Environmental magnetism and climate change

A major and pressing problem is to understand how, and how fast, the Earth's climate has changed in the past, with and without human influences on the global carbon cycle. Magnetic, remanence-acquiring, minerals, mostly iron oxides and sulphides, occur ubiquitously in sediments. They can act as sensitive recorders of past climates, because as climate has varied (from glacial to interglacial, for example), the mineralogy, magnetic domain state, composition and source of these minerals has varied. Here, the magnetic properties of windblown dust and interbedded soil layers of the Chinese Loess Plateau are used to calculate rainfall for the last million years, identifying the waxing and waning of the Southeast Asian summer monsoon. Comparison of our magnetic rainfall record on land with environmental records from the deep-sea shows that summer monsoon intensity is linked with growth and decay of continental-sized ice sheets, in turn reflecting changes in the Earth's orbit around the Sun.     

Controlling the composition and the magnetic properties of hexagonal Co2Z ferrite powders synthesized using two different methods

Polycrystalline Co₂Z hexaferrite (Ba₃Co₂Fe₂₄O₄₁) powders have been prepared via two wet chemical routes: sol gel auto-combustion (SGA) and co-precipitation (CP) methods. The effects of synthesis conditions on the crystal structure, crystallite size, morphology, and magnetic properties were systematically studied. The results revealed that single Co₂Z hexaferrite phase was obtained at relatively low temperature 1250 ^°C for 5 h via the SGA method whereas it was formed at 1300 ^°C for 6 h using the CP pathway. The microstructures of the pure powders appeared as a hexagonal platelet-like structure. The particle size of the pure Co₂Z powders by CP method was higher than as obtained by the SGA method. The soft characteristic loops were obtained for single Co₂Z hexaferrite phase synthesized using both routes. High saturation magnetization (M _s =53.7 emu/g) was achieved for the Co₂Z powder synthesized via the CP method compared with the formed single phase synthesized via the SGA method (M _s =47.0 emu/g). Good dielectric and dynamic magnetic properties were obtained for the Co₂Z powder synthesized via the SGA method in comparison with the sample synthesized via CP method. The results obtained are discussed on the basis of electromagnetic theory.     

A closed form type reduction method for piecewise linear interval type-2 fuzzy sets

In this study, a new centroid type reduction method is proposed for piecewise linear interval type-2 fuzzy sets based on geometrical approach. The main idea behind the proposed method relies on the assumption that the part of footprint of uncertainty (FOU) of an interval type-2 fuzzy set (IT2FS) has a constant width where the centroid is searched. This constant width assumption provides a way to calculate the centroid of an IT2FS in closed form by using derivative based optimization without any need of iterations. When the related part of FOU is originally constant width, the proposed method finds the accurate centroid of an IT2FS; otherwise, an enhancement can be performed in the algorithm in order to minimize the error between the accurate and the calculated centroids. Moreover, only analytical formulas are used in the proposed method utilizing geometry. This eliminates the need of using discretization of an IT2FS for the type reduction process which in return naturally improves the accuracy and the computation time. The proposed method is compared with Enhanced Karnik–Mendel Iterative Procedure (EKMIP) in terms of the accuracy and the computation time on seven test fuzzy sets. The results show that the proposed method provides more accurate results with shorter computation time than EKMIP.     

Comment to: Perturbation estimates for the nonlinear matrix equation X−A ∗ X q A=Q (0<q<1) by G. Jia and D. Gao

We show that the perturbation estimate for the matrix equation X?A ^? X ^q A=Q (0<q<1), due to G. Jia and D. Cao, published in this journal, is wrong.     

Characterization of Closed Densely Defined Semi-Browder Linear Operators

In the present paper we characterize the closed densely defined semi-Browder operators through the Kato decomposition. Furthermore, we apply the obtained results to give a new characterization of Browder’s essential defect spectrum and Browder’s essential approximate point spectrum under finite rank operator perturbations.     

Hochschild cohomology of partial relation extensions

We show how to compute the low Hochschild cohomology groups of a partial relation extension algebra.     

The fundamental groups of a triangular algebra

A finite dimensional algebra A (over an algebraically closed field) is called triangular if its ordinary quiver has no oriented cycles. To each presentation (Q I) of A is attached a fundamental group π₁(Q I), and A is called simply connected if π₁(Q I) is trivial for every presentation of A. In this paper, we provide tools for computations with the fundamental groups, as well as criteria for simple connectedness. We find relations between the fundamental groups of A and the first Hochschild cohomology H ¹ (A A).     

The heat transfer problem for inhomogeneous materials in photoacoustic applications and spectral parameter power series

A method for studying the one‐dimensional heat transfer process within an inhomogeneous spatially bounded medium in the presence of an external heat source is presented. It is based on a recently introduced technique for solving problems related to Sturm–Liouville equations that consists in the representation of solutions in the form of a spectral parameter power series. We consider a heat transfer model linked to photoacoustic and show that the introduced method, besides its relative simplicity and analytical nature, offers an efficient numerical algorithm as well as a convenient way to work separately with different physically meaningful components of the temperature distribution function. Detailed explanations and numerical examples are given. Copyright © 2013 John Wiley & Sons, Ltd.     

Existence of a ground state and scattering for a nonlinear Schrödinger equation with critical growth

We study the energy-critical focusing nonlinear Schrödinger equation with an energy-subcritical perturbation. We show the existence of a ground state in the four or higher dimensions. Moreover, we give a sufficient and necessary condition for a solution to scatter, in the spirit of Kenig and Merle (Invent Math 166:645–675, 2006).     

Synthesis,spectroscopic, thermal and electrical conductivity studies of three charge transfer complexes formed between 1,3-di[(<Emphasis Type="Italic">E</Emphasis>)-1-(2-hydroxyphenyl)methylideneamino]-2-propanol Schiff base and different acceptors

Charge-transfer complexes (CTC) resulting from interactions of 1,3-di[(E)-1-(2-hydroxyphenyl) methylideneamino]-2-propanol Schiff base with some acceptors such as iodine (I₂), bromine (Br2), and picric acid (PiA) have been isolated in the solid state in a chloroform solvent at room temperature. Based on elemental analysis, UV-Vis, infrared, and ¹H NMR spectra, and thermogravimetric analysis (TG/DTG) of the solid CTC, [(Schiff)(I₂)] (1), [(Schiff)(Br₂)] complexes with a ratio of 1:1 and [(Schiff)(PiA)₃] complexes with 1:3 have been prepared. In the picric acid complex, infrared and ¹H NMR spectroscopic data indicate that the charge-transfer interaction is associated with a hydrogen bonding, whereas the iodine and bromine complexes were interpreted in terms of the formation of dative ion pairs [Schiff⁺, I₂^∙−] and [Schiff⁺, Br₂^∙−], respectively. Kinetic parameters were obtained for each stage of thermal degradation of the CT complexes using Coats–Redfern and Horowitz–Metzger methods. DC electrical properties as a function of temperature of these charge transfer complexes have been studied.