Bipolar disorder is a neurological disorder that consists of two main factors,i.e.mania and depression.There are two main drawbacks in clinical diagnosis of the bipolar disorder.First,bipolar disorder is mostly wrongl...Bipolar disorder is a neurological disorder that consists of two main factors,i.e.mania and depression.There are two main drawbacks in clinical diagnosis of the bipolar disorder.First,bipolar disorder is mostly wrongly diagnosed as unipolar depression in clinical diagnosis.This is,because in clinical diagnosis,the first factor is often neglected due to its approach toward positivity.Consequently,the element of bipolarity vanishes and the disease becomes worse.Second,the types of bipolhr disorder are mostly misdiagnosed due to similar symptoms.To overcome these problems,the bipolar fuzzy soft set(BFS-set)and bipolar fuzzy soft mappings(BFS-mappings)are useful to tackle bipolarity and to construct a strong mathematical modeling process to diagnose this disease correctly.This technique is extensive but simple as compared to existing medical diagnosis methods.A chart(relation between different types and symptoms of bipolar disorder)is provided which contains different ranges over the interval[-1,1].A process of BFS-mappings is also provided to obtain correct diagnosis and to suggest the best treatment.Lastly,a generalized BFS-mapping is introduced which is helpful to keep patient's improvement record.The case study indicates the reliability,efficiency and capability of the achieved theoretical results.Further,it reveals that the connection of soft set with bipolar fuzzy set is fruitful to construct a connection between symptoms which minimize the complexity of the case study.展开更多
Let G be a bounded open set on the complex plane, we denote by La2(G) the totality of all analytic functions on G which is square intergrable with respect to Lebesgue measure dA on G. It’s clear that La2(G) is a Hilb...Let G be a bounded open set on the complex plane, we denote by La2(G) the totality of all analytic functions on G which is square intergrable with respect to Lebesgue measure dA on G. It’s clear that La2(G) is a Hilbert space when endowed with norm ‖f‖=(∫G|f|2dA)1/2. The bounded operator S on La2(G) which is multiplication by z will be callde Bergman operator on G. For Bergman operators we have the following properties ([1], [4]):展开更多
Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contain...Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.展开更多
文摘Bipolar disorder is a neurological disorder that consists of two main factors,i.e.mania and depression.There are two main drawbacks in clinical diagnosis of the bipolar disorder.First,bipolar disorder is mostly wrongly diagnosed as unipolar depression in clinical diagnosis.This is,because in clinical diagnosis,the first factor is often neglected due to its approach toward positivity.Consequently,the element of bipolarity vanishes and the disease becomes worse.Second,the types of bipolhr disorder are mostly misdiagnosed due to similar symptoms.To overcome these problems,the bipolar fuzzy soft set(BFS-set)and bipolar fuzzy soft mappings(BFS-mappings)are useful to tackle bipolarity and to construct a strong mathematical modeling process to diagnose this disease correctly.This technique is extensive but simple as compared to existing medical diagnosis methods.A chart(relation between different types and symptoms of bipolar disorder)is provided which contains different ranges over the interval[-1,1].A process of BFS-mappings is also provided to obtain correct diagnosis and to suggest the best treatment.Lastly,a generalized BFS-mapping is introduced which is helpful to keep patient's improvement record.The case study indicates the reliability,efficiency and capability of the achieved theoretical results.Further,it reveals that the connection of soft set with bipolar fuzzy set is fruitful to construct a connection between symptoms which minimize the complexity of the case study.
文摘Let G be a bounded open set on the complex plane, we denote by La2(G) the totality of all analytic functions on G which is square intergrable with respect to Lebesgue measure dA on G. It’s clear that La2(G) is a Hilbert space when endowed with norm ‖f‖=(∫G|f|2dA)1/2. The bounded operator S on La2(G) which is multiplication by z will be callde Bergman operator on G. For Bergman operators we have the following properties ([1], [4]):
基金Supported by the Science and Technology Foundation of Educational Committee of Tianjin (Grant No 20060402)
文摘Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.
