Long Long - Academia.edu (original) (raw)

Papers by Long Long

arXiv: Functional Analysis, 2015

In this paper, we first introduce the notion of the Orlicz space generated from a random normed m... more In this paper, we first introduce the notion of the Orlicz space generated from a random normed module EEE. Then we give a representation theorem which identify the dual of the Orlicz heart of EEE with the Orlicz space generated from the random conjugate space of EEE. Finally, we establish relations between the strict convexity and uniform convexity of this Orlicz space and the random strict convexity and random uniform convexity of the underlying random normed module, respectively.

Biomedicine & Pharmacotherapy, 2018

Cerebral ischemia-reperfusion (I/R) injury is a key contributing factor to the pathogenic mechani... more Cerebral ischemia-reperfusion (I/R) injury is a key contributing factor to the pathogenic mechanisms involved in ischemic stroke. The present study was designed to explore the effects of icariside II (ICS II) on oxygen-glucose deprivation/reoxygenation (OGD/R)-induced PC12 cell oxidative injury. The results showed that ICS II ameliorated OGD/R-induced PC12 cell injury at the concentrations of 12.5, 25, and 50 μM, as evidenced by both the increase of cell viability and the decrease of LDH leakage from 33.96% ± 0.48% to 16.78% ± 0.78%, 13.12% ± 0.17%, 12.96% ± 0.10%, respectively. Moreover, ICS II not only attenuated the reactive oxygen species (ROS) from 212.2% ± 5.45%, 168.6% ± 5.29%, 148.7% ± 9.37%, 142.7% ± 7.76%, respectively, but also decreased the overproduction of mitochondrial ROS, as well as recovered the mitochondrial membrane potential (MMP) from 60.68% ± 7.90% to 76.71% ± 2.87%, 93.69% ± 4.41%, 95.92% ± 3.97%, respectively. Furthermore, OGD/R accelerated neuronal oxidative injury and apoptosis along with reduced nucleus-Nrf2, NQO-1, HO-1, Bcl-2 protein expressions, and increased Keap1, Bax and cleaved caspase-3 contents, whereas ICS II significantly reversed the abovementioned changes. Interestingly, ICS II also restrained the OGD/ R-induced decrease in SIRT3 and IDH2 expressions. In conclusion, this study indicates that ICS II alleviates OGD/ R-induced oxidative injury in PC12 cells, and its underlying mechanisms are due to the regulation of Nrf2/SIRT3 signaling pathway.

Toxicol. Res., 2016

Sulfur mustard (SM) is a well known chemical warfare agent that poses a major threat to military ... more Sulfur mustard (SM) is a well known chemical warfare agent that poses a major threat to military personnel and also populace.

GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference, 2009

In this paper we address the multicast survivability problem of using minimum resources to provis... more In this paper we address the multicast survivability problem of using minimum resources to provision a multicast session and its protection paths (trees) in a network such that the session is protected against any single-link failure. We propose a new protection scheme, namely, Segment-based Protection Tree (SPT). In SPT scheme, a given multicast session is first provisioned as a primary multicast tree, and then each segment on the primary tree is protected by a multicast tree instead of a path, as in most existing approaches. We also analyze the recovery performance of SPT and design a Reconfiguration Calculation Algorithm to compute the average number of reconfigurations upon any link failure. We study the performance of the SPT scheme in different traffic scenarios. The numerical results show that SPT outperforms the best existing approaches. It uses less than 10% extra resources to provision a survivable multicast session over the optimal solution and 0.2-4% lower than the existing approaches in the various traffic cases and has the average number of reconfigurations 10-86% less than the best cost efficient approach.

International journal of oral science, 2014

Our previous salivary study had demonstrated an apparent T helper 2 (Th2)-predominance in saliva ... more Our previous salivary study had demonstrated an apparent T helper 2 (Th2)-predominance in saliva of oral lichen planus (OLP) patients and suggested a potential of salivary interleukin-4 (IL-4) as a biomarker for monitoring disease severity. To further determine the consistency of Th1/Th2 bias of OLP, this study investigated the expression profile of interferon-γ (IFN-γ) and IL-4 in serum and the relationship of the serum levels of these cytokines with their saliva partners. Sixty ethnic Chinese patients with OLP (40 of the erythematous/ulcerative form and 20 of the reticular form) were recruited for this study, with 40 age-sex-matched healthy volunteers as control group. IFN-γ and IL-4 levels in serum and paired saliva samples were screened by enzyme-linked immunosorbent assay. OLP patient showed a low-level IFN-γ but high-level IL-4 expression profile in both serum and saliva, with a lower IFN-γ/IL-4 ratio. Serum IL-4 level in the erythematous/ulcerative group was significantly hig...

