This paper is concerned with higher odd-order boundary value problems. We first prove that the operators associated with the problems are symmetric and the corresponding eigenvalues are real, and we give the resolvent operators related to the differential operators. Then we obtain that the eigenvalues are not only continuously but also smoothly dependent on the parameters of the problem. Moreover, the differential expressions of the eigenvalues as regards these parameters are given. In particular, we give the Frechet derivatives of the eigenvalues for the leading coefficient function q0 and coefficient functions q1,⋯,qn.

With the swift development of express delivery industry, the increasingly attention has been shifted to express delivery mechanism design. Generally, the revenue of the courier is the difference between the users' express fee and the courier's pickup cost. In order to improve the revenue of courier without increasing the user's express fee, this paper presents a low-cost package pickup covering system to find an optimal Hamiltonian pickup tour for the courier over a subset of packages, where packages who are not on the tour should be covered exactly by one package on the tour. A billing rule discounting the express fee to incentivize users to deliver their packages is also proposed. We formulate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Low-cost Package Pickup Covering (LPPC)</i> problem to maximize the revenue of the courier. Considering the complexity of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LPPC</i> , we propose a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Low-cost Package Pickup Covering Mechanism (LPPCM)</i> to solve the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LPPC</i> problem including problem transformation, hardness analyzing, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Attention Model based on Encoder-Decoder Architecture (AMEDA)</i> model design and model training. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AMEDA</i> is trained by a deep reinforcement learning algorithm in an unsupervised manner and it can directly output the solution based on the given instances. Through extensive simulations, we demonstrate that the average revenue of courier for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AMEDA</i> is at least 10.1% higher than the traditional heuristic local search and is 18.5% lower than the optimal solution on average. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AMEDA</i> provides a desired trade-off between the execution time and solution quality, which is well suited for the large-scale tasks which require quick decisions.

AbstractThis study explores the role of internal climate system forcing in the relationship between dust and tropical cyclones (TCs). Here internal climate system forcing includes the Atlantic Multidecadal Oscillation (AMO), Atlantic Meridional Mode (AMM), Sahel rainfall, North Atlantic Oscillation (NAO), and El Niño–Southern Oscillation (ENSO). The dust‐TC relationship is evaluated through statistical analyses of 42‐year (1980–2021) reanalysis and observation data sets for TCs and the Saharan dust plume over the North Atlantic. In August, the negative correlation between dust and TCs in the region east of the Florida Peninsula and north of the Caribbean Sea is inhibited by AMO, AMM, and ENSO and promoted by NAO. In September, the positive correlation between dust and TCs in the eastern US and its adjacent ocean is inhibited by Sahel rainfall and promoted by AMO, AMM, and ENSO. In October, the positive correlation between dust and TCs in the southeastern US is promoted by Sahel rainfall and inhibited by AMO, AMM, and ENSO. The leading climate mode influence on the dust‐TC relationship comes from AMO in August and September, and ENSO in October. The dust‐TC relationship in September and October indicates an increase in TC landfalls over the continental US accompanied by a strengthened Saharan dust plume, which further affects the hydrology of the continental US on an interdecadal timescale by reducing land moisture in September and increasing it in October, as determined by the location of TC landfalls, topography, and the impact of climate mode.

ABSTRACT This paper investigates the impact of different positions and angles of secondary fuel injector on the flow field characteristics, fuel-air mixing, and combustion performance of a miniature trapped vortex combustor (TVC), utilizing a combination of experimental and numerical methods. The numerical computation results show a good agreement with experimental data. Detailed computational findings highlight the significant influence of varying injector positions and angles on miniature TVC performance. Adjusting the positions and angles of secondary fuel injectors lead to notable outcomes: Adjusting the positions and angles of secondary fuel injectors leads to notable outcomes: achieving a more stoichiometric mixture within the cavity, extending the region of intense combustion, and increasing combustion efficiency by up to 3.4%. These adjustments are conductive to enhancing the overall performance of a miniature trapped vortex combustor.

This paper introduces a numerical approach for the fractional-order Rössler chaotic systems and gives error analysis. The effectiveness of the present method is determined by comparing the numerical results of the high-precision difference scheme and predictor-correctors scheme. Some complex dynamical behaviors for the fractional-order Rössler chaotic systems are shown.

In the presented work, vibrational behavior related to a curved nanopipe which is under supersonic airflow and conveying fluid flow, is examined. To model the size-dependent nanopipe, the Quasi-2D hybrid type of nonlocal strain gradient theory (QHNSGT) is presented. Formulations are obtained by means of Hamilton’s principle for bi-directional functionally graded (Bi-FG) nanopipe. Also, formulations are solved by means of the generalized differential quadrature method (GDQM). By taking into account that the fluid flow is infinite, incompressible, uniform flow, Newtonian, laminar, as well, as viscous, and with the help of the Navier-Stokes equation, the fluid-structure interaction is obtained. A quasi-2D hybrid type of higher-order shear deformation theory is employed to introduce the displacement fields. The verification section shows that the results of this paper are very near to the results of the published article in the literature. One of the important findings of the current research is critical values of the Mach number could have increased with the aid of increasing the rigidity of edges and decreasing fluid flow velocity. Another marvelous output is that opening angle and airflow stability have an indirect relation, and increasing the opening angle provides an expansion in the unstable area.