The coherent-constructible correspondence and Fourier-Mukai transforms

As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric orbifolds. In a previous paper, the authors showed that the derived category of a toric orbifold is naturally identified with a category of polyhedrally-constructible sheaves on ℝ ⁿ . In this paper we investigate and reprove some of Kawamata’s results from this perspective.     

History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics

We consider a class of subdifferential inclusions involving a history-dependent term for which we provide an existence and uniqueness result. The proof is based on arguments on pseudomonotone operators and fixed point. Then we specialize this result in the study of a class of history-dependent hemivariational inequalities. Such kind of problems arises in a large number of mathematical models which describe quasistatic processes of contact between a deformable body and an obstacle, the so-called foundation. To provide an example we consider a viscoelastic problem in which the frictional contact is modeled with subdifferential boundary conditions. We prove that this problem leads to a history-dependent hemivariational inequality in which the unknown is the velocity field. Then we apply our abstract result in order to prove the unique weak solvability of the corresponding contact problem.     

Degradation modeling of 2 fatigue‐crack growth characteristics based on inverse Gaussian processes: A case study

Most modern products that are highly reliable are complex in their inner and outer structures. This situation indicates quality characterization by the interaction of multiple performance characteristics, which motivates the utilization of robust reliability models to obtain robust estimates. It is paramount to obtaining substantial information about a product's life cycle; therefore, when multiple performance characteristics are dependent, it is important to find models that address the joint distribution of performance degradation of such. In this paper, a reliability model for products with 2 fatigue‐crack growth characteristics related to 2 degradation processes is developed. The proposed model considers the dependence among degradation processes by using copula functions considering the marginal degradation processes as inverse Gaussian processes. The statistical inference is performed by using a Bayesian approach to estimate the parameters of the joint bivariate model. A time‐scale transformation is considered to assure monotone paths of the degradation trajectories. The comparison results of the reliability analysis, under both dependent and independent assumptions, are reported with the implementation of the proposed modeling in a case study, which consists of the crack propagation data of 2 terminals of an electronic device.     

Enzyme mediated incorporation of zirconium-89 or copper-64 into a fragment antibody for same day imaging of epidermal growth factor receptor

Identification of tumors which over-express Epidermal Growth Factor Receptor (EGFR) is important in selecting patients for anti-EGFR therapies. Enzymatic bioconjugation was used to introduce positron-emitting radionuclides (⁸⁹Zr, ⁶⁴Cu) into an anti-EGFR antibody fragment for Positron Emission Tomography (PET) imaging the same day as injection. A monovalent antibody fragment with high affinity for EGFR was engineered to include a sequence that is recognized by the transpeptidase sortase A. Two different metal chelators, one for ⁸⁹Zr^IV and one for ⁶⁴Cu^II, were modified with a N-terminal glycine to enable them to act as substrates in sortase A mediated bioconjugation to the antibody fragment. Both fragments provided high-quality PET images of EGFR positive tumors in a mouse model at 3 hours post-injection, a significant advantage when compared to radiolabeled full antibodies that require several days between injection of the tracer and imaging. The use of enzymatic bioconjugation gives reproducible homogeneous products with the metal complexes selectively installed on the C-terminus of the antibody potentially simplifying regulatory approval.

Enzymatic bioconjugation to introduce positron-emitting radionuclides (⁸⁹Zr, ⁶⁴Cu) into an anti-EGFR antibody fragment allows same day imaging with positron emission tomography.     

5-(Indol-2-yl)pyrazolo[3,4-b]pyridines as a New Family of TASK-3 Channel Blockers: A Pharmacophore-Based Regioselective Synthesis

