Potential symmetries and new solutions of a simplified model for reacting mixtures

In this paper, we investigate potential symmetries of a simplified model for reacting mixtures. We find new similarity reductions and wider class of solutions through this approach. Further, we explore an invertible mapping which linearizes the reacting mixture model.

Renormalized new solutions for the massless Thirring model

We present a nonperturbative study of the (1 + 1)-dimensional massless Thirring model by using path integral methods. The regularization ambiguities - coming from the computation of the fermionic determinant - allow to find new solution types for the model. At quantum level the Ward identity for the 1PI 2-point function for the fermionic current separates such solutions in two phases or sectors, the first one has a local gauge symmetry that is implemented at quantum level and the other one without this symmetry. The symmetric phase is a new solution which is unrelated to the previous studies of the model and, in the nonsymmetric phase there are solutions that for some values of the ambiguity parameter are related to well-known solutions of the model. We construct the Schwinger-Dyson equations and the Ward identities. We make a detailed analysis of their UV divergence structure and, after, we perform a nonperturbative regularization and renormalization of the model.

CSX and the railway unions : in search of new solutions /

"BLMR 140."

Development of New Solutions in the Field of Digitization and Digital Presentation of the National Folklore Heritage

This article briefly reviews the software developments for digital presentation and preservation of Bulgarian folklore treasure created within the project “Knowledge Technologies for Creation of Digital Presentation and Significant Repositories of Folklore Heritage” by teams of the Institute of Mathematics and Informatics.

New Vacuum Solutions for Quadratic Metric-Affine Gravity - a Metric Affine Model for the Massless Neutrino?

AMS Subj. Classification: 83C15, 83C35

Exact-Solutions Of Linear Partial-Differential Equations With Variable-Coefficients

Backlund transformations relating the solutions of linear PDE with variable coefficients to those of PDE with constant coefficients are found, generalizing the study of Varley and Seymour [2]. Auto-Backlund transformations are also determined. To facilitate the generation of new solutions via Backlund transformation, explicit solutions of both classes of the PDE just mentioned are found using invariance properties of these equations and other methods. Some of these solutions are new.

New methods for generating populations in Markov network based EDAs: Decimation strategies and model-based template recombination

Methods for generating a new population are a fundamental component of estimation of distribution algorithms (EDAs). They serve to transfer the information contained in the probabilistic model to the new generated population. In EDAs based on Markov networks, methods for generating new populations usually discard information contained in the model to gain in efficiency. Other methods like Gibbs sampling use information about all interactions in the model but are computationally very costly. In this paper we propose new methods for generating new solutions in EDAs based on Markov networks. We introduce approaches based on inference methods for computing the most probable configurations and model-based template recombination. We show that the application of different variants of inference methods can increase the EDAs’ convergence rate and reduce the number of function evaluations needed to find the optimum of binary and non-binary discrete functions.

Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

Various families of exact solutions to the Einstein and Einstein-Maxwell field equations of General Relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations.

The physical situations in which such equations arise include: a) the external gravitational field of an axisymmetric, uncharged steadily rotating body, b) cylindrical gravitational waves with two degrees of freedom, c) colliding plane gravitational waves, d) the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and e) colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein-Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa.

The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables.

The new economy: Essays in network economics and two-sided markets

Following the Introduction, which surveys existing literature on the technology advances and regulation in telecommunications and on two-sided markets, we address specific issues on the industries of the New Economy, featured by the existence of network effects. We seek to explore how each one of these industries work, identify potential market failures and find new solutions at the economic regulation level promoting social welfare. In Chapter 1 we analyze a regulatory issue on access prices and investments in the telecommunications market. The existing literature on access prices and investment has pointed out that networks underinvest under a regime of mandatory access provision with a fixed access price per end-user. We propose a new access pricing rule, the indexation approach, i.e., the access price, per end-user, that network i pays to network j is function of the investment levels set by both networks. We show that the indexation can enhance economic efficiency beyond what is achieved with a fixed access price. In particular, access price indexation can simultaneously induce lower retail prices and higher investment and social welfare as compared to a fixed access pricing or a regulatory holidays regime. Furthermore, we provide sufficient conditions under which the indexation can implement the socially optimal investment or the Ramsey solution, which would be impossible to obtain under fixed access pricing. Our results contradict the notion that investment efficiency must be sacrificed for gains in pricing efficiency. In Chapter 2 we investigate the effect of regulations that limit advertising airtime on advertising quality and on social welfare. We show, first, that advertising time regulation may reduce the average quality of advertising broadcast on TV networks. Second, an advertising cap may reduce media platforms and firms' profits, while the net effect on viewers (subscribers) welfare is ambiguous because the ad quality reduction resulting from a regulatory cap o¤sets the subscribers direct gain from watching fewer ads. We find that if subscribers are sufficiently sensitive to ad quality, i.e., the ad quality reduction outweighs the direct effect of the cap, a cap may reduce social welfare. The welfare results suggest that a regulatory authority that is trying to increase welfare via regulation of the volume of advertising on TV might necessitate to also regulate advertising quality or, if regulating quality proves impractical, take the effect of advertising quality into consideration. 3 In Chapter 3 we investigate the rules that govern Electronic Payment Networks (EPNs). In EPNs the No-Surcharge Rule (NSR) requires that merchants charge at most the same amount for a payment card transaction as for cash. In this chapter, we analyze a three- party model (consumers, merchants, and a proprietary EPN) with endogenous transaction volumes and heterogenous merchants' transactional benefits of accepting cards to assess the welfare impacts of the NSR. We show that, if merchants are local monopolists and the network externalities from merchants to cardholders are sufficiently strong, with the exception of the EPN, all agents will be worse o¤ with the NSR, and therefore the NSR is socially undesirable. The positive role of the NSR in terms of improvement of retail price efficiency for cardholders is also highlighted.