Some Types of Integral Problems

This paper uses the mathematical software Maple for the auxiliary tool to study three types of integrals. We can obtain the infinite series forms of these three types of integrals by using integration term by term theorem. In addition, we propose some examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions using Maple.

This paper uses the mathematical software Maple as an auxiliary tool to study six types of definite integrals. We can obtain the infinite series forms of these definite integrals by using Parseval’s theorem. On the other hand, we provide some examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying the answers by using Maple.

This paper uses the mathematical software Maple for the auxiliary tool to study three types of definite integrals. The closed forms of these definite integrals can be obtained using Parseval’s theorem. In addition, we propose some definite integrals to do calculation practically. The research methods adopted in this study is to find solutions through manual calculations and verify these solutions using Maple.

This paper studies six types of double integrals and uses Maple for verification. The infinite series forms of these double integrals can be obtained using Taylor series expansions and integration term by term theorem. In addition, some examples are used to demonstrate the calculations.

This article considers two types of triple integrals and uses Maple for verification. The infinite series forms of the two types of triple integrals can be obtained using binomial series and integration term by term theorem. In addition, some examples are used to demonstrate the calculations.

This paper uses the mathematical software Maple for the auxiliary tool to study two types of integrals. We can obtain the infinite series forms of these two types of integrals by using binomial series and integration term by term theorem. On the other hand, we provide some examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding problem-solving methods.

he research was motivated by the desire to obtain inexpensive (optimum) and adequate capacity of structure. This study aims to determine the variation of ? value and fc' on a single reinforcement concrete beams that can produce the most optimum and economical construction. This study used optimization process that requires repetitive calculations, hence the research was categorized as applied research. This cost analysis of a single reinforced concrete beam consisted of 200 samples for each concrete compressive strength (fc') of 25-35 MPa with an increment of 2.5 MPa. The results of sample analysis produce ? interactions graphs and charts interaction between cost and fc’. In addition, the cost calculations were made assuming the cost without using formwork and using formwork of once until three time usage. This research produced graphic to observe the most optimal and economic reinforcement ratio. Based on the variation of nominal moment, the values of ? was needed for without formwork cost calculation at range of between 0.56-0.66 (times ? needed max ), and the values of ? was needed for the cost calculation by once until three times formwork assumtion at range of beetwen 0.92-1 (times ?max), 0.75-1 (times ?max), and 0.69-1 (times ?max needed) respectively.

This dissertation discusses Fano vector bundles on projective space and the quantum cohomology of the associated projective bundle. A bundle is said to be Fano if the associated projective bundle is a Fano variety. We prove a theorem that reconstructs the small quantum cohomology ring for the projective bundle from a subset of the quantum multiplication-table. Equivalently, in the spirit of Kontsevich’s first reconstruction theorem, the theorem reconstructs all genus-0 Gromov-Witten invariants from a small set of 2-point invariants. The theorem improves on Kontsevich’s reconstruction theorem, where they both apply, as the required subset of invariants is smaller. Qin and Ruan note that, unlike in the classical case, the quantum cohomology of a projectivised bundle need not be a module over the quantum cohomology of the base. The reconstruction theorem described in this thesis demonstrates that this ‘non-modularity’ contains all the essential quantum information. As an example we discuss the Fano bundle Ω(2)P4 , the second wedge of the cotangent bundle on P4, and calculate the quantum cohomology of the Fano 9-fold given by its projectivisation using the reconstruction theorem. We apply Givental formalism to this result to obtain the quantum periods for some Fano subvarieties embedded in P(Ω(2)P4). These novel calculations are of interest to the Fanosearch programme. In particular, we describe two 4-dimensional Fano subvarieties that have quantum periods suggestive of 4-folds which are not of toric complete-intersection type; they are not contained in a conjecturally complete list of such objects. We observe the presence of the Apery numbers in J-function of the Fano 9-fold P(Ω(2)P4) and comment, after Golyshev, that this may indicate hidden modularity in the J-function.

