Citric acid is an important organic substance whose marketing concerns various fields. Nevertheless, until 1997 the scientific literature reported little information about the process of crystallization by cooling thr...Citric acid is an important organic substance whose marketing concerns various fields. Nevertheless, until 1997 the scientific literature reported little information about the process of crystallization by cooling through which the commercial product is obtained. In particular, the available studies were aimed to investigate only the kinetics of nucleation and crystal growth neglecting some effective aspects of the industrial crystallization in mechanically stirred apparatus. In order to fill that sci-tech gap, the Department of Chemical Engineering at the University ＂La Sapienza＂ of Rome decided to lead a long and meticulous experimental research on the crystallization in discontinuous （batch） of CAM （citric acid monohydrate） in the allotropic form that is stable at room temperature. Due to the number of people involved in that pioneering work, carried out in the historic laboratories of＂La Sapienza＂ （Faculty of Engineering）, and motivated by the publication of related M.Sc. dissertations and research papers, such collective effort was called ＂School of Industrial Crystallization＂. Among the graduate students in Chemical Engineering that 17 years ago participated in that fruitful experience there was also the author who, under the supervision of Prof. Barbara Mazzarotta, had the specific task of assessing the effects on CAM of changing the crystallization operating conditions until their optimization; the achievements are briefly illustrated in this paper.展开更多
As expounded in some recent mathematical conferences, this research on that amazing source of algebraic ideas known as Fermat＇s equation is aimed to prove how Fermat triples can be limited until the impossible existe...As expounded in some recent mathematical conferences, this research on that amazing source of algebraic ideas known as Fermat＇s equation is aimed to prove how Fermat triples can be limited until the impossible existence through a criterion of incompatible parities related to unexplored properties of the binomial coefficients. In this paper, the authors use a technique based on the analysis of four numbers and their internal relations with three basic compulsory factors. It leads to the practical impossibility to find any triple of natural numbers candidate to satisfy Fermat＇s equation, because when the authors try to meet a condition between parity and range the authors are compelled to violate the other one, so that they are irreducibly alternative. In particular, there is a parity violation when the authors choose all the basic factors in the allowed range and the authors obtain exceeding values of one of the involved variables when the authors try to restore the parity. Since Fermat＇s last theorem would consequently be demonstrated, many readers could recall the never found elementary proof of FLT （Fermat＇s last theorem） claimed by Pierre de Fermat. The authors are not encouraging such an interpretation because this paper is intended as a journey into Fermat＇s equation and the reader＇s attitude should be towards the algebraic achievements here proposed, with their possible hidden flaws and future developments, rather than to legendary problems like Fermat＇s riddle.展开更多
Far from being equivalent to host the process, the vessels play an active role in the crystallization thanks to their differently shaped bottoms. It was clearly pointed out through a meticulous experimental research o...Far from being equivalent to host the process, the vessels play an active role in the crystallization thanks to their differently shaped bottoms. It was clearly pointed out through a meticulous experimental research on the batch crystallization of CAM （citric acid monohydrate） carried out in the years 1997-1998 by the author at the historic laboratories of＂La Sapienza＂ University of Rome. Such pioneering M.Sc. thesis, supervised by Prof. Barbara Mazzarotta （Department of Chemical Engineering）, was already summarized in an informative essay but, since the crystallization operating conditions to optimize were illustrated ＂collectively＂, it seemed necessary a further paper expounding uniquely the geometry effect. Our aim is to use all the data, collected and simulated, in order to show why the round-bottomed crystallizer performed better than the conical-bottomed one with the CAM from aqueous solutions, and why we should discard the flat-bottomed crystallizers.展开更多
