Construction of a normalized basis of a univariate quadratic $C^1$ spline space and application to the quasi-interpolation

In this paper, we use the finite element method to construct a new normalized basis of a univariate quadratic $C^1$ spline space. We give a new representation of Hermite interpolant of any piecewise polynomial of class at least $C^1$ in terms of its polar form. We use this representation for constructing several superconvergent and super-superconvergent discrete quasi-interpolants which have an optimal approximation order. This approach is simple and provides an interesting approximation. Numerical results are given to illustrate the theoretical ones.

Most general propagator in quantum field theory

One of the most important mathematical tools necessary for Quantum Field Theory calculations is the field propagator. Applications are always done in terms of plane waves and although this has furnished many magnificent results, one may still be allowed to wonder what is the form of the most general propagator that can be written. In this paper, by exploiting what is called polar form, we find the most general propagator in the case of spinors, whether regular or singular, and we give a general discussion in the case of vectors.

A study of refined neutrosophic complex numbers and their algebriac properties

This paper is dedicated to defining for the first time the concept of complex refined neutrosophic numbers as a direct application of refined neutrosophic sets and as a new generalization of neutrosophic complex numbers. Also, it presents some of their elementary properties such as conjugates, absolute values, invertibility, and algebraic operations. The importance of the definitions in this article lies in the use of them by defining the polar form of the refined neutrosophic complex numbers.

Персуазия, манипуляция и религиозный язык: теоретический аспект

This article is an attempt at a theolinguistic description of such concepts as manipulation, persuasia, and religious language. The author focuses primarily on the theoretical aspect of the stated problem. In the first part of the work, such concepts as manipulation, persuasia and speech influence are analyzed. Their hierarchy is being organized and it is concluded that persuasia and manipulation, when considered in “pure form” is the polar form of speech influence, different in means of achieving the goal: if persuasia is an open speech influence, suggesting a deliberate choice by the recipient, speech influence with the sign “+”, then the manipulation is speech influence, often using hidden mechanisms with the aim of achieving a result, do not necessarily coincident with the interests of the recipient, speech influence with the sign “–”. The second part of the work describes the religious language and its functions. Special attention is paid to the instrumental function – the function of using langu age as a means to achieve certain goals. Attention is drawn to the fact that the use of the form and content of religious language not only opens the way for various kinds of manipulations with language and with the help of language, but also for persuasia: the transfer of relevant knowledge, the formation of beliefs, ideas about true values.

Hybrid Sentiment Analyzer for Opinion Mining: Indian Admission Scenario

Social media has become one of the widely acclaimed tool for sharing information as well as expressing ideas and emotions. The work depicts the dual aspect task of analyzing and comprehending data available on Twitter platform. This is done using NLP techniques. Using Latent Dirichlet Allocation (LDA) topic technique; the major topics discussed in tweets (of data set taken), have been identified. The input for this Latent Dirichlet Allocation is given by NLP technique – Bag of Words. For further processing, identification of the underlying emotions contained in tweets using the techniques of Sentiment Analysis is done. The result of sentiment analysis is in the polar form. As a case study, a scenario of admissions in India for UG and PG has been considered. The whole process has captured the opinions of stake holders taking part in the admission process. Tweeter data of Indian Institute of Technology (IIT) admission has been used to collect the data in order to conduct the experiment. Major topics discussed in tweets and the fundamental emotions contained are obtained as results along with the polarity of the tweets

Classification of Complex Fuzzy Numbers and Fuzzy Inner Products

The paper is concerned with complex fuzzy numbers and complex fuzzy inner product spaces. In the classical complex number set, a complex number can be expressed using the Cartesian form or polar form. Both expressions are needed because one expression is better than the other depending on the situation. Likewise, the Cartesian form and the polar form can be defined in a complex fuzzy number set. First, the complex fuzzy numbers (CFNs) are categorized into two types, the polar form and the Cartesian form, as type I and type II. The properties of the complex fuzzy number set of those two expressions are discussed, and how the expressions can be used practically is shown through an example. Second, we study the complex fuzzy inner product structure in each category and find the non-existence of an inner product on CFNs of type I. Several properties of the fuzzy inner product space for type II are proposed from the modulus that is newly defined. Specfically, the Cauchy-Schwartz inequality for type II is proven in a compact way, not only the one for fuzzy real numbers. In fact, it was already discussed by Hasanhani et al; however, they proved every case in a very complicated way. In this paper, we prove the Cauchy-Schwartz inequality in a much simpler way from a general point of view. Finally, we introduce a complex fuzzy scalar product for the generalization of a complex fuzzy inner product and propose to study the condition for its existence on CFNs of type I.