In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the ...In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.展开更多
BACKGROUND Primary ciliary dyskinesia(PCD)is an inherited autosomal-recessive disorder of impaired mucociliary clearance characterized by chronic respiratory diseases,otolaryngological diseases,central nervous system ...BACKGROUND Primary ciliary dyskinesia(PCD)is an inherited autosomal-recessive disorder of impaired mucociliary clearance characterized by chronic respiratory diseases,otolaryngological diseases,central nervous system abnormalities,reproductive system abnormalities,and cardiac function abnormalities.General anesthesia in these patients is associated with a higher incidence of respiratory complications than in patients without the disease.CASE SUMMARY A 16-year-old male patient was referred to the emergency room complaining of right ankle pain due to distal tibiofibular fracture.Three years prior,he had been diagnosed with PCD.At that time,he had experienced several episodes of pneumonia,sinusitis,and chronic middle ear infections,for which he underwent surgical interventions.At the current admission,he presented with cough and sputum but no other respiratory symptoms.A chest computed tomography scan revealed centrilobular ground-glass opacities in both lower lobes and a calcified nodule in the left lower lobe.For the surgical procedure and postoperative pain management,combined spinal-epidural anesthesia was employed.The patient’s postoperative pain score was measured by the numerical rating scale(NRS).On the day of surgery,his NRS was 5 points.By the second postoperative day,the NRS score had decreased to 2–3 points.The epidural catheter was removed on the fourth day following the operation.The patient was subsequently discharged no respiratory complications.CONCLUSION We performed combined spinal-epidural anesthesia in a patient with PCD.The patient experienced no additional respiratory complications and was discharged with a low NRS score for pain.展开更多
This paper proposes a novel pair of induced IF covering approximation operators in an IF covering approximation space,and discusses some basic properties about definable IFSs.A measure is defined to describe the uncer...This paper proposes a novel pair of induced IF covering approximation operators in an IF covering approximation space,and discusses some basic properties about definable IFSs.A measure is defined to describe the uncertainty of IFSs in IF covering approximation spaces.Finally,we study the properties of reductions of an IF covering respectively based on induced IF covering approximation operators and IF covering approximation operators.展开更多
Starting from general Jacobi polynomials we derive for the Ul-traspherical polynomials as their special case a set of related polynomials which can be extended to an orthogonal set of functions with interesting proper...Starting from general Jacobi polynomials we derive for the Ul-traspherical polynomials as their special case a set of related polynomials which can be extended to an orthogonal set of functions with interesting properties. It leads to an alternative definition of the Ultraspherical polynomials by a fixed integral operator in application to powers of the variable u in an analogous way as it is possible for Hermite polynomials. From this follows a generating function which is apparently known only for the Legendre and Chebyshev polynomials as their special case. Furthermore, we show that the Ultraspherical polynomials form a realization of the SU(1,1) Lie algebra with lowering and raising operators which we explicitly determine. By reordering of multiplication and differentiation operators we derive new operator identities for the whole set of Jacobi polynomials which may be applied to arbitrary functions and provide then function identities. In this way we derive a new “convolution identity” for Jacobi polynomials and compare it with a known convolution identity of different structure for Gegenbauer polynomials. In short form we establish the connection of Jacobi polynomials and their related orthonormalized functions to the eigensolution of the Schrödinger equation to Pöschl-Teller potentials.展开更多
Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known...Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known quantities are used to characterize bounded compact approximation property.Similarly,a new quantity characterizing lower semi-Fredholm operators is introduced,investigated and used to characterize the bounded compact approximation property for dual spaces.展开更多
In this note, the explicit representations of Moore-Penrose inverses of lower triangular operator matrices are established. As an application, the explicit representations of Bott-Duffin inverses of bounded linear ope...In this note, the explicit representations of Moore-Penrose inverses of lower triangular operator matrices are established. As an application, the explicit representations of Bott-Duffin inverses of bounded linear operators on a Hilbert space with respect to a closed subspace are obtained.展开更多
基金Supported by the National Natural Science Foundation of China(11171308,61379018,51305400)
文摘In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.
文摘BACKGROUND Primary ciliary dyskinesia(PCD)is an inherited autosomal-recessive disorder of impaired mucociliary clearance characterized by chronic respiratory diseases,otolaryngological diseases,central nervous system abnormalities,reproductive system abnormalities,and cardiac function abnormalities.General anesthesia in these patients is associated with a higher incidence of respiratory complications than in patients without the disease.CASE SUMMARY A 16-year-old male patient was referred to the emergency room complaining of right ankle pain due to distal tibiofibular fracture.Three years prior,he had been diagnosed with PCD.At that time,he had experienced several episodes of pneumonia,sinusitis,and chronic middle ear infections,for which he underwent surgical interventions.At the current admission,he presented with cough and sputum but no other respiratory symptoms.A chest computed tomography scan revealed centrilobular ground-glass opacities in both lower lobes and a calcified nodule in the left lower lobe.For the surgical procedure and postoperative pain management,combined spinal-epidural anesthesia was employed.The patient’s postoperative pain score was measured by the numerical rating scale(NRS).On the day of surgery,his NRS was 5 points.By the second postoperative day,the NRS score had decreased to 2–3 points.The epidural catheter was removed on the fourth day following the operation.The patient was subsequently discharged no respiratory complications.CONCLUSION We performed combined spinal-epidural anesthesia in a patient with PCD.The patient experienced no additional respiratory complications and was discharged with a low NRS score for pain.
基金supported by the National Natural Science Foundation of China(Nos.60773174 and 60963006)Hebei Province Science and Technology Research and Development Program(No.09276158).
文摘This paper proposes a novel pair of induced IF covering approximation operators in an IF covering approximation space,and discusses some basic properties about definable IFSs.A measure is defined to describe the uncertainty of IFSs in IF covering approximation spaces.Finally,we study the properties of reductions of an IF covering respectively based on induced IF covering approximation operators and IF covering approximation operators.
文摘Starting from general Jacobi polynomials we derive for the Ul-traspherical polynomials as their special case a set of related polynomials which can be extended to an orthogonal set of functions with interesting properties. It leads to an alternative definition of the Ultraspherical polynomials by a fixed integral operator in application to powers of the variable u in an analogous way as it is possible for Hermite polynomials. From this follows a generating function which is apparently known only for the Legendre and Chebyshev polynomials as their special case. Furthermore, we show that the Ultraspherical polynomials form a realization of the SU(1,1) Lie algebra with lowering and raising operators which we explicitly determine. By reordering of multiplication and differentiation operators we derive new operator identities for the whole set of Jacobi polynomials which may be applied to arbitrary functions and provide then function identities. In this way we derive a new “convolution identity” for Jacobi polynomials and compare it with a known convolution identity of different structure for Gegenbauer polynomials. In short form we establish the connection of Jacobi polynomials and their related orthonormalized functions to the eigensolution of the Schrödinger equation to Pöschl-Teller potentials.
基金supported by the National Natural Science Foundation of China(Grant No.11971403)the Natural Science Foundation of Fujian Province of China(Grant No.2019J01024)。
文摘Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known quantities are used to characterize bounded compact approximation property.Similarly,a new quantity characterizing lower semi-Fredholm operators is introduced,investigated and used to characterize the bounded compact approximation property for dual spaces.
基金Supported bv National Natural Scieince Foundation of China (Grant No.10871224)
文摘In this note, the explicit representations of Moore-Penrose inverses of lower triangular operator matrices are established. As an application, the explicit representations of Bott-Duffin inverses of bounded linear operators on a Hilbert space with respect to a closed subspace are obtained.
