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Chinese Physics B 2010年第4期19卷 180-184页

作者： israfil i.guseinov N.Seckin Gorgun Nimet Zaim Department of Physics Faculty of Arts and SciencesOnsekiz Mart UniversityC anakkaleTurkey Department of Physics Faculty of Arts and SciencesTrakya UniversityEdirneTurkey

Using the unsymmetrical one-range addition theorems introduced by one of the authors with the help of complete orthonormal sets of $／varPsi ^／alpha $-exponential type orbitals （$／alpha = 1,0, - 1, - 2,...）$, this paper presents the sets of series expansion relations for multicentre nuclear attraction integrals over Slater-type orbitals arising in Hartree--Fock--Roothaan equations for molecules. The final results are expressed through multicentre charge density expansion coefficients and basic integrals. The convergence of the series is tested by calculating concrete cases for arbitrary values of parameters of orbitals.

关键词： Slater-type orbitals nuclear attraction integrals Hartree-Fock Roothaan equations unsymmetrical one-range addition theorems

Construction of Different Kinds of Atomic and Molecular Orbitals Using Complete Orthonormal Sets of ψ^α-ETO in Single Exponent Approximation

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Chinese Physics Letters 2008年第7期25卷 2444-2447页

作者： guseinov i. israfil Ertfirk Murat Department of Physics Faculty of Arts and Sciences Onsekiz Mart University ~anakkale Turkey

Using complete orthonormal sets of ψ^α-exponential type orbitals in single exponent approximation the new approach has been suggested for construction of different kinds of functions which can be useful in the theory of linear combination of atomic orbitals. These functions can be chosen properly according to the nature of the problems under consideration. This is rather important because the choice of the basis set may be play a crucial role in applications to atomic and molecular problems. As an example of application, different atomic orbitals for the ground states of the neutral and the first ten cationic members of the isoelectronic series of He atom are constructed by the solution of Hartree-Fock-Roothaan equations using ψ^1, ψ^0 and ψ^-1 basis sets. The cMculated results are close to the numerical Hartree-Fock values. The total energy, expansion coefficients, orbital exponents and virial ratio for each atom are presented.

关键词： the power-law exponents precipitation durative abrupt precipitation change

Ground State Energy Calculations of isoelectronic Series of He in Double-Zeta Approximation Using Coulomb Potential with Noninteger indices

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Chinese Physics Letters 2008年第3期25卷 896-898页

作者： guseinov i. israfil AKSU Hüseyin Department of Physics Faculty of Arts and Sciences Onsekiz Mart University Canakkale Turkey

Using formulae for one- and two-electron integrals of Coulomb interaction potential fk （r） = r^-k with non-integer indices k established by one of the authors with the help of complete orthonormal sets of ψ^α-exponential-type orbitals （α = 1, 0,-1,-2,…）, we perform the calculations for isoelectronic series of the He atom containing nuclear charges from 2 to 10, where k = 1 - μ （-1 〈 μ 〈 0）. For this purpose we have used the double-zeta approximation, the configuration interaction and coupled-cluster methods employing the integer-n Slater-type orbitals as basis sets. it is demonstrated that the results of calculations obtained are better than the numerical Hartree-Fock values.

关键词： SLATER-TYPE ORBiTALS MULTiCENTER iNTEGRALS ONE-ELECTRON OPEN-SHELLS SYSTEMS iNTEGER ATOMS

One-range addition theorems for generalized integer and noninteger μ Coulomb,and exponential type correlated interaction potentials with hyperbolic cosine in position,momentum,and four-dimensional spaces

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Chinese Physics B 2012年第6期21卷 137-140页

作者： i.i.guseinov Department of Physics Faculty of Arts and SciencesOnsekiz Mart UniversityCanakkaleTurkey

The formulae are established in position,momentum,and four-dimensional spaces for the one-range addition theorems of generalized integer and noninteger μ Coulomb,and exponential type correlated interaction potentials with hyperbolic cosine（GCTCP and GETCP HC）.These formulae are expressed in terms of one-range addition theorems of complete orthonormal sets of Ψα-exponential type orbitals（Ψ α-ETO）,α-momentum space orbitals（α-MSO）,and zα-hyperspherical harmonics（zα-HSH） *** one-range addition theorems obtained can be useful in the electronic structure calculations of atoms and molecules when the GCTCP and GETCP HC in position,momentum,and four-dimensional spaces are employed.

关键词： correlated interaction potentials one-range additional theorems complete orthonormalsets of orbitals overlap integrals

Unified treatment of one-range addition theorems for integer and non-integer n-STO, -GTO and -generalized exponential type orbitals with hyperbolic cosine in position, momentum and four-dimensional spaces

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Chinese Physics B 2012年第9期21卷 176-178页

作者： i. i. guseinov Department of Physics Faculty of Arts and Sciences Onsekiz Mart University

Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GETO HC, GMSO HC, and GHSH HC） in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of Ca-exponential type orbitals, Ca- momentum space orbitals and za-hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of the electronic structure of atomic and molecular systems.

