We prove that isentropic gas flow does not admit non-degenerate TVD fields on any invariant set M(r0, s0) = {r0 < r < s < s0}, where r, s are Riemann coordinates. A TVD field refers to a scalar field whose spatial variation VarX(φ(τ(t,X), u(t,X))) is nonincreasing in time along entropic solutions. The result is established under the assumption that the Riemann problem defined by an overtaking s...

The one–dimensional differential equations for the conservation mixture mass and mixture momentum coupled by a relative velocity conservation equation have been solved for an isentropic mixture of gas and liquid two–phase flow. Under certain restrictions the resulting system of partial differential equations is hyperbolic and allow discontinuous solutions. These equations have been solved by th...

An estimation problem of the mean µ of an inverse Gaussian distribution IG(µ, C µ) with known coefficient of variation c is treated as a decision problem with entropy loss function. A class of Bayes estimators is constructed, and shown to include MRSE estimator as its closure. Two important members of this class can easily be computed using continued fractions

Let α ∈ C in the upper half-plane and let I be an interval. We construct an analogue of Selberg’s majorant of the characteristic function of I that vanishes at the point α. The construction is based on the solution to an extremal problem with positivity and interpolation constraints. Moreover, the passage from the auxiliary extremal problem to the construction of Selberg’s function with vanishi...

Known as le probleme des rencontres, Montmort's problem has become a classic. Treated in almost every modern text on combinatorics, it has been recast in a variety of amusing guises including the random switching of n hats by a possibly tipsy cloakroom attendant, the random placement of n letters in n envelopes by a secretary apparently having a bad day, and even in terms of a wager on the orde...