In this paper, a new two-step Newton-type method with third-order convergence for solving systems of nonlinear equations is proposed. We construct the new method based on the integral interpolation of Newton’s method...In this paper, a new two-step Newton-type method with third-order convergence for solving systems of nonlinear equations is proposed. We construct the new method based on the integral interpolation of Newton’s method. Its cubic convergence and error equation are proved theoretically, and demonstrated numerically. Its application to systems of nonlinear equations and boundary-value problems of nonlinear ODEs are shown as well in the numerical examples.展开更多
The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△（an△^2（xn＋bnxn-τ1＋cnxn＋τ2））＋qnx^βn＋1-σ1＋pnx^^βn...The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△（an△^2（xn＋bnxn-τ1＋cnxn＋τ2））＋qnx^βn＋1-σ1＋pnx^^βn＋1＋σ2=0,where （an）, （bn}, （cn}, （qn} and （pn} are positive real sequences, β is a ratio of odd positive integers, τ1, τ2, and σ2 are positive integers. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero. Some examples are presented to illustrate the main results.展开更多
In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower soluti...In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works.展开更多
Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solution...Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.展开更多
To determine the prevalence of metabolic syndrome (MetS) in Malaysian type 2 diabetic patients using WHO, NCEP ATP III, IDF and the new Harmonized definitions, and the concordance between these definitions. This study...To determine the prevalence of metabolic syndrome (MetS) in Malaysian type 2 diabetic patients using WHO, NCEP ATP III, IDF and the new Harmonized definitions, and the concordance between these definitions. This study involved 313 patients diagnosed with type 2 diabetes mellitus (T2DM) at two Malaysian tertiary hospitals. Socio-demographic data were assessed using a pre-tested interviewer-administered structured questionnaire. Anthropometric measurements were carried out according to standard protocols. Clinical and laboratory characteristics were examined. Kappa (k) statistics were used for the agreement between the four MetS definitions. The overall prevalence rates of MetS (95% CI) were 95.8% (93.6-98.1), 96.1% (94.0-98.3), 84.8% (80.8-88.9) and 97.7% (96.1-99.4) according to the WHO, NCEP ATP III, IDF and the Harmonized definitions, respectively. The Kappa statistics demonstrated a slight to substantial agreement between the definitions (k = 0.179-0.875, p k = 0.875, p hest specificity (100%) in identifying MetS. In conclusion, the new Harmonized criteria established the highest prevalence of MetS among the four definitions applied. There was a very good concordance between the WHO and NCEP ATP III criteria. The extremely high prevalence of MetS observed in type 2 diabetic patients indicates an impending pandemic of CVD risk in Malaysia. Aggressive treatment of MetS components is required to reduce cardiovascular risk in T2DM.展开更多
文摘In this paper, a new two-step Newton-type method with third-order convergence for solving systems of nonlinear equations is proposed. We construct the new method based on the integral interpolation of Newton’s method. Its cubic convergence and error equation are proved theoretically, and demonstrated numerically. Its application to systems of nonlinear equations and boundary-value problems of nonlinear ODEs are shown as well in the numerical examples.
文摘The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△（an△^2（xn＋bnxn-τ1＋cnxn＋τ2））＋qnx^βn＋1-σ1＋pnx^^βn＋1＋σ2=0,where （an）, （bn}, （cn}, （qn} and （pn} are positive real sequences, β is a ratio of odd positive integers, τ1, τ2, and σ2 are positive integers. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero. Some examples are presented to illustrate the main results.
文摘In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works.
文摘Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.
文摘To determine the prevalence of metabolic syndrome (MetS) in Malaysian type 2 diabetic patients using WHO, NCEP ATP III, IDF and the new Harmonized definitions, and the concordance between these definitions. This study involved 313 patients diagnosed with type 2 diabetes mellitus (T2DM) at two Malaysian tertiary hospitals. Socio-demographic data were assessed using a pre-tested interviewer-administered structured questionnaire. Anthropometric measurements were carried out according to standard protocols. Clinical and laboratory characteristics were examined. Kappa (k) statistics were used for the agreement between the four MetS definitions. The overall prevalence rates of MetS (95% CI) were 95.8% (93.6-98.1), 96.1% (94.0-98.3), 84.8% (80.8-88.9) and 97.7% (96.1-99.4) according to the WHO, NCEP ATP III, IDF and the Harmonized definitions, respectively. The Kappa statistics demonstrated a slight to substantial agreement between the definitions (k = 0.179-0.875, p k = 0.875, p hest specificity (100%) in identifying MetS. In conclusion, the new Harmonized criteria established the highest prevalence of MetS among the four definitions applied. There was a very good concordance between the WHO and NCEP ATP III criteria. The extremely high prevalence of MetS observed in type 2 diabetic patients indicates an impending pandemic of CVD risk in Malaysia. Aggressive treatment of MetS components is required to reduce cardiovascular risk in T2DM.
