Special formulas involving polygonal numbers and Horadam numbers

Some convolution-type identities involving polygonal numbers and Horadam numbers are derived. The method of proof is to properly relate the generating functions to each other. Additionally, we prove a general non-convolutional result involving these number families and discuss some of the consequences

Empirical investigation to explore potential gains from the amalgamation of Phase Changing Materials (PCMs) and wood shavings

The reduction of gained heat, heat peak shifting and the mitigation of air temperature fluctuations are some desirable properties that are sought after in any thermal insulation system. It cannot be overstated that these factors, in addition to others, govern the performance of such systems thus their effect on indoor ambient conditions. The effect of such systems extends also to Heating, Ventilation and Air-conditioning (HVAC) systems that are set up to operate optimally in certain conditions. Where literature shows that PCMs and natural materials such as wood-shavings can provide efficient passive insulation for buildings, it is evident that such approaches utilise methods that are of a degree of intricacy which requires specialist knowledge and complex techniques, such as micro-encapsulation for instance. With technical and economic aspects in mind, an amalgam of PCM and wood-shavings has been created for the purpose of being utilised as a feasible thermal insulation. The amalgamation was performed in the simplest of methods, through submerging the wood shavings in PCM. An experimental procedure was devised to test the thermal performance of the amalgam and compare this to the performance of the same un-amalgamated materials. Comparative analysis revealed that no significant thermal gains would be expected from such amalgamation. However, significant reduction in the total weight of the insulation system would be achieved that, in this case, shown to be up to 20.94%. Thus, further reducing possible strains on structural elements due to the application of insulation on buildings. This can be especially beneficial in vernacular architectural approaches where considerably large amounts and thicknesses of insulations are used. In addition, cost reduction could be attained as wood shavings are significantly cheaper compared to the cost of PCMs

Додаткові співвідношення Фібоначчі-Бернуллі

We continue our study on relationships between Fibonacci (Lucas) numbers and Bernoulli numbers and polynomials. The derivations of our results are based on functional equations for the respective generating functions, which in our case are combinations of hyperbolic functions. Special cases and some corollaries will highlight interesting aspects of our findings.У цій статті ми продовжуємо наші дослідження взаємозв’язків між числами Фібоначчі і Люка та числами (многочленами) Бернуллі. Доведення результатів базується на функціональних рівняннях для відповідних генератрис, які в нашому випадку є комбінаціями гіперболічних функцій

Physical effort in treating depression in the elderly – a systematic review

Depression is the most common mental disorder among people over 65 years old, making it one of the most significant health problems for this population. Due to the fact that medications and psychological therapy are not effective in all cases, many studies in recent decades have highlighted alternative treatments for depression. In particular, physical exercise has been highlighted as a potentially beneficial form of treatment. The purpose of this paper was to conduct a review into the relationship between exercise and its effects on the treatment of depression in the elderly. Specifically, PubMed and Google Scholar were searched for articles on the effectiveness of physical activity interventions for the treatment of senile depression and the reduction of its symptoms. The results show that physical activity is effective for reducing the symptoms of depression amongst the elderly. The positive effects of physical activity in the treatment of depression in the elderly were found for both endurance and resistance exercises, and for low-, moderate- and high-intensity exercise. Positive effects were observed for both traditional and water-based forms of exercise. Aligning the type and intensity of exercise to the patient’s personal preferences also helps to enhance the effectiveness of training. Overall, it was concluded that physical exercise can serve as a valuable strategy for the protection of mental health amongst the elderly. However, more research is needed to clarify the most effective type, intensity, and frequency of exercises to treat depression

Strategic Sustainable and Smart Development Based on User Behaviour

It is clear that the field of artificial intelligence (AI) as a decision-oriented tool has recently proven to be a viable alternative approach to solve environmental challenges. For example, artificial neural networks (ANNs) and support vector machines (SVMs), which are a subset of artificial intelligence, are going to be widely used to predict energy consumption in the buildings. The work aims to explore the use of user behaviour, smart and passive systems to improve energy efficiency and indoor environmental quality (IEQ) in buildings. The presence of users within buildings can affect process improvement. For example, users can contribute to energy efficiency by switching off artificial lighting during daylight hours. Furthermore, they can reduce the use of energy by changing their behaviour to act according to principles of sustainable development. In order to evaluate the impact of user behaviour on energy consumption, development of an assessment model based on artificial intelligence (AI) can be useful. On the other hand, use of a new concept from artificial intelligence in assessment tools can not only explore the potential benefits of approach but also provide ways to achieve an optimum level of efficiency