Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Simulation research on surface growth process of positive and negative frequency detuning chromium atom lithographic gratings

Chromium atom photolithography gratings are a promising technology for the development of nanoscale length standard substances due to their high accuracy,uniformity,and consistency.However,the inherent difference between the interaction of positive and negative frequency detuning standing wave field and the atoms can cause a difference in the adjacent peak-to-valley heights of the grating in positive and negative frequency detuning chromium atom lithography,which greatly reduces its accuracy.In this study,we performed a controlled variable growth simulation using the semi-classical theoretical model and Monte Carlo method with trajectory tracking and ballistic deposition methods to investigate the influence of key experimental parameters on the surface growth process of positive and negative frequency detuning atomic lithography gratings.We established a theoretical model based on simulation results and summarized empirical equations to guide the selection of experimental parameters.Our simulations achieved uniform positive and negative frequency detuning atomic lithography gratings with a period of 1/4 of the wavelength corresponding to the atomic transition frequency,and adjacent peak-to-valley heights differing by no more than 2 nm,providing an important theoretical reference for the controllable fabrication of these gratings.

EXISTENCE OF POSITIVE SOLUTIONS FOR NEUTRAL DIFFERENCE EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS

In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature.

STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS

Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.

POSITIVE SOLUTIONS WITH HIGH ENERGY FOR FRACTIONAL SCHRODINGER EQUATIONS

In this paper, we study the Schrodinger equations (-△)^(s)u + V(x)u = a(x)|u|^(p-2)u + b(x)|u|^(q-2)u, x∈R^(N),where 0 < s < 1, 2 < q < p < 2_(s)^(*), 2_(s)^(*) is the fractional Sobolev critical exponent. Under suitable assumptions on V, a and b for which there may be no ground state solution, the existence of positive solutions are obtained via variational methods.

Hermite Positive Definite Solution of the Quaternion Matrix Equation Xm + B*XB = C

This paper discusses the necessary and sufficient conditions for the existence of Hermite positive definite solutions of the quaternion matrix equation Xm+ B*XB = C (m > 0) and its iterative solution method. According to the characteristics of the coefficient matrix, a corresponding algebraic equation system is ingeniously constructed, and by discussing the equation system’s solvability, the matrix equation’s existence interval is obtained. Based on the characteristics of the coefficient matrix, some necessary and sufficient conditions for the existence of Hermitian positive definite solutions of the matrix equation are derived. Then, the upper and lower bounds of the positive actual solutions are estimated by using matrix inequalities. Four iteration formats are constructed according to the given conditions and existence intervals, and their convergence is proven. The selection method for the initial matrix is also provided. Finally, using the complexification operator of quaternion matrices, an equivalent iteration on the complex field is established to solve the equation in the Matlab environment. Two numerical examples are used to test the effectiveness and feasibility of the given method. .

Backward Support Computation Method for Positive and Negative Frequent Itemset Mining

Association rules mining is a major data mining field that leads to discovery of associations and correlations among items in today’s big data environment. The conventional association rule mining focuses mainly on positive itemsets generated from frequently occurring itemsets (PFIS). However, there has been a significant study focused on infrequent itemsets with utilization of negative association rules to mine interesting frequent itemsets (NFIS) from transactions. In this work, we propose an efficient backward calculating negative frequent itemset algorithm namely EBC-NFIS for computing backward supports that can extract both positive and negative frequent itemsets synchronously from dataset. EBC-NFIS algorithm is based on popular e-NFIS algorithm that computes supports of negative itemsets from the supports of positive itemsets. The proposed algorithm makes use of previously computed supports from memory to minimize the computation time. In addition, association rules, i.e. positive and negative association rules (PNARs) are generated from discovered frequent itemsets using EBC-NFIS algorithm. The efficiency of the proposed algorithm is verified by several experiments and comparing results with e-NFIS algorithm. The experimental results confirm that the proposed algorithm successfully discovers NFIS and PNARs and runs significantly faster than conventional e-NFIS algorithm.

