Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficie...Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.展开更多
Objective: To discuss some key points about nursing in the use of DDG-3300K liver reserve function analyzer in patients at the department of infectious diseases. Method: DDG-3300K liver reserve function analyzer was a...Objective: To discuss some key points about nursing in the use of DDG-3300K liver reserve function analyzer in patients at the department of infectious diseases. Method: DDG-3300K liver reserve function analyzer was applied to 5464 patients at the department of infectious diseases. The reasons for failed detection and complications related to the detection were analyzed, and the measures for improving the nursing procedures were proposed. Result: Among the 5464 patients, the detections were successful at the first attempt in 5458 patients;2 patients had leakage of liquid;2 patients were poorly prepared, and 1 case failed because of mistaken selection of CO mode, which led to adverse drug reactions;1 case did not finish the detection due to anaphylactic shock;8 patients had nausea and 6 patients had skin rash on the four limbs and torso during the detection. Conclusion: It is necessary to formulate the nursing procedures for the use of DDG-3300K liver reserve function analyzer. Moreover, preparatory work, health education, refined nursing procedures and skillful operations are closely related to the success rate and accuracy of the detection.展开更多
In this paper, we obtain the convexity of new general integral operator on some classes of k-uniformly p-valent a-convex functions of complex order. These results extend some known theorems.
Common wheat(Triticum aestivum L.)is the most important crop in the world and a typical allopolyploid with a large and complex genome.Pre-harvest sprouting(PHS)leads to a significant reduction in grain quality worldwi...Common wheat(Triticum aestivum L.)is the most important crop in the world and a typical allopolyploid with a large and complex genome.Pre-harvest sprouting(PHS)leads to a significant reduction in grain quality worldwide.PHS is a complex trait with related QTL located on different chromosomes.However,the study of markers and genes related to PHS resistance is limited especially for whitegrained wheat.Four pairs of near isogenic lines(NILs)from a white-grained wheat cross of CharaDM5637B*8 targeting a major QTL for PHS resistance(Qphs.ccsu-3A.1)on wheat chromosme 3AL were genotyped using the 90K SNP Illumina iSelect array.Ten SNPs were identified,with a 75%-100%consistency between genotype and phenotype in the resistant or susceptible isolines.The 10 SNPs were converted to cost-effective kompetitive allele-specific PCR(KASP)markers.Screening of 48 wheat cultivars with different phenotypes of PHS identified four KASP markers with 81.3%-85.4%conformity between genotype and phenotype.Further investigation revealed that the four SNPs(BS00022245_51,Kukri_c49927_151,BS00022884_51 and BS00110550_51)corresponding to the four validated KASP markers are residing in three independent genes(TraesCS3A03G1072800,TraesCS3A03G1072400,TraesCS3A03G1071800)close to each other with a distance of 4.28-4.48 Mb to the targeted QTL.These three annotated genes have potential functions related to PHS resistance.Our study revealed that combined use of NILs and the 90K SNP chip is a powerful approach for developing KASP markers and mining functional genes in wheat.The KASP markers for PHS resistance on chromosome 3AL are useful for high-throughput evaluation and marker-assisted selection,and the three identified genes could lead to a better understanding of the genetic pathways controlling PHS.展开更多
In this paper. we study the average n-K width of the convolution class B_(pq)(G)(or B_(?)(G)), for which the kernel G(x) is a PF density, in the metric L_q(R)(or L_(qp)(R)) for the case 1≤q<p ≤∞, and obtain some...In this paper. we study the average n-K width of the convolution class B_(pq)(G)(or B_(?)(G)), for which the kernel G(x) is a PF density, in the metric L_q(R)(or L_(qp)(R)) for the case 1≤q<p ≤∞, and obtain some exact results.展开更多
The objective of this note is to provide some(potentially useful) integral transforms(for example, Euler, Laplace, Whittaker etc.) associated with the generalized k-Bessel function defined by Saiful and Nisar [3]. We ...The objective of this note is to provide some(potentially useful) integral transforms(for example, Euler, Laplace, Whittaker etc.) associated with the generalized k-Bessel function defined by Saiful and Nisar [3]. We have also discussed some other transforms as special cases of our main results.展开更多
