Factorials Research Articles

A Maximal Covering Problem in Supply Chain Considering Variable Radius and Gradual Coverage with the Choice of Transportation Mode

Today, supply chain management is a fundamental principle of business infrastructure implementation in the world. One of the most important pillars of the supply chain management is distribution network design. A distribution network with appropriate structure reduces costs and enhances customer-perceived service level, thereby improving competitive advantages of the company. In supply chain analysis, it is essential to focus on customers, as they greatly affect the formation of chain. This requires a balance between associated costs and the level of service provided. Variable radius and gradual radius maximal covering problem focus on the service levels in relation to the costs incurred to the system. In this study, a bi-objective mixed-integer nonlinear programming model was presented to determine optimal number, location and capacity of factories, distribution centers, and retailers, select transportation modes between the chain elements, and evaluate coverage radius of retailers, in such a way to minimize total transportation costs, maximize the covered demand, and achieve gradual coverage of facilities in a variable radius scheme. The proposed model was validated on a number of sample problems produced and solved by GAMS optimization software. Being NP-Hard, the problem was proposed to be solved via NSGA-II algorithm when its dimensions go large. Analysis of the computational results and respective comparisons indicated good performance of the presented algorithm.

Windschitl type approximation formulas for the gamma function

In this paper, we present four new Windschitl type approximation formulas for the gamma function. By some unique ideas and techniques, we prove that four functions combined with the gamma function and Windschitl type approximation formulas have good properties, such as monotonicity and convexity. These not only yield some new inequalities for the gamma and factorial functions, but also provide a new proof of known inequalities and strengthen known results.

The computational complexity of calculating partition functions of optimal medians with Hamming distance

We study the complexity of computing the partition function of medians for binary strings with Hamming distance using various weight functions. When the weight function is the factorial function, this partition function has application in bioinformatics, counting the most parsimonious scenarios on a star tree under the Single Cut-or-Join model for genome rearrangement. Although this model is computationally simple, we show that it is #P-complete to compute the partition function. Our results are also extended to binary trees as we show that it is #P-complete to calculate the most parsimonious scenarios on an arbitrary binary tree under the Single Cut-or-Join model. These results also apply to substitution models for many biological sequences.

EVALUATION OF PILOT PROJECTS IN THE MINISTRY OF STATE FOR ENVIRONMENTAL AFFAIRS AND ITS RELATIONSHIP TO SUSTAINABLE DEVELOPMENT IN EGYPT GOAL 12: ENSURE QUALITY AND SUSTAINABLE CONSUMPTION AND PRODUCTION PATTERNS

The aim of the study is to identify the successful models for the sustainability of internationally funded pilot projects and to achieve their objectives in the industrial pollution control project Phase II, The extent of the legal obligation of the establishment to environmental legislation and the setting of environmental objectives as a general framework for the activity of industrial enterprises, As well as studying the impact of the concepts of environmental economics (green) as a main input to achieve sustainable development among those concerned with industry in Egypt. The descriptive syllabus was utilized thanks to its dependence on describing the phenomenon and extracting the results through gathering the statements and information necessary for research. Data were gathered from the Ministry of State for Environmental Affairs, reports of donor countries and state of the environment reports issued by the Ministry of State for Environmental Affairs About Egyptian Pollution Abatement Project (EPAP) between 2007 and 2015. (Case Study of Industrial Pollution Control (End of Tube) (Air) Project for a number of cement production projects and a number of brick production factories in Arab Abu Sa'ed area and rehabilitation of phosphoric plant Abu Zaabal Fertilizer and Chemical Factory). The results have resulted in the adjustment of the environmental conditions of the industrial enterprises and the support of the cleaner production projects. These environmental projects contribute to reducing the use of raw materials and reducing the resulting waste, thereby reducing the cost of production, thus achieving the economic and environmental dimensions and their commitment to the social dimension of the workers inside and outside the plant. In highly polluted areas and thus improve the conditions of the local environment by encouraging private sector companies and the public sector to invest in the field of pollution control and support the applications of appropriate binding methods and inspection activities to Knapp technical capacity development within environmental institutions and the participating banks and to improve environmental awareness and performance in Egypt with a focus on the Greater Cairo and Alexandria and the strengthening of the special commitment to environmental protection law 4 of 1994, as amended, environmental authorities capabilities. But the information collected by the researcher indicates that many of these projects will be affected by the absence of international funding for the inability of companies alone or the insufficient budget allocated by the State to reduce pollution, which will be clear from the implementation of the plan of this study. The researchers recommended the activation of the law of environmental protection 4 of 1994 and its amendments to sustain the results of the pilot projects through the support of the environmental inspection of the EEAA with a number of human cadres while providing the potential to increase the inspection rates on the industrial zones to maintain the sustainability of the industrial pollution control project, Green economy and cleaner production mechanism in Egyptian industry, also an alternative to foreign grants and loans should be found in financing environmental projects and providing technical and institutional support and maintaining their sustainability through the establishment of a national fund for financing environmental projects. It should establish national banks, the Ministry of State for Environmental Affairs, the Ministry of Finance, Export Development Fund), Ministry of Investment, Social Fund for Development, provided that projects are financed with interest determined by the Central Bank of Egypt.

