Intertwined basins of attraction of dynamical systems

In this paper, we investigate a kind of intertwining phenomenon and give a new definition of intertwined attractors of the dynamical systems and get some related results.     

Solubility and activity coefficient of thallium (I) chloride in the system TlCl+HCl+NaCl+H2O at 25°C

The solubility of thallium (I) chloride has been studied in aqueous mixtures of HCl and NaCl at 25°C at ionic strengths ranging from 0.10 to 3.20 mol-kg^–1. Activity coefficients were derived and fitted to Pitzer's equations. This required values of the single-electrolyte parameters, ⁰, ¹ and C for TlCl. Since these are not available in the literature, owing to the low solubility of TlCl in water, a method has been devised for evaluating these parameters. These were then used to determine the mixing parameters, and , for the system. Consideration of the higher-order limiting law for symmetrical mixing did not improve the accuracy of the fit. The success with which the ion-interaction theory in its simplest form has been able to model the present system to such a high ionic strength shows that it is not necessary to treat ion association in the system explicitly in terms of an ion association equilibrium constant.     

EFFECT OF pH ON THE ADSORPTION OF p-AMINOBENZOIC ACID ON POLYSTYRENE-BASED ADSORBENTS

In the present study the adsorptive properties of p-aminobenzoic acid with hypercrosslinked and multi-functional polymeric adsorbents at different solution pHs were systematically investigated in accordance with the particular physicochemical characteristics of the aromatic amphoteric compound involving both Lewis acid and Lewis base functional groups. It was found that the equilibrium adsorption data of the three polymeric adsorbents fitted well in the Langmuir and Freundlich isotherm equations. Studies at various pH levels indicate that the capacity of the adsorbents for adsorption of the ionic forms of adsorbate is less than that for the corresponding neutral species. At pH 3.78, the adsorption capacities of the three adsorbents are the highest. Whereas the adsorption property of multi-functional polymeric adsorbent NJ-99 is the largest, which may be attributed to the strong hydrogen-bonding interaction between the amino groups on the resin and the carboxyl group of p-aminobenzoic acid. The trend of the adsorption capacities of the three adsorbents towards p-aminobenzoic acid with the solution pH is in accord with the dissociation curve of the neutral molecular p-aminobenzoic acid. The adsorption forces include π-π interaction, hydrogen-bonding interaction and electrostatic attraction or repulsion when there exist the molecular and ionic adsorbing species at different pHs in aqueous solution.     

Planar 2,2′-bithiophenes with 3,3′- and 3,3′,4,4′-substituents. A computational study

Ab initio calculations have shown that when carbonyl groups are incorporated into the 3- and 3′-positions of bithiophenes, as part of five-membered rings, the bithiophene system is planar. This is due to electrostatic attraction between the carbonyl oxygen and the sulfur atom in the adjacent ring. In the analogous systems containing a CH₂ group in place of the carbonyl, or containing six-membered rather than five-membered rings, the bithiophenes are twisted. This has implications for preparing planar polythiophenes.     

Oversized waveguides and resonators for millimeter waves

If real monolithic systems^* turn out to be impractical at millimeter-wave frequencies, oversized waveguides and resonators are useful alternatives in component and system design. Low losses, high Q factors, and inexpensive manufacturing are their advantages. Starting with an explanation of the term oversized, the loss reductions, Q factors, inherently oversized guides, such as the H-guide and its modifications, excitation of higher-order modes, laterally oversized H-guides, and the effects of coupling are described. A brief consideration of applications concludes the presentation.     

Use of the 2D 1H-13C HSQC NMR Methyl Region to Evaluate the Higher Order Structural Integrity of Biopharmaceuticals

The higher-order structure (HOS) of protein therapeutics is directly related to the function and represents a critical quality attribute. Currently, the HOS of protein therapeutics is characterized by methods with low to medium structural resolution, such as Fourier transform infrared (FTIR), circular dichroism (CD), intrinsic fluorescence spectroscopy (FLD), and differential scanning calorimetry (DSC). High-resolution nuclear magnetic resonance (NMR) methods have now been introduced, representing powerful approaches for HOS characterization (HOS by NMR). NMR is a multi-attribute method with unique abilities to give information on all structural levels of proteins in solution. In this study, we have compared 2D ¹H-¹³C HSQC NMR with two established biophysical methods, i.e., near-ultraviolet circular dichroism (NUV-CD) and intrinsic fluorescence spectroscopy, for the HOS assessments for the folded and unfolded states of two monoclonal antibodies belonging to the subclasses IgG1 and IgG2. The study shows that the methyl region of the ¹H-¹³C HSQC NMR spectrum is sensitive to both the secondary and tertiary structure of proteins and therefore represents a powerful tool in assessing the overall higher-order structural integrity of biopharmaceutical molecules.     

Higher-order rogue waves with controllable fission and asymmetry localized in a (3 + 1)-dimensional generalized Boussinesq equation

The purpose of this paper is to report the feasibility of constructing high-order rogue waves with controllable fission and asymmetry for high-dimensional nonlinear evolution equations.Such a nonlinear model considered in this paper as the concrete example is the(3+1)-dimensional generalized Boussinesq(gB) equation,and the corresponding method is Zhaqilao’s symbolic computation approach containing two embedded parameters.It is indicated by the(3+1)-dimensional gB equation that the embedded param...     

A coaxial HOM coupler for a superconducting RF cavity and its low-power measurement results

A resonant buildup of beam-induced fields in a superconducting radio frequency(RF)cavity may make a beam unstable or a superconducting RF cavity quench. Higher-order mode(HOM)couplers are used for damping higher-order modes to avoid such a resonant buildup. A coaxial HOM coupler based on the TTF (TESLA Test Facility)HOM coupler has been designed for the superconducting RF cavities at the Proton Engineering Frontier Project(PEFP)in order to overcome notch frequency shift and feed-through tip melting issues. In order to confirm the HOM coupler design and finalize its structural dimensions, two prototype HOM couplers have been fabricated and tested. Low-power testing and measurement of the HOM couplers has shown that the HOM coupler has good filter properties and can fully meet the damping requirements of the PEFP low-beta superconducting RF linac.     

A family of high order iterations for calculating the sign of a matrix

For the computation of a matrix sign function, a family of iterative methods is proposed. for some cases of the accelerator parameters, this method is proven to converge globally with higher rates of convergence. Its stability is discussed analytically as well. to illustrate the efficiency of the proposed methods from the family, several tests of various matrix sizes are considered to worked out.     

Sub-ODE＇s New Solutions and Their Applications to Two Nonlinear Partial Differential Equations with Higher-Order Nonlinear Terms

In the present paper, with the aid of symbolic computation, families of new nontrivial solutions of the first-order sub-ODE F12 = AF2 ＋ BF2＋p ＋ CF2＋2p （where F1= dF/dε, p 〉 0） are obtained. To our best knowledge, these nontrivial solutions have not been found in [X.Z. Li and M.L. Wang, Phys. Lett. A 361 （2007） 115] and IS. Zhang, W. Wang, and J.L. Tong, Phys. Lett. A 372 （2008） 3808] and other existent papers until now. Using these nontrivial solutions, the sub-ODE method is described to construct several kinds of exact travelling wave solutions for the generalized KdV-mKdV equation with higher-order nonlinear terms and the generalized ZK equation with higher-order nonlinear terms. By means of this method, many other physically important nonlinear partial differential equations with nonlinear terms of any order can be investigated and new nontrivial solutions can be explicitly obtained with the help of symbolic computation system Maple or Mathematics.