VMO Spaces Associated with Operators with Gaussian Upper Bounds on Product Domains

In this paper, we extend the well-known result “the predual of Hardy space \(H^1\) is VMO” to the product setting, associated with differential operators. Let \(L_i\), \(i = 1, 2\), be the infinitesimal generators of the analytic semigroups \(\{e^{-tL_i}\}\) on \(L^2({\mathbb {R}})\). Assume that the kernels of the semigroups \(\{e^{-tL_i}\}\) satisfy the Gaussian upper bounds. We introduce the VMO spaces VMO\(_{L_1, L_2}(\mathbb {R}\times \mathbb {R})\) associated with operators \(L_1\) and \(L_2\) on the product domain \(\mathbb {R}\times \mathbb {R}\), then show that the dual space of VMO\(_{L_1, L_2}(\mathbb {R}\times \mathbb {R})\) is the Hardy space \(H^1_{L_1^*, L_2^*}(\mathbb {R}\times \mathbb {R})\) associated with the adjoint operators \(L^*_1\) and \(L^*_2\).     

Contraction of the proximal mapping and applications to the equilibrium problem

In this paper, we introduce a new definition of Lipschitz-type continuity of a bifunction. Using this definition, we prove the contraction of the proximal mapping and apply it to the equilibrium problem over the fixed-point set of a nonexpansive mapping. We present a new algorithm for this problem. Under classical conditions, the convergence of the algorithm is proved. Finally, we present some numerical results for the proposed algorithm.     

On the No-Gap Second-Order Optimality Conditions for a Discrete Optimal Control Problem with Mixed Constraints

Motivated by our recent works on optimality conditions in discrete optimal control problems under a nonconvex cost function, in this paper, we study second-order necessary and sufficient optimality conditions for a discrete optimal control problem with a nonconvex cost function and state-control constraints. By establishing an abstract result on second-order optimality conditions for a mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a discrete optimal control problem. Using a common critical cone for both the second-order necessary and sufficient optimality conditions, we obtain “no-gap” between second-order optimality conditions.     

Structural variability of endotoxins from R-type isogenic mutants of Shigella sonnei

The structural variations in the rough-type endotoxins [lipopolysaccharides (LPSs)] of Shigella sonnei mutant strains (S. sonnei phase II-4303, R41, 562H and 4350) were investigated by Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS) and tandem MS. A series of S. sonnei mutants had previously been the subject of analytical studies on the biosynthesis of heptose components in the core oligosaccharide region of LPSs. This study gives a complete overview on the structures of the full core and lipid A of S. sonnei mutant strains by MS. We found that the LPSs of the isogenic rough mutants were formed in a step-like manner containing 0:1:2:3 heptose in the deep core region of 4350, 562H, R41 and 4303, respectively, and the longest LPS from the mutant S. sonnei 4303 contained also five hexoses. The structural variations in the lipid A moiety and in the oligosaccharide part of the intact LPS were followed by MALDI-TOF-MS/MS. For the dissolution and the ionization of the samples, 2,5-dihydroxybenzoic acid in citric acid solution was applied as matrix. The detailed evaluation of the mass spectra indicates heterogeneity in the lipid part due to the differences in the phosphate and fatty acid composition.     

Two-dimensional paper networks: programmable fluidic disconnects for multi-step processes in shaped paper

Most laboratory assays take advantage of multi-step protocols to achieve high performance, but conventional paper-based tests (e.g., lateral flow tests) are generally limited to assays that can be carried out in a single fluidic step. We have developed two-dimensional paper networks (2DPNs) that use materials from lateral flow tests but reconfigure them to enable programming of multi-step reagent delivery sequences. The 2DPN uses multiple converging fluid inlets to control the arrival time of each fluid to a detection zone or reaction zone, and it requires a method to disconnect each fluid source in a corresponding timed sequence. Here, we present a method that allows programmed disconnection of fluid sources required for multi-step delivery. A 2DPN with legs of different lengths is inserted into a shared buffer well, and the dropping fluid surface disconnects each leg at in a programmable sequence. This approach could enable multi-step laboratory assays to be converted into simple point-of-care devices that have high performance yet remain easy to use.     