A Full Factorial Design-Based Desirability Function Approach for Optimization of Hot Forged Vanadium Micro-alloyed Steel

The present work undertakes an experimental investigation into the influence that process parameters, namely forging temperature, percentage deformation, and cooling rate in conjunction with their interactions on the microstructure and mechanical properties of vanadium micro-alloyed steel (38MnSiVS5) undergoing hot forging operation. The variations observed in the mechanical properties are explained in terms of the microstructure obtained. A full factorial-based design has been made use of to account for all possible combinations of factors in order to obtain a thorough study. Empirical models that relate the response and process parameters have been developed from the results that have been obtained from these experiments. These models are validated by making use of analysis of variance (ANOVA). Response surface plots for each response are analyzed, and the optimal parameter setting for each response is determined. The study discovered an outsized variation in the microstructural features corresponding to the various thermomechanical conditions under examination. In order to optimize all the responses at the same time, desirability function is adopted.

Construction method for generating functions of special numbers and polynomials arising from analysis of new operators

The aim of this paper is to construct a new method related to a family of operators to define generating functions for special numbers and polynomials. With the help of this method, we investigate various properties of these special numbers and polynomials with their generating functions, functional equations, and differential equations. We also give some algorithms to calculate the values of these numbers and polynomials. Moreover, we introduce some fundamental properties of this operator. By applying integral method to this operator, we obtain integral formulas together with combinatorial sums. Moreover, by applying this operator, the Lagrange inversion formula and convolution formula to these generating functions, we derive some novel identities and relations including combinatorial sums and combinatorial numbers including these new numbers and polynomials, ie, the Apostol‐Bernoulli numbers, the Apostol‐Euler numbers, the Stirling numbers, the central factorial numbers, and the other special numbers and polynomials. In addition, we give some examples derived from relations between composita and this operator on the set of formal power series. Finally, we give complex form of the Fourier series for these generating functions. By using these Fourier series, we not only derive some series relations and trigonometric sums including trigonometric function and hyperbolic functions but also give an example for a differential equation.

Human behaviour in the Euclidean Travelling Salesperson Problem: Computational modelling of heuristics and figural effects

The Travelling Salesperson Problem (TSP) describes a situation where an imaginary individual wishes to visit multiple cities once before returning to his/her own city. This type of problem is known as a nondeterministic polynomial (NP) hard problem, since the factorial number of solutions results in it being impractical to solve using exhaustive processing. Interestingly, when presented as a Euclidean graph (i.e., ETSP), humans identify near optimal solutions almost effortlessly, despite billions of possible tours. In this study, we consider human processing of the ETSP, and introduce the reader to a number of factors that literature proposes as impacting human performance. We hypothesise that: (i) human ETSP activity may be modelled by considering the quotient relationship between node-to-node and node-to-centroid distances; and (ii) consideration of figural effects can optimise automated TSP solution generation. In this paper human processing based heuristics are developed, i.e. replacing the cost function within the nearest neighbour algorithm, to guide node selection. Results showed that the quotient relationship between node-to-node and node-to-centroid distances can be used to closely model average human performance, across a range of ETSP graphs. Interestingly, however, additional consideration of graph figural effects (e.g. distance between boundary points in the convex hull, standard deviation of distances between nodes that make up the convex hull, and number of nodes in the convex hull) results in significantly improved tour costs.

