Formal model of internal measurement: Alternate changing between recursive definition and domain equation

We sketch a paradox generally resulting from recursivity, and propose a novel model to express evolutionary processes that requires identification of an interaction with internal measurement. In this model, a paradox is not resolved and the notion of relativity of any resolution is implicit. In a dynamical system a certain transition rule is used recursively along time. If one takes the foundation (or context) of recursivity into consideration, one obtains a fixed point or one confronts a paradox. In order to resolve this paradox, we adopt Scott's technical way to identify the form of a fixed point with a domain equation and to obtain a reflective domain, however we simultaneously show that any resolution is destined to be relative. In utilizing this notion, we construct a model of dynamical process by embedding a measurement process in one time step. Any time transition involves the process of doubting the foundation of a transition rule leading to a fixed point. Solving it and obtaining a reflexive domain is used as a new transition rule. Also, this process perpetually proceeds along time, and then the system perpetually proceeds while any solution is destined to be relative. We illustrate this type of model by using a dynamically changing contraction mapping as the interface of state and transition rule. Finally, we show that one can formalize emergent properties by using this model and discuss the relationship between endo-physics and internal measurement.     

Isochroman-3-ones via site-selective ring opening of benzocyclobutenones promoted by lithium tetramethylpiperidide and reaction with aromatic aldehydes

In the presence of Li-TMP and an aromatic aldehyde, benzocyclobutenone undergoes an unusual heterolytic C(1)---C(4) bond fission, and subsequent reaction with the aldehyde gives, after acidic workup, isochroman-3-one in high yield.     

Calcium phosphate-vanadate apatite (CPVAP)-catalyzed aerobic oxidation of propargylic alcohols with molecular oxygen

Calcium phosphate-vanadate apatite (CPVAP) works effectively as a catalyst for the aerobic oxidation of propargylic alcohols to the corresponding carbonyl compounds under an atmospheric pressure of molecular oxygen. Moreover, CPVAP can be readily separated by filtration and reused at least 10 times without appreciable loss of the catalytic activity.     

Enantio- and diastereomerically pure threo-homoallylic alcohols via highly stereoselective reduction of α-methyl-β,γ-unsaturated ketones

Reduction of α-methyl-β,γ-unsaturated ketones with L-Selectride proceeded with high $\text{threo}$-selectivity to afford $\text{threo}$-β-methyl homoallylic alcohols of high enantio- and diastereomerical purities.     

Development of mast cells

Mast cells are progeny of the multipotential hematopoietic stem cell (MHSC). Mast cell-committed progenitors (MCPs) leave hematopoietic tissues, migrate in peripheral blood, invade to connective or mucosal tissue, proliferate and differentiate to morphologically identifiable mast cells. Phenotype of mast cells (connective tissue-type or mucosal type) is determined by the site of lodgment of MCPs. Most progeny of the multipotential hematopoietic stem cell lose proliferation potential after maturation, but connective tissue-type mast cells (CTMCs) possess appreciable proliferation potential after maturation. Even after functioning by degranulation, CTMCs proliferate and restore the original morphology. The most important cytokine for development and survival of mast cells is KIT ligand, and the KIT receptor tyrosine kinase is expressed through the whole developmental process of mast cells from MHSC to mature mast cells. The loss-of-function mutation of KIT gene results in depletion of mast cells, whereas its gain-of-function mutation causes mast cell tumors. Since mast cells are involved in various disease processes, intervention in development of mast cells might be beneficial to the treatment.     

The Weight Enumerator of Linear Codes over GF q m) Having Generator Matrix over GF q

We have the relationships between the Hamming weight enumerator of linear codes over GFq ^m which have generator matrices over GFq, the support weight enumerator and the -ply weight enumerator.     

Recent development of ortho-C–H functionalization of aryl sulfoxides through [3,3] sigmatropic rearrangement

Sulfoxide-promoted ortho-C–H functionalization reactions of aromatic compounds have emerged as powerful tools for organic synthesis. Among them, [3,3] sigmatropic rearrangement induced by interrupted Pummerer reaction or electrophilic activation of sulfoxides has proved to be a fruitful strategy due to its versatility and high reaction efficiency. This digest paper mainly focuses on recent progress on C–H functionalization reactions of aryl sulfoxides via [3,3] sigmatropic rearrangement of sulfonium-tethered intermediates.