Abstract Over the years a number of two-factor interest rate models have been proposed that have formed the basis for the valuation of interest rate contingent claims. This valuation equation often takes the form of a partial differential equation that is solved using the finite difference approach. In the case of two-factor models this has resulted in solving two second-order partial derivatives leading to boundary errors, as well as numerous first-order derivatives. In this article we demonstrate that using Green's theorem, second-order derivatives can be reduced to first-order derivatives that can be easily discretized; consequently, two-factor partial differential equations are easier to discretize than one-factor partial differential equations. We illustrate our approach by applying it to value contingent claims based on the two-factor CIR model. We provide numerical examples that illustrate that our approach shows excellent agreement with analytical prices and the popular Crank–Nicolson method. 相似文献
In this paper we classify Bianchi type VIII and IX space—times according to their teleparallel Killing vector fields in the teleparallel theory of gravitation by using a direct integration technique. It turns out that the dimensions of the teleparallel Killing vector fields are either 4 or 5. From the above study we have shown that the Killing vector fields for Bianchi type VIII and IX space—times in the context of teleparallel theory are different from that in general relativity. 相似文献
Black phosphorus(BP) has received attention due to its own higher carrier mobility and layer dependent electronic properties, such as direct band gap. Interestingly, the single layer black phosphorus(SLBP) has had large popularity in applications related to thermoelectric, optoelectronic, and electronic devices. Here, we investigate the phonon spectrum,thermal conductivities, and stress strain effects. Robust anisotropy was mainly observed in the thermal conductivities together with the alongside zigzag(ZZ) direction value, compared to the armchair(AC) directions. We also investigated the attitude of stress that was anisotropic in both directions, and the stress effects were two times greater across the ZZ path than those in the AC direction at a low temperature. We obtained a Young's modulus of 63.77 and 20.74 GPa in the AC and ZZ directions, respectively, for a strain range of 0.01. These results had good agreement with first principle calculations.Our study here is useful and significant for the thermal tuning of phosphorus-based nanoelectronics and thermalelectric applications of phosphorus. 相似文献
Fukuyama reaction for the synthesis of multifunctional aldehydes, secondary amines and ketones has gained considerable importance in synthetic organic chemistry because of mild reaction conditions. The use of thioesters in both Fukuyama aldehydes and ketones synthesis is highly attractive for organic chemists as they are easily accessible from corresponding carboxylic acids. Fukuyama–Mitsunobu reaction utilizes 2-nitrobenzenesulfonyl (Ns) for the protection/activation/deprotection of primary amines to afford secondary amines in good yields and high enantioselectivities. This review presents recent synthetic developments and applications of Fukuyama reaction for the synthesis of aldehydes, secondary amines and ketones.
The need for some economic strategies for increased growth and nutraceuticals of medicinal plants is well acknowledged now. It was hypothesized that external magnetic field treatment (MFT) of seeds affecting internal magnet of cells may affect growth and metabolism. In this study, seeds were subjected to pre-sowing magnetic field (50 mT at 5 mm for 5 s). At vegetative stage, the leaf growth, chlorophyll content, catalase (CAT), peroxidase (POD), amino acids, proteins, flavonoids, soluble sugars, total soluble phenolics, carotenoids, anthocyanins, phenolic profile (HPLC based), and antimicrobial activity of leaves (in terms of the minimum inhibitory concentration against Staphylococcus aureus and Pseudomonas aeruginosa) were studied. Yield was evaluated for nutritive components in fruit (peel+pulp) and peel. MFT improved germination percentage, growth, leaf chlorophyll, antimicrobial activity, peel amino acids, phenolics, and POD with negligible effect on fruit nutritive value. Moreover, photosynthetic pigments and cinnamic acid exhibited direct correlation with antimicrobial potential against both pathogens. However, sinapic acid showed positive correlation against Staphylococcus aureus only. Cinnamic acid, coumaric acid, syringic acid, and quercetin were in direct correlation against Pseudomonas aeruginosa; it was directly correlated with total flavonoids too. In conclusion, magnetic field can be used to manipulate plant cell metabolism promising improvement of growth, antimicrobial activity, and phenolics of interest.
