Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution theorem.Further, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations aswell.Moreover,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.

Mechanistic insights into the amelioration effects of diabetic cardiomyopathy by berberine:an integrated systems pharmacology study and experimental validation

Background:Diabetic cardiomyopathy(DCM)is a type of cardiomyopathy caused by long-term diabetes,characterized by abnormal myocardial structure and function,which can lead to heart failure.Berberine(BBR),a quaternary ammonium alkaloid isolated from Coptidis Rhizoma,a traditional Chinese medicine,has superior anti-diabetic and heart-protective properties.The purpose of this study is to assess the impact of BBR on DCM.Methods:This study used a systems pharmacology approach to evaluate the related proteins and signalling pathways between BBR and DCM targets,combined with experimental validation using diabetic mouse heart sections.Microstructural and pathological changes were observed using Hematoxylin-eosin,Masson’s trichrome stain and wheat germ agglutinin staining.Immunofluorescence and western blot were used to determine protein expression.Results:The results indicate that BBR and DCM share 21 core relevant targets,with cross-targets predominantly located in mitochondrial,endoplasmic reticulum,and plasma membrane components.BBR exerts its main effects in improving DCM by maintaining mitochondrial integrity,particularly involving the PI3K-AKT-GSK3βand apoptosis signalling pathways.In addition,post-treatment changes in the key targets of BBR,including cysteine aspartate specific protease(Caspase)-3,phosphoinositide 3-kinase(PI3K)and mitochondria-related proteins,are suggestive of its efficacy.Conclusion:BBR crucially improves DCM by maintaining mitochondrial integrity,inhibiting apoptosis,and modulating PI3K-AKT-GSK3βsignaling.Further studies must address animal model limitations and validate clinical efficacy to understand BBR’s mechanisms fully and its potential clinical use.

Spireoside Controls Blast Disease by Disrupting Membrane Integrity of Magnaporthe oryzae

The application of fungicides is an effective strategy for controlling plant diseases.Among these agents,plant-derived antifungal metabolites are particularly promising due to their eco-friendly and sustainable nature.Plant secondary metabolites typically exhibit broad-spectrum antifungal activity without selective toxicity against pathogens.However,only a small fraction of antifungal metabolites have been identified from the tens of thousands of known plant secondary metabolites.In this study,we conducted a metabolomic analysis on both blast-resistant(Digu)and-susceptible(Lijiangxintuanheigu)rice varieties to uncover novel metabolites that enhance blast resistance.We found that 24 and 48 h post-inoculation with Magnaporthe oryzae were critical time points for metabolomic profiling,based on the infected status of M.oryzae in rice and the observed differences in shikimate accumulation between the two varieties.Following metabolomic analysis,we identified nine flavonoids that were differentially accumulated and are considered potential candidates for disease control.Among these,apigenin-7-glucoside,rhamnetin,and spireoside were found to be effective in controlling blast disease,with spireoside demonstrating the most pronounced efficacy.We discovered that spireoside controlled blast disease by inhibiting both spore germination and appressorium formation in M.oryzae,primarily through disrupting cell membrane integrity.However,spireoside did not induce rice immunity.Furthermore,spireoside was also effective in controlling sheath blight disease.Thus,spireoside shows considerable promise as a candidate for the development of a fungicide for controlling plant diseases.

Some properties of monotone set functions defined by Choquet integral

In this paper, some properties of the monotone set function defined by theChoquet integral are discussed. It is shown that several important structural characteristics of theoriginal set function, such as weak null-additivity, strong order continuity, property (s) andpseudomelric generating property, etc., are preserved by the new set function. It is also shown thatC-integrability assumption is inevitable for the preservations of strong order continuous andpseudometric generating property.

