Analysis and Prbability over Infinite Extensions of a Local Field

We consider an infinite extension K of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. K is equipped with an inductive limit topology; its conjugate K; is a completion of K with respect to a topology given by certain explicitly written semi-norms. We construct and study a Gaussian measure, a Fourier transform, a fractional differentiation operator and a cadlag Markov process on K. If we deal with Galois extensions then all these objects are Galois-invariant.     

弦图扩张与最优排序

弦图是一类特殊的完美图,以具有完美消去顺序为特征．由弦图扩张引出一系列序列性组合优化问题,沟通了图论、数值分析及最优排序等领域的若干研究课题．本文将论述我们的一些观点和研究结果．     

Kan Extensions of Internal Functors. Algebraic Approach

We investigate the question of the Kan extension in the case when all categories and functors are internal in the category of groups. Under certain assumptions we establish the necessary and sufficient conditions for the existence of internal Kan extensions. Questions related to this problem are also discussed.     

A N. Bourbaki type General Theory and the Properties of Contracting Symbols and Corresponding Contracted Forms

A system of contracting symbols is introduced for a N. Bourbaki type general mathematical theory corresponding to a general classical mathematical theory T.     

On Generalized Friedrichs and Krein‐von Neumann Extensions and Canonical Systems

Let S be a densely defined and closed symmetric relation in a Hilbert space ℋ︁ with defect numbers (1,1), and let A be some of its canonical selfadjoint extensions. According to Krein's formula, to S and A corresponds a so‐called Q‐function from the Nevanlinna class N . In this note we show to which subclasses N _γ of N the Q‐functions corresponding to S and its canonical selfadjoint extensions belong and specify the Q‐functions of the generalized Friedrichs and Krein‐von Neumann extensions. A result of L. de Branges implies that to each function Q ∈ N there corresponds a unique Hamiltonian H such that Q is the Titchmarsh‐Weyl coefficient of the two‐dimensional canonical system J_y′ = —zHy on [0, ∞) where Weyl's limit point case prevails at ∞. Then the boundary condition y(0) = 0 corresponds to a symmetric relation T_min with defect numbers (1,1) in the Hilbert space L²_H, and Q is equal to the Q‐function with respect to the extension corresponding to the boundary condition y₁(0) = 0. If H satisfies some growth conditions at 0 or ∞, wepresent results on the corresponding Q‐functions and show under which conditions the generalized Friedrichs or Krein‐von Neumann extension exists.     

Synthesis and properties of thermally reversible polyesters

Thermally reversible polyesters were obtained by the ester formation reaction of thermoplastic polyesters with hydroxyl end groups and the diacid anhydride of tetra carboxylic acid as a thermally reversible chain extender. Typical example of the thermally reversible polyesters was obtained by the reaction of PBT (polyburylene terephthalate) and PMA (pyromellitic dianhydride). This material having twice as large molecular weight as the original PBT exhibited almost the same melt viscosity as the original. Also that thermally reversible chain extension reaction occurred without unfavorable side reaction such as cross-linking. This material shows both good processability and superior mechanical properties due to its thermally reversible characters.     

New segmented poly(ester‐urethane)s from renewable resources

The physical and mechanical properties of aliphatic homopolyesters from monomers obtainable from renewable resources, namely, 1,3‐propanediol and succinic acid, were improved by their combination with aromatic urethane segments capable of establishing strong intermolecular hydrogen bonds. Segmented poly(ester‐urethane)s were synthesized from dihydroxy‐terminated oligo(propylene succinate)s chain‐extended with 4,4′‐diisophenylmethane diisocyanate. The newly synthesized materials were exhaustively characterized by ¹H NMR spectroscopy, size exclusion chromatography, differential scanning calorimetry, dynamic mechanical analysis, and with respect to their main static mechanical properties, an Instron apparatus was used. The average repeat number of the hard segments, evaluated by NMR, ranged from 4 to 9, whereas that of the flexible segments was about 14. The degree of crystallinity, glass‐transition temperature, melting point, tensile strength, elongation, and Young's modulus were influenced by the ratio between hard and soft segments of the segmented copolymer in a predictable way. The results demonstrated that poly(ester‐urethane)s from 1,3‐propanediol and succinic acid are promising thermoplastics. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 630–639, 2001     

High‐molecular‐weight polyisobutylenes (PIBs) and PIB networks from liquid PIBs by thiol‐ene clicking

We report the synthesis of high‐molecular‐weight linear polyisobutylenes (PIBs) and PIB networks from low‐molecular‐weight PIB by thiol‐ene click chemistry. Thus, liquid allyl‐telechelic PIB was reacted with small di‐ and tri‐thiols, and the thiolated intermediates chain‐extended by UV‐ or thermally induced free radical initiation to linear and crosslinked products. PIB networks were also prepared by crosslinking SH‐telechelic PIB with a small triallyl compound. Linear products were characterized by ¹H NMR spectroscopy and GPC, and networks by FTIR spectroscopy, extractables, swelling, and permanent set. The effect of reaction conditions (nature of thiol chain extender, concentration of photo‐ and thermal initiators, UV radiation time, and reagent concentrations) on chain extension and crosslinking was investigated. Under well‐defined conditions high‐molecular‐weight PIBs and tight PIB networks were prepared. Thiol‐ene click chemistry provides novel thiolated PIB derivatives and is a useful strategy for the convenient preparation of high‐molecular‐weight rubbery PIBs and tight PIB networks from low‐molecular‐weight PIB precursors. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019