Exponents of class groups of real quadratic function fields

We show that there are polynomials with such that the ideal class group of the real quadratic extensions has an element of order .

     

Nonlocal regularization and spontaneously broken abelian gauge theories for an arbitrary gauge parameter

We study the nonlocal regularization for the case of a spontaneously broken abelian gauge theory in the R-gauge with an arbitrary gauge parameter . We consider a simple abelian-Higgs model with chiral couplings as an example. We show that if we apply the nonlocal regularization procedure (to construct a nonlocal theory with FINITE mass parameter) to the spontaneously broken R-gauge Lagrangian, using the quadratic forms as appearing in this Lagrangian, we find that a physical observable in this model, an analogue of the muon anomalous magnetic moment, evaluated to order O [g²] does indeed show -dependence. We then apply the modified form of nonlocal regularization that was recently advanced and studied for the unbroken non-abelian gauge theories and discuss the resulting WT identities and -independence of the S-matrix elements.     

Phase‐Stable CsPbI3 Nanocrystals: The Reaction Temperature Matters

High temperature colloidal synthesis for obtaining thermal, colloidal and phase‐stable CsPbI₃ nanocrystals with near‐unity quantum yield is reported. While standard perovskite synthesis reactions were carried out at 160 °C (below 200 °C), increase of another ≈100 °C enabled the alkylammonium ions to passivate the surface firmly and prevented the nanocrystals from phase transformation. This did not require any inert atmosphere storage, use of heteroatoms, specially designed ligands, or the ice cooling protocol. Either at high temperature in reaction flask or in the crude mixture or purified dispersed solution; these nanocrystals were observed stable and retained the original emission. Different spectroscopic analyses were carried out and details of the surface binding of alkyl ammonium ligands in place of surface Cs in the crystal lattice were investigated. As CsPbI₃ is one of the most demanding optical materials, bringing stability by proper surface functionalization without use of secondary additives would indeed help in wide spreading of their applications.     

Relativistic dynamics of half-spin particles in a homogeneous magnetic field: an atom with nucleus of spin 12

An investigation of the relativistic dynamics of N+1 spin-12 particles placed in an external, homogeneous magnetic field is carried out. The system can represent an atom with a fermion nucleus and N electrons. Quantum electrodynamical interactions, namely, projected Briet and magnetic interactions, are chosen to formulate the relativistic Hamiltonian. The quasi-free-particle picture is retained here. The total pseudomomentum is conserved, and its components are distinct when the total charge is zero. Therefore, the center-of-mass motion can be separated from the Hamiltonian for a neutral (N+1)-fermion system, leaving behind a unitarily transformed, effective Hamiltonian H(0) at zero total pseudomomentum. The latter operator represents the complete relativistic dynamics in relative coordinates while interaction is chosen through order alpha4mc2. Each one-particle part in the effective Hamiltonian can be brought to a separable form for positive- and negative-energy states by replacing the odd operator in it through two successive unitary transformations, one due to Tsai [Phys. Rev. D 7, 1945 (1973)] and the other due to Weaver [J. Math. Phys. 18, 306 (1977)]. Consequently, the projector changes and the interaction that involves the concerned particle also becomes free from the corresponding odd operators. When this maneuver is applied only to the nucleus, and the non-Hermitian part of the transformed interaction is removed by another unitary transformation, a familiar form of the atomic relativistic Hamiltonian H(atom) emerges. This operator is equivalent to H(0). A good Hamiltonian for relativistic quantum chemical calculations, H(Qchem), is obtained by expanding the nuclear part of the atomic Hamiltonian through order alpha4mc2 for positive-energy states. The operator H(Qchem) is obviously an approximation to H(atom). When the same technique is used for all particles, and subsequently the non-Hermitian terms are removed by suitable unitary transformations, one obtains a Hamiltonian H(T) that is equivalent to H(atom) but is in a completely separable form. As the semidiscrete eigenvalues and eigenfunctions of the one-particle parts are known, the completely separable Hamiltonian can be used in computation. A little more effort leads to the derivation of the correct atomic Hamiltonian in the nonrelativistic limit, H(nonrel). The operator H(nonrel) is an approximation to H(T). It not only retains the relativistic and radiative effects, but also directly exhibits the phenomena of electron paramagnetic resonance and nuclear magnetic resonance.     

A facile access to natural and unnatural dialkylsubstituted maleic anhydrides

A facile new route to the potential building blocks 2-bromomethyl-3-alkylmaleic anhydrides 15a/b for the synthesis of natural and unnatural dialkylsubstituted maleic anhydrides has been demonstrated, starting from dimethyl citraconate (9) via NBS-bromination, S_N2′ Grignard coupling reactions, hydrolysis, molecular bromine addition and dehydrative ring closure reactions pathway with 49-51% overall yield in 5-steps. Chemoselective allylic substitution of bromoatom in 15a/b with Grignard reagents has been described to obtain the unsymmetrical maleic anhydride 16 and symmetrically dialkylsubstituted maleic anhydrides 25a/b in 55% yield. The naturally occurring 2-carboxymethyl-3-hexylmaleic anhydride (1) has been synthesized from 16 via esterification, ozonolysis and an oxidation route. The synthesis of two naturally occurring 2-(β-carboxyethyl)-3-alkylmaleic anhydrides 2a/b have been completed via a chemoselective diethylmalonate coupling reaction followed by acid induced hydrolysis. In our hands the S_N2 or S_N2′ coupling of Grignard reagent with 21 to obtain 1 and Reformatsky reaction with 15a/b to obtain 2c/d met with failure.     

