In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbol...In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbolic conservation laws.For the purpose of designing increasingly high-order finite difference WENO schemes,the equal-sized stencils are becoming more and more wider.The more we use wider candidate stencils,the bigger the probability of discontinuities lies in all stencils.Therefore,one innovation of these new WENO schemes is to introduce a new splitting stencil methodology to divide some fourpoint or five-point stencils into several smaller three-point stencils.By the usage of this new methodology in high-order spatial reconstruction procedure,we get different degree polynomials defined on these unequal-sized stencils,and calculate the linear weights,smoothness indicators,and nonlinear weights as specified in Jiang and Shu(J.Comput.Phys.126:202228,1996).Since the difference between the nonlinear weights and the linear weights is too big to keep the optimal order of accuracy in smooth regions,another crucial innovation is to present the new mapping functions which are used to obtain the mapped nonlinear weights and decrease the difference quantity between the mapped nonlinear weights and the linear weights,so as to keep the optimal order of accuracy in smooth regions.These new MWENO schemes can also be applied to compute some extreme examples,such as the double rarefaction wave problem,the Sedov blast wave problem,and the Leblanc problem with a normal CFL number.Extensive numerical results are provided to illustrate the good performance of the new finite difference MWENO schemes.展开更多
Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 fo...Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.展开更多
Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Alta...Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, and e∞^r, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））, and the Schauder basis of the spaces e0^r△^（m））, ec^r△^（m））. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^（m））.展开更多
A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach ...A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features：（i） it enables synchronization to be achieved for both cases of n 〈 m and n 〉 m;（ii） it is rigorous,being based on theorems;（iii） it can be readily applied to any chaotic（hyperchaotic） maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map（as the drive system） and the three-dimensional hyperchaotic Wang map（as the response system）,and the three-dimensional H′enon-like map（as the drive system） and the two-dimensional Lorenz discrete-time system（as the response system）.展开更多
In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l（u, v, p; △（m））, which consist of the sequences whose generalized weighted △（m）-di...In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l（u, v, p; △（m））, which consist of the sequences whose generalized weighted △（m）-difference means are in the linear space l（p） defined by I.J.Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from l（u, v, p, △（m）） to l∞, c, and co. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space lp（U, v, △（m）） （1 ≤ p 〈 ∞）.展开更多
Difference equations arise in many fields. This article is concerned to general- ization of semiconjugacy in difference equations. In fact, H. Sedaghat in [7] investigated the semiconjugacy in difference equations whe...Difference equations arise in many fields. This article is concerned to general- ization of semiconjugacy in difference equations. In fact, H. Sedaghat in [7] investigated the semiconjugacy in difference equations where the factor maps are one-dimensional. We gen- eralize the definition of semiconjugacy of maps, where the factor map is multi-dimensional. This generalization is very useful. By this generalization, we can investigate the dynamics of many difference equations especially the dynamics of systems of higher order difference equations. Some systems of difference equations are investigated using the semiconjugacy property.展开更多
The Indian shield comprises a number of Archean–Paleoproterozoic cratonic blocks and predominantly Meso–Neoproterozoic mobile belts with Archean protoliths.All these ancient cratons were thought to be integral parts of
