1,720,994 research outputs found
On the generalized bin packing problem
Full text linkThe generalized bin packing problem (GBPP) is a novel packing problem arising in many transportation and logistic settings, characterized by multiple items and bins attributes and the presence of both compulsory and non-compulsory items. In this paper, we study the computational complexity and the approximability of the GBPP. We prove that the GBPP cannot be approximated by any constant, unless P = NP. We also study the particular case of a single bin type and show that when an unlimited number of bins is available, the GBPP can be reduced to the bin packing with rejection (BPR) problem, which is approximable. We also prove that the GBPP satisfies Bellman’s optimality principle and, exploiting this result, we develop a dynamic programming solution approach. Finally, we study the behavior of standard and widespread heuristics such as the first fit, best fit, first fit decreasing, and best fit decreasing.We show that while they successfully approximate previous versions of bin packing problems, they fail to approximate the GBPP
Japanese Temple Geometry: A Digital Sangaku About a Regular Pentagon and the Golden Ratio
Full text linkSangaku are wooden tablets depicting geometric or mathematical problems. They are objects typical of the Edo period. Since these tables were exposed in the temples, the related geometry is known as the Japanese Temple Geometry. Here we illustrate a digital approach to Sangaku. The specific problem we are discussing in the construction of a regular pentagon
Intermodalism in the Transportation Network of the Roman Empire
Full text linkIn this paper we are proposing a preliminary work for evidencing some features of intermodalism in the transportation network of the Roman Empire. We will show that intermodal terminals for oversea and overland transportations existed such as containers and shipping documents. For them, the Empire that had some specific logistic systems too
Elderly labor supply, endogenous grandparental childcare, and fertility in an OLG model
Full text linkThis paper explores how grandparental childcare influences fertility decisions, elderly labor supply, and economic development. We model the time elderly individuals allocate between work and caring for grandchildren. In high-income countries, higher wages lead to increased investments in children’s education and human capital. Interestingly, the decision to work in old age does not depend on economic development but on wage dynamics. Specifically, when the effective wage grows rapidly, grandparents are more likely
to work, even while caring for grandchildren. These findings highlight the importance of intergenerational time transfers in shaping economic outcomes. Future research could explore the long-term effects of aging populations on labor markets and family dynamics
A Mathematical Study of a Symbol: the Vesica Piscis of Sacred Geometry
Full text linkIn this paper, we are proposing a study of the Vesica Piscis, a symbol of Sacred Geometry, starting from mathematics. This study aims to give a deeper comprehension of the hidden meanings of this icon. The paper is also showing that scientific and philosophical studies can be integrated, leading to very interesting results
A Study of the Regular Pentagon with a Classic Geometric Approach
Full text linkIn this paper we will consider a regular pentagon and discuss three of its properties, which are linking side, radius, diagonal and apothem to the golden ratio. One of the properties, that regarding the ratio between the diagonal and the radius of the circumscribed circumference is strictly connected to the construction of the regular pentagon with compass and straightedge
The three-dimensional knapsack problem with balancing constraints
Full text linkTech. Rep. CIRRELT 2011-51, CIRRELT, Montreal, Canad
Symmetry and the golden ratio in the analysis of a regular pentagon
No full textThe regular pentagon had a symbolic meaning in the Pythagorean and Platonic philosophies and a subsequent important role in Western thought, appearing also in arts and architecture. A property of regular pentagons, which was probably discovered by the Pythagoreans, is that the ratio between the diagonal and the side of these pentagons is equal to the golden ratio. Here, we will study some relations existing between a regular pentagon and this ratio. First, we will focus on the group of fivefold rotational symmetry, to find the position in the complex plane of the vertices of this geometric figure. Then, we will propose an analytic method to solve the same problem based on the Cartesian coordinates, a method where we find the golden ratio without any specific geometric consideration. This study shows a comparison of the use of complex numbers, symmetries and analytic methods, applied to a subject which can be interesting for general education in mathematics. In fact, the proposed approach can convey and link several concepts, requiring only a general pre-college education, showing at the same time the richness that mathematics can offer in solving geometric problems
Educational support by grandparents and human capital growth: an OLG model with endogenous time allocation
No full textThis study explores the role of grandparents in the education of their grandchildren within an overlapping generations model. We introduce an endogenously determined time allocation, where grandparents decide how much time to dedicate to their grandchildren's education based on a trade-off between leisure and educational contributions. The model shows that grandparental involvement in education
influences the intergenerational transmission of human capital, with the potential for long-term effects on economic outcomes. By combining theoretical analysis and simulations, we highlight the dynamic relationship between grandparental education, human capital development, and the generational transmission process
Lower and upper bounds for the Generalized Bin Packing Problem with bin-dependent item profits
No full text- …