Integrated multi-factory production and distribution scheduling applying vehicle routing approach

This paper introduces a new integrated multi-factory production and distribution scheduling problem in supply chain management. This supply chain consists of a number of factories joined together in a network configuration. The factories produce intermediate or finished products and supply them to other factories or to end customers that are distributed in various geographical zones. The problem consists of finding a production schedule together with a vehicle routing solution simultaneously to minimise the sum of tardiness cost and transportation cost. A mixed-integer programming model is developed to tackle the small-sized problems using CPLEX, optimally. Due to the NP-hardness, to deal with medium- and large-sized instances, this paper develops a novel Improved Imperialist Competitive Algorithm (IICA) employing a local search based on simulated annealing algorithm. Performance of the proposed IICA is compared with the optimal solution and also with four variants of population-based metaheuristics: Imperialist Competitive Algorithm, Genetic Algorithm, Particle Swarm Optimisation (PSO), and Improved PSO. Based on the computational results, it is statistically shown that quality of the IICA’s solutions is the same as optimal ones solving small problems. It also outperforms other algorithms in finding near-optimal solutions dealing with medium and large instances in a reasonably short running time.

Exploring the Causes of Formation of Urban Heat Island and its Impacts and Effects Through Landsat: A Case Study of Satna, Madhya Pradesh

The date, the various growth and developments that have taken place in the social and physical infrastructural aspects of the society have led to a tremendous increase in the built up area and decrease in the green and open spaces. Some of this development includes the increase in the number of factories, industries and service centers, which along with it, encourages an increased number in floating population for employment; and all this has latterly led to an increase in covered and impervious surfaces in the urban fabric. These are also some of the major reasons causing the meteorological phenomenon of urban heat island, being described as the part of the metropolitan area being warmer in temperature, than its surrounding area. Rise in temperatures, warmed atmospheric levels, melting of glaciers, heat strokes are some of the major effects of the urban heat island effect, further leading to global warming and climate change. Thus, an essential technique of green infrastructure to be incorporated at city planning level is essential to reduce the effect and maintain the microclimate of any place. Remote sensing is a reported technique used to identify the urban heat island affected areas, accurately and enable the researchers to opt for best suitable intervention. The paper attempts to study broadly the presence of the urban heat island effect in various parts/ areas in the study area city of Satna, Madhya Pradesh; through processing, comparing and analyzing the Landsat imageries of the study area city for two years 1992 and 2016; and identifying the factors of formation of the phenomenon in the affected parts of the city.

The case of China’s Economic Reform: The Xi Jinping Era, a comparative analysis with Mao Zedong and Deng Xiaoping

<p style="text-align: justify;">China is a faithful example when things are done well, great results are obtained, in part thanks to the role that the same culture played in the growth it has had and still has. Work and savings have been fundamental pillars for the economic development that this country during the last decades, not leaving aside the role played by the Western economies to nurture this reality; first, with the policies implemented by Mao and Deng when the country was in a great crisis generating the necessary investment and establishing a sufficient number of factories that allow to reactivate the Chinese economy; secondly, the opening by Xi to the western region becoming the passage of time, in one of the largest consumers and at the same time the largest producers in the world in different areas.</p>
 <p style="text-align: justify;">In a certain sense, it seems as if the powers of the West have exceeded looking for more short-term benefit, but without realizing the consequences that could be faced by adopting these decisions. On the other hand, China knew how to play the cards, your business became a truly business profitable: lend money and then be reimbursed in the coffers of the country, for the concept of selling products and paying interest on loans. The work of the State in the planning of economic policies, to medium and long term, which led to the generation of a market economy socialist with Chinese characteristics, does not remain outside when defining the economic success of the Asian giant. The implementation of this new economic model, which knew how to combine some dynamics of capitalism within the communist system, it played a very important role. The fact of generating great coordination between the public and private sectors, in addition to capture the market signals in a timely manner, allowed the results and economic policies were heading towards a prosperous path.</p>
 <p style="text-align: justify;">Nor can we ignore the autonomy and independence that has had the Communist Party to make political and economic decisions with the greatest opportunism and speed possible. This is proper to have a power not shared, which has undoubtedly generated that the measures taken obtain a high degree of efficiency.</p>
 <p style="text-align: justify;">This is how the application in China of a series of dynamics is explained of capitalism that allowed it, in a succession of conditions presented, that would grow by leaps and bounds as opposed to economies of most of the industrialized countries of the West. It is also in this way that it is understood that China has been able to take from poverty to 800 million people in 30 years (World Bank, 2012) and that, currently, is in the longed for place to be the largest economy world.</p>

