Nanostructures in a binary mixture confined in slit-like pores with walls decorated with tethered polymer brushes in the form of stripes: dissipative particle dynamics study

Using dissipative particle dynamics, we investigate the behavior of a binary mixture, exhibiting demixing in a bulk phase, confined in slit-like pores with walls modified by the stripes of tethered brush of chains. Our main interest is to determine possible morphologies that can be formed inside the pore, depending on the geometrical parameters characterizing the system (the size of the pore and the width of the stripes). In order to describe the observed morphologies we calculate several characteristics, as the density and local temperature profiles, the radii of gyration for the attached polymers, and the minimum polymer-polymer distances in the direction parallel and perpendicular to the pore walls. The summary of our findings is presented as a sketch of the diagram of morphologies.     

Efficient time-dependent density functional theory approximations for hybrid density functionals: analytical gradients and parallelization

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.     

Structural evolution and properties of solid solutions of hexagonal InMnO3 and InGaO3

Solid solutions InMn(1-x)Ga(x)O(3) (0 ≤ x ≤ 1) have been investigated using magnetic, dielectric, specific heat, differential scanning calorimetry (DSC), and high-temperature powder synchrotron X-ray diffraction (HT-SXRD) measurements. It was found that samples with 0.5 ≤ x ≤ 1 crystallize in space group P6(3)/mmc with a ~ 3.32 ? and c ~ 11.9 ?, and samples with 0.0 ≤ x ≤ 0.4 crystallize in space group P6(3)cm with a ~ 5.8 ? and c ~ 11.6 ? at room temperature. HT-SXRD data revealed the existence of a P6(3)cm-to-P6(3)/mmc phase transition at about 480 K in InMn(0.6)Ga(0.4)O(3) and at 950 K in InMn(0.7)Ga(0.3)O(3). However, no dielectric, phonon, second-harmonic-generation, or DSC anomalies were found to be associated with these phase transitions. The phase transition should be improper ferroelectric from the symmetry point of view, but the above-mentioned experimental facts, together with the absence of ferroelectric hysteresis loops, revealed no evidence for ferroelectricity in the low-temperature P6(3)cm structure. We suggest that InMn(1-x)Ga(x)O(3) corresponds to a nonferroelectric phase of hexagonal RMnO(3) with P6(3)cm symmetry. The antiferromagnetic phase-transition temperature decreases from 118 K for x = 0 to 105 K for x = 0.1 and 73 K for x = 0.2, and no long-range magnetic ordering could be found for x ≥ 0.3. Specific heat anomalies associated with short-range magnetic ordering were observed for 0.0 ≤ x ≤ 0.5. InMn(1-x)Ga(x)O(3) with small Mn contents (0.8 ≤ x ≤ 0.98) has a bright-blue color.     

Toward a Clarity of the Extreme Value Theorem

We apply a framework developed by C. S. Peirce to analyze the concept of clarity, so as to examine a pair of rival mathematical approaches to a typical result in analysis. Namely, we compare an intuitionist and an infinitesimal approaches to the extreme value theorem. We argue that a given pre-mathematical phenomenon may have several aspects that are not necessarily captured by a single formalisation, pointing to a complementarity rather than a rivalry of the approaches.     

On the dimension of the space of ℝ-places of certain rational function fields

We prove that for every n ∈ ? the space M(K(x ₁, …, x _n ) of ?-places of the field K(x ₁, …, x _n ) of rational functions of n variables with coefficients in a totally Archimedean field K has the topological covering dimension dimM(K(x ₁, …, x _n )) ≤ n. For n = 2 the space M(K(x ₁, x ₂)) has covering and integral dimensions dimM(K(x ₁, x ₂)) = dim_? M(K(x ₁, x ₂)) = 2 and the cohomological dimension dim _G M(K(x ₁, x ₂)) = 1 for any Abelian 2-divisible coefficient group G.     

Complex geometry of moment-angle manifolds

Moment-angle manifolds provide a wide class of examples of non-Kähler compact complex manifolds. A complex moment-angle manifold \(\mathcal {Z}\) is constructed via certain combinatorial data, called a complete simplicial fan. In the case of rational fans, the manifold \(\mathcal {Z}\) is the total space of a holomorphic bundle over a toric variety with fibres compact complex tori. In general, a complex moment-angle manifold \(\mathcal {Z}\) is equipped with a canonical holomorphic foliation \({\mathcal {F}}\) which is equivariant with respect to the \(({\mathbb {C}}^\times )^m\)-action. Examples of moment-angle manifolds include Hopf manifolds of Vaisman type, Calabi–Eckmann manifolds, and their deformations. We construct transversely Kähler metrics on moment-angle manifolds, under some restriction on the combinatorial data. We prove that any Kähler submanifold (or, more generally, a Fujiki class \(\mathcal {C}\) subvariety) in such a moment-angle manifold is contained in a leaf of the foliation \({\mathcal {F}}\). For a generic moment-angle manifold \(\mathcal {Z}\) in its combinatorial class, we prove that all subvarieties are moment-angle manifolds of smaller dimension and there are only finitely many of them. This implies, in particular, that the algebraic dimension of \(\mathcal {Z}\) is zero.     

High-pressure study of tetramethylsilane by Raman spectroscopy

High-pressure behavior of tetramethylsilane, one of the Group IVa hydrides, was investigated by Raman scattering measurements at pressures up to 142 GPa and room temperature. Our results revealed the phase transitions at 0.6, 9, and 16 GPa from both the mode frequency shifts with pressure and the changes of the full width half maxima of these modes. These transitions were suggested to result from the changes in the inter- and intra-molecular bonding of this material. We also observed two other possible phase transitions at 49-69 GPa and 96 GPa. No indication of metallization in tetramethylsilane was found with stepwise compression to 142 GPa.     

Biomarker discovery in breast cancer serum using 2-D differential gel electrophoresis/ MALDI-TOF/TOF and data validation by routine clinical assays

In the present study, we used 2-D differential gel electrophoresis (2-D DIGE) and MS to screen biomarker candidates in serum samples obtained from 39 patients with breast cancer and 35 controls. First, we pooled the serum samples matched with age and menopausal status. Then, we depleted the two most abundant proteins albumin and IgG by immunoaffinity chromatography under partly denaturing conditions in order to enrich low-abundance proteins and proteins with low molecular weight. Concentrated and desalted samples were labeled with three different CyDyes including one internal standard, pooled from all the samples, and separated with 2-D DIGE in triplicate experiments. Biological variations of the protein expression level were analyzed with DeCyder software and evaluated for reproducibility and statistical significance. The profile of differentially expressed protein spots between patients and controls revealed proapolipoprotein A-I, transferrin, and hemoglobin as up-regulated and three spots, apolipoprotein A-I, apolipoprotein C-III, and haptoglobin alpha2 as down-regulated in patients. Finally, routine clinical immunochemical reactions were used to validate selected candidate biomarkers by quantitative determination of specific proteins in all individual serum samples. The serum level of transferrin correlated well with the 2-D-DIGE results. However, the serum levels of apolipoprotein A-I and haptoglobin could not be detected with the clinical routine diagnostic tests. This demonstrated an advantage 2-D DIGE still has over other techniques. 2-D DIGE can distinguish between isoforms of proteins, where the overall immunochemical quantification does fail due to a lack of isoform-special antibodies.