In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results fo...In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results for the simultaneous approx- imation, with the same order of accuracy, of a function and its derivatives （whenever these exist）, are obtained. The relation with neural networks and radial basis func- tions approximations is discussed. Numerical examples are given for the purpose of illustration.展开更多
Some properties for convex cones are discussed, which are used to obtain an equivalent condition and another important property for nearly cone-subconvexlike set-valued functions. Under the nearly cone-subconvexlikene...Some properties for convex cones are discussed, which are used to obtain an equivalent condition and another important property for nearly cone-subconvexlike set-valued functions. Under the nearly cone-subconvexlikeness, some characterizations of the super efficiency are given in terms of scalarization and Lagrangian multipliers. Related results are generalized.展开更多
The excitation functions of two very similar reaction channels, 58Fe＋ 208pb→ 265Hs ＋ 1n and 58Fe＋ 209Bi → 266Mt ＋1n are studied in the framework of the dinuclear system conception. The fusion probabilities are f...The excitation functions of two very similar reaction channels, 58Fe＋ 208pb→ 265Hs ＋ 1n and 58Fe＋ 209Bi → 266Mt ＋1n are studied in the framework of the dinuclear system conception. The fusion probabilities are found to be strongly subject to the structure of the driving potential. Usually the fusion probability is hindered by a barrier from the injection channel towards the compound nuclear configuration. The barrier towards the mass symmetrical direction, however, also plays an important role for the fusion probability, because the barrier hinders the quasi-fission, and therefore helps fusion.展开更多
The gl（1/1） supersymmetric vertex model with domain wall boundary conditions （DWBC） on an N × N square lattice is considered. We derive the reduction formulae for the one-point boundary correlation functions ...The gl（1/1） supersymmetric vertex model with domain wall boundary conditions （DWBC） on an N × N square lattice is considered. We derive the reduction formulae for the one-point boundary correlation functions of the model. The determinant representation for the boundary correlation functions is also obtained.展开更多
We consider the dynamics of the Robertson-Walker geometry using the point-like field-theory effective action of superstrings.The exact solutions have been found for corresponding Wheeler-DeWitt equation.These solution...We consider the dynamics of the Robertson-Walker geometry using the point-like field-theory effective action of superstrings.The exact solutions have been found for corresponding Wheeler-DeWitt equation.These solutions satisfy the needs of Hawking's and Kim’s boundary conditions for the wormhole wave function.Thus they can provide a quantum-mechanical description of wormholes in the superstring theory.展开更多
For the new subclass B of the bi-univalent functions constructed with the help of the(u,v)-Chebyshev polynomials of the second type,we get estimates for the first two initial coefficients and upper bounds of the Feket...For the new subclass B of the bi-univalent functions constructed with the help of the(u,v)-Chebyshev polynomials of the second type,we get estimates for the first two initial coefficients and upper bounds of the Fekete-Szeg o functional.展开更多
Remote sensing image super-resolution technology is pivotal for enhancing image quality in critical applications including environmental monitoring,urban planning,and disaster assessment.However,traditional methods ex...Remote sensing image super-resolution technology is pivotal for enhancing image quality in critical applications including environmental monitoring,urban planning,and disaster assessment.However,traditional methods exhibit deficiencies in detail recovery and noise suppression,particularly when processing complex landscapes(e.g.,forests,farmlands),leading to artifacts and spectral distortions that limit practical utility.To address this,we propose an enhanced Super-Resolution Generative Adversarial Network(SRGAN)framework featuring three key innovations:(1)Replacement of L1/L2 loss with a robust Charbonnier loss to suppress noise while preserving edge details via adaptive gradient balancing;(2)A multi-loss joint optimization strategy dynamically weighting Charbonnier loss(β=0.5),Visual Geometry Group(VGG)perceptual loss(α=1),and adversarial loss(γ=0.1)to synergize pixel-level accuracy and perceptual quality;(3)A multi-scale residual network(MSRN)capturing cross-scale texture features(e.g.,forest canopies,mountain contours).Validated on Sentinel-2(10 m)and SPOT-6/7(2.5 m)datasets covering 904 km2 in Motuo County,Xizang,our method outperforms the SRGAN baseline(SR4RS)with Peak Signal-to-Noise Ratio(PSNR)gains of 0.29 dB and Structural Similarity Index(SSIM)improvements of 3.08%on forest imagery.Visual comparisons confirm enhanced texture continuity despite marginal Learned Perceptual Image Patch Similarity(LPIPS)increases.The method significantly improves noise robustness and edge retention in complex geomorphology,demonstrating 18%faster response in forest fire early warning and providing high-resolution support for agricultural/urban monitoring.Future work will integrate spectral constraints and lightweight architectures.展开更多
