A Different Brachistochrone Problem with Counterintuitive Results

A problem similar to the famous brachistochrone problem is examined in which, instead of a smooth curve, the path consists of two straight-line sections, one slant and one horizontal. The condition for minimum sliding time is investigated, producing results that are both counterintuitive and interesting.

Breakdown of a Commonly Practiced Technique in Quantum Mechanics

The dynamically shifted oscillator is investigated quantum mechanically, both analytically and numerically. It is shown that the commonly used method of solving the Schrödinger equation using power series results in incorrect eigenvalues and eigenfunctions.

A Review of Native Hawaiian Benefits Received through the Inflation Reduction Act of 2022

On August 16th, 2022, Public Law 117-169, The Inflation Reduction Act of 2022, was signed into law by the President of the United States, Joseph R. Biden Jr. The Inflation Reduction Act of 2022 provides the Native Hawaiian community an opportunity to engage in activities of climate resilience and adaptation through making funds available to support such actions. This article provides a preliminary policy analysis of the Inflation Reduction Act of 2022 to identify the opportunities presented by this legislation that can provide ecological and cultural benefit to the Native Hawaiian community. Findings suggest policy language included in this Act is broad which emphasizes the need for the Senior Program Director of the Office of Native Hawaiian Relations, who is tasked with fund distribution, to rely upon the knowledge of the Native Hawaiian community and ecological experts to direct funds in a manner that best benefits the Native Hawaiian community.

A Model for Droplet Evaporation

Based on the kinetic theory of gases, a simple model for droplet vaporization, in particular mercury, is developed to study the variation of droplet radius as a function of time. This model is in agreement with more sophisticated models for water, such as the kinetic model and the Kulmala model. Findings indicate that complete evaporation of a 1-mm-radius mercury droplet, in a ventilated room at normal temperatures, should take about 1.8 × 104 seconds or 5 hours. The findings of this study can be utilized to direct further research in the field of toxin remediation.

累托石对水中扑尔敏的吸附性能

对累托石对水中扑尔敏的吸附性能进行了研究,系统地研究了吸附时间、溶液浓度、pH值对其吸附行为产生的影响。实验结果表明:累托石对扑尔敏的吸附速率先快速增大后趋于平缓,反应系统达到吸附平衡的时间约为22 h;在等温吸附研究中,室温下累托石对扑尔敏的最大吸附量为121.76 mg/g,吸附等温线方程符合Langmuir等温模型;吸附行为符合拟二级动力学方程;在pH值为2～8时,吸附量随pH值的升高而增大。

Economical effect of lumen apposing metal stents for treating benign foregut strictures

AIM To evaluate the clinical and economical efficacy of lumen apposing metal stent(LAMS) in the treatment of benign foregut strictures.METHODS A single center retrospective database of patients who underwent endoscopic treatment of benign foregut strictures between January 2014 and May 2017 was analyzed. A control group of non-stented patients who underwent three endoscopic dilations was compared to patients who underwent LAMS placement. Statistical tests performed included independent t-tests and fiveparameter regression analysis RESULTS Nine hundred and ninety-eight foregut endoscopic dilations were performed between January 2014 and May 2017. 15 patients underwent endoscopic LAMS placement for treatment of benign foregut stricture. Thirty-six patients with recurrent benign foregut strictures underwent three or more endoscopic dilations without stent placement. The cost ratio of endoscopic dilation to LAMS(stent, placement and retrieval) is 5.77. Cost effective analysis demonstrated LAMS to be economical after three endoscopic dilation overall.LAMS was cost effective after two dilations in the Postsurgical stricture subgroup. CONCLUSION Endoscopists should consider LAMS for the treatment of benign foregut strictures if symptoms persist past three endoscopic dilations. Post-surgical strictures may benefit from LAMS if symptoms persist after two dilations in a post-surgical. Early intervention with LAMS appears to be a clinically and economically viable option for durable symptomatic relief in patients with these strictures.

Damping of a Simple Pendulum Due to Drag on Its String

A basic classical example of simple harmonic motion is the simple pendulum, consisting of a small bob and a massless string. In a vacuum with zero air resistance, such a pendulum will continue to oscillate indefinitely with a constant amplitude. However, the amplitude of a simple pendulum oscillating in air continuously decreases as its mechanical energy is gradually lost due to air resistance. To this end, it is generally perceived that the main role in the dissipation of mechanical energy is played by the bob of the pendulum, and that the string’s contribution is negligible. The purpose of this research is to experimentally investigate the merit of this assumption. Thus, we experimentally investigate the damping of a simple pendulum as a function of its string diameter and compare that to the contribution from its bob. We find out that although in some cases the effect of the string might be small or even negligible, in general the string can play a significant role, and in some cases even a greater role on the damping of the pendulum than its bob.

A New Formulation of Maxwell’s Equations in Clifford Algebra

A new unification of the Maxwell equations is given in the domain of Clifford algebras with in a fashion similar to those obtained with Pauli and Dirac algebras. It is shown that the new electromagnetic field multivector can be obtained from a potential function that is closely related to the scalar and the vector potentials of classical electromagnetics. Additionally it is shown that the gauge transformations of the new multivector and its potential function and the Lagrangian density of the electromagnetic field are in agreement with the transformation rules of the second-rank antisymmetric electromagnetic field tensor, in contrast to the results obtained by applying other versions of Clifford algebras.