关键词： electronic structure generalized exponential type orbitals one-range addition theorems,Hartree-Fock-Roothaan equations

One-Range Addition Theorems in Terms of ψ^α -ETOs for STOs and Coulomb-Yukawa Like Correlated interaction Potentials of integer and Noninteger indices

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Chinese Physics Letters 2008年第12期25卷 4240-4243页

作者： i. i. guseinov Department of Physics Faculty of Arts and Sciences Onsekiz Mart University Canakkale Turkey

The expansion formulas in terms of complete orthonormal sets of ψ^α -exponential type orbitals are established for the Slater type orbitals and Coulomb-Yukawa-like correlated interaction potentials of integer and noninteger indices. These relations are used in obtaining their unsymmetrical and symmetrical one-range addition theorems. The final results are especially useful in the calculations of multicentre multielectron integrals occurring when Hartree-Fock-Roothaan and explicitly correlated methods are employed.

关键词： orthonormal set expansion formula

Unified treatment for accurate and fast evaluation of the Fermi-Dirac functions

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Chinese Physics B 2010年第5期19卷 72-77页

作者： i.i.guseinov B.A.Mamedov Department of Physics Faculty of Arts and SciencesOnsekiz Mart UniversityCanakkaleTurkey Department of Physics Faculty of Arts and SciencesGaziosmanpa sa UniversityTokatTurkey

A new analytical approach to the computation of the Fermi-Dirac （FD） functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions. This simplification and the use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Some numerical results are presented for significant mapping examples and they are briefly discussed.

关键词： statistical semiconductors plasma physics nuclear physics

On Evaluation of Overlap integrals with Noninteger Principal Quantum Numbers

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Communications in Theoretical Physics 2004年第5X期42卷 753-756页

作者： i.i.guseinov B.A.Mamedov DepartmentofPhysics FacultyofArtsandSciencesOnsekizMartUniversityCanakkaleTurkey DepartmentofPhysics FacultyofArtsandSciencesGaziosmanpasaUniversityTokatTurkey

By use of complete orthonormal sets of ψα exponential-type orbitals (ψα-ETOs, α = 1, 0,-1,-2, ...) the series expansion formulas for the noninteger n* Slater-type orbitals (NiSTOs) in terms of integer n Slater-type orbitals(iSTOs) are derived. These formulas enable us to express the overlap integrals with NiSTOs through the overlap integrals over iSTOs with the same and different screening constants. By calculating concrete cases the convergence of the series for arbitrary values of noninteger principal quantum numbers and screening constants of NiSTOs and internuclear distances is tested. The accuracy of the results is quite high for quantum numbers, screening constants and location of STOs.

关键词：指数轨道游标量子数迭代积分 NiSTOS 原子核

Arctic sea-ice extent: No record minimum in 2023 or recent years

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Atmospheric and Oceanic Science Letters 2025年第1期18卷 52-55页

作者： Ola M.Johannessen Tor i.Olaussen Nansen Scientific Society BergenNorway Nansen Environmental and Remote Sensing Center BergenNorway

Arctic sea-ice extent reaches its minimum each year in September. On 11 September 2023 the minimum was 4.969 million square kilometers(***^(2)). This was not a record low, which occurred in 2012, when the minimum was 4.175 ***^(2), 0.794 ***^(2) less than the minimum in 2023. However, the ice extent had decreased by 0.432 ***^(2) compared with 2022. Nevertheless, the summer melting in 2023 was remarkably less than expected when considering the strong heat waves in the atmosphere and ocean, with record temperatures set around the world. in general, there is a high correlation between the long-term decrease in sea-ice extent and the increasing CO_(2) in the atmosphere, where the increase of CO_(2) in recent decades explains about 80% of the decrease in sea ice in September, while the remainder is caused by natural variability.

关键词： Sea ice Arctic Minimum ice Climate

Coarse to Fine: The Role of Severe Plastic Deformation in Advancing Titanium-Based Medical implants - A Comprehensive Review

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Journal of Wuhan University of Technology(Materials Science) 2025年第1期40卷 295-306页

作者： Dragana R Mihajlović Bojan i Međo ivana Lj Cvijović-Alagić Veljko R Djokić Faculty of Technology and Metallurgy University of BelgradeKarnegijeva 411120 BelgradeSerbia Vinča institute of Nuclear Sci-ences-National institute of the Republic of Serbia University of Belgrade11001BeogradSerbia innovation Centre of the Faculty of Technology and Metallurgy Karnegijeva 411120 BelgradeSerbia

This paper describes severe plastic deformation(SPD)procedures,which are utilized to form an ultrafine-grained structure in metallic *** the SPD process,a solid material sample is subjected to very high loads without a significant change in sample *** the present work,the high-pressure torsion(HPT)process,as one of the SPD techniques,which achieves a high degree of deformation and ensures refinement of the microstructure,will be discussed in more *** that grain size control is accepted as a method to obtain materials with desired characteristics,an overview of the properties of ultrafine-grained titanium-based biomaterials to be used in medicine is ***,particular attention is dedicated to the influences of HPT process parameters,primarily hydrostatic pressure,and number of revolutions during torsion,on the grain size and physical and mechanical characteristics(modulus of elasticity,microhardness,and tensile properties),corrosion resistance,and biocompatibility of the titanium-based biomaterials.A review of the literature indicates that titanium-based materials obtained by the SPD process show improved mechanical and physical properties without losing biocompatibility and corrosion resistance,which suggests that these methods of obtaining implants are something that should be further developed in the future.

关键词： high-pressure torsion process ultrafine-grained titanium-based materials electrochemical anodization physical properties mechanical properties