(ISSN Number (Online) - 2644-3368)

(ISSN Number (Print) - 2688-8300)

This paper considers the semigroup of partial transformation P

We have reviewed the proof [1] of a conjecture posted in the Online Encyclopedia of Integer Sequences (OEIS)

At present market, with the help of science, the information technology has developed rapidly as well
as the information security as an important part of information technology is also strongly affecting
people's work and life. When the development of science and technology brings convenience to
characters, it also exposes many security issues. In recent years, information security incidents such as
information leakage, SQL injection vulnerabilities, network penetration, and hacking attacks have
triggered irreparable losses to enterprises, society, and individuals. In our paper, a symmetric key
encryption with fuzzy based session key has been proposed for satisfying the key issues like security;
increase the strength of symmetric key. Here the session key is generated using fuzzy logic. Now the
encryption is done by using this session key and symmetric key. Here a new authentication scheme is
developed to generate cipher text. Different types of experiments to test the robustness of keys and
encryption technique and comparative study with existing standard techniques have been done with
satisfactory results. This paper has taken steps to develop an attack capability for use within a cyber
challenge environment. The principles discussed within this paper aim to be applicable to all challenges
against mathematical cryptanalysis and cryptographic protocol in general and also it is used to cover
threat modeling, construction of cyber security test beds and take footsteps against offensive cyber
operations.

**Keywords:** Symmetric key, Session key, Fuzzy logic, Encryption, Decryption, Cryptanalysis.

In this paper we have tried to study the geometry of tetrahedron as a member of polyhedron family and hence calculate the face angles on each face of a tetrahedron with help of “C” Programming. We will also be looking into the applications of tetrahedron structure in chemistry in the structure of various molecules, in aviation it is used as a Wind Sock which serves as a reference to pilots indicating the direction of the wind as well as Geology where the ‘Tetrahedral Hypothesis” was used to explain the formation of earth.

When we talk about new technologies and the advancement in the field of Computer Science, the first thing that comes to our mind is Artificial Intelligence and Machine Learning. Artificial Intelligence has seen resurgence in the 21 st century because of its ability to mimic functions done by human intelligence like “problem solving” and “learning”. It is slowly becoming the area of interest of the new generation because of its modern capabilities which even human intelligence struggle to perform like competing at highest level in strategic game systems, intelligent routing, operating cars autonomously and simulations. Artificial Intelligence may look easy but there are several tools involved in making it successful. One of the main tool is “Statistical Methods”. Linear algebra and Partial Differential Equations have become the base of this field. The objective of our paper is to throw light on how Statistical Methods and Mathematical optimization provide the base for the working of Supervised Learning. Over years, algorithms inspired by Partial Differential Equations (PDE) and Linear Algebra have had an immense impact on many processing and autonomously performed tasks that involve speech, image and video data. Image processing tasks and intelligent routing done using PDE models has lead to ground-breaking contributions. The reinterpretation of many modern machine capabilities like artificial neural networks through PDE lens has been creating multiple celebrated approaches that benefit a vast area. In this paper, we have established some working of these methods in different sub- fields of Artificial Intelligence. Guided by well-established theories we demonstrate new insights and algorithms for Supervised Learning and demonstrate the competitiveness of different numerical experiments used in the sub-fields. Not only will we see the wide application of Artificial intelligence but also its ability to slowly replace human works leading to unemployment which are part of its limitation. This research will provide wider insights into the multiple mathematical processes which acts as roots to make the field of Computer Science interesting and successful.

For n ∈ N a positive integer, let f n (x) = ∑ nj=0 a n−j x n−j ; a n ≠ 0; n < 5 be a general polynomial equation of degree less than five in one variable. Before now, we are unaware of any known unified method for solving f n (x) = 0 (n < 5) in radical until Kulkarni did so in 2006. However, it is quite ironical and contradicting to observe (one among many other issues) that the method introduced by Kulkarni fails if n = 1 (since n = 1 satisfies n < 5) which is the case of general polynomial equation of degree one. It is the purpose of this paper to address this issue and many more with an approach that is quite simple and novel.

Fifth generation systems are required to fulfill the objectives like compatibility, flexibility, high speed data rate and low cost. Universal Mobile Telecommunication System (UMTS) use WCDMA as the air interface for 4th generation mobile system. The performance of wireless communication system is often limited by the radio channel models. In urban areas, channel is modeled as Rayleigh fading channel. This channel causes multipath channels and other problems resulting degraded performance. Hence, channel estimation before receiver helps to receive the transmitted signal using rake receiver. Rake receiver is a conventional receiver for DS-CDMA system. In this, channel is estimated adaptively using LMS algorithm and performance of this algorithm is studied for various multipath channels and step sizes. Moreover, the channel introduces Inter Symbol Interference (ISI) and channel equalizers are used to compensate for the ISI. In this work, BER vs. SNR performance of Zero Forcing Equalizer (ZFE), Minimum Mean Square Error (MMSE) and MMSE- Decision Feedback Equalizer (MMSE-DFE) in WCDMA downlink system are compared with conventional rake receiver for various spread factors in Rayleigh multipath fading channel with Additive White Gaussian Noise.

In the information era, a huge amount of terabytes is generated from our day to day lives. This mainly comes from our modern information system and advanced digital technologies such as internet of this and cloud computing.Since the datas are huge the analysis of these datas require a large amount of efforts at multiple levels and for multiple purposes. Therefore to cope up with this big data analysis is a current area of research. Due to rapid growth of such data solutions need to be studied and found. The ones taking the decisions also called as decision makers need to have a detailed insights about the data they are handling otherwise how can they come up with correct and best decions,which can only be provided using data analytics. As a result this article provides a platform or rather a solution or we can also call it a brief analysation of big data challenges open research issues and also some of the different methods and tools which can be used for data analytics. It also opens a new horizon for the researchers to come up with the solution.

It is plausible that language is processed by the innate spinal sign reflex mechanism. Human speech sound contains logical properties of phoneme and mora, which interact with in-brain antigen/antibody molecular structures and networking memories in the postnatally developed logical circuits optimized for signals of syllables, a character set (long lasting syllables) and electronic form (interactive and ubiquitous syllables). For grammatical decoding, sound localization function at the brainstem auditory nuclei is converted to process sound vectors of grammatical syllables. For axiomatic scientific concepts, sign reflex logic of “If A then B” must be upgraded by mathematical group logic to be acquired by learning, so that the results of interdisciplinary conceptual operations should become meaningful and productive. As electronic data is interactive, we can discover as many relevant linguistic information as possible with keyword search on the internet within a few seconds. As a result, we obtain multi-disciplinary and voluminous linguistic information but with uncertain reliability. To inherit collective human intelligence and correct any errors in linguistic information of the past, regenerative reading might be appropriate for individual ontogenesis to repeat intellectual and conceptual phylogeny. Errors cannot be corrected by the original authors posthumously but only by those who are alive now and equipped with error correction techniques for linguistic information.

This paper deals with concise study on the applications of data-structure and algorithms associated with field of computer science. It has huge significance in the proper functioning of operating system and improvement of the throughput by resource utilization. There is an amount of essential complexity in the operations related to the data and files present in computer system. No brute-force approaches can minimize and manifest it so easily by adopting to the non-harmonized methodology of the storage and management, but it can be placed so that it doesn't get in the way and it's also easy to understand. The best such place is a data structure. Data structures have many applications in the area of system development, data base design, software coding and computer-networks. In this paper, we have presented a succinct explanation about the efficiency and application of algorithms upon different domains followed by a survey of different areas.