Strict Contraction Research Articles

International Investment Law Between Commitment and Flexibility: A Contract Theory Analysis

This article analyzes international investment protection law by using tools of economic contract theory. Contract theory has been applied to international trade law, but investment law has not yet been analyzed under this methodology. International Investment Agreements may be interpreted as a mechanism for overcoming commitment problems between investor and host state in order to generate mutual benefits. States trade credibility for sovereignty as international investment law restricts the regulatory conduct of states to an unusual extent, subject to control through compulsory international adjudication. A well-known problem in contract theory is how to deal with uncertainty. Changing conditions are a prevalent characteristic in investment law. Contract theory finds that too strict and inflexible contracts may impair the joint surplus of the contracting parties. Thus, a trade-off arises between ex ante commitment on the one hand and flexibility ex post in order to uphold the efficiency of the contract on the other. Those problems become virulent in unforeseen crises, such as financial or economic ones. This article analyzes commitment and flexibility mechanisms in international investment protection law and proposes to use similar mechanisms as in WTO law to design more optimal contracts.

Positive solutions of [formula omitted]th-order impulsive boundary value problems with integral boundary conditions in Banach spaces

By using the fixed point theory for strict set contraction operator, this paper investigates the existence of positive solutions for a class of n th-order impulsive boundary value problems with integral boundary conditions in Banach spaces. Moreover, we offer some interesting discussion of the associated boundary value problems. Since the technique to deal with n th-order BVP is completely different from that of previous papers, the expression of the associated integral equation is simpler than that of relevant papers, and upper and lower bounds for these positive solutions also are given, our work is new.

Existence results for a class of [formula omitted]th order [formula omitted]-point boundary value problems in Banach spaces

By obtaining intervals of the parameter λ , this paper investigates the existence of a positive solution for a class of nonlinear m -point boundary value problems of n th order differential equations in abstract spaces. The arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator.

Solving the nonlinear matrix equation [formula omitted] via a contraction principle

In this paper we consider the nonlinear matrix equation X=Q+∑i=1mMiXδiMi∗ where Q is positive (resp. semidefinite) definite and Mi’s are arbitrary (resp. nonsingular) matrices. We prove that if δ≔max{|δi|:1⩽i⩽m}<1, then the equation has a unique positive definite solution which is realized as the unique fixed point of a strict contraction with the Lipschitz constant less than or equal to δ. Furthermore, we show that the solution map varying over the determining coefficient matrices is continuous.

Positive solutions for [formula omitted] conjugate boundary value problems in Banach spaces

The existence and multiplicity of positive solutions for a integral equation in Banach spaces are obtained. Using these results, we investigate the existence of multiple-positive solutions for ( k , n − k ) conjugate boundary value problems. The arguments are based upon a specially constructed cone and the fixed point theory in a cone for strict set contraction operators. This work gives an unified approach applicable to many boundary value problems.

Classes of tuples of commuting contractions satisfying the multivariable von Neumann inequality

We obtain a decomposition for multivariable Schur-class functions on the unit polydisk which, to a certain extent, is analogous to Agler's decomposition for functions from the Schur–Agler class. As a consequence, we show that d-tuples of commuting strict contractions obeying an additional positivity constraint satisfy the d-variable von Neumann inequality for an arbitrary operator-valued bounded analytic function on the polydisk. Also, this decomposition yields a necessary condition for solvability of the finite data Nevanlinna–Pick interpolation problem in the Schur class on the unit polydisk.

Between Commitment and Flexibility: The Fragile Stability of the International Investment Protection Regime

This article analyzes international investment protection law by using tools of economic contract theory. Contract theory has been applied to international trade law, but investment law has not yet been analyzed under this methodology. Bilateral Investment Treaties or International Investment Agreements may be interpreted as a mechanism for overcoming commitment problems between investor and host state in order to generate mutual benefits. States thereby trade credibility for sovereignty as international investment law restricts the regulatory conduct of states to an unusual extent, subject to control through compulsory international adjudication. A well-known problem in contract theory is how to deal with uncertainty. Parties cannot easily design contracts that maximize jointly beneficial investments and at the same time respond appropriately to changing conditions ex post. Changing conditions are a prevalent characteristic in investment law covering long term investments. Contract theory finds that too strict and inflexible contracts may impair the joint surplus of the contracting parties. Thus, a trade-off arises between ex ante strong commitment devices on the one hand and flexibility ex post in order to uphold the efficiency of the contract on the other hand. The article analyzes commitment and flexibility mechanism in international investment protection law and proposes to use similar mechanisms to the WTO law in order to design more optimal contracts (that is investment treaties).

Positive solutions to fourth-order singular boundary value problems with integral boundary conditions in abstract spaces

Under various weaker conditions, we establish various results on the existence of positive solutions to fourth-order singular boundary value problems with integral boundary conditions in abstract spaces. The arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator. Our results improve and extend that obtained in [X. Zhang, M. Feng, W. Ge, Existence results for nonlinear boundary value problems with integral boundary conditions in Banach spaces, Nonlinear Anal. 69 (2008) 3310–3321; Y. Liu, Multiple positive solutions to fourth-order singular boundary value problems in abstract spaces, Electron. J. Diff. Eqns. 120 (2004) 1–13], even in the scalar spaces.

