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
AIM: To explore the impact of tumor size on outcomes in patients with advanced gastric cancer in the lower third of the stomach. METHODS: We retrospectively analyzed the clinical records of 430 patients with advanced ...AIM: To explore the impact of tumor size on outcomes in patients with advanced gastric cancer in the lower third of the stomach. METHODS: We retrospectively analyzed the clinical records of 430 patients with advanced gastric cancer in the lower third of the stomach who underwent distal subtotal gastrectomy and D2 lymphadenectomy in our hospital from January 1998 to June 2004. Receiver-operating characteristic (ROC) curve analysis was used to determine the appropriate cutoff value for tumor size, which was measured as maximum tumor diameter. Based on this cutoff value, patients were divided into two groups: those with large-sized tumors (LSTs) and those with small-sized tumors (SSTs). The correlations between other clinicopathologic factors and tumor size were investigated, and the 5-year overall survival (OS) rate was compared between the two groups. Potential prognostic factors were evaluated by univariate KaplanMeier survival analysis and multivariate Cox's propor-tional hazard model analysis. The 5-year OS rates in the two groups were compared according to pT stage and pN stage. RESULTS: The 5-year OS rate in the 430 patients with advanced gastric cancer in the lower third of the stomach was 53.7%. The mean ± SD tumor size was 4.9 ± 1.9 cm, and the median tumor size was 5.0 cm. ROC analysis indicated that the sensitivity and specificity results for the appropriate tumor size cutoff value of 4.8 cm were 80.0% and 68.2%, respectively (AUC=0.795, 95%CI: 0.751-0.839, P=0.000). Using this cutoff value, 222 patients (51.6%) had LSTs (tumor size ≥ 4.8 cm) and 208 (48.4%) had SSTs (tumor size<4.8 cm). Tumor size was significantly correlated with histological type (P=0.039), Borrmann type (P=0.000), depth of tumor invasion (P=0.000), lymph node metastasis (P=0.000), tumor-nodes metastasis stage (P=0.000), mean number of metastatic lymph nodes (P=0.000) and metastatic lymph node ratio (P=0.000). Patients with LSTs had a significantly lower 5-year OS rate than those with SSTs (37.1% vs 63.3%, P=0.000). Univariate analysis showed that depth of tumor invasion (c 2=69.581, P=0.000), lymph node metastasis (c 2=138.815, P=0.000), tumor size (c 2=78.184, P=0.000) and metastatic lymph node ratio (c 2=139.034, P=0.000) were significantly associated with 5-year OS rate. Multivariate analysis revealed that depth of tumor invasion (P=0.000), lymph node metastasis (P=0.019) and tumor size (P=0.000) were independent prognostic factors. Gastric cancers were divided into 12 subgroups: pT2N0; pT2N1; pT2N2; pT2N3; pT3N0; pT3N1; pT3N2; pT3N3; pT4aN0; pT4aN1; pT4aN2; and pT4aN3. In patients with pT2-3N3 stage tumors and patients with pT4a stage tumors, 5-year OS rates were significantly lower for LSTs than for SSTs (P<0.05 each), but there were no significant differences in the 5-year OS rates in LST and SST patients with pT23N0-2 stage tumors (P > 0.05). CONCLUSION: Using a tumor size cutoff value of 4.8cm, tumor size is a prognostic factor in patients with pN3 stage or pT4a stage advanced gastric cancer located in the lower third of the stomach.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AIM: To explore the impact of tumor size on outcomes in patients with advanced gastric cancer in the lower third of the stomach. METHODS: We retrospectively analyzed the clinical records of 430 patients with advanced gastric cancer in the lower third of the stomach who underwent distal subtotal gastrectomy and D2 lymphadenectomy in our hospital from January 1998 to June 2004. Receiver-operating characteristic (ROC) curve analysis was used to determine the appropriate cutoff value for tumor size, which was measured as maximum tumor diameter. Based on this cutoff value, patients were divided into two groups: those with large-sized tumors (LSTs) and those with small-sized tumors (SSTs). The correlations between other clinicopathologic factors and tumor size were investigated, and the 5-year overall survival (OS) rate was compared between the two groups. Potential prognostic factors were evaluated by univariate KaplanMeier survival analysis and multivariate Cox's propor-tional hazard model analysis. The 5-year OS rates in the two groups were compared according to pT stage and pN stage. RESULTS: The 5-year OS rate in the 430 patients with advanced gastric cancer in the lower third of the stomach was 53.7%. The mean ± SD tumor size was 4.9 ± 1.9 cm, and the median tumor size was 5.0 cm. ROC analysis indicated that the sensitivity and specificity results for the appropriate tumor size cutoff value of 4.8 cm were 80.0% and 68.2%, respectively (AUC=0.795, 95%CI: 0.751-0.839, P=0.000). Using this cutoff value, 222 patients (51.6%) had LSTs (tumor size ≥ 4.8 cm) and 208 (48.4%) had SSTs (tumor size<4.8 cm). Tumor size was significantly correlated with histological type (P=0.039), Borrmann type (P=0.000), depth of tumor invasion (P=0.000), lymph node metastasis (P=0.000), tumor-nodes metastasis stage (P=0.000), mean number of metastatic lymph nodes (P=0.000) and metastatic lymph node ratio (P=0.000). Patients with LSTs had a significantly lower 5-year OS rate than those with SSTs (37.1% vs 63.3%, P=0.000). Univariate analysis showed that depth of tumor invasion (c 2=69.581, P=0.000), lymph node metastasis (c 2=138.815, P=0.000), tumor size (c 2=78.184, P=0.000) and metastatic lymph node ratio (c 2=139.034, P=0.000) were significantly associated with 5-year OS rate. Multivariate analysis revealed that depth of tumor invasion (P=0.000), lymph node metastasis (P=0.019) and tumor size (P=0.000) were independent prognostic factors. Gastric cancers were divided into 12 subgroups: pT2N0; pT2N1; pT2N2; pT2N3; pT3N0; pT3N1; pT3N2; pT3N3; pT4aN0; pT4aN1; pT4aN2; and pT4aN3. In patients with pT2-3N3 stage tumors and patients with pT4a stage tumors, 5-year OS rates were significantly lower for LSTs than for SSTs (P<0.05 each), but there were no significant differences in the 5-year OS rates in LST and SST patients with pT23N0-2 stage tumors (P > 0.05). CONCLUSION: Using a tumor size cutoff value of 4.8cm, tumor size is a prognostic factor in patients with pN3 stage or pT4a stage advanced gastric cancer located in the lower third of the stomach.
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.
