UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE NONLINEARITIES

This article deals with a nonlocal heat system subject to null Dirichlet bound- ary conditions, where the coupling nonlocal sources consist of mixed type asymmetric non- linearities. We at first give the criterion for simultaneous blow-up of solutions, and then establish the uniform blow-up profiles of solutions near the blow-up time. It is observed that not only the simultaneous blow-up rates of the two components u and v are asymmet- ric, but also the blow-up rates of the same component u （or v） may be in different levels under different dominations.

The Marginal Rao-Blackwellized Particle Filter for Mixed Linear/Nonlinear State Space Models

In this paper, the marginal Rao-Blackwellized particle filter （MRBPF）, which fuses the Rao-Blackwellized particle filter （RBPF） algorithm and the marginal particle filter （MPF） algorithm, is presented. The state space is divided into linear and non-linear parts, which can be estimated separately by the MPF and the optional Kalman filter. Through simulation in the terrain aided navigation （TAN） domain, it is demonstrated that, compared with the RBPF, the root mean square errors （RMSE） and the error variance of the nonlinear state estimations by the proposed MRBPF are respectively reduced by 29% and 96%, while the unique particle count is increased by 80%. It is also found that the MRBPF has better convergence properties, and analysis has shown that the existing RBPF is nothing more than a special case of the MRBPF.

Effectiveness of Darcy-Forchheimer and nonlinear mixed convection aspects in stratified Maxwell nanomaterial flow induced by convectively heated surface

The effect of nonlinear mixed convection in stretched flows of rate-type nonNewtonian materials is described. The formulation is based upon the Maxwell liquid which elaborates thermal relation time characteristics. Nanofluid properties are studied considering thermophoresis and Brownian movement. Thermal radiation, double stratification, convective conditions, and heat generation are incorporated in energy and nanoparticle concentration expressions. A boundary-layer concept is implemented for the simplification of mathematical expressions. The modeled nonlinear problems are computed with an optimal homotopy scheme. Moreover, the Nusselt and Sherwood numbers as well as the velocity, nanoparticle concentration, and temperature are emphasized. The results show opposite impacts of the Deborah number and the porosity factor on the velocity distribution.

OBLIQUE DERIVATIVE PROBLEMS FOR SECOND ORDER NONLINEAR MIXED EQUATIONS WITH DEGENERATE LINE

The present article deals with oblique derivative problems for some nonlinear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for the equations is given; next, the representation and estimates of solutions for the above problems are obtained; finally, the existence of solutions for the problems is proved by the successive iteration and the compactness principle of solutions of the problems. In this article, the author uses the complex method, namely, the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used.

THE MIXED PROBLEM FOR A CLASS OF NONLINEAR SYMMETRIC HYPERBOLIC SYSTEMS WITH DISCONTINUOUS DATA

This paper studies the nonlinear mixed problem for a class of symmetric hyperbolic systems with the boundary condition satisfying the dissipative condition about discontinuous data in higher dimension spaces, establishes the local existence theorem by using the method of a prior estimates, and obtains the structure of singularities of the solutions of such problems.

PERIODIC BOUNDARY VALUE PROBLEMS FOR NONLINEAR IMPULSIVEINTEGRODIFFERENTIAL EQUATIONS OF MIXED TYPE IN BANACH SPACES

In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.

ALGORITHM OF SOLUTIONS FOR MIXEDNONLINEAR VARIATIONAL-LIKE INEQUALITIES IN REFLEXIVE BANACH SPACE

In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, rite author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.

Responses of River Runoff to Climate Change Based on Nonlinear Mixed Regression Model in Chaohe River Basin of Hebei Province, China

Taking the nonlinear nature of runoff system into account,and combining auto-regression method and multi-regression method,a Nonlinear Mixed Regression Model (NMR) was established to analyze the impact of temperature and precipitation changes on annual river runoff process. The model was calibrated and verified by using BP neural network with observed meteorological and runoff data from Daiying Hydrological Station in the Chaohe River of Hebei Province in 1956–2000. Compared with auto-regression model,linear multi-regression model and linear mixed regression model,NMR can improve forecasting precision remarkably. Therefore,the simulation of climate change scenarios was carried out by NMR. The results show that the nonlinear mixed regression model can simulate annual river runoff well.

APPROXIMATE SOLUTION TO A CLASS OF MULTIVALUED NONLINEAR MIXED VARIATIONAL INCLUSIONS

Concerned with the existence and convergence properties of approximate solution to multivalued nonlinear mixed variational inclusion problem in a Hilbert space, we established the equivalence between the variational inclusion and the general resolvent equations, obtained three iterative algorithms, provided the convergence analysis of the algorithms. The results obtained improve and generalize a number of resent results.

