Pre-commitment or post-payment: Which worsens a line-sitting firm’s revenue?

Recently, Cui et al. (2018) investigated the economics of line-sitting, where a customer could hire a line-sitter to wait for her, and the line-sitting fee is paid at the completion of service. Usually, it is believed that the line-sitting firm benefits in the pre-commitment payment method, in which the customer still pays a pre-specified amount of fee for service even if the actual waiting time is less than the pre-committed wait. By comparing two payment mechanisms, we find that, surprisingly, under the optimal line-sitting rate, the revenue of firm worsens under pre-commitment case, but a better customer welfare can be obtained.     

A capacitated firm’s pricing strategies for strategic consumers with different search costs

This paper studies pricing strategies of a seller with budget constraints facing two types of strategic consumers with different search costs, and proposes three pricing strategies to motivate all consumers to visit his shop. These are the basic price strategy, differentiated compensation strategy and an improved differentiated compensation strategy. Based on the rational expectations paradigm, we characterize the rational expectations equilibrium in the game and propose a basic pricing strategy. In order to address the interplay between price and demand, we further propose a differentiated compensation strategy to improve the basic model. We then compare the differentiated compensation strategy to the basic pricing strategy when both are feasible. We find that selection of the optimal strategy is independent of composition of consumers but is dependent on the seller’s budget level and the difference between the two search costs. If the budget is large enough and the difference between the search costs is small enough, a differentiated compensation strategy can further improve the seller’s profitability. In addition to these findings, we first propose an improved differentiated compensation strategy to further enhance the firm’s profit. We find that the optimal strategy is to implement the improved differentiated compensation strategy when all three strategies are feasible. Interestingly, the firm may benefit from paying a high compensation to the consumers.     

Reich’s problem concerning Halpern’s convergence

We discuss Halpern’s convergence for nonexpansive mappings in Hilbert spaces. We prove that one of the conditions in [R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. (Basel), 58 (1992), 486–491] is the weakest sufficient condition among the conditions known to us. We also improve a necessary condition, which is close to Wittmann’s. This is one step to solve the problem raised by Reich in 1974 and 1983. Received: 15 July 2008     

Warfield’s Duality and Malcev’s Matrix

In this work, we investigate relations between Malcev’s matrices of a torsion-free group G of finite rank and Malcev’s matrices of groups Hom(R,G) and Hom(G,R), where G is a locally free group and R is a torsion-free group of rank 1.     

Bergmann’s Dilemma and Internalism’s Escape

Michael Bergmann has argued that internalist accounts of justification face an insoluble dilemma. This paper begins with an explanation of Bergmann??s dilemma. Next, I review some recent attempts to answer the dilemma, which I argue are insufficient to overcome it. The solution I propose presents an internalist account of justification through direct acquaintance. My thesis is that direct acquaintance can provide subjective epistemic assurance without falling prey to the quagmire of difficulties that Bergmann alleges all internalist accounts of justification cannot surmount.     

Generalizations of Sherman’s Inequality Via Fink’s Identity and Green’s Function

Ukrainian Mathematical Journal - New generalizations of Sherman’s inequality for n-convex functions are obtained with the help of Fink’s identity and Green’s function. By using...     

Kantorovich’s majorants principle for Newton’s method

We prove Kantorovich’s theorem on Newton’s method using a convergence analysis which makes clear, with respect to Newton’s method, the relationship of the majorant function and the non-linear operator under consideration. This approach enables us to drop out the assumption of existence of a second root for the majorant function, still guaranteeing Q-quadratic convergence rate and to obtain a new estimate of this rate based on a directional derivative of the derivative of the majorant function. Moreover, the majorant function does not have to be defined beyond its first root for obtaining convergence rate results. The research of O.P. Ferreira was supported in part by FUNAPE/UFG, CNPq Grant 475647/2006-8, CNPq Grant 302618/2005-8, PRONEX–Optimization(FAPERJ/CNPq) and IMPA. The research of B.F. Svaiter was supported in part by CNPq Grant 301200/93-9(RN) and by PRONEX–Optimization(FAPERJ/CNPq).     