An explicitly designed paratope of amyloid-β prevents neuronal apoptosis in vitro and hippocampal damage in rat brain

Synthetic antibodies hold great promise in combating diseases, diagnosis, and a wide range of biomedical applications. However, designing a therapeutically amenable, synthetic antibody that can arrest the aggregation of amyloid-β (Aβ) remains challenging. Here, we report a flexible, hairpin-like synthetic paratope (SP1, ∼2 kDa), which prevents the aggregation of Aβ monomers and reverses the preformed amyloid fibril to a non-toxic species. Structural and biophysical studies further allowed dissecting the mode and affinity of molecular recognition events between SP1 and Aβ. Subsequently, SP1 reduces Aβ-induced neurotoxicity, neuronal apoptosis, and ROS-mediated oxidative damage in human neuroblastoma cells (SH-SY5Y). The non-toxic nature of SP1 and its ability to ameliorate hippocampal neurodegeneration in a rat model of AD demonstrate its therapeutic potential. This paratope engineering module could readily implement discoveries of cost-effective molecular probes to nurture the basic principles of protein misfolding, thus combating related diseases.

Herein, the therapeutic potentials of an explicitly designed peptide probe are systematically illuminated in vitro and in vivo against Aβ aggregation. The probe demonstrates remarkable potency for attenuating neurotoxicity and hippocampal damage.     

First principles simulation of the UV absorption spectrum of ethylene using the vertical Franck-Condon approach

A new method which we refer to as vertical Franck-Condon is proposed to calculate electronic absorption spectra of polyatomic molecules. In accord with the short-time picture of spectroscopy, the excited-state potential energy surface is expanded at the ground-state equilibrium geometry and the focus of the approach is more on the overall shape of the spectrum and the positions of the band maxima, rather than the precise position of the 0-0 lines. The Born-Oppenheimer approximation and the separability of the excited-state potential energy surface along the excited-state normal mode coordinates are assumed. However, the potential surface is not necessarily approximated as harmonic oscillator potentials along the individual normal modes. Instead, depending upon the nature of the potential surface along a particular normal mode, it is treated either in the harmonic approximation or the full one-dimensional potential is considered along this mode. The vertical Franck-Condon approach is applicable therefore even in cases where the excited state potential energy surface is highly anharmonic and the conventional harmonic Franck-Condon approach is inadequate. As an application of the method, the ultraviolet spectrum of ethylene between 6.2 eV (50,000 cm(-1)) and 8.7 eV (70,000 cm(-1)) is simulated, using the Similarity Transformed Equation of Motion Coupled-Cluster method to describe the required features of the potential energy surfaces. The spectrum is shown to be a result of sharp doublet structures stemming from the pi --> 3s (Rydberg) state superimposed on top of a broad band resulting from the pi --> pi* (valence) state. For the Rydberg state, the symmetric C=C stretch and the torsion mode contribute to the spectrum, while the broad valence band results from excitation into the C=C stretch, CH2 scissors, and the torsion mode. For both states, the potential along the torsion mode is highly anharmonic and the full treatment of the potential along this mode in the vertical Franck-Condon method is required.     

Exact solution of the relativistic dynamics of a spin‐½ particle moving in a homogeneous magnetic field

The relativistic dynamics of one spin‐½ particle moving in a uniform magnetic field is described by the Hamiltonian $\mathbf{h}^{0}_{D}(\pi)=c\alpha\cdot\pi+\beta mc^{2}$. The discrete (and semidiscrete) eigenvalues and the corresponding eigenspinors are in principle known from the work of Dirac, Rabi, and Bloch. These are extensively reviewed here. Next, exact solutions are worked out for the recoil dynamics in relative coordinates, which involves the Hamiltonian $\mathbf{h}^{0}_{D}(-\mathbf{k})=-c\alpha\cdot\mathbf{k}+\beta mc^{2}$. Exact solutions are also explicitly calculated in the case where the spin‐½ particle has an anomalous magnetic moment such that its Hamiltonian is given by $\mathbf{h}_{D}(\pi)=\mathbf{h}^{0}_{D}(\pi)-\beta\mu_{\mathrm{ano}}\sigma\cdot\mathbf{B}$. Similar exact solutions are derived here when the recoiling particle has an anomalous magnetic moment, that is, the eigenvalues and eigenspinors of the Hamiltonian $\mathbf{h}_{D}(-\mathbf{k})=\mathbf{h}^{0}_{D}(-\mathbf{k})-\beta\mu_{\mathrm{ano}}\sigma\cdot\mathbf{B}$ are explicitly obtained. The diagonalized and separable form of the Hamiltonian h _D(π), written as $\tilde{\mathbf{h}}_{D}(\pi)$, has exceedingly simple forms of eigenspinors. Similarly, the diagonalized and separable form of the operator h _D(? k ), written as $\tilde{\mathbf{h}}_{D}(-\mathbf{k})$, has very simple eigenspinors. The importance of these exact solutions is that the eigenspinors can be used as bases in a calculation involving many spin‐½ particles placed in a uniform magnetic field. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 209–217, 2001     

A general gold-catalyzed direct oxidative coupling of non-activated arenes

A gold-catalyzed mild and general oxidative homo-coupling of arenes using PhI(OAc)2 as the oxidant is described (13 examples, 31-81% yield).     

Local density corrected three-body distribution functions for probing local structure reorganization in liquids

Three-body distribution functions are calculated for metal ions in an aqueous medium in order to investigate and characterise solvent structure reorganization. Based on the existing formulation of three body correlation function, a local density correction is introduced to enable a comparison of different sub-regions within a solvate as well as different systems, thus taking into account the varying density arising from the influence of the solute.