Multiplicative functions additive on generalized pentagonal numbers

We prove that the set GP of all nonzero generalized pentagonal numbers is an additive uniqueness set; if a multiplicative function f satisfies the equation

$f(a+b)=f(a)+f(b),$

for all $a,b\in GP$, then f is the identity function.     

Random fixed point theorems for Hardy-Rogers self-random operators with applications to random integral equations

In this paper, we prove some random fixed point theorems for Hardy–Rogers self-random operators in separable Banach spaces and, as some applications, we show the existence of a solution for random nonlinear integral equations in Banach spaces. Some stochastic versions of deterministic fixed point theorems for Hardy–Rogers self mappings and stochastic integral equations are obtained.     

Strong convergence analysis of a hybrid algorithm for nonlinear operators in a Banach space

In this paper, a hybrid algorithm is investigated for an asymptotically quasi-$\phi$-nonexpansive mapping in the intermediate sense and a bifunction. Strong convergence of the algorithm is obtained in a strictly convex, smooth and reflexive Banach space.     

Mean curvatures and Gauss maps of a pair of isometric helicoidal and rotation surfaces in Minkowski 3-space

It is proved that, in Minkowski 3-space, a CSM-helicoidal surface, i.e., a helicoidal surface under cubic screw motion is isometric to a rotation surface so that helices on the helicoidal surface correspond to parallel circles on the rotation surface. By distinguishing a CSM-helicoidal surface as three cases, that is, the case of type I, the case of type II with negative and positive pitch, the relations are discussed between the mean curvatures or Gauss maps of a pair of isometric helicoidal and rotation surface. A CSM-helicoidal surface of Case 1 or 2 and its isometric rotation surface with null axis have same mean curvatures (resp. Gauss maps) if and only if they are minimal. But each pair of isometric CSM-helicoidal surface of Case 3 and rotation surface with spacelike axis have different Gauss maps.     

Simulation in manufacturing and business: A review

This paper reports the results of a review of simulation applications published within peer-reviewed literature between 1997 and 2006 to provide an up-to-date picture of the role of simulation techniques within manufacturing and business. The review is characterised by three factors: wide coverage, broad scope of the simulation techniques, and a focus on real-world applications. A structured methodology was followed to narrow down the search from around 20,000 papers to 281. Results include interesting trends and patterns. For instance, although discrete event simulation is the most popular technique, it has lower stakeholder engagement than other techniques, such as system dynamics or gaming. This is highly correlated with modelling lead time and purpose. Considering application areas, modelling is mostly used in scheduling. Finally, this review shows an increasing interest in hybrid modelling as an approach to cope with complex enterprise-wide systems.     

An adjustable approach to fuzzy soft set based decision making

Molodtsov’s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. Recently, decision making based on (fuzzy) soft sets has found paramount importance. This paper aims to give deeper insights into decision making based on fuzzy soft sets. We discuss the validity of the Roy-Maji method and show its true limitations. We point out that the choice value designed for the crisp case is no longer fit to solve decision making problems involving fuzzy soft sets. By means of level soft sets, we present an adjustable approach to fuzzy soft set based decision making and give some illustrative examples. Moreover, the weighted fuzzy soft set is introduced and its application to decision making is also investigated.     

Support vector machines for default prediction of SMEs based on technology credit

In Korea, many forms of credit guarantees have been issued to fund small and medium enterprises (SMEs) with a high degree of growth potential in technology. However, a high default rate among funded SMEs has been reported. In order to effectively manage such governmental funds, it is important to develop an accurate scoring model for selecting promising SMEs. This paper provides a support vector machines (SVM) model to predict the default of funded SMEs, considering various input variables such as financial ratios, economic indicators, and technology evaluation factors. The results show that the accuracy performance of the SVM model is better than that of back-propagation neural networks (BPNs) and logistic regression. It is expected that the proposed model can be applied to a wide range of technology evaluation and loan or investment decisions for technology-based SMEs.     

Group-specific stochastic production frontier models with parametric specifications

This paper develops a stochastic frontier model that not only focuses more on group-specific temporal variations in technical efficiency rather than individual temporal variations, but also allows for a parametric function of the time-varying coefficient of the efficiency factor. We derived the concentrated least squares estimator and its asymptotic properties. When applied to the Penn World data set, the group-specific models yield much more variation in the temporal patterns of efficiency across countries. This application demonstrates the feasibility of applying a group-specific stochastic frontier model with a parametric function of temporal pattern to a real empirical analysis.     

Photoluminescence properties of a perfluorinated supramolecular columnar liquid crystal with a pyrene core: effects of the ordering and orientation of the columns

We investigated the effects of the alignment and ordering of pi-conjugated perfluorinated dendrimers containing pyrene moieties in their cores on their photoluminescence (PL) properties. The pyrene molecules are stacked in columns surrounded by aromatic and semifluorinated tails, which can be conjugated and act as chromophores. Polarized light microscopy (PLM), cross-sectional scanning electron microscopy (SEM), and atomic force microscopy (AFM) results show that variation of the cooling rate of the dendrimers produces variation in their orientation and ordering: Slow cooling (approximately <0.5 degrees C/min) of the isotropic melt in a sandwich glass cell results in a high degree of ordering and the vertical alignment of the columns on the substrate, in which the stacked pyrene molecules are oriented parallel to the surface over large areas. In contrast, rapid cooling (approximately >10 degrees C/min) leads to the planar alignment of the columns with significant disorder on the same substrate. UV-vis, PL, SEM, and AFM results show that the quenched columns with a planar orientation produce a broad emission band and a second weak shoulder, which indicates the presence of isolated molecules. However, the high degree of ordering of the columns with a vertical alignment produces a red-shift in the PL spectrum, with very few isolated molecules. By comparing two films with different alignments but similar ordering, we show that the ordering of this material has a greater influence on the PL spectrum than the alignment. This effect of the ordering of the columns was further verified by comparing the optical properties of the isolated dendrimers with those of small pi-conjugated molecules in solution and solid films.     

Preparation and characterization of the antibacterial Cu nanoparticle formed on the surface of SiO2 nanoparticles

Cu deposition on the surface of spherical SiO2 nanoparticles was studied to achieve the hybrid structure of Cu-SiO2 nanocomposite. SiO2 nanoparticles served as seeds for continuous Cu metal deposition. The chemical structure and morphology were studied with X-ray photoelectron spectroscopy (XPS), scanning electron microscope energy dispersive X-ray (SEM-EDX), and a transmission electron microscope (TEM). The antibacterial properties of the Cu-SiO2 nanocomposite were examined with disk diffusion assays. The homogeneously formed Cu nanoparticles on the surface of SiO2 nanoparticles without aggregation of Cu nanoparticles showed excellent antibacterial ability.