Drill wear not only affects the surface smoothness of the hole, but also influences the life of the drill. Drill wear state recognition is important in the manufacturing process, which consists of two steps: first, d...Drill wear not only affects the surface smoothness of the hole, but also influences the life of the drill. Drill wear state recognition is important in the manufacturing process, which consists of two steps: first, decomposing cutting torque components from the original signals by wavelet packet decomposition (WPD); second, extracting wavelet coefficients of different wear states (i.e., slight, normal, or severe wear) with signal features adapting to Welch spectrum. Finally, monitoring and recognition of the feature vectors of cutting torque signal are performed by using the K-means cluster and radial basis function neural network (RBFNN). The experiments on different tool wears of the multivariable features reveal that the results of monitoring and recognition are significant and effective.展开更多
Objective:To observe the effect of Taohong Siyu Decoction on the coagulation function and the signaling pathway of PI3K(phosphatidylinositol 3-kinase)/AKT(protein kinase B)/mTOR(mammalian target of rapamycin)after fem...Objective:To observe the effect of Taohong Siyu Decoction on the coagulation function and the signaling pathway of PI3K(phosphatidylinositol 3-kinase)/AKT(protein kinase B)/mTOR(mammalian target of rapamycin)after femoral artery anastomosis in rabbits.Methods:30 New Zealand white rabbits were divided into blank control group,model control group,papavine hydrochloride injection group and low,medium and high dose groups of Taohong Siwu decoction by random number table method,with 5 rabbits in each group.The rabbits in the model control group,papavine hydrochloride injection group and low,medium and high dose groups of Taohong Siwu decoction were treated with the femoral artery simple intermittent end-to-end suture model.After the successful modeling,the low,medium and high dose groups of Taohong Siwu decoction were given the Taohong Siwu decoction,while the model control group,the blank control group and papavine hydrochloride injection group were given the same amount of normal saline.APTT(activated partial thromboplastin time),FIB(fibrinogen)and PI3K/AKT/mTOR concentrations were measured in aural venous blood samples from six groups of rabbits 30min before operation and 1d,2D,3D and 7d after operation,respectively.Statistical analysis was conducted on the data of the six groups.Results:Compared with blank control group,APTT of model control group was significantly shortened 1d to 7d after operation(P<0.05),FIB values were significantly increased from 1d to 7d after operation(P<0.05);Compared with model control group,APTT in Taohong Siwu decoction low-dose,medium-dose and high-dose groups were significantly prolonged 1d to 7d after operation(P<0.05),FIB value of Taohong Siwu decoction medium and high dose groups decreased significantly from 1d to 7d after operation(P<0.05),the FIB value of Taohong Siwu decoction low-dose group was significantly decreased from 2d to 7d after surgery(P<0.05);Compared with papaverine hydrochloride injection group,APTT in Taohong Siwu decoction medium dose group was significantly prolonged 2d to 7d after surgery(P<0.05),APTT of Taohong Siwu decoction high-dose group was significantly prolonged on 1d to 7d after operation(P<0.05).FIB in Taohong Siwu decoction medium and high dose groups decreased significantly 1d to 7d after operation(P<0.05);Compared with the blank control group,the expression concentrations of PI3K,Akt and mTOR in serum of the model control group were significantly increased from 1d to 7d after surgery(P<0.05);Compared with the model control group,the expression levels of PI3K,Akt and mTOR in serum were significantly increased in the low dose group of Taohong Siwu decoction and Papaverine Hydrochloride Injection group on postoperative 7 days(P<0.05),Taohong Siwu decoction high-dose group was significantly increased from 1d to 7d after surgery(P<0.05),the expression concentrations of PI3K and Akt in Taohong Siwu decoction medium dose group were significantly increased from 2d to 7d after operation(P<0.05),mTOR expression levels were significantly increased from 3d to 7d after operation(P<0.05);Compared with papaverine hydrochloride injection group,the expression concentrations of PI3K,Akt and mTOR in serum of Taohong Siwu decoction medium dose group were significantly increased from 3d to 7d after operation(P<0.05),the expression concentrations of PI3K and mTOR in Taohong Siwu decoction high-dose group were significantly increased from 1d to 7d after operation(P<0.05),and the expression concentration of Akt increased significantly from 3d to 7d after operation(P<0.05).Conclusion:The Taohong Siwu decoction can improve the coagulation function of rabbit femoral artery anastomosis,prevent thrombosis,activate PI3K/Akt/mTOR signaling pathway,promote angiogenesis,and improve tissue ischemia after artery anastomosis.展开更多
Different technical conditions in the process of solid-state fermentation of red yeast rice has a certain impact on the production of acid-form and lactone form Monacolin K.When cultured in the loose rice medium,the a...Different technical conditions in the process of solid-state fermentation of red yeast rice has a certain impact on the production of acid-form and lactone form Monacolin K.When cultured in the loose rice medium,the acid form Monacolin K accounts for 50%-60%;while the acid form Monacolin K accounts for 80%-90%cultured in the consolidated rice medium.And we also found that the proportion of the acid form and lactone form Monacolin K will decrease with the increase of fermentation time.展开更多
