The vanishing order of certain Hecke L-functions of imaginary quadratic fields

AbstractLet −D<−4 denote a fundamental discriminant which is either odd or divisible by 8, so that the canonical Hecke character of Q(−D) exists. Let d be a fundamental discriminant prime to D. Let 2k−1 be an odd natural number prime to the class number of Q(−D). Let χ be the twist of the (2k−1)th power of a canonical Hecke character of Q(−D) by the Kronecker's symbol n↦(dn). It is proved that the vanishing order of the Hecke L-function L(s,χ) at its central point s=k is determined by its root number when |d|⪡D112−ϵ, where the constant implied in the symbol ⪡ depends only on k and ϵ, and is effective for L-functions with root number −1

Growth and Optical Properties of the Whole System of Li(Mn1−x_{1-x},Nix_{x})PO4_{4} (0 ≤ x ≤ 0.5) Single Crystals

A series of single crystals of Li(Mn$_{1-x}$,Ni$_{x}$)PO$_{4}$ (x = 0.00, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.08, 0.10, 0.15, 0.20, and 0.50) have been grown to large sizes up to 5 mm in diameter and 120 mm in length using the floating zone method for the first time. The comprehensive characterizations of the as-grown crystals were performed before further physical property measurements. The composition of the grown crystals was determined by energy-dispersive X-ray spectroscopy. The crystal structures were characterized by the X-ray powder diffraction method with a GSAS fitting for structural refinement, which reveals a high phase purity of the as-obtained crystals. The polarized microscopic images and Laue patterns prove the excellent quality of the single crystals. Oriented cuboids with sizes of 2.7 × 3.8 × 2.1 mm$3{1-x}$ along the a, b, and c crystalline directions were cut and polished for further anisotropic magnetic and transparent measurements. We also first proposed a new potential application in the non-linear optical (NLO) and laser generation application for LiMPO$_{4}$ (M = transition metal) materials. The optical and laser properties, such as the absorption spectra and the second harmonic generation (SHG), have been investigated and have furthermore confirmed the good quality of the as-grown single crystals

The Electronic Structural and Defect-Induced Absorption Properties of a Ca2_{2}B10_{10}O14_{14}F6_{6} Crystal

Comprehensive ab initio electronic structure calculations were performed for a newly developed deep-ultraviolet (DUV) non-linear optical (NLO) crystal Ca$_{2}$B$_{10}$O$_{14}$F$_{6}$ (CBOF) using the first principle method. Fifteen point defects including interstitial, vacancy, antisite, Frenkel, and Schottky of Ca, O, F, and B atoms in CBOF were thoroughly investigated as well as their effects on the optical absorption properties. Their formation energies and the equilibrium concentrations were also calculated by ab initio total energy calculations. The growth morphology was quantitatively analyzed using the Hartman–Perdok approach. The formation energy of interstitial F (Fi) and antisite defect O$_{F}$ were calculated to be approximately 0.33 eV and 0.83 eV, suggesting that they might be the dominant defects in the CBOF material. The absorption centers might be induced by the O and F vacancies (V$_{F}$, V$_{O}$), interstitial B and O (O$_{i}$, B$_{i}$), and the antisite defect O substitute of F (O$_{F}$), which might be responsible for lowering the damage threshold of CBOF. The ionic conductivity might be increased by the Ca vacancy (V$_{ca}$), and, therefore, the laser-induced damage threshold decreases

Preparation of Recombinant Human Collagen III Protein Hydrogels with Sustained Release of Extracellular Vesicles for Skin Wound Healing

