Multiobjective problems of convex geometry

Under study is the new class of geometrical extremal problems in which it is required to achieve the best result in the presence of conflicting goals; e.g., given the surface area of a convex body $ \mathfrak{x} $ \mathfrak{x} , we try to maximize the volume of $ \mathfrak{x} $ \mathfrak{x} and minimize the width of $ \mathfrak{x} $ \mathfrak{x} simultaneously. These problems are addressed along the lines of multiple criteria decision making. We describe the Pareto-optimal solutions of isoperimetric-type vector optimization problems on using the techniques of the space of convex sets, linear majorization, and mixed volumes.     

Determination of the turbulent Prandtl number in an asymptotic boundary layer with suction

The problem of heat transfer in a turbulent asymptotic boundary layer with suction is solved in the framework of the monoharmonic model. The flow is one dimensional on the average, which is why it is chosen for investigation. The theoretically determined mean and pulsation characteristics of the flow, in particular the turbulent Prandtl number, agree with the experimental results for a boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 74–79, January–February, 1981.     

Chemical synthesis and molecular recognition of phosphatase-resistant analogues of phosphatidylinositol-3-phosphate

The remodeling of phosphatidylinositol polyphosphates in cellular membranes by phosphatases and kinases orchestrates the signaling by these lipids in space and time. To provide chemical tools to study the changes in cell physiology mediated by these lipids, three new metabolically stabilized (ms) analogues of phosphatidylinositol-3-phosphate (PtdIns(3)P) were synthesized. We describe herein the total asymmetric synthesis of 3-methylphosphonate, 3-(monofluoromethyl)phosphonate and 3-phosphorothioate analogues of PtdIns(3)P. From differentially protected D-myo-inositol key intermediates, a versatile phosphoramidite reagent was employed in the synthesis of PtdIns(3)P analogues with diacylglyceryl moieties containing dioleoyl, dipalmitoyl, and dibutyryl chains. In addition, we introduce a new phosphorylation reagent, (monofluoromethyl)phosphonyl chloride, which has general applications for the preparation of "pKa-matched" monofluorophosphonates. These ms-PtdIns(3)P analogues exhibited reduced binding activities with 15N-labeled FYVE and PX domains, as significant 1H and 15N chemical shift changes in the FYVE domain were induced by titrating ms-PtdIns(3)P analogues into membrane-mimetic dodecylphosphocholine micelles. In addition, the PtdIns(3)P analogues with dioleoyl and dipalmitoyl chains were substrates for the 5-kinase enzyme PIKfyve; the corresponding phosphorylated ms-PI(3,5)P2 products were detected by radio-TLC analysis.     

The mathematical background of Lomonosov’s contribution

This is a short overview of the influence of the mathematicians of the Enlightenment on the creative contribution of Mikhaĭlo Lomonosov.     

Mathematics and economics of Leonid Kantorovich

This is a short overview of the life of Leonid Kantorovich and his contribution to the formation of the modern outlook on the interaction between mathematics and economics.     

Nonstandard tools of nonsmooth analysis

This is an overview of the basic tools of nonsmooth analysis which are grounded on nonstandard models of set theory. By way of illustration we give a criterion for an infinitesimally optimal path of a general discrete dynamic system.     

Never lie against truth

This is a short tribute to Aleksandr A. Borovkov on the occasion of his 80th birthday.     

On Infinitesimally Optimal Paths

The concept of infinitesimal optimality is specified for discrete dynamic extremal problems.     

S-tosylsulfene chloride — The first representative of a new class of sulfene halides

A representative of a previously unknown class of S-sulfonylsulfene halides — S-tosylsulfene chloride (1) — was prepared for the first time. It was shown that the reaction of sulfene chloride1 with cyclohexene yieldstrans-2-chlorocyclohexyl-p-toluene thiosulfonate, and the reaction with 1-hexene yields a mixture of 2-chlorohexyl-p-toluene thiosulfonate and 1-chloro-2-hexyl-p-toluene thiosulfonate.M. V. Lomonosov Moscow State University, 119899 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 5, pp. 1217–1218, May, 1992.