Recent Advances in Mathematical Research and Computer Science Vol. 3

In classical Diophantine approximation, uniform distribution is an important topic. The distribution of real numbers and the estimation of exponential sums using Weyl's criteria are inextricably linked.Carlitz provided an elementary definition of uniform distribution in positive characteristics (see [1]), but we will find a geometrical description.In this paper, we use the Haar measure to present a precise analogue to Weyl's criteria in the case of positive characteristics.  As an application, we demonstrate that the uniformly distributed modulo 1 for linear forms and polynomial functions.We show that in the Laurent series field, the set {m\(\theta\)}  is uniformly distributed modulo 1, where m extends over all polynomials and \(\theta\)  is a fixed irrational function.

Multi antenna transmission and reception is included in last-generation and future wireless communication standards, such as DVB-T2 or DVB-NGH, to increase bandwidth efficiency and receiver robustness. The primary goal is to combine diversity and spatial multiplexing in order to fully exploit the capacity of multiple-input multiple output (MIMO) channels. For this purpose, full-rate full-diversity (FRFD) space-time codes (STC) such as the Golden code are being investigated. Despite their higher achievable capacity, most of them have a high soft detection complexity, which prevents them from being combined with soft-input decoders in bit-interleaved coded modulation (BICM) schemes. This paper presents a study of a low complexity soft detection algorithm for receiving FRFD space-frequency block codes in BICM orthogonal frequency division multiplexing (OFDM) systems and compares performance using LDPC and Turbo codes. The proposed detector has a low and fixed complexity, avoiding the variable nature of the list sphere decoder (LSD), which is dependent on noise and channel conditions. The proposed detector performs close to the optimal log-maximum a posteriori (MAP) detection in a variety of DVB-T2 broadcasting scenarios, according to complexity and simulation-based performance results.  

Cloud Computing is a technology that utilizes internet for storing and managing data on remote servers. They can be classified as Public cloud – it’s owned and operated by a third party cloud service providers, Private cloud – It refers to computing resources used exclusively by a single business or organization, and Hybrid cloud – It combines public and private clouds, bound together that allows data and applications to be shared between them. Few applications are discussed for Cloud Computing.

Indian languages are often used in social media messages. Tamil is one of the oldest languages which has been used often in tweets. Sentiment Analysis (SA) is a multidisciplinary unit which is a part of text mining as well as natural language processing.  Sentiment analysis has gained incredible development in recent times mostly for English language. However very less work of sentiment analysis has done for Indian languages like Hindi, Tamil, Kannada etc., In this chapter, Tamil tweets are focused to find the sentiment of the Tamil movie reviews. It is essential to analyze the Tamil language content for tweets and get perception of opinion expressed by the tweets. The objective is to classify the sentiment of the Tamil movies based on Tamil tweets using Tamil SentiWordNet (TSWN). Term Frequency - Inverse Document Frequency (TF-IDF) method is proposed to find the sentiment polarity of the Tamil movie dataset. Domain specific ontology is applied to identify the primary sentiment categorization of the Tamil movies. In contextual semantic, the sentiment of a word may flip based on the neighbouring word. In this research, sentiment-bearing terms and its neighbouring terms in Tamil tweets are evaluated using contextual semantic sentiment analysis to get more accurate result for the movie sentimental classification.

In mobile ad-hoc networks nodes are freely move and communicate with each other in its frequency range wirelessly. Due to dynamic topology the routes are not stable. Hence transmitting data packets among nodes is one of the major challenge. The algorithms compatible with the changes created in the network due to the nodes’ movements are of high significance. For reducing data packet transmission time among nodes, route shortness and also route stability should be taken into consideration. More than a decade ago, that our approach to Artificial Intelligence has been widely accepted as a new development in the field of routing protocols [1,2]. In order to select the robust routing process, the reinforcement learning was used to make the best choice among the neighbor nodes at any moment to transmit data packets from source to destination. It predicts the behavior pattern of the nodes in relation to the target node through using reinforcement learning. The proposed method adopts Q-learning algorithm which has more homogeneity to estimate the value of actions [3]. 

