A collocation method for differential equations with one‐point Taylor initial conditions

This paper presents a new multistep collocation method for nth order differential equations. The interval of interest is first divided into N subintervals. By determining interval conditions in Taylor interpolation in each subinterval, Taylor polynomials are calculated with different step lengths. Then the obtained solutions in each subinterval are used as initial conditions in the next step. Optimal error is assessed using Peano lemma, which shows that the errors decay by decreasing the step length. In particular, for fixed step length h, the error is of O(m^?m), where m is the number of collocation points in each subinterval. Meanwhile, for fixed m, the error is of O(h^m). Numerical examples demonstrate the validity and high accuracy of the proposed method even for stiff problems.     

Simulating pedestrian flow through narrow exits

Introduction: The flow of pedestrians through narrow doorways is one of the most common features of crowd motions and evacuations. It is particularly an important aspect of pedestrian simulations models since their accuracy depends highly on their ability to produce realistic exit flow rates. The problem has been extensively studied in the literature, but many aspects of it have remained controversial with mixed (and often contradictory) evidence emerging from different studies and different methods. Methods: We discuss the significance of parameter calibration for accurate simulation of pedestrian flow through narrow exits using social force model. Based on sensitivity analyses, we show how simulated exit throughput rate can vastly differ by changing the value of certain parameters. We identify the two parameters that are most critical, and then calibrate them based on a set of experimental observations (at macro level). Using these calibrated parameters, we then re-examine three fundamental questions related to pedestrian flow at bottlenecks, (1) the relation between desired velocity and simulated egress time; (2) the effect of barricade at exits; and (3) the effect of exit in the corner versus the middle. Results: Our numerical analyses showed that, with the calibrated parameters, increasing the desired velocity in the social-force model results in monotonically shorter egress times (at a marginal rate that rapidly diminishes as the desired velocity increases). We showed that placing a panel-like barricade at exit can facilitate the outflow and reduces the egress time, but its effect depends on the widths of exit, as well as the size of the barricade and its distance to exit. We show that the positioning the exit in the corner is also effective in terms of reducing egress time, but only for very narrow exits. The benefit diminishes quickly as the exit becomes wider. Applications: These outcomes demonstrated the significance of parameter calibration for accurate simulation of crowd flows. The findings may also help to identify simple modifications that can facilitate crowd flows at narrow bottlenecks.     

Systematic investigation of simultaneous removal of phosphate/nitrate from water using Ag/rGO nanocomposite: Development,characterization, performance and mechanism

Research on Chemical Intermediates - The primary purpose of this study is to create a method for removal of nitrate and phosphate utilizing adsorption-based technique. To this end, the adsorption...     

Selective tetrahydropyranylation of alcohols and phenols using titanium(IV) salophen trifluoromethanesulfonate as an efficient catalyst

Titanium(IV) salophen trifluoromethanesulfonate, [Ti^IV(salophen)(OSO₂CF₃)₂], as a catalyst enables selective tetrahydropyranylation of alcohols and phenols with 3,4‐dihydro‐2H‐pyran. Using this catalytic system, primary, secondary and tertiary alcohols, as well as phenols, were converted to their corresponding tetrahydropyranyl ethers in high yields and short reaction times at room temperature. Investigation of the chemoselectivity of this method showed discrimination between the activity of primary alcohols in the presence of secondary and tertiary alcohols and phenols. This heterogenized catalyst could be reused several times without loss of its catalytic activity. Copyright © 2016 John Wiley & Sons, Ltd.     

Quantum investigation of non-bonded interaction between the B15N15 ring and BH2NBH2 (radical, cation, anion) systems: a nano molecularmotor

