Characterization of Function Spaces for the Dunkl Type Operator on the Real Line

In this work we consider the Dunkl operator on the real line, defined by $$ {\cal D}_kf(x):=f'(x)+k\dfrac{f(x)-f(-x)}{x},\,\,k\geq0. $$ We define and study Dunkl–Sobolev spaces \(L^p_{n,k}(\mathbb{R})\) , Dunkl–Sobolev spaces \({\cal L}^p_{\alpha,k}(\mathbb{R})\) of positive fractional order and generalized Dunkl–Lipschitz spaces \(\wedge^k_{\alpha,p,q}(\mathbb{R})\) . We provide characterizations of these spaces and we give some connection between them.     

Phase transition at 233 K in [(CH3)4N]2cdI4

Abstract

[(CH₃)₄N]₂cdI₄ exhibits a phase transition at 233 K from Pnma to P2 1/c as shown by single-crystal X-ray measurements and differential scanning calorimetry. The observed entropy change amounts to approximately 8.4 J.mole^?1 K^?1 and the spontaneous strain is about – 18.10^?3. The symmetry change can be interpreted in the framework of the Landau theory.     

Crystal structure of monomethylammonium tribromocadmate(II)

CH₃NH₃CdBr₃ crystallizes in the space group Ccm2₁, a = 13.693(1) Å, b = 7.906(1) Å, c = 6.886(1) Å, V = 745.46(15) ų, Z = 4, D _x = 3.42 Mg m^–3. The structure of the title compound is one-dimensional consisting of infinite chains made of face sharing CdBr₆ octahedra. The methylammonium groups are situated in the space between chains. The cations and anions are joined by hydrogen bonding.     

Space charge packets in polyethylene nano-scales under dc applied voltages

In this paper, we are interested in space charge packet phenomenon generated at submicron scales in insulating polyethylene materials that have not been extensively investigated in all previous theoretical modeling and experimental works. Indeed, a bipolar charge transport model is proposed to simulate space charge dynamics in nano-scale polyethylene material under dc high electric field. For these scales, our results show space charge packet appearance which induces new dynamics that are marked on injected and conduction current oscillations. In addition, our results also show the establishment of post breakdown phenomena that are indicated by an external current abrupt increase without saturation.     

Secondary ion yields produced by keV atomic and polyatomic ion impacts on a self-assembled monolayer surface

A suite of keV polyatomic or 'cluster' projectiles was used to bombard unoxidized and oxidized self-assembled monolayer surfaces. Negative secondary ion yields, collected at the limit of single ion impacts, were measured and compared for both molecular and fragment ions. In contrast to targets that are orders of magnitude thicker than the penetration range of the primary ions, secondary ion yields from polyatomic projectile impacts on self-assembled monolayers show little to no enhancement when compared with monatomic projectiles at the same velocity. This unusual trend is most likely due to the structural arrangement and bonding characteristics of the monolayer molecules with the Au(111). Copyright 1999 John Wiley & Sons, Ltd.     

Magnetocaloric properties in the Cr-doped La0.7Sr0.3MnO3 manganites

Single-phase polycrystalline samples of La_0.7Sr_0.3Mn_1-xCr_xO₃ with nominal composition of x=0.00, 0.20, 0.40 and 0.50 were prepared by a conventional solid-state reaction method in air. Investigations of magnetization were carried out in the temperature range 5-400 K and magnetic field range 0-8 T. It was found that the Curie temperature T_C decreases with increasing x and the maximum magnetic entropy change (−ΔS_M) for x=0.20 is ∼1.203 and ∼2.653 J/kg K, respectively for 2 and 6 T magnetic field near the temperature of 280 K.     

Critical behavior and magnetic entropy change in the La0.6Sr0.4Mn0.8Fe0.1Cr0.1O3 perovskite

Critical behavior in the La_0.6Sr_0.4Mn_0.8Fe_0.1Cr_0.1O₃ ceramics was studied using magnetization methods. Results show that the paramagnetic–ferromagnetic transition is of second order. Based on the critical behavior analysis using the Banerjee criterion and the Kouvel–Fisher method, we find the critical exponents: β=0.395±0.010, γ=1.402±0.010, and δ=5.208±0.007, for which the magnetic interaction is satisfied within the three-dimensional Heisenberg model. Results indicate the presence of short-range interactions. The magnetic entropy change (−ΔS_M) reached maximum values of 1.75, 1.45, 1.15, 0.8 and 0.43 J Kg⁻¹ K⁻¹ under a magnetic field variation of 5, 4, 3, 2 and 1 T, respectively. Nevertheless, these (−ΔS_M) values are much low for any potential application at this moment. The nature of this phenomenon is discussed in relation to the characteristics of the magnetic phase transition and critical exponents.