In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with...In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.展开更多
In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix eleme...In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.展开更多
A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided differenc...A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works.展开更多
Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike （non-diagonal case） and Kramers＇ （diagonal case） recurrence relations for arbitrary x^k which is independen...Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike （non-diagonal case） and Kramers＇ （diagonal case） recurrence relations for arbitrary x^k which is independent of the central potential V（x）. Some significant results in diagonal case are obtained for special k in xk （k ≥2）. In particular, we find the orthogonal relation 〈n1｜n2〉 = δh1,n2 （k = 0）, 〈n1[V＇（x）｜n2〉 = （En1-En2）^2〈n1｜x｜n2〉 （k = 1）, En = （n｜V＇（x）x/2｜n〉 ＋ （n｜V（x）｜n〉 （k = 2） and -4En（n｜x｜n） ~ 〈n｜V＇（x）x^2｜n〉 ＋ 4〈n｜V（x）x｜n〉 =0 （k=3）. The latter two formulas can be used directly to calculate the energy levels. We present useYul explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.展开更多
In this paper,we present the formula of a solution for a class of recurrence relations with two indices by applying iteration and induction according to the principle of solving algebraic equa-tions.It provides a conc...In this paper,we present the formula of a solution for a class of recurrence relations with two indices by applying iteration and induction according to the principle of solving algebraic equa-tions.It provides a concrete model to solve the concerned prob-lems with modern computing tools.展开更多
AIMTo characterize temporal pattern of resolution and recurrence of naive choroidal neovascularization (CNV) secondary to wet age-related macular degeneration (AMD) treated with intravitreal bevacizumab on as needed r...AIMTo characterize temporal pattern of resolution and recurrence of naive choroidal neovascularization (CNV) secondary to wet age-related macular degeneration (AMD) treated with intravitreal bevacizumab on as needed regimen, and to analyze baseline risk factors for CNV resolution or recurrence.展开更多
In this paper, the 231 earthquake data of magnitude 5 and higher, between north (39.00o-42.00o) and east (26.00o-45.00o) coordinates in Turkey from July 12, 1900 to October 23, 2011 are statistically analyzed. The pro...In this paper, the 231 earthquake data of magnitude 5 and higher, between north (39.00o-42.00o) and east (26.00o-45.00o) coordinates in Turkey from July 12, 1900 to October 23, 2011 are statistically analyzed. The probability density function and cumulative function of the magnitude are derived. It is shown that magnitude random variable is distrib-uted as the exponential distribution. The recurrence periods is also calculated. Recurrence period is estimatedapproxi-matelytwo times a year for an earthquake having magnitude 5.2. Using the Gutenberg-Richter function, the relation between magnitude and frequency is represented.展开更多
Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,f...Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,for example,time to failure of a computer system.The computation of these moments is sometimes very tedious and hence some algorithms are required.One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments.Generalized order statistics pro-vides several models of ordered data as a special case.The moments of general-ized order statistics also provide moments of order statistics and record values as a special case.In this research,the recurrence relations for single,product,inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution.These relations will be helpful for obtained moments of gen-eralized order statistics from Lindley–Weibull distribution recursively.Special cases of the recurrence relations will also be obtained.Some characterizations of the distribution will also be obtained by using moments of generalized order statistics.These relations for moments and characterizations can be used in differ-ent areas of computer sciences where data is arranged in increasing order.展开更多
AIM： To analyze, retrospectively in a populationbased study, the management and survival of patients with recurrent rectal cancer initially treated with a macroscopically radical resection obtained with total mesorec...AIM： To analyze, retrospectively in a populationbased study, the management and survival of patients with recurrent rectal cancer initially treated with a macroscopically radical resection obtained with total mesorectal excision （TME）. METHODS： All rectal carcinomas diagnosed during 1998 to 2000 and initially treated with a macroscopically radical resection （632 patients） were selected from the Amsterdam Cancer Registry. For patients with recurrent disease, information on treatment of the recurrence was collected from the medical records. RESULTS： Local recurrence with or without clinically apparent distant dissemination occurred in 62 patients （10%）. Thirty-two patients had an isolated local recurrence. Ten of these 32 patients （31%） underwent radical re-resection and experienced the highest survival （three quarters survived for at least 3 years）. Eight patients （25%） underwent non-radical surgery （median survival 24 rno）, seven patients （22%） were treated with radio- and/or chemotherapy without surgery （median survival 15 mo） and seven patients （22%） only received best supportive care （median survival 5 too）. Distant dissemination occurred in 124 patients （20%） of whom 30 patients also had a local recurrence. The majority （54%） of these patients were treated with radio- and/or chemotherapy without surgery （median survival 15 mo）. Twenty-seven percent of these patients only received best supportive care （median survival 6 mo）, while 16% underwent surgery for their recurrence. Survival was best in the latter group （median survival 32 mo）. CONCLUSION： Although treatment options and survival are limited in case of recurrent rectal cancer after radical local resection obtained with TME, patients can benefit from additional treatment, especially if a radical resection is feasible.展开更多
