Flexible sliced designs for computer experiments

Sliced Latin hypercube designs are popularly adopted for computer experiments with qualitative factors. Previous constructions require the sizes of different slices to be identical. Here we construct sliced designs with flexible sizes of slices. Besides achieving desirable one-dimensional uniformity, flexible sliced designs (FSDs) constructed in this paper accommodate arbitrary sizes for different slices and cover ordinary sliced Latin hypercube designs as special cases. The sampling properties of FSDs are derived and a central limit theorem is established. It shows that any linear combination of the sample means from different models on slices follows an asymptotic normal distribution. Some simulations compare FSDs with other sliced designs in collective evaluations of multiple computer models.     

Decay rates of solutions to thermoviscoelastic plates with memory

We consider the thermoelastic plate under the presence of along range memory. We find uniform rates of decay (in time)of the energy, provided that suitable assumptions on the relaxationfunctions are given. Namely, if the relaxation decays exponentiallythen the first order energy also decays exponentially. Whenthe relaxation g satisfies -c₁g(t)^1+1/_p g'(t) -c_og(t)^1+1/_p; and g,g^1-1/_p L¹ (R) withp > 2 then the energy decays as 1/(1+t)^p. A new Liapunov functionalis built for this problem.     

A falling body problem through the air in view of the fractional derivative approach

Recent studies have revealed that the fractional derivative can behave as a dissipative term. The analysis of a simple fractional oscillator has supported this point of view. However, other physical aspects related to fractional derivative are also important to be explored. For this purpose, in this work, we employ the fractional approach and guide ourselves by the above property to investigate the falling body problem. We show that the velocity of a falling body, in the fractional approach, can be greater (t<1) or less (t>1) than that velocity of free-fall obtained by the usual approach. Moreover, we show that the fractional derivative alone is not sufficient to attain a terminal speed. In order to provide a terminal speed into the fractional system a term, proportional to velocity, must be introduced.     

Effect of Heavy‐Atom (Br) at the Phenyl Rings of Schiff‐Base Ligands on the NIR Luminescence of their Bimetallic Zn‐Nd Complexes

Two heterobimetallic Zn‐Nd phenylene‐bridged Schiff‐base ligands complexes [ZnNd L¹ (Py)(NO₃)₃] ( 1 ) and [Zn L² Nd(Py)(NO₃)₃]·MeCN ( 2 ) (Py = pyridine, H₂L¹ = N,N′‐bis‐ (3‐methoxy‐salicylidene)phenylene‐1,2‐diamine, H₂L² = N,N′‐bis‐5‐bromo‐3‐methoxy‐salicylidene)phenylene‐1,2‐diamine) were obtained. Both 1 and 2 were structurally characterized by X‐ray crystallography, and their near‐infrared (NIR) luminescent properties were determined. For the two complexes, the occupation of pyridine at the axial position of 3d Zn²⁺ ions could effectively prevent luminescent quenching arising from OH‐, NH‐ or CH oscillators of the solvates around the 4f Nd³⁺ ions, and the heavy‐atom (Br) effect of the Schiff‐base ligands on their NIR luminescent properties is also discussed.     

Crystal structure of a non-stoichiometric channel inclusion complex of 1-benzyl-6-phenylpiperidin-2-one-5-carboxylic acid with acetonitrile

C₁₉H₁₉NO₃·x CH₃CN (x=0.3),M _r=643.35, hexagonal, space groupP6₁ (No. 169),a=23.027(5),c=5.775(1) Å,V=2652(1) ų,Z=6. The structure was solved by direct methods and refined toR=0.077 for 1562 observed MoK reflections. The title heterocyclic carboxylic acid was established as thetrans isomer, with the phenyl and carboxyl substituents occupying pseudo-equatorial and equatorial positions, respectively, of the piperidin-2-one ring in a half-chair conformation. Acid host molecules related by the 6₁ screw operation are linked by intermolecular O–H...O (cyclic amide) hydrogen bonds to generate an open channel bounded by coaxial intertwined helices each having a pitch of 5c. Within each channel of free diameterca. 6.0 Å the acetonitrile molecules partially occupy highly disordered sites which do not lie on thec axis. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82067 (13 pages).     

Contact angle measurements with liquids consisting of bulky molecules

Well-measured contact angles with different solid-liquid systems fall approximately on smooth patterns when plotted versus liquid surface tension. However, there are deviations of 1 degrees -3 degrees , which are outside the error limits. It is the purpose of this paper to elucidate the reasons for such deviations. Two types of liquids were selected for advancing contact angle measurements on Teflon AF 1600 coated surfaces: a series of n-alkanes ranging from n-hexane to n-hexadecane and five liquids consisting of bulky molecules, octamethylcyclotetrasiloxane (OMCTS), methyl salicylate, tetralin, cis-decalin, and octamethyltrisiloxane (OMTS). It was found that contact angles of the liquids with bulky molecules fall on a perfectly smooth curve corresponding to a solid surface tension of 13.64 +/- 0.1 mJ/m2. However, contact angles of n-alkanes deviated from this curve by up to 3 degrees in a complicated fashion. The observed trend suggests that more than one mechanism is responsible for the deviations. Substrate-induced rearrangement of liquid molecules in the close vicinity of the surface in the case of long-chain n-alkanes and adsorption of vapor onto the solid surface in the case of short-chain n-alkanes are the most likely explanations. The results suggest that liquids with bulky molecules appear to be suitable for contact angle measurements to characterize energetics of polymeric surfaces.     

Structural trends in first-row transition-metal bis(benzimidazole) complexes

Dimethyl-substituted bis(benzimidazole) (Me2BBZ) is a novel macrocyclic ligand that possesses an intrinsic nonplanarity. To examine how metal-ion binding affects the magnitude of this nonplanarity, we have determined the structures of a periodic series of Me2BBZ complexes bound to Mn(II), Fe(II), Co(II), Ni(II), and Cu(II). These studies demonstrate that the extent of ligand ruffling and metal doming is indeed influenced by the nature of the metal. Concomitant with the periodic decrease of the ionic radii of the encapsulated divalent metal ion, a decrease in the magnitude of both the ligand nonplanarity and the metal out-of-the-plane distance is observed. For the metal out-of-the-plane distance, this correlation persists until the metal finally moves into the mean ligand plane. For the nonplanar distortion, the extent of the nonplanarity decreases to a limiting value that is intrinsic to the Me2BBZ ligand due to steric factors. These observations indicate that the relative sizes of the metal ion and the Me2BBZ ligand cavity have profound effects on the structural features of the metal-ligand complex.     

Liquid alkoxides of a perfluorotertiary alcohol and their derivatives

Sodium and lithium alkoxides of (CF₃)₂CFOCF₂CF₂C(CF₃)₂OH have been prepared in high yields by the addition of sodium hydride to the alcohol or in the case of the lithium salt through the addition of (CF₃)₂C=O to the organolithium compound (CF₃)₃CFOCF₂CF₂Li. These salts react with active halides e.g. PCl₃ or cyanuric chloride to yield completely substituted products.