This study aims to classify the critical points of functions with 4 variables and 8 parameters, we found the caustic for the certain function with the spreading of the critical points. Finally, as an application, we found the bifurcation solutions for the equation of sixth order with boundary conditions using the Lyapunov-Schmidt method in the variational case.

Background: Glycemic control and prevention of secondary complications are the most important aims of using pharmacological treatments in diabetes mellitus. Due to the high incidence of inadequate response to insulin and, we try to evaluate the effects of adjunct use of silymarin with insulin on glycemic control, lipid profile and renal function in type 1 diabetes mellitus patients.
Patients and Methods: Placebo-controlled, doubled blinded clinical trial method is utilized through which 60 type 1 DM patients allocated into two groups, 30 patients treated with insulin and silymarin 400 mg/day in two divided doses, while the other 30 patients treated with insulin and placebo for 60 days. Fasting serum gluco

We propose two simple, rapid, and convenient spectrophotometric methods which are described for the determination of cephalexin in bulk and its pharmaceutical preparations. They are based on the measurement of the flame atomic emission of potassium ion (in the first method) and colorimetric determination of the green colored solution at 610 nm formed after the reaction of cephalexin with potassium permanganate as an oxidant agent (in the second method) in basic medium. The working conditions of the methods are investigated and optimized. Beer's law plot shows a good correlation in the concentration range of 5-40?g ml-1. The detection limits are 2.573,2.814 ?g ml-1 for the flame emission photometric method and 1.844,2.016 ?g ml-1 for colo

In this work, MWCNT in the epoxy can be prepared at room temperature and thickness (1mm) at different concentration of CNTs powder. Optical properties of multi-walled carbon nanotubes (CNTs) reinforced epoxy have been measured in the range of (300-800)nm. The electronic transition in pure epoxy and CNT/epoxy indicated direct allowed transition. Also, it is found that the energy gap of epoxy is 4.1eV and this value decreased within range of (4.1-3.5)eV when the concentration of CNT powder increased from (0.001-0.1)% respectively.
The optical constants which include (the refractive index (n), the extinction coefficient (k), real (ε1) and imaginarily (ε2) part of dielectric constant calculated in the of (300-800)nm at different concent

In this paper, isobutane (R-600a) is used as a suitable substitute for (R-134a) when changing the length of capillary tube. And the experimental data on capillary tube are obtained under different conditions such as (subcooling and ambient temperatures) on domestic refrigerator (9ft3 size), this data shows that (R-600a) a suitable substitute for (R134a) .The test presented a model for a steady state, two-phase flow in capillary tube for vapour compression system .The numerical model depends on conservation equations (mass, energy and momentum) as wall as the equation of state for refrigerant. The solution methodology was implemented by using finite difference techniques. The system results indicate that it is possible to change the refri

In projective plane over a finite field q F , a conic is the unique complete
(q 1) arc and any arcs on a conic are incomplete arc of degree less than q 1.
These arcs correspond to sets in the projective line over the same field. In this paper,
The number of inequivalent incomplete k  arcs; k  5,6, ,12, on the conic in
PG(2,23) and stabilizer group types are found. Also, the projective line
PG(1,23) has been splitting into two 12-sets and partitioned into six disjoint
tetrads.