A Mathematical Model for Spread of COVID-19 in the World

In this article, the validity of a previously developed model for Coronavirus pandemic is verified by testing it against the global infection cases complied by the World Health Organization. The results further support the validity of the model and its assumptions as was previously verified by the United States data.

Average Speed in Projectile Motion and in General Motion of a Particle

We calculate the average speed of a projectile in the absence of air resistance, a quantity that is missing from the treatment of the problem in the literature. We then show that this quantity is equal to the time-average instantaneous speed of the projectile, but different from its space-average instantaneous speed. It is then shown that this behavior is shared by general motion of all particles regardless of the dimensionality of motion and the nature of the forces involved. The equality of average speed and time-average instantaneous speed can be useful in situations where the calculation of one is more difficult than the other. Thus, making it more efficient to calculate one by calculating the other.

An Algorithm for Generating Random Numbers with Normal Distribution

A new algorithm is suggested based on the central limit theorem for generating pseudo-random numbers with a specified normal or Gaussian probability density function. The suggested algorithm is very simple but highly accurate, with an efficiency that falls between those of the Box-Muller and von Neumann rejection methods.

Numerical Solution of Differential Equations by Direct Taylor Expansion

A variation of the direct Taylor expansion algorithm is suggested and applied to several linear and nonlinear differential equations of interest in physics and engineering, and the results are compared with those obtained from other algorithms. It is shown that the suggested algorithm competes strongly with other existing algorithms, both in accuracy and ease of application, while demanding a shorter computation time.

Diffraction Pattern of a Rotated Grating

Diffraction patterns of a rotated grating are investigated from both theoretical and experimental points of view. It is shown that as the grating rotates, the angle of deviation of each diffracted line relative to the incident light goes through a minimum, and that the angle between any two successive diffracted lines goes through a minimum value which is the same for all adjacent diffracted lines. It is also shown that the angle between diffraction lines with n=1 and n=-1 is not sensitive to small variations of the grating from being normal to the incident light. Finally, a method is suggested for determining the line distance of a diffraction grating with high accuracy.

Foucault Pendulum and Other Coriolis Effects in Inertial Frames

The purpose of this research is to show that Foaucault pendulum as well as other Coriolis effects, which are normally studied in a rotating coordinate system, can also be analyzed in a fixed reference frame. To this end, Foucault pendulum and other Coriolis effects are studied in inertial reference frames. The approach is simple, yet rigorous, and the results are exactly the same as those obtained in non-inertial reference frames but without resorting to some of the assumptions that are needed in rotating coordinate systems.

The Work of a Normal Force

It is shown that an impulsive force acting on a particle perpendicular to its velocity vector cannot change its direction of motion without increasing its kinetic energy. If the particle’s kinetic energy is to remain unchanged, the impulsive force must have a component in the direction opposite to the direction of motion. This situation is also realized in the case of a continuous force acting perpendicular to the velocity vector of the particle, when the particle's motion is viewed as a sequence of infinitesimal steps.

Federal and State Land Acquisition in Hawaii: Conservation in the Epicenter of Extinction

The Land and Water Conservation Fund Act of 1965, reinstated in 2018 through the John D. Dingell, Jr. Conservation, Management, and Recreation Act, provided the United States Federal Government the ability to acquire and fund land acquisition for the purpose of preservation, development, and public enjoyment. In 2005, the state of Hawaii passed Act 156 which was later amended by Hawaii Revised Statues §173A. Established through this legislation is a land conservation fund providing the state government of Hawaii analogous land acquisition abilities to that of the federal government. It is through these laws that the federal government and state of Hawaii can reinforce the conservation of the fragile Hawaiian tropical rainforest ecosystem. This paper will identify discontinuities as well as opportunities in the implementation of this legislation to provide recommendations to improve the ability of both state and federal government to protect and conserve at risk ecosystems and lands like those present in Hawaii.

Archimedes’ Principle Revisited

Based on Newton’s third law of motion, we present a different but quite general analysis of Archimedes’ principle. This analysis explains the reduction in apparent weight of a submerged object in all cases, regardless of its position in the fluid. We also study the case in which the object rests on the bottom of the container where the net hydrostatic force on it is downward, and explain where in this case the reduction in the apparent weight comes from.

Premelting, Pressure Melting, and Regelation of Ice Revisited

In this article we review some of the most important and relevant literature on the properties of ice. We focus on three of its surface properties, namely, the slipperiness of ice, the phenomena of a string under load passing through a block of ice without cutting the block in half, and pressure melting and adhesion of blocks of ice. We then provide an argument for the most plausible factor responsible for each of these effects.

Maxwell-Boltzmann Distribution in Solids

The velocity distribution functions of particles in one- and three-dimensional harmonic solids are investigated through molecular dynamics simulations. It is shown that, as in the case of dense fluids, these distribution functions still obey the Maxwell-Boltzmann law and the assumption of molecular chaos remains valid even at low temperatures.

Approximate and Invariant Solutions of a Mathematical Model Describing a Simple One-Dimensional Blood Flow of Variable Density

We examine governing equations that could be used to model a one-dimensional blood flow within a pulsating elastic artery that is represented by a tube of varying cross-section. The model is considered from two perspectives. The first represents a singular perturbation theory providing explicit approximate solutions to the model, and the second is based on group theoretical modeling that provides exact solutions in implicit form. The main goal is to compare these two approaches and lay out the advantages and disadvantages of each approach.