According to published statistics regarding pharmaceutical industries, there has been a significant increase in the demand for cosmetics and skincare products. As a result, there has also been an increase in interest by researchers to conduct experimental and theoretical studies on these industries. The outermost layer of the skin, which is the stratum corneum, plays a key role in determining the skin permeability. This layer represents the first and main barrier against dehydration and screening from external elements and pathogens. Research efforts have been made to better understand skin permeability. Experimental methodologies play a key role in pharmaceutical and dermatology studies. However, ethical standards of using animal and human models in in-vitro permeability studies are very strict in their admission process and approval time. Furthermore, the lack of available material and financial resources for setting up, operating and repeating experiments has also limited the required progress. These problems can be addressed by developing better mathematical models on skin permeability. Progress, regarding the mathematical modelling of solute transport in skin, has been achieved in the last decades. The mathematical modelling strategy is used as a skin permeability predictor tool based on common physicochemical properties of the skin and penetrated solute molecules. Many factors play an important role in the formulation of a mathematical model and in determining how reliable the predicted results are. Therefore, the more skin physiological details are included in the model, the more computational efforts are required to interpret the solute permeation mechanisms in the dermal region and simulate a drug transport in the transdermal administration. The mathematical complexities associated with formulating a mathematical model of drug transport in skin significantly limit the utilities of such models in practice. Thus, a balance between the model’s complexity and how realistic it is in describing the solute transport processes in skin has to be achieved. Therefore, a mathematical model formulated on principles familiar to the pharmaceutical scientific community could be of value. In this thesis, we have developed a novel mathematical model using a compartmental approach. The proposed model enables for simulating solute transport across the stratum corneum (SC) in a variety of exposure scenarios in percutaneous drug delivery systems. The obtained results were compared with the diffusion model outcomes – which can be considered the current ‘golden standard’ for modelling skin transport – and showed a good agreement. The mathematical foundations of the model are relatively simple and better aligned with the physiology of the stratum corneum. In addition, this work shows that performing a numerical simulation using the compartmental model is less demanding than using the diffusing model, especially for complex exposure scenarios, and can be performed using free software, such as Python. The research findings of this thesis contribute towards a better understanding of transport phenomena across the skin. Also, the compartmental model proposed in this work can be used to describe transport phenomena in the membrane. Due to the similarity between the governing equations of diffusion and heat transfer, the proposed approach also offers a mathematical framework for studying heat transfer problems in biomaterials with minimum model development or computational efforts.

Network simulation is a technique that models network behavior by performing transaction calculations between different network entities and using mathematical formulas and taking observations of network products. A network simulator is a software program have been applied to analyze the performance of a computer network without the presence of a real network. Hardware equipment, equipment configuration, communication, and routing protocols and network traffic modeled in simulation software and the behavior of the network and its components examined from different dimensions. The user can also customize the simulation software according to their needs. Simulation software has different uses, and the user can use these tools to model their network by recognizing this software. In terms of research, it is difficult to create a network, especially large networks, in a real-time scenario, and it is not easily possible to carry out it in the real world, and it is very costly. So, simulators help network developers to control whether the network can work in real-time or not, or whether it is efficient enough. This reduces the time and cost of network application testing.Today, simulation technology is successfully used to model, design and manage a variety of intelligent systems. Numerous tools have been created in this regard. In this article, we review and compare important network simulators such as CloudSim, GloMoSim, GNS3, NS-2, Opnet, OMNet ++, NetSim, NS-3, AVRORA, Packet Tracer, QualNet, J-Sim, REAL and OptSim and their results. These comparisons express from several perspectives in the tables.