Darcy-Forchheimer flow with nonlinear mixed convection

An analysis of the mixed convective flow of viscous fluids induced by a nonlinear inclined stretching surface is addressed.Heat and mass transfer phenomena are analyzed with additional effects of heat generation/absorption and activation energy,respectively.The nonlinear Darcy-Forchheimer relation is deliberated.The dimensionless problem is obtained through appropriate transformations.Convergent series solutions are obtained by utilizing an optimal homotopic analysis method(OHAM).Graphs depicting the consequence of influential variables on physical quantities are presented.Enhancement in the velocity is observed through the local mixed convection parameter while an opposite trend of the concentration field is noted for the chemical reaction rate parameter.

A NONLINEAR GALERKIN MIXED ELEMENT METHOD AND A POSTERIORI ERROR ESTIMATOR FOR THE STATIONARY NAVIER-STOKES EQUATIONS

A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution are first discussed, and then a posteriori error estimator based on the NGME method is derived.

A NONLINEAR GALERKIN/PETROV-LEAST SQUARES MIXED ELEMENT METHOD FOR THE STATIONARY NAVIER-STOKES EQUATIONS

A nonlinear Galerkin/Petrov-least squares mixed element (NGPLSME) method for the stationary Navier-Stokes equations is presented and analyzed. The scheme is that Petrov-least squares forms of residuals are added to the nonlinear Galerkin mixed element method so that it is stable for any combination of discrete velocity and pressure spaces without requiring the Babu*lka-Brezzi stability condition. The existence, uniqueness and convergence (at optimal rate) of the NGPLSME solution is proved in the case of sufficient viscosity (or small data).

A NONLINEAR LAVRENTIEV-BITSADZE MIXED TYPE EQUATION

In this paper the Tricomi problem for a nonlinear mixed type equation is studied. The coefficients of the mixed type equation are discontinuous on the line, where the equation changes its type. The existence of solution to this problem is proved. The method developed in this paper can be applied to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.

NONLINEAR GALERKIN MIXED ELEMENT METHODS FOR STATIONARY INCOMPRESSIBLE MAGNETOHYDRODYNAMICS

A nonlinear Galerkin mixed element （NGME） method for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of the NGME solution are derived.

Optimal integration of solar home systems and appliance scheduling for residential homes under severe national load shedding

In developing countries like South Africa,users experienced more than 1030 hours of load shedding outages in just the first half of 2023 due to inadequate power supply from the national grid.Residential homes that cannot afford to take actions to mitigate the challenges of load shedding are severely inconvenienced as they have to reschedule their demand involuntarily.This study presents optimal strategies to guide households in determining suitable scheduling and sizing solutions for solar home systems to mitigate the inconvenience experienced by residents due to load shedding.To start with,we predict the load shedding stages that are used as input for the optimal strategies by using the K-Nearest Neighbour(KNN)algorithm.Based on an accurate forecast of the future load shedding patterns,we formulate the residents’inconvenience and the loss of power supply probability during load shedding as the objective function.When solving the multi-objective optimisation problem,four different strategies to fight against load shedding are identified,namely(1)optimal home appliance scheduling(HAS)under load shedding;(2)optimal HAS supported by solar panels;(3)optimal HAS supported by batteries,and(4)optimal HAS supported by the solar home system with both solar panels and batteries.Among these strategies,appliance scheduling with an optimally sized 9.6 kWh battery and a 2.74 kWp panel array of five 550 Wp panels,eliminates the loss of power supply probability and reduces the inconvenience by 92%when tested under the South African load shedding cases in 2023.

Study on Multi-stream Heat Exchanger Network Synthesis with Parallel Genetic/Simulated Annealing Algorithm

The multi-stream heat exchanger network synthesis (HENS) problem can be formulated as a mixed integer nonlinear programming model according to Yee et al. Its nonconvexity nature leads to existence of more than one optimum and computational difficulty for traditional algorithms to find the global optimum. Compared with deterministic algorithms, evolutionary computation provides a promising approach to tackle this problem. In this paper, a mathematical model of multi-stream heat exchangers network synthesis problem is setup. Different from the assumption of isothermal mixing of stream splits and thus linearity constraints of Yee et al., non-isothermal mixing is supported. As a consequence, nonlinear constraints are resulted and nonconvexity of the objective function is added. To solve the mathematical model, an algorithm named GA/SA (parallel genetic/simulated annealing algorithm) is detailed for application to the multi-stream heat exchanger network synthesis problem. The performance of the proposed approach is demonstrated with three examples and the obtained solutions indicate the presented approach is effective for multi-stream HENS.

