Convergence of an augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints

An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail.     

New Results on Generalized $c$-Distance Without Continuity in Cone $b$-Metric Spaces over Banach Algebras

In this work, some new fixed point results for generalized Lipschitz mappings on generalized $c$-distance in cone $b$-metric spaces over Banach algebras are obtained, not acquiring the condition that the underlying cone should be normal or the mappings should be continuous. Furthermore, the existence and the uniqueness of the fixed point are proven for such mappings. These results greatly improve and generalize several well-known comparable results in the literature. Moreover, some examples and an application are given to support our new results.     

Regularity of Viscosity Solutions of the Biased Infinity Laplacian Equation

In this paper, we are interested in the regularity estimates of the nonnegative viscosity super solution of the $β$−biased infinity Laplacian equation $$∆^β_∞u = 0,$$ where $β ∈ \mathbb{R}$ is a fixed constant and $∆^β_∞u := ∆^N_∞u + β|Du|,$ which arises from the random game named biased tug-of-war. By studying directly the $β$−biased infinity Laplacian equation, we construct the appropriate exponential cones as barrier functions to establish a key estimate. Based on this estimate, we obtain the Harnack inequality, Hopf boundary point lemma, Lipschitz estimate and the Liouville property etc.     

Dielectric properties of beryllia ceramics in the near-millimeter wavelength range

We report the refractive indices and absorption coefficients for four beryllia (BeO) ceramic samples. These dielectric properties have been measured over the range from 4 to 18 cm^–1 by use of a Michelson interferometer. The index n, follows the linear relationship n=0.6517 cm³/g×+0.7130 with density, , over the range 2.8<<3.0 g/cm³.     

Effect of the modification of silica on thermal properties and flammability of cross-linked butadiene-acrylonitrile rubbers

The paper presents the results of testing the thermal stability and flammability of butadiene-acrylonitrile rubber vulcanizates with different contents of combined acrylonitrile: Perbunan NT 1845 and Perbunan NT 3945 from Bayer, containing unmodified and bromine- or iodine-modified silica. The test results were obtained with the use of a derivatograph, measurements of flammability by the method of oxygen index, in air and also with the use of a cone calorimeter. The effect of the modification on the zeta potential was also examined. A considerable reduction in the flammability of nitrile rubber vulcanizates filled with silica can be obtained by the modification of filler with bromine or iodine. All the vulcanizates containing modified silica are self-extinguishing. An appropriate filling of NBR 39 vulcanizates with bromine-modified silica makes it possible to obtain non-flammable polymeric materials. They neither ignite nor glow under the action of a flame source for 30 s. The findings can be a rational basis for the synthesis of modified silica that can act as active filler and effective flame-retardant agent at the same time.     

Facets for the cut cone I

We study facets of the cut coneC _n , i.e., the cone of dimension 1/2n(n – 1) generated by the cuts of the complete graph onn vertices. Actually, the study of the facets of the cut cone is equivalent in some sense to the study of the facets of the cut polytope. We present several operations on facets and, in particular, a lifting procedure for constructing facets ofC _n+1 from given facets of the lower dimensional coneC _n . After reviewing hypermetric valid inequalities, we describe the new class of cycle inequalities and prove the facet property for several subclasses. The new class of parachute facets is developed and other known facets and valid inequalities are presented.     

Analytical chemistry and the cone penetrometer: In situ chemical characterization of the subsurface

The development of novel microanalytical techniques forin situ chemical characterization of the terrestrial subsurface environment has grown significantly over the last decade, particularly those instruments that are interfaced to the cone penetrometer. Cone penetrometer testing (CPT) has emerged as an effective means to introduce samplers and probes forin situ analysis of contaminants in soil and groundwater matrices. A variety ofin situ chemical samplers for CPT have been developed that can be driven into the subsurface to collect soil gas, groundwater, or soil samples at depth, thus providing a means of determining the vertical and horizontal extent of contamination. Cone penetrometer testing is also being explored as a means to deliverin situ subsurface sensor probes, including probes based on laser-induced fluorescence, Raman, and infrared spectroscopies for organics; on laser-induced breakdown and X-ray fluorescence spectroscopies for heavy metals; and on passive gamma-ray spectroscopy for radionuclides. The range of analytical technologies used in CPT for the determination of organic and inorganic species in the subsurface is described.     

Banach空间半线性发展方程的周期解

把上、下解方法引入到有序Ｂａｎａｃｈ空间中的半线性发展方程周期解问题，利用正算子半群特征与单调迭代程序，获得了最大周期解与最小周期解的存在性．所得的结果概括和推广了常微分方程与偏微分方程中的有关结论     

Generalized nets in neurology: an example of mathematical modelling

The purpose of this paper is to explain the basic theory of generalized nets (GNs) and their applications in the context of the differential diagnosis of neurological diseases. We define formally the concepts of a GN and transitions of a GN and also outline some remarks on their theory. The work here constructs an example which aims to trace the process of diagnosing different signs and symptoms in neurology. This will enable the interested reader to see the scope of nets in general as tools for the modelling, simulation, optimization and control of real processes.     

Conformational properties of propargyloxy-calix[4]arene tricarboxamides: NMR and DFT studies on the O-through-the-annulus rotation

The size limit of substituents allowing O-through-the-annulus rotation of substituted calix[4]arenes was further extended to the propargyloxy group in 24-propargyloxy-25,26,27-tris(N,N-dimethylcarbamoylmethoxy)-p-tert-butylcalix[4]arene by demonstrating its free but slow motion affording equilibrium between the partial cone and 1,2-alternate conformers. The effect of solvent and upper rim substituents R¹ on the conformational inversion was investigated by means of ¹H NMR. The rotational isomerisation of the parent (R¹ = H) analogue could not unambiguously be detected. The experimental results were supported by comprehensive density functional theory studies.