Groupoid Approach to Ergodic Dynamical System of Commutative von Neumann Algebra

Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L∞(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L2(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .

Integral Representations for the Price of Vanilla Put Options on a Basket of Two-Dividend Paying Stocks

This paper presents integral representations for the price of vanilla put options, namely, European and American put options on a basket of two-dividend paying stocks using integral method based on the double Mellin transform. We show that by the decomposition of the integral equation for the price of American basket put option, the integral equation for the price of European basket put option can be obtained directly.

Order Relation on the Permutation Symbols in the Ehresmann Subvariety Class Associated to the Distinguished Monomials of Flag Manifolds

In this paper, we use the theory of lexicographical and graded lexicographical orders to compare two distinguished monomials through their codes of invariants and study the effect of this comparison on their respective defining permutation symbols in the Ehresmann subvariety classes.

Fast Fourier Transform of Multi-Assets Options under Economic Recession Induced Uncertainties

A Fast Fourier transform approach has been presented by Carr & Madan (2009) on a single underlying asset. In this current research paper, we present fast Fourier transform algorithm for the valuation of Multi-asset Options under Economic Recession Induced Uncertainties. The issue of multi-dimension in both finite and infinite case of Options is part of the focus of this research. The notion of economic recession was incorporated. An intuition behind the introduction of recession induced volatility uncertainty is revealed by huge volatility variation during the period of economic recession compared to the period of recession-free. Nigeria economic recession outbreak in 2016 and its effects on the uncertainty of the payoffs of Nigeria Stocks Exchange (NSE) among other investments was among the motivating factors for proposing economic recession induced volatility in options pricing. The application of the proposed Fast Fourier Transform algorithm in handling multi-assets options was shown. A new result on options pricing was achieved and capable of yielding efficient option prices during and out of recession. Numerical results were presented on assets in 3-dimensions as an illustration taking Black Scholes prices as a bench mark for method effectiveness comparison. The key findings of this research paper among other crucial contributions could be seen in computational procedure of options valuation in multi-dimensions and uncertainties in options payoffs under the exposure of economic recession.

Spherical Functions on Fuzzy Lie Group

Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Helgason-spherical function on G is then established on .

A Sandwich Control System with Dual Stochastic Impulses

Dear editor,Along with the progress of science and technology and the development of social civilization,control system brings an increasingly significant function in daily life.The application field of control system is very wide,for instance,in mobile technology[1],artificial earth satellite[2],pest control[3],etc.Ribeiro[4]first put forward the concept of random pulse in 1967.At present,impulsive control is used in networked control[5],secure communication[6],etc.In the 21st century,the impulsive control has been used in synchronization of coupled system,intelligent fault identification,image encryption.

On a Dynamic Optimization Technique for Resource Allocation Problems in a Production Company

This paper examines the allocation of resource to different tasks in a production company. The company produces the same kinds of goods and want to allocate m number of tasks to 50 number of machines. These machines are subject to breakdown. It is expected that the breakdown machines will be repaired and put into operation. From past records, the company estimated the profit the machines will generate from the various tasks at the first stage of the operation. Also, the company estimated the probability of breakdown of the machines for performing each of the tasks. The aim of this paper is to determine the expected maximize profit that will accrue to the company over T horizon. The profit that will accrued to the company was obtained as N4,571,100,000 after 48 weeks of operation. At the infinty horizon, the profit was obtained to be N20,491,000,000 . It was found that adequate planning, prompt and effective maintainance can enhance the profitability of the company.

Interval Analytic Method in Existence Result for Hyperbolic Partial Differential Equation

Without the usual assumption of monotonicity, we establish some results on the theory of hyperbolic differential inequalities which enable us to produce a majorising interval function for the solution of the hyperbolic initial value problem. Using this function, a variation of parameters formula and interval iterative technique, the existence of solution to the problem is established.

Links Between HX-Groups and Hypergroups

The concept of an HX-group is an upgrade of the concept of a group,in which a new operation is defined on the family of non-empty subsets of a group.If this new support set together with the new operation is a group,then we call it an HX-group.On the other hand,a hyperoperation is a mapping having the same codomain as the operation of an HX-group,i.e.,the family of non-empty subsets of the initial set,but a different domain-the set itself.This could be(and was indeed)a source of confusion,which is clarified in this paper.Moreover,HX-groups naturally lead to constructions of hypergroups.The links between these two algebraic concepts are presented,with the aim of reviving the old notion of an HX-group in the current research on algebraic hyperstructures.One of such existing links and one newly established link are also discussed.