Modeling and Multi-objective Optimization of Refinery Hydrogen Network

The demand of hydrogen in oil refinery is increasing as market forces and environmental legislation, so hydrogen network management is becoming increasingly important in refineries. Most studies focused on single-objective optimization problem for the hydrogen network, but few account for the multi-objective optimization problem. This paper presents a novel approach for modeling and multi-objective optimization for hydrogen network in refineries. An improved multi-objective optimization model is proposed based on the concept of superstructure. The optimization includes minimization of operating cost and minimization of investment cost of equipment. The proposed methodology for the multi-objective optimization of hydrogen network takes into account flow rate constraints, pressure constraints, purity constraints, impurity constraints, payback period, etc. The method considers all the feasible connections and subjects this to mixed-integer nonlinear programming （MINLP）. A deterministic optimization method is applied to solve this multi-objective optimization problem. Finally, a real case study is intro-duced to illustrate the applicability of the approach.

Simulated Annealing Approach to the Optimal Synthesis of Distillation Column with Intermediate Heat Exchangers

This article presents a simulated annealing-based approach to the optimal synthesis of distillation column considering intermediate heat exchangers arrangements. T-he number of intermediate condensers and/or intermediate reboilers, the placement locations, the.operating pressure of column, and the heat duties of intermediate heat exchangers are treated as optimization variables. A novel coding procedure making use of an integer number series is proposed to represent and manipulate the structure of system and a stage-to-stage method is used for column design and cost calculation. With the representation procedure, the synthesis problem is formulated as a mixed integer nonlinear programming （MINLP） problem, which can then be solved with an improved simulated annealing algorithm. Two examples are illustrated to show the effectiveness of the suggested approach.

Tree mortality and biomass loss in drought-aff ected forests of East Texas,USA

Changes in tree mortality due to severe drought can alter forest structure,composition,dynamics,ecosystem services,carbon fl uxes,and energy interactions between the atmosphere and land surfaces.We utilized long-term(2000‒2017,3 full inventory cycles)Forest Inventory and Analysis(FIA)data to examine tree mortality and biomass loss in drought-aff ected forests for East Texas,USA.Plots that experienced six or more years of droughts during those censuses were selected based on 12-month moderate drought severity[Standardized Precipitation Evaporation Index(SPEI)-1.0].Plots that experienced other disturbances and inconsistent records were excluded from the analysis.In total,222 plots were retained from nearly 4000 plots.Generalized nonlinear mixed models(GNMMs)were used to examine the changes in tree mortality and recruitment rates for selected plots.The results showed that tree mortality rates and biomass loss to mortality increased overall,and across tree sizes,dominant genera,height classes,and ecoregions.An average mortality rate of 5.89%year−1 during the study period could be incited by water stress created by the regional prolonged and episodic drought events.The overall plot and species-group level recruitment rates decreased during the study period.Forest mortality showed mixed results regarding basal area and forest density using all plots together and when analyzed the plots by stand origin and ecoregion.Higher mortality rates of smaller trees were detected and were likely compounded by densitydependent factors.Comparative analysis of drought-induced tree mortality using hydro-meteorological data along with drought severity and length gradient is suggested to better understand the eff ects of drought on tree mortality and biomass loss around and beyond East Texas in the southeastern United States.

Multi-objective modeling and optimization for scheduling of cracking furnace systems

Cracking furnace is the core device for ethylene production. In practice, multiple ethylene furnaces are usually run in parallel. The scheduling of the entire cracking furnace system has great significance when multiple feeds are simultaneously processed in multiple cracking furnaces with the changing of operating cost and yield of product. In this paper, given the requirements of both profit and energy saving in actual production process, a multi-objective optimization model contains two objectives, maximizing the average benefits and minimizing the average coking amount was proposed. The model can be abstracted as a multi-objective mixed integer non- linear programming problem. Considering the mixed integer decision variables of this multi-objective problem, an improved hybrid encoding non-dominated sorting genetic algorithm with mixed discrete variables （MDNSGA-II） is used to solve the Pareto optimal front of this model, the algorithm adopted crossover and muta- tion strategy with multi-operators, which overcomes the deficiency that normal genetic algorithm cannot handle the optimization problem with mixed variables. Finally, using an ethylene plant with multiple cracking furnaces as an example to illustrate the effectiveness of the scheduling results by comparing the optimization results of multi-objective and single objective model.