Alternative Theorem Research Articles

Corporate Responsibility and Identity: from a Stakeholder to an Awareness Approach

ABSTRACTFirms are encouraged to manage their corporate responsibility and identity in accordance with the popular stakeholder theory. Managers are, however, confronted with the complexity of the praxis and related ethical dilemmas, as the expectations of their external stakeholders may be myriad, ambiguous and self‐contradictory, or even non‐existent in the global and dynamic business contexts. Therefore, the purpose of this paper is to (a) review and critically discuss the stakeholder approach in striving for a responsible identity and (b) introduce an alternative approach that can address its inadequacies and shortcomings. The study outlines an alternative theorem, the awareness approach to responsible identity. In the conclusions, the article proposes how firms can adopt a responsible identity that leads to a desired image and reputation, and maps out further research opportunities. Copyright © 2011 John Wiley & Sons, Ltd and ERP Environment

Approximately cubic functional equations and cubic multipliers

In this paper, we prove the Hyers-Ulam stability and the superstability for cubic functional equation by using the fixed point alternative theorem. As a consequence, we show that the cubic multipliers are superstable under some conditions. 2000 Mathematics Subject Classification: 39B82; 39B52.

On the construction of a nonnegative solution for one class of Urysohn-type nonlinear integral equations on a semiaxis

We investigate one class of Urysohn-type nonlinear integral equations with noncompact operator. It is assumed that a Wiener–Hopf–Hankel-type linear integral operator is a local minorant for the initial Urysohn operator. We prove an alternative theorem on the existence of positive solutions and investigate the asymptotic behavior of the obtained solutions at infinity.

Existence and global asymptotic stability of periodic solution for discrete and distributed time-varying delayed neural networks with discontinuous activations

In this paper, we study a general class of neural networks with discrete and distributed time-varying delays, whose neuron activations are discontinuous and may be unbounded or nonmonotonic. By using the Leray–Schauder alternative theorem in multivalued analysis, matrix theory and generalized Lyapunov-like approach, we obtain some sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the periodic solution. Moreover, when all the variable coefficients and time delays are real constants, we discuss the global convergence in finite time of the neural network dynamical system. Our results extend previous works not only on discrete and distributed time-varying delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete and distributed time-varying delayed neural networks with discontinuous activations. Two numerical examples are given to illustrate the effectiveness of our main results.

On Lagrangian duality in vector optimization: applications to the linear case

We recall a general scheme for vector problems based on separation arguments and alternative theorems, and then, this approach is exploited to study Lagrangian duality in vector optimization. We show that the vector linear duality theory due to Isermann can be embedded in this separation approach. The theoretical part of this paper serves the purpose of introducing two possible applications. Some well-known classical applications in economics are the minimization of costs and the maximization of profit for a firm. We extend these two examples to the multiobjective framework in the linear case, exploiting the duality theory of Isermann. For the former, we consider the minimization of costs and of pollution as two different and conflicting goals; for the latter, we introduce as second objective function the profit for a competitor firm. This allows us to study the relationships between the shadow prices referred to the two different goals and to introduce a new representation of the feasible region of the dual problem.

The Stochastic Dirichlet Problem Driven by the Ornstein–Uhlenbeck Operator: Approach by the Fredholm Alternative for Chaos Expansions

In this article, we prove the Fredholm alternative theorem for mappings defined on spaces of generalized stochastic processes given by their Wiener–It chaos expansion form. We apply the result to solve the stochastic Dirichlet problem with a perturbation term driven by the Ornstein–Uhlenbeck operator.

Alternative Theorems for Pseudo Almost Automorphic Problems

This paper gives alternative theorems to investigate the existence of pseudo almost automorphic solutions for semilinear evolution equations. Moreover, we consider a parabolic equation to illustrate the theorem.

ON SOLVABLE SUBGROUPS OF AUTOMORPHISM GROUPS OF RIGHT-ANGLED ARTIN GROUPS

For any right-angled Artin group, we show that its outer automorphism group contains either a finite-index nilpotent subgroup or a nonabelian free subgroup. This is a weak Tits alternative theorem. We find a criterion on the defining graph that determines which case holds. We also consider some examples of solvable subgroups, including one that is not virtually nilpotent and is embedded in a non-obvious way.

