Molecular Architecture Manipulation in Free Radical Copolymerization: An Advanced Monte Carlo Approach to Screening Copolymer Chains with Various Comonomer Sequence Arrangements

A Kinetic Monte Carlo (KMC) simulation approach has been adopted in this study to capture evolutionary events in the course of free radical copolymerization, through which batch and starved‐feed semibatch processes are compared. The implementation of the KMC code deve­loped in this work: (i) enables satisfactory control of the molecular weight of the copolymer by tracking the profiles of concentrations of macroradicals, monomers, and polymer as well as degree of polymerization, polydispersity, and chain length distribution; (ii) captures the bivariate distribution of chain length and copolymer composition; (iii) comprehensively tracks and analyzes detailed information on the molecular architecture of the growing chains, thus distinguishing between sequence length and polydispersity of chains produced in batch and starved‐feed semibatch operations; (iv) makes possible the screening of products, based on such details as the number and weight fractions of products having different comonomer units located at various positions along the copolymer chains. The aforementioned characteristics are achieved by stochastic calculations through code developed in‐house. This KMC simulator becomes a very useful tool for the development of tailored copolymers through free radical polymerization, with blocks separated with single units of a different type.

     

Norm Retrievable Frames and Their Perturbation in Finite Dimensional Complex Hilbert Spaces

In this article, we study the property of norm retrievability of spanning vectors in a finite dimensional complex Hilbert space ?. Using the set of zero trace operators on ? and two sets of self-adjoint operators on ? denoted by 𝒮^1,0 and 𝒮^1,1, we present some equivalent conditions to the norm retrievable frames in ?. We will also show that the property of norm retrievability for n-dimensional complex Hilbert space ? with n≠2 is stable under enough small perturbation of the frame set only for phase retrievable frames.     

Application of Sulfonic Acid Functionalized SBA‐15 as a New Nanoporous Acid Catalyst in the Green One‐Pot Synthesis of Spirooxindole‐4H‐pyrans

Sulfonic acid functionalized SBA‐15 (SBA‐Pr‐SO₃H) as a new nanoporous solid acid catalyst was applied in the green one‐pot synthesis of spirooxindole‐4H‐pyrans via condensation of isatins, malononitrile or methyl cyanoacetate or ethyl cyanoacetate, and 4‐hydroxycoumarin in water solvent. SBA‐Pr‐SO₃H was proved to be an efficient heterogeneous nanoporous solid acid catalyst with a pore size of 6 nm that could be easily handled and removed from the reaction mixture by simple filtration and can be recovered and reused for several times without any loss of activity. The significant merits of present methodology are its simplicity, short reaction time, good yields, and environmentally benign mild reaction condition as water was used as a green solvent.     

On the fractional derivatives of radial basis functions: Theories and applications

The paper provides the fractional integrals and derivatives of the Riemann‐Liouville and Caputo type for the five kinds of radial basis functions, including the Powers, Gaussian, Multiquadric, Matérn, and Thin‐plate splines, in one dimension. It allows to use high‐order numerical methods for solving fractional differential equations. The results are tested by solving two test problems. The first test case focuses on the discretization of the fractional differential operator while the second considers the solution of a fractional order differential equation.     

Gas phase pyrolysis of some cyclic dithioketals

A detailed analysis of the gas phase pyrolysis of 1,4-dithiaspiro[4,4]nonane(I), 1,5-dithiaspiro(5.4)decane(II), 1,4-dithiaspiro(4.5)decane(III), and 1,5-(5,5)undecane(IV) is presented. Pyrolysis resulted primarily in cleavage of the molecules to thiocyclopentanone and thiocyclohexanone. The products observed are discussed in relation to the effect of ring size in cyclic dithioketals. A definite correlation was noted between the thermal and their electron-impact-induced fragmentations of these materials.     

Effect of frit size on sintering, crystallization and electrical properties of wollastonite glass-ceramics

Wollastonite glass-ceramics were prepared through pressureless sintering. The sinterability of the prepared samples of the glassy powder in the system (SiO₂-CaO-Na₂O-Fe₂O₃-WO₃) was investigated in the temperature range 720-900 °C and soaking time of 180 min. The influence of the increase in the glass powder particle size on the sinterability and dielectric properties of the glass-ceramic samples was studied.The sintered specimens were characterized by scanning electron microscopy (SEM) and X-ray diffraction (XRD) methods. XRD analysis revealed that wollastonite was the main crystalline phase in the sintered glass-ceramics. Dielectric properties such as dielectric constant and dielectric loss were measured via a network analyzer at 10 GHz.It was observed that the increase of the glassy powder particle size improved the sinterability and dielectric properties of the glass-ceramic specimens. Wollastonite glass-ceramics with 16 μm particle size had maximum constant and minimum loss (ε_r = 10.10 and tan δ = 0.005) compared with the other glass-ceramics.     

Compact chip-scale filter based on curved waveguide Bragg gratings

We propose a method for miniaturization of filters based on curved waveguide Bragg gratings, so that long structures can be packed into a small area on a chip. This eliminates the stitching errors introduced in the fabrication process, which compromise the performance of long Bragg gratings. Our approach relies on cascading curved waveguide Bragg gratings with the same radius of curvature. An analytical model for the analysis of these devices was developed, and a filter based on this model was designed and fabricated in a silicon on insulator platform. The filter had a total length of 920μm, occupied an area of 190μm×114μm, and exhibited a stop band of 1.7nm at 1.55μm and an extinction ratio larger than 23dB.     

Robust least squares solution of linear inequalities

Least squares solution of linear inequalities appears in many disciplines such as linear separability problems and inconsistency correction. In this paper we consider this problem with uncertainty in its data. Then we prove that its robust counterpart is equivalent to a second order conic linear optimization problem, which can be efficiently solved using interior point methods.