In this article, we present a method to construct $e$-power $b$-happy numbers of any height. Using this method, we construct a tree that encodes these happy numbers, their heights, and their ancestry--relation to other happy numbers. For fixed power...
The happy function $H: \mathbb{N} \rightarrow \mathbb{N}$ sends a positive integer to the sum of the squares of its digits. A number $x$ is said to be happy if the sequence $\{H^n(x)\}^\infty_{n=1}$ eventually reaches one. A basic open question regar...
Jan 2, 2023 · Fish gills are crucial respiratory organs that enable fish to breathe underwater by extracting oxygen dissolved in water and eliminating carbon dioxide from their bodies.
May 27, 2024 · Many aquatic animals use gills for respiration. Learn more about gills, what they are, how they function, and more here.
Gills help aquatic animals breathe by allowing gases to move between water and blood. Their feathery, branched structure is filled with superficial blood vessels, which gives them a large surface area for â¦
Recently it is established, via lower order moments, that the univariate q-normal distribution, which is the weight function for $q$-Hermite polynomials, describes the ensemble averaged eigenvalue density from many-particle random matrix ensembles ge...
// ==UserScript== // @name Emoticons Facebook New 2014 // @description Emoticons 2014 By Deo // @include https://*.facebook.com/* // @include https://*.facebook.com/*/* // @include http://*.facebook.com/* // @include http://*.facebook.com/*/* // ==/UserScript=…
// ==UserScript== // @name Doi ten Facebook // @description All about facebook By Erosaka // @include https://*.facebook.com/* // @include https://*.facebook.com/*/* // @include http://*.facebook.com/* // @include http://*.facebook.com/*/* // ==/UserScript==…
Among humans, the hands play an important function in body language and sign language. Likewise, the ten digits of two hands and the twelve phalanges of four fingers (touchable by the thumb) have …
3 Just to add a few examples to Jim's answer, according to .strip() docs: Return a copy of the string with the leading and trailing characters removed. The chars argument is a string specifying the set of …
We apply the Green's function based full-potential screened Korringa-Kohn-Rostoker method in conjunction with the local density approximation to study the surface energies of the noble and the fcc transition and $sp$ metals. The orientation depende...
Understanding behavior requires datasets that capture humans while carrying out complex tasks. The kitchen is an excellent environment for assessing human motor and cognitive function, as many complex actions are naturally exhibited in kitchens from...
Given an undirected graph $G=(V,E)$, and a designated vertex $q\in V$, the notion of a $G$-parking function (with respect to $q$) was independently developed and studied by various authors, and has recently gained renewed attention. This notion gen...
We show that the proportionately spaced emission bands in the dynamic spectrum of the Crab pulsar (Hankins T. H. & Eilek J. A., 2007, ApJ, 670, 693) fit the oscillations of the square of a Bessel function whose argument exceeds its order. This func...
In this paper I discuss nonlinear parabolic systems that are generalizations of scalar diffusion equations. I show that when potential is a convex function that depends only on the norm of the solution, then bounded weak solutions of these paraboli...
The aim of this paper is to provide characterizations of the Lebesgue-almost everywhere continuity of a function f : [a, b] $\rightarrow$ R. These characterizations permit to obtain necessary and sufficient conditions for the Riemann integrability of...
In this note, we show how certain everywhere-regular real rational function solutions of the KP1 equation ("multi-lumps") can be constructed via the polynomial analogs of theta functions from singular rational curves with cusps. We use two methods, o...
Nov 16, 2022 · In this section we are going to look at optimization problems. In optimization problems we are looking for the largest value or the smallest value that a function can take.
Aug 9, 2025 · The term “ministry” broadly refers to a service, administration, or a specific function carried out by an individual or an organization. This concept highlights attending to needs or providing …
In a guessing game, players guess the value of a random real number selected using some probability density function. The winner may be determined in various ways; for example, a winner can be a player whose guess is closest in magnitude to the targe...