Bounds for sorting by prefix reversal

For a permutation σ of the integers from 1 to n, let ?(σ) be the smallest number of prefix reversals that will transform σ to the identity permutation, and let ?(n) be the largest such ?(σ) for all σ in (the symmetric group) S_n. We show that $\text{?(n)?}\text{(5n+5)}\text{3}$, and that $\text{?(n)?}\text{17n}\text{16}$ for n a multiple of 16. If, furthermore, each integer is required to participate in an even number of reversed prefixes, the corresponding function g(n) is shown to obey $\text{3n}\text{2?1}\text{?g(n)?2n+3}$.     

Multiplicative intrinsic component optimization (MICO) for MRI bias field estimation and tissue segmentation

This paper proposes a new energy minimization method called multiplicative intrinsic component optimization (MICO) for joint bias field estimation and segmentation of magnetic resonance (MR) images. The proposed method takes full advantage of the decomposition of MR images into two multiplicative components, namely, the true image that characterizes a physical property of the tissues and the bias field that accounts for the intensity inhomogeneity, and their respective spatial properties. Bias field estimation and tissue segmentation are simultaneously achieved by an energy minimization process aimed to optimize the estimates of the two multiplicative components of an MR image. The bias field is iteratively optimized by using efficient matrix computations, which are verified to be numerically stable by matrix analysis. More importantly, the energy in our formulation is convex in each of its variables, which leads to the robustness of the proposed energy minimization algorithm. The MICO formulation can be naturally extended to 3D/4D tissue segmentation with spatial/sptatiotemporal regularization. Quantitative evaluations and comparisons with some popular softwares have demonstrated superior performance of MICO in terms of robustness and accuracy.     

High-yield syntheses and reactivity studies of Fe10 "ferric wheels": structural, magnetic, and computational characterization of a star-shaped Fe8 complex

Convenient, high-yield routes have been developed to [Fe 10(OMe) 20(O 2CR) 10] ( 1) "ferric wheels" involving the alcoholysis of [Fe 3O(O 2CR) 6(H 2O) 3] (+) salts in MeOH in the presence of NEt 3. Reactivity studies have established [Fe 10(OMe) 20(O 2CMe) 10] ( 1a) to undergo clean carboxylate substitution with a variety of other RCO 2H groups to the corresponding [Fe 10(OMe) 20(O 2CR) 10] product. In contrast, the reaction with phenol causes a nuclearity change to give a smaller [Fe 8(OH) 4(OPh) 8(O 2CR) 12] ( 2) wheel. Similarly, reactions of [Fe 10(OMe) 20(O 2CR) 10] with the bidentate chelate ethylenediamine (en) cause a structural change to give either [Fe 8O 5(O 2CMe) 8(en) 8](ClO 4) 6 ( 3) or [Fe 2O(O 2CBu (t))(en) 4](NO 3) 3 ( 4), depending on conditions. Complex 3 possesses a "Christmas-star" Fe 8 topology comprising a central planar [Fe 4(mu 4-O)] (10+) square subunit edge-fused to four oxide-centered [Fe 3(mu 3-O)] (7+) triangular units. Variable-temperature, solid-state dc and ac magnetization studies on complexes 1a- 4 in the 5.0-300 K range established that all the complexes possess an S = 0 ground state. The magnetic susceptibility data for 4 were fit to the theoretical chi M versus T expression derived by the use of an isotropic Heisenberg spin Hamiltonian and the Van Vleck equation, and this revealed an antiferromagnetic exchange parameter with a value of J = -107.7(5) cm (-1). This value is consistent with that predicted by a previously published magnetostructural relationship. Theoretically computed values of the exchange constants in 3 were obtained with the ZILSH method, and the pattern of spin frustration within its core and the origin of its S = 0 ground state have been analyzed in detail.     

