By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable ...By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials.Its application in deriving the normalization for some quantum optical states is presented.展开更多
By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-seri...By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-series and Hermite polynomials, i.e.,min（m,n）∑l=0^min（m,n）n!m!（-1）^l/l!（n-1）!（m-l）!/Hn-l（x）y^m-l≡ n,m（x,y）.By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators（IWOP） we derive its generating function. The circumstance in which this new special function appears and is applicable is considered.展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
Generalized q-exponentials functions are employed to make a generalization of complete and incomplete gamma functions. We obtain a generalization of this class of special functions which are very important in the fiel...Generalized q-exponentials functions are employed to make a generalization of complete and incomplete gamma functions. We obtain a generalization of this class of special functions which are very important in the fields of probability, statistics, statistical physics as well as combinatorics and we derive some of its properties. One gets that the generalized gamma function obtained whether approaches of the standard gamma function for a specific q values such as q=q0≈0.9 value suffering a large variation with the variation of q.展开更多
The aim of this short note is to examine the properties of a special function defined by an integral which was appeared in a paper by Ersoy. It is revealed that the function for is expressed in terms of the gamma func...The aim of this short note is to examine the properties of a special function defined by an integral which was appeared in a paper by Ersoy. It is revealed that the function for is expressed in terms of the gamma function and it varies linearly with for . Its appropriate graphs are plotted and its pertinent values are tabulated.展开更多
Environments with reciprocal patchiness of resources, in which the availability of two resources such as light and soil nutrients are patchily distributed in horizontal space and negatively correlated in each patch, a...Environments with reciprocal patchiness of resources, in which the availability of two resources such as light and soil nutrients are patchily distributed in horizontal space and negatively correlated in each patch, are common in many ecosystems. The strategies by which clonal plants adapt to this type of heterogeneous environment were examined in three stoloniferous herbs,Potentilla reptans L. var. sericophylla Franch., P. anserina L. and Halerpestes ruthenica (Jacq.) Qvcz., commonly inhabiting forest understories, grasslands and low saline meadows, respectively. As pairs of connected ramets were subjected to reciprocal patchiness of light and nutrients, stolon connection between the two ramets significantly enhanced biomass of both ramet growing in low light intensity but high soil nutrient condition (LH ramet) and ramet growing in high light intensity but low soil nutrient condition (HL ramet) as well as whole ramet pairs (consisting of LH ramets and HL ramets). Additionally, stolon connection greatly increased root/shoot ratio of LH ramet while significantly decreased that of HL ramet. The results indicate that a reciprocal transportation of resources between interconnected ramets and a functional specialization of ramets in uptake of abundant resources occurred. By resource sharing and functional specialization, clonal plants can efficiently acquire locally abundant resources and buffer the stress caused by reciprocal patchiness of resources.展开更多
In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above ...In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above function,are obtained.Especially,we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions.Meanwhile,some interesting integral operators and derivative operators of this function,are also discussed.展开更多
Recent studies have made substantial progress in understanding the interactions between cognitive functions, from language to cognitive control, attention, and memory. However, dissociating these functions has been ha...Recent studies have made substantial progress in understanding the interactions between cognitive functions, from language to cognitive control, attention, and memory. However, dissociating these functions has been hampered by the close proximity of regions involved, as in the case in the prefrontal and parietal cortex. In this article, we review a series of studies that investigated the relationship between language and other cognitive functions in an alternative way - by examining their functional （co-）lateralization. We argue that research on the hemispheric lateralization of language and its link with handedness can offer an appropriate starting- point to shed light on the relationships between different functions. Besides functional interactions, anatomical asymmetries in non-human primates and those underlying language in humans can provide unique information about cortical organization. Finally, some open questions and criteria are raised for an ideal theoretical model of the cortex based on hemispheric specialization.展开更多