Construction analysis on integral lifting of steel structure by the vector form intrinsic finite element

A newnumerical method based on vector form intrinsic finite element（VFIFE） is proposed to simulate the integral lifting process of steel structures. First, in order to verify the validity of the VFIFE method, taking the steel gallery between the integrated building and the attached building of Nanjing M obile Communication Buildings for example, the static analysis was carried out and the corresponding results were compared with the results achieved by the traditional finite element method. Then, according to the characteristics of dynamic construction of steel structure integral lifting, the tension cable element was employed to simulate the behavior of dynamic construction. The VFIFE method avoids the iterative solution of the stiffness matrix and the singularity problems. Therefore, it is simple to simulate the complete process of steel structure lifting construction.Finally, by using the VFIFE, the displacement and internal force time history curves of the steel structures under different lifting speeds are obtained. The results show that the lifting speed has influence on the lifting force, the internal force, and the displacement of the structure. In the case of normal lifting speed, the dynamic magnification factor of 1. 5 is safe and reasonable for practical application.

AN NUMERICAL ALGORI THM FOR LAPLACE′S INTEGRAL BY B-SPLINE

Algorithm for Laplace ′s integral is given when the inverse image function has high order discontinui ty. The multi-node technique of B-spline is used to describe the interruption point, cusp and non-smooth point of the inverse image function. The difference quotient and de Boor algorithm are used to derive the image function of the Lapl ace′s integral under non-uniform partition. And a set of practical formula is got when the partition is quasi-uniform. The scheme enables the image function to be approximated within any prescribed tolerance. Experiments also show that g ood result is achieved. It is much faster than that of Simpsons rule, and much s impler than that of Berge method, the traditional efficient method. It is no lon ger to find the zero points and coefficients of Gauss-Laguerre or Gauss-Legend re polynomials. The image function of Laplace′s integral can also be computed while the inverse image function is hyper-function with high order discontinuity.

Forming mechanism of integral serrated high fins by plowing-extruding based on variational feed

Plowing-extruding tool was designed and plowing-extruding process was investigated.Then,a manufacturing method of integral serrated high-finned tube,plowing-extruding based on variational feed was proposed,in which plowing-extruding tool moved forward at two different feeds,f1 and f2,in turn.In this method,overlaps that are usually avoided in practical application were utilized to manufacture high fins and average height of fins was up to 1.58 mm.The critical feed(fc) of overlaps forming and terms of high fins forming were analyzed.The main technical parameters that affect the fins height were discussed.The experimental results show that the fins height increases with extruding inclination angle and plowing-extruding depth,and the fins height increases with f1 increasing when f1 is smaller than fc,and decreases with f1 increasing if f1 is larger than fc.

LINEAR SINGULAR INTEGRAL EQUATION ON DOMAINS COMPOSED BY BALLS

For domains composed by balls in C^n, this paper studies the boundary behaviour of Cauchy type integrals with discrete holomorphic kernels and the corresponding linear singular integral equation on each piece of smooth lower dimensional edges on the boundary of the domain.

Emotional inference by means of Choquet integral and λ-fuzzy measurement in consideration of ambiguity of human mentality

Research on human emotions has started to address psychological aspects of human nature and has advanced to the point of designing various models that represent them quantitatively and systematically. Based on the findings, a method is suggested for emotional space formation and emotional inference that enhance the quality and maximize the reality of emotion-based personalized services. In consideration of the subjective tendencies of individuals, AHP was adopted for the quantitative evaluation of human emotions, based on which an emotional space remodeling method is suggested in reference to the emotional model of Thayer and Plutchik, which takes into account personal emotions. In addition, Sugeno fuzzy inference, fuzzy measures, and Choquet integral were adopted for emotional inference in the remodeled personalized emotional space model. Its performance was evaluated through an experiment. Fourteen cases were analyzed with 4.0 and higher evaluation value of emotions inferred, for the evaluation of emotional similarity, through the case studies of 17 kinds of emotional inference methods. Matching results per inference method in ten cases accounting for 71% are confirmed. It is also found that the remaining two cases are inferred as adjoining emotion in the same section. In this manner, the similarity of inference results is verified.

A Method for Solving Fredholm Integral Equations of the First Kind Based on Chebyshev Wavelets

In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.

