Asymptotic behavior of bounded solutions for a system of neutral functional differential equations

AbstractConsider the system of neutral functional differential equations{(x1(t)−cx2(t−r))′=−F(x1(t))+G(x2(t−r)),(x2(t)−cx1(t−r))′=−F(x2(t))+G(x1(t−r)), where r>0, c∈[0,1), F, G∈C(R1) and F is strictly increasing on R1. It is shown that if F(x)⩾G(x) for all x∈R1 or F(x)⩽G(x) for all x∈R1, then every bounded solution of such a system tends to an equilibrium. Our results improve and extend some corresponding ones already known

Periodic solutions for nonlinear nth order differential equations with delays

AbstractBy applying the continuation theorem of coincidence degree theory, we establish the existence of 2π-periodic solutions for a class of nonlinear nth order differential equations with delays

Existence and uniqueness of periodic solutions for a kind of Liénard equation with a deviating argument

AbstractIn this work, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for a kind of Liénard equation with a deviating argument of the form x″(t)+f(x(t))x′(t)+g(t,x(t−τ(t)))=p(t)

Positive almost periodicity on SICNNs incorporating mixed delays and D operator

This article involves a kind of shunting inhibitory cellular neural networks incorporating D operator and mixed delays. First of all, we demonstrate that, under appropriate external input conditions, some positive solutions of the addressed system exist globally. Secondly, with the help of the differential inequality techniques and exploiting Lyapunov functional approach, some criteria are established to evidence the globally exponential stability on the positive almost periodic solutions. Eventually, a numerical case is provided to test and verify the correctness and reliability of the proposed findings

Qualitative Theory of Functional Differential and Integral Equations

Functional differential equations arise in many areas of science and technology: whenever a deterministic relationship involving some varying quantities and their rates of change in space and/or time (expressed as derivatives or differences) is known or postulated. This is illustrated in classical mechanics, where the motion of a body is described by its position and velocity as the time varies. In some cases, this differential equation (called an equation of motion) may be solved explicitly. In fact, differential equations play an important role in modelling virtually every physical, technical, biological, ecological, and epidemiological process, from celestial motion, to bridge design, to interactions between neurons, to interaction between species, to spread of diseases with a population, and so forth. Also many fundamental laws of chemistry can be formulated as differential equations and in economy differential equations are used to model the behavior of complex systems. However, the mathematical models can also take different forms depending on the time scale and space structure of the problem; it can be modeled by delay differential equations, difference equations, partial delay differential equations, partial delay difference equations, or the combination of these equations

Large anomalous Hall effect in a hexagonal ferromagnetic Fe5Sn3 single crystal

In this paper, we report an experimental observation of the large anomalous Hall effect (AHE) in a hexagonal ferromagnetic Fe5Sn3 single crystal with current along the b axis and a magnetic field normal to the bc plane. The intrinsic contribution of the anomalous Hall conductance sigma_AH^int was approximately 613 {\Omega}-1 cm-1, which was more than 3 times the maximum value in the frustrated kagome magnet Fe3Sn2 and nearly independent of the temperature over a wide range between 5 and 350 K. The analysis results revealed that the large AHE was dominated by a common, intrinsic term, while the extrinsic contribution, i.e., the skew scattering and side jump, turned out to be small. In addition to the large AHE, it was found the types of majority carriers changed at approximately 275 and 30 K, consistent with the critical temperatures of the spin reorientation. These findings suggest that the hexagonal ferromagnetic Fe5Sn3 single crystal is an excellent candidate to use for the study of the topological features in ferromagnets.Comment: accepted as a rapid communication in Phy. Rev.

Effect of alkaline microwaving pretreatment on anaerobic digestion and biogas production of swine manure

Microwave assisted with alkaline (MW-A) condition was applied in the pretreatment of swine manure, and the effect of the pretreatment on anaerobic treatment and biogas production was evaluated in this study. The two main microwaving (MW) parameters, microwaving power and reaction time, were optimized for the pretreatment. Response surface methodology (RSM) was used to investigate the effect of alkaline microwaving process for manure pretreatment at various values of pH and energy input. Results showed that the manure disintegration degree was maximized of 63.91% at energy input of 54 J/g and pH of 12.0, and variance analysis indicated that pH value played a more important role in the pretreatment than in energy input. Anaerobic digestion results demonstrated that MW-A pretreatment not only significantly increased cumulative biogas production, but also shortened the duration for a stable biogas production rate. Therefore, the alkaline microwaving pretreatment could become an alternative process for effective treatment of swine manure