Mediators of inflammation, 2014

Interleukin- (IL-) 23/IL-17 axis is a newly discovered proinflammatory signaling pathway and has ... more Interleukin- (IL-) 23/IL-17 axis is a newly discovered proinflammatory signaling pathway and has been implicated in the pathogenesis of many chronic inflammatory and immune disorders. Here we investigated whether the IL-23/IL-17 axis was present and functional in the lesions of oral lichen planus (OLP), a chronic inflammatory disease affecting the oral mucosa. Using immunohistochemistry and quantitative PCR, we found that the subunits of IL-23 and IL-17 were overexpressed in OLP lesions than in normal oral mucosa tissues. In addition, the expressions of IL-23 and IL-17 are positively correlated in reticular OLP tissues. Results from in vitro studies revealed that exogenous IL-23 could increase the percentage of Th17 cells and IL-17 production in the CD4+T cells from reticular OLP patients. Furthermore, we also found that exogenous IL-17 could significantly enhance the mRNA expressions of β-defensin-2, -3, CCL-20, IL-8, and TNF-α, but not β-defensin-1, CXCL-9, -10, -11, CCL-5, and IL...

Biochimica et biophysica acta, 2015

Selective PPARγ modulators (sPPARγM) retains insulin sensitizing activity but with minimal side e... more Selective PPARγ modulators (sPPARγM) retains insulin sensitizing activity but with minimal side effects compared to traditional TZDs agents, is thought as a promising strategy for development of safer insulin sensitizer. We used a combination of virtual docking, SPR-based binding, luciferase reporter and adipogenesis assays to analyze the interaction mode, affinity and agonistic activity of L312 to PPARγ in vitro, respectively. And the anti-diabetic effects and underlying molecular mechanisms of L312 was studied in db/db mice. L312 interacted with PPARγ-LBD in a manner similar to known sPPARγM. L312 showed similar PPARγ binding affinity, but displayed partial PPARγ agonistic activity compared to PPARγ full agonist pioglitazone. In addition, L312 displayed partial recruitment of coactivator CBP yet equal disassociation of corepressor NCoR1 compared to pioglitazone. In db/db mice, L312 (30 mg/kg·day) treatment considerably improved insulin resistance with the regard to OGTT, ITT, fast...

Life sciences, 2015

The aim of the study was to explore the effect of miR-200b on the development of human peripheral... more The aim of the study was to explore the effect of miR-200b on the development of human peripheral blood monocyte-deriveddendritic-cell (DC) and its mechanisms. Expression levels of miR-200b and its predicted targets were measured by real time-PCR. Protein expression of WASF3 was determined by Western blot and immunohistochemistry. Human peripheral blood mononuclear cells (PBMCs) were isolated by Ficoll-Hypaque density gradient centrifugation from the buffy coat fraction of anticoagulated blood. Monocytes were purified from PBMCs using anti-CD14 microbeads. The immunophenotypes of DCs were tested by flow cytometry. A strong reduction in miR-200b expression was associated with human peripheral blood monocyte-derivedDC differentiation. The overexpression of miR-200b significantly reduced the numbers of protruding veils in mature DCs (mDCs) that are critical for promoting antigen-specificT-cell activation. Further experiments showed that miR-200b could regulate the function of DCs by ta...