A simple and rapid spectrophotometric technique has been designed for the trace copper analysis employing 1-(2-Thiazolylazo)-2-naphthol (TAN) reagent in aqueous micellar solution of cetyl trimethylammonium bromide (CTAB) as a surfactant. Copper complexed with 1-(2-Thiazolylazo)-2-naphthol to form bis[1-(2-Thiazolylazo)-2-naphthol]copper. The present spectrophotometric technique was very important since the micellar system was used in place of the toxic, high cost and time-consuming solvent extraction steps. The technique showed an enhanced detection efficiency, specificity, and molar absorptivity. It was found that the molar absorption coefficient and sensitivity of Sandel were ε 2.45 × 104 L mol?1cm?1 and 2.6 ngcm?2 at λmax 578.4 nm. A linear calibration plot in the range 0.12–5.0 μg mL?1 was obtained; a stoichiometric metal ligand ratio [M:L] of 1:2 was found for the formation of Cu-[TAN]2. The complex was formed at pH 9.5 and was stable up to 24 h. The proposed technique has been employed to study copper from different alloys, biological, environmental and pharmaceutical samples. 相似文献
Alkene is an attractive substrate for chemists due to its easy availability and reactivity towards large number of reactants affording diverse range of organic compounds. It reacts under ionic and free radical mechanisms including single electron transfer (SET). In this review, strategies used for C–C and C-heteroatom functionalization of alkene has been discussed with emphasis on the regio, stereoselectivity, mechanistic detail and sustainability aspects. These strategies mainly follow the free radical mechanism, and the highly reactive carbon radicals show uncontrollable regio- and stereoselectivities. Thus these strategies still need to be focused; especially in the asymmetric versions. The regio- and stereoselectivities of functionalization of alkenes have been highlighted and debated. In addition, the hazardous reagents such as Cl2, Br2 I2, CO, peroxides, and benzene have also been discussed with the emphasis on their impact on the environment. Their plausible green alternatives have also been suggested, such as MX as halogen replacement; CO surrogates (formaldehyde etc.); sustainable aromatic solvents as benzene replacement. The non-green strategies relying on pre-formed silyl hydride and their green alternative strategies such as transfer hydrogenations have also been indicated. The applications of the functionalization of alkenes for the total synthesis of bioactive compounds have also been discussed in detail. In addition, future perspectives are also highlighted for further developments in the functionalization of alkenes. 相似文献
Peptide nucleic acid (PNA) is a nucleic acid analog which consists of purines, pyrimidines bases, and a neutrally charged peptide backbone. The PNA has the potential as a very useful biological probe for protein analysis since it has more in vivo biological stability as compared to DNA- or RNA-based aptamers. Usually, the addition of amino acids or peptide to the PNA backbone is used to improve its water-solubility and cell-permeability, but these modifications may affect the interaction between PNA and proteins. To date, the investigation of the interaction between PNA and proteins is rare, and there is no reported study about the effects of modifications. In this work, we designed two types of amino acid modified PNAs, (Lys)2-PNA and (Glu)2-PNA, which kept the same base sequence with 15-mer thrombin aptamer and had two basic lysine and two acidic glutamic acid residues on N-terminal of the peptide backbone, respectively. To rapidly assess the binding affinity and specificity of modified PNA and proteins, the online CE reaction method was developed to analyze the interactions of (Lys)2-PNA/(Glu)2-PNA and three proteins: thrombin (THB), single-strand DNA-binding protein (SSB) and human serum albumin (HSA). Meanwhile, the interactions of (Lys)2-PNA/(Glu)2-PNA and thrombin were compared with that of the corresponding complementary base sequence (Lys)2-cPNA/(Glu)2-cPNA and thrombin. The online CE reaction results showed that the interaction of (Lys)2-PNA and (Glu)2-PNA with three proteins was in the order of THB > SSB > HSA. However, (Lys)2-PNA and (Lys)2-cPNA showed similar binding affinity with thrombin; while the binding affinity of (Glu)2-PNA with thrombin was stronger than that of (Glu)2-cPNA with thrombin. Moreover, the binding constant Kb of (Glu)2-PNA and three proteins was determined by affinity capillary electrophoresis (ACE). The online CE reaction eliminates the requirement of incubation, and thus it is fast in detection, and easy to operate with minimum cost. The method is particularly suitable for the interaction studies of expensive modified PNAs and proteins, and can assist the design of PNA probe that binds to proteins. 相似文献