Hyperbolic Functions
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Recent papers in Hyperbolic Functions
Hyperbolic functions do not form a complete set and in general it is not possible to expand a given function as an infinite series of hyperbolic functions. Here, we take the classical problem of steady laminar flow in a rectangular duct... more
The hyperbolic and circular trigonometric functions exhibit periodicity under repeated differentiation. The hyperbolic sine and cosine functions, whilst distinct from their first derivatives, are each equal to their own second derivative.... more
Current seismic design of bridges is based on a displacement performance philosophy using nonlinear static pushover analysis. This type of bridge design necessitates that the geotechnical engineer predict the resistance of the abutment... more
Resilient modulus, shear strength, dielectric permittivity, and shear and compressional wave speed values were determined for 36 soil specimens created from the six soil samples. These values show that the soils had larger stiffnesses at... more
We propose two new definitions of the exponential function on time scales. The first definition is based on the Cayley transformation while the second one is a natural extension of exact discretizations. Our eponential functions map the... more
This paper investigates the impact of the bridge skew angle on the force-deformation characteristics of abutments and the seismic response of a two-span bridge subjected to seismic two-component ground motions with near-fault effects.... more
Tree-like structures are ubiquitous in nature. In particular, neuronal axons and dendrites have tree-like geometries that mediate electrical signaling within and between cells. Electrical activity in neuronal trees is typically modeled... more
Tree-like structures are ubiquitous in nature. In particular, neuronal axons and dendrites have tree-like geometries that mediate electrical signaling within and between cells. Electrical activity in neuronal trees is typically modeled... more
ABSTRACT Using an integral transform with a mild singularity, we obtain series representations valid for specific regions in the complex plane involving trigonometric functions and the central binomial coefficient which are analogues of... more
Several inequalities involving hyperbolic functions are derived. Some of them are obtained with the aid of Stolarsky and Gini means.