Predicting a cyclic Poisson process

We construct and investigate a (1−α)-upper prediction bound for a future observation of a cyclic Poisson process using past data. A normal based confidence interval for our upper prediction bound is established. A comparison of the new prediction bound with a simpler nonparametric prediction bound is also given.     

The limit of the partial sums process of spatial least squares residuals

We establish a functional central limit theorem for a sequence of least squares residuals of spatial data from a linear regression model. Under mild assumptions on the model we explicitly determine the limit process in the case where the assumed linear model is true. Moreover, in the case where the assumed linear model is not true we explicitly establish the limit process for the localized true regression function under mild conditions. These results can be used to develop non-parametric model checks for linear regression. Our proofs generalize ideas of a univariate geometrical approach due to Bischoff [W. Bischoff, The structure of residual partial sums limit processes of linear regression models, Theory Stoch. Process. 8 (24) (2002) 23–28] which is different to that proposed by MacNeill and Jandhyala [I.B. MacNeill, V.K. Jandhyala, Change-point methods for spatial data, in: G.P. Patil, et al. (Eds.), Multivariate Environmental Statistics. Papers Presented at the 7th International Conference on Multivariate Analysis held at Pennsylvania State University, University Park, PA, USA, May 5–9 1992, in: Ser. Stat. Probab., vol. 6, North-Holland, Amsterdam, 1993, pp. 289–306 (in English)]. Moreover, Xie and MacNeill [L. Xie, I.B. MacNeill, Spatial residual processes and boundary detection, South African Statist. J. 40 (1) (2006) 33–53] established the limit process of set indexed partial sums of regression residuals. In our framework we get that result as an immediate consequence of a result of Alexander and Pyke [K.S. Alexander, R. Pyke, A uniform central limit theorem for set-indexed partial-sum processes with finite variance, Ann. Probab. 14 (1986) 582–597]. The reason for that is that by our geometrical approach we recognize the structure of the limit process: it is a projection of the Brownian sheet onto a certain subspace of the reproducing kernel Hilbert space of the Brownian sheet. Several examples are discussed.     

Non-standard finite-difference time-domain method for solving the Schrödinger equation

The literature on chaos has highlighted several chaotic systems with special features. In this work, a novel chaotic jerk system with non-hyperbolic equilibrium is proposed. The dynamics of this new system is revealed through equilibrium analysis, phase portrait, bifurcation diagram and Lyapunov exponents. In addition, we investigate the time-delay effects on the proposed system. Realisation of such a system is presented to verify its feasibility.     

Estimating the intensity of a cyclic Poisson process in the presence of linear trend

We construct and investigate a consistent kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process in the presence of linear trend. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias, variance, and the mean-squared error of the proposed estimator are also computed. A simulation study shows that the first order asymptotic approximations to the bias and variance of the estimator are not accurate enough. Second order terms for bias and variance were derived in order to be able to predict the numerical results in the simulation. Bias reduction of our estimator is also proposed.     

A reliable synthesis of 2- and 6-amino-β-cyclodextrin and permethylated-β-cyclodextrin

A new, reliable method for the introduction of an amine group at positions 2 or 6 of β-cyclodextrin and permethyl-β-cyclodextrin is described. It involves selective tosylation followed by azide substitution and almost quantitative reduction with triphenylphosphine followed by hydrolysis of the phosphinimine intermediate.     

Synthesis and application of mono-6-(3-methylimidazolium)-6-deoxyperphenylcarbamoyl-beta-cyclodextrin chloride as chiral stationary phases for high-performance liquid chromatography and supercritical fluid chromatography

The synthesis of mono-6-(3-methylimidazolium)-6-deoxyperphenylcarbamoyl-beta-cyclodextrin chloride (MPCCD) and its application in chiral stationary phases (CSPs) for high-performance liquid chromatography (HPLC) and supercritical fluid chromatography (SFC) are being reported. This chiral selector is coated onto silica gel in different weight percentages (15, 20 and 35%, w/w) to obtain CSPs having different loading content. These new chiral stationary phases are tested using normal-phase HPLC for enantioseparation of racemic aromatic alcohols. Indeed, the enantiodiscrimination abilities of these CSPs are found to be influenced by the loading content of the chiral selector. Among the three columns (MPCCD-C15, MPCCD-C20 and MPCCD-C35), the best enantioseparation results are obtained using a column containing 20% (w/w) of MPCCD (MPCCD-C20). The resolution (R(s)) obtained for p-fluorophenylethanol, p-chlorophenylethanol, p-bromophenylethanol, p-iodophenylethanol and p-fluorophenyl-3-buten-1-ol using MPCCD-C20 ranges from 3.83 to 5.65. Good enantioseparation results are obtained for these analytes under SFC separation conditions using the MPCCD-C20 column.     