On powers of the Catalan number sequence

The Catalan number sequence is one of the most famous number sequences in combinatorics and is well studied in the literature. In this paper we further investigate its fundamental properties related to the moment problem and prove for the first time that it is an infinitely divisible Stieltjes moment sequence in the sense of S.-G. Tyan. Besides, any positive real power of the sequence is still a Stieltjes determinate sequence. Some more cases including (a) the central binomial coefficient sequence (related to the Catalan sequence), (b) a double factorial number sequence and (c) the generalized Catalan (or Fuss–Catalan) sequence are also investigated. Finally, we pose two conjectures including the determinacy equivalence between powers of nonnegative random variables and powers of their moment sequences, which is supported by some existing results.

Energy Saving Potential for Non-Designated Factories: A Case Study of Thailand

Energy saving potential for non-designated factories which are medium and small size factories was investigated. In Thailand, factories are classified into two major groups called designated and non-designated factories. Designated factories are controlled their energy consumptions by law but non-designated have no seriously enforcement in energy conservation by the government due to low level energy consumption per factory. However, the number of non-designated factories are 123,064 factories accounting for 95.58% of all 128,761 factories. Thus total energy consumption of non-designated factories is significant and should be considered for energy efficiency measures. 32 samples of non-designated factories in 4 industries: ice cube, rice mill, concrete and drinking water, that located in upper part of north-eastern Thailand were surveyed. Energy consumption data, production volume in 12 months, main energy consumed equipment and their energy conservation measures were investigated and analyzed. Linear regression method was used to determine the specific energy consumption (SEC) of each factory and compared with SEC of the same industry, then the potential of energy saving was evaluated by 2 methods i.e. comparing the SEC of each surveyed factory with the best SEC in same industry, comparing the SEC of each surveyed factory with the SEC of designated factory in same industry. Results showed that the potential of energy saving for ice cube, rice mill, concrete and drinking water industries were 608.31 toe/year, 234.87toe/year, 29.92 toe/year and 6.04 toe/year respectively. These potentials are in total of 879.14 toe/year, accounting for 40.71% of their 2,159.65 toe/year total energy consumption. The results of 32 samples suggested that non-designated factories have a great energy saving potential thus there should be a policy to cover this numerous factories for energy consumption and saving.

A cyber-physical system for production monitoring of manual manufacturing processes

The computerization of manufacturing is one of the major challenges of the so-called fourth industrial revolution or Industry 4.0. Virtualization of the smart factory should provide real-time vision, control and monitoring of production through interactive dashboards and synchronization of data coming from different factory functions. The latter characteristics are particularly difficult to implement when the manufacturing core relies on traditional manual labour rather than on automation, as in the case of manual assembly. Monitoring or even controlling the manual work in real-time is extremely difficult to put into practice. Therefore, realizing the principles of Industry 4.0 in manual or semi-automatic labour contexts means developing new production control systems that involve the worker in the monitoring process without negatively affecting the production times or the psychological status of the workers. In particular, the authors propose a computer-aided production control framework based upon multimedia manuals and smart completeness control systems that can be used to implement the principles of Industry 4.0 in manual or semi-automatic work environments. This technology has been successfully tested in laboratory on the basis of a real industrial case study. The response of the testers has been positive and the outcomes in terms of increased product quality are promising.