Background Recurrence of takotsubo cardiomyopathy （TTC） is a well-known complication. However, current literature lists only a few isolated cases. We aimed to determine the incidence and clinical significance of rec...Background Recurrence of takotsubo cardiomyopathy （TTC） is a well-known complication. However, current literature lists only a few isolated cases. We aimed to determine the incidence and clinical significance of recurrent TTC. Methods ＆ Results Our institutional database constituted a collective of 114 patients diagnosed with TTC since 2003. Close follow-up of these patients revealed a recurrence of TTC in seven of these （6.1%）. The time interval between the index event and its recurrence varied between six months and six years. Arterial hypertension was more revealed in the recurrence group of TTC compared to non-recurrence group, （P = 0.02）. Chronic obstructive pulmo- nary disease and/or asthma was more diagnosed in the recurrence group, （P = 0.04）. Clinical events like fight ventficular involvement, TTC related complications such as life-threatening arrhythmias, pulmonary congestion and in hospital death were observed more frequently in the recurrent episode. Over a mean follow-up of one year the mortality rate was similar in both groups. Conclusions Recurrence of TTC within six years after index event is not an uncommon phenomenon. In the event of right ventricular involvement in the relapse phase, it might be associated with a higher complication rate. TTC recurrence should be the first differential diagnosis in patients with a past history of TTC.展开更多
AIM： To investigate clinicopathological features of immunoglobulin G4-related ophthalmic disease（IgG4-ROD）, and analyze the recurrence rates following systemic corticosteroid administration.METHODS： We retrospecti...AIM： To investigate clinicopathological features of immunoglobulin G4-related ophthalmic disease（IgG4-ROD）, and analyze the recurrence rates following systemic corticosteroid administration.METHODS： We retrospectively searched clinical features, laboratory and histological findings based on the medical records of 21 patients with IgG4-ROD. All the patients examined in this study underwent surgical resection in the ocular adnexal lesions and underwent histological evaluation. This study further investigated clinical and histopathological features of 15 patients who received systemic corticosteroid after the resection.RESULTS： The mean age of the patients consisting of 7 males（33%） and 14 females（67%） was 61y. Fourteen patients were diagnosed as definitive, and 2 and 5 patients were probable and possible IgG4-ROD, respectively. Eyelid swelling was an initial symptom in 11 patients（52%） who did not show systemic involvements at a diagnosis. Fifteen patients received systemic corticosteroid administration, and all showed remission of inflammation. Among them, 10 patients did not recur, whereas 5 patients（33%） recurred during tapering. There were no significant difference between patients with or without recurrence in clinicopathological features.CONCLUSION： In this study, female patients are more predominant in IgG4-ROD. While inflammation recurs in one-third of patients, this study do not identify factors associated with recurrence after systemic corticosteroid administration.展开更多
For decades, kidney diseases related to inappropriate complement activity, such as atypical hemolytic uremic syndrome and C3 glomerulopathy(a subtype of membranoproliferative glomerulonephritis), have mostly been comp...For decades, kidney diseases related to inappropriate complement activity, such as atypical hemolytic uremic syndrome and C3 glomerulopathy(a subtype of membranoproliferative glomerulonephritis), have mostly been complicated by worsened prognoses and rapid progression to end-stage renal failure. Alternative complement pathway dysregulation, whether congenital or acquired, is well-recognized as the main driver of the disease process in these patients. The list of triggers include: surgery, infection, immunologic factors, pregnancy and medications. The advent of complement activation blockade, however, revolutionized the clinical course and outcome of these diseases, rendering transplantation a viable option for patients who were previously considered as non-transplantable cases.Several less-costly therapeutic lines and likely better efficacy and safety profiles are currently underway. In view of the challenging nature of diagnosing these diseases and the long-term cost implications, a multidisciplinary approach including the nephrologist, renal pathologist and the genetic laboratory is required to help improve overall care of these patients and draw the optimum therapeutic plan.展开更多
文摘In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.