The Tohoku Journal of Experimental Medicine, 2014

Integrins, which act as an important role in the connection between cells and extra-cellular envi... more Integrins, which act as an important role in the connection between cells and extra-cellular environments, are important cell surface receptors. Integrins have been demonstrated to play critical roles in many aspects of the progression of oral squamous cell carcinoma (OSCC). The aim of this study was to investigate the association between single nucleotide polymorphisms (SNPs) in microRNA-binding sites of integrin genes and the susceptibility and progression of OSCC in Chinese Han Population. We recruited 167 OSCC patients and 200 cancer-free controls from three independent medical centers. Genotyping was completed successfully for the five selected integrin SNPs: rs1062484 (integrin α3), rs11902171 (integrin α v), rs17468 (integrin β 1), rs3809865 (integrin β 3), and rs2675 (integrin β 5). The results demonstrated that the A allele of rs3809865 T/A (a T-to-A nucleotide change), a functional polymorphism in the 3′UTR of integrin β3 gene, was associated with OSCC risk (p < 0.05). In addition, the association analysis between this SNP and integrin β 3 mRNA expression level in the patients' peripheral blood mononuclear cells indicated that OSCC patients carrying the A allele would have a lower integrin β3 expression level (p = 0.047). Meanwhile, survival analysis showed that the C allele of rs2675 A/C (nucleotide change from A to C), another 3′UTR polymorphism in integrin β5 gene, was related with progression of OSCC. Overall, our results suggest that rs3809865 and rs2675 may contribute to OSCC risk and progression in Chinese Han Population. These two SNPs may be used as potential diagnostic and prognostic biomarkers for OSCC in future.

Optical Switching and Networking, 2013

The p-cycle and its Failure Independent Path Protection (FIPP) extension are known to be efficien... more The p-cycle and its Failure Independent Path Protection (FIPP) extension are known to be efficient and agile protection strategies. The p-cycle is preconfigured such that if there is a failure, only the switches at two end nodes need to be reconfigured. In this paper, we extend the p-cycle by allowing cycles to have attached links, called Parasitic Protection Links (PPL), in order to protect paths whose source and destination nodes are not only located on the cycle but also connected by the PPL to the cycle. A p-cycle with PPL is named p 2-cycle. We address the unicast service protection problems against single-link failures by using p 2-cycle in mesh networks and the problem is formulated as an Integer Linear Program (ILP). The numerical results show that the p 2-cycle scheme provides better capacity efficiency than the FIPP p-cycle scheme in all the traffic scenarios considered and consumes 2.7% − 14.8% extra total cost over the optimum, provided by Shared Backup Path Protection (SBPP) approach. Moreover, we study the failure recovery performance by comparing it to FIPP and SBPP in terms of average number of reconfigurations (NOR). The results achieved by the p 2-cycle are much better than that of SBPP and gets close to FIPP as the number of traffic demands increases. In conclusion, the p 2-cycle protection scheme provides greater overall performance over existent protection schemes, especially when the number of traffic demands is large.

Molecules, 2014

A series of 1-aryl-3-(2H-chromen-5-yl)urea and 1-aryl-3-(chroman-5-yl)urea derivatives were desig... more A series of 1-aryl-3-(2H-chromen-5-yl)urea and 1-aryl-3-(chroman-5-yl)urea derivatives were designed, synthesized and evaluated for their inhibitory activities towards TNF-α production in lipopolysaccharide-stimulated THP-1 cells. The most active compound, 40g, inhibited TNF-α release with an IC 50 value of 0.033 μM, which is equipotent to that of BIRB796 (IC 50 = 0.032 μM).

Journal of Molecular Neuroscience, 2013

Jun activation domain-binding protein (Jab1) is a multifunctional protein that participates in af... more Jun activation domain-binding protein (Jab1) is a multifunctional protein that participates in affecting signaling pathway, controlling cell proliferation and apoptosis, and regulating genomic instability and DNA repair, and acts as a key subunit of COP9 signalosome. p27kip1, a member of the Cip/Kip family of cyclin-dependent kinase inhibitors, was shown to inhibit the enzymatic activity of cyclin-CDK complexes, resulting in cell-cycle arrest at G1. Recent studies have shown that Jab1 directly binds to p27kip1 and induces nuclear export and subsequent degradation in a variety of human cancers, while the association and function of Jab1 and p27kip1 in nervous system lesion and regeneration remain unclear. Here, we performed a sciatic nerve injury model in adult rats and studied the dynamic changes of Jab1 and p27kip1 expression by Western blot. Sciatic nerve crush (SNC) resulted in a significant upregulation of Jab1 and a downregulation of p27kip1. Besides, we observed that Jab1 was expressed widely in Schwann cells (SCs) and had few co-localization in axons by double immunofluorescence staining. In addition, the peak expression of Jab1 was parallel with proliferating cell nuclear antigen (PCNA), and numerous SCs expressing Jab1 were PCNA-positive. Results obtained by co-immunoprecipitation and double labeling further showed their interaction in the sciatic nerve. Thus, these results suggested that Jab1 and p27kip1 may be involved in the pathophysiology of sciatic nerve after SNC.

