In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.

 ‎In this paper we study the existence of nontrivial‎ solutions for a variational inequality on the half-line‎. ‎Our‎ ‎approach is based on the non-smooth critical point theory‎ ‎for Szulkin-type functionals.

In this work, we dissect the performance of  two modern Perdew-Burke-Ernzerhof (PBE)-based double-hybrid (DH) density functionals to predict the isotropic and anisotropic polarizabilities of water nanoclusters (H2O)n [n = 2-6]. The considered models include the cubic integrand (CI) and quadratic integrand (QI) functions as well as the spin-opposite-scaled...

Electronic singlet excitations of stacked adenine-thymine (AT) and guanine-cytosine (GC) complexes have been investigated with respect to local excitation and charge-transfer (CT) characters. Potential energy curves for rigid displacement of the nucleobases have been computed to establish the distance dependence of the CT states. The second-order algebraic diagrammatic construction [ADC(2)] met...

the immortality of the rational soul is one of the most important issues of ibn sina’s philosophy and anthropology. he poses many arguments in proving this subject. ibn sina proves the immortality of rational soul by not having relation or position of the intelligible concepts, indefinite power of the rational soul in his actions as well as its needlessness to sensible faculties in some of its ...

The Radon transform is a fundamental tool in many areas. For example, in reconstruction of an image from its projections (CT scanning). Although it is situated in the core of many modern physical computations, the Radon transform lacks a coherent discrete definition for 2D discrete images which is algebraically exact, invertible, and rapidly computable. We define a notion of 2D discrete Radon t...

Training support vector machines (SVM) with indefinite kernels has recently attracted attention in the machine learning community. This is partly due to the fact that many similarity functions that arise in practice are not symmetric positive semidefinite, i.e. the Mercer condition is not satisfied, or the Mercer condition is difficult to verify. Previous work on training SVM with indefinite ke...