BACKGROUND： It has been proved that brain electrical activity mapping （BEAM） and transcranial Doppler （TCD） detection can reflect the function of brain cell and its diseased degree of infant patients with moderat...BACKGROUND： It has been proved that brain electrical activity mapping （BEAM） and transcranial Doppler （TCD） detection can reflect the function of brain cell and its diseased degree of infant patients with moderate to severe hypoxic-ischemic encephalopathy （HIE）. OBJECTIVE： To observe the abnormal results of HIE at different degrees detected with BEAM and TCD in infant patients, and compare the detection results at the same time point between BEAM, TCD and computer tomography （CT） examinations. DESIGN ： Contrast observation SETTING： Departments of Neuro-electrophysiology and Pediatrics, Second Affiliated Hospital of Qiqihar Medical College. PARTICIPANTS： Totally 416 infant patients with HIE who received treatment in the Department of Newborn Infants, Second Affiliated Hospital of Qiqihar Medical College during January 2001 and December 2005. The infant patients, 278 male and 138 female, were at embryonic 37 to 42 weeks and weighing 2.0 to 4.1 kg, and they were diagnosed with CT and met the diagnostic criteria of HIE of newborn infants compiled by Department of Neonatology, Pediatric Academy, Chinese Medical Association. According to diagnostic criteria, 130 patients were mild abnormal, 196 moderate abnormal and 90 severe abnormal. The relatives of all the infant patients were informed of the experiment. METHOOS： BEAM and TCD examinations were performed in the involved 416 infant patients with HIE at different degrees with DYD2000 16-channel BEAM instrument and EME-2000 ultrasonograph before preliminary diagnosis treatment （within 1 month after birth） and 1,3,6,12 and 24 months after birth, and detected results were compared between BEAM, TCD and CT examinations. MAIN OUTCOME MEASURES： Comparison of detection results of HIE at different time points in infant patients between BEAM. TCD and CT examinations. RESULTS： All the 416 infant patients with HIE participated in the result analysis. （1） Comparison of the detected results in infant patients with mild HIE at different time points after birth between BEAM, TCD and CT examinations： BEAM examination showed that the recovery was delayed, and the abnormal rate of BEAM examination was significantly higher than that of CT examination 1 and 3 months after birth [55.4%（72/130）vs. 17.0% （22/130 ）,x^2=41.66 ;29.2% （ 38/130 ） vs. 6.2% （ 8/130 ）, x^2=23.77, P 〈 0.01 ], exceptional patients had mild abnormality and reached the normal level in about 6 months. TCD examination showed that the disease condition significantly improved and infant patients with HIE basically recovered 1 or 2 months after birth, while CT examination showed that infant patients recovered 3 or 4 months after birth. （2） Comparison of detection results of infant patients with moderate HIE at different time points between BEAM, TCD and CT examinations： The abnormal rate of BEAM examination was significantly higher than that of CT examination 1,3,6 and 12 months after birth [90.8% （178/196）,78.6% （154/196）,x^2=4.32,P 〈 0.05;64.3% （126/196）,43.9% （86/196） ,x^2=16.44 ;44.9% （88/196） ,22.4% （44/196）,x^2=22.11 ;21.4% （42/196）, 10.2% （20/196）,x^2=9.27, P 〈 0.01]. BEAM examination showed that there was still one patient who did not completely recovered in the 24^th month due to the relatives of infant patients did not combine the treatment,. TCD examination showed that the abnormal rate was 23.1%（30/196）in the 1^st month after birth, and all the patients recovered to the normal in the 3^rd month after birth, while CT examination showed that mild abnormality still existed in the 24^th month after birth （1.0% ,2/196）. （3） Comparison of detection results of infant patients with severe HIE at different time points between BEAM, TCD and CT examinations： The abnormal rate of BEAM examination was significantly higher than that of CT examination in the 1^st, 3^rd, 6^th and 12^th months after birth[86.7% （78/90）,44.4% （40/90）,x^2=35.53;62.2% （56/90）,31.1% （28/90）,x^2=17.51 ;37.8% （34/90）,6.7% （6/90）, x^2=27.14, P 〈 0.01]. BEAM examination showed that mild abnormality still existed in 4 infant patients in the 24^th month after birth. TCD examination showed that the abnormal rate was 11.1% （10/90） in the 3^rd month after birth, and all the infant patients recovered in the 6^th month after birth. CT examination showed that the abnormal rate was 6.7%（6/90） in the 12^th month after birth, and all of infant patients recovered to the normal in the 24^th month after birth.CONCLUSION ： BEAM is the direct index to detect brain function of infant patients with HIE, and positive reaction is still very sensitive in the tracking detection of convalescent period. The positive rate of morphological reaction in CT examination is superior to that in TCD examination, and the positive rate is very high in the acute period of HIE in examination.展开更多
基金the NSFC grant 11872210 and the Science Challenge Project,No.TZ2016002the NSFC Grant 11926103 when he visited Tianyuan Mathematical Center in Southeast China,Xiamen 361005,Fujian,Chinathe NSFC Grant 12071392 and the Science Challenge Project,No.TZ2016002.
