课程文献中心 更多>>

关键词： Differential subordination   exact differential equation   convex functions   best dominant  

摘要： Let h be a non-vanishing convex univalent function and p be an analytic function in D. We consider the differential subordination psi(i)(p(z), zp' (z)) < h(z) with the admissible functions psi(1) := (beta p(z)+gamma)(-alpha) ((beta p(z)+gamma)/beta(1-alpha) + zp' (z)) and psi(2) := 1/root gamma beta arctan (root beta/gamma p(1-alpha) (z)) + (1-alpha/beta p(2(1-alpha))(z)+gamma zp' (z)/p(alpha)(z). The objective of this paper is to find the dominants, preferably the best dominant (say q) of the solution of the above differential subordination satisfying psi(i)(q(z), nzq'(z)) = h(z). Furthermore, we show that psi(i)(q(z), nzq' (z)) = h(z) is an exact differential equation and q is a convex univalent function in D. In addition, we estimate the sharp lower bound of Re p for different choices of h and derive a univalence criterion for functions in H (class of analytic normalized functions) as an application to our results.

关键词： fractional operator with the non-singular kernel   numerical approximation   stability analysis   convergence analysis   tumor model   chaos  

摘要： This manuscript is devoted to describing a novel numerical scheme to solve differential equations of fractional order with a non-singular kernel namely, Caputo-Fabrizio. First, we have transformed the fractional order differential equation to the corresponding integral equation, then the fractional integral equation is approximated by using the Simpson's quadrature 3/8 rule. The stability of the proposed numerical scheme and its convergence is analyzed. Further, a cancer growth Caputo-Fabrizio model is solved using the newly proposed numerical method. Moreover, the numerical results are provided for different values of the fractional-order within some special cases of model parameters.

关键词： power series solution   Riemann-Liouville fractional derivative   symmetry reduction   time-fractional Burgers equations  

摘要： Based on the Lie symmetry method and taking the generalized time-fractional Burgers equations involving the Riemann-Liouville derivative for example, we propose a new similarity transformation which converts the time-fractional Burgers equation into a fractional ordinary differential equation without containing the Erdelyi-Kober fractional differential operator. Such type of reduced equations facilitates us to study the properties as well as construct analytical solutions. Consequently, we obtain an exact solution and a new power series solution of the time-fractional Burgers equation via the reduced equation.

关键词： Integrated circuits   Maximum power point trackers   Regulators   Inverters   Topology   Power demand   Junctions   Differential power processing   integrated circuits   maximum power point tracking   optimizers   photovoltaic power systems  

摘要： This article presents a cell-level differential power processing IC to maximize the power yield under partial shading and mismatch condition in series-connected single junction photovoltaic (PV) cells. A 3-MHz bidirectional buck-boost converter is employed to realize voltage equalization technique forcing the PV cells to constantly operate close to their maximum power points. A novel and simple low-power low-area analog control circuit is proposed to maintain the high system efficiency at low and high levels of mismatch by obviating the need for power hungry blocks such as analog to digital converters, digital to analog converters, op-amps, saw-tooth generator, and regulators. The voltage of adjacent PV cells is used to drive the high-side switches through bootstrap supplies eliminating the need for voltage regulators. The performance of the proposed IC, fabricated in 130 nm CMOS process, is validated through simulation and experimental results. The converter is capable of processing mismatch currents up to 4 A while the control circuitry consumes less than 40 mW and a system efficiency above 95% is achieved.

关键词： Geosynthetics   Confined-reinforced earth   Geogrid length   Differential settlement   Cyclic load  

摘要： Reducing differential settlement between bridges and their embankments caused by an earthquake is necessary to maintain traffic, especially emergency vehicles accessing affected areas. The confined-reinforced earth (CRE) method has been proposed to strengthen the subgrade layer at the bottom of a road pavement and to ultimately reduce road surface unevenness. The method uses granular soil, geogrid layers and confining tie rods. This study presents model experiments designed to investigate the effects of embedded geogrid lengths on CRE behavior under differential settlement and cyclic (vehicle) loads. The CRE was constructed on a fixed plate to simulate a bridge abutment, and on a movable plate to simulate the settlement of an embankment. The results showed that the surface settlement distribution and the maximum surface slope of the CRE decreased with an increase in embedded geogrid length until the geogrids are sufficiently long. Beyond this length value, the deformation only changed slightly. The tensile strain in the geogrids also increased with increased embedded geogrid length under settlement, and the maximum tensile strain increased linearly with increasing settlement. The increment of tensile strain due to the cyclic load was larger for lower geogrid layers than for upper geogrid layers.

关键词： inverse problems   fractional differential equa-tions   fixed point theorems   numerical solutions  

摘要： It is a fundamental problem to determine a starting point in fractional differential equations which reveals the memory length in real life modeling. This paper describes it by an inverse problem. Fixed point theorems such as Krasnoselskii's and Schauder type's and nonlinear alternative for single- valued mappings are presented. Through existence analysis of the inverse problem, the range of the initial value points and the memory length of fractional differential equations are obtained. Finally, three examples are demonstrated to support the theoretical results and numerical solutions are provided.

