EVOLUTIONARY MATHEMATICS AND SCIENCE FOR LIFE CONTINGENCY INVESTIGATION

Tsao, Hung-ping (2019). Evolutionary mathematics and science for life contingency investigation. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 1, Number 3, March 2019; 72 pages. Lenox Institute Press, PO Box 405, Newtonville, NY, 12128-0405, USA. No. STEAM-VOL1-NUM3-MAR2019; ISBN 978-0-9890870-3-2. ---------------ABSTRACT: This chapter will start with the accumulation function and use the geometric point of view to generalize and simplify the theory of interest. Then survey the laws of mortality from both points of view of stochastic theory and traditional actuaries. There is a thorough discussion and simple visualization of Balducci and uniform distribution of deaths assumptions of mortality rates of fractional ages. Two least square-fit cubic survivorship functions for fitting the Male Table of 1958 CSO are presented. Various complicated exposure formulas for a mortality study are obtained by a simple inspection of the valuation schedule in demography. Life insurance and annuities are first introduced in three different points of view: deterministic, stochastic and dynamic. Then the uniform representation of a general life contingency function and its derivative is defined in such a fashion that deferred, term, endowment, life insurance and life annuity with level or varying benefit and premium can be treated all in one shot

EVOLUTIONARY MATHEMATICS AND ARTS FOR SUDOKU INTIMACY INVESTIGATION

Tsao, Hung-ping (2019). Evolutionary mathematics and arts for sudoku intimacy investigation. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 1, Number 4, April 2019; 103 pages. Lenox Institute Press, PO Box 405, Newtonville, NY, 12128-0405, USA. No. STEAM-VOL1-NUM4-APR2019; ISBN 978-0-9890870-3-2. ---------------ABSTRACT: This chapter contains the following unique features: 1) Providing “step-by- step” Sudoku solving procedures; 2) Recording the entire solving process by using “subscripts” and “annotations”; 3) Training the beginners into champion players with enabling “kungfu skills” coupled with surprisingly easy measures - letting you conquer down all puzzles. ---------------The Sudoku world can be divided and conquered via the following approaches: 1) Illuminating with magic mirrors; 2) Drilling with skill-sharpening puzzles; 3) Trouble-shooting with number pairing tests

EVOLUTIONARY MATHEMATICS AND SCIENCE FOR NUMBERS INTRICACY INVESTIGATION

Tsao, Hung-ping (2019). Evolutionary mathematics and science for numbers intricacy investigation. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 1, Number 2, February 2019; 160 pages. Lenox Institute Press, Newtonville, NY, 12128-0405, USA. No. STEAM-VOL1-NUM2-FEB2019; ISBN 978-0-9890870-3-2. ---------------ABSTRACT: All foreseeable approaches to derive polynomial expressions for the power-sum of the natural sequence are presented here. Throughout, binomial coefficients play as the key role of linking together the product-sums and the power-sums. The author takes the opportunity to sort out the intricate liaisons among Stirling numbers of both kinds, Euler numbers of two orders, ordered and Eulerian Bell polynomials. He further generalizes the related numbers based on the natural sequence to those that are arithmetically progressive sequence based so that various structures of triangular arrays can be built on top of different underlying bases

EVOLUTIONARY MATHEMATICS AND ARTS FOR SUDOKU PROFICIENCY INVESTIGATION

Tsao, Hung-ping (2019). Evolutionary mathematics and arts for sudoku proficiency investigation. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 1, Number 5, May 2019; 123 pages. Lenox Institute Press, PO Box 405, Newtonville, NY, 12128-0405, USA. No. STEAM-VOL1-NUM5-MAY2019; ISBN 978-0-9890870-3-2. ---------------ABSTRACT: In contract to Number 4 of Volume 1 (Sudoku 1.0) in which readers are divided into begginers and veterans, no distinction would be made here in Sudoku 2.0 based on the belief that all minds are created equal in the world of Sudoku. The unique features of this chapter are as follows: 1) Educational and situational moves are introduced for proficiency elevation. 2) Most puzzles are with 17 initial values that require 64 steps to complete. 3) Plenty of hard puzzles are provived in the end for readers to practice