Mesenchymal stromal cell transplantation is an effective and promising approach for treating various systemic and diffuse diseases.However,the biological characteristics of transplanted mesenchymal stromal cells in hu...Mesenchymal stromal cell transplantation is an effective and promising approach for treating various systemic and diffuse diseases.However,the biological characteristics of transplanted mesenchymal stromal cells in humans remain unclear,including cell viability,distribution,migration,and fate.Conventional cell tracing methods cannot be used in the clinic.The use of superparamagnetic iron oxide nanoparticles as contrast agents allows for the observation of transplanted cells using magnetic resonance imaging.In 2016,the National Medical Products Administration of China approved a new superparamagnetic iron oxide nanoparticle,Ruicun,for use as a contrast agent in clinical trials.In the present study,an acute hemi-transection spinal cord injury model was established in beagle dogs.The injury was then treated by transplantation of Ruicun-labeled mesenchymal stromal cells.The results indicated that Ruicunlabeled mesenchymal stromal cells repaired damaged spinal cord fibers and partially restored neurological function in animals with acute spinal cord injury.T2*-weighted imaging revealed low signal areas on both sides of the injured spinal cord.The results of quantitative susceptibility mapping with ultrashort echo time sequences indicated that Ruicun-labeled mesenchymal stromal cells persisted stably within the injured spinal cord for over 4 weeks.These findings suggest that magnetic resonance imaging has the potential to effectively track the migration of Ruicun-labeled mesenchymal stromal cells and assess their ability to repair spinal cord injury.展开更多
Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the m...Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the main contributions is proving this property using linear algebra instead of profound knowledge.This makes it easy to read and understand this fundamental fact.The proof of linear independence of a set of Gauss functions relies on the constructing method for one-dimensional space and on the deducing method for higher dimensions.Additionally,under the condition of preserving the same moments between the original function and interpolating function,both the interpolating existence and uniqueness are proven for GRBF in one-dimensional space.The final work demonstrates the application of the GRBF method to locate lunar olivine.By combining preprocessed data using GRBF with the removing envelope curve method,a program is created to find the position of lunar olivine based on spectrum data,and the numerical experiment shows that it is an effective scheme.展开更多
In today's era of continuous advancement in materials science,the properties of materials are constantly being enhanced,and their application fields are also expanding continuously.SAF(Super Absorbent Fiber),one s...In today's era of continuous advancement in materials science,the properties of materials are constantly being enhanced,and their application fields are also expanding continuously.SAF(Super Absorbent Fiber),one such material,stands out.Compared to traditional SAP(Super Absorbent Polymer),SAF boasts a unique fibrous form and exceptional performance,presenting broad application prospects.展开更多
In the paper,a class of functions with bounded turnings involving cardioid domain,are studied in the region of the unit disc.The bounds of|a_(5)|,|a_(6)|,|a_(7)|and the fourth Hankel determinant are obtained,which are...In the paper,a class of functions with bounded turnings involving cardioid domain,are studied in the region of the unit disc.The bounds of|a_(5)|,|a_(6)|,|a_(7)|and the fourth Hankel determinant are obtained,which are more accurate than those obtained by Srivastava.展开更多
In this paper, we introduce and investigate a new subclass of the function class ∑. of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Fu...In this paper, we introduce and investigate a new subclass of the function class ∑. of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients ｜a2｜ and ｜a3｜ for functions in the new subclass introduced here. Further Application of Hohlov operator to this class is obtained. Several （known or new） consequences of the results are also pointed out.展开更多
By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several propertie...By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several properties and characteristics including(for example)the modified Hadamard products,Holder's inequalities and convolution properties as well as some closure properties under a general family of integral transforms.展开更多
We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra.Then its super Hamiltonian structure is furnished by super trace identity.As its r...We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra.Then its super Hamiltonian structure is furnished by super trace identity.As its reduction,we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.展开更多