As former Fermatist, the author tried many times to prove Fermat＇s Last Theorem in an elementary way. Just few insights of the proposed schemes partially passed the peer-reviewing and they motivated the subsequent fr...As former Fermatist, the author tried many times to prove Fermat＇s Last Theorem in an elementary way. Just few insights of the proposed schemes partially passed the peer-reviewing and they motivated the subsequent fruitful collaboration with Prof. Mario De Paz. Among the author＇s failures, there is an unpublished proof emblematic of the FLT＇s charming power for the suggestive circumstances it was formulated. As sometimes happens with similar erroneous attempts, containing out-of-context hints, it provides a germinal approach to power sums yet to be refined.展开更多
文摘Citric acid is an important organic substance whose marketing concerns various fields. Nevertheless, until 1997 the scientific literature reported little information about the process of crystallization by cooling through which the commercial product is obtained. In particular, the available studies were aimed to investigate only the kinetics of nucleation and crystal growth neglecting some effective aspects of the industrial crystallization in mechanically stirred apparatus. In order to fill that sci-tech gap, the Department of Chemical Engineering at the University ＂La Sapienza＂ of Rome decided to lead a long and meticulous experimental research on the crystallization in discontinuous （batch） of CAM （citric acid monohydrate） in the allotropic form that is stable at room temperature. Due to the number of people involved in that pioneering work, carried out in the historic laboratories of＂La Sapienza＂ （Faculty of Engineering）, and motivated by the publication of related M.Sc. dissertations and research papers, such collective effort was called ＂School of Industrial Crystallization＂. Among the graduate students in Chemical Engineering that 17 years ago participated in that fruitful experience there was also the author who, under the supervision of Prof. Barbara Mazzarotta, had the specific task of assessing the effects on CAM of changing the crystallization operating conditions until their optimization; the achievements are briefly illustrated in this paper.
文摘As expounded in some recent mathematical conferences, this research on that amazing source of algebraic ideas known as Fermat＇s equation is aimed to prove how Fermat triples can be limited until the impossible existence through a criterion of incompatible parities related to unexplored properties of the binomial coefficients. In this paper, the authors use a technique based on the analysis of four numbers and their internal relations with three basic compulsory factors. It leads to the practical impossibility to find any triple of natural numbers candidate to satisfy Fermat＇s equation, because when the authors try to meet a condition between parity and range the authors are compelled to violate the other one, so that they are irreducibly alternative. In particular, there is a parity violation when the authors choose all the basic factors in the allowed range and the authors obtain exceeding values of one of the involved variables when the authors try to restore the parity. Since Fermat＇s last theorem would consequently be demonstrated, many readers could recall the never found elementary proof of FLT （Fermat＇s last theorem） claimed by Pierre de Fermat. The authors are not encouraging such an interpretation because this paper is intended as a journey into Fermat＇s equation and the reader＇s attitude should be towards the algebraic achievements here proposed, with their possible hidden flaws and future developments, rather than to legendary problems like Fermat＇s riddle.
文摘Far from being equivalent to host the process, the vessels play an active role in the crystallization thanks to their differently shaped bottoms. It was clearly pointed out through a meticulous experimental research on the batch crystallization of CAM （citric acid monohydrate） carried out in the years 1997-1998 by the author at the historic laboratories of＂La Sapienza＂ University of Rome. Such pioneering M.Sc. thesis, supervised by Prof. Barbara Mazzarotta （Department of Chemical Engineering）, was already summarized in an informative essay but, since the crystallization operating conditions to optimize were illustrated ＂collectively＂, it seemed necessary a further paper expounding uniquely the geometry effect. Our aim is to use all the data, collected and simulated, in order to show why the round-bottomed crystallizer performed better than the conical-bottomed one with the CAM from aqueous solutions, and why we should discard the flat-bottomed crystallizers.
文摘As former Fermatist, the author tried many times to prove Fermat＇s Last Theorem in an elementary way. Just few insights of the proposed schemes partially passed the peer-reviewing and they motivated the subsequent fruitful collaboration with Prof. Mario De Paz. Among the author＇s failures, there is an unpublished proof emblematic of the FLT＇s charming power for the suggestive circumstances it was formulated. As sometimes happens with similar erroneous attempts, containing out-of-context hints, it provides a germinal approach to power sums yet to be refined.
