The saddle point problem and the Manteuffel algorithm

In the last two decades, the augmented linear systems and the saddle point problems have been solved by many researchers who have used the conjugate gradient method or the generalized SOR iterative method and variants of them. In the latter class of methods, when the block \(A \in {\mathrm{I\!R}}^{m\times m}\) of the matrix coefficient \(\mathcal {A} = \left[ \begin{array}{cc} A &{} B \\ -B^T &{} 0\end{array}\right] \in {\mathrm{I\!R}}^{(m+n) \times (m+n)}\), \(m \ge n,\) of the linear system to be solved, is symmetric positive definite and \({\mathrm{rank}}(B) =r \le n\), convergence regions and optimal values of the parameters involved have been determined. In this work, we consider the block A to be nonsymmetric positive definite, \({\mathrm{rank}}(B) =r < n \), and use a two-level stationary iterative method whose main step is the linear second-order stationary iterative method for the solution of this class of problems. This method leads to the singular Manteuffel algorithm and the determination of its optimal parameters. As a byproduct, the optimal parameters of the Generalized Modified SSOR method in a particular case are also determined. Numerical examples verify our theoretical findings.     

Effective interaction parameter of linear/star polymer blends and comparison with that of linear/linear and star/star blends

The authors present a detailed study of the microscopic parameters, which control the miscibility in binary linear/star polymer blends. The effective interactions of linear/star polymer blends are studied by means of Monte Carlo simulations and comparison is made with linear/linear and star/star blends, which they also determined. Using the bond fluctuation model on a simple cubic lattice, the authors are able to simulate symmetric linear/linear, star/star, and, for the first time, linear/star blends with a moderate number of arms. The simulations were performed at a volume fraction of occupied lattice sites phi=0.5, which corresponds to dense polymer mixtures for this algorithm. In particular, we study star/star blends with 4, 8, and 12 arms and the respective linear/linear blends as well as linear/star blends, all having the same total number of units equal to 73 and 121. The authors find that linear/star blends are more miscible than the corresponding linear/linear blends, which is in agreement with recent experimental and theoretical results. They find that linear/star mixtures are less miscible than star/star blends, a result which is also verified by theoretical findings.     

Dielectric relaxation spectroscopy in poly(ethylene oxide)/water systems

The dielectric properties of poly(ethylene oxide) (PEO) are studied by dielectric relaxation spectroscopy measurements in wide ranges of frequency (5–2×10⁹ Hz) and temperature (193 − 300 K). PEO/water systems are also studied in a wide range of water content h (0 − 0.85 grams of water per grams of dry PEO). The measurements allow to distinguish between the dipolar secondary mechanism γ and effects related to free charge motion. The data are analyzed within the formalisms of permittivity, ϵ*, and electric modulus, M*. The water has been found to plasticize the dipolar process and to affect strongly the conduction process. A critical water content h_c, h_c = 0.13, has been found for the mechanism of charge transport.     

On the universal Gröbner bases of toric ideals of graphs

The universal Gröbner basis of an ideal is a Gröbner basis with respect to all term orders simultaneously. We characterize in graph theoretical terms the elements of the universal Gröbner basis of the toric ideal of a graph. We also provide a new degree bound. Finally, we give examples of graphs for which the true degrees of their circuits are less than the degrees of some elements of the Graver basis.     

Approximate dynamic programming for stochastic linear control problems on compact state spaces

This paper addresses Markov Decision Processes over compact state and action spaces. We investigate the special case of linear dynamics and piecewise-linear and convex immediate costs for the average cost criterion. This model is very general and covers many interesting examples, for instance in inventory management. Due to the curse of dimensionality, the problem is intractable and optimal policies usually cannot be computed, not even for instances of moderate size.     

Electronic spectroscopy and electronic structure of diatomic TiFe

Diatomic TiFe, a 12 valence electron molecule that is isoelectronic with Cr(2), has been spectroscopically investigated for the first time. In addition, the first computational study that includes the ground and excited electronic states is reported. Like Cr(2), TiFe has a (1)Σ(+) ground state that is dominated by the 1σ(2) 2σ(2) 1π(4) 1δ(4) configuration. Rotationally resolved spectroscopy has established a ground state bond length of 1.7024(3) A?, quite similar to that found for Cr(2) (r(0) = 1.6858 A?). Evidently, TiFe exhibits a high degree of multiple bonding. The vibronic spectrum is highly congested and intense to the blue of 20?000 cm(-1), while two extremely weak band systems, the [15.9](3)Π(1) ← X (1)Σ(+) and [16.2](3)Π(0+) ← X (1)Σ(+) systems, are found in the 16?000-18?500 cm(-1) region. The bond lengths, obtained by inversion of the B(e) (') values, and vibrational frequencies of the two upper states are nearly identical: 1.886?A? and 344 cm(-1) for [15.9](3)Π(1) and 1.884 A? and 349 cm(-1) for [16.2](3)Π(0+). The measured spin-orbit splitting of the (3)Π state is consistent with its assignment to the 1σ(2) 2σ(2) 1π(4) 1δ(3) 2π(1) configuration, as is also found in the ab initio calculations.     

Diblock copolymers of polystyrene‐b‐poly(1,3‐cyclohexadiene) exhibiting unique three‐phase microdomain morphologies

The synthesis and molecular characterization of a series of conformationally asymmetric polystyrene‐block‐poly(1,3‐cyclohexadiene) (PS‐b‐PCHD) diblock copolymers (PCHD: ～90% 1,4 and ～10% 1,2), by sequential anionic copolymerization high vacuum techniques, is reported. A wide range of volume fractions (0.27 ≤ ?_PS ≤ 0.91) was studied by transmission electron microscopy and small‐angle X‐ray scattering in order to explore in detail the microphase separation behavior of these flexible/semiflexible diblock copolymers. Unusual morphologies, consisting of PCHD core(PCHD‐1,4)–shell(PCHD‐1,2) cylinders in PS matrix and three‐phase (PS, PCHD‐1,4, PCHD‐1,2) four‐layer lamellae, were observed suggesting that the chain stiffness of the PCHD block and the strong dependence of the interaction parameter χ on the PCHD microstructures are important factors for the formation of this unusual microphase separation behavior in PS‐b‐PCHD diblock copolymers. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1564–1572     

Organic–inorganic bonding in chitosan–silica hybrid networks: Physical properties

Novel biomaterials are needed for bone tissue repair with improved mechanical performance compared to classical bioceramics. The objective of this work was to characterize a hybrid filler material, which is capable to coat as a thin film porous scaffolds improving their mechanical properties for bone tissue engineering. The hybrid filler material is a blend of chitosan and silica network formed through in situ sol–gel using tetraethylortosilicate and 3‐glycidoxypropyltrimethoxysilane (GPTMS) as silica precursors. The hypothesis was that the epoxy ring of GPTMS could react with the amino groups of chitosan in acidic media while it is also reacting the siloxane groups of hydrolyzed silica precursors. The formation of the hybrid organic–inorganic network was assessed by different physical techniques revealing changes in molecular mobility and hydrophilicity upon chemical reaction. Finally, the cytotoxicity of the samples was also evaluated by MTT assay. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1391–1400