Efficient Simple Tests For Primality

The tests form a general method to decide whether a given positive odd integer is composite or prime. The tests are based on the divisibility properties of the sum of two squared positive integers. The algorithms comprising the tests are polynomial- time algorithms

A Pure Mathematical Proof Of The Four Color Problem

As stated originally the four – color problem asked whether it is always possible to color the regions of a plane map with four colors such that regions which share a common boundary ( and not just a point ) receive different colors. In the long and arduous history of attacks to prove the four color theorm many attempts came close, but what finally succeeded in the Apple – Haken proof of 1976 and also in the recent proof of Robertson ,Sanders , Seymour and Thomas 1997 was a combination of some old ideas and the calculating powers of modern – day computers. Thirty years after the original proof, the situation is still basically the the same,no pure mathematical proof is in sight.Now I give in my paper such a pure mathematical proof

Efficient Simple Tests For Primality

The tests form a general method to decide whether a given positive odd integer is composite or prime. The tests are based on the divisibility properties of the sum of two squared positive integers. The algorithms comprising the tests are polynomial- time algorithms

How to prove the Riemann Hypothesis

I have already discovered a simple proof of the Riemann Hypothesis. The hypothesis states that the nontrivial zeros of the Riemann zeta function have real part equal to 0.5 . I assume that any such zero is s =a+ bi .I use integral calculus in the first part of the proof. In the second part I employ variational calculus. Through equations (50) to (59) I consider (a) as a fixed exponent , and verify that a = 0.5 .From equation (60) onward I view (a) as a parameter (a <0.5 ) and arrive at a contradiction. At the end of the proof (from equation (73)) and through the assumption that (a) is a parameter, I verify again that a = 0.

Reasons that Make Teachers of the English Language don't Use the Different Strategies, Approaches, Techniques and Methods to Teach the Activities of Text Books to their Students in Private Schools in Amman-Jordan

The research represents the study of the reasons that make teachers of the English language don't use modern strategies, approaches, techniques and methods to teach the activities of the English text books to their students. The importance of this research lies in the attempt to discover these reasons by making questionaire and then to know the medial account of each item and its percent. The questionaire consists of (31) items which represent many questions about strategies, approaches, techniques and methods. The others related to the relationship between teachers, the school administration, the educational supervision, the conditions around them and between teachers themselves. This research is limited to the English teachers in private schools in Amman-Jordan 2014-2015.This research consists of four chapters one deals with the research importance the need, the aim and the limits of the study chapter two deals with the theoretical introduction, about the educational strategies, approaches, techniques and methods and aims of using them chapter three introduces the research curricula, the procedures and the research surrounding. Chapter four represents results and their explanation. Keywords: Strategies, Approach, Technique, Methods

The Effect of Storage on Consumer Preference, Sugar Content, and Starch Content of Spiced Low-Fat Sweet Potato Flavored Yogurt.

The primary purpose of this study was to determine if addition of pumpkin pie spice to sweet potato puree would enhance consumer acceptance of sweet potato flavored yogurt. In Phase I, the effect of fat percentage, spice percentage, and addition of sweet potato pre-fermentation and post-fermentation on consumer acceptance was examined to determine the optimum treatment preferred by consumers and the effect of each treatment variable on the fermentation process. Phase II focused on the effect of storage periods of 7, 14, and 21 days on the organoleptic qualities and chemical composition of sweet potato. Analyses showed that the percentage of spice in the treatment appeared to have an effect on pH during fermentation. Treatments containing higher percentages of spice exhibited a slower drop in pH during the fermentation process. The effect was more pronounced in treatments containing .4 percent spice. Addition of sweet potato pre-fermentation and post-fermentation impacted consumer acceptance, viscosity, and glucose and sucrose content. Consumers appeared to prefer treatments with higher percentages of spice content in which sweet potato was added pre-fermentation. In addition, treatments in which sweet potato was added pre-fermentation exhibited higher viscosity regardless of fat and spice percentage and were rated higher by consumers in evaluation of texture. Analyses of Phase II data showed that consumers preferred treatments containing 5 and 6 percent sugar and storage periods of 14 days. Percent added sugar impacted pH, titratable acidity, glucose and sucrose levels. Treatments with lower percentages of added sugar exhibited lower pH values and higher titratable acidity for all storage periods. Treatments with higher percentages of added sugar prefermentation exhibited higher glucose and sucrose levels across storage periods. Dry matter exhibited a storage effect with significant increases in dry matter after 21 days of storage. Viscosity and starch content were not impacted by sugar or storage. Future research should focus on refinement of the yogurt formula to improve the organoleptic properties of the product. Other flavor or textural enhancements such as spiced granola or pecans should be explored. Additional research to determine the nature of the spice on the fermentation process is needed