文摘In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbolic conservation laws.For the purpose of designing increasingly high-order finite difference WENO schemes,the equal-sized stencils are becoming more and more wider.The more we use wider candidate stencils,the bigger the probability of discontinuities lies in all stencils.Therefore,one innovation of these new WENO schemes is to introduce a new splitting stencil methodology to divide some fourpoint or five-point stencils into several smaller three-point stencils.By the usage of this new methodology in high-order spatial reconstruction procedure,we get different degree polynomials defined on these unequal-sized stencils,and calculate the linear weights,smoothness indicators,and nonlinear weights as specified in Jiang and Shu(J.Comput.Phys.126:202228,1996).Since the difference between the nonlinear weights and the linear weights is too big to keep the optimal order of accuracy in smooth regions,another crucial innovation is to present the new mapping functions which are used to obtain the mapped nonlinear weights and decrease the difference quantity between the mapped nonlinear weights and the linear weights,so as to keep the optimal order of accuracy in smooth regions.These new MWENO schemes can also be applied to compute some extreme examples,such as the double rarefaction wave problem,the Sedov blast wave problem,and the Leblanc problem with a normal CFL number.Extensive numerical results are provided to illustrate the good performance of the new finite difference MWENO schemes.
基金Supported by the NNSF of China(11971165)the Natural Science Foundation of Zhejiang Province(LY21A010003)。
文摘Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.
文摘Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, and e∞^r, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））, and the Schauder basis of the spaces e0^r△^（m））, ec^r△^（m））. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^（m））.
文摘A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features：（i） it enables synchronization to be achieved for both cases of n 〈 m and n 〉 m;（ii） it is rigorous,being based on theorems;（iii） it can be readily applied to any chaotic（hyperchaotic） maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map（as the drive system） and the three-dimensional hyperchaotic Wang map（as the response system）,and the three-dimensional H′enon-like map（as the drive system） and the two-dimensional Lorenz discrete-time system（as the response system）.
文摘In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l（u, v, p; △（m））, which consist of the sequences whose generalized weighted △（m）-difference means are in the linear space l（p） defined by I.J.Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from l（u, v, p, △（m）） to l∞, c, and co. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space lp（U, v, △（m）） （1 ≤ p 〈 ∞）.
文摘Difference equations arise in many fields. This article is concerned to general- ization of semiconjugacy in difference equations. In fact, H. Sedaghat in [7] investigated the semiconjugacy in difference equations where the factor maps are one-dimensional. We gen- eralize the definition of semiconjugacy of maps, where the factor map is multi-dimensional. This generalization is very useful. By this generalization, we can investigate the dynamics of many difference equations especially the dynamics of systems of higher order difference equations. Some systems of difference equations are investigated using the semiconjugacy property.
