The Debt Status of Commercial Company under Gharimin Perspective

Currently, commercial entity companies are not regarded yet as one of the groups that receive the zakat. This paper examines the debt status and its micro and macro-economic implications of corporations that experienced the debt shackled in the zakat system through analogy on personal gharim (person in the burden debt). The analysis presented here has been designed on a library research, an analogy method, as well as seen from a debt trap theory. This paper particularly argues that in the twist condition of enterprises to repay their debt, a commercial company may be entitled as the recipient of zakat on behalf of gharim (the fifth group who receives the zakat). It further argues that the loan of the commercial company has a larger impact than individual gharim. Synchronizing the entity companies as “syakhsun i’tibariyun” (the legal person) to the personal obligation to pay zakat is matched to be the reasons for their gharim’s status. The results of this paper contribute to expanding the recipient of zakat on behalf of gharim and enhance the insight of zakat distribution in Islamic philanthropy institutions.

Homoclinic Orbits for Second-Order Hamiltonian Systems with Some Twist Condition

We study the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systemsq¨−L(t)q+∇qW(t,q)=0, whereL(t)is unnecessarily positive definite for allt∈ℝ, and∇qW(t,q)is of at most linear growth and satisfies some twist condition between the origin and the infinity.

Wave packet pseudomodes of variable coefficient differential operators

The pseudospectra of non-selfadjoint linear ordinary differential operators with variable coefficients are considered. It is shown that when a certain winding number or twist condition is satisfied, closely related to Hörmander's commutator condition for partial differential equations, ϵ -pseudoeigenfunctions of such operators for exponentially small values of ϵ exist in the form of localized wave packets. In contrast to related results of Davies and of Dencker, Sjöstrand & Zworski, the symbol need not be smooth. Applications in fluid mechanics, non-hermitian quantum mechanics and other areas are presented with the aid of high-accuracy numerical computations.

DEGENERATE BIFURCATIONS OF RESONANT TORI IN HAMILTONIAN SYSTEMS

The twist condition is a necessary condition in integrable Hamiltonian systems and symplectic maps to obtain Poincaré–Birkhoff bifurcations under small perturbations. When this condition does not hold, topological structures other than Poincaré–Birkhoff chains arise in phase space through bifurcations of isolated periodic orbits and reconnections of asymptotic manifolds. In this paper we construct an integrable model Hamiltonian with degeneracies suitable to observe these phenomena close to nontwist resonant tori. The generation of isochronous chains and the stability of their fixed points is determined analytically and a condition for the reconnection is found. Particular examples are given, illustrating the bifurcation and reconnection scenario for several cases of degeneracy.