The release of a new artificial intelligence(AI)model,ironically,evokes a biblical memory.What has transpired in the past few days echoes the biblical story of David versus Goliath,in which the massive and wellarmed G...The release of a new artificial intelligence(AI)model,ironically,evokes a biblical memory.What has transpired in the past few days echoes the biblical story of David versus Goliath,in which the massive and wellarmed Goliath is defeated by the comparatively puny David,who comes to the battle with only his staff and sling.展开更多
Amid overlapping crises and uncertainties as the world enters an era of turbulence and transformation,the countries of the Global South are swiftly emerging from the periphery of world politics to the forefront of int...Amid overlapping crises and uncertainties as the world enters an era of turbulence and transformation,the countries of the Global South are swiftly emerging from the periphery of world politics to the forefront of international cooperation,playing an increasingly vital role in advancing humanity’s collective progress.展开更多
The release of a new artificial intelligence(AI)model,ironically,evokes a biblical memory.What has transpired in the past few days echoes the story of David versus Goliath,in which the massive and well-armed Goliath i...The release of a new artificial intelligence(AI)model,ironically,evokes a biblical memory.What has transpired in the past few days echoes the story of David versus Goliath,in which the massive and well-armed Goliath is defeated by the comparatively puny David,who comes to the battle with only his staff and sling.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
This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ...This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.展开更多
This study describes how one can construct sets of composite natural numbers as tensorial products of the vectors created with the natural powers of prime numbers.
In this paper, it is shown that： if λ1 ,……λs axe nonzero real numbers, not all of the same sign, such that A1/A2 is irrational, then for any real number η and ε 〉 0 the inequality ｜λ1x1^2 ＋ λ2x2^2＋ λ3x3^...In this paper, it is shown that： if λ1 ,……λs axe nonzero real numbers, not all of the same sign, such that A1/A2 is irrational, then for any real number η and ε 〉 0 the inequality ｜λ1x1^2 ＋ λ2x2^2＋ λ3x3^4＋ λsx3^4＋……λsx8^4 ＋η〈 ε has infinitely many solutions in positive integers x1,... ,xs.展开更多
The incidence chromatic number of G is the least number of colors such that G has an incidence coloring. It is proved that the incidence chromatic number of Cn^p, the p-th power of the circuit graph, is 2p ＋ 1 if and...The incidence chromatic number of G is the least number of colors such that G has an incidence coloring. It is proved that the incidence chromatic number of Cn^p, the p-th power of the circuit graph, is 2p ＋ 1 if and only if n = k（2p ＋ 1）, for other cases： its incidence chromatic number is at most 2p ＋ [r/k] ＋ 2, where n = k（p ＋ 1） ＋ r, k is a positive integer. This upper bound is tight for some cases.展开更多
Utilizing translation operators we get the powers sums on arithmetic progressions and the Bernoulli polynomials of order munder the form of differential operators acting on monomials. It follows that (d/dn-d/dz) appli...Utilizing translation operators we get the powers sums on arithmetic progressions and the Bernoulli polynomials of order munder the form of differential operators acting on monomials. It follows that (d/dn-d/dz) applied on a power sum has a meaning and is exactly equal to the Bernoulli polynomial of the same order. From this new property we get the formula giving powers sums in term of sums of successive derivatives of Bernoulli polynomial multiplied withprimitives of the same order of n. Then by changing the two arguments z,n into Z=z(z-1), λ where λ designed the 1st order power sums and proving that Bernoulli polynomials of odd order vanish for arguments equal to 0, 1/2, 1, we obtain easily the Faulhaber formula for powers sums in term of polynomials in λ having coefficients depending on Z. These coefficients are found to be derivatives of odd powers sums on integers expressed in Z. By the way we obtain the link between Faulhaber formulae for powers sums on integers and on arithmetic progressions. To complete the work we propose tables for calculating in easiest manners possibly the Bernoulli numbers, the Bernoulli polynomials, the powers sums and the Faulhaber formula for powers sums.展开更多
The stopping powers of Br and C in Ag Elm have been measured with the method of elastic recoil detection in energy range 0.28-0.42MeV/amu.The results have been compared with the theoretical calculations of TRIM-90.