Using liellrami-Schaefer stress funtion in the theory of elasticity in this paper, we derive the stress functions of torsion, plane problem, axisymmetric deformation in solid of revolution and torsion on solid of revo...Using liellrami-Schaefer stress funtion in the theory of elasticity in this paper, we derive the stress functions of torsion, plane problem, axisymmetric deformation in solid of revolution and torsion on solid of revolution.展开更多
In the past decades, terahertz technology has a great development and steady improvement, which has kept discovering and developing a series of potential applications in terahertz sensing, imaging, spectroscopy, secur...In the past decades, terahertz technology has a great development and steady improvement, which has kept discovering and developing a series of potential applications in terahertz sensing, imaging, spectroscopy, security, and communication. After the recent technical breakthroughs in reliable sources and sensitive detectors, terahertz functional devices, such as waveguides, switches, filters, splitters, isolators, modulators and sensors, are indispensable for the construction of compact application systems and have become a worldwide supreme issue in research.展开更多
Special bilinear functions (SBF) proved to be applicable in many situations and for a good number of problems. Hence it is important to generalize them to a higher degree by expanding previous work. In the beginning, ...Special bilinear functions (SBF) proved to be applicable in many situations and for a good number of problems. Hence it is important to generalize them to a higher degree by expanding previous work. In the beginning, we give a quick review of SBF [or quacroms of second degree and dimension 2 x <em>n</em>];then we give a few applications based on previously published research concentrating on their use in evaluating some special functions and where we present the evaluation of Chebyshev polynomials as a new work. Following that, we define special trilinear functions (STF) of three <em>n</em>-tuples vectors, which are the generalization of SBF. Finally, a few applications, such as taking the product of three polynomials of degree <em>n</em>, are given stressing the fact that the process of taking the product of three integers using STF techniques, practically, takes place in a very efficient way and with no mentioned effort. A short discussion on the future of the subject constitutes the conclusion of our article.展开更多
In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bound...In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f（x,p,ξ）satisfying weak convexity assumption.展开更多
Mie theory is a rigorous solution to scattering problems in spherical coordinate system. The first step in applying Mie theory is expansion of some arbitrary incident field in terms of spherical harmonics fields in te...Mie theory is a rigorous solution to scattering problems in spherical coordinate system. The first step in applying Mie theory is expansion of some arbitrary incident field in terms of spherical harmonics fields in terms of spherical which in turn requires evaluation of certain definite integrals whose integrands are products of Bessel functions, associated Legendre functions and periodic functions. Here we present analytical results for two specific integrals that are encountered in expansion of arbitrary fields in terms of summation of spherical waves. The analytical results are in terms of finite summations which include Lommel functions. A concise analytical expression is also derived for the special case of Lommel functions that arise, rendering expensive numerical integration or other iterative techniques unnecessary.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11175113)
文摘By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials.Its application in deriving the normalization for some quantum optical states is presented.
基金supported by the Natural Science Fund of Education Department of Anhui Province,China(Grant No.KJ2016A590)the Talent Foundation of Hefei University,China(Grant No.15RC11)the National Natural Science Foundation of China(Grant Nos.11247009 and 11574295)
文摘By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-series and Hermite polynomials, i.e.,min（m,n）∑l=0^min（m,n）n!m!（-1）^l/l!（n-1）!（m-l）!/Hn-l（x）y^m-l≡ n,m（x,y）.By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators（IWOP） we derive its generating function. The circumstance in which this new special function appears and is applicable is considered.
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
文摘Generalized q-exponentials functions are employed to make a generalization of complete and incomplete gamma functions. We obtain a generalization of this class of special functions which are very important in the fields of probability, statistics, statistical physics as well as combinatorics and we derive some of its properties. One gets that the generalized gamma function obtained whether approaches of the standard gamma function for a specific q values such as q=q0≈0.9 value suffering a large variation with the variation of q.
文摘The aim of this short note is to examine the properties of a special function defined by an integral which was appeared in a paper by Ersoy. It is revealed that the function for is expressed in terms of the gamma function and it varies linearly with for . Its appropriate graphs are plotted and its pertinent values are tabulated.
