## The series of Semigroup Theory via Functional Calculus

Present panorama of the sequence of operators classes with their associated functional calculi , relevant in semigroup theory : the sequence of operators of halfplane , strip ,sector and parabola-type . It is shown that the basic results in the theory of C0-semigroup (the Hille-Yosida and the Trotter-kato theorem) follow easily from general functional calculus principles by Markus Haase [9] . The introduction of parabola-type sequence of operators allows to treat cosine the sequence of operators functions by functional calculus methods .

## A Neuro-Fuzzy System For Diagnosis of Soya-Beans Diseases

Soyabean is an important legume crop, extensively cultivated for food on which low-income population highly depend because of its proteineous nutrient on daily basis for food.The efforts of farmers to specifically identify the specific pests responsible for damaging of plants segment such as petioles, roots, stem, pod and leaves still remain vague and imprecise to many farmers. In this work, a neuro-fuzzy system will be built with MATLAB version 8 with 100 rules on five input parameters as linguistic variables or symptoms into the system to determine the disease type either as fungi or bacteria or virus, and to also determine intensity rate as the output in form of a crisp. The output of the system will produce results for the decision maker to provide solution regarding the treatment of the infected plant for bountiful and quality harvest.

## Chaotic Random Sequence Generated from Tent Map on Variant Maps

Chaotic sequences, have being widely used in mobile communications and cyberspace security. Using the sequences, various stochastic analysis schemes are developed. The Tent map is one of the widely used chaotic maps with good ergodic uniformity. In this paper, the variant maps are used to illustrate the Tent chaotic sequence under different lengths and control parameters to show the statistical characteristics of sequences. Results are shown that when the control parameter of Tent map is close to 0.5, the generated sequences have the symmetrical distribution, that is more stable if the sequence is longer.

## Generating New Orthogonal Binary Sequences Using Quotient Rings Z/pm Z

Orthogonal Sequences (as M-Sequences, Walsh Sequences, …) are used widely at the forward links of communication channels to mix the information on connecting to and at the backward links of these channels to sift through this information is transmitted to reach the receivers this information in a correct form, especially in the pilot channels, the Sync channels, and the Traffic channel. This research is useful to generate new sets of orthogonal sequences (with the bigger lengths and the bigger minimum distance that assists to increase secrecy of these information and increase the possibility of correcting mistakes resulting in the channels of communication) from quotient rings Z/pmZ, where Z is the integers and p is prime, replacing each event number by zero and replacing each odd number by one.

## Traffic Shaping for Congestion Control

The problem of congestion is not new to the field of telecommunications; its root can be traced back to the very foundations of the internet. Most, if not all networks, are currently faced with this problem. The distribution of resources on the network is very vital. The fact that resources are limited brought about major problem such that these limited resources would be shared among various workstations and nodes. As the network grows, and the number of workstations and nodes increases; resources become integral and if not properly managed no meaningful work will be done in such networks. Congestion control, which involved managing resources when the network utilization becomes so high, is of utmost importance so as to avoid congestion collapse. The complex calculations and computation carried out in the existing solutions, increase utilization as well as the problem of congestion. Traffic shaping algorithms provide solutions with little overhead and thus would be preferred to use in medium sized networks. This work proposes traffic shaping as a better solution for congestion control especially in medium size networks.

## Comparative Study of a Class of One-Step Methods for the Numerical Solution of Some Initial Value Problems in Ordinary Differential Equations

We emphasized explicitly on the derivation and implementation of a new one-step numerical method for the solution of initial value problems in ordinary differential equations. In this paper, we aimed at comparing the newly developed method with other existing methods such as Euler’s method, Trapezoidal rule and Simpson’s rule. Using these methods to solve some initial value problems of first order ordinary differential equations, we discovered that the results compared favorably, which led to the conclusion that the newly derived one-step numerical method is approximately correct and can be used for any related first order ordinary differential equations.

