Boundedness of the anisotropic maximal and anisotropic singular integral operators in generalized Morrey spaces

In this paper we give the conditions on the pair (ω ₁, ω ₂) which ensures the boundedness of the anisotropic maximal operator and anisotropic singular integral operators from one generalized Morrey space M_p,w1 \mathcal{M}_{p,\omega _1 } to another M_p,w2 \mathcal{M}_{p,\omega _2 }, 1 < p < g8, and from the space M_1,w1 \mathcal{M}_{1,\omega _1 } to the weak space WM_1,w2 W\mathcal{M}_{1,\omega _2 }.     

The Banach algebra generated by a C0-semigroup

Let $\mathbf{T}={\{T(t)\}}_{t?0}$ be a bounded $C_0$-semigroup on a Banach space with generator A. We define $A_{\mathbf{T}}$ as the closure with respect to the operator-norm topology of the set $\{\stackrel{?}{f}(\mathbf{T}):f\in L^1({\mathbb{R}}_{+})\}$, where $\stackrel{?}{f}(\mathbf{T})={\int }_0^{\infty }f(t)T(t)\mathrm{d}t$ is the Laplace transform of $f\in L^1({\mathbb{R}}_{+})$ with respect to the semigroup T. Then $A_{\mathbf{T}}$ is a commutative Banach algebra. It is shown that if the unitary spectrum $\sigma (A)\cap \mathrm{i}\mathbb{R}$ of A is at most countable, then the Gelfand transform of $S\in A_{\mathbf{T}}$ vanishes on $\sigma (A)\cap \mathrm{i}\mathbb{R}$ if and only if, ${\lim }_{t\to \infty }6T(t)S6=0$. Some applications to the semisimplicity problem are given. To cite this article: H. Mustafayev, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Resurrecting no-scale supergravity phenomenology

In the context of phenomenological models in which the soft supersymmetry-breaking parameters of the MSSM become universal at some unification scale, M _in, above the GUT scale, M _GUT, it is possible that all the scalar mass parameters m ₀, the trilinear couplings A ₀ and the bilinear Higgs coupling B ₀ vanish simultaneously, as in no-scale supergravity. Using these no-scale inputs in a renormalisation-group analysis of the minimal supersymmetric SU(5) GUT model, we pay careful attention to the matching of parameters at the GUT scale. We delineate the region of M _in, m _1/2 and tan?β where the resurrection of no-scale supergravity is possible, taking due account of the relevant phenomenological constraints such as electroweak symmetry breaking, m _h ,b→s γ, the neutralino cold dark matter density Ω _χ h ² and g _μ ?2. No-scale supergravity survives in an L-shaped strip of parameter space, with one side having m _1/2?200 GeV, the second (orthogonal) side having M _in?5×10¹⁶ GeV. Depending on the relative signs and magnitudes of the GUT superpotential couplings, these may be connected to form a triangle whose third side is a hypotenuse at larger M _in, m _1/2 and tan?β, whose presence and location depend on the GUT superpotential parameters. We compare the prospects for detecting sparticles at the LHC in no-scale supergravity with those in the CMSSM and the NUHM.     

Investigation of DNA cleavage activities of new oxime-type ligand complexes and molecular modeling of complex-DNA interactions

Nucleolytic activities of some new oxime-type ligand complexes were investigated by neutral agarose gel electrophoresis. Analysis of the cleavage products in agarose gel indicated that all complexes used converted supercoiled pUC18 plasmid DNA to its nicked or linear form. It was found that nucleolytic activities of the complexes depend on the complex concentration, reaction time and the presence of a cooxidant (magnesium monoperoxyphthalate, MMPP) in the reaction mixture. However, the complexes cleaved pUC18 plasmid DNA at all investigated pH values. Nucleolytic activities of complexes were investigated for different complex concentrations (0.1–100 μmol L⁻¹), pH values (6.0–10.0) and reaction times (0–60 min). Molecular modeling studies performed by the Hyperchem Software together with DNA-binding studies showed that planar sites of the complexes intercalated into double stranded DNA. It can be concluded that all oxime-type ligand complexes used can be evaluated as nuclease mimics.     