文摘Environments with reciprocal patchiness of resources, in which the availability of two resources such as light and soil nutrients are patchily distributed in horizontal space and negatively correlated in each patch, are common in many ecosystems. The strategies by which clonal plants adapt to this type of heterogeneous environment were examined in three stoloniferous herbs,Potentilla reptans L. var. sericophylla Franch., P. anserina L. and Halerpestes ruthenica (Jacq.) Qvcz., commonly inhabiting forest understories, grasslands and low saline meadows, respectively. As pairs of connected ramets were subjected to reciprocal patchiness of light and nutrients, stolon connection between the two ramets significantly enhanced biomass of both ramet growing in low light intensity but high soil nutrient condition (LH ramet) and ramet growing in high light intensity but low soil nutrient condition (HL ramet) as well as whole ramet pairs (consisting of LH ramets and HL ramets). Additionally, stolon connection greatly increased root/shoot ratio of LH ramet while significantly decreased that of HL ramet. The results indicate that a reciprocal transportation of resources between interconnected ramets and a functional specialization of ramets in uptake of abundant resources occurred. By resource sharing and functional specialization, clonal plants can efficiently acquire locally abundant resources and buffer the stress caused by reciprocal patchiness of resources.
基金Supported by The National Undergraduate Innovation Training Program(Grant No.202310290069Z).
文摘In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above function,are obtained.Especially,we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions.Meanwhile,some interesting integral operators and derivative operators of this function,are also discussed.
文摘Recent studies have made substantial progress in understanding the interactions between cognitive functions, from language to cognitive control, attention, and memory. However, dissociating these functions has been hampered by the close proximity of regions involved, as in the case in the prefrontal and parietal cortex. In this article, we review a series of studies that investigated the relationship between language and other cognitive functions in an alternative way - by examining their functional （co-）lateralization. We argue that research on the hemispheric lateralization of language and its link with handedness can offer an appropriate starting- point to shed light on the relationships between different functions. Besides functional interactions, anatomical asymmetries in non-human primates and those underlying language in humans can provide unique information about cortical organization. Finally, some open questions and criteria are raised for an ideal theoretical model of the cortex based on hemispheric specialization.
文摘Using liellrami-Schaefer stress funtion in the theory of elasticity in this paper, we derive the stress functions of torsion, plane problem, axisymmetric deformation in solid of revolution and torsion on solid of revolution.
文摘In the past decades, terahertz technology has a great development and steady improvement, which has kept discovering and developing a series of potential applications in terahertz sensing, imaging, spectroscopy, security, and communication. After the recent technical breakthroughs in reliable sources and sensitive detectors, terahertz functional devices, such as waveguides, switches, filters, splitters, isolators, modulators and sensors, are indispensable for the construction of compact application systems and have become a worldwide supreme issue in research.
文摘Special bilinear functions (SBF) proved to be applicable in many situations and for a good number of problems. Hence it is important to generalize them to a higher degree by expanding previous work. In the beginning, we give a quick review of SBF [or quacroms of second degree and dimension 2 x <em>n</em>];then we give a few applications based on previously published research concentrating on their use in evaluating some special functions and where we present the evaluation of Chebyshev polynomials as a new work. Following that, we define special trilinear functions (STF) of three <em>n</em>-tuples vectors, which are the generalization of SBF. Finally, a few applications, such as taking the product of three polynomials of degree <em>n</em>, are given stressing the fact that the process of taking the product of three integers using STF techniques, practically, takes place in a very efficient way and with no mentioned effort. A short discussion on the future of the subject constitutes the conclusion of our article.
基金the Doctorial Programme Foundation of EducationMinistry of of China(20030288002)the Science Foundation of Jiangsu Province(BK2006209)+1 种基金NaturalScience Foundation of Jiangsu Higher Education Bureau(07KJD110206)NNSF of China(10771181)
文摘In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f（x,p,ξ）satisfying weak convexity assumption.
文摘Mie theory is a rigorous solution to scattering problems in spherical coordinate system. The first step in applying Mie theory is expansion of some arbitrary incident field in terms of spherical harmonics fields in terms of spherical which in turn requires evaluation of certain definite integrals whose integrands are products of Bessel functions, associated Legendre functions and periodic functions. Here we present analytical results for two specific integrals that are encountered in expansion of arbitrary fields in terms of summation of spherical waves. The analytical results are in terms of finite summations which include Lommel functions. A concise analytical expression is also derived for the special case of Lommel functions that arise, rendering expensive numerical integration or other iterative techniques unnecessary.
