Nonexistence of eventually positive solutions of a difference inequality with multiple and variable delays and coefficients

AbstractIn this paper, we consider the nonexistence of eventually positive solutions of the difference inequality ϰn+1 − ϰn + ∑i=1mpi(n)ϰn−ki(n) ≤ 0.Let m be a positive integer. Then for each positive integer i: 1 ≤ i ≤ m, {ki(n)}∞n=0 and {pi(n)}∞n=0 are a sequence of positive integers and a sequence of nonnegative real numbers, respectively. A sufficient condition guaranteeing the nonexistence of eventually positive solutions is obtained with the help of a new method. As an application of the main result, a conjecture is proved

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

Influences of Y Addition on Mechanical Properties and Oxidation Resistance of CrN Coating

AbstractCr1-xYxN coatings were fabricated by reactive co-sputtering deposition and the Y content was changed by varying the Y target power. The influence of varying amounts of Y addition on the mechanical properties and oxidation resistance of CrN coatings has been studied. The results reveal that Y ions substitute Cr ions in Cr-N lattice forming the solid solution Cr1-xYxN coatings. Y doping has a beneficial effect on the improvements of hardness and adhesion of the coatings. After the oxidation in air at 850°C for 2h, The CrN coating with 1.2 at. % Y addition exhibits superior oxidation resistance than Y-free CrN coating, while over doping of Y produces detrimental effects on oxidation resistance of the coatings

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

Experimental and Numerical Analysis of Normal and Lateral High-Velocity Impacts on Carbon Fiber-Reinforced Polymer Laminates

This paper examines the effects of normal and lateral high-speed impacts on carbon fiber-reinforced polymer laminates. Experimental tests were conducted at varying velocities (120–200 m/s), and the differing damage modes between normal and lateral impacts were analyzed. Dynamic finite element analysis was performed to simulate the damage process using the finite element software ABAQUS. The simulation shows a good correlation with the experimental results

Measuring the efficiency and productivity of U.K. insurance market

The U.K. insurance industry has a dominant international presence, suggesting strong competitiveness and performance. Yet, its efficiency and productivity has rarely being investigated. The purpose of this paper is to provide an overview of insurers' performance in the U.K. insurance market from 1996 to 2017, using stochastic frontier analysis to measure efficiency scores and productivity at the firm level. Results show the U.K. insurance industry could improve by about 40% in terms of cost efficiency and by 70% in terms of profit efficiency. In addition, our model reveals a higher cost efficiency score compared to profit efficiency, implying that there are higher inefficiencies on the income side of the insurance industry as measured by our profit function. In terms of total factor productivity (TFP) growth, we report a steady decline over time while on average is negative. By decomposing TFP growth into its underlying components, we reveal that the reported negative trend in TFP growth over time has mainly been driven by the enhanced competition that resulted in a drop in markup, while the scale and cost efficiency has also driven TFP growth down. However, from a positive point of view, we report evidence of both β-convergence and σ-convergence in cost and profit efficiency

Any-degrees-of-freedom (anyDOF) registration for the characterization of freeform surfaces

This paper presents an any-degrees-of-freedom (anyDOF) registration method for the characterization of freeform surfaces. The method attempts to fill the research gap regarding traditional surface registration methods which are normally dedicated to solving the global optimization problem with all DOF but they lack flexibility. The proposed anyDOF method is capable of registering surfaces with any specified combination of DOF. This is particularly useful when some of the DOF are known to be unchanged according to the a priori knowledge. The anyDOF surface registration method is regarded as a typical optimization problem of finding the minimum distance from target surface to the reference surface, with constraints of the unwanted DOF. The problem is solved by the Levenberg-Marquardt method. Simulated experiments for a two-dimensional (2D) profile and a three-dimensional (3D) surface were undertaken, together with three measurement experiments including a fluid-jet polished surface, a bonnet polished surface and a diamond machined freeform surface. Experimental results show that the anyDOF registration method is highly flexible in the characterization of freeform surfaces

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

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

Zircon records of Miocene ultrapotassic rocks from southern Lhasa subterrane, Tiben Plateau

Zircons entrained in mantle-derived magmas offer a prime opportunity to reveal cryptic magmatic episodes in the deep crust. We have investigated zircons from mantle-derived ultrapotassic veins in the Xuena area, southern Lhasa subterrane. Zircons in the Xuena ultrapotassic rocks reveal four major magmatic pulses around <100Ma, 300 ~ 400Ma, 450 ~ 500Ma, and 700 ~ 850Ma. The high U / Yb ratios and low Y contents of these zircons demonstrate their continental origin. Cenozoic-Mesozoic and Late Paleozoic magmatism have been widely identified from the southern Lhasa subterrane, suggesting the contribution from overlying juvenile crust. But similar Proterozoic-Early Paleozoic age distributions (450 ~ 500Ma and 700 ~ 850Ma) between these zircon xenocrysts and those dating records in the Himalayan orogenic belt corroborate the input from underthrusted Indian continental crust. Furthermore, the Increasing (Dy / Yb) N ratio since ~ 60 Ma zircon and Rapid Decreasing epsilon Hf ( t ) values, from + 10 ~ + 5 to -10 ~ -25, are Interpreted to reflect Significant and progressive Crustal Thickening in Response to India-Asia convergence and the contribution from subducted Indian continental crust to postcollisional magmatism in the southern Lhasa sub-terrane