Existence results of positive solutions for Kirchhoff type equations via bifurcation methods

In this paper we address the following Kirchhoff type problem \begin{equation*} \left\{ \begin{array}{ll} -\Delta(g(|\nabla u|_2^2) u + u^r) = a u + b u^p& \mbox{in}~\Omega, u>0& \mbox{in}~\Omega, u= 0& \mbox{on}~\partial\Omega, \end{array} \right. \end{equation*} in a bounded and smooth domain $\Omega$ in ${\rm I}\hskip -0.85mm{\rm R}$. By using change of variables and bifurcation methods, we show, under suitable conditions on the parameters $a,b,p,r$ and the nonlinearity $g$, the existence of positive solutions.Comment: 18 pages, 1 figur

First-Principles Study on Structural and Chemical Asymmetry of a Biomimetic Water-Splitting Dimanganese Complex

Density-functional theory calculations are carried out for a biomimetic dimanganese complex, [H₂O­(terpy)­Mn^III(μ-O)₂Mn^IV(terpy)­OH₂]³⁺(<b>1</b>, terpy = 2,2′:6′,2″-terpyridine), which is a structural model for the oxygen evolving center of photosystem II. Theoretical investigations aim at elucidating the asymmetry features in the geometric and electronic structures of complex <b>1</b>, as well as their influences on the chemical functions of the two manganese centers, in the presence of water solvent. With the insight gained from the first-principles calculations, we study the oxidation state of complex <b>1</b> in the acetate buffer solution. Both the thermodynamic and kinetic aspects are explored in detail, and the structural and chemical asymmetry of the two manganese centers is fully considered. It is found that the larger steric repulsion associated with the Mn­(IV) center plays a decisive role, which leads to the predominant acetate coordination at the Mn­(III) ion. This thus resolves the existing controversy on the preferential acetate binding to complex <b>1</b>

Structural Stability of La₂Ce₂O₇ as a Proton Conductor: A First-Principles Study

As a promising candidate of a proton conductor under reducing atmosphere, La₂Ce₂O₇ has attracted considerable research interest. However, the thermodynamically stable structure of bulk La₂Ce₂O₇ has remained rather unclear. In this paper, first-principles calculations are carried out to resolve this issue. It is found that the lattice of La₂Ce₂O₇ is substantially stabilized by the formation of anion Frenkel defects, i.e., oxygen atoms displaced from their original sites to interstitial regions. Consequently, the bulk La₂Ce₂O₇ favors disordered fluorite configurations over pyrochlore structure. Our calculation results are consistent with the previously reported neutron diffraction patterns. In addition, partial disordering of cations is also likely under experimental conditions. We then explore the possible proton transfer pathways inside bulk La₂Ce₂O₇. It is revealed that the partial disordering in La₂Ce₂O₇ increases the energy barriers of proton transfer pathways

Magnet-Free Time-Resolved Magnetic Circular Dichroism with Pulsed Vector Beams

Magnetic circular dichroism (MCD) is a widely used spectroscopic technique which reveals valuable information about molecular geometry and electronic structure. However, the weak signal and the necessary strong magnets impose major limitations on its application. We propose a novel protocol to overcome these limitations by using pulsed vector beams (VBs), which consist of nanosecond gigahertz pump and femtosecond UV–vis probe pulses. By virtue of the strong longitudinal electromagnetic fields, the MCD signal detected by using the pulsed VBs is greatly enhanced compared to conventional MCD performed with plane waves. Furthermore, varying the pump–probe time delay allows monitoring the ultrafast variation of molecular properties

