The Ackermann function. a theoretical,computational, and formula manipulative study

Ackermann's function is of highly recursive nature and of two arguments. It is here treated as a class of functions of one argument, where the other argument defines the member of the class. The first members are expressed with elementary functions, the higher members with a hierarchy of primitive recursive functions. The number of calls of the function needed in a straightforward recursive computation is given for the first members. The maximum depth in the recursion during the evaluation is investigated.Results from tests with the Ackermann function of recursive procedure implementations in ALGOL-60, ALGOL W, PL/I and SIMULA-67 on IBM 360/75 and CD 6600 are given.A SYMBAL formula manipulating program, that automatically solves recurrence relations for the first members of the function class and for the number of calls needed in their straightforward computation, is given.The Ackermann rating of programming languages is discussed.     

Analytical artefacts in the speciation of arsenic in clinical samples

Urine and blood samples of cancer patients, treated with high doses of arsenic trioxide were analysed for arsenic species using HPLC-HGAFS and, in some cases, HPLC-ICPMS. Total arsenic was determined with either flow injection-HGAFS in urine or radiochemical neutron activation analysis in blood fractions (in serum/plasma, blood cells). The total arsenic concentrations (during prolonged, daily/weekly arsenic trioxide therapy) were in the μg mL⁻¹ range for urine and in the ng g⁻¹ range for blood fractions. The main arsenic species found in urine were As(III), MA and DMA and in blood As(V), MA and DMA.With proper sample preparation and storage of urine (no preservation agents/storage in liquid nitrogen) no analytical artefacts were observed and absence of significant amounts of alleged trivalent metabolites was proven. On the contrary, in blood samples a certain amount of arsenic can get lost in the speciation procedure what was especially noticeable for the blood cells although also plasma/serum gave rise to some disappearance of arsenic. The latter losses may be attributed to precipitation of As(III)-containing proteins/peptides during the methanol/water extraction procedure whereas the former losses were due to loss of specific As(III)-complexing proteins/peptides (e.g. cysteine, metallothionein, reduced GSH, ferritin) on the column (Hamilton PRP-X100) during the separation procedure. Contemporary analytical protocols are not able to completely avoid artefacts due to losses from the sampling to the detection stage so that it is recommended to be careful with the explanation of results, particularly regarding metabolic and pharmacokinetic interpretations, and always aim to compare the sum of species with the total arsenic concentration determined independently.     

Model integration and algorithmic transparency in APL

This paper aims to portray concepts like finite differences and integrations to those who lack mathematical background or access to specialized computer programs, but have access to an APL terminal.     

中国部门生产链演化趋势及动态影响分析

研究部门间生产链关系及其演化趋势和生产链上、下游顺次动态影响情况。利用中国1987～2005年不变价序列投入产出表和APL模型,计算发现1987～2005年国民经济中存在四条重要的生产链,分析了这一时期四条生产链的演化趋势。进一步,以“黑色金属矿开采业－黑色金属冶炼及压延加工业－金属制品业”生产链为例,基于向量自回归模型,运用脉冲响应函数和方差分解分析了生产链上、下游部门相互间的动态影响情况。结果有助于确定国民经济总体战略及制定相关产业政策,并在制定经济调控政策时更好地预期政策的时效性。     

Quantitative analysis with linguistic values

The concept of quantitative analysis with linguistic values is set out and discussed. An APL-implemented auxiliary language is presented which makes such analysis operational with regard to humanistic systems where the variables cannot easily be numerically measured. Special emphasis is placed on linguistic approximation which is implemented by an APL-function of 19 statements with a range of approximately 10¹⁰ linguistic values. Examples of the linguistic input-linguistic output characteristics of the language are shown.