In the present investigation, we consider two new general subclasses B∑m（T, λ; α）and B^∑m （τ λ;β） of Em consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. For functi...In the present investigation, we consider two new general subclasses B∑m（T, λ; α）and B^∑m （τ λ;β） of Em consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. For functions belonging to the two classes introduced here, we derive non-sharp estimates on the initial coefficients [a-~＋ll and │a2＋1│. Several connections to some of the earlier known results are also pointed out.展开更多
Background Evidence on the effects of different exercise interventions on cognitive function is insufficient.Aims To evaluate the feasibility and effects of remotely supervised aerobic exercise(AE)and resistance exerc...Background Evidence on the effects of different exercise interventions on cognitive function is insufficient.Aims To evaluate the feasibility and effects of remotely supervised aerobic exercise(AE)and resistance exercise(RE)interventions in older adults with mild cognitive impairment(MCI).Methods This study is a 6-month pilot three-arm randomised controlled trial.Eligible participants(n=108)were recruited and randomised to the AE group,RE group or control(CON)group with a 1:1:1 ratio.Interventions were delivered at home with remote supervision.We evaluated participants’global cognition,memory,executive function,attention,physical activity levels,physical performance and muscle strength of limbs at baseline,3 months(T1)and 6 months(T2)after randomisation.A linear mixed-effects model was adopted for data analyses after controlling for covariates.Tukey’s method was used for adjusting for multiple comparisons.Sensitivity analyses were performed after excluding individuals with low compliance rates.Results 15(13.89%)participants dropped out.The median compliance rates in the AE group and RE group were 67.31%and 93.27%,respectively.After adjusting for covariates,the scores of the Alzheimer’s Disease Assessment Scale-Cognitive subscale in the AE group decreased by 2.04(95%confidence interval(CI)−3.41 to−0.67,t=−2.94,p=0.004)and 1.53(95%CI−2.88 to−0.17,t=−2.22,p=0.028)points more than those in the CON group at T1 and T2,respectively.The effects of AE were still significant at T1(estimate=−1.70,95%CI−3.20 to−0.21,t=−2.69,p=0.021),but lost statistical significance at T2 after adjusting for multiple comparisons.As for executive function,the Stroop time interference in the RE group decreased by 11.76 s(95%CI−21.62 to−1.90,t=−2.81,p=0.015)more than that in the AE group at T2 after Tukey’s adjustment.No other significant effects on cognitive functions were found.Conclusions Both remotely supervised AE and RE programmes are feasible in older adults with MCI.AE has positive effects on global cognition,and RE improves executive function.展开更多
An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,...An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,π/2） such that Re {eiδ（1-z）2f′（z）} 〉 0, z ∈ D. For the class C（k） of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.展开更多
基金supported, in part, by the GNAMPA and the GNFM of the Italian INdAM
文摘In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results for the simultaneous approx- imation, with the same order of accuracy, of a function and its derivatives （whenever these exist）, are obtained. The relation with neural networks and radial basis func- tions approximations is discussed. Numerical examples are given for the purpose of illustration.
文摘Some properties for convex cones are discussed, which are used to obtain an equivalent condition and another important property for nearly cone-subconvexlike set-valued functions. Under the nearly cone-subconvexlikeness, some characterizations of the super efficiency are given in terms of scalarization and Lagrangian multipliers. Related results are generalized.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10505016, 10235020, and 10235030, the Knowledge Innovation Project of the Chinese Academy of Sciences under Grant Nos. KJCX2-SW-N17 and KJCX-SYW-N2, the Natural Science Foundation of Guangdong Province under Grant No. 04300874, Major State Basic Research Development Program under Grant No. 2007CB815000 and the Financial Support from DFG of Germany
文摘The excitation functions of two very similar reaction channels, 58Fe＋ 208pb→ 265Hs ＋ 1n and 58Fe＋ 209Bi → 266Mt ＋1n are studied in the framework of the dinuclear system conception. The fusion probabilities are found to be strongly subject to the structure of the driving potential. Usually the fusion probability is hindered by a barrier from the injection channel towards the compound nuclear configuration. The barrier towards the mass symmetrical direction, however, also plays an important role for the fusion probability, because the barrier hinders the quasi-fission, and therefore helps fusion.
基金National Natural Science Foundation of China under Grant No.90403019
文摘The gl（1/1） supersymmetric vertex model with domain wall boundary conditions （DWBC） on an N × N square lattice is considered. We derive the reduction formulae for the one-point boundary correlation functions of the model. The determinant representation for the boundary correlation functions is also obtained.
文摘We consider the dynamics of the Robertson-Walker geometry using the point-like field-theory effective action of superstrings.The exact solutions have been found for corresponding Wheeler-DeWitt equation.These solutions satisfy the needs of Hawking's and Kim’s boundary conditions for the wormhole wave function.Thus they can provide a quantum-mechanical description of wormholes in the superstring theory.
