In this paper, it is proved that for p≥7 an arbitrary odd prime and 3≤s 〈 p, the homotopy elements β1λs and α1λs are nontrivial in the stable homotopy groups of spheres π*S.
We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-...We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes.展开更多
In this paper, we study the invertibility of sequences consisting of finitely many bounded linear operators from a Hilbert space to others. We show that a sequence of operators is left invertible if and only if it is ...In this paper, we study the invertibility of sequences consisting of finitely many bounded linear operators from a Hilbert space to others. We show that a sequence of operators is left invertible if and only if it is a g-frame. Therefore, our result connects the invertibility of operator sequences with frame theory.展开更多
We discuss two types of maps on operator spaces. Firstly, through example we show that there is an isometry on unit sphere of an operator space cannot be extended to be a complete isometry on the whole operator space....We discuss two types of maps on operator spaces. Firstly, through example we show that there is an isometry on unit sphere of an operator space cannot be extended to be a complete isometry on the whole operator space. Secondly, we give a new characterization for complete isometry by the concept of approximate isometry.展开更多
We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettstosser.
We show that every Bessel sequence (and therefore every frame) in a separable Hilbert space can be expanded to a tight frame by adding some elements. The proof is based on a recent generalization of the frame concep...We show that every Bessel sequence (and therefore every frame) in a separable Hilbert space can be expanded to a tight frame by adding some elements. The proof is based on a recent generalization of the frame concept, the g-frame, which illustrates that g-frames could be useful in the study of frame theory. As an application, we prove that any Gabor frame can be expanded to a tight frame by adding one window function.展开更多
In this paper, some groups Ext A^s.t (Zp, Zp) with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial famil...In this paper, some groups Ext A^s.t (Zp, Zp) with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres πpnq+(s+3)pq+(s+1)q-5S which is represented (up to a nonzero scalar) by β+2bohh∈ExtA^s+5,P^nq+(n+3)pq+(n+1)q+s(Zp, Zp) in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥3, 0≤ s 〈 p - 3, q = 2(p - 1).展开更多
In this paper, we consider the optimal dividend problem for a classical risk model with a constant force of interest. For such a risk model, a sufficient condition under which a barrier strategy is the optimal strateg...In this paper, we consider the optimal dividend problem for a classical risk model with a constant force of interest. For such a risk model, a sufficient condition under which a barrier strategy is the optimal strategy is presented for general claim distributions. When claim sizes are exponentially distributed, it is shown that the optimal dividend policy is a barrier strategy and the maximal dividend-value function is a concave function. Finally, some known results relating to the distribution of aggregate dividends before ruin are extended.展开更多
We study the approximation of the inverse wavelet transform using Riemannian sums.We show that when the Fourier transforms of wavelet functions satisfy some moderate decay condition,the Riemannian sums converge to the...We study the approximation of the inverse wavelet transform using Riemannian sums.We show that when the Fourier transforms of wavelet functions satisfy some moderate decay condition,the Riemannian sums converge to the function to be reconstructed as the sampling density tends to infinity.We also study the convergence of the operators introduced by the Riemannian sums.Our result improves some known ones.展开更多
This paper studies framings in Banach spaces, a concept raised by Casazza, Han and Larson, which is a natural generalization of traditional frames in Hilbert spaces and unconditional bases in Banach spaces. The minima...This paper studies framings in Banach spaces, a concept raised by Casazza, Han and Larson, which is a natural generalization of traditional frames in Hilbert spaces and unconditional bases in Banach spaces. The minimal unconditional bases and the maximal unconditional bases with respect to framings are introduced. Our main result states that, if (xi, fi) is a framing of a Banach space X, and (eimin) and (eimax) are the minimal unconditional basis and the maximal unconditional basis with respect to (xi, fi), respectively, then for any unconditional basis (ei) associated with (xi, fi), there are A,B 〉 0 such that A||i=1∑∞aieimin||≤||i=1∑∞aiei||≤B||i=1∑∞aieimax|| for all (ai) ∈ c00.It means that for any framing, the corresponding associated unconditional bases have common upper and lower bounds.展开更多