关键词： Fractional pantograph differential equations   Caputo derivative   Riemann-Liouville fractional integration   Fractional-order Alpert multiwavelets  

摘要： In this article, we develop a new set of functions called fractional-order Alpert multiwavelet functions to obtain the numerical solution of fractional pantograph differential equations (FPDEs). The fractional derivative of Caputo type is considered. Here we construct the Riemann-Liouville fractional operational matrix of integration (Riemann-Liouville FOMI) using the fractional-order Alpert multiwavelet functions. The most important feature behind the scheme using this technique is that the pantograph equation reduces to a system of linear or nonlinear algebraic equations. We perform the error analysis for the proposed technique. Illustrative examples are examined to demonstrate the important features of the new method. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Clonal propagation   Explant   Galactans   Gracilaria salicornia   Rhodophyta   Seaweed cultivation  

摘要： The cultivation of the red algal genus Gracilaria is successful and accounts for a ca. 14% global share in farmed seaweed. Gracilaria salicornia has been used as feedstock for commercial production of galactans and plant bio-stimulant. The un-abated demand of raw material during last 5 years by domestic industries has fueled ca. 757% increase in biomass exploitation of this resource. As the farming methods heavily rely on clonal propagation of apical explants, it is imperative to check the viability of sub-apical and basal explant to increase the number of clones needed for farming operation. Here we ascertained the efficacy of two commercially available seaweed-derived plant bio-stimulants namely AMPEP and Sagarika under various concentrations and treatment times. One hundred percent survival was recorded with 0.1% AMPEP and 15-, 30-min exposure, 10% AMPEP and 15-, 30-, and 60-min exposure, while with Sagarika, it was observed in 0.01% and 60 min, 0.001% and 15, 30, and 60 min and 0.1% and 30, 60 min treatments of apical explants. The highest regeneration of 80.42 +/- 12.01% was observed in apical explants at 1% AMPEP and 15-min exposure and the highest growth of 3.66 +/- 0.32% day(-1) was found in apical explants with 1% AMPEP and 60-min exposure. The proximate composition of apical explants treated with 0.1 g L-1 AMPEP and 60-min exposure was 25.10 +/- 3.9% carbohydrate, 13.59 +/- 4.8% protein, and 4.6 +/- 1.1% lipid, while total phenol and free radical activity were 13.11 +/- 1.65% and 37.93 +/- 1.9%, respectively. Although apical explants clearly showed superiority for clonal propagation, use of sub-apical and basal explants can also be considered for commercial seedlings production in case of paucity of material to continue the operation. The sustainable production of seedlings would help in negating consequences of natural harvesting while ensuring continuous feedstock supply through cultivation.

关键词： Valves   Bending   Transducers   Regulation   Force   Ceramics   Time factors   Bending transducer   high differential pressure   piezoelectric valve   proportional control  

摘要： In this article, a piezoelectric active proportional regulation valve with high differential pressure is proposed based on a bending transducer. The output flowrate of the valve can be accurately controlled by a bending transducer. The configuration design and driving principle of the valve are presented and analyzed. The static analyses are performed to determine the structural parameters of the valve and deduce its transient overflow gap. On this basis, the overall flowrate model of the valve is established using the theory of circumferential flow and extended Bernoulli equation. The effects of differential pressure and driving voltage on output flowrate are clarified. A prototype of the valve is manufactured and the experimental setup is also established to evaluate the performances of the valve. The results indicate that the proportional regulation of the valve can be achieved by changing the driving voltage;the valve displacement and response time under no liquid-loading condition are 16.16 mu m and 340 mu s at the voltage of 300 Vp-p;the maximum output flowrate is 286.3 mL/min under the differential pressure of 344.75 kPa, and the leakage level is 0.11%;the maximum cut-off pressure of 275.8 kPa can be realized;the corresponding input power is 185 mW.

关键词： ADHD   aggression   DMDD   irritability   latent variable analysis  

摘要： Objective: Irritability is a multifaceted construct in pediatric psychopathology. It has been conceptualized as having a phasic dimension and a tonic dimension. Disruptive mood dysregulation disorder is defined by the presence of both dimensions. Severe irritability, or disruptive mood dysregulation disorder, is highly comorbid with attention-deficit/hyperactivity disorder (ADHD). However, it is unknown whether the presence of ADHD modulates the expression of phasic and tonic irritability. Method: A data-driven, latent variable approach was used to examine irritability and ADHD symptoms in a transdiagnostic pediatric sample (N 1/4 489) with primary disruptive mood dysregulation disorder, ADHD, subclinical irritability symptoms, or no diagnosis. Using latent profile analyses, we identified 4 classes: high levels of both irritability and ADHD symptoms, high levels of irritability and moderate levels of ADHD symptoms, moderate levels of irritability and high levels of ADHD symptoms, and low levels of both irritability and ADHD symptoms. Confirmatory factor analysis operationalized phasic irritability and tonic irritability. Results: As expected, the 2 latent classes characterized by high overall irritability exhibited the highest levels of both phasic and tonic irritability. However, between these 2 high irritability classes, highly comorbid ADHD symptoms were associated with significantly greater phasic irritability than were moderately comorbid ADHD symptoms. In contrast, the 2 high irritability groups did not differ on levels of tonic irritability. Conclusion: These findings suggest that phasic, but not tonic, irritability has a significant association with ADHD symptoms and that phasic and tonic might be distinct, though highly related, irritability dimensions. Future research should investigate potential mechanisms underlying this dif-ferential association.