We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-function...We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-functional. We also prove Jackson’s inequality for the approximation by trigonometric polynomials.展开更多
In this paper, we prove an analogous to a result of Erdös and Rényi and of Kelly and Oxley. We also show that there are several properties of k-balanced matroids for which there exists a threshold function.
k holomorphic functions are a type of generation of holomorphic functions.In this paper,a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in C^(2).The e...k holomorphic functions are a type of generation of holomorphic functions.In this paper,a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in C^(2).The existence of the solution for the problem is studied in detail with the help of the boundary properties of Cauchy type singular integral operators with a k holomorphic kernel.Furthermore,the integral representation for the solution is obtained.展开更多
The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><i></i></span><i><span><span><i><span style="...The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><i></i></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;">-variate survival functions for arbitrary </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2, 3, </span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">...</span><span style="font-family:Verdana;">, given all the univariate marginal survival functions. This universal form of </span></span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;">-variate probability distributions was obtained by means of “dependence functions” named “joiners” in the text. These joiners determine all the involved stochastic dependencies between the underlying random variables. However, in order that the presented formula (the form) represents a legitimate survival function, some necessary and sufficient conditions for the joiners had to be found. Basically, finding those conditions is the main task of this paper. This task was successfully performed for the case </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;"> = 2 and the main results for the case </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;"> = 3 were formulated as Theorem 1 and Theorem 2 in Section 4. Nevertheless, the hypothetical conditions valid for the general </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;"> ≥ 4 case were also formulated in Section 3 as the (very convincing) Hypothesis. As for the sufficient conditions for both the </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;"> = 3 and</span><i> </i></span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;"> ≥ 4 cases, the full generality was not achieved since two restrictions were imposed. Firstly, we limited ourselves to the, defined in the text, “continuous cases” (when the corresponding joint density exists and is continuous), and secondly we consider positive stochastic dependencies only. Nevertheless, the class of the </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;">-variate distributions which can be constructed is very wide. The presented method of construction by means of joiners can be considered competitive to the </span><span style="font-family:Verdana;"><strong></strong></span></span></span><strong><span><span><b><span style="font-family:Verdana;">copula</span></b><span style="font-family:Verdana;"></span></span></span></strong><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> methodology. As it is suggested in the paper the possibility of building a common theory of both copulae and joiners is quite possible, and the joiners may play the role of tools within the theory of copulae, and vice versa copulae may, for example, be used for finding proper joiners. Another independent feature of the joiners methodology is the possibility of constructing many new stochastic processes including stationary and Markovian.</span></span></span>展开更多
Utilization of the shift operator to represent Euler polynomials as polynomials of Appell type leads directly to its algebraic properties, its relations with powers sums;may be all its relations with Bernoulli polynom...Utilization of the shift operator to represent Euler polynomials as polynomials of Appell type leads directly to its algebraic properties, its relations with powers sums;may be all its relations with Bernoulli polynomials, Bernoulli numbers;its recurrence formulae and a very simple formula for calculating simultaneously Euler numbers and Euler polynomials. The expansions of Euler polynomials into Fourier series are also obtained;the formulae for obtaining all π<sup>m</sup> as series on k<sup>-m</sup> and for expanding functions into series of Euler polynomials.展开更多
文摘Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.