In this paper we mainly study the ruin probability of a surplus process described by a piecewise deterministic Markov process (PDMP). An integro-differential equation for the ruin probability is derived. Under a cer...In this paper we mainly study the ruin probability of a surplus process described by a piecewise deterministic Markov process (PDMP). An integro-differential equation for the ruin probability is derived. Under a certain assumption, it can be transformed into the ruin probability of a risk process whose premiums depend on the current reserves. Using the same argument as that in Asmussen and Nielsen, the ruin probability and its upper bounds are obtained. Finally, we give an analytic expression for ruin probability and its upper bounds when the claim-size is exponentially distributed.展开更多
Grochenig and Balan, Casazza, Heil, and Landau introduced the concepts of localization. The concepts were used to Gabor frames, wavelet frames and sampling theorem in recent years. Here they are applied to the frame o...Grochenig and Balan, Casazza, Heil, and Landau introduced the concepts of localization. The concepts were used to Gabor frames, wavelet frames and sampling theorem in recent years. Here they are applied to the frame of exponential windows with the conclusion that the frame of exponential windows is a Banach frame for a kind of Banach spaces, and the conclusion is also obtained about the relationship between frame bounds, frame density, measure and density of indexing set.展开更多
The homogeneous approximation property (HAP) states that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time-scale shifts. In this paper, we ...The homogeneous approximation property (HAP) states that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time-scale shifts. In this paper, we show that every wavelet frame with nice wavelet function and arbitrary expansive dilation matrix possesses the HAP. Our results improve some known ones.展开更多
The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n ×...The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n × n real expansive matrix A, the frame-sets with respect to A are a family of sets in R^n. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry.展开更多
We generalize the discrete Yamabe flow to α order. This Yamabe flow deforms the α-order curvature to a constant. Using this new flow, we manage to find discrete α-quasi-Einstein metrics on the triangulations of S3.
文摘In this paper, it is proved that for p≥7 an arbitrary odd prime and 3≤s 〈 p, the homotopy elements β1λs and α1λs are nontrivial in the stable homotopy groups of spheres π*S.
文摘We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes.
基金supported partially by the National Natural Science Foundation of China (10971105 and 10990012)the Natural Science Foundation of Tianjin (09JCYBJC01000)
文摘In this paper, we study the invertibility of sequences consisting of finitely many bounded linear operators from a Hilbert space to others. We show that a sequence of operators is left invertible if and only if it is a g-frame. Therefore, our result connects the invertibility of operator sequences with frame theory.
文摘We discuss two types of maps on operator spaces. Firstly, through example we show that there is an isometry on unit sphere of an operator space cannot be extended to be a complete isometry on the whole operator space. Secondly, we give a new characterization for complete isometry by the concept of approximate isometry.
基金This work was supported partially by the National Natural Science Foundation of China (Grant Nos. 60472042,10571089 and 60572113),the Liuhui Center for Applied Mathematics, the Program for New Century Excellent Talents in Universitiesthe Research Fund for the Doctoral Program of Higher Educationthe Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China
文摘We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettstosser.
基金supported partially by the National Natural Science Foundation of China (10571089,10671062)the Program for New Century Excellent Talents in Universities+1 种基金the Innovation Scientists and Technicians Troop Construction Projects of He'nan Province of China (084100510012)the Natural Science Foundation for the Education Department of He'nan Province of China (2008B510001)
文摘We show that every Bessel sequence (and therefore every frame) in a separable Hilbert space can be expanded to a tight frame by adding some elements. The proof is based on a recent generalization of the frame concept, the g-frame, which illustrates that g-frames could be useful in the study of frame theory. As an application, we prove that any Gabor frame can be expanded to a tight frame by adding one window function.
基金the National Natural Science Foundation of China(No.10501045,10426028)the China Postdoctoral Science Foundation and the Fund of the Personnel Division of Nankai University
文摘In this paper, some groups Ext A^s.t (Zp, Zp) with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres πpnq+(s+3)pq+(s+1)q-5S which is represented (up to a nonzero scalar) by β+2bohh∈ExtA^s+5,P^nq+(n+3)pq+(n+1)q+s(Zp, Zp) in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥3, 0≤ s 〈 p - 3, q = 2(p - 1).
