On the Upper Bound of Eigenvalues for Elliptic Equations with Higher Orders

AbstractLet Ω be a bounded domain in Rm with piecewise smooth boundary. We consider the upper bound of the (n+1)th eigenvalue λn+1 for the two problems [formula] and [formula] where l and r are positive integers with l>r, v is the unit outward normal to ∂Ω, and P(t)=al−rtl+al−r−1tl−1+ . . . +a1tr+1 with the constant coefficients al−r=1, ai≥0 for i=1, 2,..., l−r−1. The bounds of λn+1 are expressed in terms of the preceding eigenvalues. This generalizes the inequalities obtained by Payne, Polya, Weinberger, Protter, Hile, and Yeh

Periodic solutions of a single species discrete population model with periodic harvest/stock

AbstractWe discuss a discrete population model describing single species growth with periodic harvest/stock. The theory of coincidence degree is applied to show that the model equation admits two periodic solutions. Under minor technical assumptions, we show that one of these two periodic solutions is positive and attracts almost all positive solutions

Bounds of Efficiency at Maximum Power for Normal-, Sub- and Super-Dissipative Carnot-Like Heat Engines

The Carnot-like heat engines are classified into three types (normal-, sub- and super-dissipative) according to relations between the minimum irreversible entropy production in the "isothermal" processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between $\eta_C/2$ and $\eta_C/(2-\eta_C)$, $\eta_C /2$ and $\eta_C$, 0 and $\eta_C/(2-\eta_C)$, respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Lett. 98, 40001 (2012)] although the dissipative engines and the irreversible ones are inequivalent to each other.Comment: 1 figur

Unraveling the Rich Fragmentation Dynamics Associated with S-H Bond Fission Following Photoexcitation of H ₂S at Wavelengths ∼129.1 nm

H2S is being detected in the atmospheres of ever more interstellar bodies, and photolysis is an important mechanism by which it is processed. Here, we report H Rydberg atom time-of-flight measurements following the excitation of H2S molecules to selected rotational (JKaKc′) levels of the 1B1 Rydberg state associated with the strong absorption feature at wavelengths of λ ∼ 129.1 nm. Analysis of the total kinetic energy release spectra derived from these data reveals that all levels predissociate to yield H atoms in conjunction with both SH(A) and SH(X) partners and that the primary SH(A)/SH(X) product branching ratio increases steeply with ⟨Jb2⟩, the square of the rotational angular momentum about the b-inertial axis in the excited state. These products arise via competing homogeneous (vibronic) and heterogeneous (Coriolis-induced) predissociation pathways that involve coupling to dissociative potential energy surfaces (PES(s)) of, respectively, 1A″ and 1A′ symmetries. The present data also show H + SH(A) product formation when exciting the JKaKc′ = 000 and 111 levels, for which ⟨Jb2⟩ = 0 and Coriolis coupling to the 1A′ PES(s) is symmetry forbidden, implying the operation of another, hitherto unrecognized, route to forming H + SH(A) products following excitation of H2S at energies above ∼9 eV. These data can be expected to stimulate future ab initio molecular dynamic studies that test, refine, and define the currently inferred predissociation pathways available to photoexcited H2S molecules

A dementia classification framework using frequency and time-frequency features based on EEG signals.

Alzheimer's Disease (AD) accounts for 60-70% of all dementia cases, and clinical diagnosis at its early stage is extremely difficult. As several new drugs aiming to modify disease progression or alleviate symptoms are being developed, to assess their efficacy, novel robust biomarkers of brain function are urgently required. This study aims to explore a routine to gain such biomarkers using the quantitative analysis of Electroencephalography (QEEG). This paper proposes a supervised classification framework which uses EEG signals to classify healthy controls (HC) and AD participants. The framework consists of data augmentation, feature extraction, K-Nearest Neighbour (KNN) classification, quantitative evaluation and topographic visualisation. Considering the human brain either as a stationary or a dynamical system, both frequency-based and time-frequency-based features were tested in 40 participants. Results: a) The proposed method can achieve up to 99% classification accuracy on short (4s) eyes open EEG epochs, with the KNN algorithm that has best performance when compared to alternative machine learning approaches; b) The features extracted using the wavelet transform produced better classification performance in comparison to the features based on FFT; c) In the spatial domain, the temporal and parietal areas offer the best distinction between healthy controls and AD. The proposed framework can effectively classify HC and AD participants with high accuracy, meanwhile offering identification and localisation of significant QEEG features. These important findings and the proposed classification framework could be used for the development of a biomarker for the diagnosis and monitoring of disease progression in AD

Investigation of optimal Split ratio for high-speed permanent-magnet brushless machines

The split ratio, i.e., the ratio of rotor outer diameter to stator outer diameter, is one of the most vital design parameters for permanent-magnet (PM) machines due to its significant impact on the machine torque or power density. However, it has been optimized analytically in the existing papers with due account only for the stator copper loss, which is reasonable for low-to-medium speed PM machines. For high-speed PM machines (HSPMMs), the negligence of stator iron loss and the mechanical stress on the rotor will lead to a deviation of optimal split ratio and actual torque capability. In this paper, the optimal split ratio of HSPMM is investigated analytically with the consideration of stator iron loss as well as the mechanical stress on the rotor. The influence of air-gap length and rotor pole pairs on the optimal split ratio is elaborated. Both the analytical and finite-element analysis reveal that the optimal split ratio for HSPMM will be significantly reduced, when stator iron loss and mechanical constraints are taken into account

Modulation instability induced by cross-phase modulation in a dual-wavelength dispersion-managed soliton fiber ring laser

We report on the observation of modulation instability induced by cross-phase modulation in a dual-wavelength operation dispersion-managed soliton fiber ring laser with net negative cavity dispersion. The passively mode-locked operation is achieved by using nonlinear polarization rotation technique. A new type of dual-wavelength operation, where one is femtosecond pulse and the other is picosecond pulse operation, is obtained by properly rotating the polarization controllers. When the dual-wavelength pulses are simultaneously circulating in the laser ring cavity, a series of stable modulation sidebands appears in the picosecond pulse spectrum at longer wavelength with lower peak power due to modulation instability induced by cross-phase modulation between the two lasing wavelengths. Moreover, the intensities and wavelength shifts of the modulation sidebands can be tuned by varying the power of the femtosecond pulse or the lasing central wavelengths of the dual-wavelength pulses. The theoretical analysis of the modulation instability induced by cross-phase modulation in our fiber laser is also presented.Comment: 26 pages, 10 figure

Gravity on codimension 2 brane worlds

We compute the matching conditions for a general thick codimension 2 brane, a necessary previous step towards the investigation of gravitational phenomena in codimension 2 braneworlds. We show that, provided the brane is weakly curved, they are specified by the integral in the extra dimensions of the brane energy-momentum, independently of its detailed internal structure. These general matching conditions can then be used as boundary conditions for the bulk solution. By evaluating Einstein equations at the brane boundary we are able to write an evolution equation for the induced metric on the brane depending only on physical brane parameters and the bulk energy-momentum tensor. We particularise to a cosmological metric and show that a realistic cosmology can be obtained in the simplest case of having just a non-zero cosmological constant in the bulk. We point out several parallelisms between this case and the codimension 1 brane worlds in an AdS space.Comment: 24 page