EVOLUTIONARY MATHEMATICS AND ARTS FOR SUDOKU ECSTASY INVESTIGATION

Tsao, Hung-ping (2020). Evolutionary mathematics and arts for Sudoku ecstasy investigation. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 2, Number 5, May 2020; 54 pages. Lenox Institute Press, PO Box 405, Newtonville, NY, 12128-0405, USA. No. STEAM-VOL2-NUM5-MAY2020; ISBN 978-0-9890870-3-2. ---------------ABSRACT: In contract to Number 4 of Volume 1 (Sudoku 1.0) in which readers are elevated from beginners to veterans and Number 5 of Volume 1 (Sudoku 2.0) where educational and situational moves are introduced for proficiency elevation, this chapter is intended for readers to have the most fun with all puzzles with 17 initial values that require 64 steps to complete. Other than the introduction, no further instructions will be given. 63 puzzles are divided into 9 sections in such a fashion that each section contains 7 puzzles followed by their annotated solutions so that readers can steadily improve their solving skills to reach the optimal ecstasy

EVOLUTIONARY MATHEMATICS AND ARTS FOR TALK ELEGANCY INVESTIGATION

Tsao, Hung-ping (2019). Evolutionary mathematics and arts for talk elegancy investigation. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 1, Number 1, January 2019; 68 pages. Lenox Institute Press, Newtonville, NY, 12128-0405, USA. No. STEAM-VOL1-NUM1-JAN2019; ISBN 978-0-9890870-3-2. --------------- ABSTRACT: The author has been motivated by Tower of Hanoi and Einstein Riddle to provide innovative ways of solving various types of problems such as Twin knight, The ballot box, Ties in matching pennies, The theater row and Same birthday among classmates. In addition, mutual independency versus mutual exclusiveness, current life insurance models deficiency and Sudoku puzzles efficiency will be discussed

General Eulerian Numbers and Eulerian Polynomials

In this paper, we will define general Eulerian numbers and Eulerian polynomials based on general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian numbers and polynomials to the general Eulerian polynomials and numbers.Comment: 14 page

EVOLUTIONARY MATHEMATICS AND ARTS FOR EAST CLEAR WEST BRIGHT 東明西燦：業餘與職業數學家的寫照

Tsao, Hung-ping 曹恆平 (2022). Evolutionary Mathematics and Arts for East Clear West Bright 東明西燦：業餘與職業數學家的寫照 . In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 4, Number 3, March 2022; 614 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAM-VOL4-NUM3-MAR2022; ISBN 978-0-9890870-3-2. ...........ABSTRACT: This is a crisscross autobiographical narrative of two mathematicians (amateur versus professional) both born in the Spring prior to the outburst of World War II in the hostile (east vs. west) countries, respectively, and each having an extremely caring great mother. ........KEYWORDS: Mathematician, Amateur, Professional, Blind, Unorthodox, Tortuou

CRACKING SUDOKU DOWN COMPLETELY

Tsao, Hung-ping (2023). Cracking Sudoku down completely. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 5, NUMBER 6A, June 2023; 125 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAM-VOL5-NUM6A-JUN2023; ISBN 978-0-9890870-3-2. ...... ABSTRACT: This is an e-version of the author’s paperback book in Chinese published ten years ago, the English version of which will also be e-published shortly. Based on his ten years of experience in challenging numerous Sudoku puzzles devised by the world’s top-ranked masters, the author had developed a unique step-by-step puzzle solving procedure by way of using subscripts and brief annotations. This unique feature can manifest the logical underpinning of puzzle-unfolding process and thus enable readers, especially the seniors and minors, walk through with the author the clear path of how a Sudoku puzzle being solved

CARING LETTERS FROM MY LOVING MOTHER 慈暉魚雁昭

Tsao, Hung-ping 曹恆平 (2021). Caring Letters From My Loving Mother 慈暉魚雁昭 . In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. 王抗曝 and Tsao, Hung-ping 曹恆平 (editors). Volume 3, Number 12, December 2021; 111 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAM-VOL3-NUM12-DEC2021; ISBN 978-0-9890870-3-2. ............ABSTRACT: This is a collection of letters from his mother in Taiwan reflecting all sorts of hardships encountered by the author during the first ten years of study and research in a couple of the Midwestern States of America. Her caring and love of his son have been omnipresent in between lines of her unpretentious words. 個人浪跡天涯期間，慈母來信七十多封，今謹原文存真錄出，從中或可一窺遊子十年寒窗苦況斑斑歷歷如昨之實境，讀者諒能推而廣之, 見證那段歲月的台灣風貌, 以及留學生涯