文摘For the new subclass B of the bi-univalent functions constructed with the help of the(u,v)-Chebyshev polynomials of the second type,we get estimates for the first two initial coefficients and upper bounds of the Fekete-Szeg o functional.
基金This study was supported by:Inner Mongolia Academy of Forestry Sciences Open Research Project(Grant No.KF2024MS03)The Project to Improve the Scientific Research Capacity of the Inner Mongolia Academy of Forestry Sciences(Grant No.2024NLTS04)The Innovation and Entrepreneurship Training Program for Undergraduates of Beijing Forestry University(Grant No.X202410022268).
文摘Remote sensing image super-resolution technology is pivotal for enhancing image quality in critical applications including environmental monitoring,urban planning,and disaster assessment.However,traditional methods exhibit deficiencies in detail recovery and noise suppression,particularly when processing complex landscapes(e.g.,forests,farmlands),leading to artifacts and spectral distortions that limit practical utility.To address this,we propose an enhanced Super-Resolution Generative Adversarial Network(SRGAN)framework featuring three key innovations:(1)Replacement of L1/L2 loss with a robust Charbonnier loss to suppress noise while preserving edge details via adaptive gradient balancing;(2)A multi-loss joint optimization strategy dynamically weighting Charbonnier loss(β=0.5),Visual Geometry Group(VGG)perceptual loss(α=1),and adversarial loss(γ=0.1)to synergize pixel-level accuracy and perceptual quality;(3)A multi-scale residual network(MSRN)capturing cross-scale texture features(e.g.,forest canopies,mountain contours).Validated on Sentinel-2(10 m)and SPOT-6/7(2.5 m)datasets covering 904 km2 in Motuo County,Xizang,our method outperforms the SRGAN baseline(SR4RS)with Peak Signal-to-Noise Ratio(PSNR)gains of 0.29 dB and Structural Similarity Index(SSIM)improvements of 3.08%on forest imagery.Visual comparisons confirm enhanced texture continuity despite marginal Learned Perceptual Image Patch Similarity(LPIPS)increases.The method significantly improves noise robustness and edge retention in complex geomorphology,demonstrating 18%faster response in forest fire early warning and providing high-resolution support for agricultural/urban monitoring.Future work will integrate spectral constraints and lightweight architectures.
基金supported by the National Key R&D Program of China,Nos.2017YFA0104302(to NG and XM)and 2017YFA0104304(to BW and ZZ)
文摘Mesenchymal stromal cell transplantation is an effective and promising approach for treating various systemic and diffuse diseases.However,the biological characteristics of transplanted mesenchymal stromal cells in humans remain unclear,including cell viability,distribution,migration,and fate.Conventional cell tracing methods cannot be used in the clinic.The use of superparamagnetic iron oxide nanoparticles as contrast agents allows for the observation of transplanted cells using magnetic resonance imaging.In 2016,the National Medical Products Administration of China approved a new superparamagnetic iron oxide nanoparticle,Ruicun,for use as a contrast agent in clinical trials.In the present study,an acute hemi-transection spinal cord injury model was established in beagle dogs.The injury was then treated by transplantation of Ruicun-labeled mesenchymal stromal cells.The results indicated that Ruicunlabeled mesenchymal stromal cells repaired damaged spinal cord fibers and partially restored neurological function in animals with acute spinal cord injury.T2*-weighted imaging revealed low signal areas on both sides of the injured spinal cord.The results of quantitative susceptibility mapping with ultrashort echo time sequences indicated that Ruicun-labeled mesenchymal stromal cells persisted stably within the injured spinal cord for over 4 weeks.These findings suggest that magnetic resonance imaging has the potential to effectively track the migration of Ruicun-labeled mesenchymal stromal cells and assess their ability to repair spinal cord injury.
基金Supported by the National Basic Research Program of China(2012CB025904)Zhengzhou Shengda University of Economics,Business and Management(SD-YB2025085)。
文摘Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the main contributions is proving this property using linear algebra instead of profound knowledge.This makes it easy to read and understand this fundamental fact.The proof of linear independence of a set of Gauss functions relies on the constructing method for one-dimensional space and on the deducing method for higher dimensions.Additionally,under the condition of preserving the same moments between the original function and interpolating function,both the interpolating existence and uniqueness are proven for GRBF in one-dimensional space.The final work demonstrates the application of the GRBF method to locate lunar olivine.By combining preprocessed data using GRBF with the removing envelope curve method,a program is created to find the position of lunar olivine based on spectrum data,and the numerical experiment shows that it is an effective scheme.