Consecutive Factorial Base Niven Numbers

Consecutive Factorial Base Niven Numbers

Current challenges of urbanization - economic view

Сучасна економіка пов'язана з індустріалізацією, розвитком міст і нових технологій. Нова реальність - це коли валовий внутрішній продукт (ВВП) окремих міст, регіонів чи районів є більшим за його значення для деяких розвинутих країн світу, а щільність населення у такому регіоні збільшується в кілька разів за рік. Усе це формує нову економічну ситуацію, а саме, економіку пов'язану з містом як урбаністичним центром. У подальшому варто зосередити основну увагу на дослідженні факторів, які визначають успішні міста, як міста, що постійно розвиваються. Також необхідно дослідити, які економічні фактори є домінуючими у нових центрах, у противагу класичному підходу. Автори вважають доцільним дослідити також сукупність екологічних чинників, нерухомість у приміських зонах, адже вони впливають на приріст чи зменшення росту населення, і у подальшому можуть мати значну вагу при розвитку міста в урбаністичний центр. За результатами проведених досліджень, ми вважаємо за доцільне представити нове визначення поняття терміну урбанізація, базуючись на дослідженнях та гіпотезах, а також фокусуючи основну увагу на економічних факторах. Ключові слова : урбанізація, землекористування, економіка, екологія, сучасні проблеми міст.

Identities associated with Milne\u2013Thomson type polynomials and special numbers

The purpose of this paper is to give identities and relations including the Milne–Thomson polynomials, the Hermite polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the central factorial numbers, and the Cauchy numbers. By using fermionic and bosonic p-adic integrals, we derive some new relations and formulas related to these numbers and polynomials, and also the combinatorial sums.

Determinant Monte Carlo algorithms for dynamical quantities in fermionic systems

We introduce and compare three different Monte Carlo determinantal algorithms that allow one to compute dynamical quantities, such as the self-energy, of fermionic systems in their thermodynamic limit. We show that the most efficient approach expresses the sum of a factorial number of one-particle-irreducible diagrams as a recursive sum of determinants with exponential complexity. By comparing results for the two-dimensional Hubbard model with those obtained from state-of-the-art diagrammatic Monte Carlo, we show that we can reach higher perturbation orders and greater accuracy for the same computational effort.

Reduction of CO2 Emission and Production Costs by Using Pozzolans in Lamerd Cement Factory

Two major concerns for cement factories are environmental aspects and production costs. The number of cement factories is increasing in Iran which from an environmental point of view is not favorable. Different pozzolans such as brick, potted clay, volcanic rocks, sedimentary rocks and rice bran were used in the cement produced by Lamerd factory in the south of Iran. Among these additives, rice bran fails to be proper pozzolan. This research shows that using pozzolans up to 10% does not have a significant effect on the quality of Lamerd cement. Almost the similar textures of compositions for differently mixed types of cement were determined using XRD and XRF experiments. Considering these additives, volcanic and sedimentary rocks seem to be more favorable regarding both quality and price. In fact, the additives can reduce both the emission of CO2 (reduction of more than around 400 tons CO2 per day) and the production costs (the money saved is around $76000 per day) in cement factory of Lamerd.

HERITAGE OF INDUSTRIAL ARCHITECTURE IN NOWADAYS' CULTURAL ENVIRONMENT

The aim of the article is to study the concept of industrial heritage and its examples, trends in the usage of old factory buildings, to carry out theoretical analysis of industrial tourism, to evaluate the possibilities of industrial tourism in Latvia and Rezekne, by performing a survey of residents of the city.In the modern world a large number of factories and objects of industrial heritage cannot exist for their primary purpose anymore: they are demolished to clear the territory for new buildings, they are reconstructed, rebuilt, transforming the factories for various needs and purposes. Their applications nowadays are very diverse, ranging from art galleries to hotels and technical parks. This is a solution to many problems related to old factories and their territories. Transforming factory buildings and territories creates opportunities for industrial tourism, which in turn promotes regional development, provides new job opportunities in the city, and develops economy.

Combinatorial and arithmetical properties of the restricted and associated Bell and factorial numbers

Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus of the present article is the analysis of combinatorial and arithmetical properties of them. The results include several combinatorial identities and recurrences as well as some properties of their $p$-adic valuations.