Abstract:
We present a new adaptive Monte Carlo integration algorithm for ill-behaved integrands with non-factorizable singularities. The algorithm combines Vegas with multi channel sampling and performs significantly better than Vegas for a large class of integrals appearing in physics.

Abstract:
To solve the range cell migration (RCM) and spectrum spread during the integration time induced by the motion of a target, this paper proposes a new coherent integration method based on Radon non-uniform FRFT (NUFRFT) for random pulse repetition interval (RPRI) radar. In this method, RCM is eliminated via searching in the motion parameters space and the spectrum spread is resolved by using NUFRFT. Comparisons with other popular methods, moving target detection (MTD), Radon-Fourier transform (RFT), and Radon-Fractional Fourier Transform (RFRFT) are performed. The simulation results demonstrate that the proposed method can detect the moving target even in low SNR scenario and is superior to the other two methods.

Abstract:
Consistency and the weights estimation model of the interval number comparison matrix (INCM) in the analytical hierarchy process is studied under uncertainty decision-making case. Based on the weights feasible region, the local consistency definition and the local satisfactory consistency definition are given. Then, a computational model set up to test whether the INCM has the local satisfactory consistency or not. Moreover, the consistency degree based on the random crisp comparison matrix is defined as an effective index to test the consistency. Next, the upper range model, the lower range model, and the possible value model are put forward which can solve the problem that some existing approaches do not consider the consistency and its effect on the weights. According to the property of these models, a genetic algorithm is developed.

Abstract:
The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear structure in the system. The generalization is an embedding of a graph onto a multi-dimensional Euclidean space and it was used by scientists to study the multi-relational complexity of ecology. However the research went out of fashion in the 1980s and was not revisited when Network Science recently expressed interests with multi-relational networks known as multiplexes. This paper studies interval graphs from the perspective of Network Science.

Abstract:
This book has seven chapters. In chapter one we give the basics needed to make this book a self contained one. Chapter two introduces the notion of interval semigroups and interval semifields and are algebraically analysed. Chapter three introduces special types of interval semirings like matrix interval semirings and interval polynomial semirings. Chapter four for the first time introduces the notion of group interval semirings, semigroup interval semirings, loop interval semirings and groupoid interval semirings and these structures are studied. Interval neutrosophic semirings are introduced in chapter five. Applications of these structures are given in chapter six. The final chapter suggests around 120 problems for the reader.

Abstract:
In this book we introduce the notion of interval semigroups using intervals of the form [0, a], a is real. Several types of interval semigroups like fuzzy interval semigroups, interval symmetric semigroups, special symmetric interval semigroups, interval matrix semigroups and interval polynomial semigroups are defined and discussed. This book has eight chapters. The main feature of this book is that we suggest 241 problems in the eighth chapter. In this book the authors have defined 29 new concepts and illustrates them with 231 examples. Certainly this will find several applications.

Abstract:
An algorithm for integration of polynomial functions with variable weight is considered. It provides extension of the Gaussian integration, with appropriate scaling of the abscissas and weights. Method is a good alternative to usually adopted interval splitting.

Abstract:
We present a proof that any continuous function with domain including a closed interval yields an antiderivative of that function on that interval. This is done without the need of any integration comparable to that of Riemann, Cauchy, or Darboux. The proof is based on one given by Lebesgue in 1905.

Abstract:
Access to distributed, heterogeneous and autonomous information sources, becomes possible with the Internet. These information sources are distinguished by the nature of information, namely, the ontological domain to which they belong but also by the type of media they are issues, such as image, text, video, etc. With the advent of semantic web, new opportunities in multi-sources integration are emerging and many approaches are revisited with taking into account the new requirements. Also, there is the use or reuse of datawarehouses, mediators and peer-to-peer systems. Our project aim to propose a distributed and open system for indexing and searching multimedia content (DIOSYS) and especially an integration system based on the Peer-to-peer paradigm. In this study, we propose a state of the art of the integration problem by examining the most representative approaches of the three currents and we will try to summarize this study with use of tables after having presented and justified a set of criteria.

Abstract:
We present a new proof to a general result due to Kestelman. Our proof differs completely from the other proofs we know and we hope that readers will find it clearer. We also include a quite exhaustive bibliographical analysis on related results and proofs.