Secrecy versus patents: process innovations and the role of uncertainty

Whilst firms often prefer secrecy to patents and process innovations particu- larly lend themselves to secrecy, we establish a rationale for process innovators who patent. Using a simple two-period model, we show that under myopic op- timisation, the incentive to patent rather than pursue secrecy increases as the probability that the rival firm attaches to it being low-cost falls and as the pro- portion of the cost reduction due to the innovation, secured by the rival firm in the period after the patent has expired, falls. However, the gain to the innovating firm from patenting rather than secrecy strictly increases if the cost reduction due to the innovation is sufficiently small that the high-cost firm could profitably bluff that it is low-cost. Finally, allowing the low-cost firm the option of using an output signal in such cases, may make the patent strategy more or less attractive relative to the case of myopic optimisation

Measuring the Balance of Intra-Regional Trade

We introduce an original method of measuring the extent of the overall balance of migration among countries within a region which allows comparisons of the balance over time as well as between regions and various possible sub-regions

The CWKB approach to non-reflecting potential and cosmological implications

We discuss the method of calculating the reflection coefficient using complex trajectory WKB (CWKB) approximation. This enables us to give an interpretation of non-reflecting nature of the potential under certain conditions and clarify some points, reported incorrectly elsewhere [vs:ejp] for the potential $U(x)=-U_0cosh^2(x/a)$. We show that the repeated reflectios between the turning points are essential, which most authors overlooked, in obtaining the non-reflecting c ondition. We find that the considered repeated reflection paths are in conformity with Bogolubov transformation technique. We discuss the implications of the results when applied to the particle production scenario, considering $x$ as a time variable and also stress the cosmological implications of the result with reference to radiation domonated and de Sitter spacetime.Comment: 9 pages, late

On bouncing solutions in non-local gravity

A non-local modified gravity model with an analytic function of the d'Alembert operator is considered. This model has been recently proposed as a possible way of resolving the singularities problem in cosmology. We present an exact bouncing solution, which is simpler compared to the already known one in this model in the sense it does not require an additional matter to satisfy all the gravitational equations.Comment: 5 pages; v2: matching the jounral versio

On Modified Gravity

We consider some aspects of nonlocal modified gravity, where nonlocality is of the type $R \mathcal{F}(\Box) R$. In particular, using ansatz of the form $\Box R = c R^\gamma,$ we find a few $R(t)$ solutions for the spatially flat FLRW metric. There are singular and nonsingular bounce solutions. For late cosmic time, scalar curvature R(t) is in low regime and scale factor a(t) is decelerated. R (t) = 0 satisfies all equations when k = -1.Comment: added references; made some clarifications; 8 page

Inter-regional Migration: The UK experience

This paper looks at the scenario of intra-UK migration amongst its four regions. The level of intra-UK migration is significant and is increasing over time. Using several measures of the balance in migration we observe that, broadly speaking, the balance is improving. We also examine the impact of changes in the regional per capita GDPs and unemployment levels on regional migration using panel analysis. Several authors find these to be significant factors in international migration. However, it seems that neither regional per capita GDP nor the unemployment level has a significant effect on regional migration in the UK (although the regression coefficients have the correct signs). In the case of regional migration in the UK, it is other characteristics of the source and destination regions which appear to matter most

Rationality and Brauer group of a moduli space of framed bundles

We prove that the moduli spaces of framed bundles over a smooth projective curve are rational. We compute the Brauer group of these moduli spaces to be zero under some assumption on the stability parameter.Comment: 7 pages, to appear in Tbilisi Math. J; v2. reference adde

Nonlocal Gravitational Models and Exact Solutions

A nonlocal gravity model with a function $f(\Box^{-1} R)$, where $\Box$ is the d'Alembert operator, is considered. The algorithm, allowing to reconstruct $f(\Box^{-1} R)$, corresponding to the given Hubble parameter and the state parameter of the matter, is proposed. Using this algorithm, we find the functions $f(\Box^{-1} R)$, corresponding to de Sitter solutions.Comment: 5 pages, v2: refs. added, to appear in the proceedings of the International Workshop "Supersymmetries and Quantum Symmetries" (SQS'2011), Dubna, Russia, July 18-23, 2011, http://theor.jinr.ru/sqs/2011