We start from a realistic half space then use to develop a mathematical asymptotic model for thermal imaging, which we analysis well suited for the design of reconstruction algorithms. We seek to reconstruct thermal a...We start from a realistic half space then use to develop a mathematical asymptotic model for thermal imaging, which we analysis well suited for the design of reconstruction algorithms. We seek to reconstruct thermal anomalies only through their rough features. With this way our proposed algorithms are stable against measurement noise and geometry perturbations. Based on rigorous asymptotic estimates, we first obtain an approximation for the temperature profile which we then use to design noniterative detection algorithms. We show on numerical simulations evidence that they are accurate and robust. Moreover, we provide a mathematical model for ultrasonic temperature imaging, which is an important technique in cancerous tissue ablation therapy.展开更多
In this paper we obtained the asymptotic formula of the orthogonal rational function on the unit circle with respect to the weight function μ(z) with preasigned poles, which are in the exterior of the unit disk.
This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas fo...This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas for the eigenvalues of a simple boundary problem generated in a finite interval by the considered Sturm-Liouville equation.展开更多
We use the analytic methods and the properties of Gauss sums to study one kind mean value problems involving the classical Dedekind sums,and give an interesting identity and asymptotic formula for it.
Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact ...Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact result in trigonometric series.展开更多
Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair...Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.展开更多
The main purpose of this paper is to study the mean value properties of thesecond Smarandache pseudo-odd number sequence and pseudo-even number sequence, andgive some interesting asymptotic formula for them.
Let p and q be two distinct primes, epq(n) denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq(n), and give some hybrid mean value formulas f...Let p and q be two distinct primes, epq(n) denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq(n), and give some hybrid mean value formulas for epq(n) and Dirichlet divisor function d(n). Key words: largest exponent; asymptotic formula; hybrid mean value; Dirichlet divisor function d(n)展开更多
On the basis of von Karnmnequations, the axisymmetric buckling and post-buckling of annular plates on anelastic foundation is so wematically discussed byusing shooting
Let n be any positive integer, and S(n) be the cubic complements of n. The main purpose of this paper is to study the asymptotic of ∑n≤x(n/S(n))^k (k ≥ 1). And by using the elementary methods, it intends to...Let n be any positive integer, and S(n) be the cubic complements of n. The main purpose of this paper is to study the asymptotic of ∑n≤x(n/S(n))^k (k ≥ 1). And by using the elementary methods, it intends to give two sharper asymptotic formulas, and thus extends the related conclusions.展开更多
For any positive integer n,let L(n) = [1,2,...,n] be the least common multiple of the integers from 1 to n.Let k be any positive integer.The main purpose of this paper is to study the asymptotic property of L(n^k),and...For any positive integer n,let L(n) = [1,2,...,n] be the least common multiple of the integers from 1 to n.Let k be any positive integer.The main purpose of this paper is to study the asymptotic property of L(n^k),and give some interesting relevant results.展开更多
This paper is to study the distribution property of Lehmer DH number by use the estimation of general Kloostermann sum and the estimation of trigonometric sum.
The main purpose of this paper is using the analytic methods to study a limit problem involving the F Smarandache square complementary number Ssc(n), and obtain its limit value.
The main purpose of this paper is using the elementary method to study a limit problem involving the F.Smarandache square complementary number, and obtain its limit value.
The main purpose of this paper is using the analytic method to study the mean value properties of the arithmetical functions δk((m, n)), δk([m,n]/m),and give several interesting asymptotic formulae for them.
In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the wh...In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of approximation for C 2[0, 1] are O(1/n 2) but corresponding degree of ordinary Landau operators are only O(1/n).展开更多
Let m be a positive integer, g(m) be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying ( t = t(n) ) t^n+1≡t(modm).For a number x≥3, let G(x)=∑m≤tg(...Let m be a positive integer, g(m) be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying ( t = t(n) ) t^n+1≡t(modm).For a number x≥3, let G(x)=∑m≤tg(m) In this paper, we obtain the asymptotic formula: .G(x)=αx^2+O(xlogx),ax x→∞ Our result improves the corresponding result with an error term O(xlog^2 x) of Yang Zhaohua obtained in 1986展开更多
The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such op...The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.展开更多
We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz ...We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz and Poschel.展开更多
基金supported by the ANR project EchoScan(AN-06-Blan-0089)the NSF grant DMS 0707421.