Computer Networks, 2010

In WDM networks, it is important to protect connections against link failures due to the high ban... more In WDM networks, it is important to protect connections against link failures due to the high bandwidth provided by a fiber link. Although many p-cycle based schemes have been proposed for single-link failure protection, protection against two-link failures have not received much attention. In this paper, we propose p-cycle based protection schemes for two-link failures. We formulate an ILP model for the pcycle design problem for static traffic. We also propose two protection schemes for dynamic traffic, namely SPPP (Shortest Path Pair Protection) and SFPP (Short Full Path Protection). Simulation results show that SFPP is more capacity efficient than SPPP under incremental traffic. Under dynamic traffic, SPPP has lower blocking than SFPP when the traffic load is low and has higher blocking than SFPP when the traffic load is high.

Clinical and Experimental Medicine, 2013

Osteoarthritis (OA) is a complex disease characterized by cartilage degeneration, secondary synov... more Osteoarthritis (OA) is a complex disease characterized by cartilage degeneration, secondary synovial membrane inflammation and subchondral bone changes. In recent years, many studies have confirmed that interleukin-18 (IL-18) is involved in the inflammatory process of inflammatory joint diseases. In the present study, we investigated IL-18 levels in plasma, synovial fluid and articular cartilage of patients with primary knee OA (n = 33) to analyze their relationship with radiographic severity. Compared to healthy controls (n = 15), OA patients had higher plasma and synovial fluid IL-18 concentrations(45.8 ± 22.1 vs. 23.7 ± 13.6 pg/ml, P&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;0.001 and 75.2 ± 40.1 vs. 28.3 ± 11.6 pg/ml, P&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;0.001) as measured by enzyme-linked immunosorbent assay. Also,the percentage of immunofluorescent IL-18 positive cells in articular cartilage was significantly increased in OA compared to controls (46.5 ± 10.3 vs. 2.9 ± 1.7, P&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;0.001). Moreover, plasma, synovial fluid and articular cartilage IL-18 significantly positively correlated with radiographic severity, respectively (r = 0.663, P&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;0.001, r = 0.56, P = 0.001 and r = 0.884, P&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;0.001). Subsequent analysis revealed that plasma, synovial fluid and articular cartilage IL-18 levels positively correlated with each other (r = 0.632, P&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;0.001, r = 0.489, P = 0.004 and r = 0.620, P&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;0.001). These data suggested that plasma, synovial fluid and articular cartilage IL-18 levels were significantly increased in OA patients, and these elevated levels were positively correlated with radiographic severity. Accordingly, our study supports the role of IL-18 in the pathophysiology of OA.

Cellular and Molecular Neurobiology, 2013

As a novel cell cycle inhibitor, PHB2 controls the G1/S transition in cycling cells in a complex ... more As a novel cell cycle inhibitor, PHB2 controls the G1/S transition in cycling cells in a complex manner. Its aberrant expression is closely related to cell carcinogenesis. While its expression and role in peripheral nervous system lesion and repair were still unknown. Here, we performed an acute sciatic nerve crush (SNC) model in adult rats to examine the dynamic changes of PHB2. Temporally, PHB2 expression was sharply decreased after sciatic nerve crush and reached a valley at day 5. Spatially, PHB2 was widely expressed in the normal sciatic nerve including axons and Schwann cells. While after injury, PHB2 expression decreased predominantly in Schwann cells. The alteration was due to the decreased expression of PHB2 in Schwann cells after SNC. PHB2 expression correlated closely with Schwann cells proliferation in sciatic nerve post injury. Furthermore, PHB2 largely localized with GAP43 in axons in the crushed segment. Collectively, we suggested that PHB2 participated in the pathological process response to sciatic nerve injury and may be associated with Schwann cells proliferation and axons regeneration.