文摘The Indian shield comprises a number of Archean–Paleoproterozoic cratonic blocks and predominantly Meso–Neoproterozoic mobile belts with Archean protoliths.All these ancient cratons were thought to be integral parts of
文摘BACKGROUND： It has been proved that brain electrical activity mapping （BEAM） and transcranial Doppler （TCD） detection can reflect the function of brain cell and its diseased degree of infant patients with moderate to severe hypoxic-ischemic encephalopathy （HIE）. OBJECTIVE： To observe the abnormal results of HIE at different degrees detected with BEAM and TCD in infant patients, and compare the detection results at the same time point between BEAM, TCD and computer tomography （CT） examinations. DESIGN ： Contrast observation SETTING： Departments of Neuro-electrophysiology and Pediatrics, Second Affiliated Hospital of Qiqihar Medical College. PARTICIPANTS： Totally 416 infant patients with HIE who received treatment in the Department of Newborn Infants, Second Affiliated Hospital of Qiqihar Medical College during January 2001 and December 2005. The infant patients, 278 male and 138 female, were at embryonic 37 to 42 weeks and weighing 2.0 to 4.1 kg, and they were diagnosed with CT and met the diagnostic criteria of HIE of newborn infants compiled by Department of Neonatology, Pediatric Academy, Chinese Medical Association. According to diagnostic criteria, 130 patients were mild abnormal, 196 moderate abnormal and 90 severe abnormal. The relatives of all the infant patients were informed of the experiment. METHOOS： BEAM and TCD examinations were performed in the involved 416 infant patients with HIE at different degrees with DYD2000 16-channel BEAM instrument and EME-2000 ultrasonograph before preliminary diagnosis treatment （within 1 month after birth） and 1,3,6,12 and 24 months after birth, and detected results were compared between BEAM, TCD and CT examinations. MAIN OUTCOME MEASURES： Comparison of detection results of HIE at different time points in infant patients between BEAM. TCD and CT examinations. RESULTS： All the 416 infant patients with HIE participated in the result analysis. （1） Comparison of the detected results in infant patients with mild HIE at different time points after birth between BEAM, TCD and CT examinations： BEAM examination showed that the recovery was delayed, and the abnormal rate of BEAM examination was significantly higher than that of CT examination 1 and 3 months after birth [55.4%（72/130）vs. 17.0% （22/130 ）,x^2=41.66 ;29.2% （ 38/130 ） vs. 6.2% （ 8/130 ）, x^2=23.77, P 〈 0.01 ], exceptional patients had mild abnormality and reached the normal level in about 6 months. TCD examination showed that the disease condition significantly improved and infant patients with HIE basically recovered 1 or 2 months after birth, while CT examination showed that infant patients recovered 3 or 4 months after birth. （2） Comparison of detection results of infant patients with moderate HIE at different time points between BEAM, TCD and CT examinations： The abnormal rate of BEAM examination was significantly higher than that of CT examination 1,3,6 and 12 months after birth [90.8% （178/196）,78.6% （154/196）,x^2=4.32,P 〈 0.05;64.3% （126/196）,43.9% （86/196） ,x^2=16.44 ;44.9% （88/196） ,22.4% （44/196）,x^2=22.11 ;21.4% （42/196）, 10.2% （20/196）,x^2=9.27, P 〈 0.01]. BEAM examination showed that there was still one patient who did not completely recovered in the 24^th month due to the relatives of infant patients did not combine the treatment,. TCD examination showed that the abnormal rate was 23.1%（30/196）in the 1^st month after birth, and all the patients recovered to the normal in the 3^rd month after birth, while CT examination showed that mild abnormality still existed in the 24^th month after birth （1.0% ,2/196）. （3） Comparison of detection results of infant patients with severe HIE at different time points between BEAM, TCD and CT examinations： The abnormal rate of BEAM examination was significantly higher than that of CT examination in the 1^st, 3^rd, 6^th and 12^th months after birth[86.7% （78/90）,44.4% （40/90）,x^2=35.53;62.2% （56/90）,31.1% （28/90）,x^2=17.51 ;37.8% （34/90）,6.7% （6/90）, x^2=27.14, P 〈 0.01]. BEAM examination showed that mild abnormality still existed in 4 infant patients in the 24^th month after birth. TCD examination showed that the abnormal rate was 11.1% （10/90） in the 3^rd month after birth, and all the infant patients recovered in the 6^th month after birth. CT examination showed that the abnormal rate was 6.7%（6/90） in the 12^th month after birth, and all of infant patients recovered to the normal in the 24^th month after birth.CONCLUSION ： BEAM is the direct index to detect brain function of infant patients with HIE, and positive reaction is still very sensitive in the tracking detection of convalescent period. The positive rate of morphological reaction in CT examination is superior to that in TCD examination, and the positive rate is very high in the acute period of HIE in examination.
