Robustness in deterministic multi-objective linear programming with respect to the relative interior and angle deviation

This paper deals with the robustness issue in deterministic multi-objective linear programming from two new standpoints. It is shown that a robustness notion recently reported in the literature is equivalent to strict efficiency. Corresponding to an efficient solution, a new quantity, robustness order (RO) is defined with respect to the interiority order of the cost matrix in the binding cone. A linear programming problem is provided to calculate the RO of a given efficient solution. The second part of the paper is devoted to investigating the robustness with respect to the eligible angle deviation of the cost matrix in the binding cone. Theoretical results are given to obtain the maximum eligible angle deviation. Finally, the relationship between two above-mentioned robustness standpoints is established. To have a better geometrical view, we prove the results for single-objective LP problems at first, and then we extend them to the multi-objective case. In addition to the theoretical results, some clarifying examples are given.     

Computation and conversion of brain pH values obtained with two algorithms of phosphorus magnetic resonance spectroscopy data analysis

The intracellular brain pH in phosphorus magnetic resonance spectroscopy is calculated using the chemical shift between the inorganic phosphate and phosphocreatine with the Henderson–Hasselbalch equations. Researchers use various mathematical formulas that have different parameters and get various results for the same input data as a consequence. Thus, the aim of this article was to determine the mathematical formulas that allow the conversion of the pH values obtained by the most popular analysis methods to each other. To determine the relationships between pH results and the applied mathematical formula, the pH values were calculated using two algorithms for the theoretical chemical shift values. The pH results were compared with each other using the appropriate t-tests. Mathematical formulas were designed to simplify the conversion of pH values obtained by two data analysis methods to each other. The pH values with were obtained this way did not differ significantly from the pH values calculated directly from the given formula. The computed mathematical formulas will make it possible to simplify pH conversions without knowing the chemical shift between inorganic phosphate and phosphocreatine but only basing on the final pH values obtained by one of the formulas.     

Rheological Technique as a Sensitive Method to Characterize the Chain Diffusion across the Interface between Polystyrene and Carbon Black Filled Polystyrene

The mutual diffusion process and interphase development taking place at the interface between disks of polystyrene (PS) and carbon black filled polystyrene (CB-PS) in the molten state were investigated by a small-amplitude, oscillatory shear, rheological technique. The rheological method was employed to probe the thermorheological complexity of these polymer disks. It was found that the dynamic complex shear modulus, G*(t), increased with the time of contact in two time regimes at a fixed frequency. The time of transition between the two regimes was observed to be close to the time needed for the transition from the Rouse mode to the reptation mode. The results showed that the content of the carbon black and the temperature affected the slope of the G*(t) – t curve. Scanning electron microscopy revealed the interface disappeared when the diffusion process was complete.     

σ2 Hessian方程的Pogorelov型C2 内估计及应用

提出利用拉格朗日乘子法重新证明σ2算子的最优凹性,并定义了一个凸锥Γ3?=λ=(λ1,λ2,?,λn)∈Rn:σ1(λ)>0,σ2(λ|i)>0,1≤i≤n。利用σ2算子的最优凹性，给出了σ2Hessian方程Pogorelov型C2内估计，进而证明了σ2(D2u(x))=1,x∈Rn的满足二次多项式增长条件的Γ3?-凸整解为二次多项式。     

Flux and fluence dependence of disorder produced during implantation of 11B in silicon

The flux and fluence dependence of disorder produced in silicon during the implantation of ¹¹B has been investigated at room temperature, -50°C. and -120°C. Implantations were carried out with 200 keV ¹¹B ions using current densities in the range from 0.06μA/cm² to 15μA/cm², and the disorder monitored by measuring the energy spectra of backscattered protons which were incident on the sample at 450 keV parallel to a (110) axis. Significant differences in the dependence of the disorder on ¹¹B flux and fluence were observed between the implantations performed at room temperature and those carried out at the two lower temperatures.     

Super-symmetric informationally complete measurements

Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately connected with the geometry of the quantum state space and also has profound implications for foundational studies. Here we explore those SICs that are most symmetric according to a natural criterion and show that all of them are covariant with respect to the Heisenberg–Weyl groups, which are characterized by the discrete analog of the canonical commutation relation. Moreover, their symmetry groups are subgroups of the Clifford groups. In particular, we prove that the SIC in dimension 2, the Hesse SIC in dimension 3, and the set of Hoggar lines in dimension 8 are the only three SICs up to unitary equivalence whose symmetry groups act transitively on pairs of SIC projectors. Our work not only provides valuable insight about SICs, Heisenberg–Weyl groups, and Clifford groups, but also offers a new approach and perspective for studying many other discrete symmetric structures behind finite state quantum mechanics, such as mutually unbiased bases and discrete Wigner functions.     