Acta Pharmacologica Sinica, 2005

Aim: Advanced glycation endproducts (AGE) have been implicated in the pathogenesis of diabetic co... more Aim: Advanced glycation endproducts (AGE) have been implicated in the pathogenesis of diabetic complications, including diabetic cardiovascular dysfunction. 3-[2-(4-Bromo-phenyl)-1-methyl-2-oxo-ethyl]-4,5,6,7-tetrahydro-benzothiazol-3-ium bromide (C16), a novel AGE breaker, was investigated for its effects on the development of cardiovascular disease in diabetic rats. Methods: Rats that had streptozotocin-induced diabetes for 12 weeks were divided into groups receiving C16 or vehicle by gavage. Results: In hemodynamic studies of the left ventricle, C16 treatment (25 or 50 mg/kg) for 4 weeks resulted in a significant increase in left ventricular systolic pressure, +dp/dt max , and-dp/dt max as compared with vehicletreated diabetic rats. Furthermore, in hemodynamic studies of the cardiovascular system, C16 (12.5, 25, or 50 mg/kg) treatment for 4 weeks resulted in a dosedependent and significant increase in cardiac output, a reduction of total peripheral resistance, and an increase in systemic arterial compliance when compared with vehicle-treated diabetic rats. Biochemical studies showed that C16 treatment also resulted in a significant decrease in immunoglobulin G-red blood cell surface crosslink content and an increase in collagen solubility. Morphological and immunohistochemical examinations indicated that C16 was able to prevent increases of the collagen type III/I ratio in the aorta and decrease the accumulation of AGE in the aorta. Conclusion: C16 has the ability to reduce AGE accumulation in tissues in vivo, and can restore diabetes-associated cardiovascular disorders in rats. This provides a potential therapeutic approach for cardiovascular disease associated with diabetes and aging in humans.

Journal of Lightwave Technology, 2009

In this paper we address the problem of traffic grooming in WDM rings with all-to-all and its gen... more In this paper we address the problem of traffic grooming in WDM rings with all-to-all and its generalization to many-to-many service by using network coding. We consider minimizing the number of Line Terminating Equipment (LTE) on two types of unidirectional rings, namely, single-hub and unhubbed rings, as our objective. In single-hub rings, we investigate the minimum cost provisioning of uniform all-to-all traffic in two cases: where network coding is used to linearly combine data, and where it is not used and data is transmitted without coding. We generalize the service mode to many-to-many and evaluate the cost of provisioning. In un-hubbed ring, we propose a multi-hub approach to obtain the minimum cost provisioning in the case of all-to-all and many-to-many traffic. In each type of ring topology, two network scenarios are considered: first, the distinct communication groups in the ring are node-disjoint and second, the different groups may have common member nodes. From our numerical results, we find that under many-to-many traffic pattern for both scenarios, network coding can reduce the network cost by 10-20% in single-hub rings and 1-5% in un-hubbed rings in both network scenarios.

Iranian Journal of Public Health, 2019

We aimed to investigate the efficacy of paclitaxel combined with kanglaite injection in the treat... more We aimed to investigate the efficacy of paclitaxel combined with kanglaite injection in the treatment of bone metastases of lung cancer in mice. Human lung cancer cell line A549 was inoculated into 100 C57BL/6 mice to establish bone metastasis model of lung cancer. Eighty successful modeling mice were randomly divided into four groups: Kanglaite (group A), Paclitaxel (group B), Paclitaxel combined with kanglaite (group C) and 0.9% sodium chloride solution (control group), 20 in each group. The mice started taking drugs on the 5th day after inoculation. The treatment lasted for 21 days, and the changes of body weight were observed. Evaluation of the efficacy of drug therapy was performed by comparing the pain behavior of the treated mice with that of the control mice. The physical improvement rates in group A and group B were lower than that in group C (P<0.05). The bone metastasis area and tumor weight in group A, group B and group C were significantly lower than those in control...

Let (Ω,ℱ,P) be a probability space and L^0(ℱ) be the algebra of equivalence classes of real-value... more Let (Ω,ℱ,P) be a probability space and L^0(ℱ) be the algebra of equivalence classes of real-valued random variables defined on (Ω,ℱ,P). A left module M over the algebra L^0(ℱ)(briefly, an L^0(ℱ)-module) is said to be regular if any given two elements x and y in M must be equal whenever there exists a countable partition {A_n,n∈ℕ} of Ω to ℱ such that Ĩ_A_n· x=Ĩ_A_n· y for each n∈ℕ, where I_A_n is the characteristic function of A_n and Ĩ_A_n its equivalence class. The purpose of this paper is to establish the fundamental theorem of L^0-affine geometry in regular L^0(ℱ)-modules: Let V and V^' be two regular L^0(ℱ)-modules such that V contains a free L^0(ℱ)-submodule of rank 2. If T:V→ V^' is stable and invertible and maps each L^0-line segment onto an L^0-line segment, then T must be L^0-affine.