In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …...In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …, 5}, a_1,…, a_k are fixed nonzero reals when p ∈ {1,3,5} and are fixed positive reals when p ∈{2,4}.展开更多
In this paper an iterated functional equation of polynomial type which does not possess the firt order iterative term g(x) is to be discussed. The difficulties resulted from loss of the first order term are overcome b...In this paper an iterated functional equation of polynomial type which does not possess the firt order iterative term g(x) is to be discussed. The difficulties resulted from loss of the first order term are overcome by utilization of Hardy-Boedewadt's theorem.展开更多
Image analysis and computer vision are interested in suitable methods to solve the nonlinear equations. Coordinate x??for f (x)?= 0?is crucial because each equation can be transformed into f (x)?= 0. A novel method of...Image analysis and computer vision are interested in suitable methods to solve the nonlinear equations. Coordinate x??for f (x)?= 0?is crucial because each equation can be transformed into f (x)?= 0. A novel method of Hurwitz-Radon Matrices (MHR) can be used in approximation of a root of function in the plane. The paper contains a way of data approximation via MHR method to solve any equation. Proposed method is based on the family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. The operator of Hurwitz-Radon (OHR), built from these matrices, is described. Two-dimensional data are represented by discrete set of curve??f points. It is shown how to create the orthogonal OHR operator and how to use it in a process of data interpolation. MHR method is interpolating the curve point by point without using any formula or function.展开更多
Background: Air temperature affects absorptive root traits, which are closely related to species distribution.However, it is still unclear how air temperature regulates species distribution through changes in absorpti...Background: Air temperature affects absorptive root traits, which are closely related to species distribution.However, it is still unclear how air temperature regulates species distribution through changes in absorptive root traits. Seven functional traits of the absorptive roots of 240 individuals of 52 species, soil properties and air temperature were measured along an elevational gradient on Mt. Fanjingshan, Tongren City, Guizhou, and then the direct and indirect effects of these controls on species distribution were detected.Results: Absorptive roots adapted to air temperature with two strategies. The first strategy was positively associated with the specific root area(SRA) and specific root length(SRL) and was negatively associated with the root tissue density(RTD), representing the classic root economics spectrum(RES). The second strategy was represented by the trade-off between root diameter, mycorrhizal fungi colonization(MF) and SRL, representing the collaboration gradient with “do it yourself” resource uptake ranging from “outsourcing” to mycorrhizal resource uptake. Air temperature regulated species distribution in six ways: directly reducing species importance value;indirectly increasing the species importance value by reducing soil nitrogen content or increasing soil pH by reducing soil moisture inducing absorptive roots to change from “do it yourself” resource absorption to “outsourcing” resource absorption;indirectly decreasing the species importance value by decreasing soil moisture to change from“outsourcing”resource absorption to “do it yourself” resource absorption;indirectly increasing the species importance value with increasing soil pH by reducing soil moisture resulting in absorptive root traits turning into nutrient foraging traits;and indirectly decreasing the species importance value by promoting absorptive root traits to nutrient conservation traits.Conclusions: Absorptive root traits play a crucial role in the regulation of species distribution through multiapproaches of air temperature.展开更多
Properties of continuous solutions of a second order polynomial-like iterated functional equation are given by considering its characteristic.A useful method to discuss the general case is described indeed in this pro...Properties of continuous solutions of a second order polynomial-like iterated functional equation are given by considering its characteristic.A useful method to discuss the general case is described indeed in this procedure.展开更多
Polynomial functions containing terms with non-integer powers are studied to disclose possible approaches for obtaining their roots as well as employing them for curve-fitting purposes. Several special cases represent...Polynomial functions containing terms with non-integer powers are studied to disclose possible approaches for obtaining their roots as well as employing them for curve-fitting purposes. Several special cases representing equations from different categories are investigated for their roots. Curve-fitting applications to physically meaningful data by the use of fractional functions are worked out in detail. Relevance of this rarely worked subject to solutions of fractional differential equations is pointed out and existing potential in related future work is emphasized.展开更多
文摘In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …, 5}, a_1,…, a_k are fixed nonzero reals when p ∈ {1,3,5} and are fixed positive reals when p ∈{2,4}.