Occurrence of Camallanus cotti in greatly diverse fish species from Danjiangkou Reservoir in central China

Two thousand four hundred fifty-eight fish comprised of 53 species were captured in the Danjiangkou Reservoir, in the northwestern part of Hubei Province, central China during 2004, to examine Camallanus cotti infections. We found that 19 cypriniform, 3 siluriforme, and 4 perciforme fishes were infected by the nematode. Our study revealed the species, Hemiculter bleekeri bleekeri, Culter oxycephaloide, Pseudolaubuca sinensis, Acanthobrama simony, Mylopharyngodon piceus, Ctenopharyngodon idella, Gnathopogon imberbis, G. argentatus, Saurogobio dabryi, S. dumerili, Gobiobotia ichangensis, Liobagrus marginatoides, and Ctenogobius shennongensis as new hosts of the worm. The number and range of fish host species found in this survey were much greater than any of the previous investigations. The mean prevalence, prevalence, mean abundance, and intensity of infection varied in different fish species, indicating a possible host preference. Moreover, we suggest that this nematode is a native parasite of cypriniform fishes in China, perhaps initially in the reaches of the Yangtze River.Two thousand four hundred fifty-eight fish comprised of 53 species were captured in the Danjiangkou Reservoir, in the northwestern part of Hubei Province, central China during 2004, to examine Camallanus cotti infections. We found that 19 cypriniform, 3 siluriforme, and 4 perciforme fishes were infected by the nematode. Our study revealed the species, Hemiculter bleekeri bleekeri, Culter oxycephaloide, Pseudolaubuca sinensis, Acanthobrama simony, Mylopharyngodon piceus, Ctenopharyngodon idella, Gnathopogon imberbis, G. argentatus, Saurogobio dabryi, S. dumerili, Gobiobotia ichangensis, Liobagrus marginatoides, and Ctenogobius shennongensis as new hosts of the worm. The number and range of fish host species found in this survey were much greater than any of the previous investigations. The mean prevalence, prevalence, mean abundance, and intensity of infection varied in different fish species, indicating a possible host preference. Moreover, we suggest that this nematode is a native parasite of cypriniform fishes in China, perhaps initially in the reaches of the Yangtze River

Involved-field irradiation or elective-nodal irradiation in neoadjuvant chemo-radiotherapy for locally-advanced esophageal cancer: comprehensive analysis for dosimetry, treatment-related complications, impact on lymphocyte, patterns of failure and survival

PurposeTo compare the differences between involved-field irradiation (IFI) and elective nodal irradiation (ENI) in selecting the optimal target area for neoadjuvant chemoradiotherapy (nCRT) in patients with locally advanced esophageal squamous cell carcinoma (LA-ESCC).Materials and methodsWe retrospectively analyzed 267 patients with LA-ESCC, of whom 165 underwent ENI and 102 underwent IFI. Dosimetry, treatment-related complications, pathological responses, recurrence/metastasis patterns, and survival were compared between the two groups.ResultsThe median follow-up duration was 27.9 months. The R0 resection rates in the IFI and ENI groups were 95.1% and 92.7%, respectively (p=0.441), while the pathological complete response (pCR) rates were 42.2% and 34.5%, respectively (p=0.12). The ENI group received higher radiation doses to the heart (HV30:23.9% vs. 18%, p=0.033) and lungs (LV30:7.7% vs. 4.9%, p<0.001) than the IFI group. Consequently, the ENI group showed a higher incidence of grade 2 or higher radiation pneumonitis (30.3% vs. 17.6%, p=0.004) and pericardial effusion (26.7% vs. 11.8%, p=0.021) than the IFI group. Post-operation fistulas were observed in 3 (2.9%) and 17 cases (10.3%) in the IFI and ENI groups, respectively (p=0.026). In the multivariate analysis, smoking, positive lymph node involvement (pN+), and anastomotic fistula were independent predictors of overall survival (OS). The pN+ patients exhibited a greater propensity for recurrence compared to pN- patients, especially in the first year of follow-up (6.67% vs. 0.56%, p=0.003).ConclusionThe ENI group had a higher incidence of radiation-induced adverse events compared to the IFI group, likely due to the higher radiation doses to normal tissues. Considering the similar disease-free survival (DFS) and OS rates in the two groups, IFI may be suitable for nCRT in patients with LA-ESCC, although further prospective studies are warranted