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Bay beaches are common coastal landforms along the world's coastlines and have frequently been used as equilibrium coastal systems to mitigate erosion problems and stabilize coasts. Throughout the literature, several formulae can be found to obtain the static equilibrium planform (SEP) of such beaches on the leeward sides of single protruding headland structures. However, equations used to define SEP behind breakwater gaps are rare and based on a limited number of studies, especially when the obliquity angle (β) is large. This paper proposes a new formula for modelling the SEP of bay beaches that includes cases with planform shapes characterized by large obliquity angles (β > 75°) for which the SEP is almost quasi-semicircular. The formula represents a general form of the parabolic bay shape equation (PBSE) with modified coefficients to alter the planform's curvature to be quasi-semicircular, mimicking the behavior of such bays in nature. The coefficients are expressed as functions of both the obliquity angle (β) and the curvature-adjustment angle (φ), which was determined based on field observations of the best-fitting SEP of 26 bay beaches with (β > 75°) along the coasts of Spain, Portugal and Brazil. Additionally, 32 beach cases characterized by smaller obliquity angles (β < 70°) were included in the derivation of the curvature adjustment angle, which was expressed as a function of (β). The model showed good results in modelling the SEP, with an RMSE of 0.90° obtained when estimating the planform's curvature-adjustment angle (φ) to obtain quasi-semicircular planform shapes for the prototype cases, confirming its utility as a valuable tool for engineering applications. • Static equilibrium planforms (SEPs) characterized by large obliquity angles are modelled. • A new formula was derived to plot the (SEP) of bay beaches behind gaps when (β > 75°). • A curvature-adjustment angle is used to alter the SEP's curvature based on field cases. • The SEP is quasi-semicircular for pocket beaches behind breakwater gaps when (β > 75°). • The curvature-adjustment angle is directly proportional to the obliquity angle (β). [ABSTRACT FROM AUTHOR]

Abstract: 222Rn concentrations in the air in Nerja cave (Spain) (3° 52′35′′W 36° 43′50′′N) were measured by continuous monitoring using Alpha-Guard, Genitron instrument equipment. The 222Rn measurements were carried out for a complete annual cycle in the different halls: Vestibule hall from July 2003 to June 2004, Ballet hall from July 2004 to June 2005 and Mirador hall from July 2005 to June 2006. Starting from the entrance of the cave we successively find the Vestibule hall, the Ballet hall and the Mirador hall. The range of 222Rn levels were of 8–627 Bq m−3 for the Vestibule hall, 28–575 Bq m−3 for the Ballet hall and 38–578 Bq m−3 for the Mirador. The aim of this study was to detect seasonal variation patterns of 222Rn concentrations. The seasonal variations of 222Rn concentrations are discussed in relation to various meteorological factors measured inside and outside the cave. The radiation exposure levels for workers and tourists with different equilibrium factors have been evaluated. The radiation exposure levels for workers and tourists only represent a low percentage of the exposure guides for the general population. [Copyright &y& Elsevier]

Abstract: The stabilization of the Cournot equilibrium point of a duopoly by feedback control is analyzed. We give a general result which is valid for any duopoly controlled by linear feedback and study in detail the stabilization of a duopoly when the feedback is not linear. [ABSTRACT FROM AUTHOR]

Abstract: The concept of equilibrium plan form and equilibrium profile has been widely used as an engineering tool in order to design beach nourishment projects. The scope of this paper is to further explore this “equilibrium beach” concept in crenulated bays, as a long-term tool for beach nourishment projects. The proposed methodology is based on and combines the static equilibrium plan and profile for long-term analysis. This methodology includes a modified equilibrium plan form, which is able to define the orientation of the local wave front in the diffracting point, and also to locate the downcoast starting point of the static equilibrium beach from which the parabolic plan form of is valid. This methodology permits the application of any equilibrium profile formulation. An example of the application of this methodology and long-term formulations to the design of the Spanish nourishment project of Poniente Beach (Gijón) is presented. Ten years after its construction, the beach has still got a static equilibrium and remains pretty close to the predicted equilibrium beach in plan and profile. [Copyright &y& Elsevier]

Abstract: In this work, we present the values of radon concentration, measured by continuous monitoring during a complete annual cycle in the Polychromes Hall of Altamira Cave in order to undertake more precise calculations of annual effective dose for guides and visitors in tourist caves. The 222Rn levels monitored inside the cave ranges from 186 Bq m-3 to 7120 Bq m-3, with an annual average of 3562 Bq m-3. In order to more accurately estimate effective dose we use three scenarios with different equilibrium factors (, 0.7 and 1.0) together with different dose conversion factors proposed in the literature. Neither effective dose exceeds international recommendations. Moreover, with an automatic radon monitoring system the time remaining to reach the maximum annual dose recommended could be automatically updated. [Copyright &y& Elsevier]