Sharpened forms of a von Neumann inequality for $\rho$-contractions

The purpose of this paper is to give some sharpened forms of the von Neumann inequality for strict $\rho$-contractions which were obtained earlier. Also, some sharpened forms of the Schwarz inequality for strict $\rho$-contractions will be given, and as applications, corresponding inequalities for strict contractions and for uniformly stable operators will be derived. In particular, we recover the results of K. Fan covering the strict contractions, and in the scalar context we find an improved form of the interior Schwarz inequality quoted by R. Osserman .

Positivity of operator-matrices of Hua-type

Let $A_j\,\,(j = 1, 2,\ldots , n)$ be strict contractions on a Hilbert space. We study an $n \times n$ operator-matrix: \[\textbf{H}_n(A_1,A_2,\ldots ,A_n) = [(I - A^*_j A_i)^{-1}]^n_{i,j=1}.\] For the case $n = 2$, Hua [Inequalities involving determinants, Acta Math. Sinica, 5 (1955), 463-470 (in Chinese)] proved positivity, i.e., positive semi-definiteness of $\textbf{H}_2(A_1,A_2)$. This is, however, not always true for $n = 3$. First we generalize a known condition which guarantees positivity of $\textbf{H}_n$. Our main result is that positivity of $\textbf{H}_n$ is preserved under the operator M\"obius map of the open unit disc $\mathcal D$ of strict contractions.

A class of three-point boundary-value problems for second-order impulsive integro-differential equations in Banach spaces

In this paper, we consider the following boundary-value problems for second-order three-point nonlinear impulsive integro-differential equation of mixed type in a real Banach space E : x ″ ( t ) + f ( t , x ( t ) , x ′ ( t ) , ( A x ) ( t ) , ( B x ) ( t ) ) = θ , t ∈ J , t ≠ t k , Δ x | t = t k = I k ( x ( t k ) ) , Δ x ′ | t = t k = I ̄ k ( x ( t k ) , x ′ ( t k ) ) , k = 1 , 2 , … , m , x ( 0 ) = θ , x ( 1 ) = ρ x ( η ) , where θ is the zero element of E , ( A x ) ( t ) = ∫ 0 t g ( t , s ) x ( s ) d s , ( B x ) ( t ) = ∫ 0 1 h ( t , s ) x ( s ) d s , g ∈ C [ D , R + ] , D = { ( t , s ) ∈ J × J : t ≥ s } , h ∈ C [ J × J , R ] , and Δ x | t = t k denotes the jump of x ( t ) at t = t k , Δ x ′ | t = t k denotes the jump of x ′ ( t ) at t = t k . Some new results are obtained for the existence and multiplicity of positive solutions of the above problems by using the fixed-point index theory and fixed-point theorem in the cone of strict set contraction operators. Meanwhile, an example is worked out to demonstrate the main results.

Positive solutions for a class of boundary-value problem with integral boundary conditions in Banach spaces

This paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary-value problem of second-order differential equations with integral boundary conditions in ordered Banach spaces. The arguments are based upon a specially constructed cone and the fixed point theory in a cone for strict set contraction operators. The nonexistence of a positive solution is also studied.

Existence results for nonlinear boundary-value problems with integral boundary conditions in Banach spaces

This paper investigates the multiplicity of positive solutions for a class of nonlinear boundary-value problems of fourth-order differential equations with integral boundary conditions in ordered Banach spaces. The arguments are based upon a specially constructed cone and the fixed point index theory in cone for strict set contraction operator. The nonexistence of positive solution is also studied. Meanwhile, an example is worked out to demonstrate the main results.

Stochastic dynamics and Parrondo’s paradox

The Spanish physicist Juan Parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game. If a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures. The appropriate abstract setting is as follows. There is given a compact metric space ( M , d ) , and M is written as the union of certain closed subsets A 1 , … , A r . For every ρ = 1 , … , r there is prescribed a strict contraction Γ ρ : A ρ → M . A random walk ( X m ) m ∈ N 0 on M is then defined as follows. The starting position is X 0 = x 0 , where x 0 ∈ M is fixed, and if the walk at the m ’th step is at position X m ∈ M , then one chooses a ρ among the ρ with X m ∈ A ρ (with equal probability, say) and defines X m + 1 as Γ ρ ( X m ) . Associated with the walk is a gain φ ( X m ) in every round, where φ : M → R is a continuous function. The aim of the present investigations is the study of the expectation G m of φ ( X m ) as a function of m . Our main result states that the sequence ( G m ) is “eventually approximately periodic” provided that all A ρ are not only closed but also open in M : for every ε there is an l 0 ∈ N such that ( G m ) is l 0 -periodic up to an error of at most ε for sufficiently large m . In fact it turns out that the behaviour of our process can be described well with a finite Markov chain. In the general case, however, the process might behave rather chaotically. We give an example where M is the unit interval. M is written as the union of two closed subsets A 1 , A 2 , the contractions Γ 1 , Γ 2 are rather simple, but the expectations of the gains are not even Cesáro convergent.

