A variant of Shelah's characterization of Strong Chang's Conjecture

Shelah considered a certain version of Strong Chang's Conjecture which we denote , and proved that it is equivalent to several statements, including the assertion that Namba forcing is semiproper. We introduce an apparently weaker version, denoted , and prove an analogous characterization of it. In particular, is equivalent to the assertion that the the Friedman‐Krueger poset is semiproper. This strengthens and sharpens results by Cox and sheds some light on problems posed by Usuba, Torres‐Perez and Wu.     

Metal oxidation states in biological water splitting

A central question in biological water splitting concerns the oxidation states of the manganese ions that comprise the oxygen-evolving complex of photosystem II. Understanding the nature and order of oxidation events that occur during the catalytic cycle of five S_i states (i = 0–4) is of fundamental importance both for the natural system and for artificial water oxidation catalysts. Despite the widespread adoption of the so-called “high-valent scheme”—where, for example, the Mn oxidation states in the S₂ state are assigned as III, IV, IV, IV—the competing “low-valent scheme” that differs by a total of two metal unpaired electrons (i.e. III, III, III, IV in the S₂ state) is favored by several recent studies for the biological catalyst. The question of the correct oxidation state assignment is addressed here by a detailed computational comparison of the two schemes using a common structural platform and theoretical approach. Models based on crystallographic constraints were constructed for all conceivable oxidation state assignments in the four (semi)stable S states of the oxygen evolving complex, sampling various protonation levels and patterns to ensure comprehensive coverage. The models are evaluated with respect to their geometric, energetic, electronic, and spectroscopic properties against available experimental EXAFS, XFEL-XRD, EPR, ENDOR and Mn K pre-edge XANES data. New 2.5 K ⁵⁵Mn ENDOR data of the S₂ state are also reported. Our results conclusively show that the entire S state phenomenology can only be accommodated within the high-valent scheme by adopting a single motif and protonation pattern that progresses smoothly from S₀ (III, III, III, IV) to S₃ (IV, IV, IV, IV), satisfying all experimental constraints and reproducing all observables. By contrast, it was impossible to construct a consistent cycle based on the low-valent scheme for all S states. Instead, the low-valent models developed here may provide new insight into the over-reduced S states and the states involved in the assembly of the catalytically active water oxidizing cluster.     

Extreme red shifted SERS nanotags

Surfaced enhanced Raman scattering (SERS) nanotags operating with 1280 nm excitation were constructed from reporter molecules selected from a library of 14 chalcogenopyrylium dyes containing phenyl, 2-thienyl, and 2-selenophenyl substituents and a surface of hollow gold nanoshells (HGNs). These 1280 SERS nanotags are unique as they have multiple chalcogen atoms available which allow them to adsorb strongly onto the gold surface of the HGN thus producing exceptional SERS signals at this long excitation wavelength. Picomolar limits of detection (LOD) were observed and individual reporters of the library were identified by principal component analysis and classified according to their unique structure and SERS spectra.     

Reflection and transmission of a compression wave at a tunnel portal

Analyses are made of the interaction of the nonlinearly steepened, compression wavefront generated by a high-speed train in a tunnel with the tunnel portal ahead of the train. The ‘micro-pressure’ pulse emitted from the portal can rattle structures in nearby buildings, and the expansion wave reflected back towards the train can cause discomfort to passengers. It is concluded that the usual simplified approximation of one-dimensional propagation within the tunnel provides an adequate representation of interactions of the wave with the portal, and also with ‘windows’ in the tunnel wall near the portal. It is shown how a discrete distribution of windows can be used to produce a reflected expansion wave that varies linearly across the wavefront, and how the thickness of that wavefront can be made many times larger than the thickness of the incident compression wave profile. A detailed analysis of the wave radiated from the portal reveals that cumulative nonlinear effects of propagation over long distances make little or no contribution to the free-space radiation of the micro-pressure wave.     