文摘Objective: To discuss some key points about nursing in the use of DDG-3300K liver reserve function analyzer in patients at the department of infectious diseases. Method: DDG-3300K liver reserve function analyzer was applied to 5464 patients at the department of infectious diseases. The reasons for failed detection and complications related to the detection were analyzed, and the measures for improving the nursing procedures were proposed. Result: Among the 5464 patients, the detections were successful at the first attempt in 5458 patients;2 patients had leakage of liquid;2 patients were poorly prepared, and 1 case failed because of mistaken selection of CO mode, which led to adverse drug reactions;1 case did not finish the detection due to anaphylactic shock;8 patients had nausea and 6 patients had skin rash on the four limbs and torso during the detection. Conclusion: It is necessary to formulate the nursing procedures for the use of DDG-3300K liver reserve function analyzer. Moreover, preparatory work, health education, refined nursing procedures and skillful operations are closely related to the success rate and accuracy of the detection.
基金Foundation item: Supported by the Natural Science Foundation of Inner Mongolia(2009MS0113) Sup- ported by the Higher School Research Foundation of Inner Mongolia(NJzy08150)
文摘In this paper, we obtain the convexity of new general integral operator on some classes of k-uniformly p-valent a-convex functions of complex order. These results extend some known theorems.
基金funded by Global Innovation Linkage program (GIL53853) from Australian Department of Industry, Science, Energy and ResourcesAustralian Government RTP Scholarship (International)University Postgraduate Awards (UPA)
文摘Common wheat(Triticum aestivum L.)is the most important crop in the world and a typical allopolyploid with a large and complex genome.Pre-harvest sprouting(PHS)leads to a significant reduction in grain quality worldwide.PHS is a complex trait with related QTL located on different chromosomes.However,the study of markers and genes related to PHS resistance is limited especially for whitegrained wheat.Four pairs of near isogenic lines(NILs)from a white-grained wheat cross of CharaDM5637B*8 targeting a major QTL for PHS resistance(Qphs.ccsu-3A.1)on wheat chromosme 3AL were genotyped using the 90K SNP Illumina iSelect array.Ten SNPs were identified,with a 75%-100%consistency between genotype and phenotype in the resistant or susceptible isolines.The 10 SNPs were converted to cost-effective kompetitive allele-specific PCR(KASP)markers.Screening of 48 wheat cultivars with different phenotypes of PHS identified four KASP markers with 81.3%-85.4%conformity between genotype and phenotype.Further investigation revealed that the four SNPs(BS00022245_51,Kukri_c49927_151,BS00022884_51 and BS00110550_51)corresponding to the four validated KASP markers are residing in three independent genes(TraesCS3A03G1072800,TraesCS3A03G1072400,TraesCS3A03G1071800)close to each other with a distance of 4.28-4.48 Mb to the targeted QTL.These three annotated genes have potential functions related to PHS resistance.Our study revealed that combined use of NILs and the 90K SNP chip is a powerful approach for developing KASP markers and mining functional genes in wheat.The KASP markers for PHS resistance on chromosome 3AL are useful for high-throughput evaluation and marker-assisted selection,and the three identified genes could lead to a better understanding of the genetic pathways controlling PHS.
基金The author was supported by the National Natural Science Found of China.
文摘In this paper. we study the average n-K width of the convolution class B_(pq)(G)(or B_(?)(G)), for which the kernel G(x) is a PF density, in the metric L_q(R)(or L_(qp)(R)) for the case 1≤q<p ≤∞, and obtain some exact results.
