Existence and global attractivity of solutions of a nonlinear functional integral equation

In this paper we prove a result on the existence and global attractivity of solutions of a nonlinear functional integral equations with deviating arguments. The investigations are placed in the Banach space of real functions defined, continuous and bounded on the real half-axis. The main tool used in consideration is a fixed point theorem of Krasnosel’skii type. A few examples illustrating the obtained results are also included.     

Controllability of nonlinear systems to affine manifolds

Controllability to an affine manifold involves controlling a system to a target defined by the generalized boundary condition x=r, where :C ⁿ R ⁿ is a bounded linear operator on the continuous functions, as defined for ordinary differential equations by Kartsatos. In this paper, sufficient conditions are obtained for such controllability for linear systems and for a class of nonlinear perturbations of linear systems.     

Controllability of impulsive neutral integrodifferential systems with infinite delay in Banach spaces

In this paper sufficient conditions for the controllability of impulsive neutral integrodifferential systems with infinite delay are established. The results are obtained by using the Schauder fixed point theorem.     

Intrinsic localized modes in microresonator arrays and their relationship to nonlinear vibration modes

Intrinsic Localized Modes (ILMs) are defined as localizations due to strong intrinsic nonlinearity within an array of perfect, periodically repeating oscillators. Such nonlinear phenomena have been studied for a number of years in the solid-state physics literature. Energy can become localized at a specific location in a discrete system as a result of the nonlinearity of the system and not due to any defects or impurities within the considered systems. Here, such mode localization is studied in the context of microcantilever arrays and microresonator arrays, and it is explored if an ILM can be realized as a forced nonlinear normal mode or nonlinear vibration mode. The method of multiple scales and methods to construct nonlinear normal modes are used to study nonlinear vibrations of microresonator arrays. Investigations reported in this article suggest that it is possible to realize an ILM as a forced nonlinear vibration mode. These results are believed to be important for future designs of microresonator arrays intended for signal processing, communication, and sensor applications.     

A Toroidal Zr70 Oxysulfate Cluster and Its Diverse Packing Structures

Herein, we report the discovery of a toroidal inorganic cluster of zirconium(IV) oxysulfate of unprecedented size with the formula Zr₇₀(SO₄)₅₈(O/OH)₁₄₆⋅x(H₂O) (Zr₇₀), which displays different packing of ring units and thus several polymorphic crystal structures. The ring measures over 3 nm across, has an inner cavity of 1 nm and displays a pseudo-10-fold rotational symmetry of Zr₆ octahedra bridged by an additional Zr in the outer rim of the ring. Depending on the co-crystallizing species, the rings form various crystalline phases in which the torus units are connected in extended chain and network structures. One phase, in which the ring units are arranged in layers and form one-dimensional channels, displays high permanent porosity (BET surface area: 241 m² g⁻¹), and thus demonstrates a functional property for potential use in, for example, adsorption or heterogeneous catalysis.     

Concise total synthesis of (+)-lyconadin a

The total synthesis of lyconadin A from (R)-5-methylcyclohex-2-enone was accomplished. Our synthesis features the facile construction of a highly fused tetracyclic compound through a combination of an aza-Prins reaction and an electrocyclic ring opening. Transformation of the bromoalkene moiety in the tetracycle could be achieved by either a vinylogous Pummerer rearrangement or the formation and subsequent isomerization of the nitrosoalkene to furnish an α,β-unsaturated ketone, from which the pyridone ring was constructed.     

Ultrasonic enhancement of the supercritical extraction from ginger

This work examines the concurrent use of power ultrasound during the extraction of pungent compounds from a typical herb (ginger) with supercritical CO₂. A power ultrasonic transducer with an operating frequency of 20 kHz is connected to an extraction vessel and the extraction of gingerols from freeze-dried ginger particles (4–8 mm) is monitored. In the presence of ultrasound, we find that both the extraction rate and the yield increase. The higher extraction rate is attributed to disruption of the cell structures and an increase in the accessibility of the solvent to the internal particle structure, which enhances the intra-particle diffusivity. While cavitation would readily account for such enhancement in ambient processes, the absence of phase boundaries should exclude such phenomena above the critical point. Possible alternate mechanisms for the cell structure damage are discussed.     

Quantum geons and noncommutative spacetimes

Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime is the Moyal plane. The Poincaré group algebra acts on it with a Drinfel’d-twisted coproduct, however the latter is not appropriate for more complicated spacetimes such as those containing Friedman-Sorkin (topological) geons. They have rich diffeomorphisms and mapping class groups, so that the statistics groups for N identical geons is strikingly different from the permutation group S _N . We generalise the Drinfel’d twist to (essentially all) generic groups including finite and discrete ones, and use it to deform the commutative spacetime algebras of geons to noncommutative algebras. The latter support twisted actions of diffeomorphisms of geon spacetimes and their associated twisted statistics. The notion of covariant quantum fields for geons is formulated and their twisted versions are constructed from their untwisted counterparts. Non-associative spacetime algebras arise naturally in our analysis. Physical consequences, such as the violation of Pauli’s principle, seem to be one of the outcomes of such nonassociativity. The richness of the statistics groups of identical geons comes from the nontrivial fundamental groups of their spatial slices. As discussed long ago, extended objects like rings and D-branes also have similar rich fundamental groups. This work is recalled and its relevance to the present quantum geon context is pointed out.