Unitarity in Dirichlet Higgs model

We show that a five-dimensional Universal Extra Dimension model, compactified on a line segment, is consistently formulated even when the gauge symmetry is broken solely by non-zero Dirichlet boundary conditions on a bulk Higgs field, without any quartic interaction. We find that the longitudinal W ⁺ W ⁻ elastic scattering amplitude, under the absence of the Higgs zero mode, is unitarized by exchange of infinite towers of KK Higgs bosons. Resultant amplitude scales linearly with the scattering energy μ ?s\propto\sqrt{s}, exhibiting five-dimensional nature. A tree-level partial-wave unitarity condition is satisfied up to 6.7 (5.7) TeV for the KK scale m _KK=430 (500) GeV, favored by the electroweak data within 90% CL.     

DFT Study of a 5‐endo‐trig‐Type Cyclization of 3‐Alkenoic Acids by Using Pd–Spiro‐bis(isoxazoline) as Catalyst: Importance of the Rigid Spiro Framework for Both Selectivity and Reactivity

The reaction pathway of an enantioselective 5‐endo‐trig‐type cyclization of 3‐alkenoic acids catalyzed by a chiral palladium–spiro‐bis(isoxazoline) complex, Pd–SPRIX, has been studied by density functional theory calculations. The most plausible pathway involves intramolecular nucleophilic attack of the carboxylate moiety on the C?C double bond activated by Pd–SPRIX and β‐H elimination from the resulting organopalladium intermediate. The enantioselectivity was determined in the cyclization step through the formation of a π‐olefin complex, in which one of the two enantiofaces of the olefin moiety was selected. The β‐H elimination occurs via a seven‐membered cyclic structure in which the acetate ligand plays a key role in lowering the activation barrier of the transition state. In the elimination step, the SPRIX ligand was found to behave as a monodentate ligand due to the hemilability of one of the isoxazoline units thereby facilitating the elimination. Natural population analysis of this pathway showed that the more weakly electron‐donating SPRIX ligand, compared with the bis(oxazoline) ligand, BOX, facilitated the formation of the π‐olefin complex intermediate, leading to a smaller overall activation energy and a higher reactivity of the Pd–SPRIX catalyst.     

The Euler multiplicity and addition-deletion theorems for multiarrangements

The addition–deletion theorems for hyperplane arrangements,which were originally shown by Terao [J. Fac. Sci. Univ. TokyoSect. IA Math. 27 (1980) 293–320.], provide useful waysto construct examples of free arrangements. In this article,we prove addition–deletion theorems for multiarrangements.A key to the generalization is the definition of a new multiplicity,called the Euler multiplicity, of a restricted multiarrangement.We compute the Euler multiplicities in many cases. Then we applythe addition–deletion theorems to various arrangements,including supersolvable arrangements and the Coxeter arrangementof type A₃, to construct free and non-free multiarrangements.     

A function space model approach to the rational evaluation subgroups

Let f : U → X be a map from a connected nilpotent space U to a connected rational space X. The evaluation subgroup G _*(U, X; f), which is a generalization of the Gottlieb group of X, is investigated. The key device for the study is an explicit Sullivan model for the connected component containing f of the function space of maps from U to X, which is derived from the general theory of such a model due to Brown and Szczarba (Trans Am Math Soc 349, 4931–4951, 1997). In particular, we show that non Gottlieb elements are detected by analyzing a Sullivan model for the map f and by looking at non-triviality of higher order Whitehead products in the homotopy group of X. The Gottlieb triviality of a fibration in the sense of Lupton and Smith (The evaluation subgroup of a fibre inclusion, 2006) is also discussed from the function space model point of view. Moreover, we proceed to consideration of the evaluation subgroup of the fundamental group of a nilpotent space. In consequence, the first Gottlieb group of the total space of each S ¹-bundle over the n-dimensional torus is determined explicitly in the non-rational case.      

Far infrared optical properties of high Tc superconductors LnBa2Cu3Ox (Ln=Y, Ho, Er, Sm, GD, Dy, Eu, Pr)

Systematic measurements of the far infrared reflection spectra of high T_c superconductors LnBa₂Cu₃O_x for various Ln as shown in the title were performed. Infrared reflection spectra of tetragonal LnBa₂Cu₃O_x exhibit Reststrahlen vibration near 640, 590, 530, 355 and 250 cm^–1, common to these materials, and the spectra of the orthorhombic LnBa₂Cu₃O_x exhibit the characteristics of free carriers except PrBa₂Cu₃O_x with weak phonon structures near 617, 570, 317 and 285 cm^–1. PrBa₂Cu₃O_x is not a superconductor, and it has no characteristic broad band due to free carriers for all x in the range of 6 to 7. Lattice dynamical calculation was performed by the use of the shell model and the calculated results express quite well the characteristic features of infrared experiments.     

Optimal consumption models in economic growth

We study the optimal consumption problem in the one-sector model of economic growth under uncertainty. We show the existence of a classical solution of the Hamilton-Jacobi-Bellman equation associated with the stochastic optimization problem, and then give an optimal consumption policy in terms of its solution.     

Synthesis and structural revision of marine eicosanoid agardhilactone

Synthesis of the marine eicosanoid agardhilactone has been achieved. The relative and absolute configuration of agardhilactone was successfully determined.     

Reactions of lithium tributyl heteroaryl borates with allylic bromides in the presence of copper(I) cyanide

The reaction of various lithium tributylheteroarylborates with allylic bromides in the presence of copper(I) cyanide furnished the regioselective allylation at the heteroaryl ring.     

On the unstable homotopy spectral sequences

We shall study the relation between the unstable homotopy spectral sequence associated with the cell decomposition of the source space and the one associated with the Postnikov decomposition of the target space. It is proved that the Maunder's result holds for these two types of spectral sequences. This result will be exploited to study the differentials of these spectral sequences and we obtain a generalization of a theorem due to Atiyah-Hirzebruch and Dold. Making use of these spectral sequences with the convergence lemma, some results on the phantom maps and the homotopy groups of map_*(Y, X) will be proved.