Highly Elastic Melamine Graphene/MWNT Hybrid Sponge for Sensor Applications

The rapidly increased interest in multifunctional nanoelectronic devices, such as wearable monitors, smart robots, and electronic skin, motivated many researchers toward the development of several kinds of sensors in recent years. Flexibility, stability, sensitivity, and low cost are the most important demands for exploiting stretchable or compressible strain sensors. This article describes the formation and characteristics of a flexible, low-cost strain sensor by combining a commercial melamine sponge and a graphene/carbon nanotubes hybrid. The composite that emerged by doping the highly elastic melamine sponge with a highly conductive graphene/carbon nanotubes hybrid showed excellent piezoresistive behavior, with low resistivity of 22 kΩ m. Its function as a piezoresistive material exhibited a high sensitivity of 0.050 kPa⁻¹ that combined with a wide detection area ranging between 0 to 50 kPa.     

Synthesis,thermal analysis,and spectroscopic and structural characterizations of tetranuclear nickel(II) cubane-type clusters with 2-hydroxybenzaldehydes or 2-hydroxyphenones

In this study, three novel tetranuclear nickel(II) cubane-type clusters with the general formula [Ni₄(L)₄(μ₃-CH₃O)₄(CH₃OH)₄] [L: the anion of 5-methyl-2-hydroxybenzaldehyde (1), 2-hydroxypropiophenone (2), and 2-hydroxybenzophenone (3)] were synthesized and characterized by single-crystal X-ray diffraction analysis. The crystal structure of each compound contains a tetranuclear cubane core [Ni₄O₄] based on an approximately cubic array of altering nickel and oxygen atoms with intracluster metal–metal separations of 3.04–3.14 Å. Each Ni(II) atom is surrounded by two oxygen atoms from the ligand (L) and by the μ₃-CH₃O oxygen atom that bridges three Ni atoms of the cubane core. The coordination sphere of Ni is completed with one methanol molecule and making six-coordinate with a distorted octahedral geometry. These complexes were characterized also by spectroscopy (IR and UV–Vis). Simultaneous TG/DTG–DTA techniques were used to analyze their thermal behavior under inert atmosphere, with particular attention to determine their thermal degradation pathways, which was found to be a multi-step decomposition accompanied by the release of the ligand molecules. Finally, the kinetic analysis of the decomposition processes was performed for the first step of complex (3), since only this verifies the requirement of applying an isoconversional method like Kissinger–Akahira–Sunose (KAS). For this step, we found the average value E _a = 107.8 ± 4.5 kJ mol^?1.     

A convergent approach to batzelladine alkaloids. Total syntheses of (+)-batzelladine E, (−)-dehydrobatzelladine C,and (+)-batzelladine K

We recently reported a convergent strategy to access the polycyclic guanidinium alkaloid (+)-batzelladine B via an aldol addition–retro-aldol–aza-Michael addition cascade. Here we describe the application of this approach toward the total syntheses of (+)-batzelladine E, (?)-dehydrobatzelladine C, and (+)-batzelladine K. The identification of suitable methods to functionalize a common tropane core by electrophilic alkynylation and nucleophilic 1,2-addition were essential to generalizing this approach. We provide evidence for the intermediacy of an acylallene species in the cascade reaction.     

Nucleosides and nucleotides. Part 25.. Synthesis of a protected 1-(2′-deoxy-β-D-ribofuranosyl)-1 H-benzimidazole 3′-phosphate

1-(2′-Deoxy-5′-O-dimethoxytrityl-′-D -ribofuranosyl)-1 H-benzimidazole 3′-[(p-chlorophenyl)(2-cyanoethyl) phosphate] ( 6 ) has been synthesized from 1-(β-D -ribofuranosyl)-1H-benzimidazole ( 3b ) using regiospecific 2′-deoxygenation. The latter compound was obtained by glycosylation of benzimidazole with the D -ribose derivative 2 leading exclusively of the β-D -anomer.     

Novel desilylation of alpha-dimethylsilyl esters by electrochemically generated superoxide ion

Electrochemical reduction of oxygen in the presence of an alpha-dimethylsilyl ester results in removal of the dimethylsilyl group. The reaction presumably proceeds by a mechanism involving electrochemically-generated superoxide ion.