文摘In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.
基金Supported by the National Natural Science Foundation of China (10871178)the Natural Science Foundation of Zhejiang Province of China (Y606154)Foundation of the Education Department of Zhejiang Province of China (20071362)
文摘A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works.
基金Supported in part by Project 20150964-SIP-IPN,COFAA-IPN,Mexico
文摘Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike （non-diagonal case） and Kramers＇ （diagonal case） recurrence relations for arbitrary x^k which is independent of the central potential V（x）. Some significant results in diagonal case are obtained for special k in xk （k ≥2）. In particular, we find the orthogonal relation 〈n1｜n2〉 = δh1,n2 （k = 0）, 〈n1[V＇（x）｜n2〉 = （En1-En2）^2〈n1｜x｜n2〉 （k = 1）, En = （n｜V＇（x）x/2｜n〉 ＋ （n｜V（x）｜n〉 （k = 2） and -4En（n｜x｜n） ~ 〈n｜V＇（x）x^2｜n〉 ＋ 4〈n｜V（x）x｜n〉 =0 （k=3）. The latter two formulas can be used directly to calculate the energy levels. We present useYul explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.
基金Supported by the National Natural Science Foundation of China(70871094)
文摘In this paper,we present the formula of a solution for a class of recurrence relations with two indices by applying iteration and induction according to the principle of solving algebraic equa-tions.It provides a concrete model to solve the concerned prob-lems with modern computing tools.
基金NIH grants R01EY007366 and R01EY018589(WRF),R01EY020617(LC)"RPB incorporated and unrestricted funds from Jacobs Retina Center"
文摘AIMTo characterize temporal pattern of resolution and recurrence of naive choroidal neovascularization (CNV) secondary to wet age-related macular degeneration (AMD) treated with intravitreal bevacizumab on as needed regimen, and to analyze baseline risk factors for CNV resolution or recurrence.
文摘In this paper, the 231 earthquake data of magnitude 5 and higher, between north (39.00o-42.00o) and east (26.00o-45.00o) coordinates in Turkey from July 12, 1900 to October 23, 2011 are statistically analyzed. The probability density function and cumulative function of the magnitude are derived. It is shown that magnitude random variable is distrib-uted as the exponential distribution. The recurrence periods is also calculated. Recurrence period is estimatedapproxi-matelytwo times a year for an earthquake having magnitude 5.2. Using the Gutenberg-Richter function, the relation between magnitude and frequency is represented.
基金The work was funded by the University of Jeddah,Saudi Arabia under Grant Number UJ–02–093–DR.The authors,therefore,acknowledge with thanks the University for technical and financial support.
文摘Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,for example,time to failure of a computer system.The computation of these moments is sometimes very tedious and hence some algorithms are required.One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments.Generalized order statistics pro-vides several models of ordered data as a special case.The moments of general-ized order statistics also provide moments of order statistics and record values as a special case.In this research,the recurrence relations for single,product,inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution.These relations will be helpful for obtained moments of gen-eralized order statistics from Lindley–Weibull distribution recursively.Special cases of the recurrence relations will also be obtained.Some characterizations of the distribution will also be obtained by using moments of generalized order statistics.These relations for moments and characterizations can be used in differ-ent areas of computer sciences where data is arranged in increasing order.
