In the present paper, we define the S-left and the S-right essential spectra of a linear operator and we study the stability of the S-essential spectra on a Banach space.
The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-def...The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained： if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ1≤λ2≤…展开更多
Patent foramen ovale (PFO) closure for systemic hypoxemia is controversial. The first systematic, albeit retrospective, study was recently presented which showed good procedural and clinical success for PFO closure fo...Patent foramen ovale (PFO) closure for systemic hypoxemia is controversial. The first systematic, albeit retrospective, study was recently presented which showed good procedural and clinical success for PFO closure for this indication. We present a case of acute right to left intra-cardiac shunt across PFO where the shunting is not persistent. Hence making a decision on PFO closure based on the aforementioned promising trial may not have been the right decision for the patient. This case highlights that the decision on PFO closure for such indication needs to be individualized. We also review the sparse literature on PFO closure for this indication and discuss how the decision making for such indication needs to be individualized.展开更多
We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty ...We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.展开更多
文摘In the present paper, we define the S-left and the S-right essential spectra of a linear operator and we study the stability of the S-essential spectra on a Banach space.
基金Supported by the National Natural Science Foundation of China(10561005)the Doctor's Discipline Fund of the Ministry of Education of China(20040126008)
文摘The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained： if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ1≤λ2≤…
文摘Patent foramen ovale (PFO) closure for systemic hypoxemia is controversial. The first systematic, albeit retrospective, study was recently presented which showed good procedural and clinical success for PFO closure for this indication. We present a case of acute right to left intra-cardiac shunt across PFO where the shunting is not persistent. Hence making a decision on PFO closure based on the aforementioned promising trial may not have been the right decision for the patient. This case highlights that the decision on PFO closure for such indication needs to be individualized. We also review the sparse literature on PFO closure for this indication and discuss how the decision making for such indication needs to be individualized.
文摘We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.
