Nonlinear Pricing of Software with Local Demand Inelasticity

Nonlinear usage-based pricing is applied extensively in software markets. Customers of software products usually cannot vary their required usage volume, a property we label local demand inelasticity. For instance, a client firm that needs a sales force automation software either buys one user license for every salesperson or does not buy at all. It is unlikely to buy licenses for some but not all salespersons. This demand feature violates a critical assumption of the standard nonlinear pricing literature that consumers are flexible with their usage volume, and their valuation changes smoothly with usage volume. Consequently, standard nonlinear pricing solutions are inapplicable to many software products. This paper studies the optimal nonlinear usage-based pricing of software when customers' demand is locally inelastic. This unique demand feature necessitates a new approach to solve the nonlinear pricing problem. We show that under a weak ordering condition of customer types, this complex pricing problem can be decomposed into a set of much simpler subproblems with known solutions. Our pricing solution is easily implementable and applicable to a broad range of demand systems, including those described by the families of exponential and normal distributions. Moreover, local demand inelasticity has a critical impact on key efficiency results.

An Implementation of The Scalable and Correct Time-Stamped Stack

Many concurrent data structures impose real time ordering over their elements. This is needed only if the insertions modifying the data structure ran sequentially. A new approach using time stamps was proposed to avoid unneeded ordering. Our implementation is based on that time-stamped (TS) stack. Concurrent insertions can be left unordered and then ordered as necessary at removal. Because of this weak ordering, using linearizability to establish correctness is not possible. The original paper presents a new approach to proving correctness for the TS stack. This proof technique is a new, generic proof for correctness on concurrent data structures. In this paper, we highlight our general approach to re-implementing the Time-Stamped stack, discuss our modifications made to to the stack, give an overview of our implementation of a stack using software transactional memory, and analyze comparative performance graphs based on our experimental data.

Thermodynamic and Transport Properties of Molten Bi-In Alloys

We have used simple statistical theory to describe the mixing behavior of liquid Bi-In alloys in terms of energetic and structure through the study of their thermodynamic and transport properties. The structural characteristics of Bi-In melts are described by the two microscopic functions, i.e. the concentration fluctuation in long wavelength limit and the Warren-Cowley short range order parameter. The transport properties are analyzed through the diffusion coefficient ratio and viscosity. The Gibb’s free energy of mixing, enthalpy of mixing and entropy of mixing are the thermodynamic functions which are used to describe the thermodynamic behaviors. In whole analysis thermodynamic input parameter, i.e. interchange energy take important role which is temperature dependent. The computed results are in good agreement with experimental data and support a weak ordering tendency in molten Bi-In system.The Himalayan Physics Vol. 6 & 7, April 2017 (5-9)

Indicators, Chains, Antichains, Ramsey Property

We introduce two Ramsey classes of finite relational structures. The first class contains finite structures of the form , where ≤ is a total ordering on A and ⪯ is a linear ordering on the set fa 2 A : Ii (a)g. The second class contains structures of the form a , where (A,≤) is a weak ordering and ⪯ is a linear ordering on A such that A is partitioned by into maximal chains in the partial ordering ≤ and each is an interval with respect to .

QUADRATIC EQUATIONS IN HILBERTIAN OPERATORS AND APPLICATIONS

In this paper bounded linear operators in Hilbert space satisfying general quadratic equations are characterized. Necessary and sufficient conditions for sets of operators satisfying two such equations to compare relative to a weak ordering are presented. In addition, averaging operators in finite dimensional spaces are determined, and in this case it is shown that they are unitary models for all projections. It is pointed out, by an example, that the latter result does not hold in infinite dimensions. A key application to certain second order random fields of Karhunen type is given. The main purpose is to present the structure of bounded non-self adjoint operators solving quadratic equations, and indicate their use.

Why Rational Agents Should Not Be Liberal Maximizers

Hans Herzberger's 1973 essay ‘Ordinal Preference and Rational Choice’ is a classic milestone in the erosion of the idea that rational agents are maximizers of utility. By the time Herzberger wrote, many authors had replaced this claim with the thesis that rational agents are maximizers of preference. That is to say, it was assumed that at the moment of choice a rational agent has a weak ordering representing his or her preferences among the options available to the agent for choice and that the rational agent restricts choice to one of the optimal options. Such an option is an available option judged at least as good as imy other.