Scene analysis for robotic watercraft

Graphs are commonly represented as points in space connected by lines. The points in space are the vertices of the graph, and the lines joining them are the edges of the graph. A general definition of a graph is considered here, where multiple edges are allowed between two vertices and an edge is permitted to connect a vertex to itself. It is assumed that graphs are connected, i.e., any vertex in the graph is reachable from another distinct vertex either directly through an edge connecting them or by a path consisting of intermediate vertices and connecting edges. Under this visual representation, graphs can be drawn on various surfaces. The focus of my research is restricted to a class of surfaces that are characterized as compact connected orientable 2-manifolds. The drawings of graphs on surfaces that are of primary interest follow certain prescribed rules. These are called 2-cellular graph embeddings, or simply embeddings. A well-known closed formula makes it easy to enumerate the total number of 2-cellular embeddings for a given graph over all surfaces. A much harder task is to give a surface-wise breakdown of this number as a sequence of numbers that count the number of 2-cellular embeddings of a graph for each orientable surface. This sequence of numbers for a graph is known as the genus distribution of a graph. Prior research on genus distributions of graphs has primarily focused on making calculations of genus distributions for specific families of graphs. These families of graphs have often been contrived, and the methods used for finding their genus distributions have not been general enough to extend to other graph families. The research I have undertaken aims at developing and using a general method that frames the problem of calculating genus distributions of large graphs in terms of a partitioning of the genus distributions of smaller graphs. To this end, I use various operations such as edge-amalgamation , self-edge-amalgamation, and vertex-amalgamation to construct large graphs out of smaller graphs, by coupling their vertices and edges together in certain consistent ways. This method assumes that the partitioned genus distribution of the smaller graphs is known or is easily calculable by computer, for instance, by using the famous Heffter-Edmonds algorithm. As an outcome of the techniques used, I obtain general recurrences and closed-formulas that give genus distributions for infinitely many recursively specifiable graph families. I also give an easily understood method for finding non-trivial examples of distinct graphs having the same genus distribution. In addition to this, I describe an algorithm that computes the genus distributions for a family of graphs known as the 4-regular outerplanar graphs.

In mathematics and statistics, the desire to eliminate mathematical tedium and facilitate exploration has lead to computer algebra systems. These computer algebra systems allow students and researchers to perform more of their work at a conceptual level. The design of generic algorithms for tedious computations allows modelers to push current modeling boundaries outward more quickly. Probability theory, with its many theorems and symbolic manipulations of random variables is a discipline in which automation of certain processes is highly practical, functional, and efficient. There are many existing statistical software packages, such as SPSS, SAS, and S-Plus, that have numeric tools for statistical applications. There is a potential for a probability package analogous to these statistical packages for manipulation of random variables. The software package being developed as part of this dissertation, referred to as “A Probability Programming Language” (APPL) is a random variable manipulator and is proposed to fill a technology gap that exists in probability theory. My research involves developing algorithms for the manipulation of discrete random variables. By defining data structures for random variables and writing algorithms for implementing common operations, more interesting and mathematically intractable probability problems can be solved, including those not attempted in undergraduate statistics courses because they were deemed too mechanically arduous. Algorithms for calculating the probability density function of order statistics, transformations, convolutions, products, and minimums/maximums of independent discrete random variables are included in this dissertation.

Викладена суть проблеми перерахування календарних дат в часові інтервали між ними і навпаки, що виникає у процесі комп’ютерного оброблення результатів наукових досліджень, в яких задіяний часовий фактор та використовуються машинні методи обчислювальної математики. Формалізовані основні закономірності григоріанського календаря. Сформульовані й доведені чотири теореми щодо вибору потрібного варіанту хронологічних обчислень. Запропоновані алгоритми вирішення дев'яти основних та двох допоміжних хронологічних завдань.

The profitability of sales is one of the main goals of companies to measure performance leadership or management in other words efficiency and effectiveness of companies. The cost of my ingredients, how long it will last, and the cost of the factory head must be calculated quickly. Especially the overheads factory which is often overlooked in production calculations. In addition to the cost of the material and the cost of the process, the costs include the cost of overhead mill electricity, the cost of shrinking, the cost of repairing the machine, and the maintenance of the machine. All costs must be calculated quickly because they affect the profitability of sales. This research took place at Jalan General Ahmad Yani Sorong No. 24 by using a method of costing in establishing the profitability of the seller and using the deposit policy for the main factory price in the overhead charge that is charged to each product. Based on the results of a comparative data analysis, the method of the company with the full costing method has different results in the profitability of sales. Keywords: Production Costs, Profitability Sales