In this paper, by using superposition method, we aim to show that ∑^n i=1 （2/- 1）^2k-1 is the product of n2 and a rational polynomial in n2 with degree k- 1, and that ∑^ni=1 （2i - 1）^2k is the product of n（2n ...In this paper, by using superposition method, we aim to show that ∑^n i=1 （2/- 1）^2k-1 is the product of n2 and a rational polynomial in n2 with degree k- 1, and that ∑^ni=1 （2i - 1）^2k is the product of n（2n - 1）（2n ＋ 1） and a rational polynomial in （2n - 1）（2n ＋ 1） with degree k - 1. Moreover, recurrence formulas to compute the coefficients of the corresponding rational polynomials are also obtained.展开更多
Examining the B-coefficient relations between two adjacent s-simplicies with given smoothness requirements, we find a compromise technique between btp-coefficients and B-coefficients to calculate a bivariate locally s...Examining the B-coefficient relations between two adjacent s-simplicies with given smoothness requirements, we find a compromise technique between btp-coefficients and B-coefficients to calculate a bivariate locally supported spline, give another proof of the BM-splines in S_(100)(4d, 3d-1, △_2) and establish the BM-splines in S_2~1, and S_4,展开更多
An operator on formal power series of the form S μS , where μ is an invertible power series, and σ is a series of the form?t+(t2)?is called a unipotent substitution with pre-function. Such operators, denoted by a p...An operator on formal power series of the form S μS , where μ is an invertible power series, and σ is a series of the form?t+(t2)?is called a unipotent substitution with pre-function. Such operators, denoted by a pair (μ ,σ )? , form a group. The objective of this contribution is to show that it is possible to define a generalized powers for such operators, as for instance fractional powers σ for every .展开更多
Lu:If the tense situations in the Middle East and Northeast Asiabecome relaxed,it would certainly exert great influence on world politi-cal pattern.Can non-traditional security solve the contradictions in thetradition...Lu:If the tense situations in the Middle East and Northeast Asiabecome relaxed,it would certainly exert great influence on world politi-cal pattern.Can non-traditional security solve the contradictions in thetraditional security field?Will the major powers continue to cooperate inthe anti-terrorist campaign?All these issues will face challenges展开更多
Richard Powers is one of American famous contemporary writers,a rising star of American postmodernist fiction,and one of the representatives of the Generation Xers as well.He explores the impacts of some factors such ...Richard Powers is one of American famous contemporary writers,a rising star of American postmodernist fiction,and one of the representatives of the Generation Xers as well.He explores the impacts of some factors such as ecological environment,social culture,and family ethics on our modern society by use of his abundant knowledge about gene engineer,neurology,family ethics,etc.From the perspective of Marxism ecological philosophy,this paper deeply analyses The Echo Maker,Richard Powers’masterpiece and interrelates the ecological thoughts implied in this novel.This work criticizes anthropocentrism and expresses the priority of nature.Human being is part of nature which our human being bases on and human being is closely related with nature.Human being should develop ecological consciousness,respect and care nature,and try every means to keep benign interaction with nature in order to build a stable and harmonious global community.展开更多
文摘The release of a new artificial intelligence(AI)model,ironically,evokes a biblical memory.What has transpired in the past few days echoes the biblical story of David versus Goliath,in which the massive and wellarmed Goliath is defeated by the comparatively puny David,who comes to the battle with only his staff and sling.
文摘Amid overlapping crises and uncertainties as the world enters an era of turbulence and transformation,the countries of the Global South are swiftly emerging from the periphery of world politics to the forefront of international cooperation,playing an increasingly vital role in advancing humanity’s collective progress.
文摘The release of a new artificial intelligence(AI)model,ironically,evokes a biblical memory.What has transpired in the past few days echoes the story of David versus Goliath,in which the massive and well-armed Goliath is defeated by the comparatively puny David,who comes to the battle with only his staff and sling.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12471005 and 12031008)Natural Science Foundation of Shandong Province(Grant No.ZR2023MA003)。
文摘Let τk(n) be the k-th divisor function.In this paper,we derive an asymptotic formula for the sum ■where k≥4,r≥2,s≥2 and ℓ≥2r-1are integers.
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.
基金Supported by National Science Foundation of China(11971027,12171497)。
文摘This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.
文摘This study describes how one can construct sets of composite natural numbers as tensorial products of the vectors created with the natural powers of prime numbers.
基金the National Natural Science Foundation of China(10671056)
文摘In this paper, it is shown that： if λ1 ,……λs axe nonzero real numbers, not all of the same sign, such that A1/A2 is irrational, then for any real number η and ε 〉 0 the inequality ｜λ1x1^2 ＋ λ2x2^2＋ λ3x3^4＋ λsx3^4＋……λsx8^4 ＋η〈 ε has infinitely many solutions in positive integers x1,... ,xs.