文摘In today's era of continuous advancement in materials science,the properties of materials are constantly being enhanced,and their application fields are also expanding continuously.SAF(Super Absorbent Fiber),one such material,stands out.Compared to traditional SAP(Super Absorbent Polymer),SAF boasts a unique fibrous form and exceptional performance,presenting broad application prospects.
基金Supported by the Natural Science Foundation of Anhui Provincial Department of Education(Grant Nos.KJ2020A 0993KJ2020ZD74)+2 种基金the High-Level Talent Research Start-Up Project(Grant No.DC2300000286)the Foundation of Guangzhou Civil Aviation College(Grant Nos.22X041824X4412).
文摘In the paper,a class of functions with bounded turnings involving cardioid domain,are studied in the region of the unit disc.The bounds of|a_(5)|,|a_(6)|,|a_(7)|and the fourth Hankel determinant are obtained,which are more accurate than those obtained by Srivastava.
文摘In this paper, we introduce and investigate a new subclass of the function class ∑. of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients ｜a2｜ and ｜a3｜ for functions in the new subclass introduced here. Further Application of Hohlov operator to this class is obtained. Several （known or new） consequences of the results are also pointed out.
文摘By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several properties and characteristics including(for example)the modified Hadamard products,Holder's inequalities and convolution properties as well as some closure properties under a general family of integral transforms.
基金Supported by the Natural Science Foundation of China under Grant No. 60972164the Program for Liaoning Excellent Talents in University under Grant No. LJQ2011136+2 种基金the Key Technologies R&D Program of Liaoning Province under Grant No. 2011224006the Program for Liaoning Innovative Research Team in University under Grant No. LT2011019the Science and Technology Program of Shenyang under Grant No. F11-264-1-70
文摘We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra.Then its super Hamiltonian structure is furnished by super trace identity.As its reduction,we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.
文摘In the present investigation, we consider two new general subclasses B∑m（T, λ; α）and B^∑m （τ λ;β） of Em consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. For functions belonging to the two classes introduced here, we derive non-sharp estimates on the initial coefficients [a-~＋ll and │a2＋1│. Several connections to some of the earlier known results are also pointed out.
基金funded by the National Natural Science Foundation of China(81871854,72374014)the National Key R&D Program of China(2020YFC2008804)+1 种基金the Shanghai Jiao Tong University Young Talent Cultivation Program in Liberal Arts(2024QN041)the Shanghai Jiao Tong University School of Medicine:Nursing Development Program(SJTUHLXK2024).
文摘Background Evidence on the effects of different exercise interventions on cognitive function is insufficient.Aims To evaluate the feasibility and effects of remotely supervised aerobic exercise(AE)and resistance exercise(RE)interventions in older adults with mild cognitive impairment(MCI).Methods This study is a 6-month pilot three-arm randomised controlled trial.Eligible participants(n=108)were recruited and randomised to the AE group,RE group or control(CON)group with a 1:1:1 ratio.Interventions were delivered at home with remote supervision.We evaluated participants’global cognition,memory,executive function,attention,physical activity levels,physical performance and muscle strength of limbs at baseline,3 months(T1)and 6 months(T2)after randomisation.A linear mixed-effects model was adopted for data analyses after controlling for covariates.Tukey’s method was used for adjusting for multiple comparisons.Sensitivity analyses were performed after excluding individuals with low compliance rates.Results 15(13.89%)participants dropped out.The median compliance rates in the AE group and RE group were 67.31%and 93.27%,respectively.After adjusting for covariates,the scores of the Alzheimer’s Disease Assessment Scale-Cognitive subscale in the AE group decreased by 2.04(95%confidence interval(CI)−3.41 to−0.67,t=−2.94,p=0.004)and 1.53(95%CI−2.88 to−0.17,t=−2.22,p=0.028)points more than those in the CON group at T1 and T2,respectively.The effects of AE were still significant at T1(estimate=−1.70,95%CI−3.20 to−0.21,t=−2.69,p=0.021),but lost statistical significance at T2 after adjusting for multiple comparisons.As for executive function,the Stroop time interference in the RE group decreased by 11.76 s(95%CI−21.62 to−1.90,t=−2.81,p=0.015)more than that in the AE group at T2 after Tukey’s adjustment.No other significant effects on cognitive functions were found.Conclusions Both remotely supervised AE and RE programmes are feasible in older adults with MCI.AE has positive effects on global cognition,and RE improves executive function.
文摘An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,π/2） such that Re {eiδ（1-z）2f′（z）} 〉 0, z ∈ D. For the class C（k） of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.
