Renormalization Horseshoe and Rigidity for Circle Diffeomorphisms with Breaks

In this paper we build the renormalization horseshoe for the circle homeomorphisms, which are C ^2+α -smooth everywhere except for one point, and at that point have a jump in first derivative. We also show that two such homeomorphisms are C ¹-smoothly conjugate for a certain class of rotation numbers, which include non-Diophantine numbers with arbitrarily high rate of growth.     

Titanium–salan‐catalyzed asymmetric sulfoxidations with H2O2: design of more versatile catalysts

Titanium–salan complexes with 3,3’‐diphenyl substituents in the salicylidene rings of the salan ligand are efficient sulfoxidation catalysts, capable of catalyzing the asymmetric oxidation of bulky aryl benzyl sulfides with H₂O₂ with good to high enantioselectivities. In this paper, substituent effects on titanium‐salan‐catalyzed enantioselective oxidation of sulfides to sulfoxides have been systematically investigated. Titanium–salan catalysts with halogen substituents at the 5,5’‐positions (3,3’‐H₂dihydrogen substituted) have been found to catalyze the oxidation of both bulky aryl benzyl sulfides and small alkyl phenyl sulfides with good to high enantioselectivities. Kinetic data witness a direct attack of the sulfide to the electrophilic active oxygen species; a consistent reaction mechanism is proposed. Copyright © 2013 John Wiley & Sons, Ltd.     

On <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-estimates of derivatives of univalent rational functions

We study the growth of the quantity ∫_T|R′(z)|dm(z) for rational functions R of degree n which are bounded and univalent in the unit disk and prove that this quantity can grow like n ^γ , γ > 0, as n → ∞. Some applications of this result to problems of regularity of boundaries of Nevanlinna domains are considered. We also discuss a related result of Dolzhenko, which applies to general (non-univalent) rational functions.     

Limited time commitment: Does competition for providing scarce products always improve the supplies?

In addition to the fact that goods and services typically become scarce because resources are scarce, scarcity involves a psychological aspect. When a product is limited in availability, or perceived as being limited, it becomes more attractive. As a result, as long as the product is viewed as scarce, a surplus in supplies implies an increase in consumption. Motivated by fresh-water scarcity, we address the problem of dynamic interaction between two firms committing to provide water supply within a limited time horizon. We find that competition does not necessarily reduce product scarcity compared to the monopolistic industry. In particular, commitment-based market equilibrium is characterized by a critical duration of the supply contract. Duopolistic competition within this duration is reminiscent of the conventional quantity competition—the supply grows and the price drops compared to the monopolistic output. On the other hand, a longer contract leads to a different operational outcome—the monopoly becomes gradually more beneficial in terms of supplies and, as the time horizon grows, even overwhelmingly advantageous, thereby resulting in lower scarcity of the products.     

Utility of biodegradable plasmonic nanoclusters in photoacoustic imaging

Plasmonic metal nanoparticles are used in photoacoustic imaging as contrast agents because of their resonant optical absorption properties in the visible and near-IR regions. However, the nanoparticles could accumulate and result in long-term toxicity in vivo, because they are generally not biodegradable. Recently, biodegradable plasmonic gold nanoclusters, consisting of sub-5 nm primary gold nanoparticles and biodegradable polymer stabilizer, were introduced. In this Letter, we demonstrate the feasibility of biodegradable nanoclusters as a photoacoustic contrast agent. We performed photoacoustic and ultrasound imaging of a tissue-mimicking phantom with inclusions containing nanoclusters at various concentrations. The results indicate that the biodegradable gold nanoclusters can be used as effective contrast agents in photoacoustic imaging.     

How to look for supersymmetry under the LHC lamppost

We apply a model-independent, agnostic approach to the collider phenomenology of supersymmetry, in which all mass parameters are taken as free inputs at the weak scale. We consider the gauginos, Higgsinos, and the first two generations of sleptons and squarks, and analyze all possible mass hierarchies among them (4×8!=161,280 in total) in which the lightest superpartner is neutral, leading to missing energy. In each case, we identify the full set of the dominant decay chains originating from the lightest colored superpartner. Our exhaustive search reveals several quite dramatic yet unexplored multilepton signatures with up to 8 isolated leptons (plus possibly up to 2 massive gauge or Higgs bosons) in the final state. Such events are spectacular, background-free for all practical purposes, and may lead to a discovery in the very early stage (～10 pb(-1)) of LHC operations at 7?TeV.     

Ultrasound attenuation in ferrofluids

The absorption of acoustic energy by internal degrees of freedom of short chains is proposed as a new viable mechanism of ultrasound attenuation in ferrofluids. It is demonstrated that even though the volume fraction of the chains may be quite small, such an effect may reach the order of magnitude of viscous damping. In addition, by investigating the statistical properties of dimers in ferrofluids, it is shown that an applied magnetic field modifies the sound attenuation in a highly anisotropic manner. The proposed mechanism provides new insight into the fundamental issue of colloidal response, and, in particular, may lead to its utilization in novel experimental concepts.