文摘AIM： To analyze, retrospectively in a populationbased study, the management and survival of patients with recurrent rectal cancer initially treated with a macroscopically radical resection obtained with total mesorectal excision （TME）. METHODS： All rectal carcinomas diagnosed during 1998 to 2000 and initially treated with a macroscopically radical resection （632 patients） were selected from the Amsterdam Cancer Registry. For patients with recurrent disease, information on treatment of the recurrence was collected from the medical records. RESULTS： Local recurrence with or without clinically apparent distant dissemination occurred in 62 patients （10%）. Thirty-two patients had an isolated local recurrence. Ten of these 32 patients （31%） underwent radical re-resection and experienced the highest survival （three quarters survived for at least 3 years）. Eight patients （25%） underwent non-radical surgery （median survival 24 rno）, seven patients （22%） were treated with radio- and/or chemotherapy without surgery （median survival 15 mo） and seven patients （22%） only received best supportive care （median survival 5 too）. Distant dissemination occurred in 124 patients （20%） of whom 30 patients also had a local recurrence. The majority （54%） of these patients were treated with radio- and/or chemotherapy without surgery （median survival 15 mo）. Twenty-seven percent of these patients only received best supportive care （median survival 6 mo）, while 16% underwent surgery for their recurrence. Survival was best in the latter group （median survival 32 mo）. CONCLUSION： Although treatment options and survival are limited in case of recurrent rectal cancer after radical local resection obtained with TME, patients can benefit from additional treatment, especially if a radical resection is feasible.
文摘Background Recurrence of takotsubo cardiomyopathy （TTC） is a well-known complication. However, current literature lists only a few isolated cases. We aimed to determine the incidence and clinical significance of recurrent TTC. Methods ＆ Results Our institutional database constituted a collective of 114 patients diagnosed with TTC since 2003. Close follow-up of these patients revealed a recurrence of TTC in seven of these （6.1%）. The time interval between the index event and its recurrence varied between six months and six years. Arterial hypertension was more revealed in the recurrence group of TTC compared to non-recurrence group, （P = 0.02）. Chronic obstructive pulmo- nary disease and/or asthma was more diagnosed in the recurrence group, （P = 0.04）. Clinical events like fight ventficular involvement, TTC related complications such as life-threatening arrhythmias, pulmonary congestion and in hospital death were observed more frequently in the recurrent episode. Over a mean follow-up of one year the mortality rate was similar in both groups. Conclusions Recurrence of TTC within six years after index event is not an uncommon phenomenon. In the event of right ventricular involvement in the relapse phase, it might be associated with a higher complication rate. TTC recurrence should be the first differential diagnosis in patients with a past history of TTC.
文摘AIM： To investigate clinicopathological features of immunoglobulin G4-related ophthalmic disease（IgG4-ROD）, and analyze the recurrence rates following systemic corticosteroid administration.METHODS： We retrospectively searched clinical features, laboratory and histological findings based on the medical records of 21 patients with IgG4-ROD. All the patients examined in this study underwent surgical resection in the ocular adnexal lesions and underwent histological evaluation. This study further investigated clinical and histopathological features of 15 patients who received systemic corticosteroid after the resection.RESULTS： The mean age of the patients consisting of 7 males（33%） and 14 females（67%） was 61y. Fourteen patients were diagnosed as definitive, and 2 and 5 patients were probable and possible IgG4-ROD, respectively. Eyelid swelling was an initial symptom in 11 patients（52%） who did not show systemic involvements at a diagnosis. Fifteen patients received systemic corticosteroid administration, and all showed remission of inflammation. Among them, 10 patients did not recur, whereas 5 patients（33%） recurred during tapering. There were no significant difference between patients with or without recurrence in clinicopathological features.CONCLUSION： In this study, female patients are more predominant in IgG4-ROD. While inflammation recurs in one-third of patients, this study do not identify factors associated with recurrence after systemic corticosteroid administration.
文摘For decades, kidney diseases related to inappropriate complement activity, such as atypical hemolytic uremic syndrome and C3 glomerulopathy(a subtype of membranoproliferative glomerulonephritis), have mostly been complicated by worsened prognoses and rapid progression to end-stage renal failure. Alternative complement pathway dysregulation, whether congenital or acquired, is well-recognized as the main driver of the disease process in these patients. The list of triggers include: surgery, infection, immunologic factors, pregnancy and medications. The advent of complement activation blockade, however, revolutionized the clinical course and outcome of these diseases, rendering transplantation a viable option for patients who were previously considered as non-transplantable cases.Several less-costly therapeutic lines and likely better efficacy and safety profiles are currently underway. In view of the challenging nature of diagnosing these diseases and the long-term cost implications, a multidisciplinary approach including the nephrologist, renal pathologist and the genetic laboratory is required to help improve overall care of these patients and draw the optimum therapeutic plan.
