In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

in statistical quality control a very widely used measure is average run length (arl) which may be worked out by different methods like integral equation, approximations, and monte carlo simulations. the arl measure and the other related measures are of major significance in every type of production process. an omission in its computation (and hence its related measures such as extra quadratic ...

We prove that in a free group the length of the value of each variable in a minimal solution of a standard quadratic equation is bounded by 2s for orientable equation and by 12s for non-orientable equation, where s is the sum of the lengths of the coefficients.

We reformulate the dual gauge model of the long-distance Yang-Mills theory in terms of the two-point Wightman functions formalism. In the flux-tube scheme of Abelian dominance and monopole condensation, the analytic expressions of both monopole-and dual gauge boson-fields propagators are obtained. Formally, new features of higher order quadratic equations for a monopole field are given. Finally...

Small codimensional embedded manifolds defined by equations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension. This allows us to prove the Hartshorne Conjecture for manifolds defined by quadratic equations and to obtain the list of such Hartshorne manifolds.

The type II1 unprojection is, by definition, the generic complete intersection type II unprojection, in the sense of [P] Section 3.1, for the parameter value k = 1, and depends on a parameter n ≥ 2. Our main results are the explicit calculation of the linear relations of the type II1 unprojection for any value n ≥ 2 (Theorem 3.16) and the explicit calculation of the quadratic equation for the c...

We investigate the class of regular-ordered word equations. The sides of such an equation contain both exactly the same variables, occurring in the same order (but separated by potentially distinct constant factors). Surprisingly, we obtain that solving even such simple equations is NP-hard. By considerations regarding the combinatorial structure of the minimal solutions of the more general qua...

This note shows that we can recover any complex vector x0 ∈ C exactly from on the order of n quadratic equations of the form |〈ai,x0〉| = bi, i = 1, . . . ,m, by using a semidefinite program known as PhaseLift. This improves upon earlier bounds in [3], which required the number of equations to be at least on the order of n log n. Further, we show that exact recovery holds for all input vectors s...

A development quadratic model of the heterogeneous biological population consisting of a few sub-populations is investigated. The classic stabilization problem of solutions for the system of ordinary quadratic differential equations, which describing this model, is solved. Examples are given. 2013 Elsevier Inc. All rights reserved.