Extremum Strategies of Approach of Controlled Objects in Dynamic Game Problems with Terminal Payoff Function

Cybernetics and Systems Analysis - The authors propose a method for solving the problem of approach of controlled objects in dynamic game problems with a terminal payoff function. The method is...     

Resolving-Functions Method for Game Problems of Control with Integral Constraints

The method of resolving functions is investigated as applied to game problems of control with integral constraints. A scheme of the method is proposed that ensures the end of a game within a definite guaranteed time in the class of stroboscopic strategies. The results of comparison of the guaranteed times of this scheme of the resolving-functions method with those of the first direct Pontryagin method for integral constraints are shown.     

Comparison of guaranteed times in conflict-controlled motion

The paper proposes a modified scheme of the method of resolving functions for conflict-controlled processes with a cylindrical terminal set. This scheme ensures that the game is terminated in a definite guaranteed time in the class of stroboscopic strategies without any additional conditions. The guaranteed times of various schemes of the method of resolving functions are compared with that of the first Pontryagin method in terms of convex-valued mappings for a certain structure of the terminal set. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 89–100, July–August 2008.     

Thiocyanate Ion Promoted E ⇌ Z Isomerization of a-Bromo-β,β-Diactivated Electrophilic Olefins: An Apparent High Nucleofugality of NCS−

(E)-β-Chloro-α-phenylcinnamaldehyde and (E)- and (Z)-methyl α-tert-butoxycarbonyl-p-nitro-β-bromocinnamates in the presence of NCS⁻ ion in acetonitrile undergo an (E) ⇌ (Z) isomerization which is faster than the vinylic substitution. (E)- and (Z)-methyl α-cyano-β-mesyloxy- (and β-chloro-) p-nitrocinnamates undergo substitution under similar conditions without preceding isomerization. MO calculations gave the energy differences between the eclipsed and the perpendicular conformers of carbanions ⁻CH₂CH₂X and (NC)₂ČH₂X (X = Cl, NCS). These rotational barriers denote the hyperconjugation stabilization energy resulting from interaction of the C-X bond and the 2p(C⁻) orbital. Both HCA values are high, those for X = Cl being 15–20% higher than for X = NCS. The limited literature data on the nucleofugality of NCS⁻ suggests that it can have a nucleofugality which is not much lower than that of Cl⁻ or Br⁻. Consequently, NCS⁻-catalyzed isomerizations of electrophilic vinyl chlorides and bromides, which involve a 180° internal rotation followed by a faster expulsion of NCS⁻ than of Cl⁻ from the initially formed intermediate carbanion Y'Y⁻C-C(R)(Cl)SCN, are not unreasonable, especially if solvation, which was not included in the calculations, plays an important role in the nucleofuge expulsion process.     

Enthesopathy and tendinopathy in gout: computed tomographic assessment

OBJECTIVE: To establish if computed tomography (CT) imaging, which has proved helpful in detecting intra-articular tophi in gout, can also be used to document gouty enthesopathy and tendinopathy. METHODS: Three patients with tophaceous gout and clinical involvement of the Achilles tendon (two cases) or patellar tendon (one case) were assessed with CT examination and plain radiographs. RESULTS: In the first two cases, CT images revealed linear or nodular high attenuation opacities within the substance of the Achilles tendons and their calcaneal insertion. In case 3, dense linear opacities were seen within the patellar tendon and within its tibial insertion. No such opacities of the tendons and entheses were seen on standard radiographs of these patients. CONCLUSIONS: CT appears to be the imaging method of choice for demonstrating monosodium urate deposits in entheses and tendons in tophaceous gout.     

Squamous cell carcinoma of the urachus

The third documented case of primary squamous cell carcinoma of the urachus in the English literature is reported. The interesting coincidental occurrence of the dermoid cyst of the right ovary and a complete longitudinal septum of the vagina and uterine cervix is described.     

Computed tomography of the knee joint as an indicator of intraarticular tophi in gout

OBJECTIVE: To evaluate the utility of computed tomography (CT) of the knee joint for detecting intraarticular tophaceous deposits. METHODS: A prospective study of 16 patients with gout affecting the knee was conducted. A condition for inclusion in the study was the presence of needle-shaped crystals with negative birefringence in the knee joint synovial fluid. Conventional radiography and CT were performed in each case. RESULTS: Intraarticular opacities in the capsule and the synovium, consistent with the presence of tophaceous deposits, were found in 5 of the 16 patients (9 knee joints). The mean duration of gout was longer in the patients with intraarticular tophi than in those without tophi, and 2 of the patients with tophi had poor tolerance to antihyperuricemic therapy. CONCLUSION: Intraarticular opacities considered to represent tophi were observed in approximately one-third of the patients. The presence of tophi correlated with a longer duration of the disease and a poor tolerance to medication. We therefore suggest that CT of the knees could be useful in the assessment and followup of certain patients with gout.