Simple Explanation of the No-Free-Lunch Theorem and Its Implications

The no-free-lunch theorem of optimization (NFLT) is an impossibility theorem telling us that a general-purpose, universal optimization strategy is impossible. The only way one strategy can outperform another is if it is specialized to the structure of the specific problem under consideration. Since optimization is a central human activity, an appreciation of the NFLT and its consequences is essential. In this paper, we present a framework for conceptualizing optimization that leads to a simple but rigorous explanation of the NFLT and its implications.     

Designing delivery districts for the vehicle routing problem with stochastic demands

This paper considers the problem of designing districts for vehicle routing problems with stochastic demands. In particular, demands are assumed to be uncertain at the time when the districts are made, and these are revealed only after the districting decisions are determined. Tabu search and multistart heuristics for this stochastic districting problem are developed and compared. Computational results show that tabu search is superior over multistart.     

A semisynthesis of isepamicin by fragmentation method

Garamine derivative, key intermediate, was obtained from acid cleavage of sisomicin derivative. Its subsequent product was glycosylated with 6-azido-2,3,4-tri-O-benzyl-6-deoxy-α-d-glucopyranosyl chloride using silver triflate as a promoter to give isepamicin.     

Sign inversion of the rotatory power and topology of the surface of gyration of αNiSO4·6H2O

The sign inversion point of the rotatory power of the gyrotropic crystals α-NiSO₄·6H₂O (λ _l=503 nm at 300 K) has been established. The topology of the gyration surface varies greatly in the vicinity of λ _l. We have demonstrated the possibility of using this method of spectrophotometric polarimetry for precise monitoring of the mounting of a gyrotropic crystal in the system “polarizer-crystal-analyzer.” Fiz. Tverd. Tela (St. Petersburg) 40, 1608–1609 (September 1998)     

Nonclassical Field States in Quantum Optics and Particle Physics

The primary aim of the present paper is to draw the attention of particle physicists to new developments in studying squeezed and correlated states of the electromagnetic field, and those working on the latest developments to new findings about multiplicity distributions and other specific effects in quantum chromodynamics. New types of nonclassical states used in quantum optics such as squeezed states, correlated states, and even and odd coherent states (Schrödinger cat states) for one-mode and multimode interactions are reviewed. Their distribution functions are analyzed according to the method first used for multiplicity distributions in high-energy particle interactions. The phenomenon of oscillations of particle distribution functions of squeezed fields is described and related to the phenomenon of oscillations of cumulant moments of some distributions for squeezed and correlated field states. Possible extension of the method to fields different from the electromagnetic field (gluons, pions, etc.) is conjectured, and some predictions of specific effects in nucleus-nucleus interactions at high energies are presented.     

Optimal trading strategy for European options with transaction costs

The European option with transaction costs is studied. The cost of making a transaction is taken to be proportional by a factor λ to the value (in dollars) of stock traded. When there are no transaction costs (i.e. when λ=0) the well-known Black-Scholes strategy tells how to hedge the option. Since no non-trivial perfect hedging strategy exists when λ>0 (see (Ann. Appl. Probab. 5(2) (1995) 327)), we instead try to maximize the expected utility attainable. We seek to understand the effect transaction costs have on the maximum attainable expected utility over all strategies, when λ is small but non-zero. It turns out that transaction costs diminish the expected utility by an amount which has the order of magnitude λ^2/3. We will compute that correction explicitly modulo an error which is small compared to λ^2/3. We will exhibit an explicit strategy whose expected utility differs from the maximum attainable expected utility by an error small in comparison to λ^2/3.     

Multiple melting and crystallization of nylon‐66/montmorillonite nanocomposites

Nylon‐66 nanocomposites were prepared by melt‐compounding nylon‐66 with organically modified montmorillonite (MMT). The organic MMT layers were exfoliated in a nylon‐66 matrix as confirmed by wide‐angle X‐ray diffraction (WAXD) and transmission electron microscopy. The presence of MMT layers increased the crystallization temperature of nylon‐66 because of the heterogeneous nucleation of MMT. Multiple melting behavior was observed in the nylon‐66/MMT nanocomposites, and the MMT layers induced the formation of form II spherulites of nylon‐66. The crystallite sizes L₁₀₀ and L₀₁₀ of nylon‐66, determined by WAXD, decreased with an increasing MMT content. High‐temperature WAXD was performed to determine the Brill transition in the nylon‐66/MMT nanocomposites. Polarized optical microscopy demonstrated that the dimension of nylon‐66 spherulites decreased because of the effect of the MMT layers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2861–2869, 2003     

Basicities of thiazole heterocyclic compounds and the reaction of 3-methyl-2-methylimino-Δ4-thiazolines with ethyl bromoacetate and 2-bromoacetophenone

The pK_a′s of several thiazole heterocyclic compounds have been determined and represent products with significantly high values. Because of their high basicities, sometimes these compounds were able to act as not only nucleophiles but also strong organic bases. 4-Substituted-3-methyl-2-methylimino-Δ⁴-thiazolines 5a-d reacted with ethyl bromoacetate in refluxing benzene, giving the corresponding N-alkylated salts 8a-d , while the products obtained from the reaction with 2-bromoacetophenone in the presence of base were pyrrolothiazines 10b-d.