Abstract:
"Does God play dice with the Universe?" The natural width of excited hydrogen atoms are found using the Bohr's model of this atom and de Broglie's ideas. The mean life time of the excited states is a characteristic only of a statistical ensemble of many atoms.

Abstract:
The emergence of quantum theory in the early decades of the twentieth century was accompanied by a wide range of popular science books, all of which presented in words and in images new scientific ideas about the structure of the atom. The work of physicists such as Ernest Rutherford and Niels Bohr, among others, was pivotal to the so-called planetary model of the atom, which, still today, is used in popular accounts and in science textbooks. In an attempt to add to our knowledge about the popular trajectory of the new atomic physics, this paper examines one book in particular, coauthored by Danish science writer Helge Holst and Dutch physicist and close collaborator of Niels Bohr, Hendrik A. Kramers. Translated from Danish into four European languages, the book not only presented contemporary ideas about the quantum atom, but also went into rather lengthy discussions about unresolved problems. Moreover, the book was quite explicit in identifying the quantum atom with the atom as described by Bohr's theory. We argue that Kramers and Holst's book, along with other atomic books, was a useful tool for physicists and science popularisers as they grappled with the new quantum physics.

Abstract:
In this paper it is shown that if one accept assumption of de Broglie that "unitary wave-particle" exists simultaneously and this coexistence is real, then one can find the mean life time of the hydrogen atom of Bohr (intensities).

Abstract:
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including algebraic geometry), topology, probability theory, and theoretical computer science.

Abstract:
Jerald BainDepartment of Medicine, Department of Obstetrics and Gynecology, University of Toronto, Ontario, Canada; Division of Endocrinology and Metabolism, Mount Sinai Hospital, Toronto, Ontario, CanadaAbstract: Testosterone is more than a “male sex hormone”. It is an important contributor to the robust metabolic functioning of multiple bodily systems. The abuse of anabolic steroids by athletes over the years has been one of the major detractors from the investigation and treatment of clinical states that could be caused by or related to male hypogonadism. The unwarranted fear that testosterone therapy would induce prostate cancer has also deterred physicians form pursuing more aggressively the possibility of hypogonadism in symptomatic male patients. In addition to these two mythologies, many physicians believe that testosterone is bad for the male heart. The classical anabolic agents, 17-alkylated steroids, are, indeed, potentially harmful to the liver, to insulin action to lipid metabolism. These substances, however, are not testosterone, which has none of these adverse effects. The current evidence, in fact, strongly suggests that testosterone may be cardioprotective. There is virtually no evidence to implicate testosterone as a cause of prostate cancer. It may exacerbate an existing prostate cancer, although the evidence is flimsy, but it does not likely cause the cancer in the first place. Testosterone has stimulatory effects on bones, muscles, erythropoietin, libido, mood and cognition centres in the brain, penile erection. It is reduced in metabolic syndrome and diabetes and therapy with testosterone in these conditions may provide amelioration by lowering LDL cholesterol, blood sugar, glycated hemoglobin and insulin resistance. The best measure is bio-available testosterone which is the fraction of testosterone not bound to sex hormone binding globulin. Several forms of testosterone administration are available making compliance much less of an issue with testosterone replacement therapy.Keywords: testosterone, androgens, male hypogonadism, anabolic steroids

Abstract:
depression is a serious global health problem. it creates a huge economic burden on society and on families and has serious and pervasive health impacts on the individual and their families. specialized psychiatric services are often scarce and thus the bulk of care delivery for depression has fallen to primary care providers, including advanced practice nurses and experienced nurses who work in under-serviced regions. these health professionals require advanced knowledge about the many faces that depression can display. this article reviews some of the faces of depression seen by primary care providers in their practices. considering depression as a heterogeneous spectrum disorder requires attention to both the details of the clinical presentation, as well as contextual factors. recommendations around engagement and potential interventions will also be discussed, in terms of the client population as well as for the practitioner who may be isolated by geography or discipline.

Abstract:
We present explicit constructions of centrally symmetric polytopes with many faces: first, we construct a d-dimensional centrally symmetric polytope P with about (1.316)^d vertices such that every pair of non-antipodal vertices of P spans an edge of P, second, for an integer k>1, we construct a d-dimensional centrally symmetric polytope P of an arbitrarily high dimension d and with an arbitrarily large number N of vertices such that for some 0 < delta_k < 1 at least (1-delta_k^d) {N choose k} k-subsets of the set of vertices span faces of P, and third, for an integer k>1 and a>0, we construct a centrally symmetric polytope Q with an arbitrary large number N of vertices and of dimension d=k^{1+o(1)} such that least (1 - k^{-a}){N choose k} k-subsets of the set of vertices span faces of Q.

Abstract:
The quantum theory of Bohr has roots in the theories of Rutherford and J. J. Thomson on the one hand, and that of Nicholson on the other. We note that Bohr neither presented the theories of Rutherford and Thomson faithfully, nor did he refer to the theory of Nicholson in its own terms. The contrasting attitudes towards these antecedent theories is telling and reveals the philosophical disposition of Bohr. We argue that Bohr intentionally avoided the concept of model as inappropriate for describing his proposed theory. Bohr had no problem in referring to the works of others as 'models', thus separating his theory from previous theories. He was interested in uncovering 'a little piece of reality'.

Abstract:
In this note, and inspired by an article appeared recently in this journal, we discuss an example related to the theory ofthe Bohr’s atom, who illustrates the fact that erroneous expositions in the learning of Physics exist, considering thatthis concept includes the use of well internationally recognized and commonly used educational text books.

Abstract:
In a previous, primary treatise of the author the
mathematical description of electron trajectories in the excited states of the
H-atom could be demonstrated, starting from Bohr’s original model but modifying
it three dimensionally. In a subsequent treatise, Bohr’s theorem of an
unalterable angular momentum h/2π,
determining the ground state of the H-atom, was revealed as an inducement by the—unalterable—electron spin. Starting from this
presumption, a model of the H_{2}-molecule could be created which
exhibits well-defined electron trajectories, and which enabled computing the
bond length precisely. In the present
treatise, Bohr’s theorem is adapted to the atom models of helium and of
neon. But while this was feasible exactly in the case of helium, the neon atom
turned out to be too complex for a mathematical modelling. Nevertheless, a
rough ball-and-stick model can be presented, assuming electron rings instead of
electron clouds, which in the outer shell are orientated as a tetrahedron. It
entails the principal statement that the neon atom does not represent a static
construction with constant electron distances and velocities, but a pulsating
dynamic one with permanently changing internal distances. Thus, the helium atom
marks the limit for precisely describing an atom, whereby at and under this
limit such a precise description is feasible, being also demonstrated in the
author’s previous work. This contradicts the conventional quantum mechanical
theory which claims that such a—locally and temporally—precise description of any atom or molecule structure is
generally not possible, also not for the H_{2}-molecule, and not even
for the H-atom.