Determination of the primary structure and carboxyl p<Emphasis Type="Italic">K</Emphasis><Subscript>A</Subscript>s of heparin-derived oligosaccharides by band-selective homonuclear-decoupled two-dimensional <Superscript>1</Superscript>H NMR

Determination of the structure of heparin-derived oligosaccharides by ¹H NMR is challenging because resonances for all but the anomeric protons cover less than 2 ppm. By taking advantage of increased dispersion of resonances for the anomeric H¹ protons at low pD and the superior resolution of band-selective, homonuclear-decoupled (BASHD) two-dimensional ¹H NMR, the primary structure of the heparin-derived octasaccharide ∆UA(2S)-[(1 → 4)-GlcNS(6S)-(1 → 4)-IdoA(2S)-]₃-(1 → 4)-GlcNS(6S) has been determined, where ∆UA(2S) is 2-O-sulfated ∆^4,5-unsaturated uronic acid, GlcNS(6S) is 6-O-sulfated, N-sulfated β-d-glucosamine and IdoA(2S) is 2-O-sulfated α-l-iduronic acid. The spectrum was assigned, and the sites of N- and O-sulfation and the conformation of each uronic acid residue were established, with chemical shift data obtained from BASHD-TOCSY spectra, while the sequence of the monosaccharide residues in the octasaccharide was determined from inter-residue NOEs in BASHD-NOESY spectra. Acid dissociation constants were determined for each carboxylic acid group of the octasaccharide, as well as for related tetra- and hexasaccharides, from chemical shift–pD titration curves. Chemical shift–pD titration curves were obtained for each carboxylic acid group from sub-spectra taken from BASHD-TOCSY spectra that were measured as a function of pD. The pK _As of the carboxylic acid groups of the ∆UA(2S) residues are less than those of the IdoA(2S) residues, and the pK _As of the carboxylic acid groups of the IdoA(2S) residues for a given oligosaccharide are similar in magnitude. Relative acidities of the carboxylic acid groups of each oligosaccharide were calculated from chemical shift data by a pH-independent method.     

Limit-periodic arithmetical functions and the ring of finite integral adeles

In this paper, we show that the ring of finite integral adeles, together with its Borel field and its normalized Haar measure, is an appropriate probability space where limit-periodic arithmetical functions can be extended to random variables. The natural extensions of additive and multiplicative functions are studied. Besides, the convergence of Fourier expansions of limit-periodic functions is proved.     

On energy estimates for second order hyperbolic equations with Levi conditions for higher order regularity

We consider energy estimates for second order homogeneous hyperbolic equations with time dependent coefficients. The property of energy conservation, which holds in the case of constant coefficients, does not hold in general for variable coefficients; in fact, the energy can be unbounded as t → ∞ in this case. The conditions to the coefficients for the generalized energy conservation (GEC), which is an equivalence of the energy uniformly with respect to time, has been studied precisely for wave type equations, that is, only the propagation speed is variable. However, it is not true that the same conditions to the coefficients conclude (GEC) for general homogeneous hyperbolic equations. The main purpose of this paper is to give additional conditions to the coefficients which provide (GEC); they will be called as C ^k -type Levi conditions due to the essentially same meaning of usual Levi condition for the well-posedness of weakly hyperbolic equations.     

Oleanolic triterpene saponins from the roots of Panax bipinnatifidus

Ten oleanane-type saponins (1-10), including three new compounds, namely bifinosides A-C (1-3), were isolated from the roots of Panax bipinnatifidus SEEM. Their structures were elucidated on the basis of chemical and spectroscopic methods.     

Control of ZnO morphologies on carbon nanotube electrodes and electrocatalytic characteristics toward hydrazine

We controlled the morphologies of zinc oxide (ZnO) nanostructures on single-walled carbon nanotube electrodes by an electrochemical deposition method and investigated the dependence of the electrocatalytic characteristics toward hydrazine on the different morphologies. ZnO nanorods provided high electrocatalytic activity with unique electrochemical behaviours, associated with the H(+) ion generated by the electro-oxidation of hydrazine.