Characteristic polynomial

On April 15th in 1912, one of the most tragic shipwreck happened. The Titanic ship sunk under the Atlantic Ocean after colliding with an iceberg. A lot of people died during the accident. Small number of available lifeboats was one of the main reasons that led to such a high number of deaths. Such factors as sex, class, age, and others also significantly contributed to the likelihood of survival. Introducing different statistical methods, I will classify what sorts of people had a better chance…

In 1942, a doctor named Harry Kleinfelter, working in a general hospital in Boston, Massachusetts, documented abnormal symptoms in males that had not been cited before. Dr. Kleinfelter was treating males suffering from undersized testicles, gynecomastia, incomplete puberty, reduced body and facial hair, as well as other sexual developmental issues such as infertility, hypospadias, and cryptorchidism. The condition was named Kleinfelter’s Syndrome, though what brought about these symptoms was…

Adolescence, per the Merriam-Webster dictionary defines it as the state or process of growing up, the period of life from puberty to maturity terminating legally at the age of majority, a stage of development prior to maturity. It is known as the developmental stage that lies between childhood and adulthood. One is no longer considered a child, but not yet an adult. Dr. Neil K. Kaneshiro of the University Of Washington School Of Medicine says in this stage, “children develop the ability to…

Puberty transforms the body’s physical characteristics from those a child to those more typical of an adult. Sexual development can begin as early as age eight in girls and age ten in boys (Arnett 2016, p. 352). In girls, there is a huge rise in the female sex hormone estradiol, which is responsible for the development of both primary and secondary sex characteristics (Arnett 2016; p. 351) . Primary sexual characteristics are directly correlated with reproduction, and are about…

puberty and mature sexually. A two-year period of rapid physical development triggers by a surge of hormones. Usually, girls will begin at about age 11 and at about 13 in boys. About the time of adolescence, adolescents not only their primary sex characteristics---the reproductive organs and external Du…

When Do Men Stop Growing? Between the ages of 12 and 16, many biological changes occur in men. Apart from changes in body composition and sexual maturation, they usually experience rapid increases in height known as growth spurts during this time. It is generally agreed that height growth stops somewhere between ages of 16 and 20 when you reach physical adulthood. However, a man’s growth is dependent on a multitude of factors, like his genetic potential and environmental factors. So, it is…

the directories they wish to protect. Files in these directories are transparently encrypted and decrypted with the specified key without further user intervention; cleartext is never stored on a disk or sent to a remote file server. One of the characteristics of CFS is that it can use any available file system for its underlying storage without modification, including remote file servers such as NFS. System management functions, such as file backup, work in a normal manner and without knowledge…

Pricing Bonds in the Australian Market is an article, which appeared in the 33rd Australian Journal of Management in 2008. Written by Bilson et al., the article does an incredible job in highlighting issues pertaining to the modeling of the term structure of interest rates. The article begins by appreciating the fact that there are various models associated with the yield curve. The authors highlight the significance of the term structure of interest rates by offering valid examples. For…

must develop a variety of characteristics. It is essential that an athlete has the motivation to succeed, the ambition to always want to improve, outstanding mental clarity, the ability to innovate, and a knack for juggling competing responsibilities (I’m looking at you family commitments, hours spent bagging at a grocery store, and never ending school work). A list of valuable traits that an athlete probably has could simply extend forever. But these very characteristics that aid an athlete en…

\begin{abstract} It is known that Groebner bases is EXP-SPACE in general. We show that this remains true over Boolean rings. \end{abstract} \section{Boolean Rings} Let $\mathbb{F}_2 = \mathbb{Z}/(2)$. Let $R_n = \mathbb{F}_2[x_1,\ldots,x_n, y_1,\ldots,y_n, z_1,\ldots,z_n]$ and % \footnote{Over $\mathbb{F}_2$, $+$ is the same as $-$.} \[ S_n := \{c^2 -c \,\, | \,\, c \in \{x_1,\ldots,x_n, y_1,\ldots,y_n, z_1,\ldots,z_n\} \}. \] Let \[ R_n^{\rm b} := R_n / (S_n). \] This is {\em Boolean ring},…