On Functions α-Starlike with Respect to Symmetric Conjugate Points

AbstractWe introduce here the notion of functions α-starlike with respect to symmetric conjugate points and derive a convolution theorem in this class. Moreover, a sharp coefficient estimate and a structural formula are given

PINNs-Based Uncertainty Quantification for Transient Stability Analysis

This paper addresses the challenge of transient stability in power systems with missing parameters and uncertainty propagation in swing equations. We introduce a novel application of Physics-Informed Neural Networks (PINNs), specifically an Ensemble of PINNs (E-PINNs), to estimate critical parameters like rotor angle and inertia coefficient with enhanced accuracy and reduced computational load. E-PINNs capitalize on the underlying physical principles of swing equations to provide a robust solution. Our approach not only facilitates efficient parameter estimation but also quantifies uncertainties, delivering probabilistic insights into the system behavior. The efficacy of E-PINNs is demonstrated through the analysis of $1$-bus and $2$-bus systems, highlighting the model's ability to handle parameter variability and data scarcity. The study advances the application of machine learning in power system stability, paving the way for reliable and computationally efficient transient stability analysis

2-{[3-Methyl-4-(2,2,2-trifluoro­eth­oxy)pyridin-2-yl]methyl­sulfan­yl}-1H-benzimidazole monohydrate

The asymmetric unit of the title compound, C16H14F3N3OS·H2O, contains two independent mol­ecules (A and B) and two water mol­ecules, one of which is disordered over two positions in a 0.790 (8):0.210 (8) ratio. The mol­ecular conformations are close, the benzimidazole mean plane and pyridine ring forming dihedral angles of 1.8 (3) and 0.1 (2)° in mol­ecules A and B, respectively. The water mol­ecules are involved in formation of two independent hydrogen-bonded chains via N—H⋯O and O—H⋯N hydrogen bonds. Chains propagating along the a axis are formed by mol­ecule A and one independent water mol­ecule, while chains propagating along the b axis are formed by mol­ecule B and the other independent water mol­ecule. The crystal packing exhibits π–π inter­actions, as indicated by short distances of 3.607 (3) and 3.701 (3) Å between the centroids of the imidazole and pyridine rings of neighbouring mol­ecules

1,3-Dihy­droxy-2-(hy­droxy­meth­yl)propan-2-aminium formate

The title compound, C4H12NO3 +·CHO2 −, was obtained from 1,3-dihy­droxy-2-(hy­droxy­meth­yl)propan-2-aminium acetate and ethyl formate. In the crystal, the cations and anions are held together by inter­molecular N—H⋯O and O—H⋯O hydrogen bonds

Recent advances in PEG–PLA block copolymer nanoparticles

Due to their small particle size and large and modifiable surface, nanoparticles have unique advantages compared with other drug carriers. As a research focus in recent years, polyethylene glycol–polylactic acid (PEG–PLA) block copolymer and its end-group derivative nanoparticles can enhance the drug loading of hydrophobic drugs, reduce the burst effect, avoid being engulfed by phagocytes, increase the circulation time of drugs in blood, and improve bioavailability. Additionally, due to their smaller particle size and modified surface, these nanoparticles can accumulate in inflammation or target locations to enhance drug efficacy and reduce toxicity. Recent advances in PEG–PLA block copolymer nanoparticles, including the synthesis of PEG–PLA and the preparation of PEG–PLA nanoparticles, were introduced in this study, in particular the drug release and modifiable characteristics of PEG–PLA nanoparticles and their application in pharmaceutical preparations

Strong quantum fluctuation of vortices in the new superconductor MgB2MgB_2

By using transport and magnetic measurement, the upper critical field $H_{c2}(T)$ and the irreversibility line $H_{irr}(T)$ has been determined. A big separation between $H_{c2}(0)$ and $H_{irr}(0)$ has been found showing the existence of a quantum vortex liquid state induced by quantum fluctuation of vortices in the new superconductor $MgB_2$. Further investigation on the magnetic relaxation shows that both the quantum tunneling and the thermally activated flux creep weakly depends on temperature. But when the melting field $H_{irr}$ is approached, a drastic rising of the relaxation rate is observed. This may imply that the melting of the vortex matter at a finite temperature is also induced by the quantum fluctuation of vortices.Comment: 4 pages, 4 figure