We examine corresponding Cauchy-Riemann equations by using the non-commutativity for the product on split-biquaternions. Additionally, we describe the regularity of functions and properties of their differential equations on split-biquaternions. We investigate representations and calculations of the derivatives of functions of split-biquaternionic variables. c ©2016 all rights reserved.

We present an iterative method for simulating beam propagation in nonlinear media using Hamiltonian ray tracing. The Wigner distribution function of the input beam is computed at the entrance plane and is used as the initial condition for solving the Hamiltonian equations. Examples are given for the study of periodic self-focusing, spatial solitons, and Gaussian-Schell model in Kerr-effect medi...

Ionizing radiation increases the nuclear spin relaxation in the target chamber. Also known as “beam depolarization,” it is essentially a two step process. First, the beam ionizes an 3He atom which results in an free electron and an atomic ion 3He+. There is also the possibility that the atomic ion bonds with an neutral 3He atom to form an molecular ion He2 . Second, interactions with 3He ions i...

We have proposed and successfully demonstrated a two step method for localizing defects on an LSI chip. The first step is the same as a conventional laser-SQUID (L-SQUID) imaging where a SQUID and a laser beam are fixed during LSI chip scanning. The second step is a new L-SQUID imaging where a laser beam is stayed at the point, located in the first step results, during SQUID scanning. In the se...

We describe a new variant of the well known Baby-Step Giant-Step algorithm in the case of some discrete logarithms with a special structure. More precisely, we focus on discrete logarithms equal to products in groups of unknown order. As an example of application, we show that this new algorithm enables to cryptanalyse a variant of the GPS scheme proposed by Girault and Lefranc at CHES 2004 con...

Giant clams (Tridacnidae) are known to live in association with photosynthetic single cell dinoflagellate algae commonly called zooxanthellae. These algae which can be found in the mantle of the clams are capable of transferring part of their photosynthates which become an important source of energy to the host ( apart from filter feeding activity). In order to understand the basic biological p...

Aims. We report on a search for faint (R total magnitude fainter than 21) and low surface brightness galaxies (R central surface brightness fainter than ∼24) (fLSBs) in a 0.72×0.82 deg2 area centered on the Coma cluster. Methods. We analyzed deep B and R band CCD imaging obtained using the CFH12K camera at CFHT and found 735 fLSBs. The total B magnitudes, at the Coma cluster redshift, range fro...

The Giant Sequoia played several crucial roles in the founding of the modern science of tree -ring dating. These included at least two central theoretical constructs and at least two minor ones; however, historical studies of dendrochronology are actively continuing and this list is expected to expand. Second only to the importance of the ponderosa pine (Pinus ponderosa) in the earliest days of...

We review current progress in the study of the stellar populations of early-type galaxies, both locally and at intermediate redshifts. In particular, we focus on the ages of these galaxies and their evolution in hopes of determining the star formation epochs of their stars. Due to serious remaining systematic uncertainties, we are unable to constrain these epochs precisely. We discuss our resul...

The US government accumulated a large amount of debt from WWII. The government debt-to-GDP ratio in the US peaked at 108% in 1946. This ratio dropped dramatically in the following two decades, to 35% in 1966. Simultaneously, the US experienced a massive baby boom. This paper studies the relationship between these two phenomena in a modified version of the Barro-Becker model. In the model, the g...