Existing treatment methods encounter difficulties in effectively promoting skin wound healing, making this a serious challenge for clinical treatment. Extracellular vesicles (EVs) secreted by stem cells have been proven to contribute to the regeneration and repair of wound tissue, but they cannot be targeted and sustained, which seriously limits their current therapeutic potential. The recombinant human collagen III protein (rhCol III) has the advantages of good water solubility, an absence of hidden viral dangers, a low rejection rate and a stable production process. In order to achieve a site-specific sustained release of EVs, we prepared a rhCol III hydrogel by cross-linking with transglutaminase (TGase) from Streptomyces mobaraensis, which has a uniform pore size and good biocompatibility. The release profile of the rhCol III-EVs hydrogel confirmed that the rhCol III hydrogel could slowly release EVs into the external environment. Herein, the rhCol III-EVs hydrogel effectively promoted macrophage changing from type M1 to type M2, the migration ability of L929 cells and the angiogenesis of human umbilical vein endothelial cells (HUVECs). Furthermore, the rhCol III-EVs hydrogel is shown to promote wound healing by inhibiting the inflammatory response and promoting cell proliferation and angiogenesis in a diabetic rat skin injury model. The reported results indicate that the rhCol III-EVs hydrogel could be used as a new biological material for EV delivery, and has a significant application value in skin wound healing

Growth and Optical Properties of the Whole System of Li(Mn_1-<em>x</em>,Ni<em>_x</em>)PO₄ (0 ≤ x ≤ 0.5) Single Crystals

A series of single crystals of Li(Mn1-x,Nix)PO4 (x = 0.00, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.08, 0.10, 0.15, 0.20, and 0.50) have been grown to large sizes up to 5 mm in diameter and 120 mm in length using the floating zone method for the first time. The comprehensive characterizations of the as-grown crystals were performed before further physical property measurements. The composition of the grown crystals was determined by energy-dispersive X-ray spectroscopy. The crystal structures were characterized by the X-ray powder diffraction method with a GSAS fitting for structural refinement, which reveals a high phase purity of the as-obtained crystals. The polarized microscopic images and Laue patterns prove the excellent quality of the single crystals. Oriented cuboids with sizes of 2.7 × 3.8 × 2.1 mm3 along the a, b, and c crystalline directions were cut and polished for further anisotropic magnetic and transparent measurements. We also first proposed a new potential application in the non-linear optical (NLO) and laser generation application for LiMPO4 (M = transition metal) materials. The optical and laser properties, such as the absorption spectra and the second harmonic generation (SHG), have been investigated and have furthermore confirmed the good quality of the as-grown single crystals

Graphene-Assisted Electromagnetically Induced Transparency-like Terahertz Metabiosensor for Ultra-Sensitive Detection of Ovalbumin

Terahertz (THz) metamaterial (MM) biosensors are a potential method of biomolecule detection. However, there have been few reports on the detection of trace proteins. In this study, we designed a novel THz biosensor consisting of graphene, polyimide (PI), and electromagnetically induced transparency-like (EIT-like) MMs for the ultra-sensitive detection of ovalbumin (OVA). The doping analyte can influence the Fermi level and electrical conductivity of graphene, as well as the coupling of resonators in MMs. These changes are reflected in the magnitude, phase, and frequency changes in the transmission spectra. The biosensor achieved a high sensitivity function for OVA and reached a limit of detection (LoD) of 8.63 pg/mL. The results showed that by regulating the Fermi level of graphene between the valence band, Dirac point, and conduction band, the sensitivity and LoD of MM-based THz biosensors can be enhanced. Such biosensors have the potential to be used in the high-sensitivity detection of trace proteins in biomedical fields

A Terahertz Controlled-NOT Gate Based on Asymmetric Rotation of Polarization in Chiral Metamaterials

Logical operation based on polarization encoding of light is important for future data transmission and information processing. However, in the terahertz (THz) region, chiral materials with large optical activity are not available in nature, and the effective manipulation of polarization states remains challenging. Here, the authors demonstrate a double-layer bi-anisotropic metamaterial that consists of planar spiral and cut-wire layers separated by a polyimide film. Strong asymmetric polarization rotation of two orthogonal linear polarizations can be observed around 0.53 THz. By investigating the correlation between two linear polarization states before and after the spiral-wire metamaterial at this frequency, a controlled-NOT (CNOT) gate operating on two linear-polarization-based qubits is further exploited. The processing mechanism of the asymmetric rotation and CNOT gate is attributed to the scattering of dipole momentum based on classical multipole theory. This polarization processor's architecture is promising for robust and energy-efficient THz polarization control, and also provides an effective path for the development of future optical supercomputing technology