Reconstruction of Complex Materials by Integral Geometric Measures

The goal of much research in computational materials science is to quantify necessary morphological information and then to develop stochastic models which both accurately reflect the material morphology and allow one to estimate macroscopic physical properties. A novel method of characterizing the morphology of disordered systems is presented based on the evolution of a family of integral geometric measures during erosion and dilation operations. The method is used to determine the accuracy of model reconstructions of random systems. It is shown that the use of erosion/dilation operations on the original image leads to a more accurate discrimination of morphology than previous methods.

Rough Integrals Generated by Function Rough Sets

The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic.

SOLUTION OF DIFFERENT HOLES SHAPE BORDERS OF FIBRE REINFORCED COMPOSITE PLATES BY INTEGRAL EQUATIONS

Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.

DECIDING PRODUCTION TECHNIQUE STRATEGY BY INTEGRAL EVALUATION

According to overall mean square root of weighted deviation, a significant method of selecting coal mine production technique strategy has been put forward in this paper. In the given example, an index system of evaluating different mining methods has also been provided, which plays a guiding effect in production of coal mine.

Chebyshev Polynomials for Solving a Class of Singular Integral Equations

This paper is devoted to studying the approximate solution of singular integral equations by means of Chebyshev polynomials. Some examples are presented to illustrate the method.

Numerical Solution of Two-Dimensional Nonlinear Stochastic Ito-Volterra Integral Equations by Applying Block Pulse Functions

This paper investigates the numerical solution of two-dimensional nonlinear stochastic Itô-Volterra integral equations based on block pulse functions. The nonlinear stochastic integral equation is transformed into a set of algebraic equations by operational matrix of block pulse functions. Then, we give error analysis and prove that the rate of convergence of this method is efficient. Lastly, a numerical example is given to confirm the method.

Numerical Solution of Mean-Square Approximation Problem of Real Nonnegative Function by the Modulus of Double Fourier Integral

A nonlinear problem of mean-square approximation of a real nonnegative continuous function with respect to two variables by the modulus of double Fourier integral dependent on two real parameters with use of the smoothing functional is studied. Finding the optimal solutions of this problem is reduced to solution of the Hammerstein type two-dimensional nonlinear integral equation. The numerical algorithms to find the branching lines and branching-off solutions of this equation are constructed and justified. Numerical examples are presented.

Some New Subclasses of Meromorphically Multivalent Uniformly Reciprocal Starlike Functions Defined by the Generalized Dziok-Srivastava Operator and Its Integral Operator

In this paper, we introduce some new subclasses of meromorphically uniformly reciprocal starlike functions associated with the generalized Dziok-Srivastava operator and its corresponding integral operator defined by subordination. We obtain the inclusion relation, sufficient conditions and raajorization property of the class. Moreover, we point out some new and interesting corollaries of our main result. These results generalize some known results.

Exact Solutions of Two Nonlinear Partial Differential Equations by the First Integral Method

In recent years, many methods have been used to find the exact solutions of nonlinear partial differential equations. One of them is called the first integral method, which is based on the ring theory of commutative algebra. In this paper, exact travelling wave solutions of the Non-Boussinesq wavepacket model and the (2 + 1)-dimensional Zoomeron equation are studied by using the first integral method. From the solving process and results, the first integral method has the characteristics of simplicity, directness and effectiveness about solving the exact travelling wave solutions of nonlinear partial differential equations. In other words, tedious calculations can be avoided by Maple software;the solutions of more accurate and richer travelling wave solutions are obtained. Therefore, this method is an effective method for solving exact solutions of nonlinear partial differential equations.

A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method

The main aim of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. These phenomenon yields a partial differential equation namely Burger’s equation, which is solved by mixture of the new integral transform and the homotopy perturbation method under suitable conditions and the standard assumption. This method provides an analytical approximation in a rapidly convergent sequence with in exclusive manner computed terms. Its rapid convergence shows that the method is trustworthy and introduces a significant improvement in solving nonlinear partial differential equations over existing methods. It is concluded that the behaviour of concentration in longitudinal dispersion phenomenon is decreases as distance x is increasing with fixed time t > 0 and slightly increases with time t.