基金Project supported by the National Natural Science Foundation of China (No.10501045)the Tianyuan Foundation of Mathematics (No.10426028)the Fund of the Personnel Division of Nankai University
文摘这篇论文在γ _ 上计算刺地图 2 并且证明它被 2b_(2,0 ) 代表在 ASS 的 h_(1,2 ) 。作者也计算 b_(2,0 ) 微分的更高的 5 月,从哪个它被证明那γ _ 3 (b_0h_n -h_1b_(n-1 )) 为 2 ≤ s 【
p - 1 是在 ASS 的永久周期。
基金Supported by National Basic Research Program of China (973 Program) (No. 2007CB814905)National Natural Science Foundation of China (No. 10871102,10926161 and 71071088)the Research Fund for the Doctorial Program of Higher Education
文摘In this paper, we consider the optimal dividend problem for a classical risk model with a constant force of interest. For such a risk model, a sufficient condition under which a barrier strategy is the optimal strategy is presented for general claim distributions. When claim sizes are exponentially distributed, it is shown that the optimal dividend policy is a barrier strategy and the maximal dividend-value function is a concave function. Finally, some known results relating to the distribution of aggregate dividends before ruin are extended.
基金supported partially by National Natural Science Foundation of China(Grant Nos.10971105,10990012)Natural Science Foundation of Tianjin (Grant No.09JCYBJC01000)
文摘We study the approximation of the inverse wavelet transform using Riemannian sums.We show that when the Fourier transforms of wavelet functions satisfy some moderate decay condition,the Riemannian sums converge to the function to be reconstructed as the sampling density tends to infinity.We also study the convergence of the operators introduced by the Riemannian sums.Our result improves some known ones.
基金Supported by National Nature Science Foundation of China(Grant Nos.11001134,11126250 and 11201336)Fundamental Research Funds for the Central Universities and Tianjin Science and Technology Fund(Grant No.20100820)
文摘This paper studies framings in Banach spaces, a concept raised by Casazza, Han and Larson, which is a natural generalization of traditional frames in Hilbert spaces and unconditional bases in Banach spaces. The minimal unconditional bases and the maximal unconditional bases with respect to framings are introduced. Our main result states that, if (xi, fi) is a framing of a Banach space X, and (eimin) and (eimax) are the minimal unconditional basis and the maximal unconditional basis with respect to (xi, fi), respectively, then for any unconditional basis (ei) associated with (xi, fi), there are A,B 〉 0 such that A||i=1∑∞aieimin||≤||i=1∑∞aiei||≤B||i=1∑∞aieimax|| for all (ai) ∈ c00.It means that for any framing, the corresponding associated unconditional bases have common upper and lower bounds.
基金Supported by the National Natural Science Foundation of China (No. 10571092) the Research Fund for the Doctorial Program of Higher Education.
文摘In this paper we mainly study the ruin probability of a surplus process described by a piecewise deterministic Markov process (PDMP). An integro-differential equation for the ruin probability is derived. Under a certain assumption, it can be transformed into the ruin probability of a risk process whose premiums depend on the current reserves. Using the same argument as that in Asmussen and Nielsen, the ruin probability and its upper bounds are obtained. Finally, we give an analytic expression for ruin probability and its upper bounds when the claim-size is exponentially distributed.
基金Supported by the National Natural Science Foundation of China (Grant No.10571089)
文摘Grochenig and Balan, Casazza, Heil, and Landau introduced the concepts of localization. The concepts were used to Gabor frames, wavelet frames and sampling theorem in recent years. Here they are applied to the frame of exponential windows with the conclusion that the frame of exponential windows is a Banach frame for a kind of Banach spaces, and the conclusion is also obtained about the relationship between frame bounds, frame density, measure and density of indexing set.
基金Supported partially by National Natural Science Foundation of China(Grant Nos.10971105and10990012)Natural Science Foundation of Tianjin(Grant No.09JCYBJC01000)
文摘The homogeneous approximation property (HAP) states that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time-scale shifts. In this paper, we show that every wavelet frame with nice wavelet function and arbitrary expansive dilation matrix possesses the HAP. Our results improve some known ones.
基金Supported by National Natural Science Foundation of China(Grants Nos.60572113,60472042)China Postdoctoral Science Foundation(Grant No.2004036368)
文摘The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n × n real expansive matrix A, the frame-sets with respect to A are a family of sets in R^n. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry.
文摘We generalize the discrete Yamabe flow to α order. This Yamabe flow deforms the α-order curvature to a constant. Using this new flow, we manage to find discrete α-quasi-Einstein metrics on the triangulations of S3.