The electromagnetic non-bonded interactions of BH₂NBH₂ molecule inside the B₁₅N₁₅ ring has been investigated with B3LYP method using EPR-II and EPR-III basis sets. Optimized structures, relative stability, and hyperfine spectroscopic parameters, such as total atomic charges, spin densities, electrical potential, and isotropic Fermi coupling constants of radical, cationic, and anionic forms of BH₂NBH₂ in different loops and bonds have been calculated. The spectral properties have been contributed to explain the characteristics of hyperfine electronic structure. The calculation for the B₁₅N₁₅–BH₂NBH₂ system and then for adenine–thymine base pairs coupled with BH₂NBH₂ molecule inside the B₁₅N₁₅ ring (A–BNB–T) have been done and three quantized rotational frequencies for transitions among cationic, radical, and anionic have been calculated, too. All observed frequencies appeared in the IR rotational region. So, this system can be used for the measurement of rotational spectra related to electrical voltage differences existing in macromolecules such as proteins and DNA and membrane. Extensive calculations have been carried out on the radical, anionic, and cationic forms of BH₂NBH₂ to obtain data and it has been observed that the radial coordinate of the dipole moment vector (r) as well as the voltage differences (ΔV) and relative energies (ΔE) exhibited Gaussian distribution. We have obtained a relationship between dipole moments and the voltage differences and energies of system.     

Isolation and characterization of degradation products of moxidectin using LC, LTQ FT-MS, H/D exchange and NMR

This study aimed to evaluate the degradation profile and pathways, and identify unknown impurities of moxidectin under stress conditions. During the experiments, moxidectin samples were stressed using acid, alkali, heat and oxidation, and chromatographic profiles were compared with known impurities given in European Pharmacopeia (EP) monograph. Moxidectin has shown good stability under heat, while reaction with alkali produced 2-epi and ?2,3 isomers (impurities D and E in EP) by characteristic reactions of the oxahydrindene (hexahydrobenzofuran) portion of the macrocyclic lactone. Two new, previously unreported, unknown degradation products, i.e. impurity 1 and impurity 2, detected after acid hydrolysis of moxidectin (impurity 2 was also observed to a lesser extent after oxidation), were isolated from sample matrices and identified using liquid chromatography, NMR, high-resolution FT-ICR MS, and hydrogen/deuterium exchange studies. FTMS analysis showed accurate mass of molecular ion peaks for moxidectin at m/z 640.38412, impurity 1 at m/z 656.37952 and impurity 2 at m/z 611.35684, giving rise to daughter ions traceable up to the seventh levels of MSⁿ experiments and supporting the proposed structures. Both unknown impurities along with moxidectin were fully characterized by ¹H, ¹³C, 1D HMBC and 2D (NOESY, COSY and HSQC) NMR experiments. The interpretation of experimental data positively identified impurity 1 as 3,4-epoxy-moxidectin and impurity 2 as 23-keto-nemadectin. The identification of new impurities and correlation of their chromatographic profiles with the EP method is very useful to establish the stability profile of moxidectin and its preparations, as well as add value to the forthcoming moxidectin finished product European Pharmacopeia monographs.

½ Cancellation Modules and Homogeneous Idealization II

In our recent work we investigated ½ (weak) cancellation modules and ½ join principal submodules and showed via the method of idealization most questions concerning these modules can be reduced to the ideal case. The purpose of this article is to continue our study of these modules as well as we introduce and give some properties of the concept of M-join principal ideals.     

Idempotent and Nilpotent Submodules of Multiplication Modules

All rings are commutative with identity, and all modules are unital. The purpose of this article is to investigate multiplication von Neumann regular modules. For this reason we introduce the concept of nilpotent submodules generalizing nilpotent ideals and then prove that a faithful multiplication module is von Neumann regular if and only if it has no nonzero nilpotent elements and its Krull dimension is zero. We also give a new characterization for the radical of a submodule of a multiplication module and show in particular that the radical of any submodule of a Noetherian multiplication module is a finite intersection of prime submodules.     

Almost-Perfect Rings and Modules

Following [1 Amini , A. , Ershad , M. , Sharif , H. ( 2008 ). Rings over which flat covers of finitely generated modules are projective . Comm. Algebra 36 : 2862 – 2871 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]], a ring R is called right almost-perfect if every flat right R-module is projective relative to R. In this article, we continue the study of these rings and will find some new characterizations of them in terms of decompositions of flat modules. Also we show that a ring R is right almost-perfect if and only if every right ideal of R is a cotorsion module. Furthermore, we prove that over a right almost-perfect ring, every flat module with superfluous radical is projective. Moreover, we define almost-perfect modules and investigate some properties of them.