The Rasmussen invariants and the sharper slice-Bennequin inequality on knots

Rasmussen introduced a knot invariant based on Khovanov homology theory, and showed that this invariant estimates the four-genus of knots. We compare his result with the sharper slice-Bennequin inequality for knots. Then we obtain a similar estimate of the Rasmussen invariant for this inequality.     

Timing in EPR correlations

Detecting the instants of absorption of two paired EPR particles, and varying independently the distances of the detectors to the source, will experimentally display the V-shaped causal link between the two correlated occurrences.     

A PRELIMINARY STUDY ON THE IMPACT OF MESOSCALE IRRIGATION OVER ARID LAND ON MESOSCALE CLIMATE

The present study investigated the modification of mesoscale inhomogeneous distribu-tion of soil wetness, resulting from mesoscale irrigation over arid or semiarid lands in mid-latitude in the later summer or early autumn, on mesoscale climate under conditions withand without synoptic flow influence, using an interactive model between soil and atmo-sphere. The simulations indicated that after a mesoscale irrgation, a wet soil breeze circu-lation was thermally forced, which was, in many features, similar to that of the sea breezecirculation. The influence of synoptic flows on the structure of thermally--induced wet soilbreeze circulation was also discussed.     

Organometallics in the nearshore marine environment of Australia

This review draws together published information on the occurrence and biogeochemical cycling of selenium, arsenic and tin in the nearshore marine environment of Australia. The selenium content of marine organisms is well documented but little information is available on the selenium content of waters and sediments. The speciation of selenium in organisms, water and sediments is unknown although it appears that selenium is associated with proteins. The occurrence and speciation of arsenic in marine organisms has been extensively studied, with arsonobetaine being isolated as the probable end-product of arsenic metabolism in marine food chains. However, organisms can produce other organoarsenic compounds, e.g. trimethylarsine oxide, which may be metabolized to toxic end-products. Little is known about the occurrence and speciation of arsenic in waters and sediments. Arsenic(V) is dominant in oxygenated waters, with appreciable quantities of arsenic(III) in some deoxygenated waters. There are few data for tin in water, sediments or organisms and no data on naturally occurring tin species. Tributyltin has been measured in water, sediment and organisms from areas affected by boating activity.     

Indestructibility and level by level equivalence and inequivalence

If κ < λ are such that κ is indestructibly supercompact and λ is 2^λ supercompact, it is known from [4] that

• {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ violates level by level equivalence between strong compactness and supercompactness}

must be unbounded in κ. On the other hand, using a variant of the argument used to establish this fact, it is possible to prove that if κ < λ are such that κ is indestructibly supercompact and λ is measurable, then

• {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ satisfies level by level equivalence between strong compactness and supercompactness}

must be unbounded in κ. The two aforementioned phenomena, however, need not occur in a universe with an indestructibly supercompact cardinal and sufficiently few large cardinals. In particular, we show how to construct a model with an indestructibly supercompact cardinal κ in which if δ < κ is a measurable cardinal which is not a limit of measurable cardinals, then δ must satisfy level by level equivalence between strong compactness and supercompactness. We also, however, show how to construct a model with an indestructibly supercompact cardinal κ in which if δ < κ is a measurable cardinal which is not a limit of measurable cardinals, then δ must violate level by level equivalence between strong compactness and supercompactness. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Learning about multiplication by comparing algorithms: “One times one,but actually they are ten times ten”

Multiplication algorithms in primary school are still frequently introduced with little attention to meaning. We present a case study focusing on a third grade class that engaged in comparing two algorithms and discussing “why they both work”. The objectives of the didactical intervention were to foster students' development of mathematical meanings concerning multiplication algorithms, and their development of an attitude to judge and compare the value and efficiency of different algorithms. Underlying hypotheses were that it is possible to promote the simultaneous unfolding of the semiotic potential of two algorithms, considered as cultural artifacts, with respect to the objectives of the didactical intervention, and to establish a fruitful synergy between the two algorithms. As results, this study sheds light onto the new theoretical construct of “bridging sign”, illuminating students’ meaning-making processes involving more than one artifact; and it provides important insight into the actual unfolding of the hypothesized potential of the algorithms.     

Near-Boundary Stress Wave Field in Anisotropic Plates under Impulsive Load

The stress wave field and the behavior of waves near the free boundary in an orthotropic plate and at the interface between two anisotropic media are studied. The results presented were obtained using the dynamic photoelastic method and optically sensitive fibrous models. Experimental data for impulsively loaded plates with various boundary conditions are analyzed     

Effects of oxidation and surface roughness on contact angle

Contact angle is known to be a parameter that effects boiling. This study was undertaken to measure contact angle of high and low surface tension fluids on copper and aluminum surfaces.Data were taken for polished, oxidized, and rough surfaces. A simple, yet fairly accurate method of measuring the static equilibrium contact angle of a solid/liquid interface is presented. The principles of a line light source and tilting plate were modified and then combined in the design of this apparatus. The angles obtained and their variation with the solid surface properties were in good agreement with previously published data. The contact angle of distilled water o of the organic fluids and refrigerants tested were in the range of 2–5°. Roughness and oxidation reduce the contact angle. If the depth of the roughness is less than 0.5 μm contact angle. The apparatus is fairly simple in construction, is inexpensive, and has good reproductibity. The measured angles were then compared to those measured with the sessile drop method.     

Direct Imaging of Octahedral Distortion in a Complex Molybdenum Vanadium Mixed Oxide

Complex Mo,V‐based mixed oxides that crystallize in the orthorhombic M1‐type structure are promising candidates for the selective oxidation of small alkanes. The oxygen sublattice of such a complex oxide has been studied by annular bright field scanning transmission electron microscopy. The recorded micrographs directly display the local distortion in the metal oxygen octahedra. From the degree of distortion we are able to draw conclusions on the distribution of oxidation states in the cation columns at different sites. The results are supported by X‐ray diffraction and electron paramagnetic resonance measurements that provide integral details about the crystal structure and spin coupling, respectively.