文摘The objective of this note is to provide some(potentially useful) integral transforms(for example, Euler, Laplace, Whittaker etc.) associated with the generalized k-Bessel function defined by Saiful and Nisar [3]. We have also discussed some other transforms as special cases of our main results.
文摘Drill wear not only affects the surface smoothness of the hole, but also influences the life of the drill. Drill wear state recognition is important in the manufacturing process, which consists of two steps: first, decomposing cutting torque components from the original signals by wavelet packet decomposition (WPD); second, extracting wavelet coefficients of different wear states (i.e., slight, normal, or severe wear) with signal features adapting to Welch spectrum. Finally, monitoring and recognition of the feature vectors of cutting torque signal are performed by using the K-means cluster and radial basis function neural network (RBFNN). The experiments on different tool wears of the multivariable features reveal that the results of monitoring and recognition are significant and effective.
文摘Objective:To observe the effect of Taohong Siyu Decoction on the coagulation function and the signaling pathway of PI3K(phosphatidylinositol 3-kinase)/AKT(protein kinase B)/mTOR(mammalian target of rapamycin)after femoral artery anastomosis in rabbits.Methods:30 New Zealand white rabbits were divided into blank control group,model control group,papavine hydrochloride injection group and low,medium and high dose groups of Taohong Siwu decoction by random number table method,with 5 rabbits in each group.The rabbits in the model control group,papavine hydrochloride injection group and low,medium and high dose groups of Taohong Siwu decoction were treated with the femoral artery simple intermittent end-to-end suture model.After the successful modeling,the low,medium and high dose groups of Taohong Siwu decoction were given the Taohong Siwu decoction,while the model control group,the blank control group and papavine hydrochloride injection group were given the same amount of normal saline.APTT(activated partial thromboplastin time),FIB(fibrinogen)and PI3K/AKT/mTOR concentrations were measured in aural venous blood samples from six groups of rabbits 30min before operation and 1d,2D,3D and 7d after operation,respectively.Statistical analysis was conducted on the data of the six groups.Results:Compared with blank control group,APTT of model control group was significantly shortened 1d to 7d after operation(P<0.05),FIB values were significantly increased from 1d to 7d after operation(P<0.05);Compared with model control group,APTT in Taohong Siwu decoction low-dose,medium-dose and high-dose groups were significantly prolonged 1d to 7d after operation(P<0.05),FIB value of Taohong Siwu decoction medium and high dose groups decreased significantly from 1d to 7d after operation(P<0.05),the FIB value of Taohong Siwu decoction low-dose group was significantly decreased from 2d to 7d after surgery(P<0.05);Compared with papaverine hydrochloride injection group,APTT in Taohong Siwu decoction medium dose group was significantly prolonged 2d to 7d after surgery(P<0.05),APTT of Taohong Siwu decoction high-dose group was significantly prolonged on 1d to 7d after operation(P<0.05).FIB in Taohong Siwu decoction medium and high dose groups decreased significantly 1d to 7d after operation(P<0.05);Compared with the blank control group,the expression concentrations of PI3K,Akt and mTOR in serum of the model control group were significantly increased from 1d to 7d after surgery(P<0.05);Compared with the model control group,the expression levels of PI3K,Akt and mTOR in serum were significantly increased in the low dose group of Taohong Siwu decoction and Papaverine Hydrochloride Injection group on postoperative 7 days(P<0.05),Taohong Siwu decoction high-dose group was significantly increased from 1d to 7d after surgery(P<0.05),the expression concentrations of PI3K and Akt in Taohong Siwu decoction medium dose group were significantly increased from 2d to 7d after operation(P<0.05),mTOR expression levels were significantly increased from 3d to 7d after operation(P<0.05);Compared with papaverine hydrochloride injection group,the expression concentrations of PI3K,Akt and mTOR in serum of Taohong Siwu decoction medium dose group were significantly increased from 3d to 7d after operation(P<0.05),the expression concentrations of PI3K and mTOR in Taohong Siwu decoction high-dose group were significantly increased from 1d to 7d after operation(P<0.05),and the expression concentration of Akt increased significantly from 3d to 7d after operation(P<0.05).Conclusion:The Taohong Siwu decoction can improve the coagulation function of rabbit femoral artery anastomosis,prevent thrombosis,activate PI3K/Akt/mTOR signaling pathway,promote angiogenesis,and improve tissue ischemia after artery anastomosis.
