High-Q states in acoustic apple-shaped resonators

Apples play a significant role in our culture in various points of human history: starting from Adam and Eve, going on with Judgement of Paris, it also touches such great minds as Sir Isaac Newton and Alan Turing. Beyond that apples are still extremely relevant today due to Steve Jobs. In this work we study high quality (high-Q) resonant states of apple-shaped resonators. We have found that quasi bound states in continuum (quasi-BICs) are possible in the linear acoustic domain. We show that quasi-BICs are of Friedrich-Wintgen type, i.e. accompanied with avoided crossings while elongating or shrinking the apple-shaped resonator. Finally, we build a concise theory based on the group theory approach utilizing Wigner’s theorem. We illustrate that only the resonator symmetry plays major role, but not particular resonator’s shape.

Analysis of Ideas Changing in the History of Mathematical Analysis

Analysis is a branch of mathematics that deals with continuous change and with certain general types of processes that have emerged from the study of continuous change, such as limits, differentiation, and integration. In the history of mathematics, analysis is the first subject became epidemic, the development of analysis originated from the British mathematician and physicist, the Sir Isaac Newton, and the German mathematician, Gottfried Wilhelm Leibniz, who developed the theory of Calculus, with hundred-years developing, the modern analysis is now very ample and has widely applications, it has grown into an enormous and central field of mathematical research, with applications throughout the sciences and in areas such as finance, economics, and sociology. In this paper, we investigated in some detail with the changing of the ideas in mathematical analysis. By numerating historical facts and the mathematical ideas, we concluded the result that the ideas changing is because of the changing of the studying objects, the conclusion are studied detailly in the paper.

Archimedes of Syracuse and Sir Isaac Newton: On the Quadrature of a Parabola

Good mathematics stands the test of time. As culture changes, we often ask different questions, bringing new perspectives, but modern mathematics stands on ancient discoveries. Isaac Newton’s discovery of calculus (along with Leibniz) may seem old but is predated by Archimedes’ findings. Current mathematics students should be familiar with parabolas and simple curves; in our introductory calculus courses, we teach them to compute the areas under such curves. Our modern approach derives its roots from Newton’s work; however, we have filled in many of the gaps in the pursuit of mathematical rigor. What many students may not know is that Archimedes solved the area problem for parabolas long before the use of algebraic expressions became mainstream. Archimedes used the geometry of the ancient Greeks, which gave him a vastly different perspective. In this paper we provide both Archimedes’ and Newton’s proofs involving the quadrature of the parabola, trying to remain true to their original texts as much as feasible.

La Scala Graduum Caloris de Newton. Una simulación numérica

Sir Isaac Newton, en la Scala graduum Caloris, publicada en 1701, presentaba una escala “con el grado de calor” de los cuerpos que extendía las medidas muy por encima de los valores disponibles en la época. Para determinarla, Newton siguió dos caminos. El primero usando un termómetro de dilatación con aceite de linaza como líquido, cuyas medidas seguían una progresión aritmética, pero cuyo máximo estaba limitado por la inflamación del aceite. El segundo, por un método completamente nuevo, que consistía en medir los tiempos de enfriamiento de un cuerpo previamente calentado en una pequeña cocina de carbón, y relacionar esos tiempos con las temperaturas según una nueva ley, lo que daba lugar a una escala que seguía una progresión geométrica. Ambas escalas se solapaban parcialmente, lo cual le permitió extender las medidas aritméticas hasta más de seis veces el punto de ebullición del agua. Esa nueva ley se conoce como “Ley de enfriamiento Newton”. Aquí, pretendemos realizar una simulación numérica del proceso de enfriamiento del cuerpo caliente, conjeturando los instrumentos que pudo haber usado y las condiciones ambientales en que se realizó. Todo ello siguiendo lo que el propio Newton refleja en su artículo. Se terminará con unas reflexiones sobre la ley, que estimamos que la enunció en forma integral.

The Well-Tempered Spectrometer

Sir Isaac Newton is the source of our enumeration of the Colors of the Spectrum as seven. It seems that Isaac Newton used a musical scale as an analogy for the spectrum, and we have seven colors to correspond with the seven tones in the scale (exclusive of the final do). But which scale did he use to calculate the characteristic lengths associated with each color (which he would have called the “wavelengths,” had he believed in the wave theory of light)? Technically, there are several possibilities, but the biggest question is whether he opted for a Pythagorean scale, which has discrepancies if carried to several octaves, or a more modern “tempered” scale that is consistent across many octaves.

There is no special condition where a velocity of a light wave is invariance in all inertial frames.

This study of the literature reveals that the concept such as the velocity of a light wave is invariance in all inertial frames is wrong. A velocity of any motion always depends upon its reference frame. There is no special condition present in nature where the velocity is invariance in all inertial frames. Galileo Galilei defined speed is the distance covered per unit of time. Sir Isaac Newton defined velocity is the speed with direction. In the same period, physicists introduced the concept such as wavelength and frequency for measuring the speed a wave. The wave motion in which cycles are repeating after the same interval of time with the same distance between them. In 1887, Albert A. Michelson and Edward W. Morley performed an experiment to detect ether medium. But they failed to prove the existence of the ether medium and published Null Result. This Null Result has led to the creation of various new hypothetical theories. This study tries to reveal the relation between mathematics and physics and also comprehensive literature of light is a particle-wave duality in nature.

There is no special condition where a velocity of a light wave is invariance in all inertial frames.

This study of the literature reveals that the concept such as the velocity of a light wave is invariance in all inertial frames is wrong. A velocity of any motion always depends upon its reference frame. There is no special condition present in nature where the velocity is invariance in all inertial frames. Galileo Galilei defined speed is the distance covered per unit of time. Sir Isaac Newton defined velocity is the speed with direction. In the same period, physicists introduced the concept such as wavelength and frequency for measuring the speed a wave. The wave motion in which cycles are repeating after the same interval of time with the same distance between them. In 1887, Albert A. Michelson and Edward W. Morley performed an experiment to detect ether medium. But they failed to prove the existence of the ether medium and published Null Result. This Null Result has led to the creation of various new hypothetical theories. This study tries to reveal the relation between mathematics and physics and also comprehensive literature of light is a particle-wave duality in nature.

Isaac Newton’s “Active Principles, Particles” and the Cellular Dust Hypothesis; Rewriting Cytology and Histology in the Light of S.A.M.S.

A new and exciting alternative to evolution is the cellular dust/microzyman theory of origin. The cellular dust/microzyman theory of origin states that life and the cosmos came to be as a result of chemical reactions carried out by imperishable miniscule/microscopic entities called microzyma/cellular dust [1-2] This theory has far reaching implications for the present hierarchical classification of organization in the human being escpecially in the light of the Bongham corpuscles and the Primo vascular system. And how does cellular dust compare with the active principles mentioned by Sir Isaac Newton?