear in the vicinity of the crossover concentration. Shear flow corresponding to the high shear rates destroyed fullerene‐induced intermolecular crosslinks in PVP/C₆₀ solutions.     

Friedrichs Method in a Lyapunov Problem

By using the well-known Friedrichs extension and some a priori inequality, we obtain weak solutions of a Lyapunov equation. In particular, we show that the Lyapunov functions satisfying necessary and sufficient conditions in the domain of asymptotic stability of a singular point some dynamical system must be absolutely continuous.     

Proper 1-immersions of graphs triangulating the plane

In this paper we study what planar graphs are “rigid” enough such that they can not be drawn on the plane with few (1, 2, or 3) crossings per edge. A graph drawn on the plane is k$k$-immersed in the plane if each edge is crossed by at most k$k$ other edges. By a proper  k$k$-immersion of a graph we mean a k$k$-immersion of the graph in the plane such that there is at least one crossing point. We give a characterization (in terms of forbidden subgraphs) of 4-connected graphs which triangulate the plane and have a proper 1-immersion. We show that every planar graph has a proper 3-immersion.     

Multielement Order Separability in Free Products of Groups

We introduce the notion of multielement order separability and study this property for free groups and free products.     

Lévy Approximation of Increment Processes with Markov Switching

We study weak convergence of increment processes with embedded Markov chain switching in a series scheme. The limit process is a Lévy process where the jump part is a compound Poisson process. A result concerning the rate of convergence is also given. This study is motivated by risk theory and its applications.     

Topology design for on-demand dual-path routing in wireless networks

One way to achieve reliability with low-latency is through multi-path routing and transport protocols that build redundant delivery channels (or data paths) to reduce end-to-end packet losses and retransmissions. However, the applicability and effectiveness of such protocols are limited by the topological constraints of the underlying communication infrastructure. Multiple data delivery paths can only be constructed over networks that are capable of supporting multiple paths. In mission-critical wireless networks, the underlying network topology is directly affected by the terrain, location and environmental interferences, however the settings of the wireless radios at each node can be properly configured to compensate for these effects for multi-path support. In this work we investigate optimization models for topology designs that enable end-to-end dual-path support on a distributed wireless sensor network. We consider the case of a fixed sensor network with isotropic antennas, where the control variable for topology management is the transmission power on network nodes. For optimization modeling, the network metrics of relevance are coverage, robustness and power utilization. The optimization models proposed in this work eliminate some of the typical assumptions made in the pertinent network design literature that are too strong in this application context.