In this paper, we study 5d $$ \mathcal{N} $$ N = 1 Sp(N) gauge theory with Nf (≤ 2N + 3) flavors based on 5-brane web diagram with O5-plane. On the one hand, we discuss Seiberg-Witten curve based on the dual graph of the 5-brane web with O5-plane. On the other hand, we compute the Nekrasov partition function based on the topological vertex formalism with O5-plane. Rewriting it in terms of profile functions, we obtain the saddle point equation for the profile function after taking thermodynamic limit. By introducing the resolvent, we derive the Seiberg-Witten curve and its boundary conditions as well as its relation to the prepotential in terms of the cycle integrals. They coincide with those directly obtained from the dual graph of the 5-brane web with O5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane and shed light on the non-toric Calabi-Yau 3-folds including D-type singularities.

No abstract

Objective: This research aimed at examining the volume of hidden blood loss (HBL) in lumbar fusion surgery with two kinds of screw implanting techniques and evaluating HBL-related factors in the patient population receiving lumbar fusion surgeryMethods: A retrospective study was conducted targeting 104 patients with lumbar degenerative diseases and treated with TLIF from January 2017 to December 2018, and the CBT (cortical bone trajectory) technique and conventional PS (pedicle screw) technique were applied to 45 and 59 patients, respectively. The collected data covered patients’ weight, height, BMI index, and operation time. It was followed by the recording of preoperative and postoperative hematocrit (HCT) of patients, based on which the blood loss was calculated by Gross’s formula. Results: The CBT and PS groups presented no significant difference in demographic characteristics (p > 0. 05), but the average HBL of 280±227 mL and 298±232 mL as well as the average TBL of 603±232 mL and 728±321 mL, respectively. It indicated the difference of the two groups in TBL, but no significant difference in HBL. In addition, an association of HBL of two screw techniques with operation time, concomitant disease and age was found from the data analysis.Conclusion: Large total blood loss incurred in lumbar fusion surgery, specifically with a lower value by the CBT technique than by the PS technique. Nonetheless, HBL occupied a large part of the total blood loss and it was identified in both groups. Thus, a good understanding of HBL will improve postoperative rehabilitation and guarantee patients’ safety.

In this paper, we study the Ruan cohomologies of X s and X sf , the natural compactifications of V s and V sf , where V s and V sf are the two small resolutions ofthe finite group quotient of the singular conifold. There is an additive isomorphism between the Chen-Ruan cohomologies ϕ : H * CR (X s ) → H * CR (X sf ). We study the three-point orbifold Gromov-Witten invariants of the exceptional curves Γ s on X s and Γ sf on X sf and show that the corresponding Ruan cohomology ring structures on the Chen-Ruan cohomologies of X s and X sf , defined by these three-point functions, are isomorphic to each other under the map ϕ and the 2010Such a function and the orbifold Poincaré pairing define the ring structure of Ruan cohomology RH * CR (X s ) over the Chen-Ruan cohomology group. Similarly, one can define F sf (β 1 , β 2 , β 3 ) on H * CR (X sf ) and the Ruan cohomology RH * CR (X sf ). Our main theorem isi.e., q ↔ q −1 . Hence, we get the isomorphism of rings: Compactifications of the resolved orbifold conifolds and their Chen-Ruan cohomologies. Resolved orbifold conifolds and their compactifications.The well-known (smooth) conifold singularity is the complex hyperplane given byIt has an isolated singular point at the origin. Given a prime number r, let µ r = ⟨ξ⟩, the cyclic group of rth roots of 1 with ξ = exp(2πi/r), act on C 4 : ξ · (x, y, z, w) = (ξx, ξ −1 y, z, w).