This study aims to classify the critical points of functions with 4 variables and 8 parameters, we found the caustic for the certain function with the spreading of the critical points. Finally, as an application, we found the bifurcation solutions for the equation of sixth order with boundary conditions using the Lyapunov-Schmidt method in the variational case.
The primary objective of this paper is to introduce a new concept of fibrewise topological spaces on D is named fibrewise multi- topological spaces on D. Also, we entroduce the concepts of multi-proper, fibrewise multi-compact, fibrewise locally multi-compact spaces, Moreover, we study relationships between fibrewise multi-compact (resp., locally multi-compac) space and some fibrewise multi-separation axioms.
The aim of this research is to study some types of fibrewise fuzzy topological spaces. The six major goals are explored in this thesis. The very first goal, introduce and study the notions types of fibrewise topological spaces, namely fibrewise fuzzy j-topological spaces, Also, we introduce the concepts of fibrewise j-closed fuzzy topological spaces, fibrewise j-open fuzzy topological spaces, fibrewise locally sliceable fuzzy j-topological spaces and fibrewise locally sectionable fuzzy j-topological spaces. Furthermore, we state and prove several Theorems concerning these concepts, where j={δ,θ,α,p,s,b,β} The second goal is to introduce weak and strong forms of fibrewise fuzzy ω-topological spaces, namely the fibrewise fuz
... Show MoreIn this paper we introduced many new concepts all of these concepts completely
depended on the concept of feebly open set. The main concepts which introduced in
this paper are minimal f-open and maximal f-open sets. Also new types of
topological spaces introduced which called Tf min and Tf max spaces. Besides,
we present a package of maps called: minimal f-continuous, maximal f-continuous,
f-irresolute minimal, f-irresolute maximal, minimal f-irresolute and maximal firresolute.
Additionally we investigated some fundamental properties of the concepts
which presented in this paper.
The diseases presence in various species of fruits are the crucial parameter of economic composition and degradation of the cultivation industry around the world. The proposed pear fruit disease identification neural network (PFDINN) frame-work to identify three types of pear diseases was presented in this work. The major phases of the presented frame-work were as the following: (1) the infected area in the pear fruit was detected by using the algorithm of K-means clustering. (2) hybrid statistical features were computed over the segmented pear image and combined to form one descriptor. (3) Feed forward neural network (FFNN), which depends on three learning algorithms of back propagation (BP) training, namely Sca
... Show MoreThe research work is "The passive voice as a grammatical phenomenon in four selected textbooks". The research deals with the grammatical phenomenon passive in German. The research consists of two parts, the theoretical and the empirical part. The present research work is divided into 3 sections:
The first section includes the definition of passive, passive types, process passive, state passive, passive with modal verbs, and other types of passive. The second section provides illustrations of the four selected textbooks. The third chapter presents the passive voice in textbooks, namely German language teaching for foreigners by Dora Schulz and Heinz Griesbach, Delfin von Aufderstrasse H. and others, Em von Balme, M. and others and
... Show MoreIn this work we define and study new concept of fibrewise topological spaces, namely fibrewise soft topological spaces, Also, we introduce the concepts of fibrewise closed soft topological spaces, fibrewise open soft topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces.
The present study investigates the relation between the biliteral and triliteral roots which is the introduction to comprehend the nature of the Semitic roots during its early stage of development being unconfirmed to a single pattern. The present research is not meant to decide on the question of the biliteral roots in the Semitic languages, rather it is meant to confirm the predominance of the triliteral roots on these languages which refers, partially, to analogy adopted by the majority of linguists. This tendency is frequently seen in the languages which incline to over generalize the triliteral phenomenon, i. e., to transfer the biliteral roots to the triliteral room, that is, to subject it to the predominant pattern regarding the r
... Show Moreيُعد التنمر ظاهرة إجتماعية قديمة موجودة في جميع المجتمعات سواء أكان المجتمع صناعيًا أم ناميًا، كما يُعد من المفاهيم الحديثة نسبيًا، وربما يرجع لحداثة الإعتراف به نوعًا من أنواع العنف فضلاعن ندرة الدراسات التي تناولته وعدم وجود معيار محدد لتحديد السلوك الذي يعد تنمرًا أم عابرًا، لقد بدأ الأهتمام بدراسة التنمر في سبعينات القرن الماضي وأصبح موضعًا يحضى بأهتمام العديد في مختلف البلدان، وفي عصرنا الحالي تطورت
... Show MoreIn this paper, we introduced module that satisfying strongly -condition modules and strongly -type modules as generalizations of t-extending. A module is said strongly -condition if for every submodule of has a complement which is fully invariant direct summand. A module is said to be strongly -type modules if every t-closed submodule has a complement which is a fully invariant direct summand. Many characterizations for modules with strongly -condition for strongly -type module are given. Also many connections between these types of module and some related types of modules are investigated.
The main idea of this research is to study fibrewise pairwise soft forms of the more important separation axioms of ordinary bitopology named fibrewise pairwise soft