Comprehensively considering energy, volume and electronic structure of alloys, the ninth equation was determined as the interaction function of Nb-Mo alloys system in BCC structure on the basis of idea of systematic s...Comprehensively considering energy, volume and electronic structure of alloys, the ninth equation was determined as the interaction function of Nb-Mo alloys system in BCC structure on the basis of idea of systematic science of alloys, experimental lattice constants and heats of formation of disordered Nb（1-x）Mox alloys. The structural parameters and properties of Nb and Mo characteristic atoms sequences and corresponding characteristic crystals sequences were determined in Nb-Mo alloys system. The electronic structure and physical properties of disordered Nb（1-x）Mox alloys system were calculated according to concentration of characteristic atoms of disordered alloys. The change trend of physical properties is the same as that of electronic structure.展开更多
The main purpose of this paper is to introduce the general Smarandache mul- tiplicative sequence based on the Smarandache multiplicative sequence, and calculate the value of some infinite series involving these sequen...The main purpose of this paper is to introduce the general Smarandache mul- tiplicative sequence based on the Smarandache multiplicative sequence, and calculate the value of some infinite series involving these sequences.展开更多
Let λ and μ are sequence spaces and have both the signed_weak gliding hump property, (λ,μ) be the algebra of the infinite matrix operators which transform λ into μ, in this paper, we study the strong? Mackey...Let λ and μ are sequence spaces and have both the signed_weak gliding hump property, (λ,μ) be the algebra of the infinite matrix operators which transform λ into μ, in this paper, we study the strong? Mackey? weak multiplier sequentially continuous problem of infinite matrix algebras (λ,μ).展开更多
An infinite integer sequence {1 ≤ a1 〈 a2 〈 ... } is called A-sequence, if no ai is sum of distinct members of the sequence other than ai. We give an example for the A-sequence, and the reciprocal sum of element...An infinite integer sequence {1 ≤ a1 〈 a2 〈 ... } is called A-sequence, if no ai is sum of distinct members of the sequence other than ai. We give an example for the A-sequence, and the reciprocal sum of elements is∑1/ai〉 2.065436491, which improves slightly the related upper bounds for the reciprocal sums of sum-free sequences.展开更多
Two infinite sequences A and B of non-negative integers are called infinite additive complements if their sum contains all sufficiently large integers. For a sequence T of non-negative integers, let T（x） be the numb...Two infinite sequences A and B of non-negative integers are called infinite additive complements if their sum contains all sufficiently large integers. For a sequence T of non-negative integers, let T（x） be the number of terms of T not exceeding x. In 1994, Sarkozy and Szemer′edi confirmed a conjecture of Danzer by proving that, for infinite additive complements A and B, if lim sup A（x）B（x）/x 1, then A（x）B（x）-x → ＋∞ as x → ＋∞. In this paper, it is proved that, if A and B are infinite additive complements with lim sup A（x）B（x）/x〈（√4 ＋ 2）/7 = 1.093 …, then（A（x）B（x）-x）/min{A（x）, B（x）} → ＋∞ as x → ＋∞.展开更多
基金Project (50954006) supported by the National Natural Science Foundation of ChinaProject (2009GK3152) supported by the Hunan Science and Technology Department, China+1 种基金Project (201012) supported by the Hunan Provincial Construction Department, ChinaProject (K1003048-11) supported by the Changsha City Science and Technology Department, China
文摘Comprehensively considering energy, volume and electronic structure of alloys, the ninth equation was determined as the interaction function of Nb-Mo alloys system in BCC structure on the basis of idea of systematic science of alloys, experimental lattice constants and heats of formation of disordered Nb（1-x）Mox alloys. The structural parameters and properties of Nb and Mo characteristic atoms sequences and corresponding characteristic crystals sequences were determined in Nb-Mo alloys system. The electronic structure and physical properties of disordered Nb（1-x）Mox alloys system were calculated according to concentration of characteristic atoms of disordered alloys. The change trend of physical properties is the same as that of electronic structure.
文摘The main purpose of this paper is to introduce the general Smarandache mul- tiplicative sequence based on the Smarandache multiplicative sequence, and calculate the value of some infinite series involving these sequences.
文摘Let λ and μ are sequence spaces and have both the signed_weak gliding hump property, (λ,μ) be the algebra of the infinite matrix operators which transform λ into μ, in this paper, we study the strong? Mackey? weak multiplier sequentially continuous problem of infinite matrix algebras (λ,μ).
基金the Natural Science Foundation of the Education Department of Sichuan Province (No.2006C057)
文摘An infinite integer sequence {1 ≤ a1 〈 a2 〈 ... } is called A-sequence, if no ai is sum of distinct members of the sequence other than ai. We give an example for the A-sequence, and the reciprocal sum of elements is∑1/ai〉 2.065436491, which improves slightly the related upper bounds for the reciprocal sums of sum-free sequences.
基金supported by National Natural Science Foundation of China (Grant Nos. 11671211 and 11371195)the China Scholarship Council (Grant No. 201608320048)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Two infinite sequences A and B of non-negative integers are called infinite additive complements if their sum contains all sufficiently large integers. For a sequence T of non-negative integers, let T（x） be the number of terms of T not exceeding x. In 1994, Sarkozy and Szemer′edi confirmed a conjecture of Danzer by proving that, for infinite additive complements A and B, if lim sup A（x）B（x）/x 1, then A（x）B（x）-x → ＋∞ as x → ＋∞. In this paper, it is proved that, if A and B are infinite additive complements with lim sup A（x）B（x）/x〈（√4 ＋ 2）/7 = 1.093 …, then（A（x）B（x）-x）/min{A（x）, B（x）} → ＋∞ as x → ＋∞.