Utilizing Instilling Negative Pressure Wound Therapy with Vashe Wound Solution for an Infected Sternal Dehiscence: A Case Report

Utilization of negative pressure wound therapy with instillation (NPWTi) for sternal dehiscence wounds secondary to sternal wound infection after surgery has become an accepted therapy. NPWTi accelerates wound healing through macrostrain, microstrain, and cyclic fluid instillation. Wounds benefit from additional superficial infection control with the removal of microorganisms, the release of proinflammatory mediators, stimulation of angiogenesis, as well as mechanical debridement. However, very few cases of utilizing NPWTi in the treatment of sternal wound infections have been reported in the literature. This case study describes the use of NPWTi with hypochlorous acid for the treatment of a sternal wound infection.

Effects of positive thinking intervention on negative emotions and quality of life in stroke patients:a scoping review

Objective:To analyze domestic and international studies on the effects of positive thought intervention therapy on negative emotions and the quality of life of stroke patients to provide a reference for future related studies.Methods:Using the scoping review method as a guide,computer searches of PubMed,Web of Science,Embase,Cochrane Library,China National Knowledge Infrastructure,Wanfang Database,China Vipers Full Text Database and China Biomedical Literature Database were conducted to collect relevant studies on the application of positive thinking interventions in stroke patients from the establishment to January 2023,and the literature was screened according to the inclusion and exclusion criteria,and the data were extracted and analyzed by two investigators independently.Results:The search yielded 964 publications,and a total of 19 were included.The time of publication,study site,study population,study design,study length,and type of results of the included studies was summarized and analyzed.Conclusions:Positive thinking-based interventions have shown significant changes in negative emotions such as anxiety and depression in stroke patients and can reduce somatic pain,enhance their social integration,and improve their quality of life.However,interventions in the areas of self-compassion,artificial intelligence and the adoption of tailoring need to be further explored.

Semi-analytical solution for mechanical analysis of tunnels crossing strike-slip fault zone considering nonuniform fault displacement and uncertain fault plane position

The tunnel subjected to strike-slip fault dislocation exhibits severe and catastrophic damage.The existing analysis models frequently assume uniform fault displacement and fixed fault plane position.In contrast,post-earthquake observations indicate that the displacement near the fault zone is typically nonuniform,and the fault plane position is uncertain.In this study,we first established a series of improved governing equations to analyze the mechanical response of tunnels under strike-slip fault dislocation.The proposed methodology incorporated key factors such as nonuniform fault displacement and uncertain fault plane position into the governing equations,thereby significantly enhancing the applicability range and accuracy of the model.In contrast to previous analytical models,the maximum computational error has decreased from 57.1%to 1.1%.Subsequently,we conducted a rigorous validation of the proposed methodology by undertaking a comparative analysis with a 3D finite element numerical model,and the results from both approaches exhibited a high degree of qualitative and quantitative agreement with a maximum error of 9.9%.Finally,the proposed methodology was utilized to perform a parametric analysis to explore the effects of various parameters,such as fault displacement,fault zone width,fault zone strength,the ratio of maximum fault displacement of the hanging wall to the footwall,and fault plane position,on the response of tunnels subjected to strike-slip fault dislocation.The findings indicate a progressive increase in the peak internal forces of the tunnel with the rise in fault displacement and fault zone strength.Conversely,an augmentation in fault zone width is found to contribute to a decrease in the peak internal forces.For example,for a fault zone width of 10 m,the peak values of bending moment,shear force,and axial force are approximately 46.9%,102.4%,and 28.7% higher,respectively,compared to those observed for a fault zone width of 50 m.Furthermore,the position of the peak internal forces is influenced by variations in the ratio of maximum fault displacement of the hanging wall to footwall and the fault plane location,while the peak values of shear force and axial force always align with the fault plane.The maximum peak internal forces are observed when the footwall exclusively bears the entirety of the fault displacement,corresponding to a ratio of 0:1.The peak values of bending moment,shear force,and axial force for the ratio of 0:1 amount to approximately 123.8%,148.6%,and 111.1% of those for the ratio of 0.5:0.5,respectively.

