Seven common errors in finding exact solutions of nonlinear differential equations

We analyze the common errors of the recent papers in which the solitary wave solutions of nonlinear differential equations are presented. Seven common errors are formulated and classified. These errors are illustrated by using multiple examples of the common errors from the recent publications. We show that many popular methods in finding of the exact solutions are equivalent each other. We demonstrate that some authors look for the solitary wave solutions of nonlinear ordinary differential equations and do not take into account the well - known general solutions of these equations. We illustrate several cases when authors present some functions for describing solutions but do not use arbitrary constants. As this fact takes place the redundant solutions of differential equations are found. A few examples of incorrect solutions by some authors are presented. Several other errors in finding the exact solutions of nonlinear differential equations are also discussed.Comment: 42 page

Methyl Farnesoate Plays a Dual Role in Regulating \u3cem\u3eDrosophila\u3c/em\u3e Metamorphosis

Corpus allatum (CA) ablation results in juvenile hormone (JH) deficiency and pupal lethality in Drosophila. The fly CA produces and releases three sesquiterpenoid hormones: JH III bisepoxide (JHB3), JH III, and methyl farnesoate (MF). In the whole body extracts, MF is the most abundant sesquiterpenoid, followed by JHB3 and JH III. Knockout of JH acid methyl transferase (jhamt) did not result in lethality; it decreased biosynthesis of JHB3, but MF biosynthesis was not affected. RNAi-mediated reduction of 3-hydroxy-3-methylglutaryl CoA reductase (hmgcr) expression in the CA decreased biosynthesis and titers of the three sesquiterpenoids, resulting in partial lethality. Reducing hmgcr expression in the CA of the jhamt mutant further decreased MF titer to a very low level, and caused complete lethality. JH III, JHB3, and MF function through Met and Gce, the two JH receptors, and induce expression of Kr-h1, a JH primary-response gene. As well, a portion of MF is converted to JHB3 in the hemolymph or peripheral tissues. Topical application of JHB3, JH III, or MF precluded lethality in JH-deficient animals, but not in the Met gce double mutant. Taken together, these experiments show that MF is produced by the larval CA and released into the hemolymph, from where it exerts its anti-metamorphic effects indirectly after conversion to JHB3, as well as acting as a hormone itself through the two JH receptors, Met and Gce

Methyl Farnesoate Plays a Dual Role in Regulating \u3cem\u3eDrosophila\u3c/em\u3e Metamorphosis

Corpus allatum (CA) ablation results in juvenile hormone (JH) deficiency and pupal lethality in Drosophila. The fly CA produces and releases three sesquiterpenoid hormones: JH III bisepoxide (JHB3), JH III, and methyl farnesoate (MF). In the whole body extracts, MF is the most abundant sesquiterpenoid, followed by JHB3 and JH III. Knockout of JH acid methyl transferase (jhamt) did not result in lethality; it decreased biosynthesis of JHB3, but MF biosynthesis was not affected. RNAi-mediated reduction of 3-hydroxy-3-methylglutaryl CoA reductase (hmgcr) expression in the CA decreased biosynthesis and titers of the three sesquiterpenoids, resulting in partial lethality. Reducing hmgcr expression in the CA of the jhamt mutant further decreased MF titer to a very low level, and caused complete lethality. JH III, JHB3, and MF function through Met and Gce, the two JH receptors, and induce expression of Kr-h1, a JH primary-response gene. As well, a portion of MF is converted to JHB3 in the hemolymph or peripheral tissues. Topical application of JHB3, JH III, or MF precluded lethality in JH-deficient animals, but not in the Met gce double mutant. Taken together, these experiments show that MF is produced by the larval CA and released into the hemolymph, from where it exerts its anti-metamorphic effects indirectly after conversion to JHB3, as well as acting as a hormone itself through the two JH receptors, Met and Gce

Broadband laser polarization control with aligned carbon nanotubes

We introduce a simple approach to fabricate aligned carbon nanotube (ACNT) device for broadband polarization control in fiber laser systems. The ACNT device was fabricated by pulling from as-fabricated vertically-aligned carbon nanotube arrays. Their anisotropic property is confirmed with optical and scanning electron microscopy, and with polarized Raman and absorption spectroscopy. The device was then integrated into fiber laser systems (at two technologically important wavelengths of 1 and 1.5 um) for polarization control. We obtained a linearly-polarized light output with the maximum extinction ratio of ~12 dB. The output polarization direction could be fully controlled by the ACNT alignment direction in both lasers. To the best of our knowledge, this is the first time that ACNT device is applied to polarization control in laser systems. Our results exhibit that the ACNT device is a simple, low-cost, and broadband polarizer to control laser polarization dynamics, for various photonic applications (such as material processing, polarization diversity detection in communications), where the linear polarization control is necessary.Comment: 5 pages, 6 figure

A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation

A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of nonlinear equations, unifying the tanh-function type methods, the homogeneous balance method, the exp-function method, the mapping method, and the F-expansion type methods. Its key point is to search for rational solutions to variable-coefficient ordinary differential equations transformed from given partial differential equations. As an application, the construction problem of exact solutions to the 3+1 dimensional Jimbo-Miwa equation is treated, together with a B\"acklund transformation.Comment: 13 page

A Mechanistic Approach to Understanding the Factors Affecting Drug Absorption: A Review of Fundamentals

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97203/1/00970002042006005.pd

Sensing and Tactile Artificial Muscles from Reactive Materials

Films of conducting polymers can be oxidized and reduced in a reversible way. Any intermediate oxidation state determines an electrochemical equilibrium. Chemical or physical variables acting on the film may modify the equilibrium potential, so that the film acts as a sensor of the variable. The working potential of polypyrrole/DBSA (Dodecylbenzenesulfonic acid) films, oxidized or reduced under constant currents, changes as a function of the working conditions: electrolyte concentration, temperature or mechanical stress. During oxidation, the reactive material is a sensor of the ambient, the consumed electrical energy being the sensing magnitude. Devices based on any of the electrochemical properties of conducting polymers must act simultaneously as sensors of the working conditions. Artificial muscles, as electrochemical actuators constituted by reactive materials, respond to the ambient conditions during actuation. In this way, they can be used as actuators, sensing the surrounding conditions during actuation. Actuating and sensing signals are simultaneously included by the same two connecting wires