Crystal structure and vibrational spectra of two complexes of manganese(II) with glicyne

Two polymeric complexes of glicyne with manganese(II) have been prepared and characterized by means of spectroscopic and x-ray analyses. The first complex of the formula [Mn(Gly)Cl₂(H₂O)₂] crystallizes in the monoclinic space group P2₁/n with a = 6.519(2), b = 15.981(3), c = 7.893(2) Å, and = 97.18(3)°. The Mn atoms are in distorted octahedral environments with all ligands in cis positions. The adjacent manganese(II) ions are linked in polymeric chains via carboxylate groups. The second complex [Mn(Gly)₂Cl₂] crystallizes in the triclinic space group P with a = 4.968(2), b = 6.582(2), c = 7.925(3) Å, = 106.17(3), = 92.86(3), and = 107.21(3)°. The octahedral-coordinated manganese(II) ion is situated on a crystallographic center of symmetry and is bound to four carboxylate oxygen atoms from different glicyne molecules and two chloride ions.     

Dipolar relaxation in an ultra-cold gas of magnetically trapped chromium atoms

We investigate, both theoretically and experimentally, dipolar relaxation in a gas of magnetically trapped chromium atoms. We find that the large magnetic moment of 6_B results in an event rate coefficient for dipolar relaxation processes of up to 3.2×10^-11 cm³s^-1 in a magnetic field of 44 G. We present a theoretical model based on pure dipolar coupling, which predicts dipolar relaxation rates that agree with our experimental observations. This very general approach can be applied to a large variety of dipolar gases. PACS 34.50.-s; 34.50.PI; 03.65.NK; 32.80.PJ     

Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

In this paper, the boundedness of a large class of sublinear commutator operators T _b generated by a Calderón-Zygmund type operator on a generalized weighted Morrey spaces \({M_{p,\varphi }}(w)\) with the weight function w belonging to Muckenhoupt’s class A _p is studied. When 1 < p < ∞ and b ∈ BMO, sufficient conditions on the pair (φ ₁, φ ₂) which ensure the boundedness of the operator T _b from \({M_{p,\varphi 1}}(w)\) to \({M_{p,\varphi 2}}(w)\) are found. In all cases the conditions for the boundedness of T _b are given in terms of Zygmund-type integral inequalities on (φ ₁, φ ₂), which do not require any assumption on monotonicity of φ ₁(x, r), φ ₂(x, r) in r. Then these results are applied to several particular operators such as the pseudo-differential operators, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.     

Embeddings between weighted Copson and Cesàro function spaces

In this paper, characterizations of the embeddings between weighted Copson function spaces \(Co{p_{{p_1},{q_1}}}\left( {{u_1},{v_1}} \right)\) and weighted Cesàro function spaces \(Ce{s_{{p_2},{q_2}}}\left( {{u_2},{v_2}} \right)\) are given. In particular, two-sided estimates of the optimal constant c in the inequality

$${\left( {\int_0^\infty {{{\left( {\int_0^t {f{{\left( \tau \right)}^{{p_2}}}{v_2}\left( \tau \right)d\tau } } \right)}^{{q_2}/{p_2}}}{u_2}\left( t \right)dt} } \right)^{1/{q_2}}} \leqslant c{\left( {\int_0^\infty {{{\left( {\int_t^\infty {f{{\left( \tau \right)}^{{p_1}}}{v_1}\left( \tau \right)d\tau } } \right)}^{{q_1}/{p_1}}}{u_1}\left( t \right)dt} } \right)^{1/{q_1}}},$$

where p₁, p₂, q₁, q₂ ∈ (0,∞), p₂ ≤ q₂ and u₁, u₂, v₁, v₂ are weights on (0,∞), are obtained. The most innovative part consists of the fact that possibly different parameters p₁ and p₂ and possibly different inner weights v₁ and v₂ are allowed. The proof is based on the combination of duality techniques with estimates of optimal constants of the embeddings between weighted Cesàro and Copson spaces and weighted Lebesgue spaces, which reduce the problem to the solutions of iterated Hardy-type inequalities.

     

On the thermodynamic equivalence of the Dicke maser model and a certain spin system

We prove the thermodynamic equivalence of the Dicke two-level model and a van der Waals spin system. This serves to show that there are cases where the Wang-Hioe procedure and the Power-Zienau transformation may be applied in any order.