Impact of web-based positive psychological intervention on emotions,psychological capital,and quality of life in gastric cancer patients on chemotherapy

BACKGROUND Gastric cancer is a malignant digestive tract tumor that originates from the epithelium of the gastric mucosa and occurs in the gastric antrum,particularly in the lower curvature of the stomach.AIM To evaluate the impact of a positive web-based psychological intervention on emotions,psychological capital,and quality of survival in gastric cancer patients on chemotherapy.METHODS From January 2020 to October 2023,121 cases of gastric cancer patients on chemotherapy admitted to our hospital were collected and divided into a control group(n=60)and an observation group(n=61)according to the admission order.They were given either conventional nursing care alone and conventional nursing care combined with web-based positive psychological interventions,respectively.The two groups were compared in terms of negative emotions,psychological capital,degree of cancer-caused fatigue,and quality of survival.RESULTS After intervention,the number of patients in the observation group who had negative feelings toward chemotherapy treatment was significantly lower than that of the control group(P<0.05);the Positive Psychological Capital Questionnaire score was considerably higher than that of the control group(P<0.05);the degree of cancer-caused fatigue was significantly lower than that of the control group(P<0.05);and the Quality of Life Scale for Cancer Patients(QLQ-30)score was significantly higher than that of the control group(P<0.05).CONCLUSION Implementing a web-based positive psychological intervention for gastric cancer chemotherapy patients can effectively improve negative emotions,enhance psychological capital,and improve the quality of survival.

The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms

We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.

Existence of Positive Solutions of Nonlinear NeutralEquations with Positive and Negative Coefficients

A class of nonlinear neutral equations with positive and negative coefficients is considered. Seveal conditions for existence of eventually positive solutions are obtained,and they extend and improve some of the criteria existing in literature. Our conditions are necessary and suffcient when all the coeffcients of the equations are constants.

SYMMETRIC POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATIONS (AX,XB)=(C,D) AND AXB=C

The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive definite solutions are derived using the singular value and the generalized singular value decompositions. The expressions for the general symmetric positive definite solutions are given when certain conditions hold.

On the Problem of All Equal Positive Odd Number Solutions of the Dissemination of the Ends' Guess

The thesis is concerned with the problem of the dissemination of the Ends’ guess and offers the formula of all equal positive odd number solutions.

Positive Solutions of a Semilinear Elliptic Equation with Coefficient That Changes Sign

We prove the existence of a positive solution to the problem-Δu=a(x)f(u), x∈Ω, u(x)=0,x∈Ω,where Ω is a bounded domain in R n with smooth boundary, a(x) is allowed to change sign.

Existence of Multiple Positive Solutions for Higher-Order p-Laplacian Boundary Value Problems

The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.

Existence of Positive Solutions for Nonlinear Conjugate Boundary Value Problems

The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.

An Existence Theorem of Positive Solution for Fourth-order Superlinear Semipositone Eigenvalue Problems

In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.

“阴/阳”和“positive/negative”之多义现象的认知对比研究

多义现象是当今语言学研究的一个重要方面,从认知语言学的视角对多义现象进行对比研究是当今语义研究的一个热点,已取得了不少的研究成果,但是对于"阴/阳"和"positive/negative"这两组具有独特民族特色的字词的语义研究尚鲜有关注。本文从原型范畴和认知隐喻的视角,详细地分析了这两组字词的语义发展特征,发现它们的语义已经形成错综复杂的语义网状结构,既有语义重合之处,也有自己的独特之处,体现了中西文化的独特文化特征和思维特征。