文摘Different technical conditions in the process of solid-state fermentation of red yeast rice has a certain impact on the production of acid-form and lactone form Monacolin K.When cultured in the loose rice medium,the acid form Monacolin K accounts for 50%-60%;while the acid form Monacolin K accounts for 80%-90%cultured in the consolidated rice medium.And we also found that the proportion of the acid form and lactone form Monacolin K will decrease with the increase of fermentation time.
文摘We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-functional. We also prove Jackson’s inequality for the approximation by trigonometric polynomials.
文摘In this paper, we prove an analogous to a result of Erdös and Rényi and of Kelly and Oxley. We also show that there are several properties of k-balanced matroids for which there exists a threshold function.
基金the NSF of China(11571089,11871191)the NSF of Henan Province(222300420397)+1 种基金the NSF of Hebei Province(A2022208007)the Key Foundation of Hebei Normal University(L2018Z01)。
文摘k holomorphic functions are a type of generation of holomorphic functions.In this paper,a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in C^(2).The existence of the solution for the problem is studied in detail with the help of the boundary properties of Cauchy type singular integral operators with a k holomorphic kernel.Furthermore,the integral representation for the solution is obtained.
文摘The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><i></i></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;">-variate survival functions for arbitrary </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2, 3, </span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">...</span><span style="font-family:Verdana;">, given all the univariate marginal survival functions. This universal form of </span></span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;">-variate probability distributions was obtained by means of “dependence functions” named “joiners” in the text. These joiners determine all the involved stochastic dependencies between the underlying random variables. However, in order that the presented formula (the form) represents a legitimate survival function, some necessary and sufficient conditions for the joiners had to be found. Basically, finding those conditions is the main task of this paper. This task was successfully performed for the case </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;"> = 2 and the main results for the case </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;"> = 3 were formulated as Theorem 1 and Theorem 2 in Section 4. Nevertheless, the hypothetical conditions valid for the general </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;"> ≥ 4 case were also formulated in Section 3 as the (very convincing) Hypothesis. As for the sufficient conditions for both the </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;"> = 3 and</span><i> </i></span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;"> ≥ 4 cases, the full generality was not achieved since two restrictions were imposed. Firstly, we limited ourselves to the, defined in the text, “continuous cases” (when the corresponding joint density exists and is continuous), and secondly we consider positive stochastic dependencies only. Nevertheless, the class of the </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;">-variate distributions which can be constructed is very wide. The presented method of construction by means of joiners can be considered competitive to the </span><span style="font-family:Verdana;"><strong></strong></span></span></span><strong><span><span><b><span style="font-family:Verdana;">copula</span></b><span style="font-family:Verdana;"></span></span></span></strong><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> methodology. As it is suggested in the paper the possibility of building a common theory of both copulae and joiners is quite possible, and the joiners may play the role of tools within the theory of copulae, and vice versa copulae may, for example, be used for finding proper joiners. Another independent feature of the joiners methodology is the possibility of constructing many new stochastic processes including stationary and Markovian.</span></span></span>
文摘Utilization of the shift operator to represent Euler polynomials as polynomials of Appell type leads directly to its algebraic properties, its relations with powers sums;may be all its relations with Bernoulli polynomials, Bernoulli numbers;its recurrence formulae and a very simple formula for calculating simultaneously Euler numbers and Euler polynomials. The expansions of Euler polynomials into Fourier series are also obtained;the formulae for obtaining all π<sup>m</sup> as series on k<sup>-m</sup> and for expanding functions into series of Euler polynomials.