Uplifted supersymmetric Higgs region

We show that the parameter space of the Minimal Supersymmetric Standard Model includes a region where the down-type fermion masses are generated by the loop-induced couplings to the up-type Higgs doublet. In this region the down-type Higgs doublet does not acquire a vacuum expectation value at tree level, and has sizable couplings in the superpotential to the tau leptons and bottom quarks. Besides a light standard-like Higgs boson, the Higgs spectrum includes the nearly degenerate states of a heavy spin-0 doublet which can be produced through their couplings to the b quark and decay predominantly into τ ⁺ τ ^? or τν.     

On bounded elementary generation for SL<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> over polynomial rings

Let F[X] be the polynomial ring over a finite field F. It is shown that, for n ≥ 3, the special linear group SL _n (F[X]) is boundedly generated by the elementary matrices.     

Bingham Flows in Periodic Domains of Infinite Length

The Bingham fluid model has been successfully used in modeling a large class of non-Newtonian fluids. In this paper, the authors extend to the case of Bingham fluids the results previously obtained by Chipot and Mardare, who studied the asymptotics of the Stokes flow in a cylindrical domain that becomes unbounded in one direction, and prove the convergence of the solution to the Bingham problem in a finite periodic domain, to the solution of the Bingham problem in the infinite periodic domain, as the length of the finite domain goes to infinity. As a consequence of this convergence, the existence of a solution to a Bingham problem in the infinite periodic domain is obtained, and the uniqueness of the velocity field for this problem is also shown. Finally, they show that the error in approximating the velocity field in the infinite domain with the velocity in a periodic domain of length 2? has a polynomial decay in ?, unlike in the Stokes case(see [Chipot,M. and Mardare, S., Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, Journal de Math′ematiques Pures et Appliqu′ees, 90(2), 2008,133–159]) where it has an exponential decay. This is in itself an important result for the numerical simulations of non-Newtonian flows in long tubes.     

An adaptive wavelet shrinkage approach to the Spektor-Lord-Willis problem

The stereological problem of unfolding the sphere size distribution from linear sections is considered. A minimax estimator of the intensity function of a Poisson process that describes the problem is introduced and an adaptive estimator is constructed that achieves the optimal rate of convergence over Besov balls to within logarithmic factors. The construction of these estimators uses Wavelet-Vaguelette Decomposition (WVD) of the operator that defines our inverse problem.     

Generalizations of Arnold’s version of Euler’s theorem for matrices

A recent result, conjectured by Arnold and proved by Zarelua, states that for a prime number p, a positive integer k, and a square matrix A with integral entries one has ${\textrm tr}(A^{p^k}) \equiv {\textrm tr}(A^{p^{k-1}}) ({\textrm mod}{p^k})${\textrm tr}(A^{p^k}) \equiv {\textrm tr}(A^{p^{k-1}}) ({\textrm mod}{p^k}). We give a short proof of a more general result, which states that if the characteristic polynomials of two integral matrices A,  B are congruent modulo p ^k then the characteristic polynomials of A ^p and B ^p are congruent modulo p ^k+1, and then we show that Arnold’s conjecture follows from it easily. Using this result, we prove the following generalization of Euler’s theorem for any 2 × 2 integral matrix A: the characteristic polynomials of A ^Φ(n) and A ^Φ(n)-ϕ(n) are congruent modulo n. Here ϕ is the Euler function, ?_i=1^l p_i^a_i\prod_{i=1}^{l} p_i^{\alpha_i} is a prime factorization of n and $\Phi(n)=(\phi(n)+\prod_{i=1}^{l} p_i^{\alpha_i-1}(p_i+1))/2$\Phi(n)=(\phi(n)+\prod_{i=1}^{l} p_i^{\alpha_i-1}(p_i+1))/2.     

Integral conditions for exponential dichotomy: A nonlinear approach

We give new necessary and sufficient integral conditions for the existence of exponential dichotomy of skew-product flows. Our methods are based on the structure of the associated stable subspace and unstable subspace. We propose a nonlinear approach, extending the study of exponential stability in terms of integral conditions to the case of uniform exponential dichotomy. We apply the main results to the study of uniform exponential dichotomy of non-autonomous systems.     

The Rb7Bi3−3xSb3xCl16 Family: A Fully Inorganic Solid Solution with Room‐Temperature Luminescent Members

Low‐dimensional ns²‐metal halide compounds have received immense attention for applications in solid‐state lighting, optical thermometry and thermography, and scintillation. However, these are based primarily on the combination of organic cations with toxic Pb²⁺ or unstable Sn²⁺, and a stable inorganic luminescent material has yet to be found. Here, the zero‐dimensional Rb₇Sb₃Cl₁₆ phase, comprised of isolated [SbCl₆]^3? octahedra and edge‐sharing [Sb₂Cl₁₀]^4? dimers, shows room‐temperature photoluminescence (RT PL) centered at 560 nm with a quantum yield of 3.8±0.2 % at 296 K (99.4 % at 77 K). The temperature‐dependent PL lifetime rivals that of previous low‐dimensional materials with a specific temperature sensitivity above 0.06 K^?1 at RT, making it an excellent thermometric material. Utilizing both DFT and chemical substitution with Bi³⁺ in the Rb₇Bi_3?3xSb_3xCl₁₆ (x≤1) family, we present the edge‐shared [Sb₂Cl₁₀]^4? dimer as a design principle for Sb‐based luminescent materials.