S. Kristyán

activity

20172024

most citedOn the statistical distribution of prime numbers, a view from where the distribution of prime numbers is not erratic

9 citations · 18 across the 11 of their papers we have counts for

collaborators

11 papers

math.GM2024

Generalization of Cantor Pairing Polynomials (Bijective Mapping Among Natural Numbers) from N02 to N0 to Z2 to N0 and N03 to N

Sandor Kristyan

The Cantor pairing polynomials are extended to larger 2D sub-domains and more complex mapping, of which the most important property is the bijectivity. If corners are involved insi…

math.GM2024

On the Simple Divisibility Restrictions by Polynomial Equation a n+bn=cn Itself in Fermat Last Theorem for Integer/Complex/Quaternion Triples

Sandor Kristyan

The divisibility restrictions in the famous equation a n+bn=cn in Fermat Last Theorem (FLT, 1637) is analyzed how it selects out many triples to be Fermat triple (i.e. solutions) i…

physics.chem-ph2019★ 1 cited

Semi-analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian expansion of Distance Operators W= R $_{C 1}^{- n}$ R $_{D 1}^{- m}$ , R $_{C 1}^{- n}$ r $_{12}^{- m}$ , r $_{12}^{- n}$ r $_{13}^{- m}$

Sandor Kristyan

The equations derived help to evaluate semi-analytically (mostly for k=1,2 or 3) the important Coulomb integrals Int rho(r1)...rho(rk) W(r1,...,rk) dr1...drk, where the one-electro…

physics.chem-ph2019

Solving the non-relativistic electronic Schrodinger equation with manipulating the coupling strength parameter over the electron-electron Coulomb integrals

Sandor Kristyan

The non-relativistic electronic Hamiltonian, H(a)= Hkin + Hne + aHee, extended with coupling strength parameter (a), allows to switch the electron-electron repulsion energy off and…

physics.chem-ph2019

Quasi-linear buildup of Coulomb integrals via the coupling strength parameter in the non-relativistic electronic Schrodinger equation

Sandor Kristyan

The non-relativistic electronic Hamiltonian, Hkin + Hne + aHee, is linear in coupling strength parameter (a), but its eigenvalues (electronic energies) have only quasi-linear depen…

physics.chem-ph2018★ 1 cited

Numerical evaluation of Coulomb integrals for 1, 2 and 3-electron distance operators, $R_{C 1}^{- n} R_{D 1}^{- m}$ , $R_{C 1}^{- n} r_{12}^{- m}$ and $r_{12}^{- n} r_{13}^{- m}$ with real $(n, m$ ) and the Descartes product of 3 dim. common density functional numerical integration scheme

Sandor Kristyan

Analytical solutions to integrals are far more useful than numeric, however, the former is not available in many cases. We evaluate integrals indicated in the title numerically tha…

physics.chem-ph2018★ 3 cited

Optimizing single Slater determinant for Electronic Hamiltonian with Lagrange multipliers and Newton-Raphson methods as an alternative to ground state calculations via Hartree-Fock self consistent field

Sandor Kristyan

Considering the emblematic Hartree-Fock (HF) energy expression with single Slater determinant and the ortho-normal molecular orbits (MO) in it, expressed as a linear combination (L…

physics.chem-ph2017★ 2 cited

Eigenvalue equations from the field of theoretical chemistry and correlation calculations

Sandor Kristyan

Many equations have been introduced and derived by the author indicated in the title in relation to multi-electron densities between the Hohenberg-Kohn theorems and variational pri…

physics.chem-ph2017

Analytic evaluation of Coulomb integrals for one, two and three-electron distance operators, $R_{C 1}^{- n} R_{D 1}^{- m}$ , $R_{C 1}^{- n} r_{12}^{- m}$ and $r_{12}^{- n} r_{13}^{- m}$ with $n, m = 0, 1, 2$

Sandor Kristyan

The state of the art for integral evaluation is that analytical solutions to integrals are far more useful than numerical solutions. We evaluate certain integrals analytically that…

physics.chem-ph2017★ 2 cited

Generalization of Brillouin theorem for the non-relativistic electronic Schrödinger equation in relation to coupling strength parameter, and its consequences in single determinant basis sets for configuration interactions

Sandor Kristyan

The Brillouin theorem has been generalized for the extended non-relativistic electronic Hamiltonian (Hkin+ Hne+ aHee) in relation to coupling strength parameter (a), as well as for…

math.GM2017★ 9 cited

On the statistical distribution of prime numbers, a view from where the distribution of prime numbers is not erratic

Sandor Kristyan

Currently there is no known efficient formula for primes. Besides that, prime numbers have great importance in e.g., information technology such as public-key cryptography, and the…

Generalization of Cantor Pairing Polynomials (Bijective Mapping Among Natural Numbers) from N02 to N0 to Z2 to N0 and N03 to N

On the Simple Divisibility Restrictions by Polynomial Equation a n+bn=cn Itself in Fermat Last Theorem for Integer/Complex/Quaternion Triples

Semi-analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian expansion of Distance Operators W= RC1−n​RD1−m​, RC1−n​r12−m​, r12−n​r13−m​

Solving the non-relativistic electronic Schrodinger equation with manipulating the coupling strength parameter over the electron-electron Coulomb integrals

Quasi-linear buildup of Coulomb integrals via the coupling strength parameter in the non-relativistic electronic Schrodinger equation

Numerical evaluation of Coulomb integrals for 1, 2 and 3-electron distance operators, RC1−n​RD1−m​, RC1−n​r12−m​ and r12−n​r13−m​ with real (n,m) and the Descartes product of 3 dim. common density functional numerical integration scheme

Optimizing single Slater determinant for Electronic Hamiltonian with Lagrange multipliers and Newton-Raphson methods as an alternative to ground state calculations via Hartree-Fock self consistent field

Eigenvalue equations from the field of theoretical chemistry and correlation calculations

Analytic evaluation of Coulomb integrals for one, two and three-electron distance operators, RC1−n​RD1−m​, RC1−n​r12−m​ and r12−n​r13−m​ with n,m=0,1,2

Generalization of Brillouin theorem for the non-relativistic electronic Schrödinger equation in relation to coupling strength parameter, and its consequences in single determinant basis sets for configuration interactions

On the statistical distribution of prime numbers, a view from where the distribution of prime numbers is not erratic

Semi-analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian expansion of Distance Operators W= R $_{C 1}^{- n}$ R $_{D 1}^{- m}$ , R $_{C 1}^{- n}$ r $_{12}^{- m}$ , r $_{12}^{- n}$ r $_{13}^{- m}$

Numerical evaluation of Coulomb integrals for 1, 2 and 3-electron distance operators, $R_{C 1}^{- n} R_{D 1}^{- m}$ , $R_{C 1}^{- n} r_{12}^{- m}$ and $r_{12}^{- n} r_{13}^{- m}$ with real $(n, m$ ) and the Descartes product of 3 dim. common density functional numerical integration scheme

Analytic evaluation of Coulomb integrals for one, two and three-electron distance operators, $R_{C 1}^{- n} R_{D 1}^{- m}$ , $R_{C 1}^{- n} r_{12}^{- m}$ and $r_{12}^{- n} r_{13}^{- m}$ with $n, m = 0, 1, 2$