## An approximation algorithm for minimizing congestion in the single-source k-splittable flow

In the traditional multi-commodity transmission networks, the number of paths each commodity can use is unrestricted, and the commodities can use arbitrary number of paths to transmit the flow. However, in the real transmission networks, too many paths will increase the total transmission cost of the network and also cause difficulties in the management of the network. In 2002, Baier[1] proposed the-splittable flow problem, in which each commodity can only use a limited number of paths to transmit the flow. In this paper, we study the-splittable multi-commodity transmission flow problem with the objective of minimizing congestion and cost. We propose an approximation algorithm with performance ratio for congestion and cost in the single-source case, in which is the minimum value of the number of paths each commodity can use. The congestion reflects the total load of the network to some extent. The main aim of minimizing congestion is to distribute the demands of the commodities on the network in a balanced way, avoiding the case that some edge is used too much. By this way, the performance of the network as a whole can be guaranteed and more commodities can be served.

## Application of the Discrete Geometrical Invariants to the Quantitative Monitoring of the Electrochemical Background

In this paper, we apply the statistics of the fractional moments (SFM) and discrete geometrical sets/invariants (DGI) for explain of the temporal evolution of the electrochemical background. For analysis of this phenomenon, we apply the internal correlation factor (ICF) and proved that integral curves expressed in the form of voltammograms (VAGs) are more sensitive in comparison with their derivatives. For analysis of the VAGs (integral curves), we propose the set of the quantitative parameters that form the invariant DGI curves of the second and the fourth orders, correspondingly. The method of their calculation based on the generalization of the well-known Pythagor’s theorem is described. The quantitative parameters that determine these DGI allow monitoring the background of the electrochemical solution covering the period of 1-1000 measurements for two types of electrode (Pt and C) and notice the specific peculiarities that characterize each electrode material. The total set of 1000 measurements was divided on 9 parts (1-100, 101-200, 201-300, …, 901-1000) and the duration of each hundred set was 1300 sec. The proposed algorithm is sensitive and has a “universal” character. It can be applied for a wide set of random curves (experimental measurements) that are needed to be compared in terms of a limited number of the integer moments. The qualitative peculiarities of the background behavior for two types of electrodes (Pt and C) based on the DGI can be explained quantitatively.

## An Implementation of a One-Time Pad Encryption Algorithm for Data Security in Cloud Computing Environment

The cloud is a computing model used by many consumers which include individuals and organizations for data storage which hitherto demands that adequate security measures be put in place to protect the confidentiality and integrity of that information. In cases where these security measures are inefficient or in some cases non-existent, client data is prone to a number of unauthorized violations which include breach of privacy, loss of data, compromised data integrity, and data manipulation among others. This therefore necessitates the demand for efficient security measures. Encryption is a security technique adopted by many for data protection which entails concealing the information content of a message in a way that only the intended recipient can make use of it. This research paper discusses the concept of encryption, a review of different encryption schemes that have been discussed over the years, and proposes a one-time pad encryption (OTP) algorithm (FAPE’s OTP). FAPE’s OTP implements the one time pad using a key expansion process that transforms a 512 bit key to the length of the plaintext. This research was carried out through a comprehensive study of encryption and cloud processes to understand both concepts independently and determine how they can be interleaved while sustaining optimum delivery. Furthermore, our findings indicate that FAPE’s OTP has a faster speed of operation in comparison to the Advanced Encryption Standard.

## Expert System Model for Diagnosing Legume Diseases

There is a current surge in designing expert systems to solve problems like humans in different domains of research but there presently exist dearth of models that can guide designers of expert systems that can be used to accurately diagnose Soya beans diseases. Soya bean is a leguminous plant that is commonly grown in sub Saharan region and it is currently one of the legumes with high Gross Domestic Product (GDP) in the Nigerian economy, but farmers of this product are faced with serious challenges from legume ravaging diseases that are usually similar in symptoms and very difficult to diagnose by the few practising botanist available. Most models available cannot be used to guide designers who are interested in developing secured and reliable expert systems that can accurately classify, identify, diagnose and recommend treatments for Soya beans diseases. The main aim of this paper is to review existing models that are currently being used in designing expert systems and identify their limitations in other to come up with a better, more reliable and secured model. In other to identify inherent gaps from other models, research review method was adopted to critically investigate the weak points in few related and current expert models for classifying and diagnosing legumes diseases.