文摘We start from a realistic half space then use to develop a mathematical asymptotic model for thermal imaging, which we analysis well suited for the design of reconstruction algorithms. We seek to reconstruct thermal anomalies only through their rough features. With this way our proposed algorithms are stable against measurement noise and geometry perturbations. Based on rigorous asymptotic estimates, we first obtain an approximation for the temperature profile which we then use to design noniterative detection algorithms. We show on numerical simulations evidence that they are accurate and robust. Moreover, we provide a mathematical model for ultrasonic temperature imaging, which is an important technique in cancerous tissue ablation therapy.
文摘In this paper we obtained the asymptotic formula of the orthogonal rational function on the unit circle with respect to the weight function μ(z) with preasigned poles, which are in the exterior of the unit disk.
文摘This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas for the eigenvalues of a simple boundary problem generated in a finite interval by the considered Sturm-Liouville equation.
基金supported by National Natural Science Foundation of China(Grant Nos.11001218 and 11071194)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20106101120001)
文摘We use the analytic methods and the properties of Gauss sums to study one kind mean value problems involving the classical Dedekind sums,and give an interesting identity and asymptotic formula for it.
文摘Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact result in trigonometric series.
基金Supported by the Natural Science Foundation of China(12071487,11671404)the Natural Science Foundation of Anhui Province(2208085MA06)+1 种基金the Provincial Natural Science Research Project of Anhui Colleges(KJ2021A0049,KJ2021A0060)Hunan Provincial Innovation Foundation for Postgraduate(CX20200146)。
文摘Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.
文摘The main purpose of this paper is to study the mean value properties of thesecond Smarandache pseudo-odd number sequence and pseudo-even number sequence, andgive some interesting asymptotic formula for them.
文摘Let p and q be two distinct primes, epq(n) denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq(n), and give some hybrid mean value formulas for epq(n) and Dirichlet divisor function d(n). Key words: largest exponent; asymptotic formula; hybrid mean value; Dirichlet divisor function d(n)
基金Project support by the State Education Commission of the People’s Republic of China
文摘On the basis of von Karnmnequations, the axisymmetric buckling and post-buckling of annular plates on anelastic foundation is so wematically discussed byusing shooting
文摘Let n be any positive integer, and S(n) be the cubic complements of n. The main purpose of this paper is to study the asymptotic of ∑n≤x(n/S(n))^k (k ≥ 1). And by using the elementary methods, it intends to give two sharper asymptotic formulas, and thus extends the related conclusions.
文摘For any positive integer n,let L(n) = [1,2,...,n] be the least common multiple of the integers from 1 to n.Let k be any positive integer.The main purpose of this paper is to study the asymptotic property of L(n^k),and give some interesting relevant results.
基金Supported by the Education Commission Science Foundation of Shaanxi(OOJK123)
文摘This paper is to study the distribution property of Lehmer DH number by use the estimation of general Kloostermann sum and the estimation of trigonometric sum.
基金Foundation item: Supported by the National Natural Science Foundation of China(10671055)
文摘The main purpose of this paper is using the analytic methods to study a limit problem involving the F Smarandache square complementary number Ssc(n), and obtain its limit value.
文摘The main purpose of this paper is using the elementary method to study a limit problem involving the F.Smarandache square complementary number, and obtain its limit value.
基金Supported by NSF of China(10671155)Supported by SF of Education Department of Shannxi Province(08JK291)
文摘The main purpose of this paper is using the analytic method to study the mean value properties of the arithmetical functions δk((m, n)), δk([m,n]/m),and give several interesting asymptotic formulae for them.
文摘In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of approximation for C 2[0, 1] are O(1/n 2) but corresponding degree of ordinary Landau operators are only O(1/n).
文摘Let m be a positive integer, g(m) be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying ( t = t(n) ) t^n+1≡t(modm).For a number x≥3, let G(x)=∑m≤tg(m) In this paper, we obtain the asymptotic formula: .G(x)=αx^2+O(xlogx),ax x→∞ Our result improves the corresponding result with an error term O(xlog^2 x) of Yang Zhaohua obtained in 1986
文摘The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.
文摘We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz and Poschel.