The work is devoted to the numerical solution of the initial boundary value problem for the heat equation with a fractional Riesz derivative. Explicit and implicit difference schemes are constructed that approximate the boundary value problem for the heat equation with a fractional Riesz derivative with respect to the coordinate. In the case of an explicit difference scheme, a condition is obtained for the time step at which the difference scheme converges. For an implicit difference scheme, a theorem on unconditional convergence is proved. An example of a numerical calculation using an implicit difference scheme is given. It has been established that when passing to a fractional derivative, the process of heat propagation slows down.

In many cases, the expected efficiency advantages of public-private partnership (PPP) projects as a specific form of infrastructure provision did not materialize ex post. From a Public Choice perspective, one simple explanation for many of the problems surrounded by the governance of PPPs is that the public decision-makers being involved in the process of initiating and implementing PPP projects (namely, politicians and public bureaucrats) in many situations make low- cost decisions in the sense of Kirchgässner (1948–2017). That is, their decisions may have a high impact on the wealth of the jurisdiction in which the PPP is located (most notably, on the welfare of citizen-taxpayers in this jurisdiction) but, at the same time, these decisions often only have a low impact on the private welfare of the individual decision-makers in politics and bureaucracy. The latter, for example, in many settings often have a low economic incentive to monitor/control what the private-sector partners are doing (or not doing) within a PPP arrangement. The purpose of this paper is to draw greater attention to the problems created by low-cost decisions for the governance of PPPs. Moreover, the paper discusses potential remedies arising from the viewpoint of Public Choice and Constitutional Political Economy.

A geologic and geomorphologic study aimed at solving some geological and geotechnical problems, regarding the massive seepage of meteoric waters in the coastal cliffs of the Island of Procida (Naples Bay, Southern Italy) composed of both tuffs and loose pyroclastic deposits, has been carried out in the geosites of Terra Murata (Middle Ages village and coastal cliff towards the Corricella Bay) and Centane-Panoramica (coastal cliff facing on the Tyrrhenian Sea).

A detailed geologic and geomorphologic survey has allowed to suggest solutions to the applied geological and geotechnical problems related to the occurrence of massive seepages of waters at the physical interface between pyroclastic rocks and loose pyroclastic deposits, characterized by different density, permeability and porosity and also controlled by a dense network of fractures, involving the pyroclastic deposits cropping out in the selected areas.

Field sampling and geotechnical laboratory analyses have been carried out to calculate the values of main geotechnical parameters of the yellow tuffs cropping out at the Terra Murata Promontory. At the same time, a detailed monitoring of the seepages of waters has been carried out through a detailed geological survey of the tuff outcrops of the promontory. The obtained results have suggested a strong control from both the geomorphologic instability of the coastal cliff and tectonic setting. At the Centane-Panoramica geosite, the geological survey, coupled with geotechnical analyses and standard penetrometric tests, has accordingly evidenced that the geomorphologic instability was mainly concentrated in the sectors of the tuff coastal cliffs facing seawards towards the Tyrrhenian Sea.

The rise of online gambling in Indonesia has emerged as a significant public health concern, driven by various psychological, social, and regulatory factors. Despite stringent laws prohibiting gambling, the accessibility and appeal of online platforms have led to increased participation, particularly among young adults. This phenomenon is characterized by a paradoxical sense of control that users feel while gambling online, which can lead to compulsive behaviors and addiction. The structural characteristics of online gambling platforms, including fast-paced games and easy accessibility, further exacerbate this issue. Social influences, particularly through social media and peer interactions, normalize gambling behaviors, making them more appealing to adolescents. Mental health issues, such as anxiety and depression, are closely linked to online gambling addiction, as individuals may use gambling as a coping mechanism. The COVID-19 pandemic has intensified these challenges, with many individuals turning to online gambling for entertainment during lockdowns. To address the growing prevalence of online gambling addiction, comprehensive regulatory frameworks are needed, alongside responsible gambling initiatives and public awareness campaigns. Collaboration among stakeholders, including government agencies, healthcare providers, and gambling operators, is crucial for effective intervention. Continuous monitoring and evaluation of online gambling trends will inform future policies and help identify emerging risks. By adopting a multifaceted approach, Indonesian policymakers and stakeholders can work towards minimizing the risks associated with online gambling and fostering a healthier environment for its citizens.