To handle bulk of power, the AC power transmission is not economical over long distance. High-voltage direct current (HVDC) transmission system is selected as the alternative not only in economic aspects but also in stability point of view. But the operation and control of HVDC links pose a challenge for the designers to choose the proper control strategy under various operating conditions. Traditionally, PI controllers are used for the rectifier current control of the HVDC system, but due to fixed proportional (P) and integral (I) gains, these controllers can perform well only over a limited operating range. However, in controlling a nonlinear plant such as the firing angle of the rectifier side in HVDC system, the model controls such as fuzzy logic controllers show better performance to the dynamic disturbances than traditional PI controllers. The CIGRÉ model as one of the conventional methods has been studied and improves the stability HVDC system.

Most industries around the globe make use of image processing to improve their productions. On the other hand Big Data Processing is a big dataset; this required fast method to processing irrespective of Generic nature, therefore Clarification of heterogeneous images can improve the integrity of any system design. To avoid waste of time and energy, it is necessary to classify images. In a clear perspective, the objective of image classification is complex characteristic modalities to categories and label group of pixies or vector within an image based on specific rules. Big Data Processing for Generic Clarification of heterogeneous images provides fast, accurate and objectives results. In this study, the researchers classified into three category using resnet50 techniques for training dataset images. The outcome of the research is analyzing these techniques and comparison analysis on different existing image data sets as pre-trained data and test data as sample images for decision making based on their limitations and strengths.

Spectrum measurement campaigns around the world have confirmed that a significant amount of radio spectrum is underutilised. According to the literature, the majority of spectrum measurement campaigns use commercially available antennas. A novel circularly polarised wide axial ratio bandwidth circularly polarised microstrip antenna is designed for Spectrum Occupancy Measurement in this communication. The antenna has a broad -10 dB impedance bandwidth from 700 MHz to 2.9 GHz, as well as a broad -3dB axial ratio bandwidth from 1.5 GHz to 2.7 GHz.  The antenna prototype has been built, and the simulated results agree very well with the measured results. Following that, the antenna's spectrum sensing ability is validated using a spectrum sensing measurement setup, which shows excellent spectrum sensing ability, -24 to -31.5 dBm in GSM 900 MHz, LTE 2.1 GHz, and ISM 2.4 GHz bands in an outdoor environment. The proposed antenna is compact , portable, and simple to integrate into the spectrum sensing measurement setup.The spectrum sensing ability of the proposed antenna is verified through the spectrum occupancy measurement setup, and results are found better than the antenna used in literature.

Hypothesis: Any number can be decomposed and further on brought back to its original form (Second Postulate of Ternary Mathematics).

The following article presents the proof of number decomposition and isomorphism of Integers to the field of vectors [1].

In perspective we aim to adapt this principle to various number types and show the isomorphism of any given number using Ternary Maths conversion.

“Comments on Ternary Mathematics and 3D Placement of Logical Elements Justification Further Research” is not only an analysis of the previously published manuscript, it is also a look at how numbers function within any chosen system of counting In that respect its content might be interesting for Computer Scientists Mathematicians and all specialists working with numeric systems.

The article consists of 3 main parts:

1. An Introduction is where we mention an earlier discovered principle of a Ternary Mathematics
2. Results and Discussion part which basically repeats decomposition of the matrix process described in “Ternary Mathematics and 3D Placement of Logical Elements Justification"
3. Conclusion is a summary of all progress made thus far in developing of Ternary Mathematics and its principles to adjust them to the needs of Applied Maths and Computer Science

This article proposed a Poisson based continuous probability distribution called Poisson-Rayleigh distribution. The study obtained and discussed extensively the properties of the new distribution such as quantile and reliability functions and other useful measures as well as its applications. The model parameters were estimated using the method of maximum likelihood. The usefulness of the new distribution was proven empirically using real life datasets. Results from the application of the proposed model to the real life datasets reveal that the Poisson-Rayleigh distribution fits the datasets much better than the Rayleigh distribution.