The Antiproliferative and Apoptosis-Inducing Effects of the Red Macroalgae Gelidium latifolium Extract against Melanoma Cells

The red macroalga Gelidium latifolium is widely distributed in the coastal areas of Indonesia. However, current knowledge on its potential biological activities is still limited. In this study, we investigated the potential bioactive compounds in Gelidium latifolium ethanol extract (GLE), and its cytotoxic effects against the murine B16-F10 melanoma cell line. GLE shows high total phenolic content (107.06 ± 17.42 mg GAE/g) and total flavonoid content (151.77 ± 3.45 mg QE/g), which potentially contribute to its potential antioxidant activity (DPPH = 650.42 ± 2.01 µg/mL; ABTS = 557.01 ± 1.94 µg/mL). ESI-HR-TOF-MS analysis revealed large absorption in the [M-H]^- of 327.2339 m/z, corresponding to the monoisotopic molecular mass of brassicolene. The presence of this compound potentially contributes to GLE’s cytotoxic activity (IC₅₀ = 84.29 ± 1.93 µg/mL). Furthermore, GLE significantly increased the number of apoptotic cells (66.83 ± 3.06%) compared to controls (18.83 ± 3.76%). Apoptosis was also confirmed by changes in the expression levels of apoptosis-related genes (i.e., p53, Bax, Bak, and Bcl2). Downregulated expression of Bcl2 indicates an intrinsic apoptotic pathway. Current results suggest that components of Gelidium latifolium should be further investigated as possible sources of novel antitumor drugs.     

The 293 K structure of tetradehydrohaliclonacyclamine A

The polycyclic title compound {systematic name: (1S,16S,17S,31S)‐3,20‐diazatetracyclo[15.15.0^1,17.1^3,31.1^16,20]tetratriaconta‐6,8,23,25‐tetraene}, C₃₂H₅₂N₂, has recently been isolated and characterized structurally, in solution by NMR spectroscopy and in the solid state by X‐ray crystallography. At 130 K the structure is monoclinic (P2₁, Z = 4) and comprises two molecules in the asymmetric unit with distinctly different conformations in the twelve‐C‐atom bridging chains. We report that, at 250 K, a phase change from monoclinic to orthorhombic (P22₁2₁, Z = 4) occurs. The higher‐temperature phase is structurally characterized herein at 293 K. The two different conformers resolved in the monoclinic low‐temperature form merge to give a single disordered molecule in the asymmetric unit of the high‐temperature phase.     

Synthesis and application of single-isomer 6-mono(alkylimidazolium)-beta-cyclodextrins as chiral selectors in chiral capillary electrophoresis

Novel single isomers of positively charged beta-CDs were prepared via nucleophilic substitution of 6-monotosyl-beta-CD with alkylimidazoles to afford 6-mono(alkylimidazolium)-beta-CD tosylates and then 6-mono(alkylimidazolium)-beta-CD chlorides by anion exchange. The chiral resolution abilities of these cationic CDs were studied by CE using dansyl (Dns)-amino acids as model analytes. From the experimental results, it was found that both resolution and selectivity of these cationic CDs were dependent on the following parameters: concentration of chiral selectors, pH of the running buffer, counteranions of the CDs, side chain length of the n-alkyl-imidazolium cation, temperature of the capillary column, and organic modifier used. The concentration of chiral selectors required for enantioseparation varied from 3 to 30 mM. The BGE pH played an important role in the resolution of Dns-amino acids. For acidic BGEs, chiral resolution increased with pH (4.0-6.0) and reached a local maximum at pH 6.0. However, better resolutions were obtained with basic phosphate buffer at pH 9.6. Methanol was found to be an effective organic modifier for the resolution of Dns-amino acids by CE.     

A family of single-isomer positively charged cyclodextrins as chiral selectors for capillary electrophoresis: mono-6A-butylammonium-6A-deoxy-beta-cyclodextrin tosylate

A novel single-isomer positively charged beta-cyclodextrin (beta-CD), mono-6(A)-butylammonium-6(A)-deoxy-beta-cyclodextrin tosylate (BuAM-beta-CD), has been synthesized, characterized, and used for the enantioseparations of alpha-hydroxy acids, carboxylic acids, and ampholytic analytes by capillary electrophoresis in acidic aqueous background electrolytes. The effective mobilities of all studied analytes decreased with increasing concentration of CD. Satisfactory resolutions were obtained for alpha-hydroxy acids over a wide range of chiral selector concentration. The optimum CD concentration was lower than 5 mM for the carboxylic acids, while higher than 20 mM for alpha-hydroxy acids. Inclusion complexation in combination with ion pair interaction seemed to account for the chiral discrimination process. The hydrogen bonding may provide secondary contribution for the chiral resolution of alpha-hydroxy acids. In addition, BuAM-beta-CD was further proved to be an effective chiral selector for anionic analytes by the baseline enantioseparation of a six-acid mixture within 20 min.