Abstract. Associated to a newform f(z) is a Dirichlet series Lf (s) with functional equation and Euler product. Hecke showed that if the Dirichlet series F (s) has a functional equation of a particular form, then F (s) = Lf (s) for some holomorphic newform f(z) on Γ(1). Weil extended this result to Γ0(N) under an assumption on the twists of F (s) by Dirichlet characters. Conrey and Farmer exten...

Abstract. Associated to a newform f(z) is a Dirichlet series Lf (s) with functional equation and Euler product. Hecke showed that if the Dirichlet series F (s) has a functional equation of a particular form, then F (s) = Lf (s) for some holomorphic newform f(z) on Γ(1). Weil extended this result to Γ0(N) under an assumption on the twists of F (s) by Dirichlet characters. Conrey and Farmer exten...

A method is developed to calculate the ligand field (LF) parameters and multiplet spectra of local magnetic centers with open $d$ $f$ shells in solids a parameter-free way. This proceeds from density functional theory employs Wannier projections nonmagnetic band structures onto or orbitals. Energies multiplets optical, as well x-ray are determined by exact numerical diagonalization Hamiltonian ...

In this paper we have introduced and studied the subclass RI(d, α, β) of univalent functions defined by the linear operator RI n,λ,lf(z) defined by using the Ruscheweyh derivative Rf(z) and multiplier transformation I (n, λ, l) f(z), as RI n,λ,l : A → A, RI γ n,λ,lf(z) = (1 − γ)R f(z) + γI (n, λ, l) f(z), z ∈ U, where An = {f ∈ H(U) : f(z) = z+ an+1z + . . . , z ∈ U} is the class of normalized ...

We present a mechanized proof of the metatheory of LF, i.e. the decidability of typechecking and the existence and uniqueness of canonical forms. We use a syntactic approach in which we define a translation from LF to its canonical forms presentation (in which only beta-short, eta-long terms are well-formed) and prove soundness and completeness of the translation, establishing that definitional...

Heart rate variability (HRV), the beat-to-beat alterations in heart rate, comprises sympathetic and parasympathetic nerve activities of the heart. HRV analysis is used to quantify cardiac autonomic regulation. Since respiration could be a confounding factor in HRV evaluation, some studies recommend consciously controlled breathing to standardize the method. However, it remains unclear whether c...

For a map f : X → Y of quasi-compact quasi-separated schemes, we discuss quasi-perfection, i.e., the right adjoint f of Rf∗ respects small direct sums. This is equivalent to the existence of a functorial isomorphism f×OY ⊗ L Lf(− ) −→ ∼ f(−); to quasi-properness (preservation by Rf∗ of pseudo-coherence, or just properness in the noetherian case) plus boundedness of Lf (finite tor-dimensionality...

Experimental uncertainties concerning the coordination mode of trivalent plutonium in concentrated LiCl have led us to theoretically evaluate the f-f transitions of a series of rare earth aquo and chloro complexes. The calculation of Pr(III), U(III), Np(III), and Pu(III) systems' spectra was undertaken using the LFDFT (ligand field density functional theory) route that combines the backgrounds ...

Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any LF -sentence φ containing only bounded quantifiers, and any positive rational number δ, decides either “φ is true”, or “a δ-strengthening of φ is false”’. Under mild assumptions, for a C-computable signature F , the δ-decision problem for bounded Σk-sentences in LF resides in (Σ...