【正文】 家寶在 《 Science》 上發(fā)表文章說，“中國正在進(jìn)行一場人類歷史上前所未有的現(xiàn)代化進(jìn)程 。 但是，即使在大學(xué)或科研機(jī)構(gòu)，甚至科研主管部門，關(guān)于基礎(chǔ)研究“沒用”或“同實(shí)際脫離”的聲音仍不絕于耳。每一次，科學(xué)巨頭都是伴隨經(jīng)濟(jì)的極度繁盛而產(chǎn)生的。 但基礎(chǔ)研究的份額只占全部研究投入的 5%，遠(yuǎn)遠(yuǎn)低于發(fā)達(dá)國家的 20%。 基礎(chǔ)研究是以自然或社會(huì)為研究對(duì)象，探索和認(rèn)識(shí)自然社會(huì)，求真致知，其動(dòng)機(jī)為好奇。“邊建議、邊施工、邊報(bào)廢”“拍腦袋、拍手掌、拍屁股”。 歌德早就說過 : 在任何一個(gè)方向上 , 我們能夠提出的任何一個(gè)問題 , 前人都早已提出來過。 不要今天在這個(gè)領(lǐng)域工作，明天在那個(gè)領(lǐng)域工作，什么問題都敢發(fā)言。 三者至少必具其一。 3. 用好數(shù)學(xué) ?越簡單越好！ ?不要為數(shù)學(xué)而數(shù)學(xué)（對(duì)于非數(shù)學(xué)家而言），能夠解決你的問題就足夠！ ?不要畏懼?jǐn)?shù)學(xué)，只要靜下心鉆進(jìn)去就會(huì)越來越順手，就會(huì)出現(xiàn)樂趣，就發(fā)現(xiàn)那些那些長篇大論用數(shù)學(xué)來描述和演繹竟然如此簡單！復(fù)雜的社會(huì)行為抽象出來不過就是幾個(gè)數(shù)學(xué)符號(hào)在跳躍！ ?我們所學(xué)過的高等數(shù)學(xué)、統(tǒng)計(jì)概率、運(yùn)籌優(yōu)化知識(shí)，只要用好了，已經(jīng)足夠解決目前大多數(shù)的、人類所能認(rèn)識(shí)到的社會(huì)、經(jīng)濟(jì)、行為方面的研究課題。他在主流經(jīng)濟(jì)學(xué)家中最早意識(shí)到市場原教旨主義和凱恩斯經(jīng)濟(jì)學(xué)的局限，也最早發(fā)現(xiàn)中國改革的創(chuàng)新和美國地位的不再。 ?1969年第一個(gè)諾貝爾經(jīng)濟(jì)科學(xué)獎(jiǎng)發(fā)給計(jì)量經(jīng)濟(jì)學(xué)的兩位創(chuàng)始人：挪威應(yīng)用數(shù)學(xué)家出身的弗里希和荷蘭理論物理學(xué)家出身的廷伯根。 ? 數(shù)學(xué)在經(jīng)濟(jì)學(xué)的應(yīng)用稱為數(shù)理經(jīng)濟(jì)學(xué)，薩繆爾遜是開山鼻祖。才”的，沒有“如果”，就不是科學(xué)的頭腦！ 國內(nèi)不少經(jīng)濟(jì)學(xué)家不喜歡使用“如果”。 ?薩繆爾遜對(duì)經(jīng)濟(jì)問題的分析， 使經(jīng)濟(jì)學(xué)家從傳統(tǒng)的歷史描述和哲學(xué)論證，不僅上升到靜態(tài)的幾何圖像，而且上升到動(dòng)態(tài)的動(dòng)力學(xué)分析。 ?薩繆爾遜 26歲 時(shí)的博士論文，于 1947年以《 經(jīng)濟(jì)分析基礎(chǔ) 》 為名出版。 4. 寫規(guī)范的學(xué)術(shù)論文 ? 科技論文就是要“八股文”！ 科技論文不能寫成散文！ 標(biāo)題 ——摘要 ——引言 ——正文 —— 結(jié)論 ——致謝 ——文獻(xiàn) ——附錄 ? 唐詩宋詞很規(guī)范，誰寫得好，一目了然！就容易評(píng)出誰是高手。 2) the train arriving at the time desired by everyone is utilized by muters from all stations。 從前言看出作者的涉足深度和學(xué)術(shù)觀點(diǎn) 1. Introduction The growing traffic congestion in large cities worldwide has led to economic inefficiency, social disruption, excessive energy consumption and increased levels of pollution. It is generally recognized that the mitigation of these problems requires efficient provision and utilization of public transportation systems. This has bee an important issue of long standing interest to economists and transportation scientists. In the end of 1960s, scholars started to derive the optimal interstation spacings of a rapid transit system which transported the population of an area to one central point, aiming at minimizing the total travel time (Vuchic and Newell, 1968) or maximizing the number of passengers (Vuchic, 1969). ………… . …………………………………………… . The latest studies concerning the transit system modeling, analyses and management can be found in a review paper by De Cea and Fernandez (2021) and a book by Vuchic (2021). Only very limited attention has been paid to the problem of muters’ departure time choice for urban mass transit services. Sumi et al. (1990) presented a stochastic model for optimizing the muters’ departure time and route choices in a mass transit system. They assumed that departure time is mainly dependent on the system’s operational features and the travelers’ appointed time of arrival at the destination. Alfa and Chen (1995) examined a public transportation system with multiple origins and destinations and proposed an algorithm for calculating the peakhour departure time of muters, where muters ride on the first ing bus in a random order. Recently, Kraus and Yoshida (2021) and Kraus (2021) provided economic analyses about the muters’ timeofuse decision, the optimal pricing and the service in an urban mass transit system. In their analyses, apart from the fare ponent, ………………… ………………………………………………………… .. The above studies considered the capacity constraints of transit systems and assumed that if the number of muters waiting at a transit stop exceeds the number of vacant seats on the forthing transit run, then some muters will have to wait for the next run. However, this assumption is not always valid in some metro systems. ………… .. There exists a mon feature in such large cities as Beijing, Hong Kong, London, New York, Moscow and others, that during peak period, some muters continue to board the trains although they have to stand in seriously crowded vehicles. In Beijing, for transporting more muters the authority even deliberately cuts down the number of seats for each transit vehicle. The number of seats provided in each train of the Beijing No. 13 railway line is 96 only, but the maximal number of passengers allowed to board is 944 (the physical capacity). ……… . We also observed that muters are not willing to wait at platforms for a period that is longer than two scheduled headways, but change their arrival times at platforms when the invehicle crowding is extremely serious. It is thus interesting to develop a modeling approach that can consider the standingup phenomena and the invehicle crowding effect. Huang et al. (2021) introduced a crowding cost function for modeling urban mass transit services, ., In this paper, we investigate the equilibrium properties of the peakperiod muting in a mass transit system with multiple origins and a single destination. …… .. Note that the model proposed in this paper is formulated from the mute