Scarring in a driven system with wave chaos

We consider acoustic wave propagation in a model of a deep ocean acoustic waveguide with a periodic range-dependence. Formally, the wave field is described by the Schrodinger equation with a time-dependent Hamiltonian. Using methods borrowed from the quantum chaos theory it is shown that in the driven system under consideration there exists a "scarring" effect similar to that observed in autonomous quantum systems.Comment: 5 pages, 7 figure

Optimizing Triangular Parabolic Fuzzy EOQ Model with Shortage Using Nearest Interval Approximation

Many Re-searchers have introduced different topics using fuzzy numbers. Triangular parabolic, Trapezoidal parabolic, Hexagonal and octagonal fuzzy numbers are developed in such a way that their membership function attains the highest value only between an interval. If that fuzzy numbers are parabolic in shape when they attains the highest value at midpoint of an interval and called as Triangular parabolic fuzzy number. This paper deals with developing ?-cut from Triangular parabolic membership function and using Triangle shaped values with an Economic Order Quantity(EOQ)model with shortage,here the setup cost ,holding cost, shortage cost are defined as fuzzy numbers. The purpose of this research is to analyse in which point attains it�s maximum value also using midpoint of an interval. Finally numerical examples along with graphical representation of the results are presented

Multi-matrix models and emergent geometry

Encouraged by the AdS/CFT correspondence, we study emergent local geometry in large N multi-matrix models from the perspective of a strong coupling expansion. By considering various solvable interacting models we show how the emergence or non-emergence of local geometry at strong coupling is captured by observables that effectively measure the mass of off-diagonal excitations about a semiclassical eigenvalue background. We find emergent geometry at strong coupling in models where a mass term regulates an infrared divergence. We also show that our notion of emergent geometry can be usefully applied to fuzzy spheres. Although most of our results are analytic, we have found numerical input valuable in guiding and checking our results.Comment: 1+34 pages, 4 figures. References adde

Review of modern numerical methods for a simple vanilla option pricing problem

Option pricing is a very attractive issue of financial engineering and optimization. The problem of determining the fair price of an option arises from the assumptions made under a given financial market model. The increasing complexity of these market assumptions contributes to the popularity of the numerical treatment of option valuation. Therefore, the pricing and hedging of plain vanilla options under the Black–Scholes model usually serve as a bench-mark for the development of new numerical pricing approaches and methods designed for advanced option pricing models. The objective of the paper is to present and compare the methodological concepts for the valuation of simple vanilla options using the relatively modern numerical techniques in this issue which arise from the discontinuous Galerkin method, the wavelet approach and the fuzzy transform technique. A theoretical comparison is accompanied by an empirical study based on the numerical verification of simple vanilla option prices. The resulting numerical schemes represent a particularly effective option pricing tool that enables some features of options that are depend-ent on the discretization of the computational domain as well as the order of the polynomial approximation to be captured better

Ergodic directional switching in mobile insect groups

We obtain a Fokker-Planck equation describing experimental data on the collective motion of locusts. The noise is of internal origin and due to the discrete character and finite number of constituents of the swarm. The stationary probability distribution shows a rich phenomenology including non-monotonic behavior of several order/disorder transition indicators in noise intensity. This complex behavior arises naturally as a result of the randomness in the system. Its counterintuitive character challenges standard interpretations of noise induced transitions and calls for an extension of this theory in order to capture the behavior of certain classes of biologically motivated models. Our results suggest that the collective switches of the group's direction of motion might be due to a random ergodic effect and, as such, they are inherent to group formation.Comment: Physical Review Focus 26, July 201

Multi-objective economic production quantity model for fully backlogged problem where demand depend on some conditions and permissible delay in payment

For any business, inventory system takes a monumental part. Keep this aspect in mind, we formulate multi-objective displayed EPQ model consider with non-instantaneous deteriorating things where production depends on demand and variable demand pattern depends on display self-space, selling price and frequency of advertisement of the item. The customers are more attracted to buy an item by observing self-space, selling price and advertisement. Imperfect materials are now and again come back to providers for a discount or credit. Here price discount is available for deteriorated and defective items. Holding cost varies with time where shortages are allowed and fully backlogged. Fuzzy environment touches the reality instead of the crisp environment. So, we assumed the cost components as Triangular Fuzzy Numbers and Nearest Interval Approximation Method is used to defuzzify the model. Finally, numerical examples as well as  sketches are given to illustrate the model

Spatiotemporal Fuzzy-Observer-based Feedback Control for Networked Parabolic PDE Systems

Assisted by the Takagi-Sugeno (T-S) fuzzy model- based nonlinear control technique, nonlinear spatiotemporal feedback compensators are proposed in this article for exponential stabilization of parabolic partial differential dynamic systems with measurement outputs transmitted over a communication network. More specifically, an approximate T-S fuzzy partial differential equation (PDE) model with C∞-smooth membership functions is constructed to describe the complex spatiotemporal dynamics of the nonlinear partial differential systems, and its approximation capability is analyzed via the uniform approximation theorem on a real separable Hilbert space. A spatiotemporally asynchronous sampled-data measurement output equation is proposed to model the transmission process of networked measurement outputs. By the approximate T-S fuzzy PDE model, fuzzy-observer-based nonlinear continuous-time and sampled- data feedback compensators are constructed via the spatiotemporally asynchronous sampled-data measurement outputs. Given that sufficient conditions presented in terms of linear matrix inequalities are satisfied, the suggested fuzzy compensators can exponentially stabilize the nonlinear system in the Lyapunov sense. Simulation results are presented to show the effectiveness and merit of the suggested spatiotemporal fuzzy compensators