Let{X,Xn;n≥1} be a sequence of i,i.d, random variables, E X = 0, E X^2 = σ^2 〈 ∞.Set Sn=X1＋X2＋…＋Xn,Mn=max k≤n│Sk│,n≥1.Let an=O（1/loglogn）.In this paper,we prove that,for b〉-1,lim ε→0 →^2（b＋1）∑n=1...Let{X,Xn;n≥1} be a sequence of i,i.d, random variables, E X = 0, E X^2 = σ^2 〈 ∞.Set Sn=X1＋X2＋…＋Xn,Mn=max k≤n│Sk│,n≥1.Let an=O（1/loglogn）.In this paper,we prove that,for b〉-1,lim ε→0 →^2（b＋1）∑n=1^∞ （loglogn）^b/nlogn n^1/2 E{Mn-σ（ε＋an）√2nloglogn}＋σ2^-b/（b＋1）（2b＋3）E│N│^2b＋3∑k=0^∞ （-1）k/（2k＋1）^2b＋3 holds if and only if EX=0 and EX^2=σ^2〈∞.展开更多
设{X,Xn,n≥1}是独立同分布正态随机变量序列,EX=0且EX2=σ2>0,Sn=sum (Xk) form k=1 to n,λ(ε) =sum form (P(|Sn|≥ nε)) form n=1 to ∞.在本文中,我们证明了存在正常数C1和C2,使得对足够小的ε>0,成立下列不等式C1ε3 ≤ε...设{X,Xn,n≥1}是独立同分布正态随机变量序列,EX=0且EX2=σ2>0,Sn=sum (Xk) form k=1 to n,λ(ε) =sum form (P(|Sn|≥ nε)) form n=1 to ∞.在本文中,我们证明了存在正常数C1和C2,使得对足够小的ε>0,成立下列不等式C1ε3 ≤ε2λ(ε)-σ2+ε2 /2 ≤ C2ε3.展开更多
Type 1 diabetes is classically the true form of insulinopaenic diabetes usually occurring in young children below the age of 15 years and occasionally up to 20 years and characterised by very low/ negligible fasting C...Type 1 diabetes is classically the true form of insulinopaenic diabetes usually occurring in young children below the age of 15 years and occasionally up to 20 years and characterised by very low/ negligible fasting C-peptide in their blood due to extensive irreversible Beta cell damage. T1DM probably accounts for 5% to 10% of all diagnosed diabetes. The worldwide prevalence of T1DM is 0.1% to 0.3%, with 78,000 new cases every year, especially among young individuals (15. Type I diabetes is very much lower (20 times) in countries like Japan and India, than the western countries. The European Nicotinamide Diabetes Intervention Trial (ENDIT) is focused on the use of nicotinamide in the prevention of diabetes. In high doses (nicotinamide), it may cause a degree of sedation, a feeling of depression, and in very large dosages, liver toxicity. Because the vitamin cannot be marketed as a drug, the study is not getting a great deal of support from pharmaceutical companies. GAD antibodies (GADA) are a major diagnostic marker for Type 1 diabetes. Phase II clinical trials of a vaccine containing alum and recombinant GAD65, an auto antigen involved in type 1 diabetes, were promising, as of 2014 Phase III trial had failed. In our quest for improving the clinical condition & quality of life of type I DM & also to reduce the economic burden on them, we have embarked on a novel metaphysical energy therapy which we have been trying for the past 3 years at our research Centre. We have so far treated some 15 cases with this DAMM therapy. Among the 15 cases, 6 cases have shown significant improvement in fasting C-peptide levels. With the advent of this new modality of treatment (DAMM Therapy) the cost of treatment will be greatly reduced. This DAMM Therapy apparently has no side effects. This mode of treatment will open a new light in the world of Type I diabetes.展开更多
基金Research supported by National Nature Science Foundation of China:10471126
文摘Let{X,Xn;n≥1} be a sequence of i,i.d, random variables, E X = 0, E X^2 = σ^2 〈 ∞.Set Sn=X1＋X2＋…＋Xn,Mn=max k≤n│Sk│,n≥1.Let an=O（1/loglogn）.In this paper,we prove that,for b〉-1,lim ε→0 →^2（b＋1）∑n=1^∞ （loglogn）^b/nlogn n^1/2 E{Mn-σ（ε＋an）√2nloglogn}＋σ2^-b/（b＋1）（2b＋3）E│N│^2b＋3∑k=0^∞ （-1）k/（2k＋1）^2b＋3 holds if and only if EX=0 and EX^2=σ^2〈∞.
文摘设{X,Xn,n≥1}是独立同分布正态随机变量序列,EX=0且EX2=σ2>0,Sn=sum (Xk) form k=1 to n,λ(ε) =sum form (P(|Sn|≥ nε)) form n=1 to ∞.在本文中,我们证明了存在正常数C1和C2,使得对足够小的ε>0,成立下列不等式C1ε3 ≤ε2λ(ε)-σ2+ε2 /2 ≤ C2ε3.
文摘Type 1 diabetes is classically the true form of insulinopaenic diabetes usually occurring in young children below the age of 15 years and occasionally up to 20 years and characterised by very low/ negligible fasting C-peptide in their blood due to extensive irreversible Beta cell damage. T1DM probably accounts for 5% to 10% of all diagnosed diabetes. The worldwide prevalence of T1DM is 0.1% to 0.3%, with 78,000 new cases every year, especially among young individuals (15. Type I diabetes is very much lower (20 times) in countries like Japan and India, than the western countries. The European Nicotinamide Diabetes Intervention Trial (ENDIT) is focused on the use of nicotinamide in the prevention of diabetes. In high doses (nicotinamide), it may cause a degree of sedation, a feeling of depression, and in very large dosages, liver toxicity. Because the vitamin cannot be marketed as a drug, the study is not getting a great deal of support from pharmaceutical companies. GAD antibodies (GADA) are a major diagnostic marker for Type 1 diabetes. Phase II clinical trials of a vaccine containing alum and recombinant GAD65, an auto antigen involved in type 1 diabetes, were promising, as of 2014 Phase III trial had failed. In our quest for improving the clinical condition & quality of life of type I DM & also to reduce the economic burden on them, we have embarked on a novel metaphysical energy therapy which we have been trying for the past 3 years at our research Centre. We have so far treated some 15 cases with this DAMM therapy. Among the 15 cases, 6 cases have shown significant improvement in fasting C-peptide levels. With the advent of this new modality of treatment (DAMM Therapy) the cost of treatment will be greatly reduced. This DAMM Therapy apparently has no side effects. This mode of treatment will open a new light in the world of Type I diabetes.