Rational Ligand Design for an Efficient Biomimetic Water Splitting Complex

Being an important biomimetic model catalyst for water oxidation, the dimanganese molecular complex [H₂O­(terpy)­Mn^III(μ-O)₂Mn^IV(terpy)­OH₂]³⁺ (complex <b>1</b>, terpy = 2,2′:6′,2″-terpyridine) has been investigated extensively by experimentalists. By carrying out density functional theory calculations, we explore theoretically the oxygen evolution mechanisms of complex <b>1</b>. On the basis of understandings of the geometric and electronic structural features of complex <b>1</b>, we explore the possibility of improving its catalytic efficiency through a rational design of ligands coordinated to the manganese ions. Recognizing that the rate-determining step of oxygen evolution is the formation of an O–O bond at a high-valent manganese center, we design a new complex, [H₂O­(2-bpnp)­Mn^III(μ-O)₂Mn^IV(2-bpnp)­OH₂]³⁺ (complex <b>2</b>, 2-bpnp = 2-([2,2′-bipyridin]-6-yl)-1,8-naphthyridine). It is verified that the proton-accepting 2-bpnp ligand leads to stabilized hydrogen bonding with surrounding water molecules, and hence, the barrier height associated with O–O bond formation is substantially reduced. Moreover, despite its larger size, the 2-bpnp ligand does not cause steric hindrance for the release of molecular oxygen. Consequently, the proposed complex <b>2</b> is expected to outperform the existing complex <b>1</b> regarding catalytic efficiency. This work highlights the potential usefulness of rational design toward reaching the high efficiency of the oxygen evolution center in photosystem II

Unveiling the Decisive Factor for the Sharp Transition in the Scanning Tunneling Spectroscopy of a Single Nickelocene Molecule

Scanning tunneling microscopy (STM) has been utilized to realize the precise measurement and control of local spin states. Experiments have demonstrated that when a nickelocene (Nc) molecule is attached to the apex of an STM tip, the dI/dV spectra exhibit a sharp or a smooth transition when the tip is displaced toward the substrate. However, what leads to the two distinct types of transitions remains unclear, and more intriguingly, the physical origin of the abrupt change in the line shape of dI/dV spectra remains unclear. To clarify these intriguing issues, we perform first-principles-based simulations on the STM tip control process for the Cu tip/Nc/Cu(100) junction. In particular, we find that the suddenly enhanced hybridization between the d orbitals on the Ni ion and the metallic bands in the substrate leads to Kondo correlation overwhelming spin excitation, which is the main cause of the sharp transition in the dI/dV spectra observed experimentally

Delivery of radix ophiopogonis polysaccharide via sucrose acetate isobutyrate-based <i>in situ</i> forming systems alone or combined with its mono-PEGylation

<p>This work aimed to achieve long-lasting delivery of radix ophiopogonis polysaccharide (ROP) by sucrose acetate isobutyrate (SAIB)-based <i>in situ</i> forming systems (ISFSs) alone or combined with mono-PEGylation of ROP. When the ‘90%SAIB/10% solvent’ system was used, the mean residence time (MRT) of ROP was prolonged by 4.3 5 ∼ 7.00 times and the initial release rate was reduced significantly. However, this system was only suitable for days-long sustained release of ROP in short-term therapy. As to the ‘SAIB/additives/solvent’ system containing mono-PEGylated ROP, the results indicated that SAIB/poly(d,l-lactide-co-glycolide) (PLGA)/N-methyl-2-pyrrolidone (NMP) was superior to SAIB/polylactic acid (PLA)/NMP and SAIB/PLA/ethanol in controlled release. Moreover, weeks- to months-long (16–60 d) smooth release of ROP could be achieved by varying the concentration (10–30%) and molecular weight (MW) of PLGA (10–50 kDa) or by employing a moderate MW of PEGylated ROP (∼20 or ∼30 kDa). With further increasing the conjugate MW to ∼40 kDa, the contribution of drug elimination to its plasma retention seemed to surpass that of the SAIB-based system, resulting in that the system no longer had an obvious influence on the <i>in vivo</i> behavior of the conjugate. Besides, the results of host response confirmed that with less solvent being used, the SAIB-based systems showed a higher biocompatibility than the PLGA-based systems, suggesting that they could be freely chosen in the prevention and/or cure of chronic diseases.</p