On Andrunakievich’s chain and Koethe’s problem

In 1969 Andrunakievich asked whether one gets a ring without nonzero nil left ideals from an arbitrary ring R by factoring out the ideal A(R) which is the sum of all nil left ideals of R. Recently, it was shown that this problem is equivalent to Koethe’s problem. In this context one may consider the chain of ideals, which starts with A ₁(R) = A(R) ⊆ A ₂(R), where A ₂(R)/A ₁(R) = A(R/A ₁(R)), and extends by repeating this process. We study the properties of this chain and show that, assuming a negative solution of Koethe’s problem, this chain can terminate at any given ordinal number.     

How do commission rates influence a firm’s success? statistical analysis of a corporate strategy simulation experiment

The purpose of this paper is to analyse the relationship between commission rates and a firm’s success within a corporate strategic planning simulation experiment. Teams of students are assigned to the role of managers of a firm within a competitive market situation. They have the task to experience the complex situation in which they act as managers to increase the performance of a firm by setting specific parameters. Our most interesting parameter is the commission rate. The Marketing Game considers a reasonably complex and realistic situation for the participants. We examine to what extent subjects succeed in increasing a firm’s turnover and profit by varying the commission rates.     

Dedekind’s and Frege’s views on logic

A contextual and comparative analysis shows that Dedekind and Frege do not understand the terms “logic” and “arithmetic” in the same way. More specifically the meaning and the scope of the corresponding concepts are essentially different for them. Consequently Dedekind and Frege have different conceptions of the relationship between arithmetic and logic.     

A note on Stone’s,Baire’s,Ky Fan’s and Dugundji’s theorem in tvs-cone metric spaces

Recently, Ayse Sonmez [A. Sonmez, On paracompactness in cone metric spaces, Appl. Math. Lett. 23 (2010) 494–497] proved that a cone metric space is paracompact when the underlying cone is normal. Also, very recently, Kieu Phuong Chi and Tran Van An [K.P. Chi, T. Van An, Dugundji’s theorem for cone metric spaces, Appl. Math. Lett. (2010) doi:10.1016/j.aml.2010.10.034] proved Dugundji’s extension theorem for the normal cone metric space. The aim of this paper is to prove this in the frame of the tvs-cone spaces in which the cone does not need to be normal. Examples are given to illustrate the results.     

Berkson’s theorem

We give a new proof of the theorem that Amitsur’s complex for purely inseparable field extensions has vanishing homology in dimensions higher than 2. This is accomplished by computing the kernel and cokernel of the logarithmic derivativet →Dt/t mapping the multiplicative Amitsur complex to the acyclic additive one (D is a derivation of the extension field). This research was supported by National Science Foundation grant NSF GP 1649.     

Higher dimensional Schwarz’s surfaces and Scherk’s surfaces

Higher dimensional generalizations of Schwarz’s P-surface, Schwarz’s D-surface and Scherk’s second surface are constructed as complete embedded periodic minimal hypersurfaces in \(\mathbb {R}^n\).     

Bartnik’s Mass and Hamilton’s Modified Ricci Flow

We provide estimates on the Bartnik mass of constant mean curvature surfaces which are diffeomorphic to spheres and have positive mean curvature. We prove that the Bartnik mass is bounded from above by the Hawking mass and a new notion we call the asphericity mass. The asphericity mass is defined by applying Hamilton’s modified Ricci flow and depends only upon the restricted metric of the surface and not on its mean curvature. The theorem is proven by studying a class of asymptotically flat Riemannian manifolds foliated by surfaces satisfying Hamilton’s modified Ricci flow with prescribed scalar curvature. Such manifolds were first constructed by the first author in her dissertation conducted under the supervision of M. T. Wang. We make a further study of this class of manifolds which we denote Ham₃, bounding the ADM masses of such manifolds and analyzing the rigid case when the Hawking mass of the inner surface of the manifold agrees with its ADM mass.     

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