Gdel逻辑系统中的函数决定公式问题

以Gdel系统为背景,成功解决了王国俊教授提出的函数决定公式问题即满足什么条件的函数可由逻辑公式导出,或逻辑公式的真值函数的特征如何。然后,又给出了逻辑公式的真度集的特征,进而按照逻辑等价的关系将公式集进行了细致的分类。     

Interplay between local and international journals: The case of Sicily, 1880–1920

In 1884, Giovan Battista Guccia founded first the Circolo Matematico di Palermo and then some years later its journal, the Rendiconti del Circolo Matematico di Palermo. Although historians of mathematics have published a number of works on the Circolo and the Rendiconti, there are very few systematic studies on mathematics in Sicilian periodicals. In our paper, we shall investigate the relationships between the “international” Rendiconti and the “local” proceedings published by the Sicilian academies located in Catania, Messina, and Palermo. What is the image of mathematics that emerges from these journals? What is the presence of Sicilian mathematicians among the authors in the different cases? May we recognize a Sicilian dynamics in mathematics and, if so, in what sense?     

Primitive Contractions of Calabi–Yau Threefolds I

We construct examples of primitive contractions of Calabi–Yau threefolds with exceptional locus being ?¹ × ?¹, ?², and smooth del Pezzo surfaces of degrees ≤ 5. We describe the images of these primitive contractions and find their smoothing families. In particular, we give a method to compute the Hodge numbers of a generic fiber of the smoothing familly of each Calabi–Yau threefold with one isolated singularity obtained after a primitive contraction of type II. As an application, we get examples of natural conifold transitions between some families of Calabi–Yau threefolds.     

Identification of Free and Glycosidically Bound Volatiles and Glycosides by Capillary GC and Capillary GC‐MS in “Lulo del Chocó” (Solanum topiro)

The volatile constituents of lulo del Chocó (Solanum topiro) fruit pulp obtained by liquid‐liquid extraction were analyzed by capillary GC and capillary GC‐MS. In total, 30 components were identified with methyl salicylate, hexadecanoic acid, hexanal, guaiacol, ethyl butanoate, and ethyl acetate being the major components. Chirospecific MDGC analysis revealed the predominance of (R)‐ethyl‐3‐hydroxybutanoate (ee 40%) and the presence of racemic mixtures both of δ‐octalactone and of δ‐decalactone. For γ‐hexalactone, γ‐octalactone, and γ‐decalactone enantiomeric distributions of 22.4 : 77.6, 22.9 : 77.1, and 20.0 : 80.0, (R) : (S), respectively, were determined. Glycosidically bound aroma compounds were identified by capillary GC and capillary GC‐MS after isolation of the glycosidic fraction obtained by Amberlite XAD‐2 adsorption and methanol elution followed by hydrolysis with a commercial pectinase enzyme. In total 13 bound aroma compounds (aglycones) were identified. These aglycones mainly consisted of compounds exhibiting aromatic structures. Additionally, with the aid of capillary GC and capillary GC‐MS (EI and NCI) of trifluoroacetylated derivatives we identified eight glucosides: the novel 3,6‐epoxy‐7‐megastigmen‐5,9‐diol β‐D‐glucopyranoside and the hexyl, benzyl, linalyl oxide (furanic), 2‐phenylethyl, vomifolyl (isomer 1), (6S,9R)‐vomifolyl, and scopoletin β‐D‐glucopyranosides.     

G(o)del逻辑和L*逻辑中公式的真度分布

研究了G\"{o}del逻辑系统和$L^\ast$逻辑系统中公式的真度的分布情况. 结果表明在G\"{o}del逻辑系统和$L^\ast$逻辑系统中含有$n$个原子命题的公式($n$元公式)的真度集分别为$\{\frac{i}{(n+ 1)!}\vert 0 \le i \le (n + 1)! ,i \in N\}$和$\{\frac{i}{(n + 1)!}\vert 0\le i \le 2^n(n + 1)!,i \in N\}.$ 进而得到了G\"{o}del逻辑系统和$L^\ast$逻辑系统中公式的真度集均为[0,1]上的有理数集. 最后,还给出了两系统中公式的相似度,伪距离的分布情况.     

On the classification of first order Gödel logics

We characterize the recursively enumerable first order Gödel logics with △ with respect to validity and non-satisfiability. The finitely valued and four infinitely valued Gödel logics with △ are recursively enumerable, not-satisfiability is recursively enumerable if validity is recursively enumerable. This is in contrast to first order Gödel logics without △, where validity is recursively enumerable for finitely valued and two infinitely valued Gödel logics, not-satisfiability is recursively enumerable if validity is recursively enumerable or 0 isolated in the truth value set.     

Gödel type metrics in Einstein–aether theory

Aether theory is introduced to implement the violation of the Lorentz invariance in general relativity. For this purpose a unit timelike vector field is introduced to the theory in addition to the metric tensor. Aether theory contains four free parameters which satisfy some inequalities in order that the theory to be consistent with the observations. We show that the Gödel type of metrics of general relativity are also exact solutions of the Einstein–aether theory. The only field equations are the 3D Maxwell field equations and the parameters are left free except c ₁ ? c ₃ = 1.