Introduction to the theory and applications of uncertainty

We introduce the special volume “The theory and applications of uncertainty”.     

Recent applications of theory of the firm under uncertainty

This paper provides a comprehensive synthesis and analysis of the current and recent empirical implementations of the theory of the firm under uncertainty, including multiple sources of uncertainty. In so doing, it identifies the major estimation obstacles and it offers the future empirical researcher ways to derive simple estimation procedures under multiple sources uncertainty.     

Antimicrobial prospect of newly synthesized 1,3-thiazole derivatives

A new series of 1,3-thiazole and benzo[d]thiazole derivatives 10-15 has been developed, characterized, and evaluated for in vitro antimicrobial activity at concentrations of 25-200 μg/mL against Gram+ve organisms such as methicillin-resistant Staphylococcus aureus (MRSA), Gram-ve organisms such as Escherichia coli (E. coli), and the fungal strain Aspergillus niger (A. niger) by the cup plate method. Ofloxacin and ketoconazole (10 μg/mL) were used as reference standards for antibacterial and antifungal activity, respectively. Compounds 11 and 12 showed notable antibacterial and antifungal activities at higher concentrations (125-200 μg/mL), whereas benzo[d]thiazole derivatives 13 and 14 were found to display significant antibacterial or antifungal activity (50-75 μg/mL) against the Gram+ve, Gram-ve bacteria, or fungal cells used in the present study. In addition, a correlation between calculated and determined partition coefficient (log P) was established which allows future development of compounds within this series to be carried out based on calculated log P values. Moreover, compounds 13 and 14 show that the optimum logarithm of partition coefficient (log P) should be around 4.     

A New Stopping Time Model: A Solution to a Free-Boundary Problem

We present a new model of stopping times and American options. In so doing, we solve a free-boundary problem.     

Production decisions under joint price and production uncertainty

While production decisions in the presence of price uncertainty have been extensively studied, this is not so for the case in which the level of production is itself uncertain. In this paper,we provide a decision analysis under multiplicative production uncertainty, both with and without price uncertainty. We depict equilibrium and obtain comparative statics results with the aid of a diagram based on the difference between expected price and marginal cost. Comparative statics results are obtained for the model with production uncertainty alone and also for simultaneous price and production uncertainty (including two special cases). We first derive results based on the Arrow–Pratt coefficients of risk aversion, and then supplement these with the Ross measure of relative risk aversion, since this proves useful in the presence of multiple sources of uncertainty. We find that increases in risk (both price and production) or input prices reduce expected output. However, expected output supply is an increasing function of (expected) price only for “low” levels of risk aversion, and in general the relationship is ambiguous.     

Preferences estimation without approximation

We devise an estimation methodology which allows preferences estimation and comparative statics analysis without a reliance on Taylor’s approximations and the indirect utility function.     

Molecular alignment of the 4-octyl-4'-cyanobiphenyl liquid crystal filled with SiO2

The molecular dynamics and molecular alignment of the dispersed 4-octyl-4'-cyanobiphenyl (8CB) liquid crystal with 5 wt % of SiO₂ nanosphere particles have been studied using dielectric spectroscopy. The measurements were performed in the frequency range between 10²-10⁷ Hz in the SmA, N and I phases. The results show only one Debye relaxation process at high frequency (10⁵-10⁷ Hz). In the bulk material, activation energies of 40, 58 and 63 kJ mol^-1 were determined for the SmA, N and the I phases, respectively. In the dispersed sample, the activation energies were found to be 52, 76 and 81 kJ mol^-1, respectively. These results are compared with the available data in the literature. The reversible electromechanical response of the dispersed sample under the influence of an applied a.c. electric field was investigated in the SmA, N, and I phases.     

A New Approach to Stochastic Optimization

We derive general explicit solutions to the investment model without reliance on the existing duality or variational methods.     

The impact of background risk

In this paper, we introduce an incomplete-market dynamic investment model with a correlated background risk. In so doing, we show the impact of background risk on the investment decisions.     

Design and synthesis of intramolecular hydrogen bonding systems. Their application in metal cation sensing based on excited-state proton transfer reaction

We reported the design and synthesis of a new type of metal-cation probes, 3-hydroxy-4-(1,4,7,10-tetraoxa-13-azacyclopentadec-13-ylmethyl)naphthalene-2-carbaldehyde (1a) and its single hydrogen-bond analogue 1-(1,4,7,10-tetraoxa-13-azacylopentadec-13-ylmethyl)-2-naphthol (2a), in which 1-aza-15-crown-5 ether in combination with the naphthol oxygen acts as a receptor, while the mechanism of excited-state intramolecular proton transfer (ESIPT) is exploited as a signal transducer. The association constant of (2.5±0.5)×10⁴, (3.8±0.4)×10⁴, (5.5±0.5)×10³ and (1.2±0.3)×10⁴ M⁻¹ for the formation of 1a/Na⁺, 1a/Ca²⁺, 2a/Na⁺ and 2a/Ca²⁺ complexes, respectively, in CH₃CN plus drastic fluorescence changes due to the fine-tuning of ESIPT reaction upon complexation, lead 1a and 2a to be highly sensitive fluorescent sensors. The results add a new class into the category of metal-cation probes, with the perspective of designing ESIPT systems capable of sensing bio-analytes.