Alternative results and robustness for fractional evolution equations with periodic boundary conditions

In this paper, we study periodic boundary value problems for a class of linear fractional evolution equations involving the Caputo fractional derivative. Utilizing compactness of the constructed evolution operators and Fredholm alternative theorem, some interesting alternative results for the mild solutions are presented. Periodic motion controllers that are robust to parameter drift are also designed for given a periodic motion. An example is given to illustrate the results.

Picard values of p-adic meromorphic functions

We investigate Picard-Hayman behavior of derivatives of meromorphic functions on an algebraically closed field K, complete with respect to a non-trivial ultrametric absolute value. We present an analogue of the well-known Hayman’s alternative theorem both in K and in any open disk. Here the main hypothesis is based on the behaviour of |f|(r) when r tends to +∞ on properties of special values and quasi-exceptional values.We apply this study to give some sufficient conditions on meromorphic functions so that they satisfy Hayman’s conjectures for n = 1and for n = 2. Given a meromorphic transcendental function f, at least one of the two functions f′f and f′f 2 assumes all non-zero values infinitely often. Further, we establish that if the sequence of residues at simple poles of a meromorphic transcendental function on K admits no infinite stationary subsequence, then either f′ + af 2 has infinitely many zeros that are not zeros of f for every a ∈ K* or both f′ + bf 3 and f′ + bf 4 have infinitely many zeros that are not zeros of f for all b ∈ K*. Most of results have a similar version for unbounded meromorphic functions inside an open disk.

Alternative principles and their applications

In this paper we establish two alternative principles of the following type: If X and Y are convex subsets of two locally convex Hausdorff topological vector spaces and $${F,S:X \multimap Y}$$ are two set-valued mappings satisfying certain conditions, then either there exists $${x_0 \in X}$$ such that $${F(x_0) = \emptyset}$$ or $${\bigcap_{x \in X}S(x) \neq \emptyset}$$ . As first applications of the alternative principles we obtain two matching theorems of Ky Fan type. Next, are given several analytic alternatives and minimax inequalities. Finally we establish two very general alternative theorems concerning existence of solutions of a vector equilibrium problem.

Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique

The free longitudinal vibration of tapered nanowires is investigated in the context of nonlocal continuum theory. The problem is studied for the nanowires with linearly varied radii under fixed–fixed and fixed–free boundary conditions. In order to assess the problem in a more general form, a perturbation technique is proposed based on the Fredholm alternative theorem. The natural frequencies, corresponding mode shapes, and phase velocities of the tapered nanowires are derived analytically up to the second-order perturbation for different boundary conditions. The predicted results by the perturbation technique are successfully verified with those of the exact solution. The obtained results reveal that the proposed methodology is a capable one in capturing the free longitudinal dynamic response of tapered nanowires with different boundary conditions. However, the differences of the results of the perturbation technique and those of the exact solution increase with the rate of radii change. In a special case, the obtained results are also compared with those of other researchers and a reasonably good agreement is achieved. It is also observed that for higher values of the small scale effect parameter, the variation of the rate of radii change has a more effect on the variation of the natural frequencies and phase velocities, irrespective of the boundary conditions of the tapered nanowire. Additionally, a scrutiny of the presented dispersion curves indicates that for a constant wavenumber, the value of the phase velocity decreases with the small scale effect parameter, particularly for higher wavenumbers.

Effective learning strategies for real-time image-guided adaptive control of multiple-source hyperthermia applicators.

This paper investigates overall theoretical requirements for reducing the times required for the iterative learning of a real-time image-guided adaptive control routine for multiple-source heat applicators, as used in hyperthermia and thermal ablative therapy for cancer. Methods for partial reconstruction of the physical system with and without model reduction to find solutions within a clinically practical timeframe were analyzed. A mathematical analysis based on the Fredholm alternative theorem (FAT) was used to compactly analyze the existence and uniqueness of the optimal heating vector under two fundamental situations: (1) noiseless partial reconstruction and (2) noisy partial reconstruction. These results were coupled with a method for further acceleration of the solution using virtual source (VS) model reduction. The matrix approximation theorem (MAT) was used to choose the optimal vectors spanning the reduced-order subspace to reduce the time for system reconstruction and to determine the associated approximation error. Numerical simulations of the adaptive control of hyperthermia using VS were also performed to test the predictions derived from the theoretical analysis. A thigh sarcoma patient model surrounded by a ten-antenna phased-array applicator was retained for this purpose. The impacts of the convective cooling from blood flow and the presence of sudden increase of perfusion in muscle and tumor were also simulated. By FAT, partial system reconstruction directly conducted in the full space of the physical variables such as phases and magnitudes of the heat sources cannot guarantee reconstructing the optimal system to determine the global optimal setting of the heat sources. A remedy for this limitation is to conduct the partial reconstruction within a reduced-order subspace spanned by the first few maximum eigenvectors of the true system matrix. By MAT, this VS subspace is the optimal one when the goal is to maximize the average tumor temperature. When more than 6 sources present, the steps required for a nonlinear learning scheme is theoretically fewer than that of a linear one, however, finite number of iterative corrections is necessary for a single learning step of a nonlinear algorithm. Thus, the actual computational workload for a nonlinear algorithm is not necessarily less than that required by a linear algorithm. Based on the analysis presented herein, obtaining a unique global optimal heating vector for a multiple-source applicator within the constraints of real-time clinical hyperthermia treatments and thermal ablative therapies appears attainable using partial reconstruction with minimum norm least-squares method with supplemental equations. One way to supplement equations is the inclusion of a method of model reduction.

