lunar and mars landing is a crucial part of any exploration mission. its importance is manifested by the considerable interest in the past couple of decades. solution of lunar descent can be either numerical or analytical. numerical solutions are iterative and computationally demanding and some of them might not be suitable for on-board implementation. on the other hand, analytical solutions ar...

A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...

in this paper we investigate multi-objective integer linear programming (moilp) problems with unbounded feasible region and introduce recession direction for moilp problems. then we present necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of moilp problems. finally we present some examples with unbounded feasible region and fi...

efficient and on-time maintenance plays a crucial role inreducing cost and increasing the market share of an industrial unit. preventivemaintenance is a broad term that encompasses a set of activitiesaimed at improving the overall reliability and availability of a systembefore machinery breakdown. the previous studies have addressed thescheduling of preventive maintenance. these studies have co...

this article is devoted to the study of existence and multiplicity of positive solutions to aclass of nonlinear fractional order multi-point boundary value problems of the type−dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where dq0+ represents standard riemann-liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ∞...

In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...

An objective function often is only a rough approximation of the actual goals of the organization and its stakeholders. Consequently, an optimal solution may be no more interesting than other solutions that provide good values. Beyond this, a set of “good” solutions whose members have diverse characteristics can be significantly more valuable for practical analysis and planning than any single,...

Solution. (a) Since φ(3n) = 2 · 3n−1, the problem amounts to showing that 3n 23 − 1 and 3n 22·3 − 1 (when n ≥ 2). The first claim follows from reduction mod 3, and the second claim follows from the exponent lifting trick, as 3 ‖ 22−1, so that 3n−1 ‖ 22·3−1. (b) Since φ(pn) = φ(2pn) = (p − 1)pn−1, it suffices to show pn g(p−1)p − 1 and pn gdp − 1 for any divisor d of p − 1 with d < p − 1. The fi...

J U L Y / A U G U S T 2 0 1 6 InsideGNSS 29 Simulation of GNSS signals is very important to test and validate algorithms. With some algorithms, such as acquisition or tracking, we do not need to simulate a realistic constellation with actual ranges, Doppler or navigation data. We can simply simulate the signal after reception at a receiver’s front-end and only take into account and fix to desir...