On the inverse spectral theory in a non-homogeneous interior transmission problem

We study the inverse spectral problem in an interior transmission eigenvalue problem. The Cartwright’s theory in value distribution theory gives a connection between the distributional structure of the eigenvalues and the asymptotic behaviours of its defining functional determinants. Given a sufficient quantity of transmission eigenvalues, we prove a uniqueness of the refraction index in inhomogeneous medium as an uniqueness problem in entire function theory. The asymptotically periodical structure of the zero set of the solutions helps to locate infinitely many eigenvalues of infinite degree of freedom.     

Synthesis of Diquinolineno[1,3,7,9]Tetraazacyclododecine-7, 15 (14H, 16H)-Dibenzene,and DNA Binding Studies of Macrocyclic Co(II), Cu(II) Complexes: As New Class of Antimicrobial Agent

The synthesis of macrocyclic ligand, diquinolineno[1,3,7,9]tetraazacyclododecine-7, 15 (14H, 16H)-dibenzene(L), is described. The metal complexes of the type [MLX₂], where (M = Co(II) (1), Cu(II) (2) and X = (Cl), have been synthesized by the reaction of ligand(L) with the corresponding metal salts, and characterized by elemental analysis, FT-IR, ¹H-NMR and electronic spectra. The binding property of the complexes with CT-DNA was studied by absorption spectra, viscosity measurements, as well as thermal denaturation studies. The absorption spectral results indicate that the complexes (1) and (2) are binds with base pairs of DNA. The intrinsic binding constant K_b had the value 3.8 × 10⁴M ^?1 for (1 Chappell, L. L., Voss, A. D. and Morrow, J. R. 1998. Inorg. Chem., 37(16): 3989–3998.  [Google Scholar]) and 3.3 × 10⁴ M^?1 for (2), respectively, in 5 mM Tris-HCl/50 mM NaCl buffer at pH 7.2. The viscosity measurement results show the viscosity of sonicated rod-like DNA fragments increased when the complex were added to the solution of calf thymus-DNA. The synthesized ligand and its metal complexes have been screened for antibacterial and antifungal activities.     

Electrical conductivity of poly(vinylidene fluoride)/polyaniline blends under oscillatory and steady shear conditions

Blends of poly(vinylidene fluoride) (PVDF) and polyaniline (PAni) were prepared through melt blending in a batch mixer. The morphology, rheological behavior and electrical conductivity were investigated through transmission electron microscopy (TEM) and combined electro-rheological measurements. Through TEM analysis, it was possible to observe that all blends showed typical phase separation with the presence of conductive polymer aggregates. Deformations imposed during a strain sweep caused, not only disturbance of the linear viscoelastic behavior, but also changes in electrical conductivity. The oscillatory shear altered the morphology, breaking the PAni domains into smaller ones. This effect increases the distance between them and, consequently, resulted in a decrease of the electrical conductivity. The measurements under quiescent conditions and steady shear proved that the disturbance in morphology for PVDF/PAni system is non-recoverable. Through combined electrical and rheological measurements, it was possible to achieve good correlation between the electrical and flow behavior of PVDF/PAni blends.     

Optical manipulation of charged microparticles in polar fluids

In this study, we report a systematic study of the response of a charged microparticle confined in an optical trap and driven by electric fields. The particle is embedded in a polar fluid, hence, the role of ions and counterions forming a double layer around the electrodes and the particle surface itself has been taken into account. We analyze two different cases: (i) electrodes energized by a step‐wise voltage (DC mode) and (ii) electrodes driven by a sinusoidal voltage (AC mode). The experimental outcomes are analyzed in terms of a model that combines the electric response of the electrolytic cell and the motion of the trapped particle. In particular, for the DC mode we analyze the transient particle motion and correlate it with the electric current flowing in the cell. For the AC mode, the stochastic and deterministic motion of the trapped particle is analyzed either in the frequency domain (power spectral density, PSD) or in the time domain (autocorrelation function). Moreover, we will show how these different approaches (DC and AC modes) allow us, assuming predictable the applied electric field (here generated by plane parallel electrodes), to provide accurate estimation (3%) of the net charge carried by the microparticle. Vice versa, we also demonstrate how, once predetermined the charge, the trapped particle acts as a sensitive probe to reveal locally electric fields generated by arbitrary electrode geometries (in this work, wire‐tip geometry).