Investigation of drillstring vibration reduction tools

Drilling related problems such as drillstring vibration is an important cause of premature failure of drillstring components and drilling inefficiency. The vibration of drillstring interferes with measurement collected while drilling. In severe cases, drillstring vibration will lead to wellbore instability that will result in an increase in the operation cost. In the late 1980\u27s, a lot of studies and techniques were developed to mitigate drillstring vibration and downhole vibration measurements were introduced to the industry in two forms; real time measurements and memory devices measurements A study of drillstring vibration of three different wells located in the Norwegian North Sea was analyzed. The bottom hole assembly (BHA) of two wells consisted of anti-vibration technology. The study involved a verification of anti stalling technology (AST) and V-stab vibration reduction tools. Part of the study illustrates the different in lateral vibration in different wells of matching lithology which include a statistical analysis of anti-vibration tools performance. Finally, a statistical analysis was conducted on downhole vibration measurement to investigate the sampling rate of the device. Alternating lithology has a big impact on lateral vibration; however, lateral vibration is not the same for different wells in the same formations due to the difference in the BHA assemblies. The study showed that lateral vibration using the V-stab was lower than the one using the AST tool. Considering torsional vibration, the analysis reveled that V-stab has a lower stick/slip severity than the AST tool. The field study showed that the roller-cone bit generates less torsional vibration than the PDC bit due to different cutting actions. One of the important findings was that there was no correlation between drillstring vibration and mechanical specific Energy (MSE) --Abstract, page iii

Numerical and field data analysis of drill stem vibration

Drill stem vibration is a major cause of premature failure of drill stem components and drilling inefficiency. In severe cases, drill stem vibration may lead to wellbore instability that could lead to increased operational cost. Drill stem vibrations are affected by design decisions and the drilling environment. Examples are; bottom hole assembly configurations, selection of operational parameters, and frequent changes in lithology. Vibration modeling, analysis of vibration data, and specialized vibration reduction tools are methods in use to prevent and mitigate severe vibrations. A drill stem vibration model was created using nonlinear strain formulation which couples the axial, lateral and torsional vibration of the entire drill stem. The model includes the effect of geometric stiffening arising from the applied axial load, two new developed vibration reduction tools used to reduce drill stem vibrations and fluid flow inside and outside the drill stem taking into account two different fluid rheological models. The obtained equation of motion was assembled using the finite element analysis which was solved numerically in Matlab®. The sensitivity analysis using Euler-Bernoulli and Timoshenko models, showed that the Euler-Bernoulli assumption is satisfactory when modeling drill stem vibrations at typical drilling conditions. Analyzing three adjacent wells in the North Sea with different bottom hole assembly and recorded vibration data, revealed that including drill stem vibration reduction tools reduces drill stem vibration and decreases stick-slip tendency. Including drilling fluid circulation, by imposing dynamic pressures on the inside and outside of the drill stem, affect lateral natural frequencies. High flow rate and wrong selection of total flow area at the drill bit could lead to vibrations --Abstract, page iii

There is always a prime between n^2 and (n + 1 )^2

I give an answer in the affirmative to the following unanswered question : Is there always a prime between n2 and (n + 1)2 where n is a natural number. The question represents a famous unsolved problem in Mathematics. I employ some familiar ideas in Number Theory

Orthosurgical Correction of Severe Vertical Maxillary Excess: Gummy Smile

Gummy smile which is commonly described as excessive gingival display in full smile has become a major esthetic concern for patients and healthcare providers in recent years. Because of the complex etiologic factors and severity of this orofacial deformity including skeletal, dentoalveolar, muscular, and gingival, it is essential that a differential diagnosis be established so that a relevant therapy can be selected from a wide range of treatment options. The complex etiologic factors of this dentofacial deformity necessitates coordination between a team of health care providers, especially between orthodontist and maxillofacial surgeon, to improve diagnosis and treatment planning, accurately predict the outcome, and minimize orthosurgical complications. In this chapter, the author will present several clinical cases and briefly review available treatment modalities for excessive gingival display in full smile. Emphasis will be put on orthosurgical treatment of severe vertical maxillary excess as the optimal solution to restore facial balance and harmony, attractive smile, and patients’ satisfaction