文摘In this paper an iterated functional equation of polynomial type which does not possess the firt order iterative term g(x) is to be discussed. The difficulties resulted from loss of the first order term are overcome by utilization of Hardy-Boedewadt's theorem.
文摘Image analysis and computer vision are interested in suitable methods to solve the nonlinear equations. Coordinate x??for f (x)?= 0?is crucial because each equation can be transformed into f (x)?= 0. A novel method of Hurwitz-Radon Matrices (MHR) can be used in approximation of a root of function in the plane. The paper contains a way of data approximation via MHR method to solve any equation. Proposed method is based on the family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. The operator of Hurwitz-Radon (OHR), built from these matrices, is described. Two-dimensional data are represented by discrete set of curve??f points. It is shown how to create the orthogonal OHR operator and how to use it in a process of data interpolation. MHR method is interpolating the curve point by point without using any formula or function.
基金financially supported by the National Nature Science Foundation of China (No.32001248)the Characteristic Field Project of Department of Education of Guizhou Province (NO.[2019]075)+3 种基金PhD Research Start-up Foundation of Tongren University (No.trxyDH1807)Guizhou Forestry Research Project (No.[2019]014)the Science and Technology Plan Project of Guizhou Province (NO.[2019]1312,NO.[2022]general-556)the Key Laboratory Project of Guizhou Province (No.[2020]2003)
文摘Background: Air temperature affects absorptive root traits, which are closely related to species distribution.However, it is still unclear how air temperature regulates species distribution through changes in absorptive root traits. Seven functional traits of the absorptive roots of 240 individuals of 52 species, soil properties and air temperature were measured along an elevational gradient on Mt. Fanjingshan, Tongren City, Guizhou, and then the direct and indirect effects of these controls on species distribution were detected.Results: Absorptive roots adapted to air temperature with two strategies. The first strategy was positively associated with the specific root area(SRA) and specific root length(SRL) and was negatively associated with the root tissue density(RTD), representing the classic root economics spectrum(RES). The second strategy was represented by the trade-off between root diameter, mycorrhizal fungi colonization(MF) and SRL, representing the collaboration gradient with “do it yourself” resource uptake ranging from “outsourcing” to mycorrhizal resource uptake. Air temperature regulated species distribution in six ways: directly reducing species importance value;indirectly increasing the species importance value by reducing soil nitrogen content or increasing soil pH by reducing soil moisture inducing absorptive roots to change from “do it yourself” resource absorption to “outsourcing” resource absorption;indirectly decreasing the species importance value by decreasing soil moisture to change from“outsourcing”resource absorption to “do it yourself” resource absorption;indirectly increasing the species importance value with increasing soil pH by reducing soil moisture resulting in absorptive root traits turning into nutrient foraging traits;and indirectly decreasing the species importance value by promoting absorptive root traits to nutrient conservation traits.Conclusions: Absorptive root traits play a crucial role in the regulation of species distribution through multiapproaches of air temperature.
基金Supported by NSF of China,Sichuan Provincial Youth Sci-Tech Foundation and Math.Grant of CAS
文摘Properties of continuous solutions of a second order polynomial-like iterated functional equation are given by considering its characteristic.A useful method to discuss the general case is described indeed in this procedure.
文摘Polynomial functions containing terms with non-integer powers are studied to disclose possible approaches for obtaining their roots as well as employing them for curve-fitting purposes. Several special cases representing equations from different categories are investigated for their roots. Curve-fitting applications to physically meaningful data by the use of fractional functions are worked out in detail. Relevance of this rarely worked subject to solutions of fractional differential equations is pointed out and existing potential in related future work is emphasized.
