Novel Refinements via <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>n</mi> </math>–Polynomial Harmonically <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>s</mi> </math>–Type Convex Functions and Application in Special Functions

Advanced Calculus: MATH 410 Functions and Regularity

5.1. Functions. We now turn our attention to the study of real-valued functions that are defined over arbitrary nonempty subsets of R. The subset of R over which such a function f is defined is called the domain of f , and is denoted Dom(f). We will write f : Dom(f) → R to indicate that f maps Dom(f) into R. For every x ∈ Dom(f) the function f associates the value f(x). The range of f is define...

Math 254a: Zeta Functions and L-series

Theorem 1.1. Let G be a group of Dirichlet characters modulo n, and KG the associated field. Fix a prime number p, and let H1 ⊂ H2 ⊂ G be the groups of χ such that χ(p) = 1 or χ(p) 6= 0 respectively. Then G/H2 ∼= IKG,p ⊂ Gal(KG/Q), and G/H1 ∼= DKG,p (note that these are non-canonical isomorphisms). We are now ready to prove the theorem on factoring Dedekind zeta functions of sub-cyclotomic fiel...

Custom math functions for molecular dynamics

functions for molecular dynamics R. F. Enenkel B. G. Fitch R. S. Germain F. G. Gustavson A. Martin M. Mendell J. W. Pitera M. C. Pitman A. Rayshubskiy F. Suits W. C. Swope T. J. C. Ward While developing the protein folding application for the IBM Blue Genet/L supercomputer, some frequently executed computational kernels were encountered. These were significantly more complex than the linear alg...

Math 341: Convex Geometry

Fejér and Hermite-Hadamard Type Inequalities for Harmonically Convex Functions

The author introduces the concept of harmonically convex functions and establishes some Hermite-Hadamard type inequalities of these classes of functions.