Formal solutions of semilinear heat equations

We study formal power series solutions to the initial value problem for semilinear heat equation t_∂u−Δu=f(u) with polynomial nonlinearity f and prove that they belong to the formal Gevrey class G². Next we give counterexamples showing that the solution, in general, is not analytic in time at t=0.     

On universal formal power series

The point source of this work is Seleznev's theorem which asserts the existence of a power series which satisfies universal approximation properties in C^∗. The paper deals with a strengthened version of this result. We establish a double approximation theorem on formal power series using a weighted backward shift operator. Moreover we give strong conditions that guarantee the existence of common universal series of an uncountable family of weighted backward shift with respect to the simultaneous approximation. Finally we obtain results on admissible growth of universal formal power series. We especially prove that you cannot control the defect of analyticity of such a series even if there exist universal series in the well-known intersection of formal Gevrey classes.     

On the predecessor relation in abstract algebras

In this paper we generalize the Dedekind theory of order for the natural numbers N to abstract algebras with arbitrarily many finitary or infinitary operations. For any algebra ??, we introduce an algebraic predecessor relation P?? and its transitive hull P*?? coinciding in N with the unary injective successor function' resp. the >-relation. For some important classes of algebras ??, including Peano algebras (absolutely free algebras, word algebras), the algebraic predecessor relation is well-founded. Hence, its transitive hull, the natural ordering >?? of ??, is a well-founded partial order, which turns out to be a convenient device for classifying Peano algebras with respect to the number of operations and their arities. Moreover, the property of well-foundedness is an efficient tool for giving simple proofs of structure theorems as, e. g., that the class of all Peano algebras is closed under subalgebras and non-void direct products. - Finally, we will show how in the case of a formal language ??, i. e., the Peano algebra ?? of expressions (= terms & formulas), relations P??, resp. P*_?? can be used to define basic syntactical notions as occurences of free and bound variables etc. without any reference to a particular representation (“coding”) of the formal language. MSC: 03B22, 03E30, 03E75, 03F35, 08A55, 08B20.     

An expedient enyne metathesis approach to dysidiolide

A short and efficient enyne metathesis route is reported for the construction of a key intermediate required in the synthesis of dysidiolide thus completing its formal synthesis.     

Smoothness and differentials in positive characteristic

Let u: A → B be a morphism of noetherian local rings. It is known that if u is formally smooth, then Ω _B|A is formally projective. We give several cases in which the converse is true, in the case of rings containing a field of positive characteristic. Work supported by the CEEX program of the Romanian Ministry of Education and Research, Contract 2-CEx06-11-20/2006.     

Fuzzy sets and Boolean-valued universes

A connection between fuzzy sets and Boolean-valued universes is made by developing a formal axiomatic system for fuzzy sets among whose models are suitably interpreted Boolean-valued universes. The formal system is an independent first-order axiomatization of fuzzy set theory which parallels the Zermelo-Fraenkel development of classical set theory.     

New sequent calculi for Visser's Formal Propositional Logic

Two cut‐free sequent calculi which are conservative extensions of Visser's Formal Propositional Logic (FPL) are introduced. These satisfy a kind of subformula property and by this property the interpolation theorem for FPL are proved. These are analogies to Aghaei‐Ardeshir's calculi for Visser's Basic Propositional Logic.     

Neural languages

In order to provide the theoretical framework necessary to study the neural mechanisms underlying languages, we present here a mathematical formalization of some neural behaviors. In such a context: (i) the neuron is defined as a coupling of automata, dealing with the transduction and codifying processes; (ii) the coupling between neurons is measured by a membership relation defined as the ratio between the transmitted and the system entropies; (iii) the attention given to the messages arriving at the system is considered as the difference between the couplings of the excitatory and inhibitory pools of neurons; (iv) the graphs in the neural systems are described by means of these couplings and, finally (v) the semantic productions are described by the fuzzy formal languages accepted by the automata formalized on these graphs. In such a way, both the verbal and neural semantics can now be correlated and experimentally investigated.     

吲哚酚衍生物的结构——式电位关系及电氧化机理

以半经验分子轨道方法计算吲哚酚衍生物的分子结构参数.以主因子分析法和多元线性回归法研究了吲哚酚衍生物的式电位与其分子结构参数间的关系.研究发现,在所选择的19个分子结构参数中,双中心电子交换能(E     

两线阵CCD相机几何指标差异对立体测绘的影响

为了准确、全面地揭示相机几何指标在立体测绘中的误差传播规律,研究了两线阵CCD相机几何指标差异与定位准确度之间的关系.针对两线阵立体测绘特点,分析了影响测绘定位的几何指标差异参量.在前方空间交会地面点计算公式的基础上,推导并建立了两线阵相机定位准确度模型,据此研究了内方位元素标定误差间的几何指标差异对定位准确度的影响规律.结果表明:主点位置x方向误差间的差异对定位准确度影响显著,当其值从1 μm增至2.5 μm时,定位准确度明显下降了60%,焦距f误差间的差异对定位准确度的影响几乎可忽略.本文所建立的模型与相关研究结论对两线阵CCD相机指标的量化与优化设计具有重要指导意义.