Fractional Hamiltonian systems with positive semi-definite matrix

We study the existence of solutions for the following fractional Hamiltonian systems $$ \left\{ \begin{array}{ll} - _tD^{\alpha}_{\infty}(_{-\infty}D^{\alpha}_{t}u(t))-\lambda L(t)u(t)+\nabla W(t,u(t))=0,\\[0.1cm] u\in H^{\alpha}(\mathbb{R},\mathbb{R}^n), \end{array} \right. ~~~~~~~~~~~~~~~~~(FHS)_\lambda $$ where $\alpha\in (1/2,1)$, $t\in \mathbb{R}$, $u\in \mathbb{R}^n$, $\lambda>0$ is a parameter, $L\in C(\mathbb{R},\mathbb{R}^{n^2})$ is a symmetric matrix, $W\in C^1(\mathbb{R} \times \mathbb{R}^n,\mathbb{R})$. Assuming that $L(t)$ is a positive semi-definite symmetric matrix, that is, $L(t)\equiv 0$ is allowed to occur in some finite interval $T$ of $\mathbb{R}$, $W(t,u)$ satisfies some superquadratic conditions weaker than Ambrosetti-Rabinowitz condition, we show that (FHS)$_\lambda$ has a solution which vanishes on $\mathbb{R}\setminus T$ as $\lambda \to \infty$, and converges to some $\tilde{u}\in H^{\alpha}(\R, \R^n)$. Here, $\tilde{u}\in E_{0}^{\alpha}$ is a solution of the Dirichlet BVP for fractional systems on the finite interval $T$. Our results are new and improve recent results in the literature even in the case $\alpha =1$.     

Persistent Organic High‐Spin Trinitrenes

The septet ground state trinitrenes 1,3,5‐trichloro‐2,4,6‐trinitrenobenzene and 1,3,5‐tribromo‐2,4,6‐trinitrenobenzene were isolated in inert (Ar, Ne, and Xe) as well as reactive matrices (H₂, O₂, and H₂O) at cryogenic temperatures. These trinitrenes were obtained in high yields by UV photolysis of the corresponding triazides and characterized by IR and UV/Vis spectroscopy. The trinitrenes, despite bearing six unpaired electrons, are remarkably unreactive towards molecular oxygen and hydrogen and are persistent in water ice up to 160 K where the water matrix starts to sublime off.     

Bragg grating writing through the polyimide coating of high NA optical fibres with femtosecond IR radiation

Bragg gratings are written with ultrafast 800 nm radiation and a phase mask through the polyimide polymer coatings of commercially available high NA fibres that are both unloaded and loaded with high pressure hydrogen gas. For polyimide coated fibres with very high germanium core concentrations, index modulations greater than 1 × 10⁻⁴ are induced. Stable core index modulations 60% of their original value were present after 115 h at 500 °C.     

Observations of an ion-driven instability in non-neutral plasmas confined on magnetic surfaces

The first detailed experimental study of an instability driven by the presence of a finite ion fraction in an electron-rich non-neutral plasma confined on magnetic surfaces is presented. The instability has a poloidal mode number m=1, implying that the parallel force balance of the electron fluid is broken and that the instability involves rotation of the entire plasma, equivalent to ion-resonant instabilities in Penning traps and toroidal field traps. The mode appears when the ion density exceeds approximately 10% of the electron density. The measured frequency decreases with increasing magnetic field strength, and increases with increasing radial electric field, showing that the instability is linked to the E x B flow of the electron plasma. The frequency does not, however, scale exactly with E/B, and it depends on the ion species that is introduced, implying that the instability consists of interacting perturbations of ions and electrons.     

Polaritonic coupling and spin dynamics in GaAs microcavities

We have used time-resolved photoluminescence spectroscopy to study the light emission dynamics in a semiconductor microcavity as a function of excitation density and exciton-cavity detuning. We paid special attention to polariton spin relaxation by using circularly polarized excitation. We have found a striking behavior of the photoluminescence degree of polarization, which reaches its maximum value at a finite time. As the excitation density is increased and the system enters the stimulated emission regime, this maximum is followed by a negative dip, whose depth strongly depends on exciton-cavity detuning.     

Complex Powers of the Neumann Laplacian in Lipschitz Domains

Let L^q_r(Ω) be the usual scale of Sobolev spaces and let Δ_N be the Neumann Laplacian in an arbitrary Lipschitz domain Ω. We present an interpolation based approach to the following question: for what range of indices does map isomorphically onto L^q_r(Ω)/ℝ?     

Electrophysiological Responses of Bactrocera kraussi (Hardy) (Tephritidae) to Rectal Gland Secretions and Headspace Volatiles Emitted by Conspecific Males and Females

Pheromones are biologically important in fruit fly mating systems, and also have potential applications as attractants or mating disrupters for pest management. Bactrocera kraussi (Hardy) (Diptera: Tephritidae) is a polyphagous pest fruit fly for which the chemical profile of rectal glands is available for males but not for females. There have been no studies of the volatile emissions of either sex or of electrophysiological responses to these compounds. The present study (i) establishes the chemical profiles of rectal gland contents and volatiles emitted by both sexes of B. kraussi by gas chromatography–mass spectrometry (GC–MS) and (ii) evaluates the detection of the identified compounds by gas chromatography–electroantennogram detection (GC–EAD) and –electropalpogram detection (GC–EPD). Sixteen compounds are identified in the rectal glands of male B. kraussi and 29 compounds are identified in the rectal glands of females. Of these compounds, 5 were detected in the headspace of males and 13 were detected in the headspace of females. GC–EPD assays recorded strong signals in both sexes against (E,E)-2,8-dimethyl-1,7-dioxaspiro[5.5]undecane, 2-ethyl-7-mehtyl-1,6-dioxaspiro[4.5]decane isomer 2, (E,Z)/(Z,E)-2,8-dimethyl-1,7-dioxaspiro[5.5]undecane, and (Z,Z)-2,8-dimethyl-1,7-dioxaspiro[5.5]undecane. Male antennae responded to (E,E)-2,8-dimethyl-1,7-dioxaspiro[5.5]undecane, 2-methyl-6-pentyl-3,4-dihydro-2H-pyran, 6-hexyl-2-methyl-3,4-dihydro-2H-pyran, 6-oxononan-1-ol, ethyl dodecanoate, ethyl tetradecanoate and ethyl (Z)-hexadec-9-enoate, whereas female antennae responded to (E,E)-2,8-dimethyl-1,7-dioxaspiro[5.5]undecane and 2-methyl-6-pentyl-3,4-dihydro-2H-pyran only. These compounds are candidates as pheromones mediating sexual interactions in B. kraussi.     

3,5-Bis(ferrocenylmethylene)-1-methyl-4-methylenepiperidine. Synthesis and some chemical properties

3,5-Bis(ferrocenylmethylene)-1-methyl-4-methylenepiperidine, a diferrocenyltriene with a fixeds-cisoid conformation of the exocyclic double bonds, was synthesized. On heating, this compound cyclodimerizes according to the [4+2]-cycloaddition scheme; it forms Diels-Alder adducts with azodicarboxylic and maleic acidN-phenylimides. The compound easily cyclodimerizes in the presence of acids by a proton cyclodimerization mechanism to give a spiro cyclodimer. The triene also adds a 3,5-bis(ferrocenylmethylene)-1,4-dimethyl-1-azonia-4-cyclohexyl salt to the terminal methylene group yielding linear and cyclic addition products. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 511–516, March, 2000.