基金Supported by NSFC(10201022,10571124,10726008)Supported by SRCPBMCE(KM200610028002)Supported by BNSF(1012003)
文摘The incidence chromatic number of G is the least number of colors such that G has an incidence coloring. It is proved that the incidence chromatic number of Cn^p, the p-th power of the circuit graph, is 2p ＋ 1 if and only if n = k（2p ＋ 1）, for other cases： its incidence chromatic number is at most 2p ＋ [r/k] ＋ 2, where n = k（p ＋ 1） ＋ r, k is a positive integer. This upper bound is tight for some cases.
文摘Utilizing translation operators we get the powers sums on arithmetic progressions and the Bernoulli polynomials of order munder the form of differential operators acting on monomials. It follows that (d/dn-d/dz) applied on a power sum has a meaning and is exactly equal to the Bernoulli polynomial of the same order. From this new property we get the formula giving powers sums in term of sums of successive derivatives of Bernoulli polynomial multiplied withprimitives of the same order of n. Then by changing the two arguments z,n into Z=z(z-1), λ where λ designed the 1st order power sums and proving that Bernoulli polynomials of odd order vanish for arguments equal to 0, 1/2, 1, we obtain easily the Faulhaber formula for powers sums in term of polynomials in λ having coefficients depending on Z. These coefficients are found to be derivatives of odd powers sums on integers expressed in Z. By the way we obtain the link between Faulhaber formulae for powers sums on integers and on arithmetic progressions. To complete the work we propose tables for calculating in easiest manners possibly the Bernoulli numbers, the Bernoulli polynomials, the powers sums and the Faulhaber formula for powers sums.
基金Supported by Doctoral Programme Foundation of Institution of Higher Education。
文摘The stopping powers of Br and C in Ag Elm have been measured with the method of elastic recoil detection in energy range 0.28-0.42MeV/amu.The results have been compared with the theoretical calculations of TRIM-90.
基金Supported by the Natural Science Foundation of Hainan Province (Grant No.111004)
文摘In this paper, by using superposition method, we aim to show that ∑^n i=1 （2/- 1）^2k-1 is the product of n2 and a rational polynomial in n2 with degree k- 1, and that ∑^ni=1 （2i - 1）^2k is the product of n（2n - 1）（2n ＋ 1） and a rational polynomial in （2n - 1）（2n ＋ 1） with degree k - 1. Moreover, recurrence formulas to compute the coefficients of the corresponding rational polynomials are also obtained.
文摘Examining the B-coefficient relations between two adjacent s-simplicies with given smoothness requirements, we find a compromise technique between btp-coefficients and B-coefficients to calculate a bivariate locally supported spline, give another proof of the BM-splines in S_(100)(4d, 3d-1, △_2) and establish the BM-splines in S_2~1, and S_4,
文摘An operator on formal power series of the form S μS , where μ is an invertible power series, and σ is a series of the form?t+(t2)?is called a unipotent substitution with pre-function. Such operators, denoted by a pair (μ ,σ )? , form a group. The objective of this contribution is to show that it is possible to define a generalized powers for such operators, as for instance fractional powers σ for every .
文摘Lu:If the tense situations in the Middle East and Northeast Asiabecome relaxed,it would certainly exert great influence on world politi-cal pattern.Can non-traditional security solve the contradictions in thetraditional security field?Will the major powers continue to cooperate inthe anti-terrorist campaign?All these issues will face challenges
基金This article is sponsored by Chongqing Social Science Planning Project(2019WT37)Chongqing Education Committee Humanities and Social Science Research Planning Project(18SKGH152)Social Science Fund Project of Chongqing University of Science and Technology(CK2017PY001).
文摘Richard Powers is one of American famous contemporary writers,a rising star of American postmodernist fiction,and one of the representatives of the Generation Xers as well.He explores the impacts of some factors such as ecological environment,social culture,and family ethics on our modern society by use of his abundant knowledge about gene engineer,neurology,family ethics,etc.From the perspective of Marxism ecological philosophy,this paper deeply analyses The Echo Maker,Richard Powers’masterpiece and interrelates the ecological thoughts implied in this novel.This work criticizes anthropocentrism and expresses the priority of nature.Human being is part of nature which our human being bases on and human being is closely related with nature.Human being should develop ecological consciousness,respect and care nature,and try every means to keep benign interaction with nature in order to build a stable and harmonious global community.
