Cauchy problem in the class of monotone increasing functions

The paper establishes some solvability conditions of the Cauchy problem for linear differential equation in the class of monotone increasing functions. The results are applied for clarifying the possibility of flight along a given trajectory under existence of braking forces.     

Reactions of triphenylphosphine with 2,3-dihalo-2-methylpropionic acids and their methyl esters

Triphenylphosphine reacts with 2,3-dichloro-2-methylpropionic acid and its ester along the dehydrochlorination pathway with the participation of the less labile hydrogen atom from the methyl group. The subsequent reaction of the unsaturated product with triphenylphosphine yields 2-carboxypropane- and 2-methoxycarbonylpropane-1,3-diylbis(triphenylphosphonium) dichlorides, respectively. The unusual course of dehydrochlorination may be due to easier electron density transfer from the C-H bond of the methyl group as compared to the chloromethyl group in the carbocationoid intermediate. With the bromine analogs, the reaction pathways are different. The ester reacts similarly to dibromopropionic acid and its derivatives, following the debromination scheme, whereas the free acid gives the product of double nucleophilic substitution.     

Undulator with permanent ferrimagnetic magnets

Undulator for terahertz FEL is created of ferrite materials. The length of the undulator period is 9 cm and the number of periods is 27. By means of selection and redistribution of magnetic elements it was succeeded to reduce the spread in amplitudes of the magnetic field down to 7%. Additional windings in magnetic elements were used to compensate for the residual spread. The needed focusing gradient of the magnetic field is obtained by means of relative displacement, along the x-axis, of alternating poles with opposite signs of the magnetic field. The undulator parameters, including the properties of focusing in the horizontal plane, are studied.     

Detection of B-FSK signals using schmidt trigger

Possibility to record B-FSK signals with use of stochastic resonance is studied. A Schmidt trigger is employed as bistable stochastic resonator. A digital model of the detector is proposed and quantitative results are obtained by means of simulations. Dependence of the probability of correctly detected bits on the added noise power and on the low-pass filter cutoff frequency is studied. Also the stability of the detector with respect to channel-introduced phase shifts is revealed.