Generalized (,α, ρ, θ)–d–V–univex functions and non-smooth alternative theorems

Under a new kind of generalized convexity and non-smooth generalized (, α, ρ, θ)–d–V–univexity, some basic alternative theorems are established and proved. These results extend some other generalized convex alternative theorems. To illustrate their applications, we present characterizations of saddle-point type necessary optimality conditions for properly efficient solutions of vector optimization problems. To conclude, the alternative theorems are applied to yield a canonical convex alternative theorem as a corollary.

Some Equivalent Results with Yakubovich's S-Lemma

This paper presents an elementary proof of nonstrict Finsler's theorem and discusses five closely related theorems: Yakubovich's S-lemma, Yuan's alternative theorem, nonstrict Finsler's theorem, strict Finsler's theorem, and Finsler–Calabi's theorem. This paper discusses how one is related with another. At the end of this article we present some extensions of these results to an infinite-dimensional vector space.

A Note to Correct Modeling Term Structures of Defaultable Bonds

This paper briefly identifies and corrects an error in Duffie and Singleton (1999). The error to omit a variable casts doubt on the arguments of Duffie and Singleton to constitute Heath-Jarrow-Morton (1992) type term structures on defaultable bonds. The error reveals inconsistency through their model in the sense that Heath, Jarrow, and Morton construct no-arbitrage term structures composed of forward rate dynamics explicitly not depending on the market price of risk with default-free bonds. Recent studies for change methods of measures to constitute alternative fundamental theorems of asset pricing shed some light on their arguments in the Heath-Jarrow-Morton framework.

Strongly Consistent Self-Confirming Equilibrium

Fudenberg and Levine (1993a) introduced the notion of self-confirming equilibrium, which is generally less restrictive than Nash equilibrium. Fudenberg and Levine also defined a concept of consistency, and claimed in their Theorem 4 that with consistency and other conditions on beliefs, a self-confirming equilibrium has a Nash equilibrium outcome. We provide a counterexample that disproves Theorem 4 and prove an alternative by replacing consistency with a more restrictive concept, which we call strong consistency. In games with observed deviators, self-confirming equilibria are strongly consistent self-confirming equilibria. Hence, our alternative theorem ensures that despite the counterexample, the corollary of Theorem 4 is still valid.

A Fixed Point Approach to the Stability of Quadratic Equations in Quasi Normed Spaces

We use the xed alternative theorem to establish Hyers{Ulam{Rassias stabil- ity of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approx- imately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the map- ping. We also give a few applications of our results in some special cases.

GENERALIZED MINIMAX THEOREMS IN GENERALIZED CONVEX SPACES

In this work, we obtain intersection theorem, analytic alternative and von Neumann type minimax theorem in G-convex spaces. We also generalize Ky Fan minimax inequality to acyclic versions in G-convex spaces. The result is applied to formulate acyclic versions of other minimax results, a theorem of systems of inequalities and analytic alternative.

Exceptional family of elements for generalized variational inequalities

This paper introduces a new concept of exceptional family of elements for a finite-dimensional generalized variational inequality problem. Based on the topological degree theory of set-valued mappings, an alternative theorem is obtained which says that the generalized variational inequality has either a solution or an exceptional family of elements. As an application, we present a sufficient condition to ensure the existence of a solution to the variational inequality. The set-valued mapping is assumed to be upper semicontinuous with nonempty compact convex values.