On dual quermassintegrals of mixed intersection bodies

In this paper, it is shown that a family of inequalities involving mixed intersection bodies holds. The Busemann intersection inequality is the first of this family. All of the members of this family are strengthened versions of classical inequalities between pairs of dual quermassintegrals of a star body.     

On box totally dual integral polyhedra

Edmonds and Giles introduced the class of box totally dual integral polyhedra as a generalization of submodular flow polyhedra. In this paper a geometric characterization of these polyhedra is given. This geometric result is used to show that each TDI defining system for a box TDI polyhedron is in fact a box TDI system, that the class of box TDI polyhedra is in co-NP and is closed under taking projections and dominants, that the class of box perfect graphs is in co-NP, and a result of Edmonds and Giles which is related to the facets of box TDI polyhdera.Supported by a grant from the Alexander von Humboldt-Stiftung.     

3D imager using dual color-balanced lights

A novel method for grabbing 3D shape of an object is proposed. It uses a pair of color-coded light sources to create a 3D-coordinated illumination space. The intensities of two modulation colors are complementally balanced, which makes the sum of the intensities of the colors a constant. This method demonstrates the abilities of uniquely representing any point in the 3D-coordinated illumination space, reducing the measuring problems in blind area, and compensating the effect caused by changes of surface color and reflection. In addition, this method has the ability of acquiring the 3D shape information in parallel and the algorithm is fairly simple, so the 3D imaging speed is basically restricted by the frame rate of the color CCD camera.     

Revisiting Quaternion Dual Electrodynamics

Dual electrodynamics and corresponding Maxwell’s equations (in the presence of monopole only) are revisited from dual symmetry and accordingly the quaternionic reformulation of field equations and equation of motion is developed in simple, compact and consistent manner.     

Mineralization of biomimetically carboxymethylated collagen fibrils in a model dual membrane diffusion system

In the present work, we show for the first time, that N^?-carboxymethyllysine is the major product of the in vitro non-enzymatic glycation reaction between fibrillar collagen and glucuronic acid. Dual diffusion membrane system was effectively used for oriented crystal growth of octacalcium phosphate/hydroxyapatite on the biomimetically carboxymethylated collagen fibrils. We hypothesize that the function of biomimetically carboxymethylated collagen is to increase the local concentration of corresponding ions in such a way that a critical nucleus of ions can be formed, leading to the formation of the mineral under specific micro-environment conditions achieved by using diffusion membrane system.     

Critical duality

We look for a general framework in which the Ekeland duality can be formulated. We propose a scheme in which the parameter sets are provided with a coupling function which induces a conjugacy. The decision spaces are not supposed to have any special structure. We examine several examples. In particular, we consider some special classes of generalized convex functions.     

An acceleration of Erlenkotter-Körkel’s algorithms for the uncapacitated facility location problem

This contribution is focused on an acceleration of branch and bound algorithms for the uncapacitated facility location problem. Our approach is based on the well-known Erlenkotters’ procedures and Körkels’ multi-ascent and multi-adjustment algorithms, which have proved to be the efficient tools for solving the large-sized instances of the uncapacitated facility location problem. These two original approaches were examined and a thorough analysis of their performance revealed how each particular procedure contributes to the computational time of the whole algorithms. These analyses helped us to focus our effort on the most frequent procedures. The unique contribution of this paper is a new dual ascent procedure. This procedure leads to considerable acceleration of the lower bound computation process and reduces the resulting computational time. To demonstrate more efficient performance of amended algorithms we present the results of extensive numerical experiments.     

Potassium Acyltrifluoroborate (KAT) Ligations are Orthogonal to Thiol‐Michael and SPAAC Reactions: Covalent Dual Immobilization of Proteins onto Synthetic PEG Hydrogels

The covalent immobilization of peptides, proteins, and other biomolecules to hydrogels provides a biologically mimicking environment for cell and tissue growth. Bioorthogonal chemical reactions can serve as a tool for this, but the paucity of such reactions and mutual incompatibilities limits the number of distinct molecules that can be introduced. We now report that the potassium acyltrifluoroborate (KAT ) amide‐forming ligation is orthogonal to both thiol‐Michael and strain promoted azide alkyne cycloadditions (SPAAC ) and the requisite functional groups – KAT s and hydroxylamines – are stable and compatible to hydrogel formation, protein modification, and post‐assembly immobilization of biomolecules onto hydrogels. In combination these ligations enables stepwise covalent protein immobilization of multiple BSA ‐derivatives onto the hydrogel scaffold regardless of the order of addition.     

A dual chemosensor for Cu2+ and Fe3+ based on π-extend tetrathiafulvalene derivative

A new dual chemosensor (TTF-PBA) for Fe³⁺ and Cu²⁺ in different signal pathways was designed and synthesized. The absorption spectrum, fluorescence spectrum and cyclic voltammograms changed in the presence of Cu²⁺ and Fe³⁺. The optical color changed within 5 s from yellow to orange upon the addition of Cu²⁺, and it changed to dark yellow when Fe³⁺ existed. The cyclic voltammogram of Cu²⁺/TTF-PBA changed from E_ox = 0.50 V, E_red = 0.32 V to E_ox = 0.64 V, E_red = 0.80 V (vs Ag/AgCl) upon the addition of 2.0 equiv. Cu²⁺. As for Fe³⁺/TTF-PBA, its oxidation wave disappeared, and its reduction wave appeared at E_red = ?0.59 V (vs Ag/AgCl) upon the addition of 4.0 equv. Fe³⁺. The sensor displayed high selectivity for Cu²⁺ and Fe³⁺ over other ions including Pb²⁺, Zn²⁺, Ni²⁺, Ag⁺, Cr³⁺, Mn²⁺, Al³⁺, Co²⁺, Pd²⁺, Hg²⁺, Fe^2+, Cd²⁺, Ce³⁺, Bi³⁺ and Au³⁺, the detection limits for Cu²⁺ and Fe³⁺ ion reached as low as 5.33 × 10^?7 mol/L and 5.34 × 10^?7 mol/L, respectively. Furthermore, when Fe³⁺ existed, Cu²⁺ can be detected sequentially by the sensor through the absorption spectrum and the color change observed by naked-eyes.     

A pyrene-based dual chemosensor for colorimetric detection of Cu2+ and fluorescent detection of Fe3+

A pyrene based chemosensor was designed and synthesized. The pyrene fluorophore was connected with a pyridine unit through a Schiff base structure to give the sensor (L). L was tested with a variety of metal ions and exhibited high colorimetric selectivities for Cu²⁺ and Fe³⁺ over other ions. Upon binding with Cu²⁺ or Fe³⁺, L showed an obvious optical color change from colorless to pink for Cu²⁺ or orange for Fe³⁺ over a wide pH range from 3 to 12. Moreover, the fluorescence of L at 370 nm decreased sharply after bonding with Fe³⁺, while other metal ions including Cu²⁺ had no apparent interference. Thus, using such single chemosensor, Cu²⁺ and Fe³⁺ can be detected independently with high selectivity and sensitivity. The limits of detection toward Cu²⁺ and Fe³⁺ were 8.5 and 2.0 μM, respectively. DFT calculation results also proved the formation of stable coordination complexes and the phenomenon of fluorescence quenching by Fe³⁺. Furthermore, L was also successfully used as a bioimaging reagent for detection of Fe³⁺ in living cells.