Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

in this paper we consider selberg-type square matrices integrals with focus on kummer-beta types i & ii integrals. for generality of the results for real normed division algebras, the generalized matrix variate kummer-beta types i & ii are defined under the abstract algebra. then selberg-type integrals are calculated under orthogonal transformations.

Unparameterized and parameterized versions are outlined of a new method for approximating self-consistent field wavefunctions from first principles at the minimum basis set level for complex molecules containing hydrogen and first-row atoms. The Hartree-Fock self-consistent field equations for closed-shell molecules are solved, retaining all one-electron integrals, and approximating the two-ele...

A local multireference singles and doubles configuration interaction method in which Cholesky vectors are used in place of conventional two-electron integrals has been developed (CD-LMRSDCI). To reduce the overall cost associated with our linear scaling LMRSDCI method presented earlier [T. S. Chwee et al., J. Chem. Phys. 128, 224106 (2008)], we adopt a two-pronged approach. First, localized ort...

Overlap syndrome, which is known as the coexistence of chronic obstructive pulmonary disease (COPD) and obstructive sleep apnea (OSA), was first defined by Flenley. Although it can refer to concomitant occurrence of any of the pulmonary diseases and OSA, overlap syndrome is commonly considered as the coexistence of OSA and COPD. This disease has unique adverse health consequences distinct from ...

We present the contribution from potential interactions to dynamics of non-spinning binaries fourth Post-Minkowskian (4PM) order. This is achieved by computing scattering angle ${\cal O}(G^4)$ using effective field theory approach and deriving bound radial action through analytic continuation. reconstruct Hamiltonian center-of-mass momentum in an isotropic gauge. The (three-loop) integrals invo...

Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.

In this paper, quadratic rules for obtaining approximate solution of definite integrals as well as single and double integrals using spline quasi-interpolants will be illustrated. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method.

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...