Unique positive solutions for boundary value problem of p-Laplacian fractional differential equation with a sign-changed nonlinearity

This paper investigates the existence of a unique positive solution for a class of boundary value problems of p-Laplacian fractional differential equations, where its nonlinearity is signchanged and involves a fractional derivative term, and its boundary involves a nonlinear fractional integral term. By constructing an appropriate auxiliary boundary value problem and applying a generalized fixed point theorem of sum operator and properties of Mittag-Leffler function, some sufficient conditions for the existence of a unique positive solution are presented, and a monotone iterative sequence uniformly converging to the unique solution is constructed. In addition, an example is given to illustrate the main result

Spectrality of Infinite Convolutions in Rd\mathbb{R}^d

In this paper, we study the spectrality of infinite convolutions in $\mathbb{R}^d$, where the spectrality means the corresponding square integrable function space admits a family of exponential functions as an orthonormal basis. Suppose that the infinite convolutions are generated by a sequence of admissible pairs in $\mathbb{R}^d$. We give two sufficient conditions for their spectrality by using the equi-positivity condition and the integral periodic zero set of Fourier transform. By applying these results, we show the spectrality of some specific infinite convolutions in $\mathbb{R}^d$.Comment: 22 pages; update the main theorem

Parental Care System and Brood Size Drive Sex Difference in Reproductive Allocation:An Experimental Study on Burying Beetles

Life-history theory predicts that increased resource allocation in current reproduction comes at the cost of survival and future reproductive fitness. In taxa with biparental care, each parent can adjust investment on current reproduction according to changes in their partner’s effort, but these adjustments may be different for males and females as they may have different reproductive strategies. Numerous theoretical and empirical studies have proposed the mechanism underlying such adjustments. In addition, the value of the brood or litter (brood size) has also been suggested to affect the amount of care through manipulation of brood size. While the two conditions have been studied independently, the impact of their interplay on potential sex-dependent future reproductive performance remains largely unknown. In this study, we simultaneously manipulated both care system (removal of either parent vs. no removal) and brood size in a burying beetle (Nicrophorus vespilloides) to understand their joint effect on reproductive allocation and trade-off between current and future reproduction. Our results show that males compensated for mate loss by significantly increasing the level of care regardless of brood size, while females exhibited such compensation only for small brood size. Additionally, with an increase in allocation to current reproduction, males showed decreased parental investment during the subsequent breeding event as a pair. These findings imply a dual influence of parental care system and brood size on allocation in current reproduction. Moreover, the impact of such adjustments on sex-dependent differences in future reproduction (parental care, larvae number, and average larval mass at dispersal) is also demonstrated. Our findings enhance the understanding of sex roles in parental investment and highlight their importance as drivers of reproductive allocation

Multiple positive solutions for boundary value problems of second order delay differential equations with one-dimensional p-Laplacian

AbstractWe consider the boundary value problems: (ϕp(x′(t)))′+q(t)f(t,x(t),x(t−1),x′(t))=0, ϕp(s)=|s|p−2s, p>1, t∈(0,1), subject to some boundary conditions. By using a generalization of the Leggett–Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions to the above problems

Bubble Flow Analysis of High Speed Cylindrical Roller Bearing under Fluid-Solid Thermal Coupling

Heat generation model of high speed cylindrical roller bearing is constructed by calculating the local friction in the bearing. Bubble flow calculation model of roller bearing considering fluid-solid thermal coupling is constructed based on two-body fluid model and k-ε turbulent model, in which diameter and size of bubbles, breakup, and coalescence model of bubbles are considered. Using dynamic mesh method, a new method for evaluating bearing temperature is set up treating the rolling elements as moving heat sources. Based on these models and finite element method, bubble flow of a high speed roller bearing is studied based on FLUENT software. The numerical study reveals the relationship between velocity of bearing, air volume fraction, and velocity and pressure of oil-air flow. An increase of air content in the oil produces a lower pressure at the bearing outlet while the exit fluid velocity increases. When fluid-solid thermal coupling effect is considered, velocity and pressure at outlet of the bearing both become larger, while temperature of bearing is lower than that without coupling. In comparison, the coupling effects on flow pressure and temperature are obvious. For a given rotating speed, there is an optimal value for air volume fraction, such that temperature rise of the bearing reaches the lowest value. Experiments verify the outcomes of the method presented in this paper

Compromised ATP binding as a mechanism of phosphoinositide modulation of ATP-sensitive K+ channels

AbstractInhibition of ATP-sensitive K+ (KATP) channels by ATP, a process presumably initiated by binding of ATP to the pore-forming subunit, Kir6.2, is reduced in the presence of phosphoinositides (PPIs). Previous studies led to the hypothesis that PPIs compromise ATP binding. Here, this hypothesis was tested using purified Kir6.2. We show that PPIs bind purified Kir6.2 in an isomer-specific manner, that biotinylated ATP analogs photoaffinity label purified Kir6.2, and that this labeling is weakened in the presence of PPIs. Patch-clamp measurements confirmed that these ATP analogs inhibited Kir6.2 channels, and that PPIs decreased the level of inhibition. These results indicate that interaction of PPIs with Kir6.2 impedes ATP-binding activity. The PPI regulation of ATP binding revealed in this study provides a putative molecular mechanism that is potentially pivotal to the nucleotide sensitivity of KATP channels

Deep Convolution and Correlated Manifold Embedded Distribution Alignment for Forest Fire Smoke Prediction

This paper proposes the deep convolution and correlated manifold embedded distribution alignment (DC-CMEDA) model, which is able to realize the transfer learning classification between and among various small datasets, and greatly shorten the training time. First, pre-trained Resnet50 network is used for feature transfer to extract smoke features because of the difficulty in training small dataset of forest fire smoke; second, a correlated manifold embedded distribution alignment (CMEDA) is proposed to register the smoke features in order to align the input feature distributions of the source and target domains; and finally, a trainable network model is constructed. This model is evaluated in the paper based on satellite remote sensing image and video image datasets. Compared with the deep convolutional integrated long short-term memory (DC-ILSTM) network, DC-CMEDA has increased the accuracy of video images by 1.50 %, and the accuracy of satellite remote sensing images by 4.00 %. Compared the CMEDA algorithm with the ILSTM algorithm, the number of iterations of the former has decreased to 10 times or less, and the algorithm complexity of CMEDA is lower than that of ILSTM. DC-CMEDA has a great advantage in terms of convergence speed. The experimental results show that DC-CMEDA can solve the problem of small sample smoke dataset detection and recognition