Some fundamental concept and technology relating well-being systems are discussed as an advanbced studies on the communicariont facility from the standpoints of their beneficiaries and social infrastructure. We mainly mention them according to ther subjective needs of individual beneficiaries in an ageing society. Thus, the support rather than the surveillance of beneficiaries is talked with low expenses of simplified equipment in ordinary tele-health cases, community-wide medicare offering security. Emphasis is however placed on Face-to-Face communication and easy handling by beneficiaries, providing as examples such opportunities as enjoying games for the disadvantaged and for dementia patients. Then, the same technological concept based on broadband are mentioned to make it enable to have teleconferences at a distance, teleeducation for rural depopulated region. Hereby a simple technology in principle is on the basis of its safety, reliability and flexibility, reflecting past technical achievements for the well-being of the persons. and the active use of the Internet environment for the wide provision of convenience and help of daily life on public benefits. In addition are proposed some methods concerning system management and software provision to start up the computer from a distance. We present technical viewpoints from our studies with comprehensive engineering issues related to development and practical utilization of basic functions required by the Internet. From the progress in information & communication technology, appropriate systems are systematically developed for the help of daily life, amusement, guidance, health care, rehabilitation, nursing and medicare. They enabled the beneficiaries not only to ask neighbors in emergency and to have daily necessities, but also to cover effective activity and communications in remote islands and/or depopulated area where sufficient resource of medical staff might not be provided. In order to bilaterally communicate with beneficiaries, an extended functions of the proposed basic system are utilized for various systems, which are supported as the concrete methods and apparatus to communicate their concerning data. In this stuation, important methods for the help of everyday life and rescue of a lonely living person with sudden illness threatened to life are realized by the combination of the additional button-type computer with the proposed communication techniques without any complicated manipulation under the Internet environment.

We use a regular and modular version of the eight-variable Karnaugh map to demonstrate and visualize some technical details of the Boolean minimization procedures usually employed in solving problems of Qualitative Comparative Analysis (QCA). We utilize as a large running example a prominent eight-variable political-science problem of sparse diversity (involving a partially-defined Boolean function (PDBF), that is dominantly unspecified). We recover the published solution of this problem, showing that it is merely one candidate solution among a set of many equally-likely competitive solutions. We immediately obtain one of these rival solutions, which looks better than the published solution in two different aspects, namely: (a) that it is based on a smaller minimal set of supporting variables, and (b) that it provides a more compact Boolean formula. However, we deliberately refrain from claiming that our solution is a better one, but instead we stress that it is simply un-comparable with the published solution. We emphasize that the comparison between any two rival solutions should be context-specific and not be tool-specific. This paper is part of an ongoing activity striving to streamline the use of Boolean minimization techniques in QCA applications.  In fact, the Boolean minimization technique, borrowed from the area of digital design, cannot be used as it is in the somewhat different QCA context. A more suitable paradigm for QCA problems is to identify all minimal sets of supporting variables (possibly via integer programming or other equivalent approaches), and then obtain all irredundant disjunctive forms (IDFs) for each of these sets. Such a paradigm stresses inherent ambiguity, and does not seem appealing as the QCA one, which usually provides a decisive answer (irrespective of whether it is justified or not).The problem studied herein is shown to have at least four distinct minimal sets of supporting variables with various cardinalities. Each of the corresponding functions does not have any non-essential prime implicants, and hence each enjoys the desirable feature of having a single IDF that is both a unique minimal sum and the complete sum (Blake Canonical Form). Moreover, each of them is a unate function as it is expressible in terms of un-complemented literals only. Political scientists are invited to investigate the meanings of the (so far) abstract formulas we obtained, and to devise some context-specific tool to assess and compare them.

The traditional way for statistics in any statistical book starting with descriptive statistics, followed by Probability and ends with inferential Statistics. The probability is considered as the link between descriptive and inferential statistics. Inferential Statistics has wide definition and is defined as “the branch of statistics concerned with using sample data to make inferences about a population. In inferential statistics, predictions are made and conclusions are drawn for the target population based on the sample”. The main topics of inferential statistics are Estimation, Testing Hypotheses about means, variances, goodness of fit and proportions, Correlation, Regression and Time series.

In this article we are trying to organize the statistics by splitting the inferential statistics into two parts, namely Diagnostic Statistics and Predictive Statistics and explaining the importance of each part. Also we will discuss a Perspective Statistics.

Based on that we will have four levels in statistics that can be used to analyze data (Descriptive, Diagnostic, Predictive and Perspective Statistics). Descriptive statistics are primarily concerned with graphs, frequency tables, measures of central tendency, measures of variation, and measures of shape. Diagnostic statistics are primarily concerned with the effects of the Independent variables (inputs) on the Dependent (Target) variable, as measured by Tests of Correlation or Association, Tests for Mean Differences, and Tests for Classification. Predictive statistics are primarily concerned with estimation, regression techniques, and time series analysis for the dependent (target) variable. Perspective statistics mainly related to the previous three levels and acts as a prescription to how to solve or prevent the problem, which means to take a decision in advance. In this article, we will clarify idea through giving an example on a real data related to Gynecologic Cancer, and show how the perspective analytics can prevent it.