Value Chain Analysis and Strategic Alliance under Total-life-cycle Costing: An Examination of New Costing Technology

Due to competitive forces, deregulated economies and technological development, strategic alliances have become noteworthy in business. A kind of cooperative business activity without strict contract laws, strategic alliances have dramatically increased in the last decade. They have been considered as a critical way to manage activities, handle uncertainties, conduct financial and strategic planning, and make correct economic decisions. Coordination and optimization of activities within strategic alliances should be achieved by using a holistic view to organize strategic positioning and to build linkages between value-creating activities. A value chain analysis can guide firms to management interfirm linkages, to reduce internal and cross-organizational costs, and to build advantages of differentiation. With the aid of value chain analysis, firms will be able to integrate relevant relationships in the whole business cycle, to improve cost management systems (CMSs) and interfirm cost management, to facilitate information sharing, and to enhance performance across firm boundaries in the management of interfirm relationships. A structured costing approach and evaluation technique, Total-life-cycle costing (TLCC) completely addresses all cost elements in owning, maintaining, operation, and replacement related to products/services. Viewed in a value chain perspective, TLCC can be considered as a longitudinal method to recognize value relevant/irrelevant activities from the start to the end of products and services. TLCC can be used as both a cost management basis and an information-sharing technique to reduce (1) value irrelevant costs down the value chain of a product/service, and (2) value irrelevant interaction costs related to interfirm strategic alliance. This study is targeted at identifying the efficacy of value chain analysis in strategic alliances when firms adopt total-life-cycle costing on an interfirm basis. I am interested in identifying processes on the efficacy of value chain analysis in coordinating interdependent tasks, eliminating value irrelevant cost, and facilitating interfirm information sharing when TLCC is used.

Two coincidence and fixed point theorems for hybrid strict contractions

Two coincidence and fixed point theorems for hybrid strict contractions

Endpoints of set-valued dynamical systems of asymptotic contractions of Meir–Keeler type and strict contractions in uniform spaces

In this paper, we introduce the concepts of the set-valued dynamical systems of asymptotic contractions of Meir–Keeler type and set-valued dynamical systems of strict contractions in uniform spaces and we present a method which is useful for establishing conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions. The result, concerning the investigations of problems of the set-valued asymptotic fixed point theory, include some well-known results of Meir and Keeler, Kirk and Suzuki concerning the asymptotic fixed point theory of single-valued maps in metric spaces. The result, concerning set-valued strict contractions (in which the contractive coefficient is not constant), is different from the result of Yuan concerning the existence of endpoints of Tarafdar–Vyborny generalized contractions (in which the contractive coefficient is constant) in bounded metric spaces and provides some examples of Tarafdar–Yuan topological contractions in compact uniform spaces. Definitions and results presented here are new for set-valued dynamical systems in uniform, locally convex and metric spaces and even for single-valued maps. Examples show a fundamental difference between our results and the well-known ones.

"Difficult Patients" in Mental Health Care: A Review

"Difficult Patients" in Mental Health Care: A Review

Solving symmetric matrix word equations via symmetric space machinery

It has recently been proved by Hillar and Johnson [C.J. Hillar, C.R. Johnson, Symmetric word equations in two positive definite letters, Proc. Amer. Math. Soc. 132 (2004) 945–953] that every symmetric word equation in positive definite matrices has a positive definite solution (existence theorem). In this paper we partially solve the uniqueness conjecture via the symmetric space and non-positive curvature machinery existing in the open convex cone of positive definite matrices. Unique positive definite solutions are obtained in terms of geometric and weighted means and as fixed points of explicit strict contractions on the cone of positive definite matrices.

SECOND QUANTIZATION AND THE Lp-SPECTRUM OF NONSYMMETRIC ORNSTEIN–UHLENBECK OPERATORS

The spectra of the second quantization and the symmetric second quantization of a strict Hilbert space contraction are computed explicitly and shown to coincide. As an application, we compute the spectrum of the nonsymmetric Ornstein–Uhlenbeck operator L associated with the infinite-dimensional Langevin equation [Formula: see text] where A is the generator of a strongly continuous semigroup on a Banach space E and W is a cylindrical Wiener process in E. Assuming the existence of an invariant measure μ for L, under suitable assumptions on A we show that the spectrum of L in the space Lp (E, μ) (1&lt; p&lt; ∞) is given by [Formula: see text] where Aμ is the generator of a Hilbert space contraction semigroup canonically associated with A and μ. We prove that the assumptions on A are always satisfied in the strong Feller case and in the finite-dimensional case. In the latter case we recover the recent Metafune–Pallara–Priola formula for σ(L).