Generalized Elliptic Integrals and the Legendre M-function

We study monotonicity and convexity properties of functions arising in the theory of elliptic integrals, and in particular in the case of a Schwarz-Christoffel conformal mapping from a half-plane to a trapezoid. We obtain sharp monotonicity and convexity results for combinations of these functions, as well as functional inequalities and a linearization property.Comment: 28 page

Generalized Convexity and Inequalities

Let R+ = (0,infinity) and let M be the family of all mean values of two numbers in R+ (some examples are the arithmetic, geometric, and harmonic means). Given m1, m2 in M, we say that a function f : R+ to R+ is (m1,m2)-convex if f(m1(x,y)) < or = m2(f(x),f(y)) for all x, y in R+ . The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of (m1,m2)-convexity on m1 and m2 and give sufficient conditions for (m1,m2)-convexity of functions defined by Maclaurin series. The criteria involve the Maclaurin coefficients. Our results yield a class of new inequalities for several special functions such as the Gaussian hypergeometric function and a generalized Bessel function.Comment: 17 page

The mapping method as a toolbox to analyze, design, and optimize micromixers

The mapping method is employed as an efficient toolbox to analyze, design, and optimize micromixers. A new and simplified formulation of this technique is introduced here and applied to three micromixers: the staggered herringbone micromixer (SHM), the barrier-embedded micromixer (BEM), and the three-dimensional serpentine channel (3D-SC). The mapping method computes a distribution matrix that maps the color concentration distribution from inlet to outlet of a micromixer to characterize mixing in a quantitative way. Once the necessary distribution matrices are obtained, computations are fast and numerous layouts of the mixer are easily evaluated, resulting in an optimal design. This approach is demonstrated using the SHM and the BEM as typical examples. Mixing analysis in the 3D-SC illustrates that also complex flows, for example in the presence of back-flows, can be efficiently dealt with by using the new formulation of the mapping metho

Crossbred dairy cattle productivity in Arsi region, Ethiopia

Presents results of analyses carried out on a range of performance traits and productivity estimates for indigenous Arsi & Zebu cattle and their crosses with Jersey & Friesian, maintained for milk production at Asela station & on smallholder farms in the Arsi region of Ethiopia; includes data on age at first calving, calving interval, breeding efficiency, milk yield & composition and body weight

CP violation in 5D Split Fermions Scenario

We give a new configuration of split fermion positions in one extra dimension with two different Yukawa coupling strengths for up-type, $h_u$, and down-type, $h_d$, quarks at $\frac{h_u}{h_d}=36.0$. The new configurations can give enough CP violating (CPV) phase for accommodating all currently observed CPV processes. Therefore, a 5D standard model with split fermions is viable. In addition to the standard CKM phase, new CPV sources involving Kaluza-Klein(KK) gauge bosons coupling which arise from the fact that unitary rotation which transforms weak eigenstates into their mass eigenstates only holds for the zero modes which are the SM fields and not for the KK excitations. We have examined the physics of kaon, neutron, and $B/D$ mesons and found the most stringent bound on the size $R$ of the extra dimension comes from $|\epsilon_K|$. Moreover, it depends sensitively on the width, $\sigma$, of the Gaussian wavefunction in the extra dimension used to describe of the fermions. When $\sigma/R \ll 1$, the constraint will be lifted due to GIM suppression on the flavor changing neutral current(FCNC) and CPV couplings.Comment: 24 pages, 8 figure

Agronomic and silage quality traits of forage sorghum cultivars in 1995

Agronomic and silage quality traits were measure d for 37 forage sorghum cultivars and three grain sorghum hybrids. The 1995 growing season was characterized by above average rainfall in the spring and early summer, and a hard freeze on September 22. At the time of the freeze, 20 cultivars had reached the early-milk to early-dough stage, 12 were in the bloom stage, and the remaining eight were still in the early- to late-boot stage . The late planting date and low plant populations resulted in below-normal whole-plant D M and grain yields. Plant height s for the grain sorghums were near normal, but the forage sorghums were well below expected plant heights. The preensiled, whole-plan t DM contents of the 37 forage sorghums ranged from 23.0 to 39.9%. As expected , the silage nutritive value traits of CP, NDF, and ADF were most favorable for the three grain sorghum hybrids and least favorable for the eight forage sorghum hybrids that were still in the boot stage when the freeze occurred