Measuring the two-dimensional structure of a wavy water surface optically: A surface gradient detector

A new method of measuring the slopes of a water surface covered with short waves is developed. A camera is placed far above the water surface looking downward so that it receives only approximately vertical rays of light emerging from the water surface from a source below. A large lens is positioned horizontally underwater. A plane light source in the form of a translucent colored screen is placed horizontally in the focal plane below this lens. Corresponding to each value of water surface slope, regardless of observer position, there is one and only one point of origin on the color screen from which light rays can enter the camera. When the color screen has a suitable two-dimensional color pattern, we are able to detect the gradient of the surface elevation throughout the field of view of the camera. This refraction slope detector has been used to find statistical properties of short wind waves in a wind-wave channel where a broad angular beam width of capillary ripples and short gravity waves contribute to the surface slopes. In these experiments waves were generated by winds ranging from 5 m/s to 10 m/s at a fetch of 24 m. The wavenumber spectra of short wave slopes have two distinguishing features: a dip at the capillary-gravity transition and steep slopes in the capillary range. Surface shapes resembling the shape of solitary capillary-gravity waves have been found from profiles of wave elevation deduced by integration of the elevation gradient.We are especially grateful for the advice of Dr. M. Gharib on the use of the HSI color system. John Lyons provided expert help in the laboratory and materials for and advice on photography. We thank the staff of the SIO Hydraulics Laboratory for making the wind-wave channel available for our use, and the staff of UCSD library for enabling us to use the Barneyscanner photometer-digitizer. We thank an anonymous reviewer who pointed out a numerical error and improved the clarity of the text.     

On the expectations of the mathematical knowledge of first-year undergraduates

In a recent survey Sutherland and Dewhurst itemized the extent to which various types of departments expected selected mathematical topics in the background of incoming undergraduates. Using the results of diagnostic tests it is possible to estimate the actual capability of students with given prior qualifications to provide a ‘probable preparedness’ in specific topics. This paper compares expectations with probable preparedness in a range of topics. It is found that while some departments have realistic expectations about the background of their incoming students, others seem over-optimistic about the mathematical knowledge of today's students. Sometimes, topics that the department actually requires must in fact be covered ab initio with the students that they recruit.     

The effect of music participation on mathematical achievement and overall academic achievement of high school students

A study was conducted on high school students, comparing those with some music credits to those with none. No statistically significant difference was found in their mean math grade point averages (GPA) or their mean cumulative GPAs. Students were then separated into two groups based on the number of music credits. Students who had earned at least two music credits per grade level were placed into Group A. This category included ninth graders with two or more music credits, tenth graders with four or more music credits, eleventh graders with six or more music credits, and twelfth graders with eight or more music credits. The remaining students were placed into Group B. Group A students performed better than group B students. However, the differences were not statistically significant. Scatter plots indicated a slight upward trend in GPAs as the number of music credits increased. Lower GPAs were nonexistent as the music credits increased.     

The rate at which energy decays in a damped String

The energy in a string subject to positive viscous damping is known to decay exponentially in time. Under the assumption that the damping is of bounded variation, we identify the best rate of decay with the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup. We analyze the spectrum of this nonselfadjoint operator in some detail. Our bounds on its real eigenvalues and asymptotic form of its large eigenvalues translate into criteria for over/underdamping and a proof that the decay rate achieves its (negative) minimum over those dampings whose total variation does not exceed a prescribed value.     

Hybridorubrins A–D: Azaphilone Heterodimers from Stromata of Hypoxylon fragiforme and Insights into the Biosynthetic Machinery for Azaphilone Diversification

The diversity of azaphilones in stromatal extracts of the fungus Hypoxylon fragiforme was investigated and linked to their biosynthetic machineries by using bioinformatics. Nineteen azaphilone-type compounds were isolated and characterized by NMR spectroscopy and mass spectrometry, and their absolute stereoconfigurations were assigned by using Mosher ester analysis and electronic circular dichroism spectroscopy. Four unprecedented bis-azaphilones, named hybridorubrins A–D, were elucidated, in addition to new fragirubrins F and G and various known mitorubrin derivatives. Only the hybridorubrins, which are composed of mitorubrin and fragirubrin moieties, exhibited strong inhibition of Staphylococcus aureus biofilm formation. Analysis of the genome of H. fragiforme revealed the presence of two separate biosynthetic gene clusters (BGCs) hfaza1 and hfaza2 responsible for azaphilone formation. While the hfaza1 BGC likely encodes the assembly of the backbone and addition of fatty acid moieties to yield the (R)-configured series of fragirubrins, the hfaza2 BGC contains the necessary genes to synthesise the widely distributed (S)-mitorubrins. This study is the first example of two distant cross-acting fungal BGCs collaborating to produce two families of azaphilones and bis-azaphilones derived therefrom.