SmI₂‑Mediated Intermolecular Coupling of γ‑Lactam <i>N</i>‑α-Radicals with Activated Alkenes: Asymmetric Synthesis of 11-Hydroxylated Analogues of the Lead Compounds CP-734432 and PF-04475270

We report, for the first time, the synthesis of 8-aza-analogues of PGE₂. The SmI₂-mediated cross coupling reactions of γ-lactam-hemiaminal <b>9</b>, lactam 2-pyridyl sulfide <b>17</b>, and lactam 2-pyridyl sulfone <b>18</b> with activated alkenes/alkyne were first developed, giving the corresponding γ-lactams in 49–78%, 45–75%, and 75–90%, respectively. The reactions of lactam 2-pyridyl sulfide and 2-pyridyl sulfone proceeded with ≥12:1 <i>trans</i>-diastereoselectivities. This represents the first intermolecular coupling reaction of the γ-lactam <i>N</i>-α-alkyl radicals of types <b>B</b>, <b>B1</b>, and <b>B2</b> with activated alkenes. Two radical-based mechanisms were suggested. The asymmetric synthesis of the 11-hydroxylated analogue of the highly selective EP₄ receptor agonist PF-04475270 (<b>30</b>), the 11-hydroxylated analogue of ocular hypotensive CP-734432 (<b>31</b>), compounds <b>35</b> and <b>36</b> have been achieved on the basis of this method

Davydov Collective Vibrational Modes and Infrared Spectrum Features in Aniline Crystal: Influence of Geometry Change Induced by van der Waals Interactions

Intermolecular interactions have significant influences on molecular crystals, oligomers, and various van der Waals clusters. They are essential in determining the quantum optics, quantum transport, and chemical properties of complex molecular systems. In this work, we investigate the infrared spectra of aniline crystal via the density functional theory. Then we identify four intriguing collective modes that are featured by NHHN wagging vibrations and four other collective modes that are featured by NH₂ wagging vibrations. All these eight collective modes are due to Davydov splitting. To clarify the origin of such vibrational pattern, we further simulate aniline molecule and oligomers, and thoroughly analyze the spectra differences on some key vibrational modes, such as N–H wagging and torsional vibrations. Our results reveal that the chain structure of aniline crystal significantly enhances the van der Waals forces among adjacent molecules, and the intermolecular interactions are responsible for those NHHN wagging collective modes. Our study provides insights in intermolecular interactions and collective motions in aniline crystal and also establishes a standard protocol for the theoretical investigation of other van der Waals clusters

SmI₂‑Mediated Intermolecular Coupling of γ‑Lactam <i>N</i>‑α-Radicals with Activated Alkenes: Asymmetric Synthesis of 11-Hydroxylated Analogues of the Lead Compounds CP-734432 and PF-04475270

We report, for the first time, the synthesis of 8-aza-analogues of PGE₂. The SmI₂-mediated cross coupling reactions of γ-lactam-hemiaminal <b>9</b>, lactam 2-pyridyl sulfide <b>17</b>, and lactam 2-pyridyl sulfone <b>18</b> with activated alkenes/alkyne were first developed, giving the corresponding γ-lactams in 49–78%, 45–75%, and 75–90%, respectively. The reactions of lactam 2-pyridyl sulfide and 2-pyridyl sulfone proceeded with ≥12:1 <i>trans</i>-diastereoselectivities. This represents the first intermolecular coupling reaction of the γ-lactam <i>N</i>-α-alkyl radicals of types <b>B</b>, <b>B1</b>, and <b>B2</b> with activated alkenes. Two radical-based mechanisms were suggested. The asymmetric synthesis of the 11-hydroxylated analogue of the highly selective EP₄ receptor agonist PF-04475270 (<b>30</b>), the 11-hydroxylated analogue of ocular hypotensive CP-734432 (<b>31</b>), compounds <b>35</b> and <b>36</b> have been achieved on the basis of this method