TASK channels belong to the two-pore-domain potassium (K_2P) channels subfamily. These channels modulate cellular excitability, input resistance, and response to synaptic stimulation. TASK-channel inhibition led to membrane depolarization. TASK-3 is expressed in different cancer cell types and neurons. Thus, the discovery of novel TASK-3 inhibitors makes these bioactive compounds very appealing to explore new cancer and neurological therapies. TASK-3 channel blockers are very limited to date, and only a few heterofused compounds have been reported in the literature. In this article, we combined a pharmacophore hypothesis with molecular docking to address for the first time the rational design, synthesis, and evaluation of 5-(indol-2-yl)pyrazolo[3,4-b]pyridines as a novel family of human TASK-3 channel blockers. Representative compounds of the synthesized library were assessed against TASK-3 using Fluorometric imaging plate reader—Membrane Potential assay (FMP). Inhibitory properties were validated using two-electrode voltage-clamp (TEVC) methods. We identified one active hit compound (MM-3b) with our systematic pipeline, exhibiting an IC₅₀ ≈ 30 μM. Molecular docking models suggest that compound MM-3b binds to TASK-3 at the bottom of the selectivity filter in the central cavity, similar to other described TASK-3 blockers such as A1899 and PK-THPP. Our in silico and experimental studies provide a new tool to predict and design novel TASK-3 channel blockers.     

Some Novel Cobalt Diphenylphosphine Complexes: Synthesis,Characterization, and Behavior in the Polymerization of 1,3-Butadiene

Some novel cobalt diphenylphosphine complexes were synthesized by reacting cobalt(II) chloride with (2-methoxyethyl)diphenylphosphine, (2-methoxyphenyl)diphenylphosphine, and 2-(1,1-dimethylpropyl)-6-(diphenylphosphino)pyridine. Single crystals suitable for X-ray diffraction studies were obtained for the first two complexes, and their crystal structure was determined. The novel compounds were then used in association with methylaluminoxane (MAO) for the polymerization of 1,3-butadiene, and their behavior was compared with that exhibited in the polymerization of the same monomer by the systems CoCl₂(PⁿPrPh₂)₂/MAO and CoCl₂(PPh₃)₂/MAO. Some significant differences were observed depending on the MAO/Co ratio used, and a plausible interpretation for such a different behavior is proposed.     

Self-organisation of di(perfluorohexyl)hexane in Langmuir and LB films

Symmetrical triblock semifluorinated n-alkane, di(perfluorohexyl)hexane of the formula F(CF₂)₆(CH₂)₆(CF₂)₆F (abbreviated F₆H₆F₆), has been synthesised and investigated at the air/water interface. Our results show for the first time that this unusual film-forming material, completely hydrophobic in nature and possessing no polar group, is capable of stable film formation at the free water surface. The surface pressure–area isotherm of the studied compound exhibited two regions: corresponding to monotonous pressure rise, followed by a pseudo-plateau region. Visualisation of film structure with Brewster angle microscope (BAM) proved the formation of domains within the pseudo-plateau region. A closer insight into the structure of these domains with atomic force microscope (AFM) proved their ordered, circular shape. The average area of F₆H₆F₆ domain was found to depend on surface pressure value, as it is 4.98 ± 1.75 μm² at π = 1.2 mN/m to 16.54 ± 0.31 μm² at π = 1.7 mN/m. Following performed quantum-chemical calculations, it can be concluded that the observed surface aggregates from F₆H₆F₆ are formed by linear conformers with shifted CF and CH parts. The calculated domain thickness is between 20 and 21 Å, which perfectly agrees with the experimental value estimated from AFM measurements (20.3 ± 1.4 Å).     

First-order interaction energies and the basis set truncation effects

The basis set superposition error is investigated in terms of the first-order symmetry adapted perturbation theory (SAPT). The analysis of the first-order SAPT contribution to the interaction energy reveals the origin of the basis set truncation effects at both the one-electron and many-electron levels of approximation. This helps to formulate the necessary conditions which ensure that the calculated interaction energy is free of the basis set superposition contributions. At the level of the one-electron approximation used for both the interacting system and its subsystems a part of the basis set truncation errors can be eliminated by using what is called the dimer-centred basis set. In order to remove all contributions which arise from the symmetrization of the product of wave functions of the subsystems one needs to redefine their reference states. This means that for the interacting system represented by a single HF determinant, the subsystems must be considered at the level of full CI in the orbital space spanned by all occupied orbitals used to describe the dimer. Then, the interaction energy becomes completely free of the basis set superposition contributions. These general considerations are exemplified by calculations of the first-order SAPT interaction energy in helium and H₂ dimers at different